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Highlights • KAMPC takes the kinematics and trajectory tracking control as a combined problem. • KAMPC is the exploration process of intrinsic characteristics for autonomous systems. • We verified the algorithm from both theoretical analysis and real experiment. • KAMPC can reduce the average tracking residuals and has good statistical performance. Abstract Although accurate trajectory tracking of autonomous vehicles strongly depends on a precise model, it is difficult to establish a precise model for high-speed tracked vehicles under off-road conditions, due to the complicated interactions between the tracks and the terrain. This paper presents a novel trajectory tracking methodology, called kinematics-aware model predictive control (KAMPC), by combining the slip kinematic model with a trajectory tracking control strategy for skid-steered tracked vehicles. For the slip kinematic model, an online identification methodology called six-parameter slip parameter estimation (SSPE) algorithm is proposed based on the instantaneous centers of rotation. For the trajectory tracking control strategy, optimized algorithm model predictive control is used to obtain the optimal control inputs. Finally, our method is validated through extensive experiments based on a distributed electric-drive high-speed tracked vehicle test platform over different types of terrain and varied off-road surface conditions. Experiment results show that the tracked vehicle kinematic characteristics are distinctive in off-road conditions, and the slipping and skidding that occur when turning are critical to this work. Compared with the other three widely used types of methodologies, the present KAMPC approach can reduce the average tracking residuals and has the best statistical performance. [ABSTRACT FROM AUTHOR]

Highlights • Introducing modified versions of ERA and fast ERA to overcome their deficiencies in real life applications. • Introducing theoretical foundations for modified ERA and modified fast ERA. • Analyzing the theoretical results using the experimental tests. • Extracting the real parameters of the structural system. Abstract The eigensystem realization algorithm (ERA) and fast ERA are two popular methods of structural-system identification; however, these two powerful methods have deficiencies when employed in real-life identification projects. The main deficiencies of the ERA and fast ERA methods are that, when the order of the structural system is not known or is infinite, the sample time is not appropriate and/or initial condition is not zero, the identification results using these algorithms are not correct. This paper introduces a theoretical foundation called the modified ERA (mERA) and modified fast ERA (mfERA) to tackle these deficiencies. The simulation and experimental results are presented to demonstrate the validity of these analytical developments. [ABSTRACT FROM AUTHOR]

Abstract: The efficient identification of the unbalanced responses in the inner and outer rotors from the beat vibration is the key step in the dynamic balancing of a dual-rotor system with a slight rotating speed difference. This paper proposes a non-whole beat correlation method to identify the unbalance responses whose integral time is shorter than the whole beat correlation method. The principle, algorithm and parameter selection of the proposed method is emphatically demonstrated in this paper. From the numerical simulation and balancing experiment conducted on horizontal decanter centrifuge, conclusions can be drawn that the proposed approach is feasible and practicable. This method makes important sense in developing the field balancing equipment based on portable Single Chip Microcomputer (SCMC) with low expense. [Copyright &y& Elsevier]

Abstract: This paper addresses the issue of estimating the machine rotational speed based on vibration signal measurement. Advantages and limitations of existing methods are presented. Most of these methods give insufficient results when dealing either with significant variations of the rotational speed or with signals of relatively complex spectral characteristic. In order to overcome these obstacles, a new two-step method for instantaneous frequency estimation is proposed. The described method is based on principles of phase demodulation and joint time-frequency analysis, taking advantage of both of them. The paper presents the method and the algorithm for its implementation on the example of a simulated vibration signal. Finally, test rig experiment vibration data is used to test the efficiency of the method. [Copyright &y& Elsevier]

