Belief Rule Research Articles

On the Robustness of Belief-Rule-Based Expert Systems

Belief rule base (BRB) expert system has been widely used in complex system modeling. Robustness is crucial to the modeling performance and safety of BRB. For a better understanding and utility of BRB, there is thereby an urgent need to know what kind of influence each part of BRB may have when the disturbance occurs. Aiming at this, a more comprehensive analysis of BRB robustness is conducted in this article. First, the Lipschitz condition for BRB is defined. With the definitions, a new robustness analysis method of BRB is proposed, which is conducted from four aspects: 1) the input transformation; 2) the matching degree calculation; 3) the matching degree normalization; and 4) the rule aggregation. Moreover, five guidelines for BRB construction are proposed by analyzing its robustness, which can offer a practical guide for users to establish, adjust, and improve the BRB model for specific applications. The robustness analysis of the BRB expert system for the relay health-state evaluation is conducted to verify the effectiveness of the proposed method.

Health assessment of satellite storage battery pack based on solar array impact analysis

The space environment has grown more complex due to the high density of satellite missions, and the likelihood of collisions causing unexpected damage to solar arrays has increased. The current research on the assessment of battery pack health condition is based only on the data from battery packs themselves, without considering the impact of solar arrays' performance on battery packs. This would lead to an overestimation of battery packs' health, and if a satellite flight and control plan is developed based on this, it could result in excessive battery pack usage, potentially shortening the lifespan of the satellite. To address this issue, this paper proposed a novel framework for assessing the health condition of satellite battery packs, which expands the applicable scenarios of the assessment. Firstly, through an energy balance analysis of satellite power systems, the impact of solar array performance degradation on battery aging in different scenarios was discussed. Then, an Informer-based model was constructed to predict the output current of the solar array based on the decline mechanism of solar arrays. Next, a current supply and demand graph was created by combining the output current of the solar array with the load demand current, and an impact factor was defined to quantify the solar array's influence on the battery pack. A rule-based model of evidence reasoning and belief rule base was then improved by the impact factor to achieve evaluation. Finally, the telemetry data from a certain type of satellite were used to predict the current of the solar array. The prediction accuracy is significantly improved compared to traditional methods. Under the assumption of damage to the solar array, the health condition of the battery pack was evaluated, and the assessment result was consistent with the usage of the battery pack, demonstrating the effectiveness of the proposed method.

Extended belief rule base with ensemble imbalanced learning for lymph node metastasis diagnosis in endometrial carcinoma

Lymph node metastasis (LNM) constitutes one of the main prognostic factors for long-term survival in endometrial carcinoma (EC). However, the previous studies on LNM diagnosis failed to consider both model interpretability and class imbalance. In this study, the extended belief rule base (EBRB) expert system is introduced to develop a novel EBRB-based LNM diagnosis model. First, the interpretability of the EBRB expert system is investigated to demonstrate the feasibility on LNM diagnosis; Second, imbalanced learning is introduced to improve rule generation scheme for constructing base EBRBs; Third, by considering the trust of base EBRBs and base diagnoses, ensemble learning is introduced to improve rule inference scheme for diagnosing final LNM. In the case study, real EC patient data collected from Fujian Provincial Maternity and Children's Hospital are used to verify the effectiveness of the proposed EBRB-based model by comparing with the variants of rule generation schemes and rule inference schemes, as well as some machine learning-based LNM diagnosis models. The comparative results showed that the proposed EBRB-based model has better sensitivity, specificity, and geometric mean in diagnosing LNM for EC patients.

A new interpretable belief rule base model with step-length convergence strategy for aerospace relay health state assessment

Health state assessment is an important measure to maintain the safety of aerospace relays. Due to the uncertainty within the relay system, the accuracy of the model assessment is challenged. In addition, the opaqueness of the process and incomprehensibility of the results tend to lose trust in the model, especially in high security fields, so it is crucial to maintain the interpretability of the model. Thus, this paper proposes a new interpretable belief rule base model with step-length convergence strategy (IBRB-Sc) for aerospace relay health state assessment. First, general interpretability criteria for BRB are considered, and strategies for maintaining model interpretability are designed. Second, the evidential reasoning (ER) method is used as the inference machine. Then, optimization is performed based on the Interpretable Projection Covariance Matrix Adaptive Evolution Strategy (IP-CMA-ES). Finally, the validity of the model is verified using the JRC-7M aerospace relay as a case study. Comparative experiments show that the proposed model maintains high accuracy and achieves advantages in interpretability.

