Belief Rule Base Research Articles

A novel motor fault diagnosis method based on principal component analysis (PCA) with a discrete belief rule base (DBRB) system

Motor vibration signal data sets are characteristically random and nonlinear, and its features are difficult to extract for fault identification. To reduce the uncertainty of fault diagnosis, a method based on principal component analysis (PCA) and discrete belief rule base (DBRB) was developed for the first time. Initially, the vibration signal was first denoised using a wavelet threshold algorithm to eliminate interference. Second, overlapping signals were segmented into 15 time windows and a total of 13 typical time domain features and mathematical statistical features were extracted. Third, the dimensions of the features were reduced to three principal components by PCA and were taken as the antecedent attributes of the DBRB. However, the amount of information in each principal component is different, so the variance contribution rate was taken as an antecedent attribute weight to restore the original data characteristics. Fourth, a PCA-DBRB model was established, which effectively avoided the combinatorial explosion problem of rule base in the DBRB model. In addition, to obtain appropriate reference values, the k-means algorithm was introduced to take the cluster centers as reference values. The method was then validated by collecting typical fault data from motor bench experiments. The results demonstrated that compared with other traditional classifiers, this approach is more effective and superior in classification performance and more accurate in diagnosing faults from motor vibration data.

A belief rule-base approach to the assessment and improvement of seismic resilience of high-speed railway station buildings

As an important part of the railway system and the key node in the railway transportation network, the railway station undertakes the critical task of realizing convenient passenger transfer and efficient mass transportation. Resilience assessment and improvement of complex communal buildings have recently received significant attention, however, the complexity of including components, spatial structure, and engineering facilities made it challenging to find an accepted framework to assess the resilience of high-speed railway (HSR) stations. To overcome this challenge, the included subsystems for various operations of HSR stations are sorted out in detail, and the hierarchical belief rule-base (BRB) is adopted to establish the quantitative relationship between station function and each subsystem at different states after an earthquake through statistical analysis, expert knowledge, and logic analysis. Subsequently, optimization of the initial parameters in BRB is performed as a demonstration in case users need a more accurate BRB based on their experience and statistics. Finally, three subsystems repair sequential solving methods to improve the seismic resilience of HSR stations are proposed and discussed: the traversal algorithm, sensitivity-based method, and simulated annealing (SA) algorithm. The method proposed in this study paves the way for research on the resilience assessment of HSR station buildings.

Fault-tolerant control based on belief rule base expert system for multiple sensors concurrent failure in liquid launch vehicle

Fault-tolerant control based on belief rule base expert system for multiple sensors concurrent failure in liquid launch vehicle

Online health assessment method based on belief rule base with sliding time window considering input correlation and redundancy

This paper develops a new health assessment method based on belief rule base with sliding time window considering correlation and redundancy of input information (BRB-WCR). The new proposed method aims to solve four problems in health assessment of dynamic complex system: lack of system fault data, uncertainty of expert knowledge, correlation of characteristic and high real-time requirement of system. The traditional BRB model can address the first two problems while it assumes that the input characteristics are completely independent. In order to solve the two remaining problems, a new BRB-WCR model is developed, where the correlation and redundancy of characteristics are considered and the sliding time window for online training data is introduced to improve the real time performance of the model. Moreover, to address the uncertainty of expert knowledge, a new optimization model is developed to train the parameters of the BRB-WCR model. To illustrate the effectiveness of the developed method, a case study of inertial navigation platform is conducted.

A New Topology-Switching Strategy for Fault Diagnosis of Multi-Agent Systems Based on Belief Rule Base.

Effective fault-diagnosis strategies have been the focus of research on multi-agent systems (MASs). In this paper, the belief rule base (BRB)-based distributed fault-diagnosis problem for MASs is investigated, and a topology-switching strategy is developed to increase the reliability of fault-diagnosis model. Firstly, a BRB-based distributed fault-diagnosis model is constructed for the MAS with multiple faults, then expert knowledge is used to judge whether the agent is faulty. Then, considering that the system may be influenced by the fault or some other factors and thus leading to a decrease in the accuracy of the fault-diagnosis results, a topology-switching strategy based on the average distance of the output diagnosis accuracy is proposed to update the topology of the agent so that the fault-diagnosis results can be more reliable. Note that the topology-switching threshold is designed based on the average distance between the accuracy of the fault diagnosis of each agent. The method proposed in this paper can solve the problem when the fault-diagnosis accuracy of the model is affected by some common factors and thus decreases, and can improve the reliability of the fault-diagnosis model very well. Finally, the effectiveness of the BRB-based distributed fault-diagnosis model and the proposed topology-switching strategy to improve the fault-diagnosis accuracy is verified by simulation examples.