Abstract: This paper presents the Expectation Maximization algorithm (EM) applied to operational modal analysis of structures. The EM algorithm is a general-purpose method for maximum likelihood estimation (MLE) that in this work is used to estimate state space models. As it is well known, the MLE enjoys some optimal properties from a statistical point of view, which make it very attractive in practice. However, the EM algorithm has two main drawbacks: its slow convergence and the dependence of the solution on the initial values used. This paper proposes two different strategies to choose initial values for the EM algorithm when used for operational modal analysis: to begin with the parameters estimated by Stochastic Subspace Identification method (SSI) and to start using random points. The effectiveness of the proposed identification method has been evaluated through numerical simulation and measured vibration data in the context of a benchmark problem. Modal parameters (natural frequencies, damping ratios and mode shapes) of the benchmark structure have been estimated using SSI and the EM algorithm. On the whole, the results show that the application of the EM algorithm starting from the solution given by SSI is very useful to identify the vibration modes of a structure, discarding the spurious modes that appear in high order models and discovering other hidden modes. Similar results are obtained using random starting values, although this strategy allows us to analyze the solution of several starting points what overcome the dependence on the initial values used. [Copyright &y& Elsevier]

This paper presents a verification of a joint input-state estimation algorithm using data obtained from in situ experiments on a footbridge. The estimation of the input and the system states is performed in a minimum-variance unbiased way, based on a limited number of response measurements and a system model. A dynamic model of the footbridge is obtained using a detailed finite element model that is updated using a set of experimental modal characteristics. The joint input-state estimation algorithm is used for the identification of two impact, harmonic, and swept sine forces applied to the bridge deck. In addition to these forces, unknown stochastic forces, such as wind loads, are acting on the structure. These forces, as well as measurement errors, give rise to uncertainty in the estimated forces and system states. Quantification of the uncertainty requires determination of the power spectral density of the unknown stochastic excitation, which is identified from the structural response under ambient loading. The verification involves comparing the estimated forces with the actual, measured forces. Although a good overall agreement is obtained between the estimated and measured forces, modeling errors prohibit a proper distinction between multiple forces applied to the structure for the case of harmonic and swept sine excitation. [ABSTRACT FROM AUTHOR]

Abstract: The focus of this paper is Bayesian modal parameter recursive estimation based on an interacting Kalman filter algorithm with decoupled distributions for frequency and damping. Interacting Kalman filter is a combination of two widely used Bayesian estimation methods: the particle filter and the Kalman filter. Some sensitivity analysis techniques are also proposed in order to deduce a recursive estimate of modal parameters from the estimates of the damping/stiffness coefficients. [Copyright &y& Elsevier]

Abstract: The objective of this paper is to propose a vibration-based automated framework dealing with local faults occurring on bearings in the transmission of a helicopter. The knowledge of the shaft speed and kinematic computation provide theoretical frequencies that reveal deteriorations on the inner and outer races, on the rolling elements or on the cage. In practice, the theoretical frequencies of bearing faults may be shifted. They may also be masked by parasitical frequencies because the numerous noisy vibrations and the complexity of the transmission mechanics make the signal spectrum very profuse. Consequently, detection methods based on the monitoring of the theoretical frequencies may lead to wrong decisions. In order to deal with this drawback, we propose to readjust the fault frequencies from the theoretical frequencies using the redundancy introduced by the harmonics. The proposed method provides the confidence index of the readjusted frequency. Minor variations in shaft speed may induce random jitters. The change of the contact surface or of the transmission path brings also a random component in amplitude and phase. These random components in the signal destroy spectral localization of frequencies and thus hide the fault occurrence in the spectrum. Under the hypothesis that these random signals can be modeled as cyclostationary signals, the envelope spectrum can reveal that hidden patterns. In order to provide an indicator estimating fault severity, statistics are proposed. They make the hypothesis that the harmonics at the readjusted frequency are corrupted with an additive normally distributed noise. In this case, the statistics computed from the spectra are chi-square distributed and a signal-to-noise indicator is proposed. The algorithms are then tested with data from two test benches and from flight conditions. The bearing type and the radial load are the main differences between the experiences on the benches. The fault is mainly visible in the spectrum for the radially constrained bearing and only visible in the envelope spectrum for the “load-free” bearing. Concerning results in flight conditions, frequency readjustment demonstrates good performances when applied on the spectrum, showing that a fully automated bearing decision procedure is applicable for operational helicopter monitoring. [Copyright &y& Elsevier]

