Theory and Methods

Sequential Monte Carlo (SMC) methods (also known as particle filter) provide a way to solve the state estimation problem in nonlinear non-Gaussian state space models (SSM) through numerical approximation. Particle smoothing is one retrospective state estimation method based on particle filtering. In this paper, we propose a new particle smoother. The basic idea is easy and leads to a forward-backward procedure, where the Metropolis-Hastings algorithm is used to resample the filtering particles. The goodness of the new scheme is assessed using a nonlinear SSM. It is concluded that this new particle smoother is suitable for state estimation in complicated dynamical systems.

Nonlinear mixed-effects state space models with applications to HIV dynamics

The problem of sequential detection of spontaneous changes in equations for unobserved state variables and observations of linear and nonlinear multivariate state-space models is considered. We consider the case of new additive terms and the case of changing coefficients of these equations. The proposed nonparametric method uses the idea of the “moving window” of observations. In Theorem 4.1 the exponential rate of convergence to zero for type 1 error probability (a wrong decision about a change) is proved. In Theorem 4.2 we consider type 2 error probability and the normalized (by the volume N of the moving window) delay time in change-point detection. Asymptotic optimality of the proposed method is proved in Theorem 5.1. Experimental study includes Monte Carlo examples of sequentially detected changes in coefficients of linear and nonlinear state-space models.

Nonlinear state-space models are ubiquitous in modeling real-world dynamical systems. Sequential Monte Carlo (SMC) techniques, also known as particle methods, are a well-known class of parameter estimation methods for this general class of state-space models. Existing SMC-based techniques rely on excessive sampling of the parameter space, which makes their computation intractable for large systems or tall data sets. Bayesian optimization techniques have been used for fast inference in state-space models with intractable likelihoods. These techniques aim to find the maximum of the likelihood function by sequential sampling of the parameter space through a single SMC approximator. Various SMC approximators with different fidelities and computational costs are often available for sample-based likelihood approximation. In this paper, we propose a multi-fidelity Bayesian optimization algorithm for the inference of general nonlinear state-space models (MFBO-SSM), which enables simultaneous sequential selection of parameters and approximators. The accuracy and speed of the algorithm are demonstrated by numerical experiments using synthetic gene expression data from a gene regulatory network model and real data from the VIX stock price index.

Extracting latent nonlinear dynamics from observed time-series data is important for understanding a dynamic system against the background of the observed data. A state space model is a probabilistic graphical model for time-series data, which describes the probabilistic dependence between latent variables at subsequent times and between latent variables and observations. Since, in many situations, the values of the parameters in the state space model are unknown, estimating the parameters from observations is an important task. The particle marginal Metropolis–Hastings (PMMH) method is a method for estimating the marginal posterior distribution of parameters obtained by marginalization over the distribution of latent variables in the state space model. Although, in principle, we can estimate the marginal posterior distribution of parameters by iterating this method infinitely, the estimated result depends on the initial values for a finite number of times in practice. In this paper, we propose a replica exchange particle marginal Metropolis–Hastings (REPMMH) method as a method to improve this problem by combining the PMMH method with the replica exchange method. By using the proposed method, we simultaneously realize a global search at a high temperature and a local fine search at a low temperature. We evaluate the proposed method using simulated data obtained from the Izhikevich neuron model and Lévy-driven stochastic volatility model, and we show that the proposed REPMMH method improves the problem of the initial value dependence in the PMMH method, and realizes efficient sampling of parameters in the state space models compared with existing methods.

This paper describes an efficient method to teach analysis and simulation of power electronic converters to undergraduate students, using system level nonlinear state-space models. System-level modeling of power electronic converters reproduces only the ideal switching behavior of the semiconductors and is a useful concept for the numerical simulation of power converters, since simulations present no convergence problems and require little computational time. Switched state-space models, programmed in the MATLAB/SIMULINK software package, can be advantageously used to simulate power converters at the system level and also to design and study their controllers. Switched state-space nonlinear models should be obtained using a theoretical framework suitable for the enhanced control of variable structure power systems. Since the method is inherently nonlinear, no approximated linear models are needed; and since state-space models are used, modern control techniques (sliding mode, neural networks, fuzzy logic) for power converters can easily be used. This paper summarizes the proposed methodology and gives some examples.

Sparse Bayesian Learning (SBL) provides sophisticated (state) model order selection with unknown support distribution. This allows to handle problems with big state dimensions and relatively limited data by exploiting variations in parameter importance. The techniques proposed in this paper allow to handle the extension of SBL to time-varying states, modeled as diagonal first-order auto-regressive (DAR(1)) processes with unknown parameters to be estimated also. Adding the parameters to the state leads to an augmented state and a non-linear (at least bilinear) state-space model. The proposed approach, which applies also to more general non-linear models, uses a combination of belief propagation (BP), Variational Bayes (VB) or mean field (MF) techniques, and Expectation Propagation (EP) to approximate the posterior marginal distributions of the scalar factors. We propose Fisher Information Matrix analysis to determine the variable split between the use of BP and VB allowing to stay optimal in terms of Laplace approximation.

