Maximum-Likelihood-Based Adaptive and Intelligent Computing for Nonlinear System Identification

Most real-time systems are nonlinear in nature, and their optimization is very difficult due to inherit stiffness and complex system representation. The computational intelligent algorithms of evolutionary computing paradigm (ECP) effectively solve various complex, nonlinear optimization problems. The differential evolution algorithm (DEA) is one of the most important approaches in ECP, which outperforms other standard approaches in terms of accuracy and convergence performance. In this study, a novel application of a recently proposed variant of DEA, the so-called, maximum-likelihood-based, adaptive, differential evolution algorithm (ADEA), is investigated for the identification of nonlinear Hammerstein output error (HOE) systems that are widely used to model different nonlinear processes of engineering and applied sciences. The performance of the ADEA is evaluated by taking polynomial- and sigmoidal-type nonlinearities in two case studies of HOE systems. Moreover, the robustness of the proposed scheme is examined for different noise levels. Reliability and consistent accuracy are assessed through multiple independent trials of the scheme. The convergence, accuracy, robustness and reliability of the ADEA are carefully examined for HOE identification in comparison with the standard counterpart of the DEA. The ADEA achieves the fitness values of 1.43 × 10−8 and 3.46 × 10−9 for a population size of 80 and 100, respectively, in the HOE system identification problem of case study 1 for a 0.01 nose level, while the respective fitness values in the case of DEA are 1.43 × 10−6 and 3.46 × 10−7. The ADEA is more statistically consistent but less complex when compared to the DEA due to the extra operations involved in introducing the adaptiveness during the mutation and crossover. The current study may consider the approach of effective nonlinear system identification as a step further in developing ECP-based computational intelligence.

Comparing system identification techniques for identifying human-like walking controllers

While human walking has been well studied, the exact controller is unknown. This paper used human experimental walking data and system identification techniques to infer a human-like controller for a spring-loaded inverted pendulum (SLIP) model. Because the best system identification technique is unknown, three methods were used and compared. First, a linear system was found using ordinary least squares. A second linear system was found that both encoded the linearized SLIP model and matched the first linear system as closely as possible. A third nonlinear system used sparse identification of nonlinear dynamics (SINDY). When directly mapping states from the start to the end of a step, all three methods were accurate, with errors below 10% of the mean experimental values in most cases. When using the controllers in simulation, the errors were significantly higher but remained below 10% for all but one state. Thus, all three system identification methods generated accurate system models. Somewhat surprisingly, the linearized system was the most accurate, followed closely by SINDY. This suggests that nonlinear system identification techniques are not needed when finding a discrete human gait controller, at least for unperturbed walking. It may also suggest that human control of normal, unperturbed walking is approximately linear.

Wavelet Characterizations for Investigating Nonlinear Oscillators

This study investigates the wavelet-based system identification capabilities on determining the system nonlinearity based on the system impulse response function. Wavelet estimates of the instantaneous envelopes and instantaneous frequency are used to plot the system backbone curve. This wavelet estimate is then used to estimate the values of the parameter for the system. Two weakly nonlinear oscillators, which are the Duffing and the Van der Pol oscillators, have been analyzed using this wavelet approach. A case study based on a model of an oscillating flap wave energy converter (OFWEC) was also discussed in this study. Based on the results, it was shown that this technique is recommended for nonlinear system identification provided the impulse response of the system can be captured. This technique is also suitable when the system's form is unknown and for estimating the instantaneous frequency even when the impulse responses were polluted with noise.

Integrate-and-Differentiate Approach to Nonlinear System Identification

In this paper, we consider a problem of parametric identification of a piece-wise linear mechanical system described by ordinary differential equations. We reconstruct the phase space of the investigated system from accelerometer data and perform parameter identification using iteratively reweighted least squares. Two key features of our study are as follows. First, we use a differentiated governing equation containing acceleration and velocity as the main independent variables instead of the conventional governing equation in velocity and position. Second, we modify the iteratively reweighted least squares method by including an auxiliary reclassification step into it. The application of this method allows us to improve the identification accuracy through the elimination of classification errors needed for parameter estimation of piece-wise linear differential equations. Simulation of the Duffing-like chaotic mechanical system and experimental study of an aluminum beam with asymmetric joint show that the proposed approach is more accurate than state-of-the-art solutions.