Fuzzy Estimation Research Articles

Molten Steel Level Control Based on an Adaptive Fuzzy Estimator in a Continuous Caster

In this paper, we propose a molten steel level controller for a continuous caster that is based on an adaptive fuzzy estimator. The main objective of the proposed controller is to reject the bulging disturbance that occurs in the continuous casting process. If we know the bulging frequencies and phases, and the system time delay, then we can efficiently reject the bulging disturbance by using an adaptive fuzzy estimator. It generates the estimated bulging compensation signal taking the system nonlinearities and delay into account and this signal is added with the PID output to reject the real bulging disturbance efficiently. Computer simulations and experiments were executed with one-to-four-scale H/W simulator.

Design of Cascade Adaptive Fuzzy Sliding-Mode Control for Nonlinear Two-Axis Inverted-Pendulum Servomechanism

Because the dynamic characteristic of a two-axis inverted-pendulum servomechanism is a nonlinear underactuated system, it is difficult to design a suitable control scheme that realizes real-time stabilization and accurate tracking control simultaneously. In general, the techniques developed for fully actuated systems cannot be used directly in underactuated systems. In this study, a cascade adaptive fuzzy sliding-mode control (AFSMC) scheme including inner and outer control loops is investigated for the stabilizing and tracking control of a nonlinear two-axis inverted-pendulum servomechanism. The aim of the inner control loop is to design an AFSMC law with fuzzy estimators so that the stick-angle vector can fit the stick-angle command vector derived from the stick-angle reference model. In the outer loop, the reference signal vector is designed via a fuzzy path-planning scheme so that the cart position vector tracks the cart-position command vector and the stick-angle tracking-error vector converges to zero simultaneously. All adaptive algorithms in the cascade AFSMC system are derived in the sense of Lyapunov stability analysis, so that system stability can be guaranteed in the entire closed-loop system. The effectiveness of the proposed control strategy is verified by numerical simulations and experimental results, and the superiority of the cascade AFSMC system is indicated in comparison with a cascade sliding-mode control system.

A Fuzzy Estimation Theory for Available Operation of Extremely Complicated Large-Scale Network Systems

In this paper, we shall describe about a fuzzy estimation theory based on the concept of set-valued operators, suitable for available operation of extremely complicated large-scale network systems. Fundamental conditions for availability of system behaviors of such network systems are clarified in a form of β-level fixed point theorem for system of fuzzy-set-valued operators. Here, the proof of this theorem is accomplished in a weak topology introduced into the Banach space.

Configurable ultrasonic flaw classification of oil pipelines

These two papers present an innovative method of configurable flaw classification and volume estimation in oil pipelines. In part I, the ultrasonic image acquisition system is introduced and surface and volume of the flaw are estimated with fuzzy image processing. A number of real figures illustrate the system performance. The flops calculation reveals that this fuzzy estimator could be integrated in a real time flaw detection system. In part II, at first, the dynamic detection of interesting points, i.e. as feature points at different levels of images, is proposed using wavelet transform. Furthermore, a guided searching strategy is used for the best matching from the coarse level to a fine level. Then, an error reduction neural network classifies the type of flaw using the wavelet transform as well as area and volume which were produced in Part I. Finally, a statistical error analyser verifies the system outputs by distinct inputs. The numerical results indicate that significant advantages are achieved over the other neural network based flaw characterisation schemes, whereas the accuracy of the predicted flaw profile can be controlled by the resolution of the network.

Fuzzy inference to assess manufacturing process capability with imprecise data

Process capability indices provide numerical measures on whether a process conforms to the defined manufacturing capability prerequisite. These have been successfully applied by companies to compete with and to lead high-profit markets by evaluating the quality and productivity performance. The loss-based process capability index C pm , sometimes called the Taguchi index, was proposed to measure process capability, wherein the output process measurements are precise. In the present study, we develop a realistic approach that allows the consideration of imprecise output data resulting from the measurements of the products quality. A general method combining the vector of fuzzy numbers to produce the membership function of fuzzy estimator of Taguchi index is introduced for further testing process capability. With the sampling distribution for the precise estimation of C pm , two useful fuzzy inference criteria, the critical value and the fuzzy P- value, are proposed to assess the manufacturing process capability based on C pm . The presented methodology takes into the consideration of a certain degree of imprecision on the sample data and leads to the three-decision rule with the four quadrants decision-making plot. The fuzzy inference procedure presented to assess process capability is a natural generalization of the traditional test, when the data are precise the proposed test is reduced to a classical test with a binary decision.

