A Novel Evidence Theory and Fuzzy Preference Approach-Based Multi-Sensor Data Fusion Technique for Fault Diagnosis

A new D numbers’ integration rule based on pessimistic criterion

For D numbers theory, there are some drawbacks in the D numbers’ integration rule. For example, the missing information is ignored in the final decision judgment for multi-attribute decision (MADM). For this problem, some researchers have improved the D numbers’ integration rules based on optimistic criterion for overcoming the shortcoming of D numbers’ integration rule. However, optimistic and pessimistic criterion are two sides of the coin for fuzzy environment. Therefore, in this article, a new D numbers’ integration rules based on pessimistic criterion is proposed. We improve the D numbers’ integration rules to redefine the missing information distribution rules based on pessimistic criterion. The missing information is distributed in inverse proportion to each D number according to the size of the original evidence credibility. Two examples of MADM is applied by the proposed method, the results show that the proposed method can be applied to MADM.

Expert Opinion Fusion Framework Using Subjective Logic for Fault Diagnosis

Fault diagnosis plays a critical role in maintaining and troubleshooting engineered systems. Various diagnosis models, such as Bayesian networks (BNs), have been proposed to deal with this kind of problem in the past. However, the diagnosis results may not be reliable if second-order uncertainty is involved. This article proposes a hierarchical system diagnosis fusion framework that considers the uncertainty based on a belief model, called subjective logic (SL), which explicitly deals with uncertainty representing a lack of evidence. The proposed system diagnosis fusion framework consists of three steps: 1) individual subjective BNs (SBNs) are designed to represent the knowledge architectures of individual experts; 2) experts are clustered as expert groups according to their similarity; and 3) after inferring expert opinions from respective SBNs, the one opinion fusion method was used to combine all opinions to reach a consensus based on the aggregated opinion for system diagnosis. Via extensive simulation experiments, we show that the proposed fusion framework, consisting of two operators, outperforms the state-of-the-art fusion operator counterparts and has stable performance under various scenarios. Our proposed fusion framework is promising for advancing state-of-the-art fault diagnosis of complex engineered systems.

A multi-source information fusion method for ship target recognition based on Bayesian inference and evidence theory

The ship target recognition (STR) is greatly related to the battlefield situation awareness, which has recently gained prominence in the military domains. With the diversification and complexity of military missions, ship targets are mostly performed in the form of formations. Therefore, using the formation information to improve the accuracy of the ship target type recognition is worth studying. To effectively identify ship target type, we in this paper jointly consider the ship dynamic, formation, and feature information to propose a STR method based on Bayesian inference and evidence theory. Specifically, we first calculate the ship position distance matrix and the directional distance matrix with the Dynamic Time Warping (DTW) and the difference-vector algorithm taken into account. Then, we use the two distance matrices to obtain the ship formation information at different distance thresholds by the hierarchical clustering method, based on which we can infer the ship type. Thirdly, formation information and other attribute information are as nodes of the Bayesian Network (BN) to infer the ship type. Afterward, we can convert the recognition results at different thresholds into body of evidences (BOEs) as multiple information sources. Finally, we fuse the BOEs to get the final recognition. The proposed method is verified in simulation battle scenario in this paper. The simulation results demonstrate that the proposed method achieves performance superiority as compared with other ship recognition methods in terms of recognition accuracy.

Application Combining VMD and ResNet101 in Intelligent Diagnosis of Motor Faults

Motor failure is one of the biggest problems in the safe and reliable operation of large mechanical equipment such as wind power equipment, electric vehicles, and computer numerical control machines. Fault diagnosis is a method to ensure the safe operation of motor equipment. This research proposes an automatic fault diagnosis system combined with variational mode decomposition (VMD) and residual neural network 101 (ResNet101). This method unifies the pre-analysis, feature extraction, and health status recognition of motor fault signals under one framework to realize end-to-end intelligent fault diagnosis. Research data are used to compare the performance of the three models through a data set released by the Federal University of Rio de Janeiro (UFRJ). VMD is a non-recursive adaptive signal decomposition method that is suitable for processing the vibration signals of motor equipment under variable working conditions. Applied to bearing fault diagnosis, high-dimensional fault features are extracted. Deep learning shows an absolute advantage in the field of fault diagnosis with its powerful feature extraction capabilities. ResNet101 is used to build a model of motor fault diagnosis. The method of using ResNet101 for image feature learning can extract features for each image block of the image and give full play to the advantages of deep learning to obtain accurate results. Through the three links of signal acquisition, feature extraction, and fault identification and prediction, a mechanical intelligent fault diagnosis system is established to identify the healthy or faulty state of a motor. The experimental results show that this method can accurately identify six common motor faults, and the prediction accuracy rate is 94%. Thus, this work provides a more effective method for motor fault diagnosis that has a wide range of application prospects in fault diagnosis engineering.

