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

Sensor Fault Reconstruction Using Robustly Adaptive Unknown-Input Observers

Sensors are a key component in industrial automation systems. A fault or malfunction in sensors may degrade control system performance. An engineering system model is usually disturbed by input uncertainties, which brings a challenge for monitoring, diagnosis, and control. In this study, a novel estimation technique, called adaptive unknown-input observer, is proposed to simultaneously reconstruct sensor faults as well as system states. Specifically, the unknown input observer is used to decouple partial disturbances, the un-decoupled disturbances are attenuated by the optimization using linear matrix inequalities, and the adaptive technique is explored to track sensor faults. As a result, a robust reconstruction of the sensor fault as well as system states is then achieved. Furthermore, the proposed robustly adaptive fault reconstruction technique is extended to Lipschitz nonlinear systems subjected to sensor faults and unknown input uncertainties. Finally, the effectiveness of the algorithms is demonstrated using an aircraft system model and robotic arm and comparison studies.

Fault Diagnosis Method for Space Fluid Loop Systems Based on Improved Evidence Theory

Addressing the challenges posed by the complexity of the structure and the multitude of sensor types installed in space application fluid loop systems, this paper proposes a fault diagnosis method based on an improved D-S evidence theory. The method first employs the Gaussian affiliation function to convert the information acquired by sensors into BPA functions. Subsequently, it utilizes a pignistic probability transformation to convert the multiple subset focal elements into single subset focal elements. Finally, it comprehensively evaluates the credibility and uncertainty factors between evidences, introducing Bray-Curtis dissimilarity and belief entropy to achieve the fusion of conflicting evidence. The proposed method is initially validated on the classic Iris dataset, demonstrating its reliability. Furthermore, when applied to fault diagnosis in space application fluid circuit loop pumps, the results indicate that the method can effectively fuse multiple sensors and accurately identify faults.

Anomaly Detection Method for Rocket Engines Based on Convex Optimized Information Fusion

The power system, as a core component of a launch vehicle, has a crucial impact on the reliability and safety of a rocket launch. Due to the limited measurement information inside the engine, it is often challenging to realize fast and accurate anomaly detection. For this reason, this paper introduces the rocket flight state data to expand the information source for anomaly detection. However, engine measurement and rocket flight state information have different data distribution characteristics. To find the optimal data fusion scheme for anomaly detection, a data set information fusion algorithm based on convex optimization is proposed, which solves the optimal fusion parameter using the convex quadratic programming problem and then adopts the adaptive CUSUM algorithm to realize the fast and accurate anomaly detection of engine faults. Numerical simulation tests show that the algorithm proposed in this paper has a higher detection accuracy and lower detection time than the traditional algorithm.

A Circuit-Level Solution for Secure Temperature Sensor

Temperature sensors play an important role in modern monitoring and control applications. When more and more sensors are integrated into internet-connected systems, the integrity and security of sensors become a concern and cannot be ignored anymore. As sensors are typically low-end devices, there is no built-in defense mechanism in sensors. It is common that system-level defense provides protection against security threats on sensors. Unfortunately, high-level countermeasures do not differentiate the root of cause and treat all anomalies with system-level recovery processes, resulting in high-cost overhead on delay and power consumption. In this work, we propose a secure architecture for temperature sensors with a transducer and a signal conditioning unit. The proposed architecture estimates the sensor data with statistical analysis and generates a residual signal for anomaly detection at the signal conditioning unit. Moreover, complementary current-temperature characteristics are exploited to generate a constant current reference for attack detection at the transducer level. Anomaly detection at the signal conditioning unit and attack detection at the transducer unit make the temperature sensor attack resilient to intentional and unintentional attacks. Simulation results show that our sensor is capable of detecting an under-powering attack and analog Trojan from a significant signal vibration in the constant current reference. Furthermore, the anomaly detection unit detects anomalies at the signal conditioning level from the generated residual signal. The proposed detection system is resilient against any intentional and unintentional attacks, with a detection rate of 97.73%.