Abstract: The cylinder pressure is arguably the most important variable characterizing the combustion process in internal combustion engines. In light of the recent advances in combustion technologies and in engine control, the use of cylinder pressure is now frequently considered as a feedback signal for closed-loop combustion control algorithms. In order to generate an accurate pressure trace for real-time combustion control and diagnostics, the output of the in-cylinder pressure transducer must be conditioned with signal processing methods to mitigate the well-known issues of offset and noise. While several techniques have been proposed for processing the cylinder pressure signal with limited computational burden, most of the available methods still require one to apply low-pass filters or moving average windows in order to mitigate the noise. This ultimately limits the opportunity of exploiting the in-cylinder pressure feedback for a cycle-by-cycle control of the combustion process. To this extent, this paper presents an estimation algorithm that extracts the pressure signal from the in-cylinder sensor in real-time, allowing for estimating the 50% burn rate location and IMEP on a cycle-by-cycle basis. The proposed approach relies on a model-based estimation algorithm whose starting point is a crank-angle based engine combustion model that predicts the in-cylinder pressure from the definition of a burn rate function. Linear parameter varying (LPV) techniques are then used to expand the region of estimation to cover the engine operating map, as well as allowing for real-time cylinder estimation during transients. The estimator is tested on the experimental data collected on an engine dynamometer as well as on a high-fidelity engine simulator. The results obtained show the effectiveness of the estimator in reconstructing the cylinder pressure on a crank-angle basis and in rejecting measurement noise and modeling errors, with considerably low computation effort. [Copyright &y& Elsevier]

Abstract: In operational modal analysis, the modal parameters (natural frequencies, damping ratios and mode shapes), obtained with stochastic subspace identification from ambient vibration measurements of structures, are subject to statistical uncertainty. It is hence necessary to evaluate the uncertainty bounds of the obtained results, which can be done by a first-order perturbation analysis. To obtain vibration measurements at many coordinates of a structure with only a few sensors, it is common practice to use multiple sensor setups for the measurements. Recently, a multi-setup subspace identification algorithm has been proposed that merges the data from different setups prior to the identification step to obtain one set of global modal parameters, taking the possibly different ambient excitation characteristics between the measurements into account. In this paper, an algorithm is proposed that efficiently estimates the covariances on modal parameters obtained from this multi-setup subspace identification. The new algorithm is validated on multi-setup ambient vibration data of the Z24 Bridge, benchmark of the COST F3 European network. [Copyright &y& Elsevier]

Abstract: In this paper, consistent multiple-input frequency-domain estimators will be presented based on a right matrix-fraction description of the frequency response function. This matrix-fraction description leads to a fast algorithm in the same way as the least-squares complex frequency-domain estimator (LSCF). The use of multiple inputs simultaneously in the estimation (so-called polyreference estimation) has the advantage that it allows to separate closely spaced modes. The main drawback of the LSCF estimator is that it is theoretically inconsistent, i.e.the estimates do not converge to the true values when the number of measurements increases to infinity. However, the noise information available from most measurements can be used to construct a maximum likelihood-like weighting for the LSCF estimators, giving consistent estimates. The results are fast, polyreference, and consistent weighted generalised total-least-squares (WGTLS) estimators. The iterative quadratic maximum likelihood (IQML) estimator is practically consistent for high signal-to-noise ratios, with the additional advantage that it yields clear stabilisation charts. The performance of the presented WGTLS and IQML estimators is evaluated by means of ground vibration test data and demonstrated on flight flutter test data. [Copyright &y& Elsevier]

