Takagi-Sugeno Fuzzy Inference System Research Articles

New Type of Takagi-Sugeno Fuzzy Inference System as Universal Approximator

A new type of fuzzy inference systems (FIS) is presenting. It is based on Takagi-Sugeno fuzzy inference system. New FIS has been called the enhanced fuzzy regression (EFR). In opposition to the Takagi-Sugeno, new type of FIS has fuzzy coefficients in right parts of the fuzzy rules. Fuzzy approximation theorem has been proved for the EFR. We have suggested learning procedure for EFR inference system.

Robust PID TS fuzzy control methodology based on gain and phase margins specifications

This paper proposes the analysis and design of TS fuzzy robust PID control based on gain and phase margins specifications for uncertain nonlinear dynamic systems with time delay. The input-output data set of the uncertain nonlinear time delay dynamic system is decomposed into several input-output spaces by Gustafson-Kessel GK clustering algorithm, which are used to compute several linear submodels by least squares algorithm, and grouped in a Takagi-Sugeno TS fuzzy inference system. From the gain and phase margins specifications, in the frequency domain, analytical formulas are derived for fuzzy model based robust PID control design via Paralel and Distributed Compensation PDC strategy, considering the influence of the time delay. The main contribution of the paper is the proposal of two theorems related to necessary and sufficient conditions for fuzzy robust control design. The first theorem shows that the robust PID controller in the i-th rule of the fuzzy robust PID controller guarantees the gain and phase margins specifications for the corresponding linear model. The second theorem shows that the robust PID controller in the i-th rule of the fuzzy robust PID controller guarantees the stability for all linear models. A simulation example illustrates the efficiency of the fuzzy controller for control of a single link robotic manipulator when compared to others control methods. The experimental results for real-time fuzzy robust PID control of a termic process are obtained to demonstrate the effectiveness and practical viability of the proposed strategy.

Mamdani and Takagi-Sugeno fuzzy classifier accuracy improvement using enhanced particle swarm optimization

This paper discusses a method for designing a fuzzy-rule-based classifiers using enhanced particle swarm optimization EPSO. Two different fuzzy classifiers are considered and optimized. The first classifier is based on Mamdani fuzzy inference system M_EPSO fuzzy classifier. The second classifier is based on Takagi-Sugeno fuzzy inference system TS_EPSO fuzzy classifier. The parameters of the proposed fuzzy classifiers including premise antecedent parameters, consequent parameters and structure of fuzzy rules are optimized using EPSO. The performances of M_EPSO and TS_EPSO fuzzy classifiers are compared to commonly used fuzzy based classifiers. Experimental results show that higher classification accuracy can be obtained with limited number of fuzzy rules by using the proposed EPSO fuzzy classifiers. Another comparison that shows the consistency of EPSO for optimizing the proposed fuzzy classifiers over other evolutionary algorithms is also presented.

Improving real time flood forecasting using fuzzy inference system

In order to improve the real time forecasting of foods, this paper proposes a modified Takagi Sugeno (T–S) fuzzy inference system termed as threshold subtractive clustering based Takagi Sugeno (TSC-T–S) fuzzy inference system by introducing the concept of rare and frequent hydrological situations in fuzzy modeling system. The proposed modified fuzzy inference systems provide an option of analyzing and computing cluster centers and membership functions for two different hydrological situations, i.e. low to medium flows (frequent events) as well as high to very high flows (rare events) generally encountered in real time flood forecasting. The methodology has been applied for flood forecasting using the hourly rainfall and river flow data of upper Narmada basin, Central India. The available rainfall–runoff data has been classified in frequent and rare events and suitable TSC-T–S fuzzy model structures have been suggested for better forecasting of river flows. The performance of the model during calibration and validation is evaluated by performance indices such as root mean square error (RMSE), model efficiency and coefficient of correlation (R). In flood forecasting, it is very important to know the performance of flow forecasting model in predicting higher magnitude flows. The above described performance criteria do not express the prediction ability of the model precisely from higher to low flow region. Therefore, a new model performance criterion termed as peak percent threshold statistics (PPTS) is proposed to evaluate the performance of a flood forecasting model. The developed model has been tested for different lead periods using hourly rainfall and discharge data. Further, the proposed fuzzy model results have been compared with artificial neural networks (ANN), ANN models for different classes identified by Self Organizing Map (SOM) and subtractive clustering based Takagi Sugeno fuzzy model (SC-T–S fuzzy model). It has been concluded from the study that the TSC-T–S fuzzy model provide reasonably accurate forecast with sufficient lead-time.

