Combined state and parameter estimation for Hammerstein systems with time-delay using the Kalman filtering

This paper discusses the state and parameter estimation problem for a class of Hammerstein state space systems with time-delay. Both the process noise and the measurement noise are considered in the system. Based on the observable canonical state space form and the key term separation, a pseudo-linear regressive identification model is obtained. For the unknown states in the information vector, the Kalman filter is used to search for the optimal state estimates. A Kalman-filter based least squares iterative and a recursive least squares algorithms are proposed. Extending the information vector to include the latest information terms which are missed for the time-delay, the Kalman-filter based recursive extended least squares algorithm is derived to obtain the estimates of the unknown time-delay, parameters and states. The numerical simulation results are given to illustrate the effectiveness of the proposed algorithms

Least squares-based iterative identification methods for linear-in-parameters systems using the decomposition technique

By extending the least squares-based iterative (LSI) method, this paper presents a decomposition-based LSI (D-LSI) algorithm for identifying linear-in-parameters systems and an interval-varying D-LSI algorithm for handling the identification problems of missing-data systems. The basic idea is to apply the hierarchical identification principle to decompose the original system into two fictitious sub-systems and then to derive new iterative algorithms to estimate the parameters of each sub-system. Compared with the LSI algorithm and the interval-varying LSI algorithm, the decomposition-based iterative algorithms have less computational load. The numerical simulation results demonstrate that the proposed algorithms work quite well

Least Squares Based and Two-Stage Least Squares Based Iterative Estimation Algorithms for H-FIR-MA Systems

This paper studies the identification of Hammerstein finite impulse response moving average (H-FIR-MA for short) systems. A new two-stage least squares iterative algorithm is developed to identify the parameters of the H-FIR-MA systems. The simulation cases indicate the efficiency of the proposed algorithms

Highly computationally efficient state filter based on the delta operator

The Kalman filter is not suitable for the state estimation of linear systems with multistate delays, and the extended state vector Kalman filtering algorithm results in heavy computational burden because of the large dimension of the state estimation covariance matrix. Thus, in this paper, we develop a novel state estimation algorithm for enhancing the computational efficiency based on the delta operator. The computation analysis and the simulation example show the performance of the proposed algorithm

Parameter estimation algorithm for multivariable controlled autoregressive autoregressive moving average systems

This paper investigates parameter estimation problems for multivariable controlled autoregressive autoregressive moving average (M-CARARMA) systems. In order to improve the performance of the standard multivariable generalized extended stochastic gradient (M-GESG) algorithm, we derive a partially coupled generalized extended stochastic gradient algorithm by using the auxiliary model. In particular, we divide the identification model into several subsystems based on the hierarchical identification principle and estimate the parameters using the coupled relationship between these subsystems. The simulation results show that the new algorithm can give more accurate parameter estimates of the M-CARARMA system than the M-GESG algorithm

Data-driven Soft Sensors in the Process Industry

In the last two decades Soft Sensors established themselves as a valuable alternative to the traditional means for the acquisition of critical process variables, process monitoring and other tasks which are related to process control. This paper discusses characteristics of the process industry data which are critical for the development of data-driven Soft Sensors. These characteristics are common to a large number of process industry fields, like the chemical industry, bioprocess industry, steel industry, etc. The focus of this work is put on the data-driven Soft Sensors because of their growing popularity, already demonstrated usefulness and huge, though yet not completely realised, potential. A comprehensive selection of case studies covering the three most important Soft Sensor application fields, a general introduction to the most popular Soft Sensor modelling techniques as well as a discussion of some open issues in the Soft Sensor development and maintenance and their possible solutions are the main contributions of this work

Gradient-based iterative parameter estimation for bilinear-in-parameter systems using the model decomposition technique

The parameter estimation issues of a block-oriented non-linear system that is bilinear in the parameters are studied, i.e. the bilinear-in-parameter system. Using the model decomposition technique, the bilinear-in-parameter model is decomposed into two fictitious submodels: one containing the unknown parameters in the non-linear block and the other containing the unknown parameters in the linear dynamic one and the noise model. Then a gradient-based iterative algorithm is proposed to estimate all the unknown parameters by formulating and minimising two criterion functions. The stochastic gradient algorithms are provided for comparison. The simulation results indicate that the proposed iterative algorithm can give higher parameter estimation accuracy than the stochastic gradient algorithms

Comparative review of methods for stability monitoring in electrical power systems and vibrating structures

This study provides a review of methods used for stability monitoring in two different fields, electrical power systems and vibration analysis, with the aim of increasing awareness of and highlighting opportunities for cross-fertilisation. The nature of the problems that require stability monitoring in both fields are discussed here as well as the approaches that have been taken. The review of power systems methods is presented in two parts: methods for ambient or normal operation and methods for transient or post-fault operation. Similarly, the review of methods for vibration analysis is presented in two parts: methods for stationary or linear time-invariant data and methods for non-stationary or non-linear time-variant data. Some observations and comments are made regarding methods that have already been applied in both fields including recommendations for the use of different sets of algorithms that have not been utilised to date. Additionally, methods that have been applied to vibration analysis and have potential for power systems stability monitoring are discussed and recommended. � 2010 The Institution of Engineering and Technology

Development and identification of hierarchical nonlinear mixed effects models for the analysis of dynamic systems: identification and application of hierarchical nonlinear mixed effects models for the determination of steady-state and dynamic torque responses of an SI engine

Multi-level or hierarchical models present various features for dealing with data grouped at several levels. The majority of applications of hierarchical models use clustered data that is static in nature and collected over a long period of time. The purpose of this study is investigating hierarchical models for application with highly dynamic systems. Steady-state data are conventionally employed for engine torque mapping purposes. The data takes much time to collect and the dynamics of the system are routinely ignored. This valuable information could be used for better control of the system.In this study, an innovative transient spark-sweep approach is developed for collecting dynamic torque data more efficiently. The means of data collection implies a structure for which a multi-level model is best suited. A multi-model augmented D-optimal design is created, and the experimental data collected. Spark excitation is applied at speed/load points using Amplitude Modulated Pseudo Random Signal (AMPRS), and the torque response over the operating space is thus obtained. Conditional first-order linearization is used within the identification process for determining the hierarchical model parameters. The level-1 Nonlinear Auto Regressive eXogenous (NARX) models are separately determined using an Iterative Generalized Least Square (IGLS) method and the results are employed for initialisation of the covariance matrix and the model level-2 parameters. A novel gradient optimiser was established to facilitate the dynamic hierarchical model identification. Additionally, the uncertainty associated with model selection was mitigated using a multi-model approach. The model identified is evaluated and compared with experimental dynamic and steady-state data. It shows behaviour, both dynamic and steady state, providing prediction over a wider extrapolated spark range than conventional approaches. The new approach is eight time faster than current state-of-the-art approaches.</div

Partially coupled gradient estimation algorithm for multivariable equation-error autoregressive moving average systems using the data filtering technique

System identification provides many convenient and useful methods for engineering modelling. This study targets the parameter identification problems for multivariable equation-error autoregressive moving average systems. To reduce the influence of the coloured noises on the parameter estimation, the data filtering technique is adopted to filter the input and output data, and to transform the original system into a filtered system with white noises. Then the filtered system is decomposed into several subsystems and a filtering-based partially-coupled generalised extended stochastic gradient algorithm is developed via the coupling concept. In contrast to the multivariable generalised extended stochastic gradient algorithm, the proposed algorithm can give more accurate parameter estimates. Finally, the effectiveness of the proposed algorithm is well demonstrated by simulation examples