Belief Rule Base Research Articles

Fault Diagnosis for Complex Equipment Based on Belief Rule Base with Adaptive Nonlinear Membership Function

Fault diagnosis of complex equipment has become a hot field in recent years. Due to excellent uncertainty processing capability and small sample problem modeling capability, belief rule base (BRB) has been widely used in the fault diagnosis. However, previous BRB models almost did not consider the diverse distributions of observation data which may reduce diagnostic accuracy. In this paper, a new fault diagnosis model based on BRB is proposed. Considering that the previous triangular membership function cannot address the diverse distribution of observation data, a new nonlinear membership function is proposed to transform the input information. Then, since the model parameters initially determined by experts are inaccurate, a new parameter optimization model with the parameters of the nonlinear membership function is proposed and driven by the gradient descent method to prevent the expert knowledge from being destroyed. A fault diagnosis case of laser gyro is used to verify the validity of the proposed model. In the case study, the diagnosis accuracy of the new BRB-based fault diagnosis model reached 95.56%, which shows better fault diagnosis performance than other methods.

An interpretable BRB model with interval optimization strategy for lithium battery capacity prediction

AbstractAccurately predicting the capacity of lithium battery is conducive to improving its safety. Affected by complex internal electrochemical reaction and external use conditions, the prediction accuracy is difficult to guarantee; at the same time, the existing prediction methods are unexplainable, resulting in the inability to trace the prediction process. Therefore, a capacity prediction model based on belief rule base with interpretability and interval optimization strategy is proposed in this paper. First, the reasoning process is designed according to interpretability modeling criteria. Second, to achieve a balance of accuracy and interpretability, based on the whale optimization algorithm, a model parameter optimization method using interval optimization strategy is proposed. Finally, through a case study, the model's effectiveness is verified. Comparison with other models shows that the proposed model has certain advantages in accuracy and interpretability.

Learning Emotion Assessment Method Based on Belief Rule Base and Evidential Reasoning

Learning emotion assessment is a non-negligible step in analyzing learners’ cognitive processing. Data are the basis of the learning emotion assessment. However, the existing learning emotion assessment models cannot balance model accuracy and interpretability well due to the influence of uncertainty in the process of data collection and model parameter errors. Given the above problems, a new learning emotion assessment model based on evidence reasoning and a belief rule base (E-BRB) is proposed in this paper. First, the transformation matrix is introduced to transform multiple emotional indicators into the same standard framework and integrate them, which keeps the consistency of information transformation. Second, the relationship between emotional indicators and learning emotion states is modeled by E-BRB in conjunction with expert knowledge. In addition, we employ the projection covariance matrix adaptation evolution strategy (P-CMA-ES) to optimize the model parameters and improve the model’s accuracy. Finally, to demonstrate the effectiveness of the proposed model, it is applied to emotion assessment in science learning. The experimental results show that the model has better accuracy than data-driven models such as neural networks.

A new BRB model for technical analysis of the stock market

To predict the trend of stock prices, a belief rule base (BRB) assessment model based on different technical indicators is proposed in this paper. The proposed BRB-based model includes three BRBs, denoted as BRB_1, BRB_2 and BRB_3. BRB_1 is used to capture the relationship between the price trend of the moving average (MA) and buy/sell decisions. BRB_2 is used to investigate the conditions of moving average convergence and divergence (MACD). BRB_3 is employed to represent the stochastic indicator (KD) states. The above three indicators are commonly used in stock analysis, and they usually need to be used together to achieve a more accurate analysis of the stock price trend. In the BRB model, the initial values of some parameters are provided by experts to construct the elementary algorithm logic, but these are unlikely to result in an accurate assessment. Therefore, on the basis of the maximum likelihood (ML) algorithm, an optimal algorithm for training the parameters of the assessment model is further proposed. Taking the trend of the Chinese stock market as the research object, an average MSE of 0.3242 is obtained using this model. The results indicate the potential application of the proposed model in the financial industry.

A new stock market analysis method based on evidential reasoning and hierarchical belief rule base to support investment decision making.

