Evidential Reasoning Rule Research Articles

A Security Posture Assessment of Industrial Control Systems Based on Evidential Reasoning and Belief Rule Base

With the rapid advancements in information technology and industrialization, the sustainability of industrial production has garnered significant attention. Industrial control systems (ICS), which encompass various facets of industrial production, are deeply integrated with the Internet, resulting in enhanced efficiency and quality. However, this integration also introduces challenges to the continuous operation of industrial processes. This paper presents a novel security assessment model for ICS, which is based on evidence-based reasoning and a library of belief rules. The model consolidates diverse information within ICS, enhancing the accuracy of assessments while addressing challenges such as uncertainty in ICS data. The proposed model employs evidential reasoning (ER) to fuse various influencing factors and derive security assessment values. Subsequently, a belief rule base is used to construct an assessment framework, grounded in expert-defined initial parameters. To mitigate the potential unreliability of expert knowledge, the chaotic mapping adaptive whale optimization algorithm is incorporated to enhance the model’s accuracy in assessing the security posture of industrial control networks. Finally, the model’s effectiveness in security assessment was validated through experimental results. Comparative analysis with other assessment models demonstrates that the proposed model exhibits superior performance in ICS security assessment.

A Performance degradation assessment method for complex electromechanical systems based on adaptive evidential reasoning rule

A Performance degradation assessment method for complex electromechanical systems based on adaptive evidential reasoning rule

Evidential reasoning rule with dynamic reliability for performance assessment of wireless sensor network

The performance of wireless sensor network (WSN) continues to change over time, and it is required to track the WSN performance accurately. In this paper, a new assessment model known as the evidential reasoning rule with dynamic reliability (ERr-DR) is proposed. In the ERr-DR, the evidence reliability evolves from the traditional static value to a dynamic value, which can reveal the impact of external noise on network performance reasonably. As an effective extension of traditional ER rule, the ERr-DR has excellent modeling ability. Furthermore, by analysing the physical meanings of model parameters in detail, an optimization objective with targeted constraints is established. Compared with the existing optimization strategies, this not only improves the output accuracy of ERr-DR, but also maintains the interpretability of assessment results. Finally, A case study of a simulated WSN scenario validates the effectiveness of the proposed model.

Performance evaluation of complex systems based on hierarchical evidential reasoning rule considering disturbances

Performance evaluation of complex systems based on hierarchical evidential reasoning rule considering disturbances

A New Method for Oil-Immersed Transformers Fault Diagnosis Based on Evidential Reasoning Rule With Optimized Probabilistic Distributed

A New Method for Oil-Immersed Transformers Fault Diagnosis Based on Evidential Reasoning Rule With Optimized Probabilistic Distributed

Modeling, Optimization, and Robustness Analysis of Evidential Reasoning Rule Under Multidiscernment Framework

Modeling, Optimization, and Robustness Analysis of Evidential Reasoning Rule Under Multidiscernment Framework

A double inference engine belief rule base for oil pipeline leakage

Accurate prediction of oil pipeline leakage is important for energy security and environmental protection. The belief rule base (BRB) is a rule-based modeling approach that can make use of information with uncertainty to describe causal relationships in predicting oil pipeline leaks. Due to the complexity and uncertainty of oil pipeline systems, traditional BRB models produce a large rule base, which reduces the modeling capability and interpretability of BRB. Therefore, this paper proposes a double inference engine BRB (BRB-DI) model. Compared with the traditional BRB models, the new model diminishes the number of the rules from 56 to 25, while maintaining the accuracy. In the BRB-DI model, firstly, rule reduction is used to reduce the complexity of the model by comprehensively analyzing the importance of rules. Secondly, to ensure the completeness of the model rule base, a double inference engine consisting of the evidence reasoning (ER) algorithm and ER rule is proposed, and a new reasoning computation process is designed. Finally, an optimization algorithm based on projection covariance matrix adaptation evolution strategy (P-CMA-ES) is proposed to prevent the diminishing interpretability of the optimized model. In order to verify the effectiveness of the proposed method, an oil pipeline leakage prediction problem is studied as a numerical example.

