Adaptation of TS fuzzy models without complexity expansion: HOSVD-based approach

One direction of measured data-set based modeling applies fuzzy logic identification tools and results in a fuzzy rule-base model. A typical problem of fuzzy identification methods is that the complexity of the resulting fuzzy rule-base, namely the number of rules in the rule-base, explodes with the modeling accuracy. As a result, the topic of fuzzy rule-base complexity reduction techniques emerged in the last decade. A common disadvantage of fuzzy rule-base complexity reduction methods is that the resulting complexity minimized fuzzy-rule bases cannot be simply adapted to new information. If we have new information that cannot be described by the fuzzy rules of the complexity minimized fuzzy rule-base, then we have two choices. The first choice is to add new fuzzy rules to the fuzzy rule-base until the new information can be described. The second choice is to modify the new information until it can be described by the fuzzy rule-base without using additional fuzzy rules. This second case has the prominent role if the number of fuzzy rules in the fuzzy rule-base is limited. This paper proposes a method for the second choice. The proposed method minimizes the necessary modification of the new information. This paper focuses attention on a recent complexity reduction method, termed Higher Order Singular Value Decomposition (HOSVD)-based complexity reduction, and Takagi-Sugeno (TS) inference operator-based fuzzy rule-bases. An example is used to provide the validation of the proposed method. In order to demonstrate the effectiveness of the proposed method, a control system of a differential-steered automatic guided vehicle is modeled in the paper.     

基于离复位控制策略的结构振动控制研究

对于主动或半主动控制系统来说,目前有多种经典控制算法可以应用于结构控制,然而由于结构控制系统内嵌的参数不确定性、非线性行为和时变特征,这些常规算法的适用性和控制效率往往是不理想的。与之相反,模糊控制系统由于不依赖系统的精确数学模型即可有效实施控制,因而许多研究者转向考虑采用模糊控制途径实施结构控制以避免这些问题。模糊控制现阶段的难题在于控制规则的建立仍无系统的方法可循,一般采取半经验的方法。由于缺乏系统完整的分析和设计方法,模糊控制规则的建立通常需要进行反复的尝试或试验,存在一定的困难。针对这一难题,提出并发展了一种离复位控制策略,用以生成结构模糊控制系统的控制规则。以这种策略作为设计模糊控制规则库的依据,研究了一个底层设有主动拉索控制系统的多层结构的地震反应控制问题。在算例中,通过与线性二次型最优控制算法进行控制效果的对比,验证了它的合理性和有效性。     

模糊决策属性约简及其在工位评估中的应用

受粗糙集理论中知识约简的启发,在模糊多属性决策理论中提出属性约简的概念,构建属性约简方法,寻求属性集合中所有最简单的保序属性约简子集以及属性约简核.用属性约简子集代替原有的属性集合,通常可以显著简化模糊多属性决策问题.还将此属性约简方法应用到生产线工位绩效评估中,表明此属性约简算法的实用性.     

Adaptation of SVD-based fuzzy reduction via minimal expansion

Most adopted fuzzy inference techniques do not hold the universal approximation property if the numbers of antecedent sets are limited. This fact and the exponential complexity problem of widely adopted fuzzy logic techniques show the contradictory features of fuzzy rule bases in pursuit of good approximation. As a result, complexity reduction emerged in fuzzy theory. The natural disadvantage of using complexity reduction is that the adaptivity property of the reduced approximation becomes highly restricted. This paper proposes a technique for the singular value decomposition (SVD) based reduction developed by Yam et al. (see IEEE Trans. Fuzzy Syst., vol. 7, p. 120-131, Feb. 1999), which may alleviate the adaptivity restriction     

A Development of Fuzzy Encoding and Decoding Through Fuzzy Clustering

Fuzzy clustering has emerged as a fundamental technique of information granulation. In this study, we introduce and discuss multivariable encoding and decoding mechanisms (referred altogether as a reconstruction problem) expressed in the language of fuzzy sets and fuzzy relations. The underlying performance index associated with the problem helps quantify a reconstruction error that arises when transforming a numeric datum through fuzzy sets (relations) and then reconstructing it into an original numeric format. The clustering platform considered in this study concerns the well-known algorithm of Fuzzy C-Means (FCM). The main design aspects deal with the relationships between the number of clusters versus the reconstruction properties and the resulting reconstruction error. The impact of the fuzzification coefficient on the reconstruction quality is investigated. This finding is of interest, given the fact that predominantly all applications involving FCM use the value of the fuzzification coefficient equal to 2. In light of the completed experiments, we demonstrate that this selection may not be experimentally legitimate. We also carry out a comparative analysis of the reconstruction properties of the Boolean decoding that is induced by the fuzzy partition. Experimental investigations involve selected machine learning data.     

