Model order reduction using factor division algorithm and fuzzy c-means clustering technique

Abstract

This paper proposes a novel hybrid approach that combines factor division algorithm and fuzzy c-means clustering technique for reducing the model order of high-order linear time invariant system. The process of clustering is used for finding the group of objects with similar nature that can be differentiated from the other dissimilar objects. The numerator of the higher order model is reduced using the factor division algorithm and the denominator of the higher order model is reduced using the fuzzy c-means clustering technique. The stability of the model is also verified using the pole zero stability analysis and it was found that the obtained reduced order model (ROM) is stable. Further, the steady state and transient response of the ROM is found to be better than the other existing techniques. The performance of the ROM is compared to other existing techniques in terms of integral square error, integral of time multiply squared error, integral absolute error and integral time-weighted absolute error.

A novel model reduction approach for linear time-invariant systems via enhanced PSO-DV algorithm and improved MPPA method

“…At iteration g = 0, initialize the 'N'. Each of the reduced-order denominator polynomials are having 'R' unknown coefficients, and they are randomly chosen by using equation (10). During initialization, make sure that each and every reduced denominator polynomial vector must satisfy the necessary and sufficient stability conditions those are discussed in Corollary 2.…”

“…Later, check whether the updated denominator polynomial vectors have satisfied the stability conditions given in Corollary 2. If any of the ith vector among the population (N) at the iteration g does not satisfy the stability conditions or failed to improve its fitness value, then the particular ith vector is replaced with a randomly chosen vector as given by equation (10) till the stability conditions are satisfied.…”

“…[4][5][6][7][8][9] Based upon the simplicity and the enormous design methods gathered in the frequency domain, the MOR techniques of this group have become more prominent. The frequency-domain MOR methods available in the literature are briefly classified into three categories: (1) conventional-type MOR methods, [9][10][11][12] (2) stochastic search-based MOR methods and [13][14][15][16][17][18] (3) hybridization of conventional-type and stochastic search algorithm-based MOR methods. 19,20 The conventional-type MOR methods involve the mathematical procedural steps that have been originally introduced in the literature of applied mathematics, mainly in the context of rational functions, matrix algebra, differential equations and so on, to determine the ROM.…”

A new model order reduction method for the design of compensator by using moment matching algorithm

“…In MOR, the fundamental features of the original system are preserved in the lower dimensional system. In various fields of engineering and science, MOR is widely used for the simplification of higher dimensional real time systems (Gautam et al, 2018; Haider et al, 2018; Narain et al, 2014; Paul and Chang, 2018; Rosenzweig et al, 2018).…”

Batch process modeling by using temporal feature and Gaussian mixture model

“…Therefore, it is impracticable for dealing with overlapped data of different sub-models. In order to smooth the hard division, fuzzy c-means (FCM) and Gustafson-Kessel (GK) clustering algorithms assign data into different clusters with the membership degree between 0 and 1 (Gautam et al, 2019; Kim et al, 2004). Additionally, Gaussian mixture model (GMM) considers sufficient linear combinations of a single multivariate Gaussian process (GP) (Liang et al, 2018) approximating to almost any continuous process (Grbić et al, 2013; Yuan et al, 2014).…”