Adaptive network fuzzy inference system modeling for the input selection and prediction of anaerobic digestion effluent quality

This paper presents the development and evaluation of three adaptive network fuzzy inference system (ANFIS) models for a laboratory scale anaerobic digestion system outputs with varied input selection approaches. The aim was the investigation of feasibility of the approach-based-control system for the prediction of effluent quality from a sequential upflow anaerobic sludge bed reactor (UASBR) system that produced a strong nonlinearship between its inputs and outputs. As ANFIS demonstrated its ability to construct any nonlinear function with multiple inputs and outputs in many applications, its estimating performance was investigated for a complex wastewater treatment process at increasing organic loading rates from 1.1 to 5.5 g COD/L d. Approximation of the ANFIS models was validated using correlation coefficient, MAPE and RMSE. ANFIS was successful to model unsteady data for pH and acceptable for COD within anaerobic digestion limits with multiple input structure. The prediction performance showed a high feasibility of the model-based-control system on the anaerobic digester system to produce an effluent amenable for a consecutive aerobic treatment unit.     

Expert system for a nuclear power plant accident diagnosis using a fuzzy inference method

The huge and complicated plants such as nuclear power stations are likely to cause the operators to make mistakes due to a variety of inexplicable reasons and symptoms in case of emergency. That’s why the prevention system assisting the operators is being developed for. First of all, I suggest an improved fuzzy diagnosis. Secondly, I want to demonstrate that a classification system of nuclear plant’s accident investigating the causes of accidents foresees possible problems, and maintains the reliability of the diagnostic reports in spite of improper working in part. In the event of emergency in a nuclear plant, a lot of operational steps enable the operators to find out what caused the problems based on an emergent operating plan. Our system is able to classify their types within twenty to thirty seconds. As so, we expect the system to put down the accidents right after the rapid detection of the damage control-method concerned.     

Adaptive control of discrete-time chaotic systems: a fuzzy control approach

This paper discusses adaptive control of a class of discrete-time chaotic systems from a fuzzy control approach. Using the T–S model of discrete-time chaotic systems, an adaptive control algorithm is developed based on some conventional adaptive control techniques. The resulting adaptively controlled chaotic system is shown to be globally stable, and its robustness is discussed. A simulation example of the chaotic Henon map control is finally presented, to illustrate an application and the performance of the proposed control algorithm.     

A branch-and-bound algorithm with fuzzy inference for a permutation flowshop scheduling problem

This paper considers an m-machine permutation flowshop scheduling problem of minimizing the makespan. This classical scheduling problem is still important in modern manufacturing systems, and is well known to be intractable (i.e., NP-hard). In fact branch-and-bound algorithms developed so far for this problem have not come to solve large scale problem instances with over a hundred jobs. In order to improve the performance of branch-and-bound algorithms this paper proposes a new dominance relation by which the search load could be reduced, and notices that it is based on a sufficient precondition. This suggests that the dominance relation holds with high possibility even if the precondition approximately holds, thus being more realistic. The branch-and-bound algorithm proposed here takes advantage of this possibility for obtaining an optimal solution as early as possible in the branch-and-bound search. For this purpose this paper utilizes membership functions in the context of the fuzzy inference. Extensive numerical experiments that were executed through Monte Carlo simulations and benchmark tests show that the developed branch-and-bound algorithm can solve 3-machine problem instances with up to 1000 jobs with probability of over 99%, and 4-machine ones with up to 900 jobs with over 97%.     

Adaptive fuzzy sliding mode control of the cart-pole underactuated system

In this work, an intelligent control scheme is proposed for the stabilization of the cart-pole underactuated system. The adopted approach is primarily based on a smooth sliding mode controller, but an adaptive fuzzy inference system is embedded within the boundary layer in order to improve the control performance. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Prediction of output response probability of sound environment system using simplified model with stochastic regression and fuzzy inference

The traditional standard stochastic system models, such as the autoregressive (AR), moving average (MA) and autoregressive moving average (ARMA) models, usually assume the Gaussian property for the fluctuation distribution, and the well-known least squares method is applied on the basis of only the linear correlation data. In the actual sound environment system, the stochastic process exhibits various non-Gaussian distributions, and there exist potentially various nonlinear correlations in addition to the linear correlation between input and output time series. Consequently, the system input and output relationship in the actual phenomenon cannot be represented by a simple model. In this study, a prediction method of output response probability for sound environment systems is derived by introducing a correction method based on the stochastic regression and fuzzy inference for simplified standard system models. The proposed method is applied to the actual data in a sound environment system, and the practical usefulness is verified.     

