Probabilistic Modeling And Parameter Estimation For Nonlinear Systems With Measurement Constraints

Industrial automation serves as the prerequisite for intelligent manufacturing,while system modeling forms the foundation to implement majority of control and optimization strategies.With the ever-increasing scale and complexity of the system,modern industrial systems often exhibit nonlinear behaviors,and involve various problems due to complex noises,external disturbances,irregular data sampling,communication bandwidth and rate limitations,actuator and sensor malfunctions,etc.Therefore,it is usually troublesome to model and estimate the systems using traditional methods,in which case the data-driven identification approach can be a favorable alternative by exploiting abundant information revealed in the collected data.To guarantee the performance of the identification algorithm,it is crucial to capture nonlinearity of the system more accurately and tackling potential measurement constraints more effectively.Focusing on the mentioned issues,this thesis develops a series of probabilistic modeling and parameter estimation methods for nonlinear systems with measurement constraints.Linear parameter-varying(LPV)model and nonlinear state-space model(NSSM)are selected as two typical nonlinear model structures,and several problems caused by measurement constraints are comprehensively considered,such as outliers/non-Gaussian noise,time delay,missing or multi-rate data,etc.As a result,the corresponding probabilistic model can be formulated,and the unknown parameters can be estimated based on Bayesian algorithm.The main research contents are summarized as follows:Firstly,a robust estimation method is designed for LPV systems with consideration of outliers.The global nonlinearity is characterized by weighted combination of multiple local models,where each local-model identity is treated as hidden variable to represent the working mode of the system.The Laplace distribution is employed to handle outliers,and conjugate priors over latent variables are introduced to construct the probabilistic model.Finally,the formulas to iteratively update the local-model identity,the model parameters and their uncertainties are derived under variational Bayesian(VB)framework.The proposed algorithm achieves better performance than the regular approach and existing robust least squares support vector machines for the identification task in the numerical example and continuous stirred tank reactor system.Furthermore,the estimation problem for LPV time-delay systems under the mutual coupling of outliers and incomplete observations is studied.The missing part of the measurements is regarded as hidden variable,the Student’s t-distribution is introduced for robust modeling.Additionally,the categorical distribution and Dirichlet distribution are used to represent the identity and significance of time-delay,respectively.Subsequently,the probability model can be established by introducing priors over hidden variables,and the Bayesian estimation scheme for LPV systems with constraints can be designed by maximizing variational lower bound of the marginal likelihood.In such paradigm,both model parameters and their uncertainties can be quantified,and the input time-delay can be evaluated through maximizing its posterior distribution.With the introduced latent variable to reflect the significance of time-delay,the number of input delays can be automatically selected.The effectiveness of the developed approach is verified through several simulations and comparative studies.In order to describe nonlinear behaviors caused by frequent variations of operating conditions,the global identification approach for LPV dual-rate systems with random transmission delays is investigated,and the model parameters can be expressed as polynomial functions of the scheduling variable.Several commonly encountered problems are simultaneously handled: the Student’s t-distribution is utilized to suppress the influence of outliers,and a modified robust Kalman filter is formulated to estimate missing values in the fast-rate process outputs.Meanwhile,the estimation method for input time-delay is extended to tackling random transmission delay problem.The formulas to iteratively updating posterior distributions over global model parameters and the transmission delays is given.Moreover,both the identity and quantity of the delay can be automatically selected.In numerical comparison and electronic bandpass filter benchmark,it is verified that the illustrated algorithm can obtain promising parameter,time-delay and output estimation results.As another typical structure for nonlinear system,the state-space model can reflect the internal dynamics of the system by introducing hidden states,but it involves the issue of jointly estimating states and parameters.Therefore,this thesis further addresses the identification problem of NSSM with skewed measurement noise.The generalized hyperbolic skew Student’s t(GHSkewt)distribution is adopted to describe the skew or asymmetric property,and a robust identification approach is demonstrated.Based on the maximum likelihood criterion and the expectation maximization framework,the forward filtering backward simulation with rejection sampling is employed in the expectation step to efficiently estimate the posterior distribution of the state,then the conditional expectation of the complete-data log-likelihood(i.e.,Q function)is maximized to estimate unknown parameters.In the developed algorithm,the hidden variable of the GHSkewt distribution acts as the weighting factor of the observed data,which can adaptively adjust the influence of the skewed noise in estimating parameters and ensure the robustness of the algorithm.Based on the numerical example and electro-mechanical positioning system(EMPS),the efficacy of the stated algorithm and its superiority over traditional as well as the robust algorithm based on symmetric heavy-tailed distribution are validated.To measure uncertainties of the parameter estimates,a Bayesian estimation scheme for linearly parameterized nonlinear state-space model(LP-NSSM)is provided.For such special model structure,all unknown parameters are viewed as random variables with conjugate priors to establish the Bayesian model accordingly.Consequently,the posterior distributions of the states and parameters can be jointly approximated under VB framework,and the robustness of the algorithm can be further improved with consideration of outliers and missing observations.The essence of the proposed method lies in transforming the original LP-NSSM with random parameters into an augmented LP-NSSM with deterministic parameters,such that existing nonlinear inference techniques can be adopted to approximate the posterior distributions of the system states.The identification results of the numerical example,the EMPS and cascaded water tank system show that satisfactory parameter and state estimation accuracy can be attained for the presented approach,and uncertainties of the parameter estimates can be evaluated according to variance statistics.