A GMDH-based fuzzy modeling approach for constructing TS model

In this paper, a new learning algorithm based on group method of data handling (GMDH) is proposed for the identification of Takagi-Sugeno fuzzy model. Different from existing methods, the new approach, called TS-GMDH, starts from simple elementary TS fuzzy models, and then uses the mechanism of GMDH to produce candidate fuzzy models of growing complexity until the TS model of optimal complexity has been created. The main characteristic of the new approach is its ability to identify the structure of TS model automatically. Experiments on Box-Jenkins gas furnace data and UCI datasets have shown that the proposed method can achieve satisfactory results and is more robust to noise in comparison with other TS modeling techniques such as ANFIS.     

An advanced dynamic process model for industrial horizontal anode baking furnace

The global aluminum industry is facing new challenges due to new technological developments. Carbon anodes, consisting of mainly petroleum coke and coal tar pitch, are used in the electrolytic production of aluminum. High amperage utilization in the electrolytic cells with the objective of increasing production requires high quality carbon anodes. The anode quality depends both on raw material quality, anode recipe as well as forming and baking conditions of anode manufacturing process. The cost of the baking process constitutes 15 to 25% of the total aluminum production cost [1]. The industrial challenge is to produce better quality anodes consuming less energy, and reducing environmental emissions.A transient two dimensional (2D⁺) process model for horizontal anode baking furnace was developed during this study. The main objective was to develop an efficient furnace model with low computation load and time, using the transient Finite Difference Method and simplified furnace geometry. The model represents several phenomena involved during the anode baking process such as heat transfer (convection, radiation and conduction), fuel combustion, volatile matter (tar, methane and hydrogen) generation and combustion, air infiltration and energy loss to the atmosphere from the walls, the top of the furnace and the foundation. The model was developed using two coupled sub-models; the first one describes the thermal conduction through the solid materials (brick refractory wall, packing coke and anode block) as well as the volatile release, and the second one describes the gas flow, heat and mass transfer as well as the combustion of fuel and volatiles in the flue. Compared to the existing process models (where the gas flow in flue is assumed as unidirectional along the horizontal furnace direction), the present model also considers the gas flow in vertical direction and uses four vertical planes per pit section to predict the temperature of the solids. The model predicts 2D temperature distribution within the flue gas (xy plane) and the pit solid materials (yz plane) allowing then the prediction of the pseudo tridimensional distribution of the solid temperature. This model is a useful tool for the continuous monitoring of anode temperature and studying of the horizontal anode baking furnace behaviour. The effect of any change in operational parameters and the energy consumption on the furnace operation can be predicted.     

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.     

Dynamics of fuzzy impulsive bidirectional associative memory neural networks with time-varying delays

Complex nonlinear systems can be represented to a set of linear sub-models by using fuzzy sets and fuzzy reasoning via ordinary Takagi-Sugeno (TS) fuzzy models. In this paper, the exponential stability of TS fuzzy bidirectional associative memory (BAM) neural networks with impulsive effect and time-varying delays is investigated. The model of fuzzy impulsive BAM neural networks with time-varying delays established as a modified TS fuzzy model is new in which the consequent parts are composed of a set of impulsive BAM neural networks with time-varying delays. Further the exponential stability for fuzzy impulsive BAM neural networks is presented by utilizing the Lyapunov-Krasovskii functional and the linear matrix inequality (LMI) technique without tuning any parameters. In addition, an example is provided to illustrate the applicability of the result using LMI control toolbox in MATLAB.     

Operation strategy optimization of desulfurization system based on data mining

Desulfurization systems in coal-fired power stations often suffer the problem of high operating costs caused by a rule-of-thumb control strategy, which implies great potential for optimization of the operation. Due to the complex desulfurization mechanism, frequently fluctuating unit load, and severe disturbance, it is challenging to determine the optimal operating parameters based on the traditional mechanistic models, and the operating parameters are closely related to the operational efficiency of the flue gas desulfurization system. In this paper, an operation strategy optimization method for the desulfurization process is proposed based on a data mining framework, which is able to determine online the optimal operating parameter settings from a large amount of historical data. First, Principal Component Analysis (PCA) is used to reduce data redundancy by mapping the data into a new vector space. Based on the new vector space, an enhanced fuzzy C-means clustering (Enhanced-FCM) is developed to cluster the historical data into groups sharing similar characteristics. Taking sulfur dioxide emission concentration as a constraint condition, the system is optimized with economic benefits and desulfurization efficiency as the objective function. When performing optimization, the group that current operating conditions belong to is determined first, then the operating parameters of the best performance are searched within the group and provided as the optimization results. The method is validated and tested based on the data from a wet flue gas desulfurization (WFGD) system of a 1000 MWe supercritical coal-fired power plant in China. The results indicate that the proposed operation strategy can appropriately obtain operating parameter settings at different conditions, and effectively reduce the desulfurization cost under the constraint of meeting emission requirements.     