Multi-sensor data fusion based on soft likelihood functions and OWA aggregation and its application in target recognition system

Multi-sensor data fusion plays an irreplaceable role in actual production and application. Dempster-Shafer theory (DST) is widely used in numerous fields of information modeling and information fusion due to the flexibility and effectiveness of processing uncertain information and dealing with uncertain information without prior probabilities. However, when highly contradictory evidence is combined, it may produce results that are inconsistent with human intuition. In order to solve this problem, a hybrid method for combining belief functions based on soft likelihood functions (SLFs) and ordered weighted averaging (OWA) operators is proposed. More specifically, a soft likelihood function based on OWA operators is used to provide the possibility to fuse uncertain information compatible with each other. It can characterize the degree to which the probability information of compatible propositions in the collected evidence is affected by unknown uncertain factors. This makes the results of using the Dempster's combination rule to fuse uncertain information from multiple sources more comprehensive and credible. Experimental results manifest that this method is reliable. Example and application show that this method has obvious advantages in solving the problem of conflict evidence fusion in multi-sensor. In particular, in target recognition, when three pieces of evidence are fused, the target recognition rate is 96.92%, etc.

Fusion Method and Application of Several Source Vibration Fault Signal Spatio-Temporal Multi-Correlation

Combined with other signal processing methods, related algorithms are widely used in the diagnosis and identification of rotor faults. In order to solve the problem that the vibration signal of a single sensor is too single, a new multi-source vibration signal fusion method is proposed. This method explores the correlation between vibration sensors at different locations by using multiple cross-correlations of spatial locations. First, wavelet noise reduction and linear normalization are used to process the original data. Then, the signal energy correlation function between the sensors is established, and the adaptive weight is obtained. Finally, the data fusion result is obtained. Taking rotor bearing and gear failures at different speeds as an example, the data of three vibration sensors at different positions are fused using the spatio-temporal multiple correlation fusion method (STMF). Through the intelligent fault diagnosis method stacked auto encoder (SAE), compared with single sensor data, average weighted fusion data and neural network fusion data, STMF method can reach a diagnosis accuracy of more than 94% at 700 rpm, 900 rpm and 1100 rpm. It is concluded that the result of the STMF method is more effective and superior.

Dempster-Shafer Theory for Modeling and Treating Uncertainty in IoT Applications Based on Complex Event Processing

The Internet of Things (IoT) has emerged from the proliferation of mobile devices and objects connected, resulting in the acquisition of periodic event flows from different devices and sensors. However, such sensors and devices can be faulty or affected by failures, have poor calibration, and produce inaccurate data and uncertain event flows in IoT applications. A prominent technique for analyzing event flows is Complex Event Processing (CEP). Uncertainty in CEP is usually observed in primitive events (i.e., sensor readings) and rules that derive complex events (i.e., high-level situations). In this paper, we investigate the identification and treatment of uncertainty in CEP-based IoT applications. We propose the DST-CEP, an approach that uses the Dempster–Shafer Theory to treat uncertainties. By using this theory, our solution can combine unreliable sensor data in conflicting situations and detect correct results. DST-CEP has an architectural model for treating uncertainty in events and its propagation to processing rules. We describe a case study using the proposed approach in a multi-sensor fire outbreak detection system. We submit our solution to experiments with a real sensor dataset, and evaluate it using well-known performance metrics. The solution achieves promising results regarding Accuracy, Precision, Recall, F-measure, and ROC Curve, even when combining conflicting sensor readings. DST-CEP demonstrated to be suitable and flexible to deal with uncertainty.

Some aggregation operators of neutrosophic Z-numbers and their multicriteria decision making method

As the generalization of the classical fuzzy number, the concept of Z-number introduced by Zadeh indicates more ability to depict the human knowledge and judgments of both restraint and reliability as an order pair of fuzzy numbers. In indeterminacy and inconsistent environment, a neutrosophic set is described by the truth, falsity, and indeterminacy degrees, but they lack measures related to reliability. To describe the hybrid information of combining the truth, falsity and indeterminacy degrees with their corresponding reliability degrees, this paper first proposes the concept of a neutrosophic Z-number (NZN) set, which is a new framework of neutrosophic values combined with the neutrosophic measures of reliability, as the generalization of the Z-number and the neutrosophic set. Then, we define the operations of neutrosophic Z-numbers (NZNs) and a score function for ranking NZNs. Next, we present NZN weighted arithmetic averaging (NZNWAA) and NZN weighted geometric averaging (NZNWGA) operators to aggregate NZN information and investigate their properties. Regarding the NZNWAA and NZNWGA operators and the score function, a multicriteria decision making (MDM) approach is developed in the NZN environment. Finally, an illustrative example about the selection problem of business partners is given to demonstrate the applicability and effectiveness of the developed MDM approach in NZN setting.