Adaptive tuning of the fuzzy controller for robots

An adaptive tuning algorithm of the fuzzy controller is developed for a class of serial-link robot arms. The algorithm can on-line tune parameters of premise and consequence parts of fuzzy rules of the fuzzy basis function (FBF) controller. The main part of the fuzzy controller is a fuzzy basis function network to approximate unknown rigid serial-link robot dynamics. Under some mild assumptions, a stability analysis guarantees that both tracking errors and parameter estimate errors are bounded. Moreover, a robust technique is adopted to deal with uncertainties including approximation errors and external disturbances. Simulations of the proposed controller on the PUMA-560 robot arm demonstrate the effectiveness.     

An adaptive neuro‐fuzzy inference system for islanding detection in wind turbine as distributed generation

This article proposes a new integrated diagnostic system for islanding detection by means of a neuro‐fuzzy approach. Islanding detection and prevention is a mandatory requirement for grid‐connected distributed generation (DG) systems. Several methods based on passive and active detection scheme have been proposed. Although passive schemes have a large non‐detection zone (NDZ), concern has been raised on active method due to its degrading power‐quality effect. Reliably detecting this condition is regarded by many as an ongoing challenge as existing methods are not entirely satisfactory. The main emphasis of the proposed scheme is to reduce the NDZ to as close as possible and to keep the output power quality unchanged. In addition, this technique can also overcome the problem of setting the detection thresholds inherent in the existing techniques. In this study, we propose to use a hybrid intelligent system called ANFIS (the adaptive neuro‐fuzzy inference system) for islanding detection. This approach utilizes rate of change of frequency (ROCOF) at the target DG location and used as the input sets for a neuro‐fuzzy inference system for intelligent islanding detection. This approach utilizes the ANFIS as a machine learning technology and fuzzy clustering for processing and analyzing the large data sets provided from network simulations using MATLAB software. To validate the feasibility of this approach, the method has been validated through several conditions and different loading, switching operation, and network conditions. The proposed algorithm is compared with the widely used ROCOF relays and found working effectively in the situations where ROCOF fails. Simulation studies showed that the ANFIS‐based algorithm detects islanding situation accurate than other islanding detection algorithms. © 2014 Wiley Periodicals, Inc. Complexity 21: 10–20, 2015     

Looking for a good fuzzy system interpretability index: An experimental approach

Interpretability is acknowledged as the main advantage of fuzzy systems and it should be given a main role in fuzzy modeling. Classical systems are viewed as black boxes because mathematical formulas set the mapping between inputs and outputs. On the contrary, fuzzy systems (if they are built regarding some constraints) can be seen as gray boxes in the sense that every element of the whole system can be checked and understood by a human being. Interpretability is essential for those applications with high human interaction, for instance decision support systems in fields like medicine, economics, etc. Since interpretability is not guaranteed by definition, a huge effort has been done to find out the basic constraints to be superimposed during the fuzzy modeling process. People talk a lot about interpretability but the real meaning is not clear. Understanding of fuzzy systems is a subjective task which strongly depends on the background (experience, preferences, and knowledge) of the person who makes the assessment. As a consequence, although there have been a few attempts to define interpretability indices, there is still not a universal index widely accepted. As part of this work, with the aim of evaluating the most used indices, an experimental analysis (in the form of a web poll) was carried out yielding some useful clues to keep in mind regarding interpretability assessment. Results extracted from the poll show the inherent subjectivity of the measure because we collected a huge diversity of answers completely different at first glance. However, it was possible to find out some interesting user profiles after comparing carefully all the answers. It can be concluded that defining a numerical index is not enough to get a widely accepted index. Moreover, it is necessary to define a fuzzy index easily adaptable to the context of each problem as well as to the user quality criteria.     

