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This paper presents a virtual sensor scheme for vibroacoustic radiation applications based on experimental modal state-space models and sparse measurements. A Kalman filter is used for the estimation combining data from the acoustical and the structural domain together with the numerical modal process model. It is proposed to use Gramians, as an energy-related measure of a system's observability which enables assessing the observability of the coupled vibroacoustic system in the modal state-space domain and the physical state domain counterpart. This Gramian-based observability metric reveals modes or states of high observability, which ensure good estimation results in the subsequent estimation. The proposed method is validated using an industrial test setup for which, due to its high complexity, modelling with first-principle techniques is not feasible. The estimation results demonstrate improved performance compared to a pure forward use of the identified model, indicating the effectiveness of the virtual sensor approach. Additionally, the newly proposed Gramian-based observability criterion outperforms state-of-the-art metrics for sensor placement in terms of estimation accuracy for particular states of interest, as demonstrated in a sensor placement task. Overall, this paper provides a promising approach for virtual sensing for vibroacoustic applications, enabling accurate and efficient system monitoring and control. [Display omitted] • Virtual sensor for vibroacoustics using modal state-space models & sparse measurements. • Fusion of acoustical and structural data via a Kalman filter. • Novel Gramian-based observability metric improves the estimation accuracy. • Investigating the relation between the observability in modal and physical coordinates. [ABSTRACT FROM AUTHOR]

• A novel unscented Kalman filter without direct feedthrough is proposed for the identification of joint input-system without direct feedthrough. • According to the uncertainty of the identified unknown inputs, two algorithms of the proposed method are presented. • The proposed method is verified by linear/nonlinear hysteretic shear structures under external or seismic excitations. Given the difficulty of accurately measuring external inputs acting on structures, the research on joint input-system identification has gained significant attention in recent years. Among them, several unscented Kalman filters under unknown input (UKF-UI) based methods have been proposed for joint input and system identification. However, the existing UKF-UI methods require unknown inputs to be presented in the observation equations, which is not always available in practical engineering. To solve this problem, an unscented Kalman filter under unknown input without direct feedthrough (UKF-UI-WDF) is proposed in this paper for real-time joint input and system identification of structural systems without direct feedthrough using limited response measurements. The proposed UKF-UI-WDF is derived for recursive identification of the structural states, parameters, and unknown inputs by integrating unknown input estimation into the conventional UKF framework. In each identification step, the unknown inputs are first identified by minimizing posterior residuals of measurements, and then the structural states and parameters are identified by a traditional unscented Kalman filtering using the identified unknown inputs. According to whether the uncertainty of the identified unknown inputs can be quantitatively described or not, two implementation algorithms are provided in this paper. In algorithm 1, only the mean values of unknown inputs can be identified. In algorithm 2, the unknown inputs are identified as a set of sigma points, so not only the mean values but also the variance of the unknown inputs can be estimated. The effectiveness of the proposed method is examined by the joint input and system identification of various case studies of linear and nonlinear hysteretic shear structures subjected to unknown external or base excitations, respectively. The results show that the proposed UKF-UI-WDF method can effectively perform real-time joint input-system identification of structural systems without direct feedthrough using limited response measurements. [ABSTRACT FROM AUTHOR]

• An AEKF-UM approach is proposed for identifying time-variant parameters with unknown mass distribution. • A real-time updating procedure is presented for improving the process and measurement noise covariance matrices. • An index is defined basing on dramatic increase of measurement noise covariance for damage instant detection. • The covariance resetting technique is used to enhance the tracking capability for effectively capturing the time-varying parameters. Although the extended Kalman filter (EKF) provides a promising way for structural state estimation, it cannot effectively track time-varying parameters online. Besides, the structural mass distribution is usually assumed to be known in advance for many EKF-based methods, limiting their applications. In this paper, by using limited observations, an adaptive EKF with unknown mass coefficients (AEKF-UM) approach is proposed for the identification of time-variant parameters and mass distribution at the same time. A real-time updating procedure is presented for improving the process and measurement noise covariance matrices at each time step to assure the stability and accuracy of convergence results. Based on the dramatic increase of measurement noise covariance, an index is defined for determining the damage instant. A covariance resetting technique is then used to enhance the tracking capability for the purpose of effectively capturing the time-varying parameters. The unknown mass coefficients can be estimated at the same time by adding them into the extended state vector. To validate the effectiveness of the proposed approach, two numerical cases are considered, i.e. (i) the Phase I ASCE structural health monitoring benchmark building structure, and (ii) a four-story nonlinear structure equipped with a magneto-rheological (MR) damper. Experimental tests on a four-story building model subject to base excitation are also conducted to investigate the performance of the proposed approach. Results show that the proposed approach is capable of satisfactorily tracking abrupt changes of stiffness parameters with unknown mass distributions. [ABSTRACT FROM AUTHOR]

This study proposes a novel filtering method for unbiased minimum variance state estimation. A key challenge in the development of digital twinning and system identification of operational civil infrastructure is the difficulties associated with measurement of the often nonstationary, and stochastic unknown input to the system, e.g. traffic, earthquake, and wind loads. Herein a novel algorithm is presented for an unbiased output-only state estimation for linear state space systems with direct feedthrough. In this paper, the problem of state estimation for discrete time systems with unknown input, where no previous assumption is made regarding the probability distribution of the input, is addressed. In this regard, a two-stage output-only filter is proposed. The unbiasedness of the estimation is demonstrated, and the error covariance propagation over time is derived. It is shown that the unknown input of the system can be subsequently reconstructed via the system matrices, the measured responses, and the estimated state vector. A closed-form solution is provided for the parameters associated with pseudo-inverse in gain calculations to ensure the numerical stability of the filter. Three case studies including simulated and laboratory experiments for verification, validation, and cross comparison of the proposed method are presented. The first case study corresponds to a simulated shear building subjected to two different load time histories, a parametric sinusoidal load, and an earthquake ground acceleration. The second case study shows the results for a simulated experiment on a steel railway bridge subjected to a concentrated load. The third case study corresponds to a laboratory shear building subjected to ground motion and observed through accelerometers. The results of the experiments show a good agreement between the "true response" and the filter state estimation. Moreover, the proposed method is compared against a state-of-the-art algorithm. [ABSTRACT FROM AUTHOR]

The fault diagnosis of variable displacement axial piston pumps has attracted huge attention since they are the power source of the hydraulic system. A notable superiority of the variable displacement pump is the capability of changing the swashplate angle to meet the requirements of different system loads. In most current research on the fault diagnosis of the variable displacement pump, however, the fixed displacement is usually postulated in a single test. Actually, time-variant displacement arouses the complex dynamic response, as well as unanticipated system state variations, which may confuse the classifier. In this paper, the fault detection of a variable displacement pump under random time-variant working conditions is investigated for the first time. The unscented Kalman filter with unknown input is utilized to estimate the system state and calculate the residual. The residual dynamic is then modelled by the sparse variational Gaussian process regression model. The extreme function theory gives a suitable threshold for determining whether the sample is faulty or not. The experimental investigation examines five fault types while tracking the random time-variant signal. Results with different fault sizes and noise levels validate the effectiveness of the proposed method. The comparative study demonstrates the proposed method achieves superior classification performance by an optimal trade-off between fault sensitivity and false alarm rate. [ABSTRACT FROM AUTHOR]

Vehicle on-board monitoring methods use responses of running vehicles to identify track irregularity in real time. But the parameters of both the bridges and the vehicles in such processes may have a non-negligible degree of uncertainty or randomness that will inevitably lead to uncertainty in the track irregularity identification. Quantifying such uncertainty is a great challenge as the vehicle-bridge system (VBS) to be treated with is time-dependent and random. This paper proposes an on-board track irregularity identification algorithm that realizes an inverse random dynamic analysis of the VBS to quantify estimation uncertainty by using a Bayesian Kalman filter technology. The proposed algorithm utilizes sigma point sets to simulate the random parameters and the noises, and is therefore capable of implementing high-fidelity probability density propagation in the nonlinear state transfer and observation functions describing the VBS. The proposed algorithm is validated by numerical examples with various running states and parameter uncertainty levels. [ABSTRACT FROM AUTHOR]

Unbalance is the most common fault of rotating machines and efforts devoted to developing balancing techniques are the goal of several researchers around the world. The most common balancing approach is the well-known influence coefficient method, which requires the use of trial weights to determine the relationship between unbalance forces and vibration responses of the rotor; consequently, it is time-consuming regarding industrial applications. The present contribution investigates the augmented Kalman filter (AKF) technique to balance a flexible rotor without using trial weights. There are few studies in this area and the majority of the previous research works are dedicated to theoretical studies using simple or reduced rotor models. This paper considers a finite element (FE) model of a realistic rotor system and investigates the effectiveness of the AKF as a balancing technique by considering several unbalance conditions. Therefore, the novelty of the present contribution is characterized by a complete numerical and experimental AKF based balancing procedure that is performed by using a realistic rotor system. As mentioned above, limited experimental contributions are found in the literature involving real-world applications. Additionally, a sensitivity analysis on the force covariance matrix is proposed to investigate the most favorable conditions to apply the AKF technique in the context of rotor balancing. The methodology proved to be effective to deal with a variety of rotor balancing applications. [ABSTRACT FROM AUTHOR]

