A Health State Prediction Model Based on Belief Rule Base and LSTM for Complex Systems

In industrial production and engineering operations,the health state of complex systems is critical,and predicting it can ensure normal operation.Complex systems have many monitoring indicators,complex coupling structures,non-linear and time-varying characteristics,so it is a challenge to establish a reliable prediction model.The belief rule base(BRB)can fuse observed data and expert knowledge to establish a nonlinear relationship between input and output and has well modeling capabilities.Since each indicator of the complex system can reflect the health state to some extent,the BRB is built based on the causal relationship between system indicators and the health state to achieve the prediction.A health state prediction model based on BRB and long short term memory for complex systems is proposed in this paper.Firstly,the LSTMis introduced to predict the trend of the indicators in the system.Secondly,the Density Peak Clustering(DPC)algorithmis used todetermine referential values of indicators for BRB,which effectively offset the lack of expert knowledge.Then,the predicted values and expert knowledge are fused to construct BRB to predict the health state of the systems by inference.Finally,the effectiveness of the model is verified by a case study of a certain vehicle hydraulic pump.

Safety Assessment of Liquid Launch Vehicle Structures Based on Interpretable Belief Rule Base

A liquid launch vehicle is an important carrier in aviation,and its regular operation is essential to maintain space security.In the safety assessment of fluid launch vehicle body structure,it is necessary to ensure that the assessmentmodel can learn self-response rules from various uncertain data and not differently to provide a traceable and interpretable assessment process.Therefore,a belief rule base with interpretability(BRB-i)assessment method of liquid launch vehicle structure safety status combines data and knowledge.Moreover,an innovative whale optimization algorithm with interpretable constraints is proposed.The experiments are carried out based on the liquid launch vehicle safety experiment platform,and the information on the safety status of the liquid launch vehicle is obtained by monitoring the detection indicators under the simulation platform.The MSEs of the proposed model are 3.8000e-03,1.3000e-03,2.1000e-03,and 1.8936e-04 for 25%,45%,65%,and 84%of the training samples,respectively.It can be seen that the proposed model also shows a better ability to handle small sample data.Meanwhile,the belief distribution of the BRB-i model output has a high fitting trend with the belief distribution of the expert knowledge settings,which indicates the interpretability of the BRB-i model.Experimental results show that,compared with other methods,the BRB-i model guarantees the model’s interpretability and the high precision of experimental results.

A New Prediction System Based on Self-Growth Belief Rule Base with Interpretability Constraints

Prediction systems are an important aspect of intelligent decisions.In engineering practice,the complex system structure and the external environment cause many uncertain factors in the model,which influence the modeling accuracy of the model.The belief rule base(BRB)can implement nonlinear modeling and express a variety of uncertain information,including fuzziness,ignorance,randomness,etc.However,the BRB system also has two main problems:Firstly,modeling methods based on expert knowledge make it difficult to guarantee the model’s accuracy.Secondly,interpretability is not considered in the optimization process of current research,resulting in the destruction of the interpretability of BRB.To balance the accuracy and interpretability of the model,a self-growth belief rule basewith interpretability constraints(SBRB-I)is proposed.The reasoning process of the SBRB-I model is based on the evidence reasoning(ER)approach.Moreover,the self-growth learning strategy ensures effective cooperation between the datadriven model and the expert system.A case study showed that the accuracy and interpretability of the model could be guaranteed.The SBRB-I model has good application prospects in prediction systems.