Data-driven fuzzy models for nonlinear identification of a complex heat exchanger

This paper presents and discusses experimental results on nonlinear model identification method applied to a real pilot thermal plant. The aim of this work is to develop a moderately complex model with interpretable structure for a complex parallel flow heat exchanger which is the main component of the thermal plant using a fuzzy clustering technique. The proposed Takagi–Sugeno-type (TS) fuzzy rule-based model is derived through an iterative fuzzy clustering algorithm using a set of input–output measurements. It is shown that the identified multivariable fuzzy rule-based model captures well the key dynamical properties of the physical plant over a wide operating range and under varying operating conditions. For validation, the model is run in parallel and series-parallel configurations to the real process. The experimental results show clearly the high performance of the proposed fuzzy model in achieving good prediction of the main process variables.     

基于观测器的模糊Delta算子系统的控制器设计

对于非线性模糊系统控制器和观测器的分析和设计,提出一种统一方法。利用Delta域离散T—S模糊模型对非线性系统建模,并基于李雅普诺夫稳定性理论给出模糊状态反馈控制器和观测器的设计策略,将所得结果归结为求解一组线性矩阵不等式。同时结论表明:分离性原理对Delta算子T—S模糊系统仍然成立。所得结果可将现有关于连续和离散T—S模糊系统的相关结论统一于Delta算子框架内。     

Stability analysis of Takagi–Sugeno fuzzy Cohen–Grossberg BAM neural networks with discrete and distributed time-varying delays

In this paper, the global asymptotic stability problem of Takagi–Sugeno (TS) fuzzy Cohen–Grossberg Bidirectional Associative Memory neural networks (FCGBAMNNs) with discrete and distributed time-varying delays is considered. A novel LMI-based stability criterion is obtained by using Lyapunov functional theory to guarantee the asymptotic stability of FCGBAMNNs which are represented by TS fuzzy models. Our results can be easily verified and are also less restrictive than previously known criteria and can be applied to Cohen–Grossberg neural networks, recurrent neural networks and cellular neural networks. Finally, the proposed stability conditions are demonstrated with a numerical example.     

Dynamic fuzzy reliability models of degraded hold-down structures for folded solar array

The hold-down structures are of considerable importance to the launch of solar array. Due to the difficulties in obtaining sufficient load specimen, it is imprecise to construct the stress as random variables. Therefore, dynamic fuzzy reliability models are developed in this paper, which resolve the problems in dealing with the interaction between the fuzzy stress process and the stochastic strength process. Even for a deterministic fuzzy stress process, the influences of material statistical properties on reliability can be affected by the level α of fuzzy stress. Meanwhile, the level α relates to investment in the collection of information about the fuzzy stress on hold-down bar. Hence, the models can be used for the economic analysis and optimal design of hold-down bar. Finally, key fuzzy parameters of stress, which have significant influences on both the reliability behavior and the effects of material statistical properties on reliability, are identified and some suggestions for the reliability enhancement of hold-down bar are provided in this paper.     

Cost,Revenue and Profit Efficiency Models in Generalized Fuzzy Data Envelopment Analysis

One of the most important information given by data envelopment analysis models is the cost, revenue and profit efficiency of decision making units (DMUs). Cost efficiency is defined as the ratio of minimum costs to current costs, while revenue efficiency is defined as the ratio of maximum revenue to current revenue of the DMU. This paper presents a framework where data envelopment analysis (DEA) is used to measure cost, revenue and profit efficiency with fuzzy data. In such cases, the classical models cannot be used, because input and output data appear in the form of ranges. When the data are fuzzy, the cost, revenue and profit efficiency measures calculated from the data should be uncertain as well. Fuzzy DEA models emerge as another class of DEA models to account for imprecise inputs and outputs for DMUs. Although several approaches for solving fuzzy DEA models have been developed, numerous deficiencies including the $\alpha$-cut approaches and types of fuzzy numbers must still be improved. This scheme embraces evaluation method based on vector for proposed fuzzy model. This paper proposes generalized cost, revenue and profit efficiency models in fuzzy data envelopment analysis. The practical application of these models is illustrated by a numerical example.     