Abstract: Modal parameter estimation requires a lot of user interaction, especially when parametric system identification methods are used and the modes are selected in a stabilization diagram. In this paper, a fully automated, generally applicable three-stage clustering approach is developed for interpreting such a diagram. It does not require any user-specified parameter or threshold value, and it can be used in an experimental, operational, and combined vibration testing context and with any parametric system identification algorithm. The three stages of the algorithm correspond to the three stages in a manual analysis: setting stabilization thresholds for clearing out the diagram, detecting columns of stable modes, and selecting a representative mode from each column. An extensive validation study illustrates the accuracy and robustness of this automation strategy. [Copyright &y& Elsevier]

Abstract: Modal strain energy has been widely utilized as a damage-sensitive feature to detect structural damage. Based on the closed-form of element modal strain energy sensitivity, a statistic structural damage detection algorithm is proposed in this paper. The method is oriented to the ambient vibration measurements where only the operational mode shapes are available. The established element damage equations are incorporated with the modal scaling factors so that the damage and modal scaling factor can be solved simultaneously. The statistic analysis is implemented to take into account the uncertainties existing in the structural model and measured structural modal parameters. The sensitivity formulas of system matrix and residual vector with respect to noise are derived. The proposed statistics based element damage equations have a compact algebraic form, which does not require a large computation time and a high storage capacity. The method is verified by a numerical simply supported beam with different assumed damage. The effects of noise and damage levels on damage detection are investigated. It is demonstrated that the proposed method can identify most likely damaged elements. [Copyright &y& Elsevier]

Abstract: It is important but still challenging to detect structural damage with limited input and output measurement signals. In this paper, an algorithm is proposed for detecting structural damage with limited input and output measurement signals. The algorithm is based on sequential application of an extended Kalman estimator for the extended state vector of a structure and least-squares estimation of its unknown external excitations. Analytical recursive solutions for the identification of structural parameters and unknown excitations are derived. Such straightforward derivation and analytical solutions are not available in the previous literature. Structural damage can be detected from the degradation of the identified element stiffness. Numerical examples of detecting damage of some small size structural systems are used to demonstrate the performances of the proposed algorithm. Then, the algorithm is extended to detect structural damage of large size structural systems based on substructure approach. Inter-connection effect between adjacent substructures is considered by ‘additional unknown inputs’ to substructures. It is shown that the ‘additional unknown inputs’ can be estimated by the algorithm without the measurements of the substructure interface DOFs, which is superior to previous identification approaches. A numerical example of detecting structural damage of a large size truss illustrates the efficiency of the proposed algorithm. [Copyright &y& Elsevier]

Abstract: Modal-based damage detection algorithms are well-known techniques for structural health assessment, but they are not commonly used due to the lack of automated modal identification and tracking procedures. Development of such procedures is not a trivial task since traditional modal identification requires extensive interaction from an expert user. Nevertheless, computational efforts have to be carefully considered. If fast on-line data processing is crucial for quickly varying in time systems (such as a rocket burning fuel), a number of vibration-based condition monitoring applications are performed at very different time scales, resulting in satisfactory time steps for on-line data analysis. Moreover, promising results in the field of automated modal identification have been recently achieved. In the present paper, a literature review on this topic is presented and recent developments concerning fully automated output-only modal identification procedures are described. Some case studies are also reported in order to validate the approach. They are characterized by different levels of complexity, in terms of mode coupling, dynamic interaction effects and level of vibration. Advantages and drawbacks of the proposed approach will be pointed out with reference to available experimental results. The final objective is the implementation of a fully automated system for vibration-based structural health monitoring of civil engineering structures and identification of adequate requirements about sensor number and layout, record duration and hardware characteristics able to ensure a reliable low-cost health assessment of constructions. Results of application of the proposed methodology to modal parameter estimation in operational conditions and during ground motions induced by the recent L’Aquila earthquake will be finally presented and discussed. [Copyright &y& Elsevier]