This paper proposes a nonlinear state space model (SSM) to estimate the health degradation and predict the remaining useful life(RUL) of industry asset. Expectation Maximization (EM) algorithm and particle filtering (PF) are introduced to estimate SSM parameters. A case study is utilized to predict RUL of industry asset.

On the basis of a previous expectation maximization (EM) algorithm, this paper applies the particle Markov chain Monte Carlo (MCMC) technique to estimate nonlinear state-space models (SSMs). The smoothed simultaneous particles for joint states are generated by importance resampling (IR) and are directly used to compute a log-likelihood function and its Jacobian vector and Hessian matrix. As a result, a relatively less computational load can thus be obtained, which is crucial to practical applications of the particle MCMC. In addition, the SSM parameters can be recursively iterated by the more efficient Newton method, in which an optimal step length for parameter update in each iteration is optimized by a 1-D search method. This presented identification method has a good global parameter convergence in case iteration parameters are initialized from quite large intervals of their respective true values. Finally, a numerical simulation for identification of a classical SSM is used to show the effectiveness of the studied identification method.

In this study, identification of nonlinear aerodynamic systems based on an improved nonlinear state-space modeling approach is presented to predict transonic aeroelastic behaviors of aircraft structures. It starts with identifying a linear state-space aerodynamic model by using the eigensystem realization algorithm and observer/Kalman filter identification methods. Subsequently, the remaining parameters of the nonlinear state-space aerodynamic model are determined through an output error-minimization procedure, based on a new training data generation methodology. To illustrate the approach, two- and three-dimensional transonic aeroelastic configurations are studied. The transonic aeroelastic behaviors predicted via the proposed approach agree well with those obtained via computational fluid dynamics technique in the interested range of dynamic pressure.

Voltage stability is of essential importance for power grids. The emergence of distributed energy generators, controllable loads, and local-area energy storage capabilities have introduced new scenarios for distribution networks in which classical frameworks for voltage stability may be inadequate. This paper introduces a control-theoretic framework for studying voltage stability and its robustness, as well as optimal power management in distribution systems composed of networked microgrids. The framework involves descriptions of the loads and generators by nonlinear state space models and the network connections by a set of topology-based algebraic equations. The integration of the combined system leads to a general nonlinear state space model for the microgrid systems. Simplified microgrids are used to illustrate the concepts.

GAIN SCHEDULING CONTROL FOR COMBINED FOUR WHEEL STEERING AND INDIVIDUAL WHEEL BRAKING

We consider the generalized state space model (GSSM) which is an extension of the state space model to the non-Gaussian and non-linear model. There are serious problems in the GSSM approach because of the need for numerical integration over a state space. A Monte Carlo method for filtering and smoothing, called the Monte Carlo Filter (MCF), has been proposed to overcome this numerical problem. It has been pointed out that there exists a close relationship between the MCF and the genetic algorithm (GA) and that an essential structure involved in the MCF is quite similar to that in the GA. In this study, we try to replace the step of the prediction by the mutation and crossover operators in the GA, and demonstrate their performance as the system noise. We furthermore propose a smoothing algorithm in which a massively simple parallel procedure plays an important role. The proposed method is first applied to a simple problem and then to a seasonal adjustment for quarterly data sets in order to illustrate its broad applicability.

In permanent magnet synchronous machine, high-frequency (HF) signal injection has been extensively investigated for permanent magnet temperature (PMT) estimation, in which PMT is estimated from the temperature-dependent HF resistance. Existing studies require prior knowledge on the HF resistance and neglect the fact that PMT is temporally correlated. This paper proposes a state-space model for PMT estimation, in which PMT is modeled with a piecewise linear equation to explore the temporal correlation. The state-space model is nonlinear due to unknown model parameters, which is required to be known in existing studies. This paper proposes to use expectation maximization particle filter (EM-PF) for simultaneous PMT and model parameter estimation. After EM-PF estimation, the state-space model becomes linear, so Kalman filter is employed for online PMT estimation. The proposed EM-PF along with a Kalman-filter-based approach can explore the temporal correlation among PMTs to improve the estimation performance, which can be hardly achieved in existing studies regarding PMT as a time-independent parameter. It should be noted that EM-PF is for initial PMT and model parameter estimation, while Kalman filter is for online PMT estimation ensuring computation efficiency and real-time capability. Our approach is validated with both numerical and experimental investigations.

A data-driven nonlinear state-space model of the unsteady lift force on a pitching wing