Evolutionary Parametric Identification of Dynamic Systems

Parametric system identification of dynamic systems is the process of building mathematical, time domain models of plants, based on excitation and response signals. In contrast to its nonparametric counterpart, this model based procedure leads to fixed descriptions, by means of finitely parameterized transfer function representations. This fact provides increased flexibility and makes model-based identification a powerful tool with growing significance, suitable for analysis, fault diagnosis and control applications (Mrad et al, 1996, Petsounis & Fassois, 2001). Parametric identification techniques rely mostly on Prediction-Error Methods (Ljung, 1999). These methods refer to the estimation of a certain model’s parameters, through the formulation of one-step ahead prediction errors sequence, between the actual response and the one computed from the model. The evaluation of prediction errors is taking place throughout the mapping of the sequence to a scalar-valued index function (loss function). Over a set of candidate sets with different parameters, the one which minimizes the loss function is chosen, with respect to the corresponding fitness to data. However, in most cases the loss function cannot be minimized analytically, due to the non-linear relationship between the parameter vector and the prediction-error sequence. The solution then has to be found by iterative, numerical techniques. Thus, PEM turns into a non-convex optimization problem, whose objective function presents many local minima. The above problem has been mostly treated so far by deterministic optimization methods, such as Gauss-Newton or Levenberg-Marquardt algorithms. The main concept of these techniques is a gradient-based, local search procedure, which requires smooth search space, good initial ‘‘guess’’, as well as well-defined derivatives. However, in many practical identification problems, these requirements often cannot be fulfilled. As a result, PEM stagnate to local minima and lead to poorly identified systems. To overcome this difficulty, an alternative approach, based in the implementation of stochastic optimization algorithms, has been developed in the past decade. Several techniques have been formulated for parameter estimation and model order selection, using mostly Genetic Algorithms. The basic concept of these algorithms is the simulation of a natural evolution for the task of global optimization, and they have received considerable interest since the work done (Kristinsson & Dumont, 1992), who applied them to the identification of both continuous and discrete time systems. Similar studies are reported in literature (Tan & Li, 2002, Gray et al. , 1998, Billings & Mao, 1998, Rodriguez et al., 1997). Fleming & Purshouse, 2002 have presented an extended survey on these techniques, while Schoenauer & Sebag, 2002 address the use of domain knowledge and the choice of fitting