Stock market analysis is helpful for investors to make reasonable decisions and maintain market stability, and it usually involves not only quantitative data but also qualitative information, so the analysis method needs to have the ability to deal with both types of information comprehensively. In addition, due to the inherent risk of stock investment, it is necessary to ensure that the analysis results can be traced and interpreted. To solve the above problems, a stock market analysis method based on evidential reasoning (ER) and hierarchical belief rule base (HBRB) is proposed in this paper. First, an evaluation model is constructed based on expert knowledge and ER to evaluate stock market sentiment. Then, a stock market decision model based on HBRB is constructed to support investment decision making, such as buying and selling stocks and holding positions. Finally, the Shanghai Stock Index from 2010 to 2019 is used as an example to verify the applicability and effectiveness of the proposed stock market analysis method for investment decision support. Experimental research demonstrates that the proposed method can help analyze the stock market comprehensively and support investors to make investment decisions effectively.

Computer-aided diagnosis of primary membranous nephropathy using expert system

BackgroundThe diagnosis of primary membranous nephropathy (PMN) often depends on invasive renal biopsy, and the diagnosis based on clinical manifestations and target antigens may not be completely reliable as it could be affected by uncertain factors. Moreover, different experts could even have different diagnosis results due to their different experiences, which could further impact the reliability of the diagnosis. Therefore, how to properly integrate the knowledge of different experts to provide more reliable and comprehensive PMN diagnosis has become an urgent issue.MethodsThis paper develops a belief rule-based system for PMN diagnosis. The belief rule base is constructed based on the knowledge of the experts, with 9 biochemical indicators selected as the input variables. The belief rule-based system is developed of three layers: (1) input layer; (2) belief rule base layer; and (3) output layer, where 9 biochemical indicators are selected as the input variables and the diagnosis result is provided as the conclusion. The belief rule base layer is constructed based on the knowledge of the experts. The final validation was held with gold pattern clinical cases, i.e., with known and clinically confirmed diagnoses.Results134 patients are used in this study, and the proposed method is defined by its sensitivity, specificity, accuracy and area under curve (AUC), which are 98.0%, 96.9%, 97.8% and 0.93, respectively. The results of this study present a novel and effective way for PMN diagnosis without the requirement of renal biopsy.ConclusionsThrough analysis of the diagnosis results and comparisons with other methods, it can be concluded that the developed system could help diagnose PMN based on biochemical indicators with relatively high accuracy.Graphical

A new method for disease diagnosis based on hierarchical BRB with power set

Disease diagnosis occupies an important position in the medical field. The diagnosis of the disease is the basis for choosing the right treatment plan. Doctors must first diagnose what the patient has based on the clinical characteristics of various diseases, and then they can administer the right medicine. When building models for disease diagnosis, models are required to be able to handle various uncertainty information. The belief rule base (BRB) can effectively handle various information under uncertainty by introducing belief distributions. However, in current research, BRB-based disease diagnosis models still have problems of combinatorial rule explosion and inability to deal with local ignorance effectively. Therefore, a hierarchical BRB with power set (H-BRBp)-based disease diagnosis model is proposed in this paper. First, the physiological indexes and data of the patients were analyzed, and the data were preprocessed using the principal component regression (PCR) algorithm. Second, the H-BRBp disease diagnosis model was constructed to solve the deficiencies in the above BRB disease diagnosis model. Finally, the validity and advantages of the model were verified by experiments on lumbar spine disease diagnosis and a large number of comparison experiments.

Belief rule-base expert system with multilayer tree structure for complex problems modeling

Belief rule-base (BRB) expert system is one of recognized and fast-growing approaches in the areas of complex problems modeling. However, the conventional BRB has to suffer from the combinatorial explosion problem since the number of rules in BRB expands exponentially with the number of attributes in complex problems, although many alternative techniques have been looked at with the purpose of downsizing BRB. Motivated by this challenge, in this paper, multilayer tree structure (MTS) is introduced for the first time to define hierarchical BRB, also known as MTS-BRB. MTS-BRB is able to overcome the combinatorial explosion problem of the conventional BRB. Thereafter, the additional modeling, inferencing, and learning procedures are proposed to create a self-organized MTS-BRB expert system. To demonstrate the development process and benefits of the MTS-BRB expert system, case studies including benchmark classification datasets and research and development (R&D) project risk assessment have been done. The comparative results showed that, in terms of modelling effectiveness and/or prediction accuracy, MTS-BRB expert system surpasses various existing, as well as traditional fuzzy system-related and machine learning-related methodologies.