A Networked Method for Multi-Evidence-Based Information Fusion

Dempster-Shafer evidence theory is an effective way to solve multi-sensor data fusion problems. After developing many improved combination rules, Dempster-Shafer evidence theory can also yield excellent results when fusing highly conflicting evidence. However, these approaches still have deficiencies if the conflicting evidence is due to sensor malfunction. This work presents a combination method by integrating information interaction graph and Dempster-Shafer evidence theory; thus, the multiple evidence fusion process is expressed as a network. In particular, the credibility of each piece of evidence is obtained by measuring the distance between the evidence first. After that, the credibility of the evidence is evaluated, keeping the unreliable evidence out of the information interaction network. With the fusion of connected evidence, the accuracy of the fusion result is improved. Finally, application results show that the presented method is effective.

Measuring Uncertainty in the Negation Evidence for Multi-Source Information Fusion

Dempster-Shafer evidence theory is widely used in modeling and reasoning uncertain information in real applications. Recently, a new perspective of modeling uncertain information with the negation of evidence was proposed and has attracted a lot of attention. Both the basic probability assignment (BPA) and the negation of BPA in the evidence theory framework can model and reason uncertain information. However, how to address the uncertainty in the negation information modeled as the negation of BPA is still an open issue. Inspired by the uncertainty measures in Dempster-Shafer evidence theory, a method of measuring the uncertainty in the negation evidence is proposed. The belief entropy named Deng entropy, which has attracted a lot of attention among researchers, is adopted and improved for measuring the uncertainty of negation evidence. The proposed measure is defined based on the negation function of BPA and can quantify the uncertainty of the negation evidence. In addition, an improved method of multi-source information fusion considering uncertainty quantification in the negation evidence with the new measure is proposed. Experimental results on a numerical example and a fault diagnosis problem verify the rationality and effectiveness of the proposed method in measuring and fusing uncertain information.

An Oversampling Method of Unbalanced Data for Mechanical Fault Diagnosis Based on MeanRadius-SMOTE

With the development of machine learning, data-driven mechanical fault diagnosis methods have been widely used in the field of PHM. Due to the limitation of the amount of fault data, it is a difficult problem for fault diagnosis to solve the problem of unbalanced data sets. Under unbalanced data sets, faults with little historical data are always difficult to diagnose and lead to economic losses. In order to improve the prediction accuracy under unbalanced data sets, this paper proposes MeanRadius-SMOTE based on the traditional SMOTE oversampling algorithm, which effectively avoids the generation of useless samples and noise samples. This paper validates the effectiveness of the algorithm on three linear unbalanced data sets and four step unbalanced data sets. Experimental results show that MeanRadius-SMOTE outperforms SMOTE and LR-SMOTE in various evaluation indicators, as well as has better robustness against different imbalance rates. In addition, MeanRadius-SMOTE can take into account the prediction accuracy of the overall and minority class, which is of great significance for engineering applications.

Application of Improved MFDFA and D-S Evidence Theory in Fault Diagnosis

To improve the accuracy of centrifugal pump fault diagnosis, a novel fault diagnosis method based on improved multiple fractal detrended fluctuation analysis (MFDFA), the fusion of multi-sensing information derived from the back propagation (BP) neural network and the Dempster–Shafter (D-S) evidence theory, is accordingly proposed. Firstly, the multifractal spectral parameters of four sensor signals under four different operating conditions were extracted as centrifugal pump fault feature vectors using improved MFDFA and input to the BP neural network. Then, the basic trust assignment function was constructed by calculating trustworthiness (both local and global) as priori information, which is based on the output results of the neural networks specific to of each group of sensors. Finally, the basic trust assignment function was fused with decision processing in accordance with the D-S evidence combination rule in order to effectively achieve the multi-sensor information fusion centrifugal pump fault diagnosis. The experimental results show the multiple fractal spectrum feature parameters extracted by the improved MFDFA can accurately reflect the signal essence, and can be used as the fault feature vector. On this basis, this multi-sensor fault diagnosis reduces the uncertainty of fault classification and demonstrates improved accuracy compared to the single-sensor fault diagnosis thanks to being based on a combination of the BP neural networks and D-S evidence theory. Thereby, this method can facilitate accurate diagnosis of the centrifugal pump fault type with high confidence, subsequently providing a novel and alternative method to existing methods of diagnosis.