Accurate road slope information is of paramount importance for optimizing vehicle control and enhancing energy efficiency. In the context of heavy-duty vehicles (HDVs), the precise estimation of road slope presents a formidable challenge. This challenge is rooted in the coupling between vehicle mass and road slope, the robustness of road slope estimation methods across diverse driving styles, and the generalizability of algorithms to real-world road scenarios. To address these challenges, this paper proposes an innovative road slope estimation scheme that comprehensively considers the influences of multiple source factors in a real-world HDV transportation scenario. Firstly, in order to solve the problem of road slope estimation error under complex road types and different driving styles, a complex road slope estimation method based on the nonlinear predictive filter (NPF) combined with the Cubature Kalman filter (CKF) is constructed. To eliminate the problem of vehicle power fluctuation in special traffic scenarios, we propose a special scenario road slope estimation method based on the combination of a low-pass filter (LPF) and the NPF_CKF algorithm. To address the error problem when using low-cost Inertial Measurement Unit (IMU) sensors, we designed a Kalman filter (KF)-based multi-sensor fusion correction method. Finally, we conduct real-world experiments on complex roads at the test site to verify the accuracy of the proposed estimation method and its insensitivity to model parameters. The robustness and applicability of the proposed method are also verified in free-driving experiments conducted in real-world road scenarios. [ABSTRACT FROM AUTHOR]

This paper investigates the application, design, and implementation of different adaptive sigma-point Kalman filters for nonlinear dynamic systems. It is a well-known fact that the performance of nonlinear Kalman filters depends on a prior knowledge of system noise statistics. In real-time applications, this knowledge is difficult and in some cases impossible to predefine. Therefore, an adaptation mechanism based on the random weighting method is proposed in this work to estimate, simultaneously, noise covariance and the state of the system. On the other hand, for real time execution, the computational efficiency of such filters should also be considered to minimize the burden on computational resources. Based on these two factors, in this paper, four different variants of the adaptive sigma-point Kalman filter are studied in detail: (I) an Adaptive Unscented Kalman filter (AUKF), (II) an Adaptive Square-root Unscented Kalman filter (ASr-UKF) with an Unscented Transformation sigma-point selection strategy, (III) an Adaptive Scaled Spherical Simplex Unscented Kalman filter (AS3UKF), and (IV) an Adaptive Square-root Scaled Spherical Simplex Unscented Kalman filter (ASr-S3UKF) with scaled spherical simplex sigma-point selection strategy. The performance of these adaptive sigma-point Kalman filters is analyzed here in depth and discussed for application to a simulated rigid–flexible four-bar linkage mechanism and a practical servo-hydraulic actuator setup under different scenarios. The simulation and the experimental results indicated that, for the cases studied in this article, the filters are competitive and present advantages and disadvantages that should be dealt with according to the requirements of the problem. [ABSTRACT FROM AUTHOR]

• Α novel prognostic strategy for the Rolling Element Bearings (REB) is proposed. • The method integrates Support Vector Data Description with Moving Horizon Estimation. • Various advanced entropy and sparsity Health Indicators (HIs) are applied. • The proposed methodology is evaluated on two publicly available datasets. • Results demonstrate that the MHE outperforms the Kalman and Particle filter. The prediction of the Remaining Useful Life (RUL) of rotating machinery targets the avoidance of sudden machine failures and the optimization of the maintenance schedules as well as the management of repairs and replacements. A number of statistical model-based prognostics methodologies have been proposed in recent literature but a number of open challenges still exist, blocking their integration in the industry: (i) The extraction of a high-quality Health Indicator (HI) is critical for bearings' prognostics but till now the trend of many classic HIs is often disturbed; deviating from a monotonical increase or decrease. (ii) The detection of the Start Prediction Time (SPT) on the HI is usually required in order to improve the accuracy of the RUL estimation but it can be incorrect especially when distinct random outliers occur. (iii) The widely applied RUL estimators, e.g. the Kalman filter (KF) and the Particle filter (PF), belong to the category of single-step estimation techniques that assume that the current step estimation depends only on the state of the previous step. However, the occurrence of bearings' damage is usually not a sudden change but an accumulated process. Therefore a novel prognostic strategy for Rolling Element Bearings (REB) is proposed in this paper, which integrates a robust anomaly detection technique, the Support Vector Data Description (SVDD), with a multi-step estimation method, the Moving Horizon Estimation (MHE). Various advanced entropy and sparsity HIs are extracted by signals filtered at different frequency bands. By comparing all the extracted HIs based on a proposed criterion, a premium prognostic HI is chosen from a specific frequency band. Moreover, the SVDD, deployed and combined with several proposed constraints, can robustly detect the occurrence of a bearing fault and decide the proper SPT. Furthermore, the MHE is combined with two popular exponential statistical models and a second-order polynomial model for bearings' prognostics. Experimental results from fifteen degraded bearings demonstrate that the MHE outperforms the classic Kalman filter and Particle filter. Moreover, the polynomial model achieves a better RUL estimation compared to the two classic exponential models in combination with the MHE. [ABSTRACT FROM AUTHOR]

Lane change trajectory prediction is crucial for autonomous vehicles (AVs) to assess their own driving safety in advance. However, there are significant uncertainties in the implementation of such prediction, including different behaviors caused by agent–agent interaction and driving styles of drivers. While prototype trajectories can serve as a means to represent typical motion patterns and enhance trajectory prediction performance, their utilization in modeling motion patterns tends to overlook the influence of agent–agent interactions and vehicle dynamics. This paper proposes a fusion algorithm that considers driving style and vehicle dynamics to address these uncertainties. The algorithm involves a long short-term memory (LSTM) lane change behavior recognition model that mines key features of agent–agent interaction through the attention mechanism. The Gaussian process (GP) motion modeling trajectory prediction (GPMM-TP) algorithm considers the driving style of the prototype trajectory based on the behavior recognition results. To further improve short-term and long-term prediction, the interactive multi-model (IMM) algorithm is used to assign probability weights to the GP model and the Extended Kalman Filter (EKF) model based on prediction accuracy, taking into account the driving styles and the vehicle dynamics. The proposed algorithm provides a promising approach to improving the accuracy of lane change trajectory prediction for AVs, and its effectiveness is demonstrated using the HighD dataset. [ABSTRACT FROM AUTHOR]

[Display omitted] • Precision MIMO vibration control with model uncertainties. • Comprehensive position/force model contains displacement, load, and force characteristics. • Robust MIMO control strategy with additive perturbation and mixed sensitivity. • Various experiments and validations. This paper presents dynamic modeling and robust vibration control for a high-speed macro–micro gripping system comprised of an air-floating macro-positioning stage and a compliant piezoelectric microgripper. A dynamic displacement coupling model is established considering rigid-flexible coupled macro-micromechanical structures, electromechanical properties containing the piezoelectric actuator and power amplifier, and hysteresis nonlinearity. Then, a comprehensive position/force model is proposed by integrating displacement, load, and force characteristics to describe the position and gripping force of micro-objects. Regarding system disturbances and model uncertainties, robust control strategies for pure displacement and position/force cooperation are devised utilizing perturbation H ∞ controllers and Kalman filters. Experimental results indicate that measurement noises for pure displacement and position/force are effectively reduced. Position/force disturbances arising from sudden mutual changes are decreased from 14.39 μm and 7.25 mN to 0.82 μm and 0.85 mN. Also, position/force vibrations excited by high-speed macro motion are suppressed by 31.99 % and 58.06 %. Both precision tracking and vibration suppression are still well achieved, even at significant parameter perturbation. Thus, experiments verify the feasibility of the proposed control strategy. [ABSTRACT FROM AUTHOR]