Asynchronous optimization approach for evidential reasoning rule-based classifier

Data classification is an important and challenging issue encountered in many practical applications. The classifier based on Evidential Reasoning Rule (ER Rule) can well handle the uncertainty in classification and obtain competitive accuracy. However, there are many parameters to be optimized, and the computation cost of the usually adopted optimization strategy is relatively high. This fact weakens the application advantage of ER Rule classifier. To address this challenge, an asynchronous optimization approach is proposed. In the original ER Rule classifier, feature referential values and evidence weights are optimized synchronously; while in the proposed method, these two types of parameters are optimized separately based on their essential impacts on the classification results. For the optimization of feature referential values, the objective function measures the quality of belief matrix, which is the critical strategy to improve the computational efficiency. Three types of feasible objective functions are constructed. After obtaining optimal referential values, evidence weights are optimized based on the actual classification effect, and the required iterations decrease. Various experiments on 14 publicly available datasets verify the computational efficiency and classification performance of the proposed method.

Quality classification of stored wheat based on evidence reasoning rule and stacking ensemble learning

Classification of stored wheat quality is extremely important for reducing wheat storage losses and ensuring food security. However, the limitations of conventional single models and the uncertainties in the decision-making process have brought great challenges to the quality classification of stored wheat. To solve this problem, an accurate classification model for stored wheat quality based on Evidence Reasoning rule and Stacking ensemble learning (ER-Stacking) is proposed. Firstly, the base learners of the ensemble model are selected by the fusion measurement method of diversity and classification performance. Then, the importance weight and reliability factor of the evidence are obtained by the Differential Evolution (DE) algorithm and probability distance similarity, respectively. Finally, the ER rule is used to fuse the evidences optimized by weight and reliability to complete the identification and classification of stored wheat quality. In order to verify the validity of the method, experiments are conducted using the structured data on physiological and biochemical indicators of stored wheat. The experimental results show that the ER-Stacking ensemble model achieves 88.1%, 88.05%, 89.31% and 88.4% in the accuracy, precision, recall and f1-score, respectively, whose classification performance is significantly higher than that of the conventional single models. Compared with the models using other integration methods or different combination strategies of base learners, the proposed model also has obvious advantages, which can effectively improve the accuracy and reliability of the classification results of stored wheat quality.

Inference, Optimization, and Analysis of an Evidential Reasoning Rule-Based Modeling Approach

The evidential reasoning (ER) rule, with its strict probabilistic reasoning and superior uncertainty handling ability, has been widely used in the evaluation, diagnosis, and decision-making. Recently, a modeling approach based on the ER rule that combines the evidence constituted by a single attribute (SA_ER) has gradually attracted scholars' attention due to its good scalability and flexibility. However, in the SA_ER, the frame of discernment (FoD) is composed of a series of singleton propositions and the universal set of these propositions. Since the SA_ER has a special form of evidence structure, its reflection on the system output is incomplete. The existing FoD is unable to quantify this incompleteness, which greatly limits the development of SA_ER. In this paper, an improved SA_ER approach that extends the FoD to the power set (PSA_ER) is proposed. Meanwhile, combined with the physical meaning of the model parameters, the expressions of evidence weight and reliability are deduced respectively. Then, an intelligent optimization algorithm is used to optimize partial parameters to enhance the performance of PSA_ER. Further, the basic properties of PSA_ER are analyzed in detail from the parameter level to promote its engineering application. Finally, an engineering example is intended to demonstrate the effectiveness of the proposed approach.

Likelihood Analysis of Imperfect Data

This article investigates how to make use of imperfect data gathered from different sources for inference and decision making. Based on Bayesian inference and the principle of likelihood, a likelihood analysis method is proposed for acquisition of evidence from imperfect data to enable likelihood inference within the framework of the evidential reasoning (ER). The nature of this inference process is underpinned by the new necessary and sufficient conditions that when a piece of evidence is acquired from a data source it should be represented as a normalized likelihood distribution to capture the essential evidential meanings of data. While the explanation of sufficiency of the conditions is straightforward based on the principle of likelihood, their necessity needs to be established by following the principle of Bayesian inference. It is also revealed that the inference process enabled by the ER rule under the new conditions constitutes a likelihood inference process, which becomes equivalent to Bayesian inference when there is no ambiguity in data and a prior distribution can be obtained as a piece of independent evidence. Two examples in decision analysis under uncertainty and a case study about fault diagnosis for railway track maintenance management are examined to demonstrate the steps of implementation and potential applications of the likelihood inference process.