A Data-Driven Method Using BRB With Data Reliability and Expert Knowledge for Complex Systems Modeling

The reliability of data is important for complex systems modeling. However, it remains to be a great challenge mainly due to the lack of effective measurement of data reliability. On the condition that there exist the actual result and gold standard in a piece of data simultaneously, a data-driven method is proposed using the belief rule base (BRB) with data reliability and expert knowledge. In the proposed method, gold standards are used to indicate the degree to which the actual results are correct and, thus, the reliability of each piece of data is defined as the similarity between its actual result and the corresponding gold standard. According to the reliability of each piece of data, the training dataset is divided into multiple clusters. Each cluster of data is separately used to construct and optimize a BRB model. The weight and reliability of each model are then calculated using the data in the respective cluster with the consideration of the reliabilities of the data. Finally, the estimated results of the models are integrated using the evidential reasoning rule to generate the integrated results. The proposed method is applied to help radiologists diagnose thyroid nodules, in which historical examination reports are collected from a tertiary hospital located in Hefei, Anhui, China. Its superior performance is verified by experiments.

BRN: A belief rule network model for the health evaluation of complex systems

A belief rule base (BRB) expert system provides a generic inference framework for approximating the complicated nonlinear relationships between inputs and outputs. Such systems have been widely applied in the system health management community. However, limited by the method of construction rules, existing methods encounter the combinatorial explosion problem in the modeling of complex systems. Thus, determining how to effectively use the collected signals, system mechanism, and expert knowledge to realize the health evaluation of complex systems has become a key issue limiting the development of BRB systems. To solve this problem, a modified micro belief rule structure is proposed, and a new belief rule network (BRN) model is developed. Then, the cautious conjunctive rule is introduced to realize the fusion and reasoning of the nonindependent nodes in the BRN. In addition, the structure and parameter learning strategies of the proposed BRN are given, thereby providing a systemic mechanism to enhance the capability of the BRN when both expert knowledge and observed data are available. The effectiveness of the BRN model is verified in an aerospace relay experiment.

A wireless sensor network node fault diagnosis model based on belief rule base with power set

Wireless sensor network (WSN) is inevitably subject to node failures due to their harsh operating environments and extra-long working hours. In order to ensure reliable and correct data collection, WSN node fault diagnosis is necessary. Fault diagnosis of sensor nodes usually requires the extraction of data features from the original collected data. However, the data features of different types of faults sometimes have similarities, making it difficult to distinguish and represent the types of faults in the diagnosis results, these indistinguishable types of faults are called ambiguous information. Therefore, a belief rule base with power set (PBRB) fault diagnosis method is proposed. In this method, the power set identification framework is used to represent the fuzzy information, the evidential reasoning (ER) method is used as the reasoning process, and the projection covariance matrix adaptive evolution strategy (P-CMA-ES) is used as the parameter optimization algorithm. The results of the case study show that PBRB method has higher accuracy and better stability compared to other commonly used fault diagnosis methods. According to the research results, PBRB can not only represent the fault types that are difficult to distinguish, but also has the advantage of small sample training. This makes the model obtain high fault diagnosis accuracy and stability.

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.

Transparent Digital Twin for Output Control Using Belief Rule Base.

A transparent digital twin (DT) is designed for output control using the belief rule base (BRB), namely, DT-BRB. The goal of the transparent DT-BRB is not only to model the complex relationships between the system inputs and output but also to conduct output control by identifying and optimizing the key parameters in the model inputs. The proposed DT-BRB approach is composed of three major steps. First, BRB is adopted to model the relationships between the inputs and output of the physical system. Second, an analytical procedure is proposed to identify only the key parameters in the system inputs with the highest contribution to the output. Being consistent with the inferencing, integration, and unification procedures of BRB, there are also three parts in the contribution calculation in this step. Finally, the data-driven optimization is performed to control the system output. A practical case study on the Wuhan Metro System is conducted for reducing the building tilt rate (BTR) in tunnel construction. By comparing the results following different standards, the 80% contribution standard is proved to have the highest marginal contribution that identifies only 43.5% parameters as the key parameters but can reduce the BTR by 73.73%. Moreover, it is also observed that the proposed DT-BRB approach is so effective that iterative optimizations are not necessarily needed.

Novel Intelligent Approach for the Early Warning of Rainfall-Type Landslides Based on the BRB Model

This work attempts to apply belief rule-based (BRB) model in information fusion method to landslides, to improve the accuracy and efficiency for early warning of landslides. Taking a typical rainfall-type landslide as the experimental area, the monitoring results find that the surface displacement is the most sensitive monitoring data. It is determined that the monitoring data of surface displacement change rate and rainfall intensity could be used as the input parameter of the BRB model. An initial BRB model is established by setting up the rule base for discriminating warning levels. The data from three monitoring points are collected for the optimization of the initial BRB model, and verification of the optimized BRB models. Results shows the optimized BRB model can accurately describe the nonlinear relationship between the selected monitoring data and the warning level, which provides an intelligent method for landslide prevention and has a strong application prospect.