An ensemble belief rule base model for pathologic complete response prediction in gastric cancer

It is well known that the decision-making on treating gastric cancer is usually the summary of several experts’ advice. Moreover, the interpretability and reliability of a model used to assist doctors with final decisions are very important in gastric cancer. Thus, this paper designed an ensemble belief rule base (EnBRB) model to ensemble multiple BRB models and predict the statement of pathological complete response (pCR), aiming to simulate the expert consultation widely used for clinical decisions on gastric cancer. In EnBRB, five BRB models were built individually using experts’ knowledge and trained through patient treatment information. Furthermore, the final output was calculated via the evidential reasoning (ER) based ensemble strategy on the results of each BRB for a more reliable decision. Then, to improve the model’s performance, a two-stage approach with a differential evolution (DE) algorithm was designed to enhance the performance of EnBRB. The experimental results demonstrated that a higher accuracy (0.9296±0.0521) and AUC (0.9570±0.0368) were obtained by our EnBRB. Moreover, the difference between sensitivity and specificity achieved by EnBRB was smaller than other comparison methods.

Combination of linguistic Z-numbers and IF-THEN rules based on rectangular coordinate system

There is a growing body of literature that recognises the importance of Z-numbers proposed by Prof Zadeh. However, due to the complicated structure and short presentation time, many unknowns about Z-numbers still exist. To fill these gaps, this study aims to make use of rectangular coordinate system to express linguistic Z-numbers. Simultaneously, this study sets out to design a score function to quantify the information contained in different Z-numbers. Subsequently, distance measure and similarity measure are also presented from the perspective of coordinate system. Besides, linguistic discrete Z-numbers and belief rule base (BRB) model are combined to construct a novel reasoning model on the basis of implication operators. To verify the validity of the proposed method, three representative examples of epidemic level assessment, multicriteria group decision-making (MCGDM), and network security assessment are employed. The comparison with other widely used methods are performed to further demonstrate the superiority of the proposed method.

Resilient Formation Reconfiguration for Leader–Follower Multi-UAVs

Among existing studies on formation reconfiguration for multiple unmanned aerial vehicles (multi-UAVs), the majority are conducted on the assumption that the swarm scale is stationary. In fact, because of emergencies, such as communication malfunctions, physical destruction, and mission alteration, the scale of the multi-UAVs can fluctuate. In these cases, the achievements of formation reconfiguration for fixed-scale multi-UAVs are no longer applicable. As such, in this article, the formation reconfiguration problem of leader–follower multi-UAVs is investigated with a variable swarm scale taken into consideration. First, a streamlined topological structure is designed on the basis of the parity of the vertex numbers. Then, three formation reconfiguration strategies corresponding to the scenarios covering leader disengagement, follower detachment, and new member additions are developed with the aim of reducing the frequency of connection changes. Moreover, in terms of the leader election link of the leader disengagement scenario, a knowledge-based performance assessment model for UAVs is constructed with the help of the hierarchical belief rule base (BRB). Finally, the proposed formation reconfiguration strategies for leader disengagement, new member addition, and follower disengagement are demonstrated through simulations. The connection retention rate (CRR) for swarm communication topology under the three formation reconfiguration strategies can reach 67%, 90%, and 100%, respectively.

A fast belief rule base generation and reduction method for classification problems

The belief rule-based (BRB) system has been one of the most significant rule-based systems for its ability to deal with various kinds of information under uncertainty, and it has shown great potential for classification problems. However, the combinatorial explosion problem hugely limits the application of the BRB system as excessive rules could not only increase the computation cost, but also impact the performance of the BRB system. Therefore, motivated by this problem, this paper proposed a fast and accurate belief rule base generation and reduction method. Firstly, a fast belief rule base generation method is introduced, where similar rules are grouped and combined to ensure all the possible situations are covered without generating excessive rules. Then, a redundancy-based belief rule base reduction method is proposed, where the redundancy degree of the belief rule that represents the degree to which a belief rule is affected by other rules is introduced, and it is calculated to identify redundant rules. Furthermore, the conventional evidential reasoning (ER)-based inference process is retained from conventional BRB systems. Thirty classification benchmarks from the well-known UCI machine learning repository are tested to validate the effectiveness of the proposed method, and the results are compared with other rule-based systems, improved BRB systems, and other machine learning methods. Comparison results show that the proposed method could effectively reduce the size of the BRB without costing its accuracy. Furthermore, sensitivity analysis and robustness analysis are conducted, which further show the effectiveness and robustness of the proposed method.