A Processor Performance Prediction Method Based on Interpretable Hierarchical Belief Rule Base and Sensitivity Analysis

The prediction of processor performance has important referencesignificance for future processors. Both the accuracy and rationality of theprediction results are required. The hierarchical belief rule base (HBRB)can initially provide a solution to low prediction accuracy. However, theinterpretability of the model and the traceability of the results still warrantfurther investigation. Therefore, a processor performance prediction methodbased on interpretable hierarchical belief rule base (HBRB-I) and globalsensitivity analysis (GSA) is proposed. The method can yield more reliableprediction results. Evidence reasoning (ER) is firstly used to evaluate thehistorical data of the processor, followed by a performance prediction modelwith interpretability constraints that is constructed based on HBRB-I. Then,the whale optimization algorithm (WOA) is used to optimize the parameters.Furthermore, to test the interpretability of the performance predictionprocess, GSA is used to analyze the relationship between the input and thepredicted output indicators. Finally, based on the UCI database processordataset, the effectiveness and superiority of the method are verified. Accordingto our experiments, our prediction method generates more reliable andaccurate estimations than traditional models.

Milling Fault Detection Method Based on Fault Tree Analysis and Hierarchical Belief Rule Base

Expert knowledge is the key to modeling milling fault detection systems based on the belief rule base.The construction of an initial expert knowledge base seriously affects the accuracy and interpretability of the milling fault detection model.However,due to the complexity of the milling system structure and the uncertainty of the milling failure index,it is often impossible to construct model expert knowledge effectively.Therefore,a milling system fault detection method based on fault tree analysis and hierarchical BRB(FTBRB)is proposed.Firstly,the proposed method uses a fault tree and hierarchical BRB modeling.Through fault tree analysis(FTA),the logical correspondence between FTA and BRB is sorted out.This can effectively embed the FTA mechanism into the BRB expert knowledge base.The hierarchical BRB model is used to solve the problem of excessive indexes and avoid combinatorial explosion.Secondly,evidence reasoning(ER)is used to ensure the transparency of the model reasoning process.Thirdly,the projection covariance matrix adaptation evolutionary strategies(P-CMA-ES)is used to optimize the model.Finally,this paper verifies the validity model and the method’s feasibility techniques for milling data sets.

A New Safety Assessment Method Based on Belief Rule Base With Attribute Reliability

Safety assessment is one of important aspects in health management.In safety assessment for practical systems,three problems exist:lack of observation information,high system complexity and environment interference.Belief rule base with attribute reliability(BRB-r)is an expert system that provides a useful way for dealing with these three problems.In BRB-r,once the input information is unreliable,the reliability of belief rule is influenced,which further influences the accuracy of its output belief degree.On the other hand,when many system characteristics exist,the belief rule combination will explode in BRB-r,and the BRB-r based safety assessment model becomes too complicated to be applied.Thus,in this paper,to balance the complexity and accuracy of the safety assessment model,a new safety assessment model based on BRB-r with considering belief rule reliability is developed for the first time.In the developed model,a new calculation method of the belief rule reliability is proposed with considering both attribute reliability and global ignorance.Moreover,to reduce the influence of uncertainty of expert knowledge,an optimization model for the developed safety assessment model is constructed.A case study of safety assessment of liquefied natural gas(LNG)storage tank is conducted to illustrate the effectiveness of the new developed model.

Operational effectiveness evaluation based on the reduced conjunctive belief rule base

To address the issue of rule premise combination explosion in the construction of the traditional complete conjunctive belief rule base(BRB),this paper introduces an orthogonal design method to reduce the conjunctive BRB.The reasoning method based on reduced conjunctive BRB is designed with the help of the conversion technology from conjunctive BRB to disjunctive BRB.Finally,the operational mission effectiveness evaluation is taken as an example to verify the proposed method.The results show that the method proposed in this paper is feasible and effective.

A new interpretable fault diagnosis method based on belief rule base and probability table

It is vital to establish an interpretable fault diagnosis model for critical equipment.Belief Rule Base(BRB)is an interpretable expert system gradually applied in fault diagnosis.However,the expert knowledge cannot be utilized to establish the initial BRB accurately if there are multiple referential grades in different fault features.In addition,the interpretability of BRB-based fault diagnosis is destroyed in the optimization process,which reflects in two aspects:deviation from the initial expert judgment and over-optimization of parameters.To solve these problems,a new interpretable fault diagnosis model based on BRB and probability table,called the BRB-P,is proposed in this paper.Compared with the traditional BRB,the BRB-P constructed by the probability table is more accurate.Then,the interpretability constraints,i.e.,the credibility of expert knowledge,the penalty factor and the rule-activation factor,are inserted into the projection covariance matrix adaption evolution strategy to maintain the interpretability of BRB-P.A case study of the aerospace relay is conducted to verify the effectiveness of the proposed method.

