Real-time parameter estimation for degrading and pinching hysteretic models

Many civil and mechanical structures exhibit hysteresis with degradation and/or pinching when subject to severe cyclic loadings such as earthquakes, wind, or sea waves. The modeling and identification of non-linear hysteretic systems with degradation and pinching is therefore a practical problem encountered in the engineering mechanics field. On-line identification of degrading and pinching hysteretic systems is quite a challenging problem because of its complexity. A recently developed technique, the unscented Kalman filter (UKF) which is capable of handling any functional non-linearity, is applied to the on-line parametric system identification of hysteretic differential models with degradation and pinching. Simulation results show that the UKF is efficient and effective for the real-time state estimation and parameter identification of highly non-linear hysteretic systems with degradation and pinching.     

Bayesian System Identification using auxiliary stochastic dynamical systems

Bayesian approaches to statistical inference and system identification became practical with the development of effective sampling methods like Markov Chain Monte Carlo (MCMC). However, because the size and complexity of inference problems has dramatically increased, improved MCMC methods are required. Dynamical systems based samplers are an effective extension of traditional MCMC methods. These samplers treat the posterior probability distribution as the potential energy function of a dynamical system, enabling them to better exploit the structure of the inference problem. We present an algorithm, Second-Order Langevin MCMC (SOL-MC), a stochastic dynamical system based MCMC algorithm, which uses the damped second-order Langevin stochastic differential equation (SDE) to sample a posterior distribution. We design the SDE such that the desired posterior probability distribution is its stationary distribution. Since this method is based upon an underlying dynamical system, we can utilize existing work to develop, implement, and optimize the sampler's performance. As such, we can choose parameters which speed up the convergence to the stationary distribution and reduce temporal state and energy correlations in the samples. We then apply this sampler to a system identification problem for a non-linear hysteretic structure model to investigate this method under globally identifiable and unidentifiable conditions.     

Sequential non-linear least-square estimation for damage identification of structures

An early detection of structural damage is an important goal of any structural health monitoring system. In particular, the ability to detect damages on-line, based on vibration data measured from sensors, will ensure the reliability and safety of the structures. In this connection, innovative data analysis techniques for the on-line damage detection of structures have received considerable attentions recently, although the problem is quite challenging. In this paper, we proposed a new data analysis method, referred to as the sequential non-linear least-square (SNLSE) approach, for the on-line identification of structural parameters. This new approach has significant advantages over the extended Kalman filter (EKF) approach in terms of the stability and convergence of the solution as well as the computational efforts involved. Further, an adaptive tracking technique recently proposed has been implemented in the proposed SNLSE to identify the time-varying system parameters of the structure. The accuracy and effectiveness of the proposed approach have been demonstrated using the Phase I ASCE structural health monitoring benchmark building, a non-linear elastic structure and non-linear hysteretic structures. Simulation results indicate that the proposed approach is capable of tracking on-line the changes of structural parameters leading to the identification of structural damages.     

Sequential non-linear least-square estimation for damage identification of structures with unknown inputs and unknown outputs

The detection of structural damages real-time on-line, based on vibration data measured from sensors, is an important but challenging research topic, and it has received considerable attentions recently. Due to practical limitations, it is highly desirable to install as few sensors as possible in the structural health monitoring system, leading to incomplete measurements of structural responses and excitations. The traditional time-domain analysis techniques, such as the least-square estimation (LSE) method and the extended Kalman filter (EKF) approach, require that all the external excitations (inputs) be available, which may not be the case for most structural health monitoring systems. Recently, the adaptive sequential non-linear least-square estimate (SNLSE) method has been proposed for the on-line identification of structural damages. In this paper, we extend the SNLSE method to cover the general case with unknown (unmeasured) excitations (inputs) and unknown (unmeasured) acceleration responses (outputs) in order to reduce the number of sensors required in the structural health monitoring system, referred to as the SNLSE-UI-UO. Analytic recursive solutions for the new approach are derived and presented. The accuracy and effectiveness of the proposed approach have been demonstrated using the Phase I ASCE structural health monitoring benchmark building, a 5-degree-of-freedom non-linear hysteretic building model, and a 3-story steel frame finite-element model. Simulation results indicate that the proposed approach is capable of tracking the changes of structural parameters leading to the identification of damages.     

水下滑翔器位姿估计的改进高斯混合粒子滤波器设计与验证（英文）

近年用于水下滑翔器的低成本导航系统成为研究热点,导航器件的成本与精度之间的折中问题仍然是目前的难题。针对因使用低成本的导航元件而造成低精度位姿估计的问题,提出用于位姿估计的改进高斯混合粒子滤波(IGMPF)方法。用高斯混合模型来估计非高斯噪声,改进的粒子滤波进一步提高位姿估计精度。为了验证其效果,该方法应用于自主设计的水下滑翔器导航系统中并做了车载实验,实验结果表明所提IGMPF方法在实际应用中比传统的EKF和UKF表现更优,姿态角和位移误差比EKF和UKF减小了至少30%。     

Identification and parameter estimation of a bilinear oscillator using Volterra series with harmonic probing

Identification of non-linear systems is mainly limited to polynomial form non-linearities. Among the non-polynomial forms, bilinear oscillator constitutes an important class of non-linear systems and it has been used for modeling of various physical systems, particularly for structural elements with a breathing crack. An identification procedure is presented here for the class of bilinear oscillator, using higher order FRFs derived from Volterra series under harmonic excitation. The procedure addresses the problem of both; identification of the non-linearity structure as well as estimation of the bilinear parameter, which can be correlated to the crack severity and structural degradation. The procedure is illustrated with numerical simulation and the estimation results indicate that even a weakly bilinear state introduced by a small crack size can be accurately identified and measured.     

Instrumental variables approach to identification of a class of MIMO Wiener systems

A new approach to identification of multi-input multi-output (MIMO) Wiener systems using the instrumental variables method is presented. It is assumed that static nonlinear elements are invertible and their inverse characteristics can be expressed or approximated by polynomials of known orders. It is also assumed that the linear part of the Wiener system can be represented by a matrix polynomial form. Based on these assumptions, the Wiener system is transformed introducing a new parameterization and its parameters are estimated using a linear-in-parameters model. To solve the problem of non-consistency of least squares parameter estimates, an instrumental variables method is employed. A numerical example is included to show the effectiveness and the practical feasibility of the presented approach.