Optimization Models for Training Belief-Rule-Based Systems

A belief rule-base inference methodology using the evidential reasoning approach (RIMER) has been developed recently, where a new belief rule representation scheme is proposed to extend traditional IF-THEN rules. The belief rule expression matrix in RIMER provides a compact framework for representing expert knowledge. However, it is difficult to accurately determine the parameters of a belief rule base (BRB) entirely subjectively, particularly, for a large-scale BRB with hundreds or even thousands of rules. In addition, a change in rule weight or attribute weight may lead to changes in the performance of a BRB. As such, there is a need to develop a supporting mechanism that can be used to train, in a locally optimal way, a BRB that is initially built using expert knowledge. In this paper, several new optimization models for locally training a BRB are developed. The new models are either single- or multiple-objective nonlinear optimization problems. The main feature of these new models is that only partial input and output information is required, which can be either incomplete or vague, either numerical or judgmental, or mixed. The models can be used to fine tune a BRB whose internal structure is initially decided by experts' domain-specific knowledge or common sense judgments. As such, a wide range of knowledge representation schemes can be handled, thereby facilitating the construction of various types of BRB systems. Conclusions drawn from such a trained BRB with partially built-in expert knowledge can simulate real situations in a meaningful, consistent, and locally optimal way. A numerical study for a hierarchical rule base is examined to demonstrate how the new models can be implemented as well as their potential applications.     

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.     

基于规则推理网络的分类模型

为了缓解神经网络的“黑盒子”机制引起的算法可解释性低的问题,基于使用证据推理算法的置信规则库推理方法(以下简称RIMER)提出了一个规则推理网络模型.该模型通过RIMER中的置信规则和推理机制提高网络的可解释性.首先证明了基于证据推理的推理函数是可偏导的,保证了算法的可行性;然后,给出了规则推理网络的网络框架和学习算法,利用RIMER中的推理过程作为规则推理网络的前馈过程,以保证网络的可解释性;使用梯度下降法调整规则库中的参数以建立更合理的置信规则库,为了降低学习复杂度,提出了“伪梯度”的概念;最后,通过分类对比实验,分析了所提算法在精确度和可解释性上的优势.实验结果表明,当训练数据集规模较小时,规则推理网络的表现良好,当训练数据规模扩大时,规则推理网络也能达到令人满意的结果.     

Belief rule-base inference methodology using the evidential reasoning Approach-RIMER

In this paper, a generic rule-base inference methodology using the evidential reasoning (RIMER) approach is proposed. Existing knowledge-base structures are first examined, and knowledge representation schemes under uncertainty are then briefly analyzed. Based on this analysis, a new knowledge representation scheme in a rule base is proposed using a belief structure. In this scheme, a rule base is designed with belief degrees embedded in all possible consequents of a rule. Such a rule base is capable of capturing vagueness, incompleteness, and nonlinear causal relationships, while traditional if-then rules can be represented as a special case. Other knowledge representation parameters such as the weights of both attributes and rules are also investigated in the scheme. In an established rule base, an input to an antecedent attribute is transformed into a belief distribution. Subsequently, inference in such a rule base is implemented using the evidential reasoning (ER) approach. The scheme is further extended to inference in hierarchical rule bases. A numerical study is provided to illustrate the potential applications of the proposed methodology.     

数据驱动的置信规则库构建与推理方法

针对Liu等(LIU J, MARTINEZ L, CALZADA A, et al. A novel belief rule base representation, generation and its inference methodology. Knowledge-Based Systems, 2013, 53: 129-141)提出的扩展置信规则库(BRB)推理精度不够高的问题,提出了一种改进的规则库构建与推理方法。在Liu等提出的规则库构建方法的基础上,给出了一种新的生成规则前件与计算规则权重的方法;同时为了避免大量不必要的规则被激活,引入80/20法则改进规则激活策略,并最终形成完整的置信规则库构建与推理方法。通过输油管道检漏的实例对所提方法的准确性和效率进行对比分析。实验结果表明,所提方法能够在保证低耗时的同时,将系统平均绝对误差(MAE)降低到0.17342,具有较高的效率和精度。     

Applying a belief rule-base inference methodology to a guideline-based clinical decision support system

Abstract: A critical issue in the clinical decision support system (CDSS) research area is how to represent and reason with both uncertain medical domain knowledge and clinical symptoms to arrive at accurate conclusions. Although a number of methods and tools have been developed in the past two decades for modelling clinical guidelines, few of those modelling methods have capabilities of handling the uncertainties that exist in almost every stage of a clinical decision-making process. This paper describes how to apply a recently developed generic rule-base inference methodology using the evidential reasoning approach (RIMER) to model clinical guidelines and the clinical inference process in a CDSS. In RIMER, a rule base is designed with belief degrees embedded in all possible consequents of a rule. Such a rule base is capable of capturing vagueness, incompleteness and non-linear causal relationships, while traditional IF–THEN rules can be represented as a special case. Inference in such a rule base is implemented using the evidential reasoning approach which has the capability of handling different types and degrees of uncertainty in both medical domain knowledge and clinical symptoms. A case study demonstrates that employing RIMER in developing a guideline-based CDSS is a valid novel approach.     

