An analysis on parameter optimisation for a belief rules-based classification system

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

In engineering practice, to ensure the safety of complex engineering systems, the life prediction has attracted an increasing attention. In previous studies, few effective methods can be used to establish the life prediction model of a type of systems that have the following features: (1) the storage lives are much longer than the working lives, (2) lots of quantitative testing data are not available, (3) some expert knowledge can be used, and (4) the system’s performance degradation cannot be observed directly. As such, a life prediction method is constructed on the basis of belief rule base (BRB) and the accelerated degradation test, where two BRBs are involved, expressed by BRB_1 and BRB_2 respectively. Moreover, BRB_1 is employed to describe the relevance between the external stress and the hidden working state. BRB_2 is applied to establish the forecasting model of hidden working states. Once the predicted hidden working state achieves the boundary line, the corresponding working time is the life of the equipment and some measures need to be taken to maintain or change the equipment. Some uncertain parameters exist in the prediction model which can be determined by experts and it can lead to the inaccuracy of the model. Thus, an algorithm is proposed for updating parameters based on the maximum likelihood (ML). An experiment of the life prediction for aerospace relay is used to prove the reasonability of the life prediction model.KeywordsBelief rule base (BRB)Life predictionAccelerated degradation test

The combinatorial explosion problem is a great challenge for belief rule base (BRB) when a complex system has overnumbered attributes and/or referenced values for the attributes. This is because the BRB is conventionally constructed under the conjunctive assumption, conjunctive BRB, which requires covering each possible combination of all referenced values for all attributes. To solve this challenge, this study proposes a generic modeling, inferencing, and optimization approach for BRB under the disjunctive assumption, disjunctive BRB, that can significantly reduce its size. First, a disjunctive BRB is defined based on the mathematical description of the BRB space. The minimum size requirement for a disjunctive BRB is also discussed in comparison to a conjunctive one. Building on this, the generic disjunctive BRB modeling and inferencing procedures are proposed. Furthermore, an improved optimization model with further relaxed restrictions is constructed, and an optimization algorithm is developed in which only the new rule is optimized and its referenced values range is determined by the optimal solution in the former round optimization. The new optimization algorithm is more efficient with fewer variables and a more concise solution space. The results of three case studies confirm that by integrating both experts' knowledge and historic data, the modeling and inferencing processes can be well understood. Moreover, optimization can further improve the modeling accuracy while it facilitates downsizing the BRB in comparison with previous studies and other approaches.

A new aeronautical relay health state assessment method based on generic belief rule base with attribute reliability

Data-driven Extraction Method of Belief Rule for Reagent Addition in Antimony Rougher Flotation

Online updating belief rule based system for pipeline leak detection under expert intervention

Running gear, which is one of crucial element of high-speed train, is vital to security and dependability of the whole high-speed train. For the sake of guaranteeing normal running of running gear, it is very necessary to accurately estimate the health state of running gear. Consequently, this thesis presents a novel state evaluation model based on belief rule base (BRB). Considering the problem of combinatorial explosion in BRB. In the proposed evaluation model based on BRB and canonical correlation analysis (CCA), which is used to select core attributes by calculating the correlation between features. The results demonstrate that the model based on BRB and CCA can exactly estimate the health state of running gear.

Health state prediction is an effective way to improve the reliability for sensors. In the process of sensor degradation, it is difficult to obtain more effective monitoring data. And in the classification of health states, how to identify the adjacent state is also a problem. This paper proposed a health state prediction model based on belief rule base (BRB) and membership function (MF), which is called BRB-MF. In the model, BRB can make full use of expert knowledge and poor effective data. In the prediction results of BRB, it may be not completely logical or not entirely appropriate facing adjacent states of sensor. In order to solve the problem, MF is used to continue the analysis of the predicted results of BRB. In the BRB-MF model, the covariance matrix adaptation evolutionary strategies (CMA-ES) optimization algorithm is used to update the model parameters to make up for the uncertainty of expert knowledge. In the end, the brightness sensor of the rail vehicle LED lighting system is taken as a case study. The results show that the BRB-MF model can predict the health state of sensor with a high accuracy and a reasonable state.

