Basic Probability Assignment Function Research Articles

Overall Assessment of Technical Conditions for Vessels

Overall assessment of technical conditions for a vessel is the major guarantees of ships’ combat capability. They are created and completed based on data and information of vessel which are complicated and numerous, so the structure of the vessel system, the subsystems and equipment of the vessel should be investigated accurately and precisely. In this paper, three models, such as the key equipment, the subsystem and the vessel system are given to assess the technical conditions of the vessel by using D-S evidence theory, fuzzy theory and gray relative analysis. The basic probability assignment functions of the key equipment are obtained. The assessment matrix of the vessel for subsystem is given, and the relational degrees of the reference and comparison sequences of the vessel are derived in order to calculate the assessment value. Taking an equipment and a vessel for example, the numerical results show that multi-hierarchy assessment is a useful method for investigating the vessel technical conditions because it can take advantage of the assessment parameters to model and calculate effectively. The influence of the technical parameters of some key equipment for the vessel are considered in the assessment, the reliabilities of the procedures and the results of the assessment are promoted significantly based on D-S evidence theory. The present assessment methods are expected to be useful in the maintenance and management of the vessel and equipment.

An approach using Dempster–Shafer evidence theory to fuse multi-source observations for dam safety estimation

Considering the limitations existing in the single-effect quantity analysis method of dam service behavior reasoning, the dam service behavior multi-effect quantities fusion reasoning model is built and implemented based on the study of improved methods about classic Dempster–Shafer (D–S) evidence fusion technologies. Focusing on the problems that classic D–S evidence fusion rules fail or the reasoning results are contrary to the intuition and convention due to the high-conflict evidences, the calculation methods of compatibility coefficient measurement matrices between any two basic probability assignment functions of evidences (E-BPAF) and between any two basic probability assignment functions of focal elements (FE-BPAF) are provided, respectively, based on the compatibility analysis of any two E-BPAFs and any two FE-BPAFs. The weight matrices about any two E-BPAFs and any two FE-BPAFs for initial BPAFs are defined, respectively, through compatibility coefficient matrices. Then, the comprehensive weight matrix for initial BPAFs is introduced to unify weight matrices. By analyzing and comparing some examples and existing study results, the performance test of the proposed method is conducted and the correctness and rationality are also verified. Finally, combining with an instance of a gravity arch dam project, the proposed method is utilized to fuse the multi-information from measuring points on the dam abutment, and the reasonable reasoning results are obtained about the dam service behavior.

A New Method of Cognitive Signal Recognition Based on Hybrid Information Entropy and D-S Evidence Theory

The automatic modulation recognition of communication signal has been widely used in many fields. However, it is very difficult to recognize the modulation in low SNR. Based on information entropy features and Dempster-Shafer evidence theory, a novel automatic modulation recognition methods is proposed in this paper. Firstly, Renyi entropy and singular entropy is used to obtain the modulation feature. Secondly, based on the normal test theory, a novel basic probability assignment function(BPAF) is presented. Finally, Dempster-Shafer evidence theory is used as a classifier. Experiment results indicate that the new approach can obtain a higher recognition result in low SNR.

A Non-Parametric Method to Determine Basic Probability Assignment Based on Kernel Density Estimation

Dempster–Shafer evidence theory has been extensively applied in a variety of fields due to its ability to solve knowledge reasoning and decision-making problem under uncertain environments. Nevertheless, it is still an open issue about how to determine the basic probability assignment (BPA). In this paper, a new non-parametric method based on kernel density estimation is proposed to determine BPA. First, the probability density function of each attribute is calculated, which can be regarded as the probability model for the related attribute using the training sample. Then, a nested BPA function is constructed using the intersections point of test sample and probability models. Finally, Dempster’s combination rule is used to combine multiple BPAs to get the final BPA. Some classification experiments are conducted on several datasets. The experimental results demonstrate that the proposed method is more effective and reasonable in determining BPAs, which has a better classification performance than the existing method.

Research on fault diagnosis methods for the reactor coolant system of nuclear power plant based on D-S evidence theory

Great attention is paid to nuclear safety which occupies the key position in the development of nuclear power plant. At present, nuclear industry is in a momentous period of strategic opportunities for development in China. Fault diagnosis systems are widely applied to guarantee the safety of nuclear power plants, and how to improve their quality is vital. D-S evidence theory has been used widely in fault diagnosis due to its effectiveness and flexibility in dealing with uncertain and subjective information. In this paper, a new fault diagnosis method for the main coolant system of nuclear power plant based on D-S evidence theory is presented. Firstly, a triangle fuzzy function is built according to historical data of the symptoms. Secondly, the basic probability assignment functions (BPAs) are constructed based on the triangle fuzzy function of symptoms and the relationship between symptoms and faults. Finally, Dempster’s combination rule is used to gain the fused BPA for decision. Examples of typical fault diagnosis in the main coolant system of a nuclear power plant are illustrated to show the use and effectiveness of the proposed method. The results demonstrate that the proposed model can not only get more accurate judgments under some cases, but also provide flexibility in dealing with uncertain information.

