New model for system behavior prediction based on belief rule based systems

To predict the behavior of a complex engineering system, a model can be built and trained using historical data. However, it may be difficult to obtain a complete and accurate set of data to train the model. Consequently, the model may be incapable of predicting the future behavior of the system with reasonable accuracy. On the other hand, expert knowledge of a qualitative nature and partial historical information about system behavior may be available which can be converted into a belief rule base (BRB). Based on the unique features of BRB, this paper is devoted to overcoming the above mentioned difficulty by developing a forecasting model composed of two BRBs and two recursive learning algorithms, which operate together in an integrated manner. An initially constructed forecasting model has some unknown parameters which may be manually tuned and then trained or updated using the learning algorithms once data become available. Based on expert intervention which can reflect system operation patterns, two algorithms are developed on the basis of the evidential reasoning (ER) algorithm and the recursive expectation maximization (EM) algorithm with the former used for handling judgmental outputs and the latter for processing numerical outputs, respectively. Using the proposed algorithms, the training of the forecasting model can be started as soon as there are some data available, without having to wait until a complete set of data are all collected, which is critical when the forecasting model needs to be updated in real-time within a given time limit. A numerical simulation study shows that under expert intervention, the forecasting model is flexible, can be automatically tuned to predict the behavior of a complicated system, and may be applied widely in engineering. It is demonstrated that if certain conditions are met, the proposed recursive algorithms can converge to a local optimum. A case study is also conducted to show the wide potential applications of the forecasting model.     

基于变速粒子群优化的置信规则库参数训练方法

针对置信规则库(BRB)中参数优化模型的求解问题,引入群智能算法中的粒子群优化(PSO)算法,提出一种新的参数训练方法。将参数优化模型求解问题转换为带约束条件的非线性优化问题,在迭代寻优时限制粒子在搜索空间中,对失去速度的粒子重新赋予速度,维持种群中粒子多样性,从而实现参数训练。在输油管道检漏问题仿真实验中,训练后系统的平均绝对误差(MAE)为0.166478。实验结果表明,所提方法有理想的收敛精度,可用于置信规则库参数训练。     

Credal classification rule for uncertain data based on belief functions

In this paper we present a new credal classification rule (CCR) based on belief functions to deal with the uncertain data. CCR allows the objects to belong (with different masses of belief) not only to the specific classes, but also to the sets of classes called meta-classes which correspond to the disjunction of several specific classes. Each specific class is characterized by a class center (i.e. prototype), and consists of all the objects that are sufficiently close to the center. The belief of the assignment of a given object to classify with a specific class is determined from the Mahalanobis distance between the object and the center of the corresponding class. The meta-classes are used to capture the imprecision in the classification of the objects when they are difficult to correctly classify because of the poor quality of available attributes. The selection of meta-classes depends on the application and the context, and a measure of the degree of indistinguishability between classes is introduced. In this new CCR approach, the objects assigned to a meta-class should be close to the center of this meta-class having similar distances to all the involved specific classes? centers, and the objects too far from the others will be considered as outliers (noise). CCR provides robust credal classification results with a relatively low computational burden. Several experiments using both artificial and real data sets are presented at the end of this paper to evaluate and compare the performances of this CCR method with respect to other classification methods.     

基于规则聚类和参数学习的扩展置信规则库推理模型

扩展置信规则库(EBRB)中的规则数量和参数取值共同影响EBRB推理模型的决策准确性和计算效率. 基于此,提出一种基于规则聚类和参数学习的改进EBRB推理模型,称为RCPL-EBRB模型.所提出模型的基本原理如下:首先,依据密度聚类分析对EBRB进行规则聚类来识别EBRB中无效的扩展置信规则和优化传统EBRB的建模过程;然后,以聚类所得到的规则簇(即Sub-EBRB)进行参数学习和规则推理,保证激活规则集合的一致性,从而提高RCPL-EBRB模型的决策准确性和计算效率;最后,引入非线性函数拟合和基准分类问题数据集开展模型的有效性检验和参数灵敏度分析.实验结果表明,所提出RCPL-EBRB模型比现有EBRB推理模型和传统机器学习方法具有更高的决策准确性.     