Abstract: As an important issue, we first address in this paper the problem of a regression matrix with non-homogeneous physical units in the parameter estimation of multibody systems. This matrix contains the most important information about the motion of the system. Attention must be paid to this before implementing any parameter estimation algorithm due to the unit inconsistency in matrix multiplication required in such algorithms. A procedure to treat this problem in a proper way will be proposed. An experiment on a six degrees of freedom (DOF) robotic device, whose reference link follows a desired trajectory, is performed. The data collected from the experiment are then used for sensitivity analysis of inertial parameters based on the unit-homogenized regression matrix of the system. In this way, we characterize the influence of each selected inertial parameter on the dynamics of the system using unit-consistent mathematical manipulations. [Copyright &y& Elsevier]

The least-squares complex frequency-domain (LSCF) estimator—commercially known as the PolyMAX estimator—nowadays is used intensively in various modal analysis applications. The main advantages are the very clear stabilization diagrams and even more important, the speed. In this paper it is shown that confidence intervals of the modal parameter estimates can be derived without major additional calculations, if the frequency response functions are uncorrelated and noise information (e.g. the coherence function) is available. This approach is also applied to the iterative quadratic maximum likelihood (IQML) estimator, indicating strong analogies to the maximum likelihood (ML) estimator. The algorithm is evaluated by means of Monte Carlo simulations. [Copyright &y& Elsevier]

Using the well-known bandwidth formula and the half power bandwidth formula [R.E.D. Bishop, G.M.L. Gladwell, An investigation into the theory of resonance testing, Philosophical Transactions of the Royal Society of London A 255 (1963) 241–280], in particular, is the simplest way to estimate modal damping for engineers. By using the half power bandwidth formula, the damping factor is estimated to be approximately the half bandwidth at the half power points. One of the major limitations that restrict the use of this method is the coupling effect between closely spaced modes. In this paper, the dependence of the damping estimation accuracy on the selected power ratios is studied with both analytical and experimental data of frequency response functions. The results show that by selecting adequate power ratio values, the coupling effect can be minimized and the estimation accuracy can be significantly improved for closely spaced modes. A further improvement of accuracy can be obtained by applying the algorithm of mode isolation [H.P. Yin, D. Duhamel, Substraction technique and finite difference formulas for modal parameter estimation, Mechanical Systems and Signal Processing 18 (2004) 1497–1503; M.S. Allen, J.H. Ginsberg, A global, single-input-multi-output (SIMO) implementation of the algorithm of mode isolation and application to analytical and experimental data, Mechanical Systems and Signal Processing 20 (2006) 1090–1111]. Also an exact bandwidth formula in case of a single degree of freedom system is presented and the link between the exact formula and the classical approximated formula is indicated. The exact bandwidth formula provides a new theoretical basis of the bandwidth method for the damping estimation from frequency response functions. [Copyright &y& Elsevier]

Abstract: This study investigates the performance of a time-domain parameter estimation algorithm aimed at identifying modal parameters from excitation and response data corrupted with significant measurement noise and unmeasured sources of periodic and random excitation. The parameters of an autoregressive moving average with exogenous excitation (ARMAX) model are estimated using an iterative multistage estimation algorithm. The use of backwards autoregressive with exogenous excitation (ARX) models in the multistage algorithm allows vibrational modes to be distinguished from spurious numerical poles and is also the basis of a model selection criterion. A diagonal parameterisation of the autoregressive (AR) polynomial matrices allows the MIMO ARMAX model to be separated into a number of MISO systems, and permits simple manipulation and stabilisation of the estimated model. Measurement noise and sources of unmeasured random and periodic excitations are accounted for by the ARMAX model structure. In this paper, the theory and algorithm of the ARMAX model is given. [Copyright &y& Elsevier]

Abstract: This paper presents a frequency domain method for estimating the parameters of a multi-frequency signal from the discrete-time observations corrupted by additive noise. With two weak restrictions on the window function used, a concise non-linear least squares-based parameter estimation model, which exploits the joint information carried by the spectral samples nearby each spectrum peak, is established, and utilising its particular structure an efficient two-step iterative algorithm is developed to solve it. The derived analytical expressions of the estimator variances indicate that this approach has superior accuracy over other computationally efficient frequency domain estimation methods. Simulation results confirm the validity of the presented method. [Copyright &y& Elsevier]