A Novel Belief Rule-Based Fault Diagnosis Method with Interpretability

Fault diagnosis plays an irreplaceable role in the normal operation of equipment.A fault diagnosis model is often required to be interpretable for increasing the trust between humans and the model.Due to the understandable knowledge expression and transparent reasoning process,the belief rule base(BRB)has extensive applications as an interpretable expert system in fault diagnosis.Optimization is an effective means to weaken the subjectivity of experts in BRB,where the interpretability of BRB may be weakened.Hence,to obtain a credible result,the weakening factors of interpretability in the BRB-based fault diagnosis model are firstly analyzed,which are manifested in deviation from the initial judgement of experts and over-optimization of parameters.For these two factors,three indexes are proposed,namely the consistency index of rules,consistency index of the rule base and over-optimization index,tomeasure the interpretability of the optimizedmodel.Considering both the accuracy and interpretability of amodel,an improved coordinate ascent(I-CA)algorithmis proposed to fine-tune the parameters of the fault diagnosis model based on BRB.In I-CA,the algorithm combined with the advance and retreat method and the golden section method is employed to be one-dimensional search algorithm.Furthermore,the random optimization sequence and adaptive step size are proposed to improve the accuracy of the model.Finally,a case study of fault diagnosis in aerospace relays based on BRB is carried out to verify the effectiveness of the proposed method.

Sensor Fault Diagnosis and Tolerant Control Based on Belief Rule Base for Complex System

This paper develops a new fault diagnosis and tolerant control framework of sensor failure(SFDTC)for complex system such as rockets and missiles.The new framework aims to solve two problems:The lack of data and the multiple uncertainty of knowledge.In the SFDTC framework,two parts exist:The fault diagnosis model and the output reconstruction model.These two parts of the new framework are constructed based on the new developed belief rule base with power set(BRB-PS).The multiple uncertainty of knowledge can be addressed by the local ignorance and global ignorance in the new developed BRB-PS model.Then,the stability of the developed framework is proved by the output error of the BRB-PS model.For complex system,the sensor state is determined by many factors and experts cannot provide accurate knowledge.The multiple uncertain knowledge will reduce the performance of the initial SDFTC framework.Therefore,in the SFDTC framework,to handle the influence of the uncertainty of expert knowledge and improve the framework performance,a new optimization model with two optimization goals is developed to ensure the smallest output uncertainty and the highest accuracy simultaneously.A case study is conducted to illustrate the effectiveness of the developed framework.

Real-time fault detection method based on belief rule base for aircraft navigation system

Real-time and accurate fault detection is essential to enhance the aircraft navigation system’s reliability and safety. The existent detection methods based on analytical model draws back at simultaneously detecting gradual and sudden faults. On account of this reason, we propose an online detection solution based on non-analytical model. In this article, the navigation system fault detection model is established based on belief rule base （BRB）, where the system measuring residual and its changing rate are used as the inputs of BRB model and the fault detection function as the output. To overcome the drawbacks of current parameter optimization algorithms for BRB and achieve online update, a parameter recursive estimation algorithm is presented for online BRB detection model based on expectation maximization （EM） algorithm. Furthermore, the proposed method is verified by navigation experiment. Experimental results show that the proposed method is able to effectively realize online parameter evaluation in navigation system fault detection model. The output of the detection model can track the fault state very well, and the faults can be diagnosed in real time and accurately. In addition, the detection ability, especially in the probability of false detection, is superior to offline optimization method, and thus the system reliability has great improvement.