Reliable Estimation of Urban Link Travel Time Using Multi-Sensor Data Fusion

Travel time is one of the most critical indexes to describe urban traffic operating states. How to obtain accurate and robust travel time estimates, so as to facilitate to make traffic control decision-making for administrators and trip-planning for travelers, is an urgent issue of wide concern. This paper proposes a reliable estimation method of urban link travel time using multi-sensor data fusion. Utilizing the characteristic analysis of each individual traffic sensor data, we first extract link travel time from license plate recognition data, geomagnetic detector data and floating car data, respectively, and find that their distribution patterns are similar and follow logarithmic normal distribution. Then, a support degree algorithm based on similarity function and a credibility algorithm based on membership function are developed, aiming to overcome the conflicts among multi-sensor traffic data and the uncertainties of single-sensor traffic data. The reliable fusion weights for each type of traffic sensor data are further determined by integrating the corresponding support degree with credibility. A case study was conducted using real-world data from a link of Jingshi Road in Jinan, China and demonstrated that the proposed method can effectively improve the accuracy and reliability of link travel time estimations in urban road systems.

A Novel Evidence Conflict Measurement for Multi-Sensor Data Fusion Based on the Evidence Distance and Evidence Angle

As an important method for uncertainty modeling, Dempster-Shafer (DS) evidence theory has been widely used in practical applications. However, the results turned out to be almost counter-intuitive when fusing the different sources of highly conflicting evidence with Dempster's combination rule. In previous researches, most of them were mainly dependent on the conflict measurement method between the evidence represented by the evidence distance. However, it is inaccurate to characterize the evidence conflict only through the evidence distance. To address this issue, we comprehensively consider the impacts of the evidence distance and evidence angle on conflicts in this paper, and propose a new method based on the mutual support degree between the evidence to characterize the evidence conflict. First, the Hellinger distance measurement method is proposed to measure the distance between the evidence, and the sine value of the Pignistic vector angle is used to characterize the angle between the evidence. The evidence distance indicates the dissimilarity between the evidence, and the evidence angle represents the inconsistency between the evidence. Next, two methods are combined to get a new method for measuring the mutual support degree between the evidence. Afterward, the weight of each evidence is determined by using the mutual support degree between the evidence. Then, the weights of each evidence are utilized to modify the original evidence to achieve the weighted average evidence. Finally, Dempster's combination rule is used for fusion. Some numerical examples are given to illustrate the effectiveness and reasonability for the proposed method.

A New Method of Two-stage Planetary Gearbox Fault Detection Based on Multi-Sensor Information Fusion

Due to their high transmission ratio, high load carrying capacity and small size, planetary gears are widely used in the transmission systems of wind turbines. The planetary gearbox is the core of the transmission system of a wind turbine, but because of its special structure and complex internal and external excitation, the vibration signal spectrum shows strong nonlinearity, asymmetry and time variation, which brings great trouble to planetary gear fault diagnosis. The traditional time-frequency analysis technology is insufficient in the condition monitoring and fault diagnosis of wind turbines. For this reason, we propose a new method of planetary gearbox fault diagnosis based on Compressive sensing, Two-dimensional variational mode decomposition (2D-VMD) and full-vector spectrum technology. Firstly, the nonlinear reconstruction and noise reduction of the signal is carried out by using compressed sensing, and then the signal with multiple degrees of freedom is adaptively decomposed into multiple sets of characteristic scale components by using 2D-VMD. Then, Rényi entropy is used as the optimization index of 2D-VMD analysis performance to extract the effective target intrinsic mode function (IMF) component, reconstruct the dynamics signal in the planetary gearbox, and improve the signal-to-noise ratio. Then, using the full-vector spectrum technique, the homologous information collected by numerous sensors is data layer fused in the spatial domain and the time domain to increase the comprehensiveness and certainty of the fault information. Finally, the Teager–Kaiser energy operator is used to demodulate the potential low-frequency dynamics frequency characteristics from the high-frequency domain and detect the fault characteristic frequency. Furthermore, the correctness and validity of the method are verified by the fault test signal of the planetary gearbox.

Negation of Belief Function Based on the Total Uncertainty Measure

The negation of probability provides a new way of looking at information representation. However, the negation of basic probability assignment (BPA) is still an open issue. To address this issue, a novel negation method of basic probability assignment based on total uncertainty measure is proposed in this paper. The uncertainty of non-singleton elements in the power set is taken into account. Compared with the negation method of a probability distribution, the proposed negation method of BPA differs becausethe BPA of a certain element is reassigned to the other elements in the power set where the weight of reassignment is proportional to the cardinality of intersection of the element and each remaining element in the power set. Notably, the proposed negation method of BPA reduces to the negation of probability distribution as BPA reduces to classical probability. Furthermore, it is proved mathematically that our proposed negation method of BPA is indeed based on the maximum uncertainty.