During their lifetime, structures are usually subjected to some mechanical shocks that generate high levels of vibration that can damage the structure itself as well as the embedded devices. However, the characteristics of these shocks (location, time history, maximum intensity, etc.) are often unknown due to the inaccessibility of the excitation region for direct force measurements or the inability to instrument the system. Therefore, inverse methods have been developed to quantify these complex excitations. Recently, a Bayesian formulation of the input-state estimation problem for linear systems has been proposed by the authors, which unifies most of the state-of-the-art filters. In this paper, we present two novel Bayesian filters derived from this framework: (a) the Correlated Dual Kalman Filter (CDKF), which is one of the filters that naturally follows from the unified Bayesian formulation, and (b) the Component Bayesian Filter (CBF), which promotes spatial sparsity of the input vector. Essentially, these filters differ in the prior distributions used to convey information about the spatial distribution of the input vector to be identified. The performance of these filters is evaluated through a numerical experiment and a real-world application aimed at reconstructing a sparse and transient excitation acting on a linear structure. A comparison of these original filters with other Bayesian filters proposed in the literature is also proposed. In particular, the numerical experiment allows to study the performance of the proposed filters in different scenarios, such as the number of sensors, the measurement noise level or the sensor configuration, while the real-world application allows to test them in operational conditions. More specifically, it is shown that filters promoting the spatial sparsity of the input vector, such as CBF, lead to a consistent identified excitation profile when acceleration measurements are the only available data. • Two particular filters deriving from a more general and generic Bayesian formulation are proposed. • The hyperparameters of each filter are obtained from optimization. • Numerical and experimental validations are performed and comparisons with AKF and a filter belonging to the same family are proposed. • One of the proposed methods avoids the drift effect and is robust to measurement noise. [ABSTRACT FROM AUTHOR]

• A particle filter-based prognostic method combining multiple features is shown. • An online feature selection criterion is proposed based on bias estimation. • The method is tested by fatigue testing of an Aluminum lug joint with Lamb wave monitoring. • The robustness of the proposed method is tested on different specimens. Damage prognosis generally resorts to damage quantification functions and evolution models to quantify the current damage state and to predict the future states and the remaining useful life (RUL). The former typically consists of a function describing the relationship between the damage state and a statistical feature extracted from the measured signals, thus the prognostic performance will strongly depend on the selection of a proper feature. Given the best feature may vary for different specimens or even at each time instant for the same specimen during damage progression, such selection is a challenging task but has received little investigation so far. In this context, this paper proposes a particle filter-based damage prognosis framework, which involves an online feature fusion and selection scheme. A prognostic model is considered for each feature, with a multivariate process equation, formulated using both a damage degradation function and a bias parameter, and a measurement equation linking the damage state and that feature considering a data-driven model and the bias. One PF is used to estimate the damage state, its evolution parameters, and the bias for each model. Then, at each step, the feature with the smallest estimated bias is selected as the best feature providing the most likely state vectors and is used to select the most likely samples of the damage state and growth parameters for predicting the RUL and for calculating the prior at the next step. The proposed prognostic framework is demonstrated by an experimental study, where an aluminum lug structure subject to fatigue crack growth is monitored by a Lamb wave measurement system. [ABSTRACT FROM AUTHOR]

A novel instantaneous frequency (IF) tracking method for non-stationary measured signals with single-frequency, multi-frequency, and harmonic-frequency is presented in this paper. Firstly, the deficiency of the mainstream time-domain IF tracking methods, such as adaptive notch filter (ANF) and Extended Kalman Filter (EKF), etc., are analyzed. Then the relationship of the amplitude, frequency, and signal value of a periodic signal in adjacent time intervals is derived, the influence of amplitude change on IF tracking results is verified, and a new state-space model for the IF tracking of a non-stationary measured signal is constructed by using the adjacent non-stationary measured signal, signal amplitude, and frequency, and the EKF is used to update the state of the model. After that, a series of non-stationary signals whose amplitude, frequency, and phase change linearly, nonlinearly, and mutation over time are designed to verify the IF tracking performance of the proposed algorithm. From the simulation results and 1000 times Monte Carlo simulation results, the proposed algorithm has faster convergence speed, higher convergence accuracy, and better robustness, compared with mainstream time-domain frequency tracking algorithms, such as ANF and EKF. Based on the proposed single-frequency IF tracking model, a multi-frequency signal IF tracking model is constructed to track the IF of non-stationary measured signals containing multiple frequency components. The effectiveness of the proposed multi-frequency IF tracking algorithm for multi-frequency signal and harmonic signal IF tracking is verified by simulation cases. After that, some experimental cases are given to further verify the feasibility of the proposed IF tracking algorithm. From the experimental results, the effectiveness of the proposed algorithm is compared with other time-domain algorithms. In addition, the initial value of frequency is set to zero in all the processes of simulation and experiment, which effectively avoids the influence of the initial condition of frequency on the IF tracking result. [ABSTRACT FROM AUTHOR]

• Robust real-time input and state estimation for systems without direct feedthrough. • Optimal sensor placement algorithm (OSPA) to meet essential system properties. • Strong observability, strong* detectability, and invertibility conditions are utilized. • The OSPA ensures stable and accurate estimations for both MVUIS and ASKF. • Verification using numerical, laboratory, and real-world building structures. Simultaneous real-time input and state estimation and optimal sensor placements are investigated in this paper, focusing on systems without direct feedthrough, such as earthquake-excited building structures with absolute floor acceleration measurements. Current studies showed that system properties such as strong observability, strong* detectability (the asterisk distinguishes strong* detectability from strong detectability), and invertibility conditions are crucial to the stability and convergence of unknown input and state estimation, but they can often be violated in practice. Consequently, uncertainties such as modeling errors and measurement noise can greatly degrade the accuracy and stability of the estimations. Estimation in this case has remained challenging due to the above reasons. To fill this gap, this paper develops an optimal sensor placement algorithm (OSPA) for real-time unknown input and state estimation, which ensures the required system conditions are met. The developed OSPA is integrated with two optimal real-time Kalman-based filters, a minimum-variance unbiased input and state estimation filter (MVUIS) and an Augmented State Kalman Filter (ASKF), for simultaneous input and state estimation. In particular, the MVUIS is presented in a recursive three-step structure without using the arbitrary matrix in the gain, which makes no assumptions on the input but requires strong* detectability. To avoid the requirement, ASKF is derived from the MVUIS by incorporating prior knowledge of the input. The developed OSPA along with the MVUIS and ASKF provide the optimal input and state estimation in real-time without incurring low-frequency drift or unstable estimations. Notably, the OSPA improves the performance of MVUIS by reducing amplitude errors and enhances the accuracy of ASKF by reducing phase errors. The developed OSPA integrated with the MVUIS and ASKF are validated through numerical and experimental studies as well as a real-world instrumented building structure under earthquakes using incomplete absolute acceleration measurements. [ABSTRACT FROM AUTHOR]

The number of timely diagnoses based on condition monitoring data is increasing with the growing usage of monitoring systems. In most of the methods used in these systems, a pre-established fault detection threshold is needed, while there are no specific limit values or thresholds in many cases, especially when the machine is unique. Also, in most actual applications, due to the kind of process and harsh environment, the noise inherent in the observed process exhibits non-Gaussian characteristics, making it a challenging task for diagnostics based on condition monitoring (CM) data. Therefore, this paper introduced a robust methodology based on the switching maximum correntropy Kalman filter (SMCKF) to address the mentioned problems (threshold and online diagnostics in the presence of non-Gaussian noise by using CM data). This approach uses multiple dynamic system models to explain different degradation stages, utilizing robust Bayesian estimation. As this approach is based on dynamic behavior, a threshold for diagnostics is no longer needed. Ultimately, the proposed approach is applied to the online diagnosis of simulated and actual data sets. The results of both simulated and real data sets prove the method's efficacy. [ABSTRACT FROM AUTHOR]

Virtual sensing techniques have gained traction in applications to the structural health monitoring of monopile-based offshore wind turbines, as the strain response below the mudline, which is a primary indicator of fatigue damage accumulation, is impractical to measure directly with physical instrumentation. The Gaussian process latent force model (GPLFM) is a generalized Bayesian virtual sensing technique which combines a physics-driven model of the structure with a data-driven model of latent variables of the system to extrapolate unmeasured strain states. In the GPLFM, unknown sources of excitation are modeled as a Gaussian process (GP) and endowed with a structured covariance relationship with response states, using properties of the GP covariance kernel as well as correlation information supplied by the mechanical model. It is shown that posterior inference of the latent inputs and states is performed by Gaussian process regression of measured accelerations, computed efficiently using Kalman filtering and Rauch–Tung–Striebel smoothing in an augmented state-space model. While the GPLFM has been previously demonstrated in numerical studies to improve upon other virtual sensing techniques in terms of accuracy, robustness, and numerical stability, this work provides one of the first cases of in-situ validation of the GPLFM. The predicted strain response by the GPLFM is compared to subsoil strain data collected from an operating offshore wind turbine in the Westermeerwind Park in the Netherlands. A number of test cases are conducted, where the performance of the GPLFM is evaluated for its sensitivity to varying operational and environmental conditions, to the instrumentation scheme of the turbine, and to the fidelity of the mechanical model. In particular, this paper discusses the capacity of the GPLFM to achieve relatively robust strain predictions under high model uncertainty in the soil-foundation system of the offshore wind turbine by attributing sources of model error to the estimated stochastic input. [ABSTRACT FROM AUTHOR]