Performance evaluation of non-repairable cyclic phased-mission systems using evidential reasoning rule and multi-valued decision diagrams

Phased-mission systems (PMS) often perform different missions that have multiple consecutive, non-overlapping phases. Many recent studies have focused on the reliability analysis for PMS. However, not much attention has been paid to the PMS performance evaluation and the phase cycle characteristic of PMS. In this paper, a performance evaluation method of non-repairable cyclic phased-mission systems (CPMS) is proposed. Considering the uncertainty caused by the change of phase duration and component performance degradation, the average duration of each phase and the fuzzy state probability vector of each component are obtained by the evidential reasoning rule (ER rule). Then, the multi-valued decision diagrams (MDD) manipulation rules suitable for cyclic phase conditions are proposed, and the component state composition path generation method based on cycle-end component states is developed. On the above basis, MDD models for CPMS (CPMS-MDD) in different states are established, and the system performance is evaluated by the continuous time Markov chains (CTMC). A phase duration adjustment strategy is further proposed based on the evaluation results. The effectiveness and correctness of the proposed method are verified by case studies on performance evaluation of satellite turntable system. Comparative study shows the concise and efficient of the proposed method.

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.

Evidential reasoning rule for environmental governance cost prediction with considering causal relationship and data reliability

Evidential reasoning rule for environmental governance cost prediction with considering causal relationship and data reliability

A New Evidential Reasoning Rule Considering Interval Uncertainty and Perturbation.

The evidential reasoning (ER) rule has been widely applied in the multiple attribute decision making (MADM), which makes the decision-making process transparent and credible by using a belief structure. To improve the ability of the ER rule in dealing with the interval uncertainty, a new interval ER (IER) rule is proposed in this article. The interval uncertainty is described as the interval grade in the new frame of discernment (FoD) to model the local ignorance. It is proved that the IER rule is a generalization of the ER rule. To study the influence of perturbation on the IER rule, the perturbation is first introduced to the belief structure, and the perturbation analysis (PA) is conducted for the IER rule. An optimization model is established to estimate the perturbation threshold, which can measure the effectiveness of the inference result under perturbation. Two numerical examples and a case study are carried out, respectively, to show the implementation process of the proposed IER rule and validate its effectiveness in different decision-making scenarios.

Health Status Evaluation of Welding Robots Based on the Evidential Reasoning Rule

It is extremely important to monitor the health status of welding robots for the safe and stable operation of a body-in-white (BIW) welding production line. In the actual production process, the robot degradation rate is slow and the effective data are poor, which can reflect a degradation state in the large amount of obtained monitoring data, which causes difficulties in health status evaluation. In order to realize the accurate evaluation of the health status of welding robots, this paper proposes a health status evaluation method based on the evidential reasoning (ER) rule, which reflects the health status of welding robots by using the running state data monitored in actual engineering and through the qualitative knowledge of experts, which makes up for the lack of effective data. In the ER rule evaluation model, the covariance matrix adaptive evolutionary strategy (CMA-ES) algorithm is used to optimize the initial parameters of the evaluation model, which improved the accuracy of health status evaluations. Finally, a BIW welding robot was taken as an example for verification. The results show that the proposed model is able to accurately estimate the health status of the welding robot by using the monitored degradation data.