Dombi weighted aggregation operators of neutrosophic Z-numbers for multiple attribute decision making in equipment supplier selection

Advances in multiple attribute decision making (MADM) require the development of information aggregation operations flexible enough to deal with neutrosophic Z-number (NZN) information. In this situation, new operations of NZNs are needed to aggregate NZNs with different values of operational parameter and to realize the MADM flexibility. Motivated by the Dombi operations, this study proposes the Dombi operations and some Dombi weighted aggregation operators of NZNs to solve a gap of flexible MADM in the setting of NZNs. Thus, the main aims of this article are (i) to propose several Dombi operations of NZNs, (ii) to present the NZN Dombi weighted arithmetic averaging (NZNDWAA) and NZN Dombi weighted geometric averaging (NZNDWGA) operators for aggregating NZN information and their properties, (iii) to establish a MADM approach based on the NZNDWAA and NZNDWGA operators for solving MADM problems under the environment of NZNs, and (iv) to give a MADM example and related comparative analysis on the issue of equipment supplier selection for indicating the applicability and efficiency of the developed MADM approach. However, the proposed MADM approach is more flexible for the selection of decision makers’ preferences and the actual requirements in MADM applications.

Multiattribute Decision-Making Problems in terms of the Weighted Mean Operation of Two Aggregation Operators of Orthopair Z-Numbers

The Z number defined by Zadeh can depict the fuzzy restriction/value and reliability measure by an ordered pair of fuzzy values to strengthen the reliability of the fuzzy restriction/value. However, there exist truth and falsehood Z-numbers in real life. Thus, the Z number cannot reflect both. To indicate both, this study presents an orthopair Z-number (OZN) set to depict truth and falsehood values (intuitionistic fuzzy values) and their reliability levels in uncertain and incomplete cases. Next, we define the operations, score and accuracy functions, and sorting rules of OZNs. Further, the OZN weighted arithmetic mean (OZNWAM) and OZN weighted geometric mean (OZNWGM) operators are proposed based on the operations of OZNs. According to the weighted mean operation of the OZNWAM and OZNWGM operators, a multiattribute decision-making (MADM) model is established in the case of OZNs. Lastly, a numerical example is presented to reflect the flexibility and rationality of the presented MADM model. Comparative analysis indicates that the presented MADM model can indicate its superiority in the reliability and flexibility of decision results. Meanwhile, the resulting advantage of this study is that the presented MADM model can strengthen the reliability level of orthopair fuzzy values and make the decision results more reliable and flexible.

A Novel Conflict Management Method Based on Uncertainty of Evidence and Reinforcement Learning for Multi-Sensor Information Fusion

Dempster-Shafer theory (DST), which is widely used in information fusion, can process uncertain information without prior information; however, when the evidence to combine is highly conflicting, it may lead to counter-intuitive results. Moreover, the existing methods are not strong enough to process real-time and online conflicting evidence. In order to solve the above problems, a novel information fusion method is proposed in this paper. The proposed method combines the uncertainty of evidence and reinforcement learning (RL). Specifically, we consider two uncertainty degrees: the uncertainty of the original basic probability assignment (BPA) and the uncertainty of its negation. Then, Deng entropy is used to measure the uncertainty of BPAs. Two uncertainty degrees are considered as the condition of measuring information quality. Then, the adaptive conflict processing is performed by RL and the combination two uncertainty degrees. The next step is to compute Dempster's combination rule (DCR) to achieve multi-sensor information fusion. Finally, a decision scheme based on correlation coefficient is used to make the decision. The proposed method not only realizes adaptive conflict evidence management, but also improves the accuracy of multi-sensor information fusion and reduces information loss. Numerical examples verify the effectiveness of the proposed method.