Interface optimality in fuzzy inference systems

In this paper we address the issue of designing optimal fuzzy interfaces, which are fundamental components of a fuzzy inference system. Due to the different roles of input and output interfaces, optimality conditions are analyzed separately for the two types of interface. We prove that input interfaces are optimal when based on a particular class of fuzzy sets called “bi-monotonic”, provided that mild conditions hold. The class of bi-monotonic fuzzy sets covers a broad range of fuzzy sets shapes, including convex fuzzy sets, so that the provided theoretical results can be applied to several fuzzy models. Such theoretical results are not applicable to output interfaces, for which a different optimality criterion is proposed. Such criterion leads to the definition of an optimality degree that measures the quality of a fuzzy output interface. Illustrative examples are presented to highlight the features of the proposed optimality degree in assessing the quality of output interfaces.     

Process planning in a fuzzy environment

Mixed-integer optimization models for chemical process planning typically assume that model parameters can be accurately predicted. As precise forecasts are difficult to obtain, process planning usually involves uncertainty and ambiguity in the data. This paper presents an application of fuzzy programming to process planning. The forecast parameters are assumed to be fuzzy with a linear or triangular membership function. The process planning problem is then formulated in terms of decision making in a fuzzy environment with fuzzy constraints and fuzzy net present value goals. The model is transformed to a deterministic mixed-integer linear program or mixed-integer nonlinear program depending on the type of uncertainty involved in the problem. For the nonlinear case, a global optimization algorithm is developed for its solution. This algorithm is applicable to general possibilistic programs and can be used as an alternative to the commonly used bisection method. Illustrative examples and computational results for a petrochemical complex with 38 processes and 24 products illustrate the applicability of the developed models and algorithms.     

Modelling and simulation of moving interfaces in gas-assisted injection moulding process

The mathematical models of gas–liquid two-phase flow are introduced, in which the multi-mode eXtended Pom–Pom (XPP) model is selected to predict the viscoelastic behavior of polymer melt. The gas-penetration process is simulated using Level Set/SIMPLEC methods, which can capture the moving interfaces at different time, including the gas–melt interface and the melt front. The physical features such as velocity, temperature and elasticity are described at different time. The influences of gas delay time and injection pressure on gas-penetration time and penetration length are analyzed. The numerical results show that the Level Set/SIMPLEC methods can precisely trace the two moving interfaces in gas-penetration process, the fractional coverage increases at very low Deborah numbers, while at higher Deborah numbers the fractional coverage decreases, and the penetration length is affected significantly by gas delay time and injection pressure.     

Fuzzy efficiency ranking in fuzzy two-stage data envelopment analysis

Data envelopment analysis (DEA) is a useful tool for efficiency measurement of firms and organizations. Many production systems in the real world are composed of two processes connected in series. Measuring the system efficiency without taking the operation of each process into consideration will obtain misleading results. Two-stage DEA models show the performance of individual processes, thus is more informative than the conventional one-stage models for making decisions. When input and output data are fuzzy numbers, the derived efficiencies become fuzzy as well. This paper proposes a method to rank the fuzzy efficiencies when the exact membership functions of the overall efficiencies derived from fuzzy two-stage model are unknown. By incorporating the fuzzy two-stage model with the fuzzy number ranking method, a pair of nonlinear program is formulated to rank the fuzzy overall efficiency scores of DMUs. Solving the pair of nonlinear programs determines the efficiency rankings. An example of the ranking of the 24 non-life assurance companies in Taiwan is illustrated to explain how the proposed method is applied.     

Estimations of trout density and biomass: a neural networks approach

In this paper, we report the use of artificial neural networks to predict the density and biomass of trout in the Pyrenees mountains from 8 physical parameters of the environment. The results obtained with a three-layered neural network are presented. Studies have been undertaken with 1 or 4 variables in the output layer of the network. Results on the test set (generalization of models) are satisfactory with determination coefficients R² exceeding 0.76.     

Intelligent data analysis and model interpretation with spectral analysis fuzzy symbolic modeling

This paper proposes fuzzy symbolic modeling as a framework for intelligent data analysis and model interpretation in classification and regression problems. The fuzzy symbolic modeling approach is based on the eigenstructure analysis of the data similarity matrix to define the number of fuzzy rules in the model. Each fuzzy rule is associated with a symbol and is defined by a Gaussian membership function. The prototypes for the rules are computed by a clustering algorithm, and the model output parameters are computed as the solutions of a bounded quadratic optimization problem. In classification problems, the rules’ parameters are interpreted as the rules’ confidence. In regression problems, the rules’ parameters are used to derive rules’ confidences for classes that represent ranges of output variable values. The resulting model is evaluated based on a set of benchmark datasets for classification and regression problems. Nonparametric statistical tests were performed on the benchmark results, showing that the proposed approach produces compact fuzzy models with accuracy comparable to models produced by the standard modeling approaches. The resulting model is also exploited from the interpretability point of view, showing how the rule weights provide additional information to help in data and model understanding, such that it can be used as a decision support tool for the prediction of new data.     