Application of firefly algorithm and ANFIS for optimisation of functionally graded beams

Volume fraction optimisation of functionally graded beams is studied for maximising the fundamental natural frequency by applying a new meta-heuristic nature-inspired algorithm called firefly algorithm (FA) which is based on the flashing behaviour of fireflies. Nature-inspired algorithms are among the most powerful algorithms for optimisation of engineering problems. The primary optimisation variables are the three parameters in the power-law distribution. Since the search space is large, the optimisation processes becomes so complicated and too much time consuming. Thus, a suitable Adaptive Neuro-Fuzzy Inference System (ANFIS) that is based on Takagi–Sugeno fuzzy inference system is combined with FA to reproduce the behaviour of the structure in free vibration. The ANFIS improves the speed of optimisation process by a considerable amount. The results are compared with those obtained by imperialist competitive algorithm, genetic algorithm and Artificial Neural Networks proposed in our previous work. Results show that the combination of FA and ANFIS is capable of yielding better optimal solution in comparison with other available techniques. It is believed that new results are of interest to the scientific and engineering community in the area of engineering design.

Elasto-geometrical modeling and calibration of robot manipulators: Application to machining and forming applications

This paper proposes an original elasto-geometrical calibration method to improve the static pose accuracy of industrial robots involved in machining, forming or assembly applications. Two approaches are presented respectively based on an analytical parametric modeling and a Takagi–Sugeno fuzzy inference system. These are described and then discussed. This allows to list the main drawbacks and advantages of each of them with respect to the task and the user requirements. The fuzzy logic model is used in a model-based compensation scheme to increase significantly the robot static pose accuracy in a context of incremental forming application. Experimental results show the efficiency of the fuzzy logic model while minimizing development and computational resources.

A mathematical modeling for incorporating energy price hikes into total natural gas consumption forecasting

In some countries that energy prices are low, price elasticity of demand may not be significant. In this case, large increase or hike in energy prices may impact energy consumption in a way which cannot be drawn from historical data. This paper proposes an integrated adaptive fuzzy inference system (FIS) to forecast long-term natural gas (NG) consumption when prices experience large increase. To incorporate the impact of price hike into modeling, a novel procedure for construction and adaptation of Takagi–Sugeno fuzzy inference system (TS-FIS) is suggested. Linear regressions are used to construct a first order TS-FIS. Furthermore, adaptive network-based FIS (ANFIS) is used to forecast NG consumption in power plants. To cope with random uncertainty in small historical data sets, Monte Carlo simulation is utilized to generate training data for ANFIS. To show the applicability and usefulness of the proposed model, it is applied for forecasting of annual NG consumption in Iran where removing energy subsidies has resulted in a hike in NG prices.

A new adaptive fuzzy inference system for electricity consumption forecasting with hike in prices

Large increase or hike in energy prices has proven to impact electricity consumption in a way which cannot be drawn from historical data, especially when price elasticity of demand is not significant. This paper proposes an integrated adaptive fuzzy inference system (FIS) to estimate and forecast long-term electricity consumption when prices experience large increase. To this end, first a novel procedure for construction and adaptation of Takagi–Sugeno fuzzy inference system (TS-FIS) is suggested. Logarithmic linear regressions are estimated with historical data and used to construct an initial first-order TS-FIS. Then, in the adaptation phase, expert knowledge is used to define new fuzzy rules which form a new secondary FIS for electricity forecasting. To show the applicability and usefulness of the proposed model, it is applied for forecasting of annual electricity consumption in Iran where removing energy subsidies has resulted in a hike in electricity prices. Gross domestic product (GDP), population and electricity price are three inputs for the initial TS-FIS. A questionnaire survey was conducted to collect the expert estimation on possible change in electricity per capita, change in electricity intensity and the ratio of GDP elasticity to population elasticity when price hikes. Based on the information collected, a fuzzy rule base is formed and used to construct the secondary FIS which is used for electricity forecasting until 2016. Furthermore, the performance of the proposed model of this paper is compared with three other models namely ANFIS, ANN and one-stage regression in terms of their mean absolute percentage error. The comparison shows a superior performance for the proposed FIS model.