An improved BRB-based anomaly detection method of drive end bearings

The anomaly detection research of drive end bearings (DEBs) is of great significance to the safe and reliable operation of hoist. This paper proposes an anomaly detection method of DEBs based on the linear weighted sum combines with the belief rule base. First, in order to improve the accuracy of anomaly detection, the time-domain features and frequency-domain features are integrated by linear weighted sum (LWS) respectively. Then, belief rule base (BRB) method is provided for anomaly detection using fused features. Meanwhile, the covariance matrix adaption evolution strategy (CMA-ES) is utilized to optimize the parameters of belief rule base model. Finally, the validity of the proposed method is verified by the vibration data, which are acquired from the condition monitoring system of hoist in body-in-white (BIW) welding production line. The proposed method achieves a high detection accuracy. It is proved that the proposed method is suitable for anomaly detection of DEBs in the actual BIW welding production line.

An interpretable model for stock price movement prediction based on the hierarchical belief rule base

Stock price movement prediction is the basis for decision-making to maintain the stability and security of stock markets. It is important to generate predictions in an interpretable manner. The Belief Rule Base (BRB) has certain interpretability based on IF-THEN rule semantics. However, the interpretability of BRB in the whole process of stock prediction modeling may be weakened or lost. Therefore, this paper proposes an interpretable model for stock price movement prediction based on the hierarchical Belief Rule Base (HBRB-I). The interpretability of the model is considered, and several criteria are constructed based on the BRB expert system. First, the hierarchical structure of BRB is constructed to ensure the interpretability of the initial modeling. Second, the interpretability of the inference process is ensured by the Evidential Reasoning (ER) method as a transparent inference engine. Third, a new Projection Covariance Matrix Adaptive Evolution Strategy (P-CMA-ES) algorithm with interpretability criteria is designed to ensure the interpretability of the optimization process. The final mean squared error value of 1.69E-04 was obtained with similar accuracy to the initial BRB and enhanced in terms of interpretability. This paper is for short-term stock forecasting, and more data will be collected in the future to update the rules to enhance the forecasting capability of the rule base.

An interpretable method for inertial platform fault diagnosis based on combination belief rule base

As a key component of navigation equipment, the inertial platform needs high reliability, so an accurate and interpretable method for fault diagnosis is necessary. The belief rule base (BRB) has strong interpretability and its ability to process semi-quantitative information. However, the high complexity of inertial platforms leads to the existence of multiple indicators for use in fault diagnosis, which leads to the combinatorial explosion of rules problem in BRB. Considering this problem, an interpretable method for inertial platform fault diagnosis based on combination BRB is proposed here. This paper provides two main contributions: 1) A BRB optimization method considering the correlation coefficient is proposed, which maintains the interpretability of sub-BRBs in the combination BRB, and 2) a method is proposed to calculate the sub-BRB weights based on the precision of the sub-BRBs and the occurrence times of repeated indicators, thus ensuring that the fusion process is explainable when the ER algorithm is used for the fusion of sub-BRBs. The proposed method ensures the interpretability of the final result during fault diagnosis while maintaining the reliability of the inertial platform. Finally, the effectiveness of the proposed method is verified against state-of-the-art methods using actual operation data from an inertial platform.

Measurement and optimization of rule consistency in a belief rule base system

As a rule-based expert system, good interpretability is one of the prominent advantages and characteristics of the belief rule base (BRB) system, and consistency is one of the important indicators of interpretability. However, the modeling of the BRB system in current research and applications usually focuses only on accuracy but ignores rule consistency. In this paper, the concept and connotation of consistency in the BRB system are first discussed. On this basis, a dynamic measurement formula of rule consistency is designed to determine whether a pair of rules is consistent and thus identify inconsistent rules. Then, an optimization process of inconsistent rules is proposed, in which expert experience or optimization algorithms can be utilized as the optimization tool. In particular, a conflict degree-based sorting method is presented to determine the optimization sequence of inconsistent rules. The proposed measurement and optimization process of rule consistency in the BRB system is validated by two cases, namely, pipeline leakage detection and remaining useful life estimation. The experimental results show that the process can effectively identify and eliminate inconsistencies in the BRB system and further ensures the effectiveness and interpretability of BRB systems in practical applications.

