Basic Probability Assignment Research Articles

Information fusion for large-scale multi-source data based on the Dempster-Shafer evidence theory

There exists many large-scale multi-source data, ranging from genetic information to medical records, and military intelligence. The inherent intricacies and uncertainties embedded within these data sources pose significant challenges to the process of information fusion. Owing to its exceptional capacity to represent data uncertainty, Dempster-Shafer (D-S) evidence theory has emerged as a widely utilized approach in information fusion. However, the evidence theory encounters three significant issues when applied to multi-source data information fusion: (1) the conversion of sample information into evidence and the construction of the basic probability assignment (BPA) function; (2) the resolution of conflicting evidence; and (3) the mitigation of exponential explosion in computation. Addressing the aforementioned challenges, this paper delves into the information fusion strategies for large-scale multi-source data based on Dempster-Shafer evidence theory. Initially, the concept of support matrix is introduced and the data matrix is transformed into a support matrix to address the construction challenges associated with BPA. Next, a method for addressing evidence conflicts is introduced by incorporating an additional data source composed of average values. Furthermore, a solution for mitigating high computational complexity is presented through the utilization of a hierarchical fusion approach. Finally, experimental results show that compared with other five advanced information fusion methods, our information method has improved the classification accuracy by 4.66% on average and reduced the time by 66.35% on average. Hence, our method is both efficient and effective, demonstrating exceptional performance in information fusion.

An algorithm for belief rule induction with partial ignorance

Belief rules are an extension of fuzzy rules that consider belief degrees. They are widely applied due to their traceability, interpretability, and flexibility. However, current belief rules only consider residual support and global ignorance while ignoring partial ignorance. In this paper, we proposed a novel belief rule-based classification system called partial ignorance belief rule induction algorithm (PIBRIA). The consequent part of belief rules takes into account not only the residual support and global ignorance but also partial ignorance of evidence. The belief degrees in the consequent part of each belief rule collectively form a genuine basic probability assignment (BPA). Based on fuzzy unordered rule induction algorithm (FURIA), we propose the learning algorithm for belief rules with partial ignorance, which helps the novel proposed PRIBIA achieve a balance between accuracy and complexity. The inference method employs the Dempster’s combination rule and Shafer’s discounting operation, where the discounting operation can resolve evidence conflicts in the combination rule. The effectiveness and superiority of PIBRIA in handling classification tasks have been validated by comparing it to some state-of-the-art rule-based models. The results of statistical tests show that PIBRIA outperforms all other methods in terms of classification accuracy. Whereas its computational complexity and model complexity are moderate.

A Tunnel Fire Detection Method Based on an Improved Dempster-Shafer Evidence Theory

Tunnel fires are generally detected using various sensors, including measuring temperature, CO concentration, and smoke concentration. To address the ambiguity and inconsistency in multi-sensor data, this paper proposes a tunnel fire detection method based on an improved Dempster-Shafer (DS) evidence theory for multi-sensor data fusion. To solve the problem of evidence conflict in the DS theory, a two-level multi-sensor data fusion framework is adopted. The first level of fusion involves feature fusion of the same type of sensor data, removing ambiguous data to obtain characteristic data, and calculating the basic probability assignment (BPA) function through the feature interval. The second-level fusion derives basic probability numbers from the BPA, calculates the degree of evidence conflict, normalizes the BPA to obtain the relative conflict degree, and optimizes the BPA using the trust coefficient. The classical DS evidence theory is then used to integrate and obtain the probability of tunnel fire occurrence. Different heat release rates, tunnel wind speeds, and fire locations are set, forming six fire scenarios. Sensor monitoring data under each simulation condition are extracted and fused using the improved DS evidence theory. The results show that there is a 67.5%, 83.5%, 76.8%, 83%, 79.6%, and 84.1% probability of detecting fire when it occurs, respectively, and identifies fire occurrence in approximately 2.4 s, an improvement from 64.7% to 70% over traditional methods. This demonstrates the feasibility and superiority of the proposed method, highlighting its significant importance in ensuring personnel safety.