Estimation of convergence of a high-speed railway tunnel in weak rocks using an adaptive neuro-fuzzy inference system (ANFIS) approach

Estimation of tunnel diameter convergence is a very important issue for tunneling construction, especially when the new Austrian tunneling method (NATM) is adopted. For this purpose, a systematic convergence measurement is usually implemented to adjust the design during the whole construction, and consequently deadly hazards can be prevented. In this study, a new fuzzy model capable of predicting the diameter convergences of a high-speed railway tunnel was developed on the basis of adaptive neuro-fuzzy inference system (ANFIS) approach. The proposed model used more than 1 000 datasets collected from two different tunnels, i.e. Daguan tunnel No. 2 and Yaojia tunnel No. 1, which are part of a tunnel located in Hunan Province, China. Six Takagi-Sugeno fuzzy inference systems were constructed by using subtractive clustering method. The data obtained from Daguan tunnel No. 2 were used for model training, while the data from Yaojia tunnel No. 1 were employed to evaluate the performance of the model. The input parameters include surrounding rock masses (SRM) rating index, ground engineering conditions (GEC) rating index, tunnel overburden (H), rock density (ρ), distance between monitoring station and working face (D), and elapsed time (T). The model’s performance was assessed by the variance account for (VAF), root mean square error (RMSE), mean absolute percentage error (MAPE) as well as the coefficient of determination (R2) between measured and predicted data as recommended by many researchers. The results showed excellent prediction accuracy and it was suggested that the proposed model can be used to estimate the tunnel convergence and convergence velocity.

Adaptive fuzzy parameter scheduling scheme for GSA based optimal proportional integral derivative and lag-lead control of a DC attraction type levitation system

Magnetic levitation system is inherently unstable and strongly nonlinear in nature. Fixed optimal gain controllers designed at some nominal operating conditions fail to provide the best control performance over a wide range of off-nominal operating conditions. In this paper, an adaptive fuzzy parameter scheduling scheme for Gravitational Search Algorithm (GSA) based optimal Proportional Integral Derivative (PID) and Lag-Lead controllers has been proposed to control a single actuator based DC Attraction type Levitation System (DCALS). A Takagi-Sugeno (T-S) fuzzy inference system is used in the proposed controllers. The inference system is extremely well suited to the task of smoothly interpolating linear gains across the input space when a strongly non-linear DCALS moves around in its operating space. Simulation results show that both proposed adaptive fuzzy PID and Lag-Lead controllers offer better performance than fixed gain controllers at different operating conditions.

Dynamic modelling and control of a twin-rotor system using adaptive neuro-fuzzy inference system techniques

This article presents an online non-linear dynamic modelling and control approach based on adaptive neuro-fuzzy inference system (ANFIS) for a twin-rotor multi-input multi-output system (TRMS), in the vertical plane motion. The TRMS can be considered as a flexible aerodynamic test rig that resembles the behaviour of a helicopter. The TRMS and similar manoeuvring systems are often subjected to random disturbances arising from various sources such as driving motors and external environmental sources. For such highly non-linear systems with varying operating conditions, adaptive control approaches are suitable tools to cope with plant uncertainties. An inverse-model control of the TRMS is developed using online ANFIS learning algorithm. The consequent and antecedent parameters of a Takagi–Sugeno fuzzy inference system are optimized online using recursive least squares and gradient descent algorithms, respectively. In order to reduce the computation complexity, the training process is minimized based on global system error tolerance. The optimal initialization of the ANFIS parameters is achieved through an off-line training process. The developed strategy is compared to other control laws in terms of tracking performance, disturbance rejection, and response to external noise. The obtained simulation results demonstrate the efficiency of the online inverse control scheme.