Health condition assessment of satellite li-ion battery pack considering battery inconsistency and pack performance indicators

Assessing the health condition of satellite li-ion battery pack accurately is critical for determining the safety of satellite power supply and ensuring that satellite satisfies its service life. Since the limitations of space environment make satellite battery special in operation and maintenance, misjudgments may occur when using existing assessment methods. To solve this problem, a novel health condition assessment indicator system that integrates battery inconsistency and pack performance indicators is built according to the performance requirement of battery pack. Based on the typical strategy of satellite battery pack performance degradation management, equalization and bypass state are employed as factors to make assessment result more accurate and comprehensive. Then, a method based on ER (evidential reasoning) and BRB (belief rule base) is proposed to achieve inconsistencies fusion and rule-based assessment. And the results can be expressed as belief degree distribution or score. Finally, the health condition of a certain type of in-orbit satellite's li-ion battery pack is assessed using telemetry data. The results are consistent with the battery's actual working state, which proves the effectiveness of the proposed method.

A novel optimization method for belief rule base expert system with activation rate

Although the belief rule base (BRB) expert system has many advantages, such as the effective use of semi-quantitative information, objective description of uncertainty, and efficient nonlinear modeling capability, it is always limited by the problem of combinatorial explosion. The main reason is that the optimization of a BRB with many rules will consume many computing resources, which makes it unable to meet the real-time requirements in some complex systems. Another reason is that the optimization process will destroy the interpretability of those parameters that belong to the inadequately activated rules given by experts. To solve these problems, a novel optimization method for BRB is proposed in this paper. Through the activation rate, the rules that have never been activated or inadequately activated are pruned during the optimization process. Furthermore, even if there is a complete data set and all rules are activated, the activation rate can also be used in the parallel optimization process of the BRB expert system, where the training data set is divided into some subprocesses. The proposed method effectively solves the combinatorial explosion problem of BRB and can make full use of quantitative data without destroying the original interpretability provided by experts. Case studies prove the advantages and effectiveness of the proposed method, which greatly expands the application fields of the BRB expert system.

Disjunctive belief rule-based reasoning for decision making with incomplete information

Witnessing the growth of inaccurate data with uncertainty and ambiguity, the belief rule base system is attracting increasing research interest because of its usage in decision-making problems as a disjunctive paradigm particularly when there is incomplete information. In this paper, we devise a novel method that employs fuzzy association rules to optimize disjunctive belief rule base (DBRB) systems regarding incomplete information in decision-making and achieve a significant performance improvement compared to the existing ones. First, we devise a method for constructing a fuzzy representation base from history data by using the triangular membership functions to blur history information. Then, a method is proposed to construct association rules based on the fuzzy representation base, in which the association rules are found regarding the missing input information by carrying out reasoning to complete the data and then making decisions on the data filled with DBRB system. Lastly, we evaluate the effectiveness of our proposed method against the public test data set, demonstrating that our method outperforms other baselines for decision-making with incomplete information.

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, to measure the interpretability of the optimized model. Considering both the accuracy and interpretability of a model, an improved coordinate ascent (I-CA) algorithm is 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.

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 base with 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 data-driven 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 WSN Node Fault Diagnosis Model Based on BRB with Self-Adaptive Quality Factor

Wireless sensor networks (WSNs) operate in complex and harsh environments; thus, node faults are inevitable. Therefore, fault diagnosis of the WSNs node is essential. Affected by the harsh working environment of WSNs and wireless data transmission, the data collected by WSNs contain noisy data, leading to unreliable data among the data features extracted during fault diagnosis. To reduce the influence of unreliable data features on fault diagnosis accuracy, this paper proposes a belief rule base (BRB) with a self-adaptive quality factor (BRB-SAQF) fault diagnosis model. First, the data features required for WSN node fault diagnosis are extracted. Second, the quality factors of input attributes are introduced and calculated. Third, the model 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 effectiveness of the proposed model is verified by comparing the commonly used fault diagnosis methods for WSN nodes with the BRB method considering static attribute reliability (BRB-Sr). The experimental results show that BRB-SAQF can reduce the influence of unreliable data features. The self-adaptive quality factor calculation method is more reasonable and accurate than the static attribute reliability method.