This paper presents a recursive Bayesian inference framework for digital twinning of an offshore wind turbine (OWT) in the Block Island Wind Farm (BIWF), the first commercial offshore wind farm in the U.S. with jacket substructure. The framework employs a window-based extended Kalman filter (EKF) to jointly estimate the dynamic input loads and unknown model parameters of the finite element (FE) model of the turbine using sparse output-only measurements. The estimation of input loads on the OWT is critical for fatigue life estimation, foundation monitoring and control strategy. In the proposed joint estimation algorithm, unknown input time histories are divided into overlapping windows and the current window of inputs is concatenated with uncertain model parameters to form an augmented state vector. To account for the uncertainty about wind direction and misalignment between wind direction and the turbine yaw angle, two independent horizontal wind load time histories in X and Y directions are estimated at the nacelle level. A numerical validation study is first performed in which wind loads of the OWT are simulated using the multi-physics platform FAST, and structural vibration responses are generated using the FE model in OpenSees. The window-based EKF is implemented using the simulated measurements, and the estimations of structural stiffness as the updating model parameter and input loads are observed to have high accuracy. The proposed algorithm is then validated using in-situ measurements on one of the OWT in BIWF. To investigate the effectiveness and robustness of the method under different environmental and operational conditions, four cases are considered in which the turbine is operating at the rated rotor speed (region 3 of power generation), below the rated rotor speed (region 2), idling rotor state (region 1 or no power), and region 4 beyond cut-out wind speed. Accurate predictions of acceleration and strain data are obtained using the proposed algorithm, and the estimations of model parameter are consistent and close to their nominal value under different conditions. These results from numerical and experimental studies validate the proposed window-based EKF for joint parameter-input estimation and digital twinning for long-term structural health monitoring of the OWT. [ABSTRACT FROM AUTHOR]

High-frequency global navigation satellite system (GNSS) is one of the most effective means for structural health monitoring. At present, most of the GNSS-based structural health monitoring research focuses on the positioning method, however, the unmodeled error caused by the complex monitoring environment and the receiver are always ignored by such technology. Most of the displacement extraction algorithms based on GNSS kinematic positioning are based on the Kalman filter and its variants, and the research on the effective determination of the process noise matrix and the measurement noise matrix is still limited. This paper aims to explore a displacement extraction method with automatic parameter tuning for structural health monitoring. An auto-tuning Kalman smoother has been introduced for extracting vibration displacement from GNSS kinematic positioning. Specifically, we divide the GNSS kinematic positioning results into a training set and a validation set, then use non-convex optimization to obtain the hyperparameters of the Kalman smoother. Finally, we extract the displacement from Kalman smoother with the tuned hyperparameters. Simulation and field experiments were carried out to verify the proposed method. The results show the feasibility and effectiveness of the method for vibration displacement extraction. For real-time kinematic positioning, the displacement extraction accuracy is improved by 9.58% compared to the traditional Kalman smoother; for precise point positioning, the displacement extraction accuracy is improved by 15.36%. The influence of the proportion of training set on the proposed method is discussed, and suggestion for the training set proportion is given. [ABSTRACT FROM AUTHOR]

• A current harmonic supperssion strategy based on extended Kalman filter is proposed. • An extended Kalman filter based harmonic suppression strategy is designed to suppress the current harmonic of all frequencies. • A mixed H 2 /H ∞ robust controller is designed to improve the road feeling torque tracking performance. • The experiment verifies the effectiveness of the road feeling control strategy proposed in this paper. In this paper, a hierarchical control strategy is proposed to improve the quality of road feeling control of a steer-by-wire system. The upper layer proposed a road feeling torque control method of uncertain system, and the lower layer suppresses the current harmonics produced in the road feeling control process. Firstly, the dynamic model of the steer-by-wire system and the vehicle are established. Secondly, considering the influence of uncertain system parameters, uncertain harmonic torque ripple, and uncertain sensor noise on the road feeling torque control, a road feeling torque control strategy based on mixed H 2 /H ∞ robust control theory is designed. Then, a current harmonic suppression strategy based on the extended Kalman filter is proposed in the lower layer to suppress the current harmonics of all frequencies. Finally, the simulation is conducted using MATLAB/Simulink, and the experimental verification is carried out on the steer-by-wire experimental platform. Simulation and experimental results show that the proposed road feeling control strategy is robust to nonlinear system uncertainties, and the proposed current harmonic suppression strategy can suppress current harmonics in all frequency ranges. [ABSTRACT FROM AUTHOR]

• A method is proposed in this paper to construct a regularized penalty matrix based on the magnitude of singular values. • Compared with the unit matrix used in ridge estimation, the constructed penalty matrix can introduce an appropriate amount of bias according to the magnitude of singular values. This reduces the variance of parameter estimation under the condition that the system bias remains approximately unchanged. • The constructed penalty matrix is applied to the source strength solution and sound field reconstruction of equivalent source near-field acoustic holography. The results show that the regularization method using the new penalty matrix enhances the stability of the source strength solution and improves the reconstruction accuracy of the sound field. Tikhonov regularization improves the ill-conditioning of the original transfer matrix by using regularization parameters and a penalty matrix. When the penalty matrix is a unit matrix, Tikhonov regularization is known as ridge estimation. Using the mean value and variance analysis of ridge estimation, it can be observed that the ridge estimation uses a regularization parameter to filter small singular values, and introduces system bias independent of the measurement error. However, due to the large order of magnitude difference between the singular values, the fixed regularization parameter cannot effectively suppress the variance component corresponding to large singular values. As a result, the variance of the estimation increases and the stability of the solution reduces. In view of the above defects, a method is proposed in this paper to construct a regularized penalty matrix based on the magnitude of singular values. Compared with the unit matrix used in ridge estimation, the constructed penalty matrix can introduce an appropriate amount of bias according to the singular values. This reduces the variance of parameter estimation under the condition that the system bias remains approximately unchanged. Finally, the constructed penalty matrix is applied to the source strength solution and sound field reconstruction of equivalent source near-field acoustic holography. The results show that the regularization method using the new penalty matrix enhances the stability of the source strength solution and improves the reconstruction accuracy of the sound field. [ABSTRACT FROM AUTHOR]

The estimation of external loads acting on mechanic structures is of paramount importance for the design, operation, and control of these systems. In many cases, external loads cannot be measured directly due to the intrusive nature or the high costs of adequate sensors. Model-based estimation techniques yield the possibility to estimate external loads in an indirect manner using indirect measurements. These methods usually assume an optimal sensor behaviour over the entire frequency range of the estimator application, which not necessarily has to be the case due to sensor bandwidth limitations. Therefore, model-based sensor fusion is constrained to sensors and applications that share the same bandwidth. This paper proposes a novel non-intrusive approach to estimating external loading in the presence of incongruent measurement regimes of the involved sensors using Kalman filters. The method uses existing model-based estimation techniques to establish a broadly applicable framework for the fusion of multiple sensors with non-coinciding measurement bandwidths. A promising application of this new approach is not only the combination of sensors that measure the same quantity in different frequency regimes but also the combination of sensor types which are not being used together due to different measurement regimes. The newly formulated approach is tested both numerically and with a validation experiment in which accelerometer and gyroscope measurement are combined. In both cases, the new method shows improved behaviour in terms of estimations quality of an unknown force over traditional Kalman filter formulations in the presence of prominent sensor dynamics and over a wide frequency range. [ABSTRACT FROM AUTHOR]

• Curvature is identified from dynamic and quasi-static acceleration response. • Filtering and empirical mode decomposition provide curvature influence lines. • Sparse modal parameters and dense influence lines are fused using Kalman filter. • The system state represents dense and robust curvature estimate. • Monitoring the state evolution allows high-resolution damage localization. Curvature is one of the most popular damage-sensitive features in vibration-based structural health monitoring applications, typically calculated from identified modal features. While the relevant strategic or historical importance of bridges may justify dense sensor networks, a limited budget is generally assigned to monitor "minor" viaducts, thus involving inexpensive devices or extremely sparse sensing solutions. Modal parameters can only be obtained at instrumented locations. Thereby, damage assessment methods based on identified features typically have a low spatial resolution, especially when using low-cost monitoring setups with a modest number of sensing devices. This paper proposes an original identification method for the curvature of bridges based on sparse acceleration measurements that can be collected using standard accelerometers. The raw acceleration signal is processed through a particular filter bank that extracts dynamic and quasi-static signal components. The first components are employed to identify modal parameters, from which sparse yet robust estimates of the structural curvature are retrieved. On the other hand, the quasi-static acceleration generated by the structural deflection induced by traffic load is used to identify the curvature influence lines of the bridge, which are fused with modal estimates using a Kalman filter. The state variable of the analyzed system, representing a dense curvature profile of the structure subjected to concentrated loads, can be used as a damage-sensitive feature for high-resolution damage localization. The method is applied to a steel truss bridge subject to different damage configurations. [ABSTRACT FROM AUTHOR]