Multi-item inventory models with price dependent demand under flexibility and reliability consideration and imprecise space constraint: A geometric programming approach

In this paper, multi-item economic production quantity (EPQ) models with selling price dependent demand, infinite production rate, stock dependent unit production and holding costs are considered. Flexibility and reliability consideration are introduced in the production process. The models are developed under two fuzzy environments–one with fuzzy goal and fuzzy restrictions on storage area and the other with unit cost as fuzzy and possibility–necessity restrictions on storage space. The objective goal and constraint goal are defined by membership functions and the presence of fuzzy parameters in the objective function is dealt with fuzzy possibility/necessity measures. The models are formed as maximization problems. The first one—the fuzzy goal programming problem is solved using Fuzzy Additive Goal Programming (FAGP) and Modified Geometric Programming (MGP) methods. The second model with fuzzy possibility/necessity measures is solved by Geometric Programming (GP) method. The models are illustrated through numerical examples. The sensitivity analyses of the profit function due to different measures of possibility and necessity are performed and presented graphically.     

Application of fuzzy time series in prediction of time between failures &; faults in software reliability assessment

Since last seventies, various software reliability growth models (SRGMs) have been developed to estimate different measures related to quality of software like: number of remaining faults, software failure rate, reliability, cost, release time, etc. Most of the exiting SRGMs are probabilistic. These models have been developed based on various assumptions. The entire software development process is performed by human being. Also, a software can be executed in different environments. As human behavior is fuzzy and the environment is changing, the concept of fuzzy set theory is applicable in developing software reliability models. In this paper, two fuzzy time series based software reliability models have been proposed. The first one predicts the time between failures (TBFs) of software and the second one predicts the number of errors present in software. Both the models have been developed considering the software failure data as linguistic variable. Usefulness of the models has been demonstrated using real failure data.     

Analyses on 3-D gas flow and heat transfer in ladle furnace lid

In order to verify the reasonableness of off-gas pressure and wall temperature, a mathematical model for gas flow and heat transfer in ladle furnace (LF) lid is developed based on 3-D Navier–Stokes equations and k–ε two equation turbulent models as well as energy conservation equation. The gas velocity vector distribution of skirt clearance between the top edge of ladle and furnace lid and electrode gaps between three graphite electrodes and furnace lid, the gas flow line distribution, pressure and temperature distribution on the furnace lid wall are simulated. Simulation results show that appropriate off-gas pressures are 200 Pa, 200 Pa and 150 Pa when electric arc emerges from molten steel surface and alloy hole is unsealed, electric arc emerges from molten steel surface and alloy hole is closure, electric arc immerges into molten steel surface and alloy hole is closure, respectively. The maximum temperature presents in the middle of LF lid in all of heating conditions, and the temperature value are 563, 603 and 343 K. Finally, the relations between gas volume and off-gas pressure are analyzed in different width of skirt clearance, and some relevant mathematical expressions are obtained. By comparing both simulation results and practical data, the advice on reducing off-gas pressure is proposed, and the maximum temperatures of furnace lid wall have good agreement with actual data.     

Robust fuzzy fault detection and isolation approach applied to surge in centrifugal compressor modeling and control

This work presents the results of applying an advanced fault detection and isolation technique to centrifugal compressor; this advanced technique uses physics models of the centrifugal compressor with a fuzzy modeling and control solution method. The fuzzy fault detection and isolation has become an issue of primary importance in modern process engineering automation as it provides the prerequisites for the task of fault detection. In this work, we present an application of this approach in fault detection and isolation of surge in compression system. The ability to detect the surge is essential to improve reliability and security of the gas compressor plants. We describe and illustrate an alternative implementation to the compression systems supervision task using the basic principles of fuzzy fault detection and isolation associated with fuzzy modeling approach. In this supervision task, the residual generation is obtained from the real input-output data process and the residual evaluation is based on fuzzy logic method. The results of this application are very encouraging with relatively low levels of false alarms and obtaining a good limitation of surge in natural gas pipeline compressors.