An Integrated Processing Method for Fatigue Damage Identification in a Steel Structure Based on Acoustic Emission Signals

This paper presents an integrated processing method that applies principal component analysis (PCA), artificial neural network (ANN), information entropy and information fusion technique to analyze acoustic emission signals for identifying fatigue damage in a steel structure. Firstly, PCA is used to build different data spaces based on the damage patterns. Input information from each sensor is diagnosed locally through ANN in the data space. The output of the ANNs is used for basic probability assignment. Secondly, the first fusion operation adopts Dempster-Shafer (D-S) evidence theory to combine the basic probability assignment value of ANNs in the different data space of a sensor. Finally, the fusion results of each sensor are combined by D-S evidence theory for the second fusion operation. In this paper, information entropy is used to calculate the uncertainty and construct basic probability assignment function. The damage identification method is verified through four-point bending fatigue tests of Q345 steel. Validation results show that the damage identification method can reduce the uncertainty of the system and has a certain extent of fault tolerance. Compared with ANN and ANN combined with information fusion methods, the proposed method shows a higher fatigue damage identification accuracy and is a potential for fatigue damage identification.

Information System Security Risk Evaluation Model Based on Improved Dempster-Shafer Evidence Theory

To deal with the uncertainty of information system security risk evaluation, a risk evaluation model combining Dempster-Shafer evidence theory and grey relational analysis is proposed. In this model, an evaluation index system is established. The risk evaluation rate of information system security is educed by using improved Dempster-Shafer theory. For each risk rating, the Basic Probability Assignment(BPA) function in Dempster-Shafer theory is get by calculating the grey relational grades, so the difficult issue of determining the BPA with Dempster-Shafer theory is solved. The Dempster-Shafer fusion strategy was applied to fuse the evaluation ratings in different data sources for evaluation conclusion. Finally, a case proves that the method is feasible and effective.

Rape Plant Disease Recognition Method of Multi-Feature Fusion Based on D-S Evidence Theory

In view of the low accuracy and uncertainty of the traditional rape plant disease recognition relying on a single feature, this paper puts forward a rape plant disease recognition method based on Dempster-Shafer (D-S) evidence theory and multi-feature fusion. Firstly, color matrix and gray-level co-occurrence matrix are extracted as two kinds of features from rape plant images after processing. Then by calculating the Euclidean distance between the test samples and training samples, the basic probability assignment function can be constructed. Finally, the D-S combination rule of evidence is used to achieve fusion, and final recognition results are given by using the variance. This method is used to collect rape plant images for disease recognition, and recognition rate arrives at 97.09%. Compared with other methods, experimental results show that the method is more effective and with lower computational complexity.

A Method for Recognizing Fatigue Driving Based on Dempster-Shafer Theory and Fuzzy Neural Network

This study proposes a method based on Dempster-Shafer theory (DST) and fuzzy neural network (FNN) to improve the reliability of recognizing fatigue driving. This method measures driving states using multifeature fusion. First, FNN is introduced to obtain the basic probability assignment (BPA) of each piece of evidence given the lack of a general solution to the definition of BPA function. Second, a modified algorithm that revises conflict evidence is proposed to reduce unreasonable fusion results when unreliable information exists. Finally, the recognition result is given according to the combination of revised evidence based on Dempster’s rule. Experiment results demonstrate that the recognition method proposed in this paper can obtain reasonable results with the combination of information given by multiple features. The proposed method can also effectively and accurately describe driving states.

A method to determine basic probability assignment in the open world and its application in data fusion and classification

Under the circumstance of the complete frame of discernment, There are quantities sufficient researches applying the Dempster-Shafer evidence theory (D-S theory) to process uncertain information. However, in most real cases, the frame of discernment is not complete, and the classic evidence theory is not applicable in some degree, including the basic probability assignment (BPA) generation method. In this paper, under the assumption of the open world, the BPA determination issue is focused originally, and a new method based on triangular fuzzy member is proposed to determine BPA. First, the mean value, standard deviation, extreme values as well as the triangular membership function of each attribute can be determined. Then, a nested structure BPA function with an assignment for the null set can be constructed, using the intersection point of one test sample and the models above. Experiments are conducted with the proposed method to determine BPA, through which the classification accuracy rates are computed, analyzed and compared with those generated by other BPA determination methods, which demonstrates the efficiency of the proposed method both in the open world and in the closed world.