A new belief rule base inference methodology with interval information based on the interval evidential reasoning algorithm

A new belief rule base inference methodology with interval information based on the interval evidential reasoning algorithm

Two-Step Optimal-Setting Control for Reagent Addition in Froth Flotation Based on Belief Rule Base

Reagent addition is an important operation in the froth flotation process. In most plants, it is manually regulated according to the operator’s experience, by observing the surface features of the froth. Due to the drawbacks of manual operation, large fluctuations in the process are common, resulting in unexpected process indexes. Thus, we investigated the relationship between reagent addition, feed conditions (including ore properties, slurry density, and slurry flow rate), and froth image features based on the mechanism of froth flotation and production technology of gold-antimony flotation. Then, we proposed a two-step optimal-setting control strategy for reagent addition, which included a basic dosage pre-setting model and a feedback reagent addition compensation model. According to operating conditions and ore properties, the pre-setting model was developed using a belief rule base (BRB) method based on an evidential reasoning approach (RIMER), which could effectively address the uncertainties of operator experience and historical data. The model parameters of the BRB were then optimized using a state transition algorithm (STA). In terms of the offsets of the froth image features, the feedback compensation model using rule-based reasoning (RBR) was built. Simulation results using a STA-optimized BRB, GA-optimized BRB, least squares support vector machine (LSSVM), and artificial neural network (ANN) were compared. Finally, industrial test results confirmed that the reagent addition system based on the proposed method could satisfy the requirements for automatic reagent addition in an industrial production environment. This is of great significance for improving the production efficiency of flotation plants.

Data-Driven Thyroid Nodule Diagnosis Using Belief Rule Base.

Doctors’ diagnosis preferences are different, which makes them adopt different assumptions in medical decision making. Taking the diagnosis of thyroid nodules as an example, this study compares three assumptions, namely deletion, imputation based on the distribution (distribution), and benign by default (benign). For deletion, which is the most used assumption, the clinical reports with missing features would be deleted. For distribution, the missing features would be replaced with a distribution of features with respective probabilities. Besides the two assumptions, certain doctors have also stated that they leave benign features unrecorded because they think that such benign features are irrelevant to the final diagnosis. Under the benign assumption, the missing features would be replaced with benign features. The three assumptions are tested comparatively. Moreover, the belief rule base (BRB) is used to construct the diagnostic model under the three assumptions since it is essentially a white-box approach that can provide good interpretability and direct access to doctors and patients. A total of 3766 clinical reports on thyroid nodule diagnosis were collected from ten radiologists over a seven-year period. Case study results validate that the benign by default assumption has produced the optimal results, although different doctors could present varied tendencies towards different assumptions. Guidance and suggestions for doctors’ practical work have been made based on the study results to improve work efficiency and diagnostic accuracy.

A Unified BRB-Based Framework for Real-Time Health Status Prediction in High-Speed Trains

The health status of the running gear in high-speed trains changes dynamically with time in a complete life cycle. Running gear systems composed of many coupled components are complex, and health statuses of which are difficult to predict in real time through a traditional health status prediction scheme. Lately, belief rule base (BRB), which is able to combine quantitative information and expert knowledge, has shown excellent expression in modeling complex systems. In the procedure of health status prediction, expert expertise can sufficiently enhance the accuracy and efficiency of this model. Therefore, this paper puts forwards a real-time health status prediction framework based on a multi-layer BRB with priority scheduling strategies for running gears. In the first-layer BRB, a time-series prediction model of multiple module BRB considering complete features is established. In the second-layer model, grey relation analysis (GRA) is employed in priority scheduling strategies of features. The third-layer BRB is used for assessing the health status of running gears by combining the features. In addition, the initial parameters of all module BRB given by experts may not be precise. Accordingly, the initial parameters in the BRB are updated by the recursive algorithm online. Finally, the proposed method is tested on the testing platform in running gears. The results make it clear the proposed method can predict the health status of running gears with much accuracy in real time.

