Parameter estimation of delay differential equations: An integration-free LS-SVM approach

Fault detection and diagnosis method for cooling dehumidifier based on LS-SVM NARX model

“…Due to the advantages for disposing of small sample and nonlinear problem, LS-SVM can well be applied to the fields such as model building for nonlinear system regression, prediction for time series and fault diagnosis (Khalil and Bardini 2011;Dong and Luo 2013;Mehrkanoon et al 2014). Compared with the standard SVM, the LS-SVM learning speed is faster; compared with the ANNs, the LS-SVM generalization ability is more favorable.…”

Two-stage parameter estimation applied to ordinary differential equation models

“…Using simulation experiments, the two-stage parameter estimation for differential equations, developed in this work, can provide the user with an efficient and easy-to-use parameter estimation algorithm. The idea of employing the estimated parameters, obtained by minimizing the squared residuals in the differential form of the underlying model, as an initial guess for the conventional approach has already been introduced in the literatures [17][18][19]. Further, many two-stage parameter estimation (or identification) methods have been proposed in the system identification field [20][21][22][23][24][25][26].…”

Maximum Likelihood Inference for Univariate Delay Differential Equation Models with Multiple Delays

“…Further, Wang and Cao consider only univariate DDEMs with a single delay parameter. An estimation method based on Least Squares Support Vector Machines (LS-SVMs) for approximating constant as well as time-varying parameters in deterministic parameter-affine DDEMs is presented by Mehrkanoon et al [8]. We note that Mehrkanoon performs parameter estimation only; no standard errors of estimates or confidence intervals are reported.…”

“…MLE can be developed for a large variety of estimation situations and is asymptotically efficient, which means that for large samples it produces the most precise estimates compared to non-MLE based methods (such as [8]). These are the reasons why we preferred using MLE over all other estimators for DDEMs in this paper.…”

“…We note that Mehrkanoon performs parameter estimation only; no standard errors of estimates or confidence intervals are reported. Further, only single delays (either constant or time varying) are considered in [8].…”