Configurable ultrasonic flaw classification of oil pipelines

To make a decision on the nature of a flaw within a pipeline, it is necessary to detect suspicious regions in ultrasonic inspection images reliably and to, derive geometrical parameters such as shape, position and orientation from each measured signal and finally to collate these parameters intelligently by associating each measured signal with a possible flaw type. These two papers present an innovative method of configurable flaw classification and volume estimation in oil pipelines. This method includes: (1) An adaptive thresholding selection for estimation of the area and volume of the flaws, (2) Dynamic detection of interesting points as feature points at different levels of images by wavelet transform, (3) A guided searching strategy for the best matching from the coarse level to a fine level with configurable classes of flaws, (4) A neural network error reducer using the area and volume of flaws and (5) A statistical error analyser to verify system outputs by distinct inputs. In part I, at first, the ultrasonic scan system acquires ultrasonic flaw signals. Then, the preprocessing module performs tasks such as filtering and smoothing. In addition, adaptive thresholding selection based on compactness measures of fuzzy S-functions is performed and the area and volume of flaws are estimated through a number of real images illustrating the performance of system. Comparing the proposed fuzzy edge detection method with the other well-known methods demonstrate the compatibility of approach in nondestructive ultrasonic inspection imaging. Flops calculation demonstrates that the proposed fuzzy estimator could be integrated into a real time flaw detection system. In part II, feature extractors such as wavelet transform, volume of the flaw, flaw classification and statistical error analysis are proposed, through acquired and preprocessed image.

Fuzzy Estimation of Parameters in Statistical Models

Using a set of confidence intervals, we develop a common approach, to construct a fuzzy set as an estimator for unknown parameters in statistical models. We investigate a method to derive the explicit and unique membership function of such fuzzy estimators. The proposed method has been used to derive the fuzzy estimators of the parameters of a Normal distribution and some functions of parameters of two Normal distributions, as well as the parameters of the Exponential and Poisson distributions. Keywords—Confidence interval. Fuzzy number. Fuzzy estimation.

Speed control for a two-mass drive system using integrated fuzzy estimator and hybrid fuzzy PD/PI controller

This paper presents a novel speed control scheme for a 2- mass motor drive system. The speed controller is based on the estimated state feedback compensation. The integrated fuzzy observer can give a fast and accuracy estimation of the unmeasured states. Two kinds of hybrid fuzzy proportional-derivative and proportional-integral (HF PD/PI) are proposed to cope with this speed control problem. The first is the static HF PD/PI controller and the second is the dynamic one. Simulation results show that the developed integrated fuzzy observer provide the better estimation performance than that of the Kalman filter and the proposed control schemes can effectively track the desired speed in the presence of load disturbance.

On theoretical pricing of options with fuzzy estimators

In this paper we present an application of a new method of constructing fuzzy estimators for the parameters of a given probability distribution function, using statistical data. This application belongs to the financial field and especially to the section of financial engineering. In financial markets there are great fluctuations, thus the element of vagueness and uncertainty is frequent. This application concerns Theoretical Pricing of Options and in particular the Black and Scholes Options Pricing formula. We make use of fuzzy estimators for the volatility of stock returns and we consider the stock price as a symmetric triangular fuzzy number. Furthermore we apply the Black and Scholes formula by using adaptive fuzzy numbers introduced by Thiagarajah et al. [K. Thiagarajah, S.S. Appadoo, A. Thavaneswaran, Option valuation model with adaptive fuzzy numbers, Computers and Mathematics with Applications 53 (2007) 831–841] for the stock price and the volatility and we replace the fuzzy volatility and the fuzzy stock price by possibilistic mean value. We refer to both cases of call and put option prices according to the Black & Scholes model and also analyze the results to Greek parameters. Finally, a numerical example is presented for both methods and a comparison is realized based on the results.

Identification and Control of Chaos Using Fuzzy Clustering and Sliding Mode Control in Unmodeled Affine Dynamical Systems

In this paper, a combination of fuzzy clustering estimation and sliding mode control is used to control a chaotic system, which its mathematical model is unknown. It is assumed that the chaotic system has an affine form. At first, the nonlinear noninput part of the chaotic system is estimated by a fuzzy model, without using any input noise signal. Without loss of generality, it is assumed that chaotic behavior is appeared in the absence of input signal. In this case, the recurrent property of chaotic behavior is used for estimating its model. After constructing the fuzzy model, which estimates the noninput part of the chaotic system, control and on-line identification of the input-related section are applied. In this step, the system model will be estimated in normal form, such that the dynamic equations can be used in sliding mode control. Finally, the proposed technique is applied to a Lur’e-like dynamic system and the Lorenz system as two illustrative examples of chaotic systems. The simulation results verify the effectiveness of this approach in controlling an unknown chaotic system.