An ensemble method with DenseNet and evidential reasoning rule for machinery fault diagnosis under imbalanced condition

Fault diagnosis is of significant importance for intelligent manufacturing as it can increase production efficiency and decrease the uncertain breakdown risk of machines. Previous studies have extensively utilized different types of shallow statistical features as well as deep representation features to comprehensively describe the fault information for achieving better performances of fault diagnosis. However, making full use of the combination of such shallow statistical features and deep representation features under the class-imbalance situation in real-world applications becomes a challenge in current research of fault diagnosis. To remedy the above issue, an Imbalanced Ensemble Method with DenseNet and Evidential Reasoning Rule, namely IEMD-ER, is proposed to incorporate both human experience and machine wisdom for machinery fault diagnosis under the class-imbalance situation. To this end, the shallow statistical features with human experience are extracted by several signal processing techniques, while the modified DenseNet is adopted to extract the deep representation features with machine wisdom. Based on these features, multiple diverse base classifiers are produced by leveraging the importance of different features. The outputs of each base classifier are adaptively fused using the Evidential Reasoning Rule as the final fault diagnosis results. Extensive experiments are conducted on the real-world bearing datasets collected by Paderborn University to validate the proposed method. The experimental results proved the superiority of the proposed IEMD-ER.

Fault diagnosis of marine electric thruster bearing based on fusing multi-sensor deep learning models

The data-driven fault diagnosis of bearings is important in the marine electric thruster. For avoiding information loss when manually extracting features and unreliable diagnosis by a single sensor, a novel method of fusing multi-sensor deep learning models is proposed. The improved one-dimensional convolution network (1DCNN) can adaptively extract features from single-sensor signals and use them for preliminary fault diagnosis at first. Then, the diagnosis results of different sensors are fused by the evidential reasoning (ER) rule. We found that the diagnosis accuracy at the training set size of 40 % is 99.4 %, which is better than four machine learning methods and ten state-of-the-art deep learning methods. Furthermore, at different noise levels (0–10 dB), the diagnostic accuracy is higher than 89 %, showing more robustness than single-sensor deep learning methods. Meanwhile, its suitability is further validated under different torque conditions.

A New Ensemble Learning Method for Multiple Fusion Weighted Evidential Reasoning Rule

Ensemble learning, as a kind of method to improve the generalization ability of classifiers, is often used to improve the model effect in the field of deep learning. However, the present ensemble learning methods mostly adopt voting fusion in combining strategies. This strategy has difficulty mining effective information from the classifiers and cannot effectively reflect the relationship between different classifiers. Ensemble learning based on the evidential inference rule (ER rule) can effectively excavate the internal relationships among different classifiers and has a certain interpretability. However, the ER rule depends on the weight distribution of different combination strategies, and the setting of the evidence weight will affect the accuracy and stability of the model. Therefore, this paper proposes a new ensemble learning method based on multiple fusion weighted evidential reasoning rules and constructs an ensemble learning framework for data fusion and decision mapping. This framework takes the evidence weight, confidence, and feature data of each classifier as input and the integration results as output. The weight of evidence was determined by multiple fusion weights of the entropy weight method and order relation method. Finally, the integrated learning process is set up by the ER algorithm. The method proposed in this paper is verified by multiple datasets. Experimental results show that the surface construction model has good performance, and the defects of single weighting instability are greatly improved under the premise of improving the integration effect.

On the evidential reasoning rule for dependent evidence combination

Evidential Reasoning (ER) rule, which can combine multiple pieces of independent evidence conjunctively, is widely applied in multiple attribute decision analysis. However, the assumption of independence among evidence is often not satisfied, resulting in ER rule inapplicable. In this paper, an Evidential Reasoning rule for Dependent Evidence combination (ERr-DE) is developed. Firstly, the aggregation sequence of multiple pieces of evidence is determined according to evidence reliability. On this basis, a calculation method of evidence Relative Total Dependence Coefficient (RTDC) is proposed using the distance correlation method. Secondly, as a discounting factor, RTDC is introduced into the ER rule framework, and the ERr-DE model is formulated. The aggregation process of two pieces of dependent evidence by ERr-DE is investigated, which is then generalized to aggregate multiple pieces of non-independent evidence. Thirdly, sensitivity analysis is carried out to investigate the relationship between the model output and the RTDC. The properties of sensitivity coefficient are explored and mathematically proofed. The conjunctive probabilistic reasoning process of ERr-DE and the properties of sensitivity coefficient are verified by two numerical examples respectively. Finally, the practical application of the ERr-DE is validated by a case study on the performance assessment of satellite turntable system.