A novel multi-source information fusion method for emergency spatial resilience assessment based on Dempster-Shafer theory

In the midst of today's intricate and ever-changing natural and social landscape, this study is committed to proposing a novel multi-source information fusion method for assessing the spatial resilience of urban emergency evacuation and rescue. Its overarching aim is to uncover latent challenges and contribute to the enhancement of a city's capacity to respond to emergencies. To achieve this, we have devised a comprehensive assessment indicator system, capable of not only quantifying a city's spatial resilience but also offering indispensable guidance for urban emergency evacuation and rescue spatial planning. Furthermore, we have introduced an innovative evaluation methodology framework. This framework includes the establishment of the basic probability assignment (BPA) model, a pioneering method for generating BPA for observed values, and the novel application of hierarchical weighting and fusion techniques. By extending the Dempster-Shafer theory, we have not only enhanced the method's ability to express and integrate uncertain information but also significantly improved the precision of the evaluation. Ultimately, we conducted a quantitative assessment using Shenzhen, China, as a case study, identifying existing issues and proposing highly-targeted improvement strategies. These research findings not only provide robust support for the augmentation of urban emergency capabilities in Shenzhen but also offer pioneering insights for the quantitative assessment and advancement of emergency spatial resilience in cities across the globe.

A wide area backup protection algorithm based on fault current comparison and evidence theory fusion

Abstract Wide-area backup protection using information in the area to determine the fault location comprehensively requires a high fault tolerance ability. However, the traditional wide area backup protection algorithm based on evidence theory assigns a separate value to each adjacent line for its fault probability, and the performance of the algorithm degrades in the condition of more information loss or errors. To solve these problems, this paper proposed a wide area backup protection algorithm based on fault current comparison and improved evidence theory fusion. The proposed method first selects the suspected fault lines by sequence voltage sorting. Then, the information on the fault current sequence component and traditional protection action is collected and preprocessed to form the evidence set, and its basic probability assignment is calculated. Finally, the improved evidence theory is used for fusion to identify fault lines. Simulation results show that the algorithm can accurately identify fault lines under complex operating conditions, multiple information loss and errors, and has high fault tolerance.

A new approximate belief mutual information derived from the developed fuzzy mutual information considering belief negation

The Dempster combination rule relies on fundamental assumption that evidences are mutually independent. However, this idealized prerequisite is frequently challenging to fulfill in real-world scenarios. How to measure belief mutual information to investigate dependence among evidence sources is a critical and significant issue. Inspired by fuzzy mutual information based on D–S evidence theory, a method of approximate belief mutual information (BMI) is developed to partially represent the dependence among the sources of evidence. In the BMI model, an interval correlation method considering the basic probability assignment (BPA) and its negation are proposed. Several examples are used to illustrate the availability of the BMI, which shows the developed BMI has better fault tolerance. Finally, the proposed method obtains higher recognition accuracy in pattern recognition tasks. The proposed method can maintain stable and reliable recognition results even when the data is disturbed, verifying the effectiveness of the proposed method.

Research on the Three-Level Integrated Environmental Evaluation Model for Multi-Greenhouse Potatoes

Aiming at the problems of large error and redundancy in the multi-node data acquisition of multi-greenhouse photo growth environmental information, a three-level fusion algorithm based on adaptive weighting, an LMBP network, and an improved D-S theory is proposed. The box-and-line graph method recognizes the original data and then replaces it based on the mean value method; the air temperature, humidity, and light intensity measurements are unbiased estimations of the true value to be estimated, so the first level of fusion chooses the adaptive weighted average algorithm to find the optimal weights of each sensor under the condition of minimizing the total mean-square error and obtains the optimal estimation of the weights of the homogeneous sensors of a greenhouse. The Levenberg–Marquardt algorithm was chosen for the second level of fusion to optimize the weight modification of the BP neural network, i.e., the LMBP network, and the three environmental factors corresponding to “suitable”, “uncertain” and “unsuitable” potato growth environments were trained for the three environmental factors in the reproductive periods. The output of the hidden layer was converted into probability by the Softmax function. The third level is based on the global fusion of evidence theory (also known as D-S theory), and the network output is used as evidence to obtain a consistent description of the multi-greenhouse potato cultivation environment and the overall scheduling of farming activities, which better solves the problem of the difficulty in obtaining basic probability assignments in the evidence theory; in the case of a conflict between the evidence, the BPA of the conflicting evidence is reallocated, i.e., the D-S theory is improved. Example validation shows that the total mean square error of the adaptive weighted fusion value is smaller than the variance of each sensor estimation, and sensors with lower variance are assigned lower weights, which makes the fusion result not have a large deviation due to the failure of individual sensors; when the fusion result of a greenhouse feature level is “unsuitable”, the fusion result of each data level is considered comprehensively, and the remote control agency makes a decision, which makes full use of the complementary nature of multi-sensor information resources and solves the problem of fusion of multi-source environmental information and the problem of combining conflicting environmental evaluation factors. Compared with the traditional D-S theory, the improved D-S theory reduces the probability of the “uncertainty” index in the fusion result again. The three-level fusion algorithm in this paper does not sacrifice data accuracy and greatly reduces the noise and redundancy of the original data, laying a foundation for big data analysis.