A calibration approach based on Takagi–Sugeno fuzzy inference system for digital electronic compasses

Recently, the development of industrial processes brought on the outbreak of technologically complex systems. This development generated the necessity of research relative to the mathematical techniques that have the capacity to deal with project complexities and validation. Fuzzy models have been receiving particular attention in the area of nonlinear systems identification and analysis due to it is capacity to approximate nonlinear behavior and deal with uncertainty. A fuzzy rule-based model suitable for the approximation of many systems and functions is the Takagi–Sugeno (TS) fuzzy model. TS fuzzy models are nonlinear systems described by a set of if then rules which gives local linear representations of an underlying system. Such models can approximate a wide class of nonlinear systems. In this paper a performance analysis of a system based on TS fuzzy inference system for the calibration of electronic compass devices is considered. The contribution of the evaluated TS fuzzy inference system is to reduce the error obtained in data acquisition from a digital electronic compass. For the reliable operation of the TS fuzzy inference system, adequate error measurements must be taken. The error noise must be filtered before the application of the TS fuzzy inference system. The proposed method demonstrated an effectiveness of 57% at reducing the total error based on considered tests.

Uma abordagem baseada em sistemas de inferência Fuzzy Takagi-Sugeno aplicada ao planejamento da operação de sistemas hidrotérmicos de geração

O planejamento da operação de sistemas hidrotérmicos de geração, em sistemas com grande participação hidráulica, como é o caso do sistema brasileiro, visa determinar uma política de operação que especifique como as usinas hidroelétricas devem ser operadas, de forma que os recursos hidroelétricos sejam utilizados com economia e confiabilidade. Este trabalho apresenta uma aplicação de sistemas de inferência fuzzy do tipo Takagi-Sugeno, responsável por obter uma política de operação (PBSIF - Política Baseada em Sistema de Inferência Fuzzy) que represente a operação otimizada de reservatórios para geração de energia elétrica, bem como da análise desta política e sua aplicação na simulação da operação de sistemas hidroelétricos. A política proposta é obtida pela otimização da operação energética das usinas hidroelétricas. Desta otimização extraem-se as relações entre a energia armazenada do sistema e o volume do reservatório de cada usina. Estas relações estão representadas nos parâmetros dos consequentes das regras linguísticas fuzzy do modelo de inferência de Takagi-Sugeno. De forma a ilustrar a eficácia da PBSIF, ela foi avaliada por meio da comparação do seu desempenho com a política de operação em paralelo; com a política de operação baseada em aproximações funcionais, que utiliza funções polinomiais e exponenciais, obtidas através do método dos mínimos quadrados; e também com o resultado obtido através da operação otimizada a usinas individualizadas. Com a metodologia proposta, procura-se demonstrar a viabilidade da obtenção e aplicação da PBSIF, e com os resultados obtidos, pretende-se ilustrar a eficácia e os ganhos energéticos advindos.