Change detection of bitemporal multispectral images based on FCM and D-S theory

In this paper, we propose a change detection method of bitemporal multispectral images based on the D-S theory and fuzzy c-means (FCM) algorithm. Firstly, the uncertainty and certainty regions are determined by thresholding method applied to the magnitudes of difference image (MDI) and spectral angle information (SAI) of bitemporal images. Secondly, the FCM algorithm is applied to the MDI and SAI in the uncertainty region, respectively. Then, the basic probability assignment (BPA) functions of changed and unchanged classes are obtained by the fuzzy membership values from the FCM algorithm. In addition, the optimal value of fuzzy exponent of FCM is adaptively determined by conflict degree between the MDI and SAI in uncertainty region. Finally, the D-S theory is applied to obtain the new fuzzy partition matrix for uncertainty region and further the change map is obtained. Experiments on bitemporal Landsat TM images and bitemporal SPOT images validate that the proposed method is effective.

Evidence combination based on credibility and non-specificity

This paper addresses the combination of unreliable evidence sources which provide uncertain information in the form of basic probability assignment (BPA) functions. We proposed a novel evidence combination rule based on credibility and non-specificity of belief functions. Following a review of all existing non-specificity measures in evidence theory, a non-specificity measure for evidence theory is discussed. It is claimed that the non-specificity degree of a BPA is related to its ability of pointing to one and only one element. Based on the difference between the largest belief grades and other belief grades, a non-specificity measure is defined. Properties of the proposed non-specificity measure are put forward and proved mathematically. Illustrative examples are employed to show the properties of non-specificity measure. After providing a procedure for the evaluation of evidence credibility, we propose a novel evidence combination rule. Numerical example and application in target identification are applied to demonstrate the performance of our proposed evidence combination rule.

A risk assessment approach for failure mode and effects analysis based on intuitionistic fuzzy sets and evidence theory

Failure mode and effects analysis (FMEA) is an extensively used engineering technique for defining, identifying and prioritizing the potential failure modes. Traditionally the Risk Priority Number (RPN) is used to rank the potential failure modes. In this paper, a new risk assessment methodology which combines intuitionistic fuzzy sets (IFSs) with evidence theory is proposed to analyze the potential failure modes. The risk factors S, O, and D are evaluated by using linguistic variables and intuitionistic fuzzy numbers, which can be transformed into the basic probability assignment functions. The Jousselme distance is used to compute the weights of decision makers in order to efficiently combine highly conflicting evidence. The weighted average of evidence is obtained and the classical Dempster's combination rule is used to combine the mass functions modified. The proposed approach is applied thereafter to the prioritization of failure modes. A numerical example for risk assessment is given to illustrate the effectiveness and rationality of the proposed method finally.

Driver behavior assessment based on the G-G diagram in the DVE system

This paper proposes a driving risk model based on the information given from the Driver-Vehicle-Environment (DVE) entities. It develops a two-level strategy to evaluate the driving risk. The first level aims to assess the risk locally in each entity and the second one concludes the global risk. The advantage of this approach is the simultaneous consideration of the parameters related to the DVE system regardless of information type (dynamic and static). It uses the Dempster-Shafer Theory (DST) for information fusion at each level. The approach uses Fuzzy Theory (FT) to design Basic Probability Assignment (BPA) functions, which is the significant part of the belief theory. The drivers’ information for the driver risk evaluation the age and gender. Two parameters in the Vehicle entity are used in the cases of lane keeping and a left/right turn scenarios with utilizing two different developed Fuzzy Inference Systems (FIS). The first system uses an Euclidean acceleration-norm and the velocity of the vehicle; while, the second one, uses lateral/longitudinal acceleration based on G-G diagram and a proposed risk indicator.The results of different scenarios validate the developed risk models using the sixth version of the Proportional Conflict Redistribution (PCR6) combination algorithm.

Fault-Tolerant Event Detection in Wireless Sensor Networks using Evidence Theory

Event detection is one of the key issues in many wireless sensor network (WSN) applications. The uncertainties that are derived from the instability of sensor node, measurement noise and incomplete sampling would influence the performance of event detection to a large degree. Many of the present researches described the sensor readings with crisp values, which cannot adequately handle the uncertainties inhered in the imprecise sensor readings. In this paper, a fault-tolerant event detection algorithm is proposed based on Dempster-Shafer (D-S) theory (also called evidence theory). Instead of crisp values, all possible states of the event are represented by the Basic Probability Assignment (BPA) functions, with which the output of each sensor node are characterized as weighted evidences. The combination rule was subsequently applied on each sensor node to fuse the evidences gathered from the neighboring nodes to make the final decision on whether the event occurs. Simulation results show that even 20% nodes are faulty, the accuracy of the proposed algorithm is around 80% for event region detection. Moreover, 97% of the error readings have been corrected, and an improved detection capability at the boundary of the event region is gained by 75%. The proposed algorithm can enhance the detection accuracy of the event region even in high error-rate environment, which reflects good reliability and robustness. The proposed algorithm is also applicable to boundary detection as it performs well at the boundary of the event.