A new complex system fault detection method based on belief rule base for unreliable interval values

Failures to equipment such as milling machines and inertial navigation systems (INSs) can affect their normal operation, resulting in economic losses and personal injury in severe cases. Therefore, fault detection is of great importance. Belief rule base (BRB) is an expert system that plays an important role in fault detection. The traditional BRB has some problems in the explosion of the number of combination rules, the process of model inference, and the process of parameter optimization. To better deal with the above problems, this paper proposes a complex system fault detection method based on an interval-valued BRB fault detection interval-valued (FDIV) and provides the construction and inference process of the method. In the method construction, the form of interval value and disjunction rules are introduced to solve the problem of the number explosion of combination rules, the indicator reliability is added to improve the accuracy of the method, and a new calculation method of rule availability is proposed. In the inference process, twice fusions are made based on evidence reasoning (ER) analysis algorithm and ER rule algorithm respectively to deal with the interval uncertainties. Moreover, the proposed FDIV method is optimized by the projection covariance matrix adaptive evolutionary strategy algorithm projection covariance matrix adaptive evolutionary strategy (P-CMA-ES). Finally, the effectiveness of the proposed method was verified through the research on milling fault detection and the experimental verification of INS fault detection. The superiority of the model was also confirmed through comparative experiments.

A new intrusion detection model for industrial control system based on hierarchical interval-based BRB

Because the flow data generated by industrial control networks have the characteristics of large quantity, large feature dimension, and obvious class imbalance, the traditional industrial control intrusion detection model has difficulty accurately identifying attack flow. To solve the above problems, a hierarchical interval-based belief rule base (HIBRB) model has been proposed in this paper, which can improve the detection rate of attack flow while maintaining high accuracy. First, interval-based BRB (IBRB) model is used as the basic model to solve the problem that too many antecedent attributes will lead to combinatorial explosion. By changing reference points into reference intervals and conjunctive to disjunctive in IF-THEN rules, the number of rules can be effectively reduced, and expert knowledge can be involved. Second, to solve the problem of class imbalance, a two-layer BRB structure is used for modeling. In the first layer, a main model (main-IBRB) is used for multiclassification to determine the possible class of samples. In the second layer, the sub model (sub-IBRB) is used for binary classification to obtain the final class. To improve the performance of the whole model, XGBoost is used to select the optimal feature subset for main-IBRB and each sub-IBRB according to the different classification targets. Through two-layer BRB structure and XGBoost feature selection, HIBRB can effectively alleviate the class imbalance problem and improve the detection rate of attack flow. Finally, the intrusion detection model is established by using the data set of the natural gas pipeline control system, and the validity of this model is verified.

A new interval constructed belief rule base with rule reliability

A new interval constructed belief rule base with rule reliability

A new belief rule base based distributed online fault diagnosis method for multi‐agent systems

AbstractIn this paper, based on belief rule base (BRB), we studied the distributed online fault diagnosis problem of multi‐agent systems (MASs). To begin with, considering the distributed nature of MASs, by using the relative information between an agent and its neighbors, a distributed online fault diagnosis model is constructed. Next, for the results of fault diagnosis, when an agent doesn't get enough relative information to diagnose the fault, the fault diagnosis result may be inaccurate, and if there exist too many neighbors of an agent, the number of attributes of the proposed BRB fault diagnosis model will be too large, which will lead to large computation. To improve the performance of the proposed distributed online fault diagnosis model, a real‐time communication topology switching strategy was proposed. Under the constructed distributed fault diagnosis model, the real‐time performance and the accuracy of fault diagnosis for agents can be guaranteed simultaneously. Finally, a simulation is given to validate the effectiveness and advancement of the distributed online fault diagnosis method proposed in this paper.