MODELING PNEUMATIC MUSCLE ACTUATORS: ARTIFICIAL INTELLIGENCE APPROACH

Robot human interaction requires use of safe, compliant and light weight actuators. Conventional linear motors and pneumatic cylinders are normally used to actuate robots to assist and augment human motions. Lately it has been realized that these actuators are not suitable and safe for applications involving human actor. Their large weight, size and stiffer design raise concerns. Pneumatic muscle actuators (PMA) on the other hand are very light weight, compact and have inherent compliance which make them potential candidate for applications involving robot human interaction. Taking on the advantages, these actuators are now being experimented for a variety of medical and rehabilitation applications. However they are not very popular due to their highly nonlinear and time dependent behavior which poses control problems. In this paper, an attempt is being made to accurately predict the uncertain and ambiguous characteristics of PMA using Artificial Intelligence (AI). Conventional tools such as analytical and numerical methods can only model a nonlinear system which is time independent. Time varying nonlinear system characteristics can be best modeled using artificial intelligence-based regression models. In this research, Artificial Neural Network (ANN), Mamdani Fuzzy Inference System (FIS) and Takagi-Sugeno (TS)-based fuzzy system are developed after carefully analyzing the time series data obtained from a real system. To achieve higher accuracy from these models, their parameters are tuned. Parameters of ANN are tuned using back propagation algorithm whereas fuzzy parameters are tuned using three different methods, namely, gradient descent method (GD), genetic algorithms (GA) and Modified Genetic Algorithm (MGA). It was found that the TS fuzzy inference system tuned by MGA provides better accuracy and can also model the time dependent behavior of PMA. The proposed TS fuzzy system is found to perform better in terms of accuracy and maximum deviation when compared to the previous approaches in the literature.

Comparison of fuzzy inference systems for streamflow prediction

A comparison of the Mamdani and the Takagi-Sugeno (TS) fuzzy inference systems is presented for predicting streamflow values. The TS fuzzy rule base uses linear functions of inputs to predict the output, whereas the Mamdani version of inference determines outputs through fuzzy sub-sets. A genetic algorithm-trained Mamdani system is applied for streamflow forecasting. All the uncertainties and model complications are treated in linguistic expressions in the form of IF—THEN statements. Fuzzy membership functions, rules and the type of defuzzification method are adjusted until the best correlation between measured and predicted values is reached. The two methods are then applied to flow predictions on the Euphrates River in Turkey, without employing exogenous variables such as rainfall. The advantages and disadvantages of the models are discussed using the case study. It is shown that the Mamdani type of fuzzy inference modelling outperforms the Takagi-Sugeno approach in terms of error criteria comparisons, but neither of the two outperforms a standard ARMA(2, 2) model.

A fuzzy inference system for modelling streamflow: Case of Letaba River, South Africa

Streamflow modelling of Letaba River in South Africa is complicated by several factors including the existence of dams and other storage structures whose releases are intermittent and based on rules of thumb depending on the irrigation demands and the need to maintain the flow required in the Kruger National park (KNP). The KNP is located about a hundred kilometres downstream of the main storage and water flows through an alluvial aquifer where complex surface–groundwater interactions occur. Farmers abstract water intermittently along the route directly from the river or indirectly from the alluvial aquifer complicating the flow patterns even more. Consequently, the streamflow series in the river shows very little similarity to what would be considered as natural. The actual abstractions are not measured and only monthly estimates of the abstractions currently exist. Like in many other basins in South Africa, streamflow, groundwater level, rainfall and evaporation data in Letaba is sparse and not very reliable. The Takagi–Sugeno fuzzy inference system using subtractive clustering, an approach which are capable of dealing with vague and inadequate information and data has therefore been used to develop a daily streamflow model for Letaba River. In order to take into account the spatial variability and to maximize the use of the available data, the model is applied in a semi-distributed manner consisting of three river reaches. The shuffled complex evolution (SCE-UA) optimizer has been used to calibrate the model. Six years of data from March 2002 to April 2008 has been used for model calibration and verification. To maximize the Nash-Sutcliffe efficiency, the minimum number of clusters required was found to be 10 for 1000 data points in calibration. An analysis of the location of the cluster centers, the coefficients relating the inputs with the simulated streamflow, and the degrees of membership indicates that no single cluster can be associated to the simulation of a specific hydrologic process or component of the streamflow hydrograph (e.g. high flows or low flows). The fuzzy model does not therefore provide any evidence that it is not a pure black box.The Nash–Sutcliffe efficiency results obtained in calibration and verification showed average values of 0.658 and 0.535 with poor values on the first river reach. Very low percent bias values averaging to −0.4% and −2.7% in calibration and verification are obtained highlighting the model’s potential for applications where mass balance considerations are most important.

