Linear discrete-time models predominate in process system identification, but suffer from some drawbacks. An appealing alternative is to identify continuous-time linear models, expressed as differential equations or Laplace transforms. Two problems must be solved in a computationally feasible way for continuous-time transfer function identification: the model structure must be determined and, subsequently, values for parameters associated with the structural description must be estimated. Our approach to the identification of continuous-time models integrates two technologies. We use the nonlinear classification capabilities of neural networks for structure determination. For parameter estimation we use a nonlinear identification algorithm. A second neural network is employed to provide the algorithm initial conditions, thereby improving its convergence properties. Network training is greatly facilitated by the dynamic generation of examples—overparametrization and overfitting concerns are alleviated entirely. A system identifier targeted for petrochemical applications has been developed. Some details of the implementation are described and experimental results presented. These demonstrate that both accurate and efficient identification of continuous-time models is feasible.
[1]
D. Marquardt.
An Algorithm for Least-Squares Estimation of Nonlinear Parameters
,
1963
.
[2]
Kurt Hornik,et al.
Multilayer feedforward networks are universal approximators
,
1989,
Neural Networks.
[3]
N.V. Bhat,et al.
Modeling chemical process systems via neural computation
,
1990,
IEEE Control Systems Magazine.
[4]
P. Werbos,et al.
Beyond Regression : "New Tools for Prediction and Analysis in the Behavioral Sciences
,
1974
.
[5]
Geoffrey E. Hinton,et al.
Learning internal representations by error propagation
,
1986
.
[6]
Tariq Samad,et al.
Parameter estimation for process control with neural networks
,
1991,
Defense + Commercial Sensing.