The Parameters Identification of Time - Delay Models of Heat Transfer Systems From Input-Output Measurements Available to Purchase

The paper presents the identification issues and proposes a parameter identification algorithm that separates the system parameters from the time-delays for a class of single input single output (SISO) linear time delay systems (LTDS). The presence of the unknown time delay greatly complicates the parameters estimation problem, because the parameters of the model are not linear with respect to the time-delay. However, once the time delay is determined, the model becomes linear for the other parameters and hence the common least square method can be utilized directly. Motivated by the nonlinear least squares problem developed in the paper Golub and Pereyra (1973), a novel modification of the so-called variable projection functional is worked out for identification of time delays. In this way, the parameters estimation is separated from the estimation of time delays and the large errors in the parameter estimates, in the case of presence of errors in the time-delay identified values, are avoided. Namely, the small error in the time-delay identified values may often cause a large error in the system parameters identification. A hybrid optimalization method combining a Genetic Algorithm and Nelder-Mead technique is used for minimization of variable projection functional for the identification of time delays. This approach is illustrated by a particular application in the field of heat transfer, concretely on the time-delay model of the recuperative heat exchanger.