Bayesian system reliability assessment under fuzzy environments

The Bayesian system reliability assessment under fuzzy environments is proposed in this paper. In order to apply the Bayesian approach, the fuzzy parameters are assumed as fuzzy random variables with fuzzy prior distributions. The (conventional) Bayes estimation method will be used to create the fuzzy Bayes point estimator of system reliability by invoking the well-known theorem called ‘Resolution Identity’ in fuzzy sets theory. On the other hand, we also provide the computational procedures to evaluate the membership degree of any given Bayes point estimate of system reliability. In order to achieve this purpose, we transform the original problem into a nonlinear programming problem. This nonlinear programming problem is then divided into four subproblems for the purpose of simplifying computation. Finally, the subproblems can be solved by using any commercial optimizers, e.g. GAMS or LINGO.     

Frequency de-aliased FFT analysis of step-like functions

The authors present a method for decreasing aliasing error in the fast Fourier transform (FFT) of step-like functions. This technique substantially decreases the sole remaining significant error in the extended function FFT (EF-FFT) method and is implemented by multiplying the EF-FFT spectral results with a simple de-aliasing function based on a piecewise linear model for the shape of the original function between data points. The attractive features of the aliasing error reduction method introduced, compared to increasing the sampling rate, are that data reacquisition is not required, computer requirements are small, and the spectra are of high accuracy up to the Nyquist frequency. The applicability is limited to functions that can be modeled with linear transitions between data points, as opposed to step transitions unless the precise timing and shape of the step transitions are known. Since most data sets are comprised of samples from slowly varying analog signals, the de-aliasing procedure provides enhanced spectral accuracy with minor additional mathematical complexity     

An extended CREAM model based on analytic network process under the type-2 fuzzy environment for human reliability analysis in the high-speed train operation

Human error is one of the largest contributing factors to unsafe operation and accidents in high-speed train operation. As a well-known second-generation human reliability analysis (HRA) technique, the cognitive reliability and error analysis method (CREAM) has been introduced to address HRA problems in various fields. Nevertheless, current CREAM models are insufficient to deal with the HRA problem that need to consider the interdependencies between the Common Performance Conditions (CPCs) and determine the weights of these CPCs, simultaneously. Hence, the purpose of this paper is to develop a hybrid HRA model by integrating CREAM, the interval type-2 fuzzy sets, and analytic network process (ANP) to overcome this drawback. Firstly, the interval type-2 fuzzy sets are utilized to express the highly uncertain information of CPCs. Secondly, the ANP is incorporated into the CREAM to depict the interdependencies between the CPCs and determine their weights. Furthermore, human error probability (HEP) can be calculated based on the obtained weights. Finally, an illustrative example of the HRA problem in high-speed train operation is proposed to demonstrate the application and validity of the proposed HRA model. The results indicate that experts prefer to express their preferences by fuzzy sets rather than crisp values, and the interdependences between the CPCs can be better depicted in the proposed model.     

一种基于软计算的转子故障诊断方法

提出了一种基于软计算的转子故障诊断方法。该方法充分利用软计算中的模糊集合理论,人工神经网 络,粗糙集理论和遗传算法等计算方法优势,弥补它们相互的不足,进行故障诊断。首先利用粗糙集理论对样本数据进 行初步规则获取,并计算规则的依赖度和条件覆盖度,然后根据这些规则进行网络设计,其中,网络隐层节点的数目等于 规则的数目,初始网络权重由规则的依赖度和条件覆盖度确定,最后用遗传算法对模糊神经网络参数进行优化。使用该 网络对转子类常见故障进行诊断。实验表明,和一般模糊神经网络相比,这种基于软计算的诊断方法具有训练时间短、 诊断准确率高的特点。     

On the comparison of bilinear, cubic spline, and fuzzy interpolation techniques for robotic position measurements