Ship collision risk assessment: A multi-criteria decision-making framework based on Dempster–Shafer evidence theory

Ship collision risk modelling is dominated by the utilization of the experts’ experiential insights and knowledge. To construct an effective assessment model for evaluating potential ship collision risks grounded in expert judgments, this paper introduces a novel multi-criteria decision-making framework based on Dempster–Shafer evidence theory (DSET). Firstly, a novel index-based assessment system is provided to generate the potential collision risk value of ships based on automatic identification system (AIS) data, which encompasses ship condition parameters, deviation coefficient, and frequency coefficient. Further, to generate the weights of these indicators, a framework to extract expert opinions is provided, which includes two parts: a) converting experts’ opinions into D-S framework through hesitant fuzzy linguistic terms and b) generating experts’ opinions using improved DSET. Regarding part a, a methodology is proposed to evaluate the trustworthiness of experts by considering both the level of uncertainty in their opinions and the degree of similarity between their viewpoints. Concerning part b, strategies are integrated to ascertain the most suitable weight for the basic probability assignment, thereby mitigating conflicts within the evidence. Finally, based on the collected AIS data, the proposed framework has been applied to six of the world's busiest waterways: (1) the Strait of Malacca, (2) the English Channel, (3) the Panama Canal, (4) the Suez Canal, (5) the Danish Straits, and (6) the Strait of Hormuz. Subsequently, comprehensive analytical results and recommendations are furnished, such as wide and smooth channels showing elevated risk.

A new distance measure between two basic probability assignments based on penalty coefficient

Uncertainty information processing is a challenging topic in information science. Dempster-Shafer evidence theory shows excellent performance when dealing with uncertainty in information representation, fusion, and processing. The measurement of the distance between the basic probability assignments (BPA) in Dempster-Shafer evidence theory is a powerful tool that deals with uncertainty in evidential information processing. Most of the existing methods are based on the difference in the assessment of evidential degree for different hypotheses, with a notable example Belief-Jensen-Shannon (BJS) divergence. However, these methods ignore the information that is carried by different units in the power sets that represent the hypotheses, i.e., the difference on the hypotheses themselves that include in the evidential degree assessment of different BPA should be considered in the distance measurement. Therefore, in this paper, a novel method grounded in BJS divergence and incorporating a penalty coefficient to rectify the distance between basic probability assignments is proposed. This methodology showcases commendable properties, including symmetry, boundedness, and adherence to the triangle inequality. To demonstrate the efficiency of the proposed distance measurement method between BPAs, we apply it to two common-used machine learning data sets: Iris data set and Dry Beans data set. Compared to the represented existing evidence distance measurement approaches, the proposed method yields superior performance in both data sets with respect to classification accuracy.