Looking for a good fuzzy system interpretability index: An experimental approach

Interpretability is acknowledged as the main advantage of fuzzy systems and it should be given a main role in fuzzy modeling. Classical systems are viewed as black boxes because mathematical formulas set the mapping between inputs and outputs. On the contrary, fuzzy systems (if they are built regarding some constraints) can be seen as gray boxes in the sense that every element of the whole system can be checked and understood by a human being. Interpretability is essential for those applications with high human interaction, for instance decision support systems in fields like medicine, economics, etc. Since interpretability is not guaranteed by definition, a huge effort has been done to find out the basic constraints to be superimposed during the fuzzy modeling process. People talk a lot about interpretability but the real meaning is not clear. Understanding of fuzzy systems is a subjective task which strongly depends on the background (experience, preferences, and knowledge) of the person who makes the assessment. As a consequence, although there have been a few attempts to define interpretability indices, there is still not a universal index widely accepted. As part of this work, with the aim of evaluating the most used indices, an experimental analysis (in the form of a web poll) was carried out yielding some useful clues to keep in mind regarding interpretability assessment. Results extracted from the poll show the inherent subjectivity of the measure because we collected a huge diversity of answers completely different at first glance. However, it was possible to find out some interesting user profiles after comparing carefully all the answers. It can be concluded that defining a numerical index is not enough to get a widely accepted index. Moreover, it is necessary to define a fuzzy index easily adaptable to the context of each problem as well as to the user quality criteria.     

Adaptive fuzzy control for a class of chaotic systems with nonaffine inputs

A robust adaptive fuzzy control scheme is presented for a class of chaotic systems with nonaffine inputs, modeling uncertainties and external disturbances by using backstepping approach. Fuzzy logic systems (FLS) are employed to approximate the unknown parts of the virtual control and practical controls. The main characteristics of the scheme are that the number of the online adaptive parameters is no more than two times of the order of chaotic system and the tracking errors are guaranteed to be uniformly asymptotically stable with the aid of additional adaptive compensation terms. Lorenz system, Chen system, Lü system and Liu system are presented to illustrate the feasibility and effectiveness of the proposed control technique.     

Adaptive fuzzy tracking control for the chaotic permanent magnet synchronous motor drive system via backstepping

An adaptive fuzzy control method is developed to suppress chaos in the permanent magnet synchronous motor drive system via backstepping technology. Fuzzy logic systems are used to approximate unknown nonlinearities and an adaptive backstepping technique is employed to construct controllers. Compared with the conventional backstepping, the designed fuzzy controllers’ structure is very simple. The simulation results indicate that the proposed control scheme can suppress the chaos of PMSM drive systems and track the reference signal successfully even under the parameter uncertainties.     

On the use of double cross-validation for the combination of proteomic mass spectral data for enhanced diagnosis and prediction

We consider a proteomic mass spectrometry case-control study for the calibration of a diagnostic rule for the detection of early-stage breast cancer. For each patient, a pair of two distinct mass spectra is recorded, each of which is derived from a different prior fractionation procedure on the available patient serum. We propose a procedure for combining the distinct spectral expressions from patients for the calibration of a diagnostic discriminant rule. This is achieved by first calibrating two distinct prediction rules separately, each on only one of the two available spectral data sources. A double cross-validatory approach is used to summarize the available spectral data using the two classifiers to posterior class probabilities, on which a combined predictor can be calibrated.     

Adaptive synchronization for a unified chaotic system with uncertainty

A new adaptive controller is designed to synchronize of a unified chaotic system with uncertainty (unknown parameter, noise perturbation, etc.). It is implemented by using variable structure control. The controller designed here only uses the derivative information of the uncertainty. Even if the uncertainty is time-varying or unbounded, as long as its derivative is bounded, the adaptive controller can guarantee the synchronization of the unified chaotic system with uncertainty. Finally, digital simulation is carried out for Lorenz system, and the results verify the effectiveness of the proposed method.     

An approximation-based approach for fuzzy multi-period production planning problem with credibility objective

This paper develops a fuzzy multi-period production planning and sourcing problem with credibility objective, in which a manufacturer has a number of plants or subcontractors. According to the credibility service levels set by customers in advance, the manufacturer has to satisfy different product demands. In the proposed production problem, production cost, inventory cost and product demands are uncertain and characterized by fuzzy variables. The problem is to determine when and how many products are manufactured so as to maximize the credibility of the fuzzy costs not exceeding a given allowable invested capital, and this credibility can be regarded as the investment risk criteria in fuzzy decision systems. In the case when the fuzzy parameters are mutually independent gamma distributions, we can turn the service level constraints into their equivalent deterministic forms. However, in this situation the exact analytical expression for the credibility objective is unavailable, thus conventional optimization algorithms cannot be used to solve our production planning problems. To overcome this obstacle, we adopt an approximation scheme to compute the credibility objective, and deal with the convergence about the computational method. Furthermore, we develop two heuristic solution methods. The first is a combination of the approximation method and a particle swarm optimization (PSO) algorithm, and the second is a hybrid algorithm by integrating the approximation method, a neural network (NN), and the PSO algorithm. Finally, we consider one 6-product source, 6-period production planning problem, and compare the effectiveness of two algorithms via numerical experiments.     