A new belief rule base knowledge representation scheme and inference methodology using the evidential reasoning rule for evidence combination

In this paper, we extend the original belief rule-base inference methodology using the evidential reasoning approach by i) introducing generalised belief rules as knowledge representation scheme, and ii) using the evidential reasoning rule for evidence combination in the rule-base inference methodology instead of the evidential reasoning approach. The result is a new rule-base inference methodology which is able to handle a combination of various types of uncertainty.Generalised belief rules are an extension of traditional rules where each consequent of a generalised belief rule is a belief distribution defined on the power set of propositions, or possible outcomes, that are assumed to be collectively exhaustive and mutually exclusive. This novel extension allows any combination of certain, uncertain, interval, partial or incomplete judgements to be represented as rule-based knowledge. It is shown that traditional IF-THEN rules, probabilistic IF-THEN rules, and interval rules are all special cases of the new generalised belief rules.The rule-base inference methodology has been updated to enable inference within generalised belief rule bases. The evidential reasoning rule for evidence combination is used for the aggregation of belief distributions of rule consequents.     

Inference analysis and adaptive training for belief rule based systems

Belief rule base (BRB) systems are an extension of traditional IF-THEN rule based systems and capable of capturing complicated nonlinear causal relationships between antecedent attributes and consequents. In a BRB system, various types of information with uncertainties can be represented using belief structures, and a belief rule is designed with belief degrees embedded in its possible consequents. For a set of inputs to antecedent attributes, inference in BRB is implemented using the evidential reasoning (ER) approach. In this paper, the inference mechanism of the ER algorithm is analyzed first and its patterns of monotonic inference and nonlinear approximation are revealed. For a practical BRB system, it is difficult to determine its parameters accurately by using only experts’ subjective knowledge. Moreover, the appropriate adjustment of the parameters of a BRB system using available historical data can lead to significant improvement on its prediction performance. In this paper, a training data selection scheme and an adaptive training method are developed for updating BRB parameters. Finally, numerical studies on a multi-modal function and a practical pipeline leak detection problem are conducted to illustrate the functionality of BRB systems and validate the performance of the adaptive training technique.     

专家干预下置信规则库参数训练的差分进化算法

传统关于置信规则库参数训练模型的求解主要采用FMINCON函数及群智能算法,但在算法设计中并未涉及所有的置信规则库参数,且缺少必要的专家干预.为解决这些问题,首先在现有参数模型的基础上进一步扩宽参与参数训练的置信规则库参数,然后设计出符合思维逻辑的专家干预的约束条件,最后结合差分进化算法提出具有更高收敛精度的置信规则库参数训练方法.在实验分析中,首先在多极值函数的实例中分析该方法的有效性,再在输油管道检漏的实例中检验专家干预的合理性及对比现有的其他参数训练方法.实验结果表明,该方法是有效可行的.     

A graph-based approach for rule integrity and maintainability in expert system maintenance

Just as conventional software systems have maintenance costs far exceeding development costs, so too do rule-based expert systems. They are frequently developed by an incremental and iterative method, where knowledge and decision rules are extracted and added to the system in a piecemeal manner throughout system evolution. Thus, ensuring the correctness and consistency of the rule base (RB) becomes an important, though challenging task. However, most research work in expert systems has focused on building and validating rule bases, leaving the maintenance issue unexplored. We propose a graph-based approach, called the object classification model (OCM), as a methodology for RB maintenance. An experiment was conducted to compare the OCM with traditional RB maintenance methods. The results show that the OCM helps knowledge engineers retain rule-base integrity and, thus, increase rule-base maintainability.     

A methodology to generate a belief rule base for customer perception risk analysis in new product development

New product development (NPD) is crucial for a company’s success in a competitive market. Meanwhile, NPD is a process associated with great complexity and high risk. To ensure its smooth operation, risks involved in an NPD process need to be analyzed in a proper way. In this paper, a novel method is proposed to generate a belief rule base (BRB), which is the basis of the Belief Rule-Base Inference Methodology using the Evidential Reasoning (RIMER). Due to its capability in dealing with complex reasoning problems under uncertainty, RIMER is then applied to assess customer perception risk (CPR) in an NPD process. To test and validate the method proposed in this paper, a case study of an “Interactive Doll” is conducted at the end of the paper.     