Defect Identification of Pipeline Ultrasonic Inspection Based on Multi-Feature Fusion and Multi-Criteria Feature Evaluation

This paper presents a novel model for ultrasonic defect identification relying on multi-feature fusion and multi-criteria feature evaluation (MFF-MCFE). Based on feature extraction, feature selection, pattern recognition and data fusion algorithm, this model analyzes ultrasonic echo signal data from single-probe ultrasonic inspection, and based on wavelet packet transform (WPT), empirical mode decomposition (EMD) and discrete wavelet transform (DWT), the main features from the collected ultrasonic echo signals are also extracted. These features are also evaluated by means of Representation Entropy (RE), Fisher’s ratio (FR) and Mahalanobis distance (MD), and the results are fused with Dempster–Shafer (D-S) evidence theory and the corresponding feature subsets are formed according to the fusion result. The support vector machine (SVM) is used as the classifier to recognize the defect signal, and the subsequent classification results are integrated by D-S evidence theory, which leads to the final recognition results. On this basis, a series of experiments were carried out to compare the performance of the developed model with that of the models using single feature sets and single feature evaluation criterion. Meanwhile, the principal component analysis (PCA) was also involved in the corresponding comparative analysis. The experimental results showed that this model is suitable for the identification and diagnosis of pipeline defects, and its classification accuracy could be reached up to 96.29% with stronger robustness and stability.

Human reliability analysis in de-energization of power line using HEART in the context of Z-numbers

Investigation reveals that a high percentage of incident causes are ascribed to some forms of human error. To effectively prevent incidents from happening, Human Reliability Analysis (HRA), as a structured way to represent unintentional operator contribution to system reliability, is a critical issue. Human Error Reduction and Assessment Technique (HEART) as a famous HRA technique, provides a straightforward method to estimate probabilities of human error based on the analysis of tasks. However, it faces varying levels of uncertainty in assigning of weights to each error producing condition (EPC), denoted as assessed proportion of affect (APOA), by experts. To overcome this limitation and consider the confidence level (reliability or credibility) of the experts, the current study aimed at proposing a composite HEART methodology for human error probability (HEP) assessment, which integrates HEART and Z-numbers short for, Z-HEART. The applicability and effectiveness of the Z-HEART has been illustrated in the de-energization power line as a case study. Furthermore, a sensitivity analysis is fulfilled to investigate the validity of the proposed methodology. It can be concluded that Z-HEART is feasible for assessing human error, and despite the methodological contributions, it offers many advantages for electricity distribution companies.

An Improved Approach of Incomplete Information Fusion and Its Application in Sensor Data-Based Fault Diagnosis

The Dempster–Shafer evidence theory has been widely used in the field of data fusion. However, with further research, incomplete information under the open world assumption has been discovered as a new type of uncertain information. The classical Dempster’s combination rules are difficult to solve the related problems of incomplete information under the open world assumption. At the same time, partial information entropy, such as the Deng entropy is also not applicable to deal with problems under the open world assumption. Therefore, this paper proposes a new method framework to process uncertain information and fuse incomplete data. This method is based on an extension to the Deng entropy in the open world assumption, negation of basic probability assignment (BPA), and the generalized combination rule. The proposed method can solve the problem of incomplete information under the open world assumption, and obtain more uncertain information through the negative processing of BPA, which improves the accuracy of the results. The results of applying this method to fault diagnosis of electronic rotor examples show that, compared with the other uncertain information processing and fusion methods, the proposed method has wider adaptability and higher accuracy, and is more conducive to practical engineering applications.