Distributed multi‐station target tracking based on unscented particle filter and Dempster‐Shafer theory

AbstractIn a distributed multi‐station system, the observations received by local radar nodes for a single target will have a large signal‐to‐noise ratio (SNR) bias due to inconsistent radar cross‐sections from distinct angles, different distances from the target, various local interference such as harsh weather, and dissimilar background noise. Integrating heterogeneous information in dynamic and uncertain environments can be challenging for the fusion centre. Moreover, the particles in the basic particle filter (PF) may degrade after many iterations, making it difficult to achieve accurate target state estimation in the local tracking process. To address these issues, the authors propose a novel method named DS‐UPF based on the Dempster–Shafer (DS) theory and the unscented particle filter (UPF). By updating the important density function, the UPF efficiently suppresses particle degradation. The weighted Basic Probability Assignments (BPAs) are proposed and integrated under the new synthesis formula. The weight‐modified DS method restrains the impact of significant local estimation errors on weighted BPAs fusion result, improving robustness without local interference prior knowledge. The experimental results demonstrate that the DS‐UPF outperforms the unscented Kalman filter, PF, and UPF in tracking tasks under various local interference. This indicates that the proposed algorithm can improve estimation precision in dynamic and uncertain environments.

A Three-Zone Identification Method for Coal Mine Area Based on DS Evidence Theory

As coal ore and other resources are continuously mined, a three-zone structure is formed underground consisting of a sagging zone, fault zone, and caving zone. The use of well-logging data to identify the three zones is important for production safety and environmental management. Owing to the scarcity of data that can reflect three zones in normal coal mining, conventional identification and prediction methods face challenges when extracting data features, incurring a degree of uncertainty within prediction results. Accordingly, the accurate identification of the three zones has become a critical objective in daily production. To address this issue, we developed a method called a method called backpropagation neural networks with Dempster–Shafer (DS) evidence theory. Initially, we preprocessed the training data and deployed two backpropagation neural networks (BPNNs) to predict the three zones according to two parameters. According to these prediction results, the local and global credibility of each prediction is calculated and used to obtain the basic probability assignment function required for the DS evidence theory. Finally, the DS evidence theory is used to fuse the two BPNNs prediction results, thereby producing the final prediction results. The proposed method was demonstrated to improve prediction accuracy by 6.4% compared to a conventional neural network.

A neural network copula function approach for solving joint basic probability assignment in structural reliability analysis

AbstractApplying evidence theory to structural reliability analysis under epistemic uncertainty, it is necessary to consider the correlation of evidence variables. Among them, solving the joint basic probability assignment (BPA) of the evidence variables is a crucial link. In this study, a solution method of joint BPA based on neural network copula function is proposed. This method is to automatically construct copula function through neural network, which avoids the process of selecting the optimal copula function. Firstly, the neural network copula function is constructed based on the sample set of evidence variables. Then, the expression for solving the joint BPA using the neural network copula function is derived through vectors. Furthermore, the expression is used to map the marginal BPA of evidence variables to joint BPA, thus realizing the solution of joint BPA. Finally, the effectiveness of this method is verified by three examples. The results show that the neural network copula function describes the data distribution better than the optimal copula function selected by the traditional method. In addition, there is actually an error in solving the reliability intervals using the traditional optimal copula function method, whereas the results of this paper's neural network copula function method are more accurate and better for decision making.

Rolling bearing fault diagnosis based on multi-source data fusion

In this paper, a fault diagnosis method is proposed based on multi-source data fusion to address the inaccurate results caused by single evidence used for decision-making. First, empirical mode decomposition is performed using sensor data to extract fault features, and a fault feature matrix and a diagnostic matrix are established. Then the deviation vector is defined to obtain the difference between the diagnostic sample and the fault sample, and then the basic probability assignment is obtained for each diagnostic sample. Finally, the Dempster combination rule is used for fusion. The effectiveness and accuracy of this method in fault diagnosis of rolling bearings have been verified through examples of rolling bearings.

Improved Evidence Fusion Theory for the Safety Assessment of Prestressed Concrete Bridges

The safety condition assessment of prestressed concrete bridges is currently subject to great uncertainty due to the subjectivity of data collection and data types. This study proposes an improved evidence fusion method, improving the conventional Dempster–Shafer fusion method to reduce assessment inaccuracies caused by data uncertainty. Firstly, the uncertain analytic hierarchy process was applied to construct a three-level safety assessment model for 15 different indicators with their initial weights. Secondly, the fuzzy matter element theory was proposed to obtain basic probability assignments required for the evidence fusion. Finally, an improved evidence fusion method was proposed based on the evidence credibility and preprocessing corrections for highly conflicting evidence. In this study, a prestressed concrete bridge in eastern China was used as a case study to perform a comprehensive safety assessment and verify the effectiveness and practicality of the proposed method. The assessment results demonstrate that the improved fusion method in this study can deal with conflicting evidence better than existing fusion methods. Compared with conventional fuzzy AHP method, it has greater sensitivity to certain indicators with severe damages, which prevents those indicators from being overshadowed by other well-performing ones in the overall assessment.

