Yongchuan Tang

Sensor Data Fusion with Z-Numbers and Its Application in Fault Diagnosis

Sensor data fusion technology is widely employed in fault diagnosis. The information in a sensor data fusion system is characterized by not only fuzziness, but also partial reliability. Uncertain information of sensors, including randomness, fuzziness, etc., has been extensively studied recently. However, the reliability of a sensor is often overlooked or cannot be analyzed adequately. A Z-number, Z = (A, B), can represent the fuzziness and the reliability of information simultaneously, where the first component A represents a fuzzy restriction on the values of uncertain variables and the second component B is a measure of the reliability of A. In order to model and process the uncertainties in a sensor data fusion system reasonably, in this paper, a novel method combining the Z-number and Dempster–Shafer (D-S) evidence theory is proposed, where the Z-number is used to model the fuzziness and reliability of the sensor data and the D-S evidence theory is used to fuse the uncertain information of Z-numbers. The main advantages of the proposed method are that it provides a more robust measure of reliability to the sensor data, and the complementary information of multi-sensors reduces the uncertainty of the fault recognition, thus enhancing the reliability of fault detection.

Failure mode and effects analysis based on a novel fuzzy evidential method

Abstract Failure mode and effect analysis (FMEA) has been widely applied to examine potential failures in systems, designs, and products. The risk priority number (RPN) is the key criteria to determine the risk priorities of the failure modes. Traditionally, the determination of RPN is based on the risk factors like occurrence ( O ), severity ( S ) and detection ( D ), which require to be precisely evaluated. However, this method has many irrationalities and needs to be improved for more applications. To overcome the shortcomings of the traditional FMEA and better model and process uncertainties, we propose a FMEA model based on a novel fuzzy evidential method. The risks of the risk factors are evaluated by fuzzy membership degree. As a result, a comprehensive way to rank the risk of failure modes is proposed by fusing the feature information of O , S and D with Dempster–Shafer (D–S) evidence theory. The advantages of the proposed method are that it can not only cover the diversity and uncertainty of the risk assessment, but also improve the reliability of the RPN by data fusion. To validate the proposed method, a case study of a micro-electro-mechanical system (MEMS) is performed. The experimental results show that this method is reasonable and effective for real applications.

Sensor Data Fusion Based on a New Conflict Measure

Dempster-Shafer (D-S) evidence theory has been widely used in various fields. However, how to measure the degree of conflict (similarity) between the bodies of evidence is an open issue. In this paper, in order to solve this problem, firstly we propose a modified cosine similarity to measure the similarity between vectors. Then a new similarity measure of basic probability assignment (BPAs) is proposed based on the modified cosine similarity. The new similarity measure can achieve the reasonable measure of the similarity of BPAs and then efficiently measure the degree of conflict among bodies of evidence. Numerical examples are used to illustrate the effectiveness of the proposed method. Finally, a weighted average method based on the new BPAs similarity is proposed, and an example is used to show the validity of the proposed method.

Ranking Z-numbers with an improved ranking method for generalized fuzzy numbers

Z-number, a new concept describes both the restriction and the reliability of evaluation, is more applicable than fuzzy numbers in the fields of decision making, risk assessment etc. However, how to deal with the restriction and the reliability properly is still a problem which is discussed few and inadequately in the existing literatures. In this paper, firstly, a new improved method for ranking generalized fuzzy numbers where the weight of centroid points, degrees of fuzziness and the spreads of fuzzy numbers are taken into consideration is proposed, which can overcome some drawbacks of exiting methods and is very efficient for evaluating symmetric fuzzy numbers and crisp numbers. Then, a procedure for evaluating Znumbers with the method for ranking generalized fuzzy numbers is presented, which considers the status of two parts ((A,B)) of Z-numbers and gives the principles of ranking Z-numbers. The main advantage of the proposed method is utilization of Z-numbers which can express more vague information compared with the fuzzy number. In addition, instead of converting B to a crisp number as the existing methods of ranking Z-numbers did, the proposed method retains the fuzzy information of B which can reduce the loss of information. Finally, several numerical examples are provided to illustrate the superiority and the rationality of the proposed procedure. 6

Ordered visibility graph average aggregation operator: An application in produced water management.