The difficulty in quantifying the benefit of Structural Health Monitoring (SHM) for decision support is one of the bottlenecks to an extensive adoption of SHM on real-world structures. In this paper, we present a framework for such a quantification of the value of vibration-based SHM, which can be flexibly applied to different use cases. These cover SHM-based decisions at different time scales, from near-real time diagnostics to the prognosis of slowly evolving deterioration processes over the lifetime of a structure. The framework includes an advanced model of the SHM system. It employs a Bayesian filter for the tasks of sequential joint deterioration state-parameter estimation and structural reliability updating, using continuously identified modal and intermittent visual inspection data. It also includes a realistic model of the inspection and maintenance decisions throughout the structural life-cycle. On this basis, the Value of SHM is quantified by the difference in expected total life-cycle costs with and without the SHM. We investigate the framework through application on a numerical model of a two-span bridge system, subjected to gradual and shock deterioration, as well as to changing environmental conditions, over its lifetime. The results show that this framework can be used as an a-priori decision support tool to inform the decision on whether or not to install a vibration-based SHM system on a structure, for a wide range of SHM use cases. [ABSTRACT FROM AUTHOR]

The establishment of a Digital Twin of an operating engineered system can increase the potency of Structural Health Monitoring (SHM) tools, which are then bestowed with enhanced predictive capabilities. This is particularly relevant for wind energy infrastructures, where the definition of remaining useful life is a main driver for assessing the efficacy of these systems. In order to ensure a proper representation of the physical structure, the monitored response of the Digital Twin should match the one experienced by the actual system throughout the complete spectrum of its operational conditions. In most typical SHM configurations, it is only possible to rely on output-only measurements, acquired from finite positions within a structure, which naturally raises the challenge of recovering the full-field operational response, including unmeasured locations. This problem, also known as Virtual Sensing (VS), has been treated using different schemes, including Bayesian filtering and Modal Expansion (ME). In this paper, the Augmented Kalman Filter (AKF) is exploited to this end; a tool which allows for simultaneous full-field response and unmeasured input prediction. The common issue of Bayesian filtering relies on calibration of the filters defining parameters, namely the assumed measurement and process noise covariance levels. While the first is directly related to the accuracy of the employed physical sensors, the latter often acts as a tuning parameter for improving the reliability of the prediction. The process noise covariance adjustment is often performed in an offline fashion, either by making use of regularization methods, e.g., the L-curve method, or via trial and error. In this work, we propose a methodology for automated process noise covariance adaptation, relying on response estimates recovered by means of an improved ME approach. The method is validated on experimental data from a large scale research Wind Turbine (WT) blade made of glass fiber reinforced plastics. [ABSTRACT FROM AUTHOR]

This paper presents for variable stiffness tuned mass dampers (VS-TMDs) a vibration control algorithm combined with a nonlinear system identification method. The objective of the proposed approach is the control of multistory shear frame structures, which exhibit abrupt stiffness degradations. A stiffness variable control (SVC) algorithm is developed to control the stiffness of the VS-TMD, which is based on the mitigation of the potential energy of the structure. For the identification of the system parameters, an adaptive unscented Kalman filter (A-UKF) scheme is utilized. The paper describes the theoretical background of the proposed approach with its governing equations and conducts performance studies on a semi-actively controlled 2-story shear frame structure. Harmonic, white noise and earthquake excitation scenarios including seismic aftershock effects are investigated. Sensitivity studies are conducted. With the proposed approach, the abrupt stiffness changes of the structure are detected and the damper stiffness is adapted successfully. The results show that the SVC together with the A-UKF clearly outperforms the passive TMD control. [Display omitted] • For the stiffness control of semi-active TMDs, a control algorithm is proposed. • A potential energy based cost function is derived and minimized by gradient descent. • The algorithm is coupled with an adaptive UKF for identification of abrupt changes. • Harmonic, white noise and seismic excitation with aftershocks are investigated. • A superior and robust control performance is observed. [ABSTRACT FROM AUTHOR]

Bearing is one of the most important component of rotary machine, and its health state is directly related to the safety of industrial production. In this paper, health state assessment of bearing is investigated with feature enhancement and prediction error compensation. Specially, health state assessment consists of time-to-start prediction point detection and remaining useful life (RUL) prediction. In the first stage, variance feature based on Kalman filter is introduced to detect the time-to-start prediction point. Subsequently, complete ensemble empirical mode decomposition with adaptive noise is employed to reconstruct the degradation trend, and cumulative function is adopted to realize the feature enhancement, then efficient health indicator can be constructed. In the RUL prediction stage, degradation model and adaptive extended Kalman filter are fused to achieve the prediction, and bidirectional gated recurrent unit neural network is chosen to compensate the prediction error. Finally, experimental studies based on PRONOSTIA and XJTU-SY datasets are conducted to validate the effectiveness of the proposed method and its superiority over the traditional methods. • The proposed method provides a new solution to determine the prediction start time. • The cumulative function is used to establish the trend health indicator. • The adaptive EKF and Bi-GRU are fused to predict the RUL of bearing. • Different bearing datasets are used to verify the effectiveness of proposed method. [ABSTRACT FROM AUTHOR]

In this paper, a new data assimilation framework for correcting finite element models from datasets acquired on-the-fly in low-frequency dynamics is presented. An Unscented Kalman filter algorithm is coupled with a modified Constitutive Relation Error (mCRE) observer, leading to a Modified Dual Kalman Filter algorithm (MDKF). Built as a Hermitian data-to-model distance written in the frequency domain enriched with a CRE residual accounting for model bias, the mCRE functional has shown interesting assets for model updating purposes, in particular enhanced convexity and robustness to measurement noise. The proposed data assimilation strategy integrates the latter through a metric change in the measurement update equation. It thus differs from classical nonlinear Kalman filtering for parameter estimation as the comparison between measurements and model predictions is achieved through the mCRE functional itself. Besides, the calibration of MDKF internal parameters is facilitated by a set of general guidelines that ensure the performance of the algorithm. The methodology is applied to two earthquake engineering examples. The performances of MDKF are first assessed using synthetic measurements from a plane frame subjected to random ground acceleration. Actual measurements from the SMART2013 benchmark are then assimilated in a real-time context to monitor the eigenfrequency drop of a reinforced-concrete structure submitted to a sequence of gradually damaging shaking-table tests. The nice correlation with (i) data-driven identification results, and (ii) sequential mCRE-based model updating results, illustrates the relevance of this new approach and suggests promising use of MDKF for on-the-fly adaptive control prospects and applications involving data-to-model interaction. • A new Kalman Filter approach is proposed for structural monitoring in dynamics. • The mCRE functional is integrated as observer in a Dual Unscented Kalman Filter. • General guidelines are provided for easy calibration of decisive internal parameters. • The robustness of the methodology is assessed from highly noisy synthetic data. • Actual measurements of the SMART2013 project are processed in a real-time context. [ABSTRACT FROM AUTHOR]

A combined approach is proposed for estimating forces and states based on a sequential implementation of an impulse response matrix deconvolution and a Kalman filter. The deconvolution is formulated from an experimental identification to compute the system inputs while the Kalman filter employs an updated model to estimate the states. The split implementation allows for improved input estimates that current joint estimation techniques struggle to determine when model mismatches are introduced. The enhanced forces are later on incorporated into the Kalman filter to generate estimates of the states at any particular location of the geometric domain, covering the deficiency of the impulse response filter to estimate unmeasured states. This methodology is reliant on measurements of commonly used sensors for experimental modal analysis and thus they can be complementarily acquired during the process of model updating. The approach alleviates the adverse effects induced by model inaccuracies, typical of structures with complex boundary conditions, large frequency bands of interest and high modal density. Additionally, this paper proposes an optimization procedure of the covariance matrix entries in order to minimize the error between observations and the Kalman filter estimates. The optimization circumvents the problem of accuracy loss in the Kalman filtering estimates in absence of prior knowledge of the system uncertainties. An industrial example of a complex mechanical component is analyzed in order to demonstrate the effectiveness of the current approach. • A framework to address complex boundary conditions and high modal density is proposed. • The CIRKF methodology circumvents estimation errors typical of model-based techniques. • An optimization algorithm is introduced to reduce state estimation errors. • Results are validated on a complex mechanical component. [ABSTRACT FROM AUTHOR]

