Dempster-Shafer (DS) Evidence Theory
Since the 1970s, AP Dempster proposed the prototype of evidence theory, and then his student G. Shafer improved and developed it on the basis of his research, forming the current evidence theory, which is aimed at dealing with uncertain problems, distinguishing The impact of uncertain information and unknown information on the system can better deal with information from multiple sources of independent evidence sources, effectively eliminate the one-sided uncertainty of evidence, and obtain more accurate results. During the development of evidence theory, there are two main problems at the theoretical level: one is that when there is contradictory information in the evidence, the obtained results may produce paradoxes; the other is that evidence theory exists in the form of a set , when the number of focal elements in the set is too large, the problem of information explosion may occur in the process of data analysis.
DS Evidence Theory Advantages
Advantages of DS evidence theory: because the prior data required in evidence theory are more intuitive and easier to obtain than those in probability reasoning theory, and the Dempster synthesis formula can synthesize knowledge or data from different experts or data sources, which makes evidence The theory has been widely used in expert systems, information fusion and other fields.
Fields of application of DS evidence theory: information fusion, expert system, pattern recognition, intelligence analysis, legal case analysis, multi-attribute decision-making analysis, etc.
DS Evidence Theory Limitations
Limitations of DS evidence theory:
(1) It is required that the evidence must be independent, which is sometimes not easy to meet;
(2) There is no very solid theoretical support for the rules of evidence synthesis, and there are still disputes about its rationality and validity;
(3) Computational There is a potential exponential explosion problem.
DS Evidence Theory Used in Fault Diagnosis
In recent years, fault diagnosis technology based on multi-sensors has been continuously developed and has been applied in various fields. Its greatest progress lies in the use of more fault symptom parameters to more accurately and timely identify faults. After the joint rule of DS evidence theory was put forward in the 1970s, it was widely used in the field of multi-sensor data fusion. The fusion algorithm is basically fixed, but the method of obtaining the distribution of the reliability function is not the same. The final fusion result is the same as the obtained The assignment of reliability functions is closely linked.
The main advantage of evidence theory is that it has a strong theoretical foundation, can continuously narrow the search space through the accumulation of evidence, and satisfies an axiom system weaker than probability theory, and can distinguish between unknown and uncertain situations. Under certain conditions, the time complexity of evidential reasoning may be low. Its shortcomings are mainly manifested in: different interpretations of evidence theory may have different results, the true meaning of DS composition rules is still unclear, the combination results sometimes lack stability, and DS evidence theory has potential complexity, requiring elements in the ensemble to satisfy mutual The exclusion condition is not suitable to be realized in the actual system. Due to the fixity of fusion rules in DS evidence theory, the distribution of reliability functions is related to the final fusion results. The assignment of reliability function represents the degree of support for the target model, which has a certain subjective color. Different construction methods and different subjective judgments will construct different assignments of reliability function.
For large-scale equipment and high-end equipment, such electromechanical equipment with few fault samples and complicated working conditions, the distribution law of typical samples can be fitted through the statistics of past historical operation data, and the density function of the distribution law can be used to establish the reliability function density to obtain Reliability function, obtain the corresponding basic probability distribution, carry out the fusion of Dempster-Shafer (DS) evidence theory, use more fault symptom parameters to judge the fault category more accurately and timely in real time, and obtain the objective reliability function to achieve the goal correctly The key to mode discrimination, and can reduce subjective judgment.