Complex networks are widely used in modeling complex system. How to aggregate data in complex systems is still an open issue. In this paper, an ordered visibility graph average aggregation operator is proposed which is inspired by the complex network theory and Newtons law of universal gravitation. First of all, the argument values are ordered in descending order. Then a new support function is proposed to measure the relationship among values in a visibility graph. After that, a weighted network is constructed to determine the weight of each value. Compared with the other operators, the new operator fully takes into account not only the information of orders but also the correlation degree between the values. Finally, an application of produced water management is illustrated to show the efficiency of the proposed method. The new method provides a universal way to aggregate data in complex systems.

A New Fuzzy-Evidential Controller for Stabilization of the Planar Inverted Pendulum System

In order to realize the stability control of the planar inverted pendulum system, which is a typical multi-variable and strong coupling system, a new fuzzy-evidential controller based on fuzzy inference and evidential reasoning is proposed. Firstly, for each axis, a fuzzy nine-point controller for the rod and a fuzzy nine-point controller for the cart are designed. Then, in order to coordinate these two controllers of each axis, a fuzzy-evidential coordinator is proposed. In this new fuzzy-evidential controller, the empirical knowledge for stabilization of the planar inverted pendulum system is expressed by fuzzy rules, while the coordinator of different control variables in each axis is built incorporated with the dynamic basic probability assignment (BPA) in the frame of fuzzy inference. The fuzzy-evidential coordinator makes the output of the control variable smoother, and the control effect of the new controller is better compared with some other work. The experiment in MATLAB shows the effectiveness and merit of the proposed method.

Conflicting evidence combination based on uncertainty measure and distance of evidence

Dempster–Shafer evidence theory is widely used in many fields of information fusion. However, the counter-intuitive results may be obtained when combining with highly conflicting evidence. To deal with such a problem, we put forward a new method based on the distance of evidence and the uncertainty measure. First, based on the distance of evidence, the evidence is divided into two parts, the credible evidence and the incredible evidence. Then, a novel belief entropy is applied to measure the information volume of the evidence. Finally, the weight of each evidence is obtained and used to modify the evidence before using the Dempster’s combination rule. Numerical examples show that the proposed method can effectively handle conflicting evidence with better convergence.

A Modified Model of Failure Mode and Effects Analysis Based on Generalized Evidence Theory

Due to the incomplete knowledge, how to handle the uncertain risk factors in failure mode and effects analysis (FMEA) is still an open issue. This paper proposes a new generalized evidential FMEA (GEFMEA) model to handle the uncertain risk factor, which may not be included in the conventional FMEA model. In GEFMEA, not only the conventional risk factors, the occurrence, severity, and detectability of the failure mode, but also the other incomplete risk factors are taken into consideration. In addition, the relative importance among all these risk factors is well addressed in the proposed method. GEFMEA is based on the generalized evidence theory, which is efficient in handling incomplete information in the open world. The efficiency and some merit of the proposed method are verified by the numerical example and a real case study on aircraft turbine rotor blades.

An Improved Belief Entropy and Its Application in Decision-Making

Uncertainty measure in data fusion applications is a hot topic; quite a few methods have been proposed to measure the degree of uncertainty in Dempster-Shafer framework. However, the existing methods pay little attention to the scale of the frame of discernment (FOD), which means a loss of information. Due to this reason, the existing methods cannot measure the difference of uncertain degree among different FODs. In this paper, an improved belief entropy is proposed in Dempster-Shafer framework. The proposed belief entropy takes into consideration more available information in the body of evidence (BOE), including the uncertain information modeled by the mass function, the cardinality of the proposition, and the scale of the FOD. The improved belief entropy is a new method for uncertainty measure in Dempster-Shafer framework. Based on the new belief entropy, a decision-making approach is designed. The validity of the new belief entropy is verified according to some numerical examples and the proposed decision-making approach.

A modified belief entropy in Dempster-Shafer framework

How to quantify the uncertain information in the framework of Dempster-Shafer evidence theory is still an open issue. Quite a few uncertainty measures have been proposed in Dempster-Shafer framework, however, the existing studies mainly focus on the mass function itself, the available information represented by the scale of the frame of discernment (FOD) in the body of evidence is ignored. Without taking full advantage of the information in the body of evidence, the existing methods are somehow not that efficient. In this paper, a modified belief entropy is proposed by considering the scale of FOD and the relative scale of a focal element with respect to FOD. Inspired by Deng entropy, the new belief entropy is consistent with Shannon entropy in the sense of probability consistency. What’s more, with less information loss, the new measure can overcome the shortage of some other uncertainty measures. A few numerical examples and a case study are presented to show the efficiency and superiority of the proposed method.