基于置信规则库的海基系统性能退化机理分析与预测

海基系统性能退化机理分析和预测对于提高海基系统的生存能力具有重要意义,但需要考虑不确定条件下的多种类型信息,传统方法在处理海基系统的不确定性时效果欠佳,而置信规则库(BRB)作为证据推理方法中的知识库又无法同时处理参数精度优化和组合爆炸问题.对此,采用BRB参数与结构联合优化方法,建立双层优化的海基系统置信规则库最优决策结构,以AIC(Akaike information criterion)为外层模型优化目标,MSE(Mean square error)为内层模型优化目标,实现同时优化的目的.对比模型输出和实际输出,并采用支持向量机(SVM)进行实验,结果表明,采用具有最优决策结构的海基系统置信规则库建模不仅可以降低模型中规则的数量,也可提高建模精度,验证了所提出方法的有效性.     

置信规则库规则约简的粗糙集方法

针对置信规则中规则数的"组合爆炸"问题,目前的解决方法主要是基于特征提取的规则约简方法,有效性依赖于专家知识.鉴于此,提出基于粗糙集理论的无需依赖规则库以外知识的客观方法,按照等价类划分思想逐条分析置信规则,进而消除冗余的候选值.最后,以装甲装备能力评估作为实例进行分析,分别从规则约简数、决策准确性方面与具有代表性的主观方法进行对比,结果表明,所提出方法是有效可行的,且优于现有规则约简主观方法.     

A belief classification rule for imprecise data

The classification of imprecise data is a difficult task in general because the different classes can partially overlap. Moreover, the available attributes used for the classification are often insufficient to make a precise discrimination of the objects in the overlapping zones. A credal partition (classification) based on belief functions has already been proposed in the literature for data clustering. It allows the objects to belong (with different masses of belief) not only to the specific classes, but also to the sets of classes called meta-classes which correspond to the disjunction of several specific classes. In this paper, we propose a new belief classification rule (BCR) for the credal classification of uncertain and imprecise data. This new BCR approach reduces the misclassification errors of the objects difficult to classify by the conventional methods thanks to the introduction of the meta-classes. The objects too far from the others are considered as outliers. The basic belief assignment (bba) of an object is computed from the Mahalanobis distance between the object and the center of each specific class. The credal classification of the object is finally obtained by the combination of these bba’s associated with the different classes. This approach offers a relatively low computational burden. Several experiments using both artificial and real data sets are presented at the end of this paper to evaluate and compare the performances of this BCR method with respect to other classification methods.     

Neural network based on adaptive resonance theory with continuous training for multi-configuration transient stability analysis of electric power systems

This work presents a methodology to analyze electric power systems transient stability for first swing using a neural network based on adaptive resonance theory (ART) architecture, called Euclidean ARTMAP neural network. The ART architectures present plasticity and stability characteristics, which are very important for the training and to execute the analysis in a fast way. The Euclidean ARTMAP version provides more accurate and faster solutions, when compared to the fuzzy ARTMAP configuration. Three steps are necessary for the network working, training, analysis and continuous training. The training step requires much effort (processing) while the analysis is effectuated almost without computational effort. The proposed network allows approaching several topologies of the electric system at the same time; therefore it is an alternative for real time transient stability of electric power systems. To illustrate the proposed neural network an application is presented for a multi-machine electric power systems composed of 10 synchronous machines, 45 buses and 73 transmission lines.     

Condition-based maintenance of dynamic systems using online failure prognosis and belief rule base

Condition-based maintenance has attracted an increasing attention both academically and practically. If the required physical models to describe the dynamic systems are unknown and the monitored information only reflects part of the state of the dynamic systems, expert knowledge is a source of valuable information to be used. However, expert knowledge is usually in a qualitative form, and therefore, needs to be transformed and combined with the measured characteristic information to provide effective prognosis. As such, this paper focuses on developing a novel approach to deal with the problem. In the proposed approach, a belief rule base (BRB) for the failure prognostic model is constructed using the expert knowledge and the analysis of the failure mechanism. An online failure prognostic algorithm is then proposed on the basis of the currently available characteristic variable information. The failure prognostic model is finally used in a condition based decision model to support the replacement decision of the dynamic systems. A case example is examined to demonstrate the implementation and potential applications of the proposed failure prognostic algorithm and the condition-based replacement model.     