Fusion of High-Dynamic and Low-Drift Sensors Using Kalman Filters

In practice, a high-dynamic vibration sensor is often plagued by the problem of drift, which is caused by thermal effects. Conversely, low-drift sensors typically have a limited sample rate range. This paper presents a system combining different types of sensors to address general drift problems that occur in measurements for high-dynamic vibration signals. In this paper, the hardware structure and algorithms for fusing high-dynamic and low-drift sensors are described. The algorithms include a drift state estimation and a Kalman filter based on a linear prediction model. Key issues such as the dimension of the drift state vector, the order of the linear prediction model, are analyzed in the design of algorithm. The performance of the algorithm is illustrated by a simulation example and experiments. The simulation and experimental results show that the drift can be removed while the high-dynamic measuring ability is retained. A high-dynamic vibration measuring system with the frequency range starting from 0 Hz is achieved. Meanwhile, measurement noise was improved 9.3 dB through using the linear-prediction-based Kalman filter.

Bayesian Update with Information Quality under the Framework of Evidence Theory

Bayesian update is widely used in data fusion. However, the information quality is not taken into consideration in classical Bayesian update method. In this paper, a new Bayesian update with information quality under the framework of evidence theory is proposed. First, the discounting coefficient is determined by information quality. Second, the prior probability distribution is discounted as basic probability assignment. Third, the basic probability assignments from different sources can be combined with Dempster's combination rule to obtain the fusion result. Finally, with the aid of pignistic probability transformation, the combination result is converted to posterior probability distribution. A numerical example and a real application in target recognition show the efficiency of the proposed method. The proposed method can be seen as the generalized Bayesian update. If the information quality is not considered, the proposed method degenerates to the classical Bayesian update.

Interval-valued distributed preference relation and its application to group decision making

As an important way to help express the preference relation between alternatives, distributed preference relation (DPR) can represent the preferred, non-preferred, indifferent, and uncertain degrees of one alternative over another simultaneously. DPR, however, is unavailable in some situations where a decision maker cannot provide the precise degrees of one alternative over another due to lack of knowledge, experience, and data. In this paper, to address this issue, we propose interval-valued DPR (IDPR) and present its properties of validity and normalization. Through constructing two optimization models, an IDPR matrix is transformed into a score matrix to facilitate the comparison between any two alternatives. The properties of the score matrix are analyzed. To guarantee the rationality of the comparisons between alternatives derived from the score matrix, the additive consistency of the score matrix is developed. In terms of these, IDPR is applied to model and solve multiple criteria group decision making (MCGDM) problem. Particularly, the relationship between the parameters for the consistency of the score matrix associated with each decision maker and those for the consistency of the score matrix associated with the group of decision makers is analyzed. A manager selection problem is investigated to demonstrate the application of IDPRs to MCGDM problems.

Energy and Entropy Measures of Fuzzy Relations for Data Analysis

We present a new method for assessing the strength of fuzzy rules with respect to a dataset, based on the measures of the greatest energy and smallest entropy of a fuzzy relation. Considering a fuzzy automaton (relation), in which A is the input fuzzy set and B the output fuzzy set, the fuzzy relation R₁ with greatest energy provides information about the greatest strength of the input-output, and the fuzzy relation R₂ with the smallest entropy provides information about uncertainty of the input-output relationship. We consider a new index of the fuzziness of the input-output based on R₁ and R₂. In our method, this index is calculated for each pair of input and output fuzzy sets in a fuzzy rule. A threshold value is set in order to choose the most relevant fuzzy rules with respect to the data.

A Weighted Combination Method for Conflicting Evidence in Multi-Sensor Data Fusion

Dempster⁻Shafer evidence theory is widely applied in various fields related to information fusion. However, how to avoid the counter-intuitive results is an open issue when combining highly conflicting pieces of evidence. In order to handle such a problem, a weighted combination method for conflicting pieces of evidence in multi-sensor data fusion is proposed by considering both the interplay between the pieces of evidence and the impacts of the pieces of evidence themselves. First, the degree of credibility of the evidence is determined on the basis of the modified cosine similarity measure of basic probability assignment. Then, the degree of credibility of the evidence is adjusted by leveraging the belief entropy function to measure the information volume of the evidence. Finally, the final weight of each piece of evidence generated from the above steps is obtained and adopted to modify the bodies of evidence before using Dempster’s combination rule. A numerical example is provided to illustrate that the proposed method is reasonable and efficient in handling the conflicting pieces of evidence. In addition, applications in data classification and motor rotor fault diagnosis validate the practicability of the proposed method with better accuracy.