Automatic Construction of Linear Stochastic Dynamic Models For Stationary Industrial Processes with Random Disturbances Using Operating Records

We describe a new technique for automatic identification of stationary, linear systems with a single output. This class of models includes all linear, time-invariant, stochastic, difference equations driven by arbitrary inputs and having stationary, normal disturbances with rational spectra.The parameters of the model are estimated by the method of maximum likelihood. A numerical algorithm for solving the likelihood equations is presented. The algorithm is essentially a modified Newton-Raphson algorithm, which takes advantage of the particular structure of the problem.Conditions for consistency and asymptotic efficiency of the estimates are given for increasing sample length. It is shown that these properties are exclusively determined by the information matrix. An estimate of the latter is obtained without additional computations. The information matrix also yields an estimate of the accuracy of the estimates in each. case.The approach has been tested on artificially generated input/output data. It is also immediately applicable to power spectrum analysis of time series, having advantages over ordinary non-parametric methods in that it always gives a non-negative estimate without the problems of trend removal and of the choice of spectral windows turning up.The basic idea can be extended to larger classes of systems. Also the identification is easily done recursively, which implies that the method is well suited for real time modelling