A comparative study of the MAX and SUM machine-learning algorithms using virtual fuzzy sets

Neural-based nonlinear system identification and control suffers from the problem of slow convergence, and selection of a suitable architecture for a problem is made through trial and error. There is the need for an algorithm that would provide an efficient solution to these problems. This paper presents one possible solution. Unlike the backpropagation algorithm that trains a fixed structure, in the algorithm presented in this paper, the network is built slowly in a step-by-step fashion. This evolving architecture methodology permits an optimal allocation of hidden nodes that avoids training on outliers and at the same time, provides sufficient complexity for the approximation of a data set. Through simulation examples we show that this algorithm also exhibits faster convergence properties than the usual multi- layered neural network algorithms. Finally, we examine some common ideas between this architecture and fuzzy logic systems.

Adaptive identification and control algorithms for nonlinear bacterial growth systems

Fractional calculus extends the scope of adaptive algorithms supporting the design of novel fractional methods that outperform standard strategies in various applications arising in applied physics and engineering. In this study, a momentum fractional least-mean-square (M-FLMS) algorithm for nonlinear system identification using a first and fractional-order gradient information is proposed. The M-FLMS avoids being trapped in local minima and provides faster convergence than the standard FLMS. The convergence and complexity analysis of the M-FLMS are given along with simulation results of a benchmark nonlinear system identification problem. The M-FLMS accuracy is verified through a parameter estimation problem for a nonlinear Hammerstein structure, modeling an electrically stimulated muscle (ESM) for rehabilitation of paralyzed muscles. The proposed method is studied in detail for different levels of noise variance, fractional orders and proportion of gradients used in the current update.

ROBUST IDENTIFICATION WITH NEURAL NETWORKS USING MULTIOBJECTIVE CRITERIA

In this paper an extension of the established training algorithm for nonlinear system identification called Lolimot is presented [9]. It is a heuristic tree-construction method that trains a local linear neuro-fuzzy network. Due to its very simple partitioning strategy, Lolimot is a fast and robust modeling approach, but has a limited flexibility. Therefore a new merging approach for regression tasks is presented, that can rearrange the local model structure in the input space, without harming the global model complexity.

This paper presents a novel methodology for systematically designing a fault detection, isolation, and identification algorithm for nonlinear systems with known model structure but uncertainty in p...

A globally consistent nonlinear least squares estimator for identification of nonlinear rational systems

A normalized robust mixed-norm (NRMN) algorithm for system identification in the presence of impulsive noise is introduced. The standard robust mixed-norm (RMN) algorithm exhibits slow convergence, requires a stationary operating environment, and employs a constant step-size that needs to be determined a priori. To overcome these limitations, the proposed NRMN algorithm introduces a time-varying learning rate and, thus, no longer requires a stationary environment, a major drawback of the RMN algorithm. The proposed NRMN exhibits increased convergence rate and substantially reduces the steady-state coefficient error, as compared to the least mean square (LMS), normalized LMS (NLMS), least absolute deviation (LAD), and RMN algorithm.

A new adaptive algorithm for system identification and adaptive signal processing has been proposed in this paper. The algorithm can be viewed as a combination of the output-error type and the equation-error type of identifier (that is, a combination of the IIR adaptive filter and the FIR adaptive filter in signal-processing applications). It has been shown both mathematically and by computer simulation that the proposed algorithm can guarantee the globally asymptotical stability. The transient behaviour of the algorithm is better than the conventional output-error type of identifier, especially in the case where the system (signal model) has its eigenvalues on the unit circle. Under certain conditions on the system model (signal model), no moving average (MA) smoothing of the generalized error is needed for the strictly positive realness (SPR) conditions.

