Particle Swarm Optimization Iterative Identification Algorithm and Gradient Iterative Identification Algorithm for Wiener Systems with Colored Noise

Abstract

This paper considers the parameter identification of Wiener systems with colored noise. The difficulty in the identification is that the model is nonlinear and the intermediate variable cannot be measured. Particle swarm optimization is an artificial intelligence evolutionary method and is effective in solving nonlinear optimization problem. In this paper, we obtain the identification model of the Wiener system and then transfer the parameter identification problem into an optimization problem. Then, we derive a particle swarm optimization iterative (PSOI) identification algorithm to identify the unknown parameter of the Wiener system. Furthermore, a gradient iterative identification algorithm is proposed to compare with the particle swarm optimization iterative algorithm. Numerical simulation is carried out to evaluate the performance of the PSOI algorithm and the gradient iterative algorithm. The simulation results indicate that the proposed algorithms are effective and the PSOI algorithm can achieve better performance over the gradient iterative algorithm.

Weight Least Squares Algorithm for Rational Models with Outliers

“…Remark 2. Based on equations (12) and 13, we can get that each cost function has different weights, and the latest data have larger weights. Taking the conditional expectation on both sides of (13) yields…”

“…Once the structure is determined, parameter estimation is involved [5][6][7]. Recently, a lot of parameter estimation algorithms are proposed, including the least squares (LS) algorithm [8,9], the gradient algorithm [10,11], the particle swarm optimization algorithm, and the expectation maximization algorithm [12,13]. Among these algorithms, the LS algorithm is to find a vector that is a local minimizer to a function that is a sum of squares; thus, it is the simplest algorithm and is widely used.…”

Identification of Wiener Model with Internal Noise Using a Cubic Spline Approximation-Bayesian Composite Quantile Regression Algorithm

“…It is di cult to identify the Wiener model because of its nonlinear characteristic. Additionally, the existing research studies are mostly related to the system without noise or only with the output noise [7][8][9]. Lamia et al described the Wiener model using the polynomial nonlinear state space (PNLSS) model and developed an output error identi cation method for the nonlinear block [10].…”

Hierarchical Newton Iterative Parameter Estimation of a Class of Input Nonlinear Systems Based on the Key Term Separation Principle

“…The core idea of adaptive parameter estimation is to recursively adjust the parameters by using the residuals, which makes the estimates approximately approach the true value. Under this framework of adaptation, the recursive least squares algorithms [13,14], the stochastic gradient algorithms [15], and the iterative algorithms [16,17] are well developed and underpin several heuristic or bioinspired learning algorithms [18][19][20]. For example, we use the adaptive algorithms such as gradient descent algorithm for learning the weights in the neural networks or training the fitness in the genetic algorithms.…”

“…In this simulation, the input vector u t is taken as an uncorrelated persistent excitation signal sequence with zero mean and v t as a white noise sequence with zero mean and variances σ 2 = 0 10 2 and σ 2 = 0 50 2 . Taking the data length L = 1000 data, we apply the proposed E-NI algorithm in (17), (18), (19), (20) Tables 1-3, and their parameter estimation errors δ ≔ θ t − θ / θ and δ ≔ ϑ t − ϑ / ϑ versus t of each algorithm are illustrated in Figures 1-3.…”