The present paper introduces a novel Bayesian filter for estimating mechanical excitation sources in the time domain from a set of vibration measurements. The proposed filter is derived from a very general Bayesian formulation, unifying most of the state-of-the-art recursive filters developed in the last decade for solving input-state estimation problems. More specifically, the proposed Bayesian filter allows promoting the spatial sparsity of the estimated input vector, by assuming that the predicted input vector is a random vector with independent and identically distributed components following a generalized Gaussian distribution. To properly estimate the most probable parameters of the latter probability distribution, a nested Bayesian optimization is implemented. The validity of the proposed approach, called Sparse adaptive Bayesian Filter, is assessed both numerically and experimentally. In particular, the comparisons performed with some state-of-the-art filters show that the proposed strategy outperforms the existing filters in terms of input estimation accuracy and avoids the so-called drift effect. • Bayesian formulations of joint and sequential input-state estimation problems are proposed. • State of the art methods are derived from the proposed Bayesian framework. • A new method promoting the sparsity of the excitation field is developed. • Numerical and experimental validations are performed and comparisons with standard methods are proposed. • The proposed method avoids the drift effect and is robust to sensors' density and measurement noise. [ABSTRACT FROM AUTHOR]

[Display omitted] This paper reports electromechanical dynamics modeling and microscopic vibration suppression for a high-speed macro–micro manipulator with structural flexibility and parameter perturbation. The macro–micro manipulator contains an air-floating macro-motion platform and a macro-fiber-composite (MFC) micromanipulator. The electromechanical dynamics model is derived by combining the assumed mode method and the asymmetric Prandtl-Ishlinskii hysteresis model. Then, a robust control strategy combining a perturbation H -infinity controller with a Kalman filter is proposed to compensate for the hysteresis nonlinearity and suppress the microscopic vibration during and after the macro motion. In particular, an additive perturbation is used to estimate the model uncertainties from the varying end mass and all other unknown dynamics. Also, the Kalman filter is designed to improve the signal-to-noise ratio of the displacement detection based on the process and measurement noises. Several experiments are conducted to validate the effectiveness and feasibility of the proposed dynamic model and robust controller. The elastic vibrations during and after macro motion are significantly suppressed even with the parameter perturbation. Thus, the proposed control strategy can improve the manipulation stability, robustness, and accuracy. [ABSTRACT FROM AUTHOR]

• A mmSHM system is proposed to achieve multi-scale and full-field vibration measurement. • An adaptive segmented phase demodulation method to track vibrations spanning from μm to dm scales. • Full-field vibration measurement method and thoroughly experimental validations. • The accuracy of the mmWave sensing method reaches μm-level. Vibration measurement is of great significance for structural health monitoring (SHM). The emerging microwave vibration measurement technology has distinct advantages over the laser and vision-based approaches, such as long-range, low-power consumption and environmental adaptability. However, it has critical limitations on multi-scale and full-field vibration measurement, especially for SHM of large structures. To overcome these drawbacks, in this paper, we propose mmSHM, a mmWave radar-based vibration measurement approach for SHM. An adaptive segmented phase demodulation (ASPD) method is developed to effectively quantify the displacement variation, allowing accurate displacement measurement spanning from µm to dm scales. What's more, to eliminate the coupling and aliasing interferences from adjacent targets in full field of view, an improved interferometric phase evolution tracking method is presented to extract the vibration displacement from the range-angle joint dimensions. To be specific, the basic principle of vibration measurement using linear frequency-modulated continuous wave (LFMCW) radar is firstly depicted. Then, the detailed procedures of multi-scale and full-field vibration measurement method are illustrated. Finally, with the built prototype of mmSHM, experimental results under different scenarios show that our method can achieve multi-scale and full-field synchronous vibration measurement with µm-level accuracy. The proposed method can be expected to provide a promising approach for contactless vibration measurement in SHM. [ABSTRACT FROM AUTHOR]

Prognostics has become an important strategy for system maintenance, however, the inevitable uncertainty will reduce the reliability of prognostic result. In order to solve this problem, a prognostic technique with the capability of uncertainty management is proposed in this paper. The implementation of proposed prognostic strategy consists of two phases. In the first phase, the methods of neural network, particle swarm optimization and sample entropy theory are used to construct the interval of the historical degradation and reduce the uncertainty of the constructed interval. In the second phase, the unscented Kalman filter is adopted to obtain the prognostic result. In order to examine the performance of the proposed prognostic method, comparative experiments between different prognostic schemes based on degradation datasets of lithium-ion battery and bearing are performed. The experimental results show that the proposed strategy is an effective prognostic method which can ensure the reliability of the prognostic result. • The proposed prognostic method provides a new solution for uncertainty management. • A cost function for NN is adopted to construct the historical degradation interval. • The CEEMD and sample entropy are utilized to reduce the uncertainty of interval. • Two types of datasets are used to verify the effectiveness of the prognostic method. [ABSTRACT FROM AUTHOR]

An augmented Kalman filter for torque estimation in marine propulsion-system drive trains is presented. Propeller and motor excitations and torque responses are estimated based on a dynamical model of the system and inboard shaft measurements. Input excitations affecting marine propulsion systems are signals whose statistical properties vary between finite time intervals. Hence, in this paper, excitations are characterized as quasi-stationary signals with bounded power spectral density. Given that upper bounds on the spectral densities are known prior to estimation, it is shown that a linear time-invariant input-and-state observer, minimizing the worst-case power of the estimation errors, can be synthesized by conventional Kalman-filtering techniques. Experiments have been conducted on a laboratory-scale test bench to assess the applicability of the proposed observer for use in marine propulsion systems. The test bench was built to emulate the behavior of a full-scale propulsion system operated in ice and other high load conditions. Estimation results from a full-size underwater mountable azimuthing thruster are also presented. Experiment results show that torque excitations and torque responses at all locations of interest on the engine-propeller drivetrain can be estimated with high accuracy based on a few indirect measurements at convenient locations on the motor shaft. [ABSTRACT FROM AUTHOR]

• A recursive window-based Bayesian inference approach is formulated and validated. • It is implemented for joint input-parameter estimation of an offshore structure. • Strain time histories at hotspots are accurately predicted through virtual sensing. • The proposed method outperform modal expansion method for virtual sensing. This paper presents a recursive Bayesian inference framework for joint parameter-input identification, and virtual sensing for strain time history prediction of an offshore platform using sparse output-only measurements. The studied offshore platform, known as FINO3, is in the North Sea and is instrumented with a variety of sensors, including accelerometers and strain gauges. Offshore platforms are fatigue critical structures due to harsh marine environmental conditions and continuous cyclic wind and wave loads. Therefore, continuous monitoring of strain time histories at hotspot locations of offshore structures is important for reducing maintenance cost and avoiding unexpected failures. A windowed unscented Kalman filter (UKF) is employed to estimate an uncertain modeling parameter (foundation stiffness) and unknown input load time histories using output-only acceleration and strain measurements. The input loads are divided into overlapping windows, and windowed inputs and model parameters are combined as an augmented state vector in the UKF framework. Then strain time histories at critical locations are estimated through a virtual sensing strategy using the estimated input loads and model parameter. A traditional modal expansion approach combined with model updating is also implemented for the purpose of verification and comparison. The proposed method is first demonstrated through a numerical study using a finite element model of FINO3, where accurate model parameter and input estimations are obtained. Then the approach is further investigated using the actual measurements on FINO3. More accurate strain predictions are provided by the UKF than the modal expansion approach, which recommends the proposed UKF method for fatigue monitoring and input estimation. [ABSTRACT FROM AUTHOR]

• Identification of operating forces. • Using measurement of acceleration responses only. • ARX time series model in conjuction with Kalman fiter is applied • The robustness against noise is investigated by numerical simulations. • The modal parameters are identified. Multi-axial flexible manipulators are structures typically employed in the maintenance of large hydropower equipment such as turbine runners. This kind of multi-process robot was specifically designed for repair jobs related to material removal via grinding or polishing. In general, the estimation of the contact forces between the grinding cup and the workpiece is crucial for improving the robot's performance and minimizing unwanted vibration at the end effector. However, due to working in a harsh environment, the direct force measurements cannot be implemented. This paper introduces a new method using a Kalman filter based on a time series Auto-Regressive with eXogenous excitation (ARX) modelling to deal with the inverse problem, where ARX model is modified by employing ambient vibration data only. The recursive least squares algorithm is adopted to reduce the effect of high random noises, thus allowing to identify the excitation forces in multiple directions under grinding operations. The proposed method was illustrated via different examples with numerical simulations and experiments on a cantilever beam and on a flexible manipulator. The numerical simulations allow for investigating the robustness of the method against noise, while its ability to identify the forces and the modal properties of structures is also presented. [ABSTRACT FROM AUTHOR]