Estimation of friction coefficient of asphalt concrete road surfaces using the fuzzy logic approach

Vehicle speeds have increased very dramatically with new developments in today’s automotive industry, and thus the friction behavior of roads has become very important from the safety point of view. The main aim of this paper is to estimate the friction behavior of asphalt concrete road surfaces at any speed using the fuzzy logic approach. Friction is defined in the paper, and the effects of road surface characteristics, mainly macrotexture and microtexture properties, on the friction behavior of asphalt concrete road surfaces are explained. The data measured from the different asphalt concrete road pavements (on Belgium road networks) representing different road surface characteristics are analyzed for estimating the friction behavior of roads. Both the multiple linear regression analysis and the fuzzy logic approach are used to estimate the friction coefficient of asphalt concrete road surfaces. The two approaches are compared, and it is shown that the fuzzy logic approach precisely estimates the friction coefficient of asphalt concrete road surfaces at any speed better than multiple linear regression analysis. It is possible that there is a strong relation between the asphalt concrete road surface characteristics, mainly macrotexture and microtexture, and friction.Key words: asphalt concrete road surfaces, friction, fuzzy estimation.

Statistical and fuzzy optimal decisions: II. Fuzzy decisions

In the paper, methods for optimal possibility-theoretical decisions are considered on examples of fuzzy identification and fuzzy estimation. The quality of the decision is determined in terms of the risk of losses accompanying the decision and is characterized by the values of possibility and/or inevitability of losses.

Stable direct adaptive neural network controller with a fuzzy estimator of the control error for a class of perturbed nonlinear systems

A state feedback direct adaptive control algorithm for single input single output perturbed nonlinear systems in affine form using single hidden layer neural network is introduced. The weights adaptation laws are based on an estimated control error provided by a fuzzy inference system composed of heuristically determined rules. It provides a bounded estimate of the control error, which affects only the step size of the updating laws. It is shown that under mild conditions the state variables and the control input are bounded and the tracking error and its derivatives converge to a bounded compact set. The method does not require any preliminary off line training of the network weights. All states are supposed to be measurable. Two simulation studies are presented for testing the proposed algorithm.

Contextual Algorithm for Decision of Fuzzy Estimation Problems with Network-Like Structure of Criteria on the Basis of Fuzzy Measures Sugeno

In this article the algorithm for the decision of alternatives' estimation problems for following conditions is considered. Values of alternative's characteristics (properties) are fuzzy. They are formalized as fuzzy sets. The estimation criteria structure is network-like and is formalized as the oriented graph with one source and many drains. The alternative's estimation result is calculated in criterion-source. Connections between criteria are formalized by fuzzy measures Sugeno. Upper-level criteria are considered as contexts for lower-level criteria. Fuzzy integrals Sugeno or Choquet are used as aggregation operator. In article also the properties of fuzzy measure and fuzzy integrals (Sugeno and Choquet) are analyzed. Properties of fuzzy measure and integrals are comparing with properties of other mathematical tools. As example the car's estimation problem is presented.

Artificial Intelligence based DTC Controlled Matrix Converter Cage Drive System

Matrix converter induction motor drive system operated with a direct torque control (DTC) shows a sluggish response during startup and under changes of torque command. Fuzzy logic is used in conjunction with direct torque control to minimize these problems. A fuzzy logic controller chooses the switching states based on a set of fuzzy variables. Flux position, error in flux magnitude and error in torque are used as fuzzy state variables. Fuzzy rules are determined by observing the vector diagram of flux and currents. The operation of the direct torque controller becomes difficult at low speeds due to the effect of change in stator resistance on the flux measurements. To improve the system performance at low speeds a fuzzy resistance estimator is proposed to eliminate the error due to the change in stator resistance. At constant flux and torque commands any change in stator resistance of the induction machines causes an error in stator current. This error is utilized by the fuzzy resistance estimator to correct the stator resistance used by the controller to match the machine resistance. Both fuzzy controller and fuzzy resistance estimator are implemented using DSP TMS320C6711 for a 3 hp induction motor drive system. Results demonstrate enhanced performance.