Controlling a drone: Comparison between a based model method and a fuzzy inference system

The work describes an automatically on-line self-tunable fuzzy inference system (STFIS) of a new configuration of mini-flying called XSF (X4 Stationnary Flyer) drone. A fuzzy controller based on on-line optimization of a zero order Takagi–Sugeno fuzzy inference system (FIS) by a back propagation-like algorithm is successfully applied. It is used to minimize a cost function that is made up of a quadratic error term and a weight decay term that prevents an excessive growth of parameters. Thus, we carried out control for the continuation of simple trajectories such as the follow-up of straight lines, and complex (half circle, corner, and helicoidal) by using the STFIS technique. This permits to prove the effectiveness of the proposed control law. Simulation results and a comparison with a static feedback linearization controller (SFL) are presented and discussed. We studied the robustness of the two controllers used in the presence of disturbances. We presented two types of disturbances, the case of a breakdown of an engine as well as a gust of wind.

Fuzzy shape-memory snakes for the automatic off-line signature verification problem

This paper introduces an adapted fuzzy snake approach for efficiently solving some of the practical constraints in the off-line signature verification problem. Our method is called fuzzy shape-memory snakes due to its resemblance to shape-memory alloys, which are metals that in high-temperature conditions can remember their original shape. In our approach, the snake also “remembers” its geometry during its iterative adjustment to a test signature. Off-line signature verification aims to establish the degree of genuineness of a given test signature when compared to a reference signature. Due to the shape and size variability in signatures of the same subject, a system with tolerance to imprecision and also with some “memory” of its initial configured shape, would be very useful for this complex verification problem. To our knowledge, snakes and other active contour models have not been previosly applied to the offline signature verification problem. We consider that they could be properly adapted to be useful for this task. Consequently, we have developed a fuzzy snake framework for signature verification which takes into account some practical constraints of this problem when applied to bank checks. Over other signature verification systems, our approach has the advantage of using only one training signature per person. We introduce the fuzziness for the considered signature verification problem in a double direction. First, when iteratively adjusting a shape-memory snake (which is obtained from the training signature) to a considered test signature. Second, when measuring the similarity degree between the snake and the test signature after the adjustment (or verification task) using a Takagi–Sugeno fuzzy inference system, which is trained with three signature features (coincidence, distance and energy) provided by the adjustment. Some advantages of our approach are that: some involved parameters in the internal (shape) snake energy are now eliminated, and a more efficient and natural snake adjustment to the test signature is achieved. This paper also provides a study of the biometric classification errors when comparing our off-line signature verification approach to other non-fuzzy ones using the same signature database.

Discussion on “Takagi–Sugeno fuzzy inference system for modeling stage–discharge relationship” by A.K. Lohani, N.K. Goel, and K.K.S. Bhatia

Discussion on “Takagi–Sugeno fuzzy inference system for modeling stage–discharge relationship” by A.K. Lohani, N.K. Goel, and K.K.S. Bhatia

A fuzzy logic approach for estimation of permeability and rock type from conventional well log data: an example from the Kangan reservoir in the Iran Offshore Gas Field

Permeability and rock type are the most important rock properties which can be used as input parameters to build 3D petrophysical models of hydrocarbon reservoirs. These parameters are derived from core samples which may not be available for all boreholes, whereas, almost all boreholes have well log data. In this study, the importance of the fuzzy logic approach for prediction of rock type from well log responses was shown by using an example of the Vp to Vs ratio for lithology determination from crisp and fuzzy logic approaches. A fuzzy c-means clustering technique was used for rock type classification using porosity and permeability data. Then, based on the fuzzy possibility concept, an algorithm was prepared to estimate clustering derived rock types from well log data. Permeability was modelled and predicted using a Takagi-Sugeno fuzzy inference system. Then a back propagation neural network was applied to verify fuzzy results for permeability modelling. For this purpose, three wells of the Iran offshore gas field were chosen for the construction of intelligent models of the reservoir, and a forth well was used as a test well to evaluate the reliability of the models. The results of this study show that fuzzy logic approach was successful for the prediction of permeability and rock types in the Iran offshore gas field.