In this paper we propose a constructive procedure to determine the radial pretension in an axially-symmetric orb-web, on the basis of one eigenfrequency and its corresponding vibration mode. The method can be applied both to axisymmetric modes, corresponding to the solution of a regular Sturm–Liouville problem, and to non-axisymmetric modes, corresponding to the solution of a singular Sturm–Liouville problem. In the absence of measurement errors of the eigenfunction, the identification of the pretension field is almost perfect. On the contrary, if the measurement presents some noise, then identification is imprecise. In this case, a regularization technique applied to the measurement of the eigenfunction, or to its derivative, is proposed, as well as a filtering process, which significantly improves the reconstruction of the pretension field. The fundamental mode of vibration, sampled with a suitable number of points, is the one that provides the lowest identification error. • The problem is solved by the knowledge of the first eigen-pair. • We propose a constructive procedure to determine the radial pretension in a spider orb-web. • The method can be applied both to axisymmetric modes and to non-axisymmetric modes. • A regularization technique and a filtering process are proposed. • The regularization technique is used to measure the eigenfunction and its derivative. [ABSTRACT FROM AUTHOR]

The actual trend of railway industry on track surveying is heading up the development of fast automated methods for continuous monitoring of track quality. This paper presents a model-based methodology for the estimation of lateral and vertical track irregularities from different sensors mounted on a Track Recording Vehicle (TRV): an Inertial Measurement Unit (IMU), a gauge sensor and a position encoder. The proposed methodology, based on the Kalman filtering technique, allows a fast and accurate measurement of track irregularities, without the use of a total station (which usually makes the measurement process very slow). The proposed method has been validated through an experimental campaign carried out on a 90 m long 1:10, scaled track facility and a scaled TRV at the University of Seville. The use of the scaled TRV allows the measurement of the 90 metres long scaled track at an operation velocity of V = 0.7 m/s in only two minutes. The results of the estimation of track irregularities have been compared with a previous measurement of the mentioned scaled track using manual means, showing a good agreement: with errors lower than 0.7 mm in the short wavelength range D1, which is the most influential in the dynamic behaviour of the vehicle. Additionally, the obtained results have been analysed and compared in the different wavelength ranges, according to standards. • A brand new track recording vehicle instrumented with inertial sensors is presented. • The scaled track recording vehicle is used to measure track irregularities. • A new methodology for surveying a track based on Kalman filter is presented. • The method proposed is validated experimentally in a 5-inch-wide scaled track. • The method shows good performance, with errors lower than 0.7 mm in the D1 range. [ABSTRACT FROM AUTHOR]

In this paper a virtual sensor is derived that can perform full field estimation of the sound field radiating from a number of loudspeakers in the time domain. The virtual sensor scheme contains two parts: Firstly, a time-domain physics-based numerical system level model that includes both the electro-mechanical behavior of the loudspeaker and the resulting wave propagation. Secondly, a Kalman filter in which the numerical model and a limited set of microphone measurements are combined to perform full field estimation. The loudspeaker dynamics are captured in a lumped parameter model and the resulting wave propagation is captured in a finite element model. To reduce the calculational complexity of the system level model, Krylov subspace based reduced order modeling is applied on the finite element model, leading to a significant reduction of the number of states. The system level model is brought to a discrete time state–space format, which allows for efficient implementation in the Kalman filter. The method is validated using two setups that use both vented and closed box loudspeakers, leading to improved estimation results as compared to pure simulation results, thus showing the merits of the virtual sensor. Furthermore, the importance of including the lumped parameter speaker model in the system level model is shown by comparing the estimation results with and without the inclusion of the lumped parameter model. • A system level model is derived for modeling the sound radiation from a speaker. • The model combines lumped parameter models with reduced order finite element models. • The model is combined with microphone measurements in a Kalman filter. • The Kalman filter performs full field estimation, thus acts as a virtual sensor. • The lumped parameter speaker model has a positive impact on the estimation results. [ABSTRACT FROM AUTHOR]

• Augmented Kalman filter based on sparse constraint theory is proposed. • Force estimation is transformed into constrained optimization based on the l 1 -norm. • Drift problem in the force estimation is solved in the proposed method. • Robustness and identification accuracy are improved by the sparse constraint. • New augmented state-space model is developed using the precise integration method. To ensure the accurate analysis and evaluation of structural integrity and vibration responses, a novel technique is required for load identification with minimal error. Accordingly, this paper presents an augmented Kalman filter (AKF) based on sparse constraint theory for solving state and input estimation problems. In the scheme developed in this study, the space-sparse characteristic of the force (as prior information) is introduced into the AKF via a pseudo- measurement equation. The unconstrained optimization of the AKF is transformed into constrained optimization based on the l 1 -norm. The proposed method solves the force drift problem in AKF more effectively than classical dummy measurements. Moreover, the stability of the system and its estimation accuracy are significantly increased. Additionally, a new augmented state-space model was established based on the augmented precise integration method, which can be applied more extensively than the zero-order hold model. To assess the performance of the proposed method, three cases were examined, namely, two numerical simulations and an experiment involving a three-story shear building. The results indicated that the proposed method outperforms the traditional dummy measurement method under a non-underdetermined and collocated sensor configuration. [ABSTRACT FROM AUTHOR]

• A parameter identification framework is developed for multirotor UAVs. • A hybrid model is utilized with three sequential excitation steps and extended Kalman filters. • Parameters of a new arm stretchable morphing MUAV is demonstrated for identification. • Identification and flight performance of the MUAV are experimentally validated. This paper presents a new framework to identify the dynamic characteristics of a multirotor unmanned aerial vehicle (MUAV). In particular, the identification framework is applied for an arm stretchable morphing MUAV. This MUAV is capable of adjusting the arm length during flight to maximize performance as well as stability. However, it is challenging to develop a flight controller without understanding several parameters of the MUAV, even though it has similar dynamic characteristics compared to conventional MUAVs. The framework consists of three sequentially operated steps: constrained roll dynamics on the ground, yaw dynamics, and roll/pitch dynamics in flight. A system is excited safely by a designed command for each step. Then, the Extended Kalman Filter (EKF) is utilized to estimate the unknown parameters that can best match the motion data with the dynamic model. The identification framework offers an effective means to design the controller by providing its dynamic characteristics. It is validated by numerical simulations and experiments with the arm stretchable MUAV. Furthermore, the identified parameters are utilized to maximize control performance using particle swarm optimization (PSO) in experiments. The flight performance along with the identified parameters has been experimentally demonstrated. [ABSTRACT FROM AUTHOR]

• A real-time simultaneous input-state-parameter estimation method is proposed. • The unknown inputs are modeled as modulated colored noise. • The low-frequency drift in the inputs and displacements estimation is eliminated. • The proposed method does not require the stationarity of the input/response. This paper introduces a novel method for real-time simultaneous input-state-parameter estimation with modulated colored noise excitation. In this method, the unknown inputs are modeled as modulated colored noise, which is realistic for real environmental excitations. By considering this input model, the typical problem of low-frequency drifts in the inputs and displacement responses estimation can be eliminated. The proposed approach provides a joint input-state-parameter estimation algorithm in a real-time manner by introducing the corresponding modeling equation for the unknown inputs into the extended Kalman filter. A Bayesian methodology is utilized to recursively update the noise covariance matrices in the filtering so stationarity of the input/response is not required for the proposed algorithm. Examples using truss and bridge models under different stationary scenarios are investigated. Compared with other existing methods that suffer from severe low-frequency drifts using only noisy acceleration measurements, the presented approach achieves substantially stable and accurate estimation for inputs, structural states and parameters. [ABSTRACT FROM AUTHOR]

In recent years, a new research direction in structural condition assessment has been focusing on developing automated or semi-automated procedures to identify a structure's modal parameters from its response measurements. This is because long-term structural monitoring systems rely on the implementation of system identification methodologies that often involve the intervention of an expert user with an acquired experience in the field. This paper aims to offer a semi-automated methodology for extracting the modal parameters independently of the chosen parametric system identification technique with minimum user involvement in the parameter selection process. Here, the framework is applied to two different parametric system identification algorithms: Data-Driven Stochastic Subspace Identification (DD-SSI) and Output Only Observer Kalman Filter (O/O OKID). The procedure can be represented as a multi-stage strategy where unsupervised tools and three clustering options are offered to the user to reach a reliable estimate of the modal parameters. The proposed procedure is validated with an application in the operational modal analysis of an existing hospital structure located in Italy. The results demonstrated excellent accuracy and robust performance of the methodology, even in the presence of closely spaced modes. The proposed procedure helps to improve the data analysis process in continuous monitoring, where usually, the algorithm's parameters need to be constantly updated by the user. • Semi-automated operational modal analysis with low user interaction • Methodology independent from the parametric system identification algorithm adopted • Three clustering techniques available to the user: two k-means approaches and DBSCAN • Application on the analysis of vibration data recorded on a RC hospital structure • Validation using two system identification algorithms: DD-SSI and O/O OKID [ABSTRACT FROM AUTHOR]