Intelligent maintenance of the working status of large equipment has gradually become a new research hotspot in the field of fault diagnosis. The assessment of equipment performance degradation is an important part of intelligent maintenance technology, and it is also the basis for making a reasonable prediction of equipment operating status. Generally speaking, from the beginning of equipment performance degradation to the complete failure of the equipment, it usually goes through a series of different performance degradation states. If the degree of equipment performance degradation can be identified during the process of equipment performance degradation, production and equipment maintenance can be organized in a targeted manner to prevent abnormal equipment failures. The equipment targeted for performance degradation assessment is often a key large-scale machinery with multiple measuring points and multi-channel monitoring. The performance evaluation of this type of equipment is different from the partial evaluation based on parts, but requires the use of information fusion technology to synthesize the status information from each part, and at the same time eliminate the redundancy and contradiction between the information of each part and reduce the uncertainty. So as to obtain the actual performance evaluation. The performance degradation stage of equipment usually lasts for a long time. Therefore, when evaluating the performance of equipment, the state of equipment can be divided into normal state, initial degradation state and deep degradation state. The Dempster-Shafer evidence theory is a method to fuse the belief functions of different observations according to the combination rule. The DS evidence theory is used to fuse the evaluation information from the local area, and eliminate the data redundancy and contradiction between multi-source information, so as to obtain the performance evaluation of the whole equipment. Although in the process of performance degradation, the data from different components will reflect the changes in equipment performance to varying degrees, but the evaluation of the overall performance of the equipment is a comprehensive consideration of the operating status of each component, and the operating status of the components is only the status of the equipment. local manifestation. The evaluation method of equipment performance degradation based on information fusion technology can realize the evaluation idea of first part and then the whole, which can not only accurately describe the process of equipment performance change, but also eliminate the influence of state contradictions between components on the overall evaluation of equipment, so that the evaluation The reliability of the results has been improved. At the same time, consider introducing the concept of component importance, distinguish between primary and secondary, and improve the influence of key parts on the overall performance evaluation value of equipment, so as to provide effective reference for actual equipment maintenance in a more targeted manner. A large number of fault data samples are required to participate in training for the performance degradation evaluation of equipment fault diagnosis sets, but in practical applications, it is difficult to obtain a large number of data samples of various types of equipment faults and different severities of the same fault, or equipment faults can be simulated , but the cost is relatively expensive, so there is a problem of serious missing fault data.
DS Evidence Theory Information Uncertainty Modeling and Information Fusion
Dempster-Shafer (DS) evidence theory is an effective method widely used in information uncertainty modeling and information fusion, but it also has some defects: (1) All
possible assumptions need to be known in advance. DS evidence theory needs to consider all possible assumptions, and these assumptions need to be selected on the basis of prior knowledge, if the assumptions are not comprehensive, it will affect the accuracy of the results.
(2) The theoretical calculation and analysis are more complicated. In the DS evidence theory, a large number of conditional probabilities and combination rules need to be calculated in the process of evidence fusion, so complex mathematical analysis and calculation are required, and the implementation is a lot of work.
(3) Higher requirements for trust in the source of evidence. The DS evidence theory requires that the credibility of the evidence provided by each evidence source is high enough, otherwise it will affect the result of fusion.
(4) Only a limited amount of evidence can be processed. Due to the complexity of evidence combination rules, DS evidence theory can only deal with a limited amount of evidence (2 to the nth power minus 1). As the number of evidence increases, the amount of calculation and the complexity of combination rules will increase.
Intelligent Integrated Fault Diagnosis of Power Generation Equipment Based on Information Fusion
A lot of research work has been done on large-scale equipment and high-end equipment at home and abroad, and many products and technologies have been well applied in practice. However, affected by many factors, there are still some problems in intelligent fault diagnosis and maintenance decision support. Many deficiencies. Due to the small number of fault samples of large-scale equipment and high-end equipment, the complexity of itself and the uncertainty of the operating environment, the equipment information reflected by the sensor is uncertain. The existence of these uncertainties will inevitably lead to a decrease in the accuracy of fault diagnosis. , and even missed and misdiagnosed.
The traditional fault diagnosis method is only done through some simple mathematical criteria. The traditional way to solve complex problems is highlighted in the misjudgment of the critical fuzzy state, the root of which lies in the insufficient or insufficient amount of information. As large-scale equipment and high-end equipment tend to be high-parameter, large-capacity, and complex, the types and numbers of sensors increase sharply, and numerous sensors form a sensor group. Due to the different combinations of sensors, information on different parts and types of equipment is provided. The traditional fault diagnosis method only analyzes one or several types of information in the equipment state information, and extracts characteristic information about equipment behavior from it. Although one type of information can sometimes diagnose equipment failures, in many cases the resulting diagnosis is unreliable. Only by obtaining multi-dimensional information about the same object from multiple aspects and using it comprehensively can a more reliable and accurate diagnosis of the device be made.
Multi-source information fusion technology has achieved great success in processing large amounts of information, target recognition and fuzzy control by using statistics or modern mathematical methods. The development of multi-source information fusion technology provides a new way to solve the uncertainty of complex system fault diagnosis. The fault diagnosis technology of large-scale equipment and high-end equipment is a comprehensive research subject of multi-disciplinary cross penetration. In order to improve the reliability of fault diagnosis, it is necessary to carry out research on fault diagnosis of large-scale equipment and high-end equipment based on information fusion technology.
In conclusion, the Dempster-Shafer (DS) evidence theory has a strong ability in information uncertainty and information fusion, but still has the above-mentioned defects. To sum up, when applying multi-sensor information fusion method for fault diagnosis, it is necessary to deeply understand the principles and characteristics of different information fusion theories, and make reasonable application according to the specific conditions of the fault diagnosis system.