A Text-Oriented Fault Diagnosis Method for Electromechanical Device Based on Belief Rule Base

At present, quantitative data is often used for fault diagnosis of electromechanical devices, while qualitative data in the form of text is rarely used. In order to integrate qualitative data in the form of text and quantitative data in the fault diagnosis of an electromechanical device, a text-oriented fault diagnosis method based on belief rule base (BRB) is proposed in this paper. Specifically, the key information of fault diagnosis is extracted from the text through natural language processing (NLP) and then converted into belief rules. Then, a rule supplement method is adopted to add the extracted belief rules to the BRB for the completion of the BRB construction. This method applies qualitative data in the form of text to the process of BRB construction, which is a new attempt at the BRB construction method. It not only solves the problem that BRB cannot use qualitative data in text form but also improves the modeling accuracy and data comprehensive processing ability of BRB. To verify the effectiveness of the algorithm, we designed an experiment of asynchronous motor fault diagnosis in the case study. The experimental result shows that the proposed method can use qualitative data in text form to construct BRB and effectively diagnose faults of asynchronous motors. The MSE of the proposed method is 0.0451, which is better than that of traditional BRB (0.1461), BP (0.0613), and SVR (0.0974) under the same experimental conditions.

Fault Diagnosis for Body-in-White Welding Robot Based on Multi-Layer Belief Rule Base

Fault diagnosis for body-in-white (BIW) welding robots is important for ensuring the efficient production of the welding assembly line. As a result of the complex mechanism of the body-in-white welding robot, its strong correlation of components, and the many types of faults, it is difficult to establish a complete fault diagnosis model. Therefore, a fault diagnosis model for a BIW-welding robot based on a multi-layer belief rule base (BRB) was proposed. This model can effectively integrate monitoring data and expert knowledge to achieve an accurate fault diagnosis and facilitate traceability. First, according to the established fault tree, a fault mechanism was determined. Second, based on the multi-layer relationship of a fault tree, we established a multi-layer BRB model. Meanwhile, in order to improve the accuracy of the model parameters, the projection covariance matrix adaptive evolutionary strategy (P-CMA-ES) algorithm was used to optimize and update the parameters of the fault diagnosis model. Finally, the validity of the proposed model was verified by a simulation experiment for the BIW-welding robot.

Research and application of park multi-source synergistic and complementary heating system and its coordinated control method

The integration of solar thermal collectors (STC) and air source heat pump (ASHP) heating systems has been widely used for building heating. However, these systems have the problems that the STC cannot fully utilize the solar energy at weak radiation, and the ASHP has insufficient output as well as low coefficient of performance (COP) under extreme cold conditions. In this study, a multi-source synergistic and complementary heating system (MSSCHS) with a heating mode selection model based on belief rule base and evidential reasoning (BRB-ER) method is designed. First, the MSSCHS composed of the STC and the ASHP as the main heat sources, and the water source heat pump as the auxiliary heat source, along with its three heating modes under different operating conditions were proposed. Then, a system heating mode selection model based on the BRB-ER method was establish to achieve mode switching. Finally, the MSSCHS with BRB-ER heating mode selection model was tested experimentally. The results show that compared with the conventional ASHP + STC heating system, the solar energy utilization rate of the MSSCHS had increased by 19.3 %, 16.6 % and 8.2 % respectively in three typical days, and the ASHP's COP had increased by 37.7 %- 55.6 % under extreme cold conditions. The high efficiency and stability of the MSSCHS were verified through operational tests during the heating period. Furthermore, by applying in different types of buildings, it is verified that the MSSCHS can meet different heating requirements and has a good applicability. It was demonstrated that the proposed MSSCHS has more efficient heating mode and more accurate mode selection method, which can provide a new research idea for building heating.

Lithium-ion battery health assessment method based on belief rule base with interpretability

Health assessment is important for the safe and reliable operation of lithium-ion battery. However, there exist two typical issues in existing health assessment models for lithium-ion battery: uncertainty of the chemical reaction inside the battery and lack of interpretability of the evaluation results. The belief rule base (BRB) is a rule-based modelling approach and can deal with uncertain information in health state assessment. However, the interpretability of the lithium-ion battery health state assessment model based on BRB needs to be preserved effectively. Thus, a new lithium-ion battery health state assessment model based on belief rule base with interpretability (BRB-I) is proposed in this paper. In the BRB-I model, both structural interpretability and optimization interpretability are constructed through the mechanism analysis of lithium-ion batteries. Moreover, a new interpretability evaluation criterion is defined as the objective function to achieve a balanced optimization between interpretability and accuracy. In addition, an improved optimization method based on the whale optimization algorithm (WOA) is proposed to enhance the interpretability of the model and the optimization process. A case study on the health state assessment of B0006 lithium-ion battery is conducted to illustrate the effectiveness of the proposed method.