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• 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]

This paper investigates the problem of parametric identification of highly uncertain bolted connections. The unknown parameters representing stiffness of the connections are estimated using two commonly accepted methods: (1) the traditional mode matching approach and (2) a probabilistic Bayesian framework based on the maximum a posteriori (MAP) formulation. Additionally, the uncertainties of the unknown parameters are also estimated and compared for both methods. A numerical example and a real lab-scale frame structure with highly uncertain bolted connections were used in the tests. In the experimental case, the system eigenvalues (squares of the natural frequencies) and the mode shapes measured in a broad frequency range were employed. The measured mode shapes were strongly disturbed by assembly discrepancies of the bolted connections. Finally, both methods were compared in terms of computational efficiency on a large-scale FE model (31,848 degrees of freedom). Despite the sophistication of the Bayesian approach in treating the trade-off between measurement errors and expected modeling errors, the results indicate that the two tested methods yield similar values for the unknown parameters. The Bayesian approach requires numerical regularization to calculate the parameter covariance matrix, which may decrease its reliability. In contrast, the mode matching method avoids such numerical difficulties. Furthermore, the Bayesian approach requires a much larger number of iterations and a careful selection of the weighting parameters. • A comparison between the mode matching and Bayesian approach for model updating. • Stiffness parameters for multiple highly-uncertain bolted connections are identified. • A numerical and experimental case study is conducted based on measured modal data. • Parameter uncertainties are estimated using both methods. • Ill-conditioning and convergence problems are discussed and addressed. [ABSTRACT FROM AUTHOR]

Estimation and variable selection in partially linear models for massive data has been discussed by several authors. However, there does not seem to exist an established procedure for other semiparametric models, such as the semiparametric varying-coefficient linear model, the single index regression model, the partially linear errors-in-variables model, etc. In this paper, we propose a general procedure for variable selection in high-dimensional general semiparametric models by penalized semiparametric estimating equations. Under some regularity conditions, the oracle property is established, which the number of parameters is allowed to diverge. Furthermore, we also propose a split-and-conquer variable selection procedure for high-dimensional general semiparametric models with massive data. Under some weak regularity conditions, we establish the oracle property of the proposed procedure when the number of subsets does not grow too fast. What is more, the split-and-conquer procedure enjoys the oracle property as the penalized estimator by using all the dataset, and can substantially reduce computing time and computer memory requirements. The performance of the proposed method is illustrated via a real data application and numerical simulations. [ABSTRACT FROM AUTHOR]

• A novel Bayesian formulation for the uncertainty quantification in modal identification was developed. • The proposed formulation is tailor-made for modal identification using seismic data. • The proposed formulation is computational efficient, and it is applicable under both well-separated and closely-spaced modes situations. • The proposed formulation was verified using data collected from shaking table tests and field tests on a real building. Modal identification is an important step to evaluate the basic modal properties of structures using measured data. In this process, the existence of modeling error and measurement noise will inevitably lead to uncertainty in modal identification. A Bayesian framework was established to determine the optimal values of modal parameters efficiently based on the structural response under earthquake excitations. In this paper, in the same framework, a new method is presented to determine the analytical formulation for carrying out uncertainty evaluation of modal parameters utilizing seismic structural responses. Based on Bayes' Theorem, the covariance matrix can be calculated based on the Hessian matrix determined using the negative log-likelihood function (NLLF). In this work, for determining the Hessian matrix, a series of formulations were derived analytically. Simulated data of a six-story building were generated to investigate the new formulations. The noise effects on the posterior uncertainty were investigated. After the verification, applications were carried out using the data in a shaking table test model under laboratory conditions and a real building from a field test. The modal properties and their uncertainty obtained by the proposed method were studied under different earthquake excitations. [ABSTRACT FROM AUTHOR]

• Using vibration data, both mass and stiffness are updated with addressing the coupling effect. • Multiple Markov chains are parallelly run to estimate complex posterior PDF. • Damage location and severity are reliably and probabilistically identified using vibration data. Damage detection inevitably involves uncertainties originated from measurement noise and modeling error. It may cause incorrect damage detection results if not appropriately treating uncertainties. To this end, vibration-based Bayesian model updating (VBMU) is developed to utilize vibration responses or modal parameters to estimate structural parameters and the associated uncertainties of those estimates. However, traditional VBMU often assumes that mass is well known and invariant because simultaneous identification of mass and stiffness may yield an unidentifiable problem due to the coupling effect of the mass and stiffness. In addition, the posterior PDF in VBMU is usually approximated by single Markov Chain Monte Carlo (MCMC), leading to a low acceptance rate and limited capability for complex structures. This paper proposed a novel VBMU to address the coupling effect and identify mass and stiffness by adding known mass. Two vibration data sets are acquired from original and modified systems with added mass, giving the new characteristic equations. Then, the posterior PDF is reformulated by measured data and predicted counterparts from new characteristic equations. For efficiently approximating the posterior PDF, Differential Evolutionary Adaptive Metropolis (DREAM) algorithm is adopted to draw samples by running multiple Markov chains parallelly to enhance acceptance rate and sufficiently explore possible solutions. Finally, a numerical example with a ten-story shear building and a laboratory-scale three-story frame structure are utilized to demonstrate the efficacy of the proposed VBMU framework. The results show that the proposed method can successfully identify both mass and stiffness, and their uncertainties. Reliable probabilistic damage detection can also be achieved. [ABSTRACT FROM AUTHOR]