In this paper, the skewed output noise is considered and we propose a lightweight robust algorithm for nonlinear state-space system identification based on the generalized hyperbolic variance gamma (GHVG) distribution, which enhances the robustness of the proposed algorithm. To facilitate the realization of the proposed algorithm, the hidden variables are introduced to decompose the GHVG distribution into the Gaussian gamma mixture (GGM) distribution, which improves the computational efficiency of the proposed algorithm. The expectation maximization (EM) and the particle smoothing (PS) approaches are combined to solve the hidden variables and unknown states problems, which contributes to derive the estimation formulas of the model parameters and noise parameters simultaneously. To further reduce the computational burden of PS method for estimating the nonlinear states, a novel nearest neighbor idea is used in the identification process which ensures the performance of the proposed algorithm while reducing the number of particles involved in the calculation of the cost function. Finally, the verification results are fairly carried out to demonstrate the effectiveness of the proposed algorithm. Note to Practitioners—The nonlinear state-space model (NSSM) is widely applied in industrial processes due to its ability to characterize the internal dynamics of the system. For probability-based identification of NSSM, the Gaussian or heavy-tailed distributions with symmetric statistical properties are commonly used, which may limit their application in practical industrial settings. Motivated by this problem, this paper proposes a lightweight robust identification algorithm of NSSM based on GHVG distribution. An improved PS method based on nearest neighbor idea is also introduced to reduce the computational efficiency of the algorithm while ensuring its performance. This means that the proposed method is not only robust to the outliers and the skewed output noise, but also greatly reduces the running time of the algorithm, which can extend its application in real industrial processes.

Fuzzy concepts are represented by fuzzy sets, so a fuzzy knowledge is defined to be a collection of fuzzy sets (concepts) which includes two constants, 1 (true) and 0 (false). Abstractly, a logical derivation is a finite series of logical operations acting on a given knowledge. In fuzzy world, logical operations are defined by mathematical operations. So fuzzy logical derivations are mathematical derivations, and vice versa In this paper, the closure of fuzzy reasoning is characterized by fuzzy rough sets, and by topologies (neighborhood systems). A new fuzzy concept F N is derivable from the old knowledge K iff the membership function of F N is continuous in K-topology, or equivalently, iff F N is a rough fuzzy set (concept) of I N D(K),or plainly, iff the membership function of F N is a “step” function in the sense that it takes a constant value in each equivalence class of I N D(K).A fuzzy set L partitions the universe into equivalence classes; each equivalence class consists of those elements which have the same degree of membership. The indiscernibility relation I N D(K)over K is the “intersection” of all the equivalence relations induced by the fuzzy sets in K. The membership function of a fuzzy set is a real valued function, so U can be given the minimal topology such that the membership function of each fuzzy set in K is a continuous function. Such topology is called K-topology.

A narrow band interval type-2 fuzzy approach for image segmentation

The aim of this research is a software implementation of the adaptive heavy-loaded trajectory identification algorithm by development of the program and its testing at controlled sections of 500 kV power grid. Previously, developed algorithm of the adaptive heavy-loaded trajectory identification makes it possible to identify the heavy-loaded trajectory using a current power system digital model relatively to a current power system state. The algorithm, in calculating limited active power flows in terms of small-signal aperiodic stability and monitoring small signal aperiodic stability violation in the researched controlled section precisely, uses such criteria as voltage levels at the ends of researched and adjacent controlled sections connections, as well as normalized angles through these connections. A software implementation of the adaptive heavy-loaded trajectory identification algorithm is performed using the object-oriented programming language C# in the development environment Microsoft Visual Studio applying AstraLib library of RastrWin3 software. The program is tested at controlled section No.1, which is the part of 500 kV transit of the chain structure. Calculated values of limited active power flows manually and using the program applying the adaptive heavy-loaded trajectory identification algorithm differ by 62 MW or 2.3%, which does not exceed 5% error value. Developed “Adaptive heavy-loaded trajectory identification” program allows calculating values of limited active power flows for a current power system state automatically. A promising direction of the program development is decreasing the running time of program operation and program modification for the identification of the adaptive heavy-loaded trajectory in circular and multi-closed structures.

A highly modular adaptive lattice algorithm for multichannel least squares filtering

Sparse constraint Least Mean Square (LMS) is a recently proposed efficient adaptive algorithm for sparse system identification. However, its computational complexity is quite high especially when the filter length is long and convergence is slow for colored input signal. This paper extends the idea of sparse constraint into multidelay frequency adaptive filter (MDF) algorithm and proposes the sparse MDF algorithm for echo cancellation. The proposed algorithm perserves both the advantage of sparse LMS which has fast convergence performance for sparse system and MDF algorithm which has temporal decorrelation effect with lower implementation complexity. Two typical sparse constraints, l 1 -norm and an approximate l 0 -norm, are employed. And their performances of various aspects are simulated. Experiments show they have better performance than existing algorithms.