This paper describes a novel technique for position error compensations of robots based on a fuzzy error interpolation method. A traditional robot calibration implements either model or modelless methods. The compensation of position error in a model-less method is to move the robot's end-effector to a target position in the robot workspace, and to find the target position error online based on the measured neighboring four-point errors around the target position. For this purpose, a stereo camera or other measurement device can be used to measure offline the position errors of the robot's end-effector at predefined grid points. By using the proposed fuzzy error interpolation technique, the accuracy of the position error compensation can be greatly improved, which is confirmed by the simulation results given in this paper. A comparison study among various interpolation methods, such as bilinear, cubic spline, and the fuzzy error interpolation technique is also made via simulation. The simulation results show that more accurate compensation results can be achieved using the fuzzy error interpolation technique compared with its bilinear and cubic spline counterparts.     

A fuzzy linear programming approach for municipal solid-waste management under uncertainty

In this study, a fuzzy linear programming (FLP) method is developed for dealing with uncertainties expressed as fuzzy sets that exist in the constraints’ left-hand and right-hand sides and the objective function. A direct transforming algorithm is advanced for solving the FLP model that improves upon the existing method through provision of a quantitative expression for uncertain relationships among a large number of fuzzy sets. The proposed solution method can greatly reduce computational requirements, which is particularly meaningful for the application of FLP to large-scale practical problems with many fuzzy sets. The developed FLP method is applied to a case of long-term waste-management planning. The results indicate that reasonable solutions have been obtained. They can be used for generating decision alternatives and to help managers identify desired policies for waste management under uncertainty. Compared with the conventional interval-parameter linear programming approach, FLP can provide more information for solutions, containing not only the lower and upper bounds but also the most possible value for decision variables and objective function.     

Prediction Model for BTA Deep-Hole Machining using Fuzzy Clustering Approach: Experimental Study

In this article, a subtractive clustering-based fuzzy identification method and a Sugeno-type fuzzy inference system are used for modeling in metal cutting. This approach is considered with its application on the experimental study of Boring and Trepanning Association (BTA) deep-hole drilling. The model for the surface roughness is identified by using the cutting speed and feed as input data and roughness as the output data. Using subtractive clustering in both input and output spaces performs the model-building process. Minimum error model is obtained through enumerative search of clustering parameters. The fuzzy model obtained is capable of predicting the surface roughness for a given set of inputs (speed and feed). Therefore, the operator can predict the quality of the surface for a given set of working parameters and will then be able to set the machining parameters to achieve a certain surface quality. The fuzzy model is verified experimentally by further experimentation using different sets of inputs. The tool life is also investigated using the same approach. The fuzzy inference system obtained is capable of predicting the tool life for a given set of cutting parameters. Therefore, the operator will be able to predict how many minutes the cutting tool is going to last and will set the time for the next tool change.     

A hybrid interval-parameter fuzzy robust programming method and its application to filter management strategy in fluid power systems

An interval-parameter fuzzy robust programming (IFRP) method is developed for the assessment of filter allocation and replacement strategies in a fluid power system (FPS) under uncertainty. The developed IFRP can effectively handle the uncertainties expressed as fuzzy sets, interval values, and their combinations, which exist in contaminant ingression/generation of the system and contaminant-holding capacity of filter without making assumptions on their probabilistic distributions. The fuzzy decision space can be delimited into a more robust one with the uncertainties being specified through dimensional enlargement of the original fuzzy constraints, leading to enhanced robustness for the optimization process. Results indicate that the developed IFRP can not only help decision-maker to identify optimal filter allocation and replacement strategies to control the contamination level of FPS with a minimized system-cost and system-failure risk under multiple uncertainties, but also mitigate uncertainties through abating interval widths of the replacement periods and service life under different contamination ingression/generation rates.     

Assessment of Structural Damage Condition Based on Fuzzy Pattern Recognition

This paper presents a new method of damage condition assessment that allows accommodating other types of uncertainties due to ambiguity, vagueness, and fuzziness that are statistically non-describable. In this method, healthy observations are used to construct a fuzzy set representing sound performance characteristics. Additionally, the bounds on the similarities among the structural damage states are prescribed by using the state similarity matrix. Thus, an optimal group fuzzy sets representing damage states such as little, moderate, and severe damage can be inferred as an inverse problem from healthy observations only. The optimal group of damage fuzzy sets is used to classify a set of observations at any unknown state of damage using the principles of fuzzy pattern recognition based on an approximate principle. This method can be embedded into the system of Structural Health Monitoring (SHM) to give advice about structural maintenance and life prediction. Finally, a case study, which comes from Reference [9] for damage pattern recognition is presented and discussed. The compared result illustrates our method is more effective and general, so it is very practical in engineering.     