Belief Inaccuracy Information Measures and Their Extensions

This work introduces belief inaccuracy information (BII) and Jensen–belief inaccuracy information (JBII), grounded in the foundational concept of basic probability assignment. The significance of these novel methodologies lies in their potential to advance the field by providing valuable insights into belief accuracy assessment. The research not only establishes these measures but also highlights their relevance in addressing critical challenges within the realm of probability assignment. Further, some results associated with these proposed information measures were established. In addition, the BII and JBII measures were examined for escort and generalized escort of basic probability assignment functions, where an escort basic probability assignment with order [Formula: see text] is constructed based on the power [Formula: see text] of a baseline basic probability assignment with a normalizing constant. Finally, this paper presents compelling results derived from the application of BII and JBII measures. A detailed simulation of Conway’s game of life cellular automaton is described, showcasing the utility of these measures in analyzing belief inaccuracies within complex dynamic systems. Furthermore, an application to ozone time series is explored, employing belief Kullback–Leibler and belief chi-square divergences. This application specifically focuses on the study of station discrepancies, revealing the versatility of the proposed measures in addressing diverse scenarios.

Large-scale group hierarchical DEMATEL method with automatic consensus reaching

Decision-making trial and evaluation laboratory (DEMATEL) is widely used because of its ability to effectively analyze nonlinear relationships between factors in complex systems. With the increasing complexity of decision-making problems, large-scale group decision-making (LSGDM) has become the norm. Most existing DEMATEL methods are only suitable for small-scale groups and simple systems. This study, therefore, proposes a large-scale group hierarchical DEMATEL method that considers consensus reaching. The DEMATEL method for LSGDM faces three challenges: large differences in knowledge structures, difficulty coordinating expert opinions, and slow group-consensus convergence. To address these challenges, first, we use hierarchical decomposition to decompose the complex system into simple systems with different levels to reduce the difficulty of decision-making in complex systems. Second, considering the limitations of expert knowledge and experience, we use the basic probability assignment function to extract the opinions of experts at different levels of subsystems and factors. Third, we divide experts into different clusters using K-means clustering to solve the problem of difficult expert-opinion coordination. Fourth, we design two types of consensuses (intrasubgroup and intersubgroup consensus) and an efficient new type of opinion autocorrection mechanism to solve the problem of the slow convergence of intragroup consensus and improve the efficiency of consensus reaching. Finally, we demonstrate the superiority of the proposed method through data analysis and method comparison.

Air pollution concentration fuzzy evaluation based on evidence theory and the K-nearest neighbor algorithm

Background: Air pollution, characterized by complex spatiotemporal dynamics and inherent uncertainty, poses significant challenges in accurate air quality prediction, and current methodologies often fail to adequately address these complexities.Objective: This study presents a novel fuzzy modeling approach for estimating air pollution concentrations.Methods: This fuzzy evaluation method integrates an improved evidence theory with comprehensive weighting and the K-nearest neighbor (KNN) interval distance within the framework of the matter-element extension model. This involves generating the basic probability assignment (BPA) based on interval similarity, performing sequential fusion using the Dempster–Shafer evidence theory, enhancing the fusion results via comprehensive weighting, and conducting fuzzy evaluation of air pollution concentrations using the matter-element extension KNN interval distance.Results: Our method achieved significant improvements in monitoring air pollution concentrations, incorporating spatiotemporal factors and pollutant concentrations more effectively than existing methods. Implementing sequential fusion and subjective–objective weighting reduced the error rate by 38% relative to alternative methods.Discussion: Fusion of multi-source air pollution data via this method effectively mitigates inherent uncertainty and enhances the accuracy of the KNN method. It produces more comprehensive air pollution concentration fusion results, improving accuracy by considering spatiotemporal correlation, toxicity, and pollution levels. Compared to traditional air-quality indices, our approach achieves greater accuracy and better interpretability, making it possible to develop more effective air quality management strategies. Future research should focus on expanding the dataset to include more diverse geographical and meteorological conditions, further refining the model to integrate external factors like meteorological data and regional industrial activity, and improving computational efficiency for real-time applications.