A new unmanned aerial vehicle intrusion detection method based on belief rule base with evidential reasoning

With the growing security demands in the public, civil and military fields, unmanned aerial vehicle (UAV) intrusion detection has attracted increasing attention. In view of the shortcomings of the current UAV intrusion detection model using Wi-Fi data traffic in terms of detection accuracy, sample size reduction, and model interpretability, this paper proposes a new detection algorithm for UAV intrusion. This paper presents an interpretable intrusion detection model for UAVs based on the belief rule base (BRB). BRB can effectively use various types of information to establish any nonlinear relationship between the model input and output. It can model and simulate any nonlinear model and optimize the model parameters. However, the rule combination explosion problem is encountered in BRB if there are too many attributes. Therefore, an evidential reasoning (ER) algorithm is proposed for solving this problem. By combining the capabilities of the ER and the BRB methodologies, a new evaluation model, named the EBRB-based model, is proposed here for predicting UAV intrusion detection, even in the case of a massive number of attributes. The global optimization of the model is ensured. A new interpretable and globally optimized UAV intrusion detection model is proposed, which is the main contribution of this paper. An experimental case is used to demonstrate the implementation and application of the proposed UAV intrusion detection method.

A New Multilayer Belief Rule Base Model for Complex System Modeling

Belief rule base (BRB) model suffers from the rule explosion problem when it is applied in modeling complex systems. The rule explosion problem makes it difficult to establish and optimize the BRB model effectively. Aiming at this problem, a new multilayer BRB (MLBRB) model is proposed, which consists of the extracting block and the processing block. In the extracting block, the inputs are first divided into two groups, and then each group is used to construct a hierarchical BRB model. The outputs of extracting block are treated as the inputs of the processing block. To obtain the optimal MLBRB, the layerwise learning strategy and the layer adaptive growth strategy are proposed to optimize these two blocks, respectively. A case study for the safety assessment of the liquefied natural gas storage tank is conducted to verify the effectiveness of the proposed method.

A novel data-driven decision model based on extended belief rule base to predict China's carbon emissions.

Global warming and climate change are gaining traction in recent years. As a major cause of global warming, carbon emissions were centered to China's climate change policy initiatives. Nevertheless, the existing policy discourse has yet reached a consensus on the optimal modeling method for carbon emissions prediction that is well-informed of both policy goals and the time-series pattern of carbon emissions. This paper fills the gap by promoting a novel data-driven decision model for carbon emissions prediction that is based on the extended belief rule base (EBRB) inference model. The new decision model consists of three components: 1) an indicator integration method, which aims to generate a few group indicators from a large number of statistical indicators; 2) a new EBRB construction method, which aims to consider the management policy goals for constructing EBRB; 3) a new ER-based inference method, which aims to predict carbon emissions based on time series change of relevant factors. The effectiveness of the proposed decision model has been tested against carbon emissions management data from 30 provinces in China. Experimental results demonstrate that the model will offer powerful reference value in the policy decision-making process, which will help to meet policy requirements for carbon emissions.

Deep belief rule based photovoltaic power forecasting method with interpretability

Accurate prediction of photovoltaic (PV) output power is of great significance for reasonable scheduling and development management of power grids. In PV power generation prediction system, there are two problems: the uncertainty of PV power generation and the inexplicability of the prediction result. The belief rule base (BRB) is a rule-based modeling method and can deal with uncertain information. Moreover, the modeling process of BRB has a certain degree of interpretability. However, rule explosion and the inexplicability of the optimized model limit the modeling ability of BRB in complex systems. Thus, a PV output power prediction model is proposed based on a deep belief rule base with interpretability (DBRB-I). In the DBRB-I model, the deep BRB structure is constructed to solve the rule explosion problem, and inefficient rules are simplified by a sensitivity analysis of the rules, which reduces the complexity of the model. Moreover, to ensure that the interpretability of the model is not destroyed, a new optimization method based on the projection covariance matrix adaptation evolution strategy (P-CMA-ES) algorithm is designed. Finally, a case study of the prediction of PV output power is conducted to illustrate the effectiveness of the proposed method.

Generative knowledge-based transfer learning for few-shot health condition estimation

In the field of high-end manufacturing, it is valuable to study few-shot health condition estimation. Although transfer learning and other methods have effectively improved the ability of few-shot learning, they still cannot solve the lack of prior knowledge. In this paper, by combining data enhancement, knowledge reasoning, and transfer learning, a generative knowledge-based transfer learning model is proposed to achieve few-shot health condition estimation. First, with the effectiveness of data enhancement on machine learning, a novel batch monotonic generative adversarial network (BM-GAN) is designed for few-shot health condition data generation, which can solve the problem of insufficient data and generate simulated training data. Second, a generative knowledge-based transfer learning model is proposed with the performance advantages of the belief rule base (BRB) method on few-shot learning, which combines expert knowledge and simulated training data to obtain a generalized BRB model and then fine-tunes the generalized model with real data to obtain a dedicated BRB model. Third, through uniform sampling of NASA lithium battery data and simulating few-shot conditions, the generative transfer-belief rule base (GT-BRB) method proposed in this paper is verified to be feasible for few-shot health condition estimation and improves the estimation accuracy of the BRB method by approximately 17.3%.