A New Model for Network Security Situation Assessment of the Industrial Internet

To address the problem of network security situation assessment in the Industrial Internet, this paper adopts the evidential reasoning (ER)algorithm and belief rule base (BRB) method to establish an assessment model. First, this paper analyzes the influencing factors of the Industrial Internet and selects evaluation indicators that contain not only quantitative data but also qualitative knowledge. Second, the evaluation indicators are fused with expert knowledge and the ER algorithm. According to the fusion results, a network security situation assessment model of the Industrial Internet based on the ER and BRB method is established, and the projection covariance matrix adaptive evolution strategy (P-CMA-ES) is used to optimize the model parameters. This method can not only utilize semiquantitative information effectively but also use more uncertain information and prevent the problem of combinatorial explosion. Moreover, it solves the problem of the uncertainty of expert knowledge and overcomes the problem of low modeling accuracy caused by insufficient data. Finally, a network security situation assessment case of the Industrial Internet is analyzed to verify the effectiveness and superiority of the method. The research results show that this method has strong applicability to the network security situation assessment of complex Industrial Internet systems. It can accurately reflect the actual network security situation of Industrial Internet systems and provide safe and reliable suggestions for network administrators to take timely countermeasures, thereby improving the risk monitoring and emergency response capabilities of the Industrial Internet.

Online Fault Diagnosis and Tolerance Based on Multiexpert Joint Belief Rule Base for Sensor Failures of Vehicles

As sensors readings are used for vehicle flight control, their reliability directly affects the flight performance. This paper develops a new fault diagnosis and tolerance method for sensor failures of vehicles by addressing three problems:unavailable faulty data, difficulty in establishing analytical system, and inconsistence of expert cognitive ability. For the purpose, a new belief rule base model with multi-expert joint (BRB-ME) is proposed. The first two problems are handled by combining the small size of observation data and the uncertain knowledge from multiple experts in BRB-ME. For the third problem, a new multi-expert joint strategy is proposed in the BRB-ME model. The experts first construct their own models, and then the models are fused with different weights according to the experts’ ability, such as research fields, the working time and etc. Then, a new fault diagnosis and tolerance framework is developed based on BRB-ME for detecting vehicles’ sensor failures, where the sensor failures are tolerated by the reconstruction strategy for faulty sensor output. Moreover, in order to address the influence of the uncertain expert knowledge, an optimization model is constructed for obtaining the optimal solutions for the framework. An experimental illustration is conducted for accelerometer failure. The diagnosis accuracy is 97.50%, and the developed framework can ensure the navigation accuracy of the vehicle under accelerometer failure.

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 Fault Diagnosis Method Based on Belief Rule Base With Attribute Reliability Considering Multi-Fault Features

A New Fault Diagnosis Method Based on Belief Rule Base With Attribute Reliability Considering Multi-Fault Features

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 assessment model 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.

Safety-Oriented Credibility-Based Fuzzy Incremental Learning for Predicting Dependent Outputs

Guaranteeing the safety of nearby buildings is essential in tunnel construction. In practice, it is implemented by closely monitoring the daily and accumulated settlements, which are dependent outputs. To accurately predict such outputs, a new approach using two features is proposed. First, a new concept of data credibility is proposed to represent the different levels of consistency among the multiple dependent outputs. Second, the training dataset is developed using data gathered from multiple phases based on the fuzzy number. The new approach is named credibility-based fuzzy incremental learning approach using the belief rule base (BRB), CI-BRB. The key contributions of the proposed CI-BRB approach are: 1) data credibility is defined and calculated rather than blindly assuming all data are accurate by default and 2) the training dataset is more representative as it includes both the current phase and more prior phases. Subsequently, a numerical case with three dependent outputs is designed to provide a detailed illustration, and a practical case is studied in a more comprehensive fashion. The case study results show that the proposed approach can produce superior results for modeling that adopts a none strategy. Additionally, further investigations validate the effectiveness of the strategy over incremental learning.