Maximum likelihood principal components regression on wavelet-compressed data

Maximum likelihood principal component regression (MLPCR) is an errors-in-variables method used to accommodate measurement error information when building multivariate calibration models. A hindrance of MLPCR has been the substantial demand on computational resources sometimes made by the algorithm, especially for certain types of error structures. Operations on these large matrices are memory intensive and time consuming, especially when techniques such as cross-validation are used. This work describes the use of wavelet transforms (WT) as a data compression method for MLPCR. It is shown that the error covariance matrix in the wavelet and spectral domains are related through a two-dimensional WT. This allows the user to account for any effects of the wavelet transform on spectral and error structures. The wavelet transform can be applied to MLPCR when using either the full error covariance matrix or the smaller pooled error covariance matrix. Simulated and experimental near-infrared data sets are used to demonstrate the benefits of using wavelets with the MLPCR algorithm. In all cases, significant compression can be obtained while maintaining favorable predictive ability. Considerable time savings were also attained, with improvements ranging from a factor of 2 to a factor of 720. Using the WT-compressed data in MLPCR gave a reduction in prediction errors compared to using the raw data in MLPCR. An analogous reduction in prediction errors was not always seen when using PCR.     

模糊粗糙集在轴承故障模式识别中的应用

提出一种基于模糊粗糙集理论的模式识别方法,将动态聚类法和方差分析法引入连续属性模糊化,获取模糊隶属函数,避开了粗糙集理论属性离散化过程带来的信息丢失;利用F检验判断分类的合理性,克服了人为确定分类数目的缺点;应用模糊化得到的模糊决策表进行条件属性约简,通过属性值约简,提取了清晰、简明的故障模式规则。轴承故障模式识别结果表明,该方法对比一般粗糙集理论,有效地提高了模式识别精度,在实际模式识别中具有很好的应用价值。     

Multiple SVM-RFE for gene selection in cancer classification with expression data

This paper proposes a new feature selection method that uses a backward elimination procedure similar to that implemented in support vector machine recursive feature elimination (SVM-RFE). Unlike the SVM-RFE method, at each step, the proposed approach computes the feature ranking score from a statistical analysis of weight vectors of multiple linear SVMs trained on subsamples of the original training data. We tested the proposed method on four gene expression datasets for cancer classification. The results show that the proposed feature selection method selects better gene subsets than the original SVM-RFE and improves the classification accuracy. A Gene Ontology-based similarity assessment indicates that the selected subsets are functionally diverse, further validating our gene selection method. This investigation also suggests that, for gene expression-based cancer classification, average test error from multiple partitions of training and test sets can be recommended as a reference of performance quality.     

随机模糊信息系统的知识约简

利用模糊逻辑中的R-型蕴涵算子定义随机模糊信息系统对象集上的模糊等价关系,进而实现对随机模糊信息系统知识的近似表示。讨论随机模糊下近似、上近似集的模糊概率与模糊信任测度、模糊似然测度之间的关系。给出基于模糊信任测度和模糊似然测度的随机模糊信息系统知识约简的方法。     

车用雨刮簧片三辊成形方式探究

为了探究车用无骨雨刮可用于实际批量加工生产的加工方式,以专用的簧片滚弯加工机器为研究对象,对其进行模型简化处理,借鉴板材的滚弯加工以及回弹理论,并通过结构有限元非线性静力仿真成形。所探究出的等比拟合方式更加接近于实际成形的簧片,在误差允许的范围内,这种三辊的滚弯加工方式是能够用于雨刮簧片的大批量加工生产的。     

基于模糊决策的供应商选择方法

在分析建立供应商评价指标体系所应遵循的三大原则的基础上，提出了一套供应商评价指标体系。由于供应商选择问题中包含大量的不确定和模糊因素，为此将模糊集合论的思想和方法引入供应商评价中，建立了供应商模糊评价模型，最后给出实例予以验证。