퍼지 PI+D 제어기를 이용한 설계변수와 이득의 자기동조에 관한 연구

본 논문에서는 설계변수와 제어기 이득의 자기 동조를 사용한 PI+D 제어기 설계법을 제안한다. 사용된 퍼지 PI+D 제어기는 일반적인 연속 시간 선형 PI+D 제어기를 근사화하여 사용하였고, 퍼지화는 퍼지싱글톤으로, 비퍼지화는 간략화된 무게중심법을 사용하였다. 퍼지추론 결과는 분리된 퍼지 변수로서 다른 작용 성분으로 계산되고, 그 결과는 설계변수에 해당하는 함수의 형태로 결정되어 제어이득을 결정한다. 따라서 제안된 방법은 빠른 동조 성능을 가지며, 퍼지 입력변수의 증가에도 쉽게 적용될 수 있고, 재생 오차를 줄이는 이점을 가진다. 이 제어기는 설계변수와 제어기 이득의 사용으로 보다 높은 효율성과 개선점을 가지고 있다. This paper proposes a design method of the PI(Proportional-Integral)+D(Derivative) controller using self-tuning of the design variables and controller gains. The used fuzzy PI+D controller is the approximated conventional continuos time linear PI+D controller and the used fuzzification method is the fuzzy single tone and the adapted defuzzification method is the simplified tenter of gravity. Fuzzy estimation result would be calculated in the other function elements from the classified fuzzy variables and the result determined by the design variables decides the controller gains. As a result, the proposed method shows the capability of the high speed tuning and can be applied to the case of input variables with many fuzzy partitions and also can bring out the advantage to reduce the reconstruction(digital sampling reconstruction) error. Most simulation results show that this controller makes much bettor efficiency and improvement by using design variables and controller gains.

Fuzzy linear regression model based on fuzzy scalar product

The new concept and method of imposing imprecise (fuzzy) input and output data upon the conventional linear regression model is proposed in this paper. We introduce the fuzzy scalar (inner) product to formulate the fuzzy linear regression model. In order to invoke the conventional approach of linear regression analysis for real-valued data, we transact the ?-level linear regression models of the fuzzy linear regression model. We construct the membership functions of fuzzy least squares estimators via the form of "Resolution Identity" which is a well-known formula in fuzzy sets theory. In order to obtain the membership value of any given least squares estimate taken from the fuzzy least squares estimator, we transform the original problem into the optimization problems. We also provide two computational procedures to solve the optimization problems.

Computing the minimum-support for mining frequent patterns

Frequent pattern mining is based on the assumption that users can specify the minimum-support for mining their databases. It has been recognized that setting the minimum-support is a difficult task to users. This can hinder the widespread applications of these algorithms. In this paper we propose a computational strategy for identifying frequent itemsets, consisting of polynomial approximation and fuzzy estimation. More specifically, our algorithms (polynomial approximation and fuzzy estimation) automatically generate actual minimum-supports (appropriate to a database to be mined) according to users’ mining requirements. We experimentally examine the algorithms using different datasets, and demonstrate that our fuzzy estimation algorithm fittingly approximates actual minimum-supports from the commonly-used requirements.

Use of Fuzzy Logic in Lignite Inventory Estimation

Seam thickness is one of the most important parameters for reserve estimation of a lignite deposit. This paper addresses a case study on fuzzy estimation of lignite seam thickness from spatial coordinates. From the relationships between input (Cartesian coordinates) and output (thickness) parameters, fuzzy clustering and a fuzzy rule-based inference system were designed. Data-driven fuzzy model parameters were derived from numerical values directly. In addition, estimations of the fuzzy model were compared with kriging estimations. It was concluded that the performance of the fuzzy model was more satisfactory. The results indicated that the fuzzy modeling approach is very reliable for the estimation of lignite reserves.

A new adaptive fuzzy controller with saturation employing influential rule search scheme (IRSS)

The present paper describes the development of a new adaptive fuzzy logic controller (AFLC), which can directly employ an adaptive fuzzy/neuro/neuro-fuzzy function approximator to develop a desired controller, based on an ideal controller input-output data set. The system also proposes the development of the AFLC based on a new adaptive fuzzy system, called influential rule search scheme (IRSS), as a pure function approximation tool. The proposed AFLC employs two additional sub-modules: i) a new static fuzzy resetting action controller (FRAC), which fuzzily changes the resetting action of the controller at each sampling instant, to enhance system performance, and ii) a new fuzzy inverse process estimator, based on IRSS as a function approximator itself. Simulation studies are shown to demonstrate the effectiveness of the proposed controller scheme over conventional PID controllers and other existing fuzzy and neural network based controllers.