In this paper, linear spatial autoregressive (SAR) models with covariate measurement errors are studied. A three-stage least squares (3SLS) estimation method both with Berkson's and classical types of instrumental variables is proposed and asymptotic normality of the proposed estimator using each type of instrumental variables is derived under mild conditions. Simulation studies are conducted to investigate the finite sample performance of the proposed estimator. A real data example is used to illustrate the developed method. [ABSTRACT FROM AUTHOR]

By utilizing intermediate Gaussian approximations, this paper establishes asymptotic linear representations of nonparametric deconvolution estimators for the classical measurement error model with repeated measurements. Our result is applied to derive confidence bands for the density and distribution functions of the error-free variable of interest and to establish faster convergence rates of the estimators than the ones obtained in the existing literature. Due to slower decay rates of the linearization errors, however, our bootstrap counterparts for confidence bands need to be constructed by subsamples. [ABSTRACT FROM AUTHOR]

• A nonlinear system identification method using Harmonic Balance is developed. • The proposed method is capable of accurately identifying non-smooth nonlinearity. • The performance of proposed method is demonstrated numerically and experimentally. • The method can deal with the effects of higher harmonics in input force and outputs. • The effect of model error and measurement noise in the proposed method is shown. Testing nonlinear structures to characterise their internal nonlinear forces is challenging. Often nonlinear structures are excited by harmonic forces and yield a multi-harmonic response. In many systems, particularly ones with strong nonlinearities, the effect of higher harmonics in the force and responses cannot be ignored. Even if the intended excitation is a single frequency sinusoidal force, the interaction of the shaker and the nonlinear structure can lead to harmonics in the applied force. The effects of these higher harmonics of the input force on nonlinear model identification in structural dynamics are often neglected. The objective of this study is to introduce an identification method, motivated by the alternating frequency/time approach using harmonic balance (AFTHB), which is able to consider both multi-harmonic forces and multi-harmonic responses of the system. The proposed AFTHB method can include all significant harmonics by selecting an appropriate time step and sampling frequency to guarantee the accuracy of the results. An analytical harmonic-balance-based (AHB) approach is also considered for comparison. However, the inclusion of all significant harmonics of the response in the analytical expansion of the nonlinear functions is often cumbersome. Furthermore, the AFTHB method can easily cope with complex nonlinearities such as Coulomb friction and with multi-degree of freedom nonlinear systems. Including the effect of higher harmonics in the identification process reduces the approximation error due to truncation and very accurate approximation of the balanced equations of each harmonic is obtained. The proposed identification method requires prior knowledge or an appropriate estimation of the type of system nonlinearities. However, the method of model selection may be used for a set of candidate models, and avoiding a dictionary of arbitrary candidate basis functions significantly reduces the computational costs. This paper highlights the important features of the AFTHB method to ensure accurate estimation using four simulated and two experimental examples. The effects of the number of harmonics considered, the modelling error, measurement noise and the frequency range on the quality of the estimated model are demonstrated. [ABSTRACT FROM AUTHOR]

• A hybrid prognostic framework consisting of GRU and Wiener process is proposed. • The adaptive Wiener process model considers four variability sources. • Both the available measurements and predicted observations by GRU are utilized. • A Kalman filtering algorithm is developed for updating machinery state. • The exponentially weighted average is used to account for the drift adaptivity. Remaining useful life (RUL) prediction is fundamental to prognostics and health management (PHM). Considering the advantages of both model-based and data-driven prognostic approaches, this paper develops a hybrid prognostic method for machinery degradation. First, a 3σ criterion-based algorithm is introduced to detect the initial timepoint of degradation. Second, gated recurrent unit (GRU) network is utilized to learn the degradation characteristics based on the available data and thereby predict the long-term degradation trend by a multi-prediction procedure. Then, an adaptive Wiener process model considering measurement errors is constructed. The states of this model consisting of the drift rate and the underlying degradation value are updated adaptively based on the monitored observations and the predictions by GRU using a Kalman filtering algorithm. The predicted values of the RUL can be determined according to the underlying degradation and the failure threshold. Finally, to account for the drift adaptivity in the future degradation, exponentially weighted average method is adopted to aggregate the estimated drift sequence from the current time until failure for the derivation of real-time RUL distributions. The effectiveness and superiority are illustrated by a simulation study and an application to rolling element bearings. [ABSTRACT FROM AUTHOR]