A novel combination belief rule base model for mechanical equipment fault diagnosis

Due to the excellent performance in complex systems modeling under small samples and uncertainty,Belief Rule Base(BRB)expert system has been widely applied in fault diagnosis.However,the fault diagnosis process for complex mechanical equipment normally needs multiple attributes,which can lead to the rule number explosion problem in BRB,and limit the efficiency and accuracy.To solve this problem,a novel Combination Belief Rule Base(C-BRB)model based on Directed Acyclic Graph(DAG)structure is proposed in this paper.By dispersing numerous attributes into the parallel structure composed of different sub-BRBs,C-BRB can effectively reduce the amount of calculation with acceptable result.At the same time,a path selection strategy considering the accuracy of child nodes is designed in C-BRB to obtain the most suitable submodels.Finally,a fusion method based on Evidential Reasoning(ER)rule is used to combine the belief rules of C-BRB and generate the final results.To illustrate the effectiveness and reliability of the proposed method,a case study of fault diagnosis of rolling bearing is conducted,and the result is compared with other methods.

A WSN Node Fault Diagnosis Model Based on BRB with Self-Adaptive Quality Factor

Wireless sensor networks (WSNs) operate in complex and harshenvironments;thus, node faults are inevitable. Therefore, fault diagnosis ofthe WSNs node is essential. Affected by the harsh working environment ofWSNs and wireless data transmission, the data collected by WSNs containnoisy data, leading to unreliable data among the data features extracted duringfault diagnosis. To reduce the influence of unreliable data features on faultdiagnosis accuracy, this paper proposes a belief rule base (BRB) with a selfadaptivequality factor (BRB-SAQF) fault diagnosis model. First, the datafeatures required for WSN node fault diagnosis are extracted. Second, thequality factors of input attributes are introduced and calculated. Third, themodel inference process with an attribute quality factor is designed. Fourth,the projection covariance matrix adaptation evolution strategy (P-CMA-ES)algorithm is used to optimize the model’s initial parameters. Finally, the effectivenessof the proposed model is verified by comparing the commonly usedfault diagnosis methods for WSN nodes with the BRB method consideringstatic attribute reliability (BRB-Sr). The experimental results show that BRBSAQFcan reduce the influence of unreliable data features. The self-adaptivequality factor calculation method is more reasonable and accurate than thestatic attribute reliability method.

基于累积置信规则库推理的台风灾害直接经济损失预测

针对台风灾害直接经济损失预测问题,现有的解决方法大多是基于时间序列或评估数据的预测模型,忽略了在建模过程中对历史数据的应用和模型的可解释性。鉴于此,该文将扩展置信规则库模型(EBRB)应用于台风灾害直接经济损失预测,并针对可能存在规则过量和组合爆炸问题,提出基于聚类方法与证据推理(ER)相结合的累积置信规则库(C-BRB)台风灾害经济损失预测模型。最后基于收集到的台风灾害数据进行直接经济损失预测,并通过与已有研究成果进行比较,验证基于C-BRB的台风灾害直接经济损失预测模型的有效性和可行性。

基于BRB-PSO的船舶舵机模型参数辨识方法研究

文中提出一种基于BRB-PSO的船舶舵机模型参数辨识方法.构造关于船舶舵机模型参数的BRB-PSO辨识模型,以描述模型输入(指令舵角和实际舵角信号)与模型输出(舵机模型参数)之间的非线性关系;建立置信规则库(BRB),通过置信规则推理得到惯性权重变化量的估计值并更新惯性权重;基于该惯性权重调整粒子群算法(PSO)中粒子的速度、位置等参数,依次迭代,直到达到停止要求,实现舵机模型参数的辨识.通过与其他典型参数辨识方法的实验结果对比,进一步说明BRB-PSO辨识方法在舵机模型参数辨识方面的优越性.