Quantification Classification Algorithm of Multiple Sources of Evidence

Although Dempster–Shafer (D–S) evidence theory and its reasoning mechanism can deal with imprecise and uncertain information by combining cumulative evidences for changing prior opinions of new evidences, there is a deficiency in applying classical D–S evidence theory combination rule when conflict evidence appear — conflict evidence causes counter-intuitive results. To address this issue, alternative combination rules have been proposed for resolving the appeared conflicts of evidence. An underlying assumption is that conflict evidences exist, which, however, is not always true. Moreover, it has been verified that conflict factors may not be accurate to characterize the degree of conflict. Instead, the Jousselme distance has been regarded as a quantification criterion for the degree of conflict because of its promising properties. To avoid the counter-intuitive results, multiple sources of evidence should be classified first. This paper proposes a novel algorithm to quantify the classification of multiple sources of evidence based on a core vector method, and the algorithm is further verified by two examples. This study also explores the relationship between complementary information and conflicting evidence and discusses the stochastic interpretation of basic probability assignment functions.

Structural reliability analysis using a copula-function-based evidence theory model

Evidence theory contains powerful features for uncertainty analysis and can be effectively employed to address the epistemic uncertainty, which is attributed to a lack of information in complex engineering problems. This paper presents an evidence theory model based on the copula function and the related structural reliability analysis method. It is an effective tool for uncertainty modeling and reliability analysis with dependent evidence variables. In the evidence theory model, a canonical maximum likelihood (CML) method was adopted to estimate the correlation parameter, and the Akaike information criterion (AIC) was utilized to select a reasonable Archimedean copula function and whereby construct the joint basic probability assignment (BPA) for the multidimensional evidence variables. Based on the joint BPA function, a procedure for reliability analysis was formulated to compute the reliability interval on the structure with evidence uncertainty. Four numerical examples were provided to verify the effectiveness of the proposed method.

Condition Assessment for Power Transformer Based on Improved Evidence Combination Rule

In view of the uncertainty transformer state information, state of transformer hierarchical evaluation model is established. Firstly, index system of transformer state is formed; Secondly, in order to get comprehensive index of state, grey clustering method is used for monomial index clustering analysis; Finally in the basis of improving synthesis rules of conflict evidence of D - S evidence theory , clustering coefficient is used as the basic probability assignment function to evaluate the overall state of transformer. Example analysis results show that the proposed evaluation model can accurately grasp the running state of transformer and provide guidance for transformer condition overhaul.

A non-parametric method to determine basic probability assignment for classification problems

As an important tool for knowledge representation and decision-making under uncertainty, Dempster-Shafer evidence theory (D-S theory) has been used in many fields. The application of D-S theory is critically dependent on the availability of the basic probability assignment (BPA). The determination of BPA is still an open issue. A non-parametric method to obtain BPA is proposed in this paper. This method can handle multi-attribute datasets in classification problems. Each attribute value of the dataset sample is treated as a stochastic quantity. Its non-parametric probability density function (PDF) is calculated using the training data, which can be regarded as the probability model for the corresponding attribute. The BPA function is then constructed based on the relationship between the test sample and the probability models. The missing attribute values in datasets are treated as ignorance in the framework of the evidence theory. This method does not have the assumption of any particular distribution. As a result, it can be flexibly used in many engineering applications. The obtained BPA can avoid high conflict between evidence, which is desired in data fusion. Several benchmark classification problems are used to demonstrate the proposed method and to compare against existing methods. The constructed classifier based on the proposed method compares well to the state-of-the-art algorithms.

Evidential Reasoning Method for Decision of Program Maliciousness

Considering the fact that the determination of the executable file maliciousness is hard to achieve,an approach based on the evidence theory is presented in this paper.First,a model for determining the maliciousness is established.Then characters compromising security are extracted to construct the set of program behaviors through decompiling the program.The model is trained using the BP neural network to gain the basic probability assignment functions(BPAF) of each behavior,and the weighted sum method is applied to combine the program behaviors,determining the executable file maliciousness.Experimental results demonstrate the validity of the approach which uses the evidence theory to determine the maliciousness of program.