基于置信规则库专家系统的司控器开关量健康状态评估

微动开关是轨道车辆司控器常用的开关设备,对其健康状态评估是保证轨道车辆运行安全的前提.针对司控器微动开关数据样本少、诊断信号具有波动性和非线性、健康状态评估困难等问题,提出一种基于置信规则库专家系统(BRB)的司控器开关量健康状态评估方法.首先,分析微动开关失效机理与故障特征的关系;然后,采用置信规则库将定性知识与定量信息有效结合,采用证据推理(ER)算法进行知识推理,并对所建立的模型初始参数进行优化,得到最优的参数集合,从而提高轨道车辆微动开关健康状态评估的准确性.通过对模型训练及测试,所得结果表明,所提出的方法能准确地评估微动开关状态,便于早期发现故障、跟踪故障发展趋势和及时更换失效部件.     

Online updating belief rule based system for pipeline leak detection under expert intervention

A belief rule base inference methodology using the evidential reasoning approach (RIMER) has been developed recently, where a new belief rule base (BRB) is proposed to extend traditional IF-THEN rules and can capture more complicated causal relationships using different types of information with uncertainties, but these models are trained off-line and it is very expensive to train and re-train them. As such, recursive algorithms have been developed to update the BRB systems online and their calculation speed is very high, which is very important, particularly for the systems that have a high level of real-time requirement. The optimization models and recursive algorithms have been used for pipeline leak detection. However, because the proposed algorithms are both locally optimal and there may exist some noise in the real engineering systems, the trained or updated BRB may violate some certain running patterns that the pipeline leak should follow. These patterns can be determined by human experts according to some basic physical principles and the historical information. Therefore, this paper describes under expert intervention, how the recursive algorithm update the BRB system so that the updated BRB cannot only be used for pipeline leak detection but also satisfy the given patterns. Pipeline operations under different conditions are modeled by a BRB using expert knowledge, which is then updated and fine tuned using the proposed recursive algorithm and pipeline operating data, and validated by testing data. All training and testing data are collected from a real pipeline. The study demonstrates that under expert intervention, the BRB expert system is flexible, can be automatically tuned to represent complicated expert systems, and may be applied widely in engineering. It is also demonstrated that compared with other methods such as fuzzy neural networks (FNNs), the RIMER has a special characteristic of allowing direct intervention of human experts in deciding the internal structure and the parameters of a BRB expert system.     

On the influence of an adaptive inference system in fuzzy rule based classification systems for imbalanced data-sets

Classification with imbalanced data-sets supposes a new challenge for researches in the framework of data mining. This problem appears when the number of examples that represents one of the classes of the data-set (usually the concept of interest) is much lower than that of the other classes. In this manner, the learning model must be adapted to this situation, which is very common in real applications.In this paper, we will work with fuzzy rule based classification systems using a preprocessing step in order to deal with the class imbalance. Our aim is to analyze the behaviour of fuzzy rule based classification systems in the framework of imbalanced data-sets by means of the application of an adaptive inference system with parametric conjunction operators.Our results shows empirically that the use of the this parametric conjunction operators implies a higher performance for all data-sets with different imbalanced ratios.     

异常信息的智能分类算法研究

信息处理过程中对异常信息的智能化处理是一个前沿的且富有挑战性的研究方向;针对所获取的信息由于噪声干扰等因素存在缺失这一异常现象,提出了一种不完整(缺失)数据的智能分类算法;对于某一个不完整样本,该方法首先根据找到的近邻类别信息得到单个或多个版本的估计样本,这样在保证插补的准确性的同时能够有效地表征由于缺失引起的不精确性,然后用分类器分类带有估计值的样本;最后,在证据推理框架下提出一种新的信任分类方法,将难以划分类别的样本分配到对应的复合类来描述由于缺失值引起的样本类别的不确定性,同时降低错误分类的风险;用UCI数据库的真实数据集来验证算法的有效性,实验结果表明该算法能够有效地处理不完整数据分类问题.     

