J.B. Gomm

Selecting radial basis function network centers with recursive orthogonal least squares training

Recursive orthogonal least squares (ROLS) is a numerically robust method for solving for the output layer weights of a radial basis function (RBF) network, and requires less computer memory than the batch alternative. In this paper, the use of ROLS is extended to selecting the centers of an RBF network. It is shown that the information available in an ROLS algorithm after network training can be used to sequentially select centers to minimize the network output error. This provides efficient methods for network reduction to achieve smaller architectures with acceptable accuracy and without retraining. Two selection methods are developed, forward and backward. The methods are illustrated in applications of RBF networks to modeling a nonlinear time series and a real multiinput-multioutput chemical process. The final network models obtained achieve acceptable accuracy with significant reductions in the number of required centers.

Adaptive neural network model based predictive control for air-fuel ratio of SI engines

The dynamics of air manifold and fuel injection of the spark ignition engines are severely nonlinear. This is reflected in nonlinearities of the model parameters in different regions of the operating space. Control of the engines has been investigated using observer-based methods or sliding-mode methods. In this paper, the model predictive control (MPC) based on a neural network model is attempted for air-fuel ratio, in which the model is adapted on-line to cope with nonlinear dynamics and parameter uncertainties. A radial basis function (RBF) network is employed and the recursive least-squares (RLS) algorithm is used for weight updating. Based on the adaptive model, a MPC strategy for controlling air-fuel ratio is realised to a nonlinear simulation of the engines, and its control performance is compared with that of a conventional PI controller. A reduced Hessian method, a new developed sequential quadratic programming (SQP) method for solving nonlinear programming (NLP) problems, is implemented to speed up the nonlinear optimisation in MPC.

Implementation of neural network predictive control to a multivariable chemical reactor

Abstract Implementation of a neural network model-based predictive control scheme to a laboratory-scaled multivariable chemical reactor is described in this paper. Three variables are controlled in the reactor—temperature, pH and dissolved oxygen. The reactor exhibits common features of industrial systems including non-linear dynamics, coupling effects among variables and is without a mathematical model. Multi-input, single-output sub-system models are developed using neural networks and combined to form a parallel process model for simulation and on-line prediction. The process modelling, model-based control simulation, implementation of the on-line control and performance evaluations are investigated and reported in detail in the paper.

Sensor fault diagnosis in a chemical process via RBF neural networks

Abstract Radial basis function (RBF) neural networks are investigated here for process fault diagnosis. The use of the output prediction error, between a neural network model and a non-linear dynamic process, as a residual for diagnosing actuator, component and sensor faults is analysed. It is found that this residual for a dependent neural model is less sensitive to sensor faults than actuator or component faults. This is confirmed in experiments for a real, multivariable chemical reactor. A scheme is then developed utilising a semi-independent neural model to generate enhanced residuals for diagnosing the sensor faults in the reactor. A second neural-network classifier is developed to diagnose the sensor faults from the residuals generated, and results are presented to demonstrate the satisfactory detection and isolation of sensor faults achieved using this approach.

Solution to the Shell standard control problem using genetically tuned PID controllers

Abstract A solution to the Shell standard control problem is presented in this paper, based on genetic algorithms (GAs). The proposed scheme includes two discrete-time PID controllers with integral anti-windup and a multivariable Smith predictor to provide the required process output regulation, while the process input minimisation problem is analytically solved on-line, by estimating the unmeasured disturbances entering the process and solving the associated linear programming problem. This, as well as the presence of constraints in the process manipulated variables, results in a complex, non-linear closed-loop system and hence, the manual tuning of the PID controllers according to some given performance specifications becomes a difficult task. GAs are successfully applied to the automatic tuning of the PID controllers according to the given specifications, using a specially formulated objective function which quantifies the controller performance in terms of time-domain bounds on the closed-loop system responses. Simulation results are presented to demonstrate the effectiveness of the proposed control scheme.

A Recursive Orthogonal Least Squares Algorithm for Training RBF Networks

A recursive orthogonal least squares (ROLS) algorithm for multi-input, multi-output systems is developed in this paper and is applied to updating the weighting matrix of a radial basis function network. An illustrative example is given, to demonstrate the effectiveness of the algorithm for eliminating the effects of ill-conditioning in the training data, in an application of neural modelling of a multi-variable chemical process. Comparisons with results from using standard least squares algorithms, in batch and recursive form, show that the ROLS algorithm can significantly improve the neural modelling accuracy. The ROLS algorithm can also be applied to a large data set with much lower requirements on computer memory than the batch OLS algorithm.

Experiment design considerations for non-linear system identification using neural networks

Although the non-linear modelling capability of neural networks is widely accepted there remain many issues to be addressed relating to the design of a successful identification experiment. In particular, the choices of process excitation signal, data sample time and neural network model structure all contribute to the success, or failure, of a neural networks ability to reliably approximate the dynamic behaviour of a process. This paper examines the effects of these design considerations in an application of a multi-layered perceptron neural network to identifying the non-linear dynamics of a simulated pH process. The importance of identification experiment design for obtaining a network capable of both accurate single step and long range predictions is illustrated. The use of model parsimony indices, model validation tests and histogram analysis of training data for design of a neural network identification experiment are investigated.

Neural model input selection for a MIMO chemical process

Abstract In modelling non-linear systems using neural networks (NN), a commonly used method for the selection of network inputs, or to determine system order and time-delay, is to try different combinations of the system input–output data and choose the best one, giving minimum prediction error. The method is increasingly difficult to apply to industrial systems, due to their multivariable nature and complexity. A systematic method for the selection of model order and time-delay is developed in this paper, and applied to the neural modelling of a multivariable chemical process rig. The method is much simpler compared to the structure identification of the Non-linear Auto-Regressive with eXogenous inputs model (NARX), since the latter also needs to determine the significant terms from a linear-in-parameters polynomial. The orders and delays for system input and output are determined by identifying linearised models of the system. The method can also be applied to other approximations of a MIMO non-linear system, such as fuzzy logic models, etc. The application example demonstrates the selection procedure. Finally, the process rig is modelled using NNs according to the chosen structure, and the modelling error is compared with that of models with different structures to show the effectiveness of the method.

Development and performance of a neural-network predictive controller

Abstract Neural-network techniques are investigated in an application to the identification and subsequent on-line control of a process exhibiting non-linearities and typical disturbances. The design and development of a neural-network process model from measured data is described, and practical aspects of the identification procedure are discussed. Results demonstrate that the developed neural-network representation of the process dynamics is sufficiently accurate to be used independently from the process, emulating the process response from only process input information. Accurate long-range predictions from the neural-network model are mainly due to the use of a novel spread encoding technique for representing data in the network. Implementation of a predictive control strategy incorporating the identified neural-network model is described, and on-line results illustrate the improvements in control performance that can be achieved when compared to conventional proportional-plus-integral control.

Neural model adaptation and predictive control of a chemical process rig

An adaptation algorithm for Gaussian radial basis function (RBF) network models is proposed. The model structure is adapted to cope with operating region change, while the weight parameters are updated to model time varying dynamics or uncertainties. The special feature is that the modeling accuracy is maintained during adaptation and, therefore, the control performance will not be degraded when the model structure changes. A localized forgetting method is proposed to deal with nonlinearities in different operating regions, and is implemented with the recursive orthogonal least squares (ROLS) training algorithm. The developed adaptive model is evaluated by real data modeling of a three-input three-output chemical process rig. Online model predictive control (MPC) of the rig is also conducted. Improved tracking performance with the adaptive model is demonstrated in comparison with nonadaptive model-based control and decentralized propotional-integral-differential (PID) control