Phase prediction of high-entropy alloys based on machine learning and an improved information fusion approach

The phase design of high entropy alloys (HEAs) is an important issue since the phase structure affects the comprehensive properties of HEAs. Accurate prediction of phase classification can accelerate material design. In this paper, a new phase prediction framework is proposed using machine learning (ML) and an improved information fusion approach based on the Dempster-Shafer (DS) evidence theory. Considering that the classification results of different ML algorithms may conflict, and the traditional DS evidence theory cannot solve the problem of high conflict, we propose an improved information fusion approach based on the DS evidence theory. The basic probability assignment function is constructed using the ML algorithms. 761 HEAs samples are collected consisting of amorphous phase (AM), solid solution (SS), intermetallic compound (IM), and a mixture of SS and IM (SS + IM). For the small dataset of HEAs, we use a conditional generative adversarial network (CGAN) for data augmentation. Based on the enhanced dataset, the ML model is optimized by sparrow search algorithm (SSA), which can accelerate searching speed of model hyperparameters and improve the performance of the model. The results show that the proposed information fusion method performs better than several other existing techniques on the test set, and the prediction accuracy reaches 94.78 %. Meanwhile, the prediction accuracy of the proposed method is higher than that of the existing technology (93.17 %). It is proved that the proposed method can solve the high conflict problem effectively. Moreover, we present the interpretability analysis of the features by the Shapley additive explanations (SHAP) and the sensitivity matrix. A smaller atomic size difference δ (<6.6 %) is conducive to the formation of SS phase, while a larger δ (>6.6 %) is conducive to the formation of AM phase. A smaller enthalpy of mixing ΔHmix tends to form AM phase. In binary and ternary alloy systems, IM phase can be extracted by the mixing enthalpy ΔSmix < 10. In addition, we find that mean bulk modulus (K) and standard deviation of melting temperature (σT) are critical features to distinguish between SS and SS + IM.

A two-level fusion model of vibro-acoustic signals for centrifugal fan blade crack detection

Blade crack detection is the key to ensuring the smooth and safe operation of centrifugal fans. However, a single vibration signal is difficult to fully reflect the health state of the blade and is susceptible to noise interference in the industrial field, which makes it difficult to detect blade cracks. Therefore, a two-level fusion model of vibro-acoustic signals is proposed for blade crack detection of centrifugal fans. Firstly, based on the designed correlated degree of cyclostationarity fusion rule, the data-level fusion of multi-source homogeneous vibro-acoustic signals is completed, and the fused signals with more obvious fault features are obtained. Then, a one-dimensional feature pyramid network is proposed to extract the vibro-acoustic features and generate initial decisions. Finally, a basic probability assignment acquisition method based on the precision of the initial classifiers and a weighted average method based on the Pignistic probability distance are proposed to minimize the conflict between multi-source evidence, and the Dempster-Shafer evidence theory method is used to obtain the blade crack detection results. The effectiveness of the proposed method is verified by the centrifugal fan blade crack detection experiments. Compared with other related methods, the proposed method has better detection performance and stronger robustness.

A Partial-Label U-Net Learning Method for Compound-Fault Diagnosis With Fault- Sample Class Imbalance

In the operation process of the rotating machinery, compound faults have various combination forms and are difficult to reproduce, which results in the scarcity of training samples of various compound faults. In this paper, a method of partial-label learning and classification fusion is proposed to investigate the above problems. Wavelet packet transformation (WPT) and dimensionless parameterization (DP) are utilized to extract features in high-dimensional space. A label-specific feature learning architecture is proposed to make up for the shortage of handcrafted features. An improved focal loss is exploited for learning prominent compound-fault characteristics and imbalanced fault samples. Basic probability assignments (BPA) about fault classes are generated from each partial classifier and combined to obtain a final inference about fault types. Experimental results of single-fault and compound-fault classification illustrate the effectiveness of the proposed method.