A belief maintenance scheme for hierarchical knowledge-based image analysis systems

A variety of belief maintenance schemes for image analysis have been suggested and used to date. In the recent past, several researchers have suggested the use of the Dempster-Shafer theory of evidence for representation of belief. This approach appears to be particularly suited for knowledge-based image analysis systems because of its intuitively convincing ways of representing beliefs, support, plausibility, ignorance, dubiety, and a host of other measures that can be used for the purpose of decision making. It also provides a very attractive technique to combine these measures obtained from disparate knowledge sources. In this article, we show how the Dempster-Shafer theoretic concepts of refinement and coarsening can be used to aggregate and propagate evidence in a multi-resolution image analysis system based on a hierarchical knowledge base.     

基于聚类集成和激活因子的扩展置信规则库推理模型

规则约减和规则激活是扩展置信规则库(EBRB)推理模型优化研究中的两个重要方向.然而,现有研究成果大多存在方法参数确定主观性强和计算复杂度高等不足.为此,通过引入聚类集成和激活因子提出改进的EBRB推理模型,称为CEAF-EBRB模型.该模型先基于聚类集成对历史数据进行多次的数据聚类分析,再以簇为单位将所有历史数据生成扩展置信规则;同时,通过激活因子修正个体匹配度计算公式以及离线的方式计算激活因子取值,以确保高效地激活一致性的规则.最后,在非线性函数拟合、模式识别、医疗诊断等常见问题中验证了所提CEAF-EBRB模型的可行性和有效性,从而为决策者提供更准确的决策支持.     

基于置信规则库的飞控系统故障诊断

针对传统飞控系统故障诊断中存在的因引入专家知识引起的主观偏差问题和使用数据驱动方法因数据量不足导致的过拟合问题,提出了基于置信规则库推理的飞控系统故障诊断。根据已有故障知识构建飞控系统故障诊断置信规则库,利用测试过程中获得的故障数据,以数值样本优化学习模型对置信规则库参数进行训练。实例表明,经少量样本训练后的置信规则库可以很好地解决初始置信规则库参数存在主观偏差的问题,经实验证明该方法能够实现高效可靠的飞控系统故障诊断。     

基于置信规则库的工业控制系统安全状态评估

当前工业控制系统存在严重安全问题,针对现有工业控制系统安全状态评估模型存在的不足,提出一种基于置信规则库(BRB)专家系统的工业控制系统安全状态评估方法.该方法首先利用置信规则库专家系统将工业控制系统中定性知识与定量监测数据相结合.然后采用证据推理(ER)算法进行知识推理,并对所建立的BRB模型初始参数进行优化.最后以...     

基于改进规则激活率的扩展置信规则库推理方法

数据驱动的扩展置信规则库系统,是在传统置信规则库的基础上利用关系数据来生成规则,使用该方法构建规则库简单有效。然而,该方法激活的规则存在不一致与不完整,并且该方法无法处理零激活的输入。鉴于此,本文提出基于改进规则激活率的扩展置信规则库方法,通过高斯核改进个体匹配度计算方法,权衡激活规则的一致性与完整性,并利用k近邻思想解决规则零激活问题。最后,本文选取非线性函数拟合实验和输油管道检漏实验来检验所提方法的效率和准确度。实验结果表明该方法既保证了扩展置信规则库系统的推理效率,也提高了推理结果的精度。     

Subsystem inference representation for fuzzy systems based uponproduct-sum-gravity rule

A new representation which expresses a product-sum-gravity (PSG) inference in terms of additive and multiplicative subsystem inferences of single variable is proposed. The representation yields additional insight into the structure of a fuzzy system and produces an approximate functional characterization of its inferred output. The form of the approximating function is dictated by the choice or polynomial, sinusoidal, or other designs of subsystem inferences. With polynomial inferences, the inferred output approximates a polynomial function the order of which is dependent on the numbers of input membership functions. Explicit expressions for the function and corresponding error of approximation are readily obtained for analysis. Subsystem inferences emulating sinusoidal functions are also discussed. With proper scaling, they produce a set of orthonormal subsystem inferences. The orthonormal set points to a possible “modal” analysis of fuzzy inference and yields solution to an additive decomposable approximation problem. This work also shows that, as the numbers of input membership functions become large, a fuzzy system with PSG inference would converge toward polynomial or Fourier series expansions. The result suggests a new framework to consider fuzzy systems as universal approximators