Iterative learning belief rule-base inference methodology using evidential reasoning for delayed coking unit

Evaluation of user satisfaction using evidential reasoning-based methodology

When making maintenance decisions for diesel engines, the safety assessment plays a crucial role. Belief rule base (BRB) is a rule-based model embedded in expert knowledge with the advantage of being interpretable. However, due to the complexity of diesel engine systems and the impact of potential failures, their safety assessment faces the following challenges: (1) The interpretability of BRBs is often weakened during the building and optimization process. (2) Existing BRB models for safety assessment lack effective interpretability quantification methods. To address the above challenges, a diesel engine safety assessment method based on an interpretable BRB with the metric is proposed in this paper. First, an interpretability metric method for the interpretable BRB model for diesel engine safety assessment is proposed to quantify the interpretability of the entire modeling process. Second, a new statistical-based method for calculating the credibility of expert knowledge is proposed. Third, on the basis of these, three new interpretability maintenance strategies are designed to correct behaviors that destroy the interpretability of the model. The validity of the proposed model is verified through a case study of the safety assessment of a WD615 diesel engine.

Correlation-oriented complex system structural risk assessment using Copula and belief rule base

A framework for modelling the safety of an engineering system using a fuzzy rule-based evidential reasoning (FURBER) approach has been recently proposed, where a fuzzy rule-base designed on the basis of a belief structure (called a belief rule base) forms a basis in the inference mechanism of FURBER. However, it is difficult to accurately determine the parameters of a fuzzy belief rule base (FBRB) entirely subjectively, in particular for complex systems. As such, there is a need to develop a supporting mechanism that can be used to train in a locally optimal way a FBRB initially built using expert knowledge. In this paper, the methods for self-tuning a FBRB for engineering system safety analysis are investigated on the basis of a previous study. The method consists of a number of single and multiple objective nonlinear optimization models. The above framework is applied to model the system safety of a marine engineering system and the case study is used to demonstrate how the methods can be implemented.

Health status assessment is crucial for ensuring the reliability and safety of complex systems. Belief rule bases (BRBs) are widely used in complex system modeling because of it advanced causal reasoning capabilities. However, traditional BRB-based assessment models often rely on fixed triangular membership functions (MFs), which limit their flexibility and inference performance. Thus, a new adaptive interval type II belief rule base (AII-BRB) is proposed. Firstly, a shape coefficient of the MF is defined, which can effectively adjust its shape according to the observed measurement data. Based on this, an adaptive interval Type II MF is constructed. Thus, the reasoning process of the BRB model changes from quantitative value reasoning to interval probability reasoning. Furthermore, the basic performance of the AII-BRB is explored to illustrate its rationality. AII-BRB model not only provides point estimate of the health status, but also provides the interval range of health status. Finally, the health status assessments of spacecraft flywheel systems and lithium batteries are used as case studies to validate the effectiveness of the AII-BRB method.

Fault diagnosis is crucial for complex system health management. The intelligent fault diagnosis model based on belief rule bases (BRB) effectively handles small sample data and uncertain information. However, due to the limitations of expert knowledge, simply utilizing this knowledge to construct initial rules may not fully capture the highly nonlinear relationships between inputs and outputs in complex systems, resulting in reduced model accuracy. While optimization algorithms can dynamically adjust the parameters and structure of the rule base to improve model accuracy, the iterative process of seeking an optimal solution can inevitably compromise the model's interpretability. To address the aforementioned issues, a fault diagnosis model based on interpretable BRB with fault tree analysis (FTA) has been proposed. In this model, initial rules are constructed through a structured representation of fault relationships using FTA. Additionally, interpretability constraints are introduced during optimization to limit the range of parameters, ensuring that the optimization results align with real-world situations. A case study on a CNC milling machine was conducted to validate the proposed method. The results indicate that the model identifies fault states in complex systems more effectively and accurately than existing models, maintaining a balance between accuracy and interpretability throughout the diagnosis process.