Valerie Haggan-Ozaki

A parameter optimization method for radial basis function type models

This paper considers the nonlinear systems modeling problem for control. A structured nonlinear parameter optimization method (SNPOM) adapted to radial basis function (RBF) networks and an RBF network-style coefficients autoregressive model with exogenous variable model parameter estimation is presented. This is an off-line nonlinear model parameter optimization method, depending partly on the Levenberg-Marquardt method for nonlinear parameter optimization and partly on the least-squares method using singular value decomposition for linear parameter estimation. When compared with some other algorithms, the SNPOM accelerates the computational convergence of the parameter optimization search process of RBF-type models. The usefulness of this approach is illustrated by means of several examples.

RBF-ARX model-based nonlinear system modeling and predictive control with application to a NOx decomposition process

Abstract This paper considers the modeling and control problem for nonstationary nonlinear systems whose dynamic characteristics depend on time-varying working-points and may be locally linearized. It is proposed to describe the system behavior by the RBF-ARX model, which is an ARX model with Gaussian radial basis function (RBF) network-style coefficients depending on the working-points of a system. The RBF-ARX model is constructed as a global model, and is estimated off-line so as to avoid the possible failure of on-line parameter estimation during real-time control. A receding horizon predictive control (RBF-ARX-MPC) strategy based on the RBF-ARX model that does not require on-line parameter estimation for the nonlinear system is presented. The local linearization of the system at each working-point may be easily obtained from the global RBF-ARX model and so the use of nonlinear programming techniques to solve the on-line optimization problem with constraints in RBF-ARX-MPC is also avoided. A fast-converging estimation method is applied to optimize the RBF-ARX model parameters. A case study and example of an industrial experiment on the nitrogen oxide (NOx) decomposition process in thermal power plants are given to demonstrate the modeling precision and control performance.

A nonlinear exponential ARX model-based multivariable generalized predictive control strategy for thermal power plants

Presents a modeling and control method for thermal power plants having nonlinear dynamics varying with load. First, a load-dependent exponential ARX (Exp-ARX) model that can effectively describe the plant nonlinear properties and requires only off-line identification is presented. The model is then used to establish a constrained multivariate multistep predictive control (ExpMPC) strategy whose effectiveness is illustrated by a simulation study of a 600 megawatt (MW) thermal power plant. Although the predictive control algorithm may be used without resorting to online parameter estimation, it is much more reliable, and displays much better control performance than the usual generalized predictive control (GPC) algorithm.

An Akaike State-Space Controller for RBF-ARX Models

Radial basis function autoregressive with exogenous inputs (RBF-ARX) models have been shown to be useful in modeling the nonlinear behavior of a variety of complex systems. In particular, Peng have shown how the RBF-ARX model may be used to model the selective catalytic reduction (SCR) process for real data from a thermal power plant, and have simulated control of the plant using the generalized predictive control (GPC) method of Clarke very effectively. However, the GPC approach requires constrained nonlinear optimization at each control step, which is time-consuming and computationally very expensive. Here, in place of the GPC approach, the authors use a variation of the Kalman state-space approach to control, which involves only the solution of a set of Riccati equations at each step. As is well known, the usual Kalman state-space representation breaks down when we need to control a system depending on inputs extending several lags into the past, but to avoid this problem, we have used the state-space approach of Akaike and Nakagawa. Although this was originally developed for the linear case, here we show how the representation may be extended for use with the nonlinear RBF-ARX model. The straightforward tuning procedure is illustrated by several examples. Comparisons with the GPC method also show the effectiveness and computational efficiency of the Akaike state-space controller method. The robustness of the method is demonstrated by showing how the RBF-ARX model fitted to one data sequence from the SCR process may be used to construct a high performance controller for other sequences taken from the same process. Akaike state-space control may also be easily extended to the multi-input-multi-output case, making it widely applicable in practice.

Structured parameter optimization method for the radial basis function-based state-dependent autoregressive model

An off-line structured nonlinear parameter optimization method (SNPOM) for accelerating the computational convergence of parameter estimation of the radial basis function-based state-dependent autoregressive (RBF-AR) model is proposed. Using the method, all the parameters of the RBF-AR model may be optimized automatically and simultaneously. The proposed method combines the advantages of the Levenberg-Marquardt algorithm in nonlinear parameter optimization and the least-squares method in linear parameter estimation. Case studies on two complex time series and a nonlinear chemical reaction process show that the proposed parameter optimization method exhibits significantly accelerated convergence when compared with the classic version of the Levenberg-Marquardt algorithm, and to some hybrid algorithms such as the evolutionary programming algorithm.

Modeling and control of nonlinear nitrogen oxide decomposition process

This paper presents a modeling and predictive control approach for a non-stationary nonlinear nitrogen oxide (NO/sub x/) decomposition process whose dynamics depend on the time-varying working-points and may be locally linearized. An off-line identified hybrid pseudo-linear ARX model (RBF-ARX model), which is composed of Gaussian radial basis function (RBF) networks and linear ARX model structure, is utilized to describe the process behavior. On the basis of the RBF-ARX model, a long range predictive control (RBF-ARX-MPC) strategy that does not require on-line parameter estimation is investigated for this kind of nonlinear process. Stability of the controller proposed under certain condition is discussed. Particularly, an industrial experiment result is also given to show satisfactory modeling precision and control performance obtained by the proposed approach in real industrial application.

RBF-ARX MODELING FOR PREDICTION AND CONTROL

Abstract This paper presents a systematic approach to the complex problem of RBF-ARX modeling. First, we point out that many of the nonlinear features of a time series may be represented by a relatively simple RBF-ARX model. A method for estimating the number of RBF centers is then proposed based on the behavior of the state variable, and initial values for the centers are found. Linear estimation methods are implemented to select the initial lag orders of candidate models. Model parameters are found by nonlinear estimation and candidate models are compared using AIC, SBC criteria and other diagnostic checks. The modeling approach is shown to work well in practice by estimating optimum RBF-ARX models for real and simulated time series data and comparing the results with those of previous authors. Diagnostic checking also confirms the validity of the method.

THE RBF-ARX MODEL BASED MODELING AND PREDICTIVE CONTROL FOR A CLASS OF NONLINEAR PROCESSES

Abstract This paper considers modeling and control problems of the non-stationary nonlinear processes whose dynamics depends on the working point. A hybrid RBF-ARX model-based predictive control (MPC) strategy without resorting to on-line parameter estimation for this kind of processes is presented. The RBF-ARX model is composed of the RBF networks and a rather general form of ARX model, which is identified off-line, and whose local linearization may be easily obtained. A quickly-convergent estimation method is applied to optimize the RBF-ARX model parameters. The modeling validity and the MPC performance is illustrated by an application to Nitrogen Oxide (NOx) decomposition process in thermal power plants.