邮轮内装物资物流集配风险评估

为量化邮轮内装物资物流集配风险并科学配置管控资源,结合置信规则库和贝叶斯网络,用于解决具有不确定性和模糊性的风险评价信息.辨识影响邮轮内装物资物流集配的关键风险因素,多维度细化风险参数表达,基于风险参数结构及权重,建立包含置信度的规则库表示风险参数与风险状态之间的对应关系;融合模糊评价数据,利用贝叶斯推理技术,得出风险因素在风险状态上的置信度分布,引入效用函数实现概率值向精确值的转换,并得到风险因素的排序结果;通过敏感性分析验证该模型的逻辑性、适用性和准确性.结果表明:邮轮内装物资物流集配风险排序位列前三的分别为内装总包商对供应商及物流服务商监管不善、参与主体权责划分不明确、以及仓储设施不满足物资存放要求.

基于置信规则库的干式空心电抗器状态评估方法研究

针对电力设备故障样本少且获取困难等问题,提出了基于置信规则库的干式空心电抗器状态评估方法。通过搭建多工况下干式空心电抗器电气及温升特性试验平台,获取不同工况下电抗器有功功率和最热点温升率数据样本集,建立基于置信规则库和证据推理的电抗器状态评估模型。为了减小因专家主观经验对状态评估模型预测结果的影响,提出置信规则库优化方法,并采用证据推理算法将电抗器输入特征信息转化为输出状态等级。利用测试数据对评估模型进行测试,结果验证了基于小训练样本的干式空心电抗器状态评估方法的有效性和准确性。

基于属性可靠度置信规则库的轴承故障诊断研究

轴承故障诊断是旋转器械健康管理中的一个关键问题。然而,在工程实践中,轴承的观测数据可能会受到一些干扰因素的影响,包括传感器质量和环境中的噪声等。在传统置信规则库(BRB)中,其模型推理假定输入数据完全可靠,但不可靠的观测数据会使BRB精度降低。具有属性可靠度的置信规则库模型(BRB-r)提供了一种建模框架和分析方法,是一个能够聚合不可靠定量数据和专家知识的系统。为提高轴承故障诊断精度,提出一种基于BRBr的轴承故障诊断模型。首先,基于统计方法计算属性可靠度;然后,使用证据推理作为模型的推理机;最后,采用投影协方差矩阵自适应进化策略(P-CMA-ES)对模型进行参数优化。验证实验结果表明,BRB-r在一定程度上能够消除观测数据中不确定性信息的影响,并对不可靠数据进行有效处理,具备良好的诊断效果。

基于置信规则的村镇应急避难场所暴雨灾害链风险诊断

为解决村镇应急避难场所面临暴雨灾害时的风险问题,基于故障树和置信规则库推理方法,提出暴雨灾害链和村镇应急避难场所功能破坏链相结合的场所避难功能失效风险诊断模型。根据事故致因理论推理灾害节点变量,通过故障树描述灾害链,运用关联规则从历史灾害数据中挖掘规则,建立置信规则库系统,构建村镇应急避难场所功能失效风险诊断模型,并以四川省某寄宿制学校为例进行模型验证。研究结果表明:该模型可实现不同证据组合下村镇应急避难场所功能失效风险的诊断推理;实例的模型诊断结果与实际情况吻合,证实该模型能够科学地诊断村镇应急避难场所面临暴雨等恶劣自然条件时存在的风险,可为村镇应急避难场所规划设计和应急管理提供理论支撑。

传感器网络的最优维护决策模型

传感器网络最优维护决策的目标为用户提供最优的维护时机,维护决策的精度直接决定了传感器网络的可靠性。基于置信规则库(belief rule base,BRB)专家系统提出的最优维护决策模型解决两个问题:检测数据不足和复杂的系统机理。模型由健康状态评估和预测两部分组成:基于BRB模型对传感器网络的健康状态进行评估;根据当前的健康评估状态,利用Wiener过程预测传感器网络的健康状态,以获得最优的维护时机。基于Wiener过程的健康状态预测模型中,由专家提供传感器网络健康状态的最小阈值,以确定最佳的维护时机。为验证模型的有效性,进行了原油存储罐无线传感器网络的最优维护决策实验研究。