基于平行多种群与冗余基因策略的置信规则库优化方法

置信规则库(Belief rule base, BRB)的参数学习和结构学习共同影响着置信规则库的建模精度和复杂度.为了提高BRB结构学习和参数学习的优化效率,本文提出了一种基于平行多种群(Parallel multi-population)策略和冗余基因(Redundant genes)策略的置信规则库优化方法.该方法采用平行多种群策略以实现对具有不同数量规则BRB同时进行优化的目的,采用冗余基因策略以确保具有不同数量规则的BRB能够顺利进行(交叉,变异等)相关优化操作.最终自动生成具有不同数量规则BRB的最优解,并得出帕累托前沿(Pareto frontier),决策者可以根据自身偏好和实际问题需求,综合权衡并在帕累托前沿中筛选最优解.最后以某输油管道泄漏检测问题作为示例验证本文提出方法的有效性,示例分析结果表明本文提出的方法可以一次生成具有多条规则BRB的最优解,并且可以准确绘制出帕累托前沿,为综合决策提供较强的决策支持.     

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.     

Inference and learning methodology of belief-rule-based expert system for pipeline leak detection

Belief rule based expert systems are an extension of traditional rule based systems and are capable of representing more complicated causal relationships using different types of information with uncertainties. This paper describes how the belief rule based expert systems can be trained and used for pipeline leak detection. Pipeline operations under different conditions are modelled by a belief rule base using expert knowledge, which is then trained and fine tuned using pipeline operating data, and validated by testing data. All training and testing data are collected and scaled from a real pipeline. The study demonstrates that the belief rule based system is flexible, can be adapted to represent complicated expert systems, and is a valid novel approach for pipeline leak detection.     

Belief rule-based methodology for mapping consumer preferences and setting product targets

Rapid and accurate identification of consumer demands and systematic assessment of product quality are essential to success for new product development, in particular for fast moving consumer goods such as food and drink products. This paper reports an investigation into a belief rule-based (BRB) methodology for quality assessment, target setting and consumer preference prediction in retro-fit design of food and drink products. The BRB methodology can be used to represent the relationships between consumer preferences and product attributes, which are complicated and nonlinear. A BRB system can initially be established using expert knowledge and then optimally trained and validated using data generated from consumer or expert panel assessments or from tests and experiments. The established BRBs can then be used to predict the consumer acceptance of new products or set product target values in retro-fit design. The proposed BRB methodology is applied to the design of a lemonade drink product using real data provided by a sensory product manufacturer in the UK. The results show that the BRB methodology can be used to predict consumer preferences with high accuracy and to set optimal target values for product quality improvement.     

基于进化信度规则库的故障预测

在假设信度规则库(BRB)的输入为均匀分布的情况下,已有文献提出了一种序贯自适应的学习算法以实现BRB的参数在线辨识和结构的自适应调整.然而在实际问题中,信度规则库的输入一般是未知的、难以得到的,这在一定程度上限制了序贯自适应学习算法的实用性,因此就需要研究一种改进的BRB学习算法以实现参数和结构的同时辨识.本文在序贯自适应方法的基础上,通过定义BRB的完整性准则,提出了改进的BRB进化策略.与现有方法相比,该方法可以实现信度规则的自动增减,且无需输入样本的概率密度函数.此外,该方法继承了BRB的特点,仅需要部分的输入输出信息.基于改进的进化策略,提出了一种新的故障预测算法,最后通过陀螺仪故障预测实验验证了本文方法的有效性.     

面向最佳决策结构的置信规则库结构学习方法

针对置信规则库中初始结构不合理的问题,现有的解决方法仍存在不具备可重复性或受数据完备性和等级效用值相关联的制约等方面的不足。鉴于此,对置信规则库的参数学习进行了理论分析和实验验证,总结出不合理结构下置信规则库中易出现结构欠完备问题或结构过完备问题;将DBSCAN算法和误差分析嵌入到现有参数学习方法中用于解决上述问题,进而提出了面向最佳决策结构的结构学习方法;通过实验分别在过完备结构和欠完备结构的置信规则库下验证了新方法,并对比了结构改变时误差的变化。实验结果表明所提方法是有效可行的。     

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...     

基于置信规则库专家系统的发动机故障诊断

针对发动机故障原因和征兆之间存在的复杂非线性关系,利用RIMER(基于证据推理算法的置信规则库推理方法)对发动机进行故障诊断,克服了传统专家系统或神经网络技术只能单一利用专家知识或训练数据的缺点,将定性知识与定量数据有效结合,对发动机故障原因进行了研究,给维修人员提供了重要参考依据,仿真实验结果表明该方法可行有效.     

Adaptive Rule Weights in Neuro-Fuzzy Systems

Neuro-fuzzy systems have recently gained a lot of interest in research and application. They are approaches that use learning techniques derived from neural networks to learn fuzzy systems from data. A very simple ad hoc approach to apply a learning algorithm to a fuzzy system is to use adaptive rule weights. In this paper, we argue that rule weights have a negative effect on the linguistic interpretation of a fuzzy system, and thus remove one of the key advantages for applying fuzzy systems. We show how rule weights can be equivalently replaced by modifying the fuzzy sets of a fuzzy system. If this is done, the actual effects that rule weights have on a fuzzy rule base become visible. We demonstrate at a simple example the problems of using rule weights. We suggest that neuro-fuzzy learning should be better implemented by algorithms that modify the fuzzy sets directly without using rule weights.