RM approach for ranking of generalized trapezoidal fuzzy numbers

Ranking of fuzzy numbers play an important role in decision making, optimization and forecasting etc. Fuzzy numbers must be ranked before an action is taken by a decision maker. In this paper, with the help of several counter examples, it is proved that ranking method proposed by Chen and Chen (Expert Systems with Applications 36 (3): 6833) is incorrect. The main aim of this paper is to propose a new approach for the ranking of generalized trapezoidal fuzzy numbers. The proposed ranking approach is based on rank and mode so it is named as an RM approach. The main advantage of the proposed approach is that the proposed approach provides the correct ordering of generalized and normal trapezoidal fuzzy numbers and also the proposed approach is very simple and easy to apply in the real life problems. It is shown that proposed ranking function satisfies all the reasonable properties of fuzzy quantities proposed by Wang and Kerre (Fuzzy Sets and Systems 118 (3): 375).     

A new error estimation approach based on fuzzy logic system for H-R adaptive boundary element method

Conventional adaptive boundary element method cannot be universally applied to solve many more problems than the subject it discussed, and different error estimation formulas need to be designed for varied problems. This paper put forward a new error analysis method based on the fuzzy logic system, which is able to make error estimation effectively using human expert experience, and solve the two classical elasticity problems in conjunction with the H-R adaptive boundary element method. Numerical examples have illustrated the effectiveness, superiority and potential of a fuzzy logic approach in the adaptive boundary element method.     

Adaptive fuzzy output constrained decentralized control for switched nonlinear large-scale systems with unknown dead zones

In this paper, an adaptive fuzzy output-feedback control design with output constrained is investigated for a class of switched uncertain nonlinear large-scale systems with unknown dead zones and immeasurable states. Based on dynamic surface backstepping control design technique and incorporated by the average dwell time method and the prescribed performance theory, a new adaptive fuzzy output-feedback control method is developed. It is strictly proved that the resulting closed-loop system is stable in the sense of uniformly ultimately boundedness and both transient and steady-state performances of the outputs are preserved. Comparison simulation studies illustrate the effectiveness of the proposed approach.     

Adaptive fuzzy output feedback control for a class of uncertain nonlinear systems with unknown backlash-like hysteresis

An output feedback controller is proposed for a class of uncertain nonlinear systems preceded by unknown backlash-like hysteresis, where the hysteresis is modeled by a differential equation. The unknown nonlinear functions are approximated by fuzzy systems based on universal approximation theorem, where both the premise and the consequent parts of the fuzzy rules are tuned with adaptive schemes. The proposed approach does not need the availability of the states, which is essential in practice, and uses an observer to estimate the states. An adaptive robust structure is used to cope with lumped uncertainties generated by state estimation error, approximation error of fuzzy systems and external disturbances. Due to its adaptive structure the bound of lumped uncertainties does not need to be known and at the same time the chattering is attenuated effectively. The strictly positive real (SPR) Lyapunov synthesis approach is used to guarantee asymptotic stability of the closed-loop system. In order to show the effectiveness of the proposed method simulation results are illustrated.     

Adaptive fuzzy backstepping control for a class of MIMO switched nonlinear systems with unknown control directions

In this article, an adaptive fuzzy output tracking control approach is proposed for a class of multiple‐input and multiple‐output uncertain switched nonlinear systems with unknown control directions and under arbitrary switchings. In the control design, fuzzy logic systems are used to identify the unknown switched nonlinear systems. A Nussbaum gain function is introduced into the control design and the unknown control direction problem is solved. Under the framework of the backstepping control design, fuzzy adaptive control and common Lyapunov function stability theory, a new adaptive fuzzy output tracking control method is developed. It is proved that the proposed control approach can guarantee that all the signals in the closed‐loop system are bounded and the tracking error remains an adjustable neighborhood of the origin. A numerical example is provided to illustrate the effectiveness of the proposed approach. © 2015 Wiley Periodicals, Inc. Complexity 21: 155–166, 2016