This paper presents an approach to solve the 2019/2020 NASA Langley UQ challenge problem on optimization under uncertainty. We define an uncertainty model (UM) as a pair f a | e , E , where f a | e is a probability density over a for each e ∈ E , and proceed to infer f a | e in a Bayesian fashion. Special attention is given to dimensionality reduction of the functional (time-series) data, to obtain a finite dimensional representation suitable for robust Bayesian inversion. Reliability analysis is performed using f a | e , whereas for design optimization we approximate f a | e using truncated Gaussians and a Gaussian copula. We apply an unscented transform (UT) in the standard normal space to estimate moments of the limit state, which is numerically very efficient. Design optimization is performed with this procedure to obtain negligible failure probability in g 1 and g 3 and acceptable failure probability and severity in g 2. • An approach to solve the NASA Langley UQ challenge on optimization under uncertainty. • Bayesian inference with functional (time-series) data. • Numerically efficient approximations that enable searching for optimal solutions. • A risk-based method for optimal control under aleatory and epistemic uncertainty. [ABSTRACT FROM AUTHOR]

Smart living spaces gather real-time sensor data and use the data to infer, predict, and make decisions. One important way of informing smart living systems is by localizing and tracking occupants. This paper utilizes floor vibration data generated by occupant footsteps—captured by a network of underfloor accelerometers—for passive occupant localization and tracking. A novel maximum likelihood (ML) footstep location estimator is proposed, based on received signal strength/power (RSS) at each sensor location. Localization error variance analysis related to sensor layout (a form of geometric dilution of precision) is studied through deriving and analyzing the theoretical Cramér–Rao lower bound. The proposed localization method does not require knowledge of floor properties, propagation velocity, nor damping. Occupant path tracking is achieved via a Kalman filtering scheme, assuming that an occupant has a zero-mean acceleration. The proposed ML localization method is evaluated using Monte Carlo simulations and using single-occupant walking experiments for 2 different test subjects on a 16 m × 2 m instrumented floor section. Results show superiority of the proposed method to previous RSS footstep localization methods. • Human footstep impacts are located via signals from hidden floor accelerometers • Received signal strength (RSS) at sensors determine an initial footstep location • Location estimates are more accurate than previous RSS methods • Knowledge of floor-dependent properties, such as damping, is not required • A Kalman filter incorporates walking kinematics to track an occupant's path • Localization error variance is analyzed via Mote Carlo simulations and the Cramér–Rao bound [ABSTRACT FROM AUTHOR]

• MEMS-INS, GPS and polarization compass are integrated together for navigation. • A multi-rate algorithm is proposed to solve the problem caused by different sampling frequencies. • Singular value decomposition is used to improve the numerical stability of the algorithm. The microelectromechanical system-inertial navigation system (MEMS-INS) is one of the most widely used sensor systems in navigation but must be used with other sensors because of its error accumulation characteristics. The information fusion method for integrated navigation systems based on filtering technology is thus very important. This paper introduces a new adaptive Kalman filter for nonlinear integrated systems. An improved multi-rate strong tracking square-root cubature Kalman filter (MR-STSCKF) for a MEMS-INS/Global Positioning System (GPS)/polarization compass integrated navigation system is proposed. The proposed filter is used to estimate the system covariance adaptively. The proposed approach can overcome the problem of the inconsistency between the sampling frequencies of different sensors while maintaining the high precision of the integrated navigation results. Experimental results demonstrate that the proposed MR-STSCKF algorithm is effective in improving the accuracy of the MEMS-INS/GPS/polarization compass integrated navigation system with a high sampling frequency. [ABSTRACT FROM AUTHOR]

• The method calibrates the inner and outer lever-arm errors simultaneously by utilizing the velocity differences of two RINSs. • The method designs the asynchronous rotation schemes of two RINSs distinctively and particularly. • The method could achieve the autonomous calibration of inner and outer lever-arm errors in dynamic conditions. • The method could enhance the linear motion information fusion accuracy of two RINSs in practical applications. Rotational inertial navigation system (RINS) can enhance navigation accuracy by gimbals rotation. In marine applications, two or more RINSs are usually employed in the same vessel to further improve the navigation performance through information fusion. However, fusion accuracy of linear motion information is influenced by the lever-arm effect errors caused by the inner lever-arm errors between the accelerometers and axes of rotation of RINS and the outer lever-arm errors between two RINSs, which should be accurately calibrated and compensated for high-precision applications. In this paper, the calibration method for inner and outer lever-arm errors of two RINSs is proposed. The method only utilizes the navigation information of two RINSs instead of external reference information to realize the calibration of the inner and outer lever-arm errors of two RINSs. The lever-arm models are deduced, and the asynchronous rotation schemes are designed by the characteristics of lever-arm errors of two RINSs. Then Kalman filter with velocity differences of two RINSs as measurements is constructed to estimate all inner and outer lever-arm errors. The method is adequately verified by simulations and experiments. Results indicate that the inner and outer lever-arm errors could be accurately calibrated and the standard deviations of calibration results are less than 1 mm. The oscillations of velocity differences of two RINSs could be obviously restrained and even disappear after the compensation of calibration results, which demonstrates the effectiveness of the proposed calibration method. [ABSTRACT FROM AUTHOR]

• Five different identification methods (FDD, OKID, SSI, SRIM, ARX) are performed to extract structural modal features. • A quantitative, ranking-based collocation framework is pursued to merge different algorithm findings and reduce method-specific modal identification uncertainties with quantified confidence on the outranking method. • The framework is verified with a numerical example and applied on two realistic testbeds, one large-scale shaking table test of a reinforced concrete bridge and another steel pedestrian bridge. • The applications demonstrate improved identification results, including damage and no damage cases in terms of true positives and true negatives. This paper presents multiple system identification of large-scale bridge structures proposing the combined usage of different modal parameter findings, namely from Frequency Domain Decomposition, Observer Kalman Filter Identification/Eigensystem Realization Algorithm, Combined Deterministic Stochastic Subspace Identification, System Realization Using Information Matrix, and Autoregressive Exogenous Model. A method-centric democratic ranking approach visualizes and quantifies the harmony among different system identification methods in terms of modal parameters, then ranks them based on the correlation among each other, and consequently complies with the highest rank modal parameter outputs. The synergistic scheme is applied on a numerical beam and two bridge structures including one healthy and another subjected to progressive damage. Looking at the top-rank selections, one can see that outlier identification results from a population of modal parameters can intuitively become extinct. The collaboration among methods is dependent on the chosen methods; therefore, method selection relies on care and fair representation of the identification features. Lack of agreement between methods can indicate low confidence in the outranking method and is quantified by median absolute deviation. Nevertheless, the majority of the algorithm population agrees on specific results, which are valuable to produce state knowledge despite low signal to noise ratio, especially without the presence of a reference. Thus, the collaborative usage of multiple methods in a systematic and ranking-based manner reduces significant error and outlier possibilities in modal identification due to algorithm-related issues, which is the novel contribution of this study. [ABSTRACT FROM AUTHOR]

• Optimal Sensor Placement in the framework of Augmented Kalman Filter estimation. • Two new metrics are proposed based on error covariance and estimator bandwidth. • The methods are compared with the existing Optimal Sensor Placement strategy. • Numerical validation on an industrial Finite Element Model is shown. The direct measurement of the external loads acting on a mechanical component represents often a challenge in many engineering applications. In this context, the attention of many researchers is focused on the field of inverse load identification. Several techniques are proposed in literature to address this problem by means of experimental methodologies, often coupled with simulation solutions. In this paper, a Kalman-based methodology is considered, which solves the problem of inverse load identification in a predictive manner. The common issue of most of the techniques is the selection of an optimal set of sensors which gives the best load estimation. In the Kalman-filtering framework, an Optimal Sensor Placement (OSP) strategy has been proposed by the authors and it aims to find the best set of sensors in terms of system observability, which is the minimum requirement of a stable estimation. However, this does not guarantee the most accurate load estimation. In this contribution, two alternative metrics are proposed, based on: i) steady-state error covariance of the estimation, ii) estimator bandwidth, with respect to the available set of measurements. Both criteria will be included in the existing OSP to improve the sensors selection. A comparison of the three strategies for multiple input/state estimation is discussed on an industrial-scale Finite Element Model, in order to show the improvement in the accuracy of the estimated quantities. [ABSTRACT FROM AUTHOR]