Measuring the Uncertainty in the Original and Negation of Evidence Using Belief Entropy for Conflict Data Fusion

Dempster-Shafer (DS) evidence theory is widely used in various fields of uncertain information processing, but it may produce counterintuitive results when dealing with conflicting data. Therefore, this paper proposes a new data fusion method which combines the Deng entropy and the negation of basic probability assignment (BPA). In this method, the uncertain degree in the original BPA and the negation of BPA are considered simultaneously. The degree of uncertainty of BPA and negation of BPA is measured by the Deng entropy, and the two uncertain measurement results are integrated as the final uncertainty degree of the evidence. This new method can not only deal with the data fusion of conflicting evidence, but it can also obtain more uncertain information through the negation of BPA, which is of great help to improve the accuracy of information processing and to reduce the loss of information. We apply it to numerical examples and fault diagnosis experiments to verify the effectiveness and superiority of the method. In addition, some open issues existing in current work, such as the limitations of the Dempster-Shafer theory (DST) under the open world assumption and the necessary properties of uncertainty measurement methods, are also discussed in this paper.

Multicriteria Decision-Making Method and Application in the Setting of Trapezoidal Neutrosophic Z-Numbers

The information expression and modeling of decision-making are critical problems in the fuzzy decision theory and method. However, existing trapezoidal neutrosophic numbers (TrNNs) and neutrosophic Z-numbers (NZNs) and their multicriteria decision-making (MDM) methods reveal their insufficiencies, such as without considering the reliability measures in TrNN and continuous Z-numbers in NZN. To overcome the insufficiencies, it is necessary that one needs to propose trapezoidal neutrosophic Z-numbers (TrNZNs), their aggregation operations, and an MDM method for solving MDM problems with TrNZN information. Hence, this study first proposes a TrNZN set, some basic operations of TrNZNs, and the score and accuracy functions of TrNZN and their ranking laws. Then, the TrNZN weighted arithmetic averaging (TrNZNWAA) and TrNZN weighted geometric averaging (TrNZNWGA) operators are presented based on the operations of TrNZNs. Next, an MDM approach using the proposed aggregation operators and score and accuracy functions is established to carry out MDM problems under the environment of TrNZNs. In the end, the established MDM approach is applied to an MDM example of software selection for revealing its rationality and efficiency in the setting of TrNZNs. The main advantage of this study is that the established approach not only makes assessment information continuous and reliable but also strengthens the decision rationality and efficiency in the setting of TrNZNs.

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.

Incomplete Information Management Using an Improved Belief Entropy in Dempster-Shafer Evidence Theory

Quantifying uncertainty is a hot topic for uncertain information processing in the framework of evidence theory, but there is limited research on belief entropy in the open world assumption. In this paper, an uncertainty measurement method that is based on Deng entropy, named Open Deng entropy (ODE), is proposed. In the open world assumption, the frame of discernment (FOD) may be incomplete, and ODE can reasonably and effectively quantify uncertain incomplete information. On the basis of Deng entropy, the ODE adopts the mass value of the empty set, the cardinality of FOD, and the natural constant e to construct a new uncertainty factor for modeling the uncertainty in the FOD. Numerical example shows that, in the closed world assumption, ODE can be degenerated to Deng entropy. An ODE-based information fusion method for sensor data fusion is proposed in uncertain environments. By applying it to the sensor data fusion experiment, the rationality and effectiveness of ODE and its application in uncertain information fusion are verified.

A New Belief Entropy in Dempster-Shafer Theory Based on Basic Probability Assignment and the Frame of Discernment

Dempster–Shafer theory has been widely used in many applications, especially in the measurement of information uncertainty. However, under the D-S theory, how to use the belief entropy to measure the uncertainty is still an open issue. In this paper, we list some significant properties. The main contribution of this paper is to propose a new entropy, for which some properties are discussed. Our new model has two components. The first is Nguyen entropy. The second component is the product of the cardinality of the frame of discernment (FOD) and Dubois entropy. In addition, under certain conditions, the new belief entropy can be transformed into Shannon entropy. Compared with the others, the new entropy considers the impact of FOD. Through some numerical examples and simulation, the proposed belief entropy is proven to be able to measure uncertainty accurately.

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.

Overcoming randomness does not rule out the importance of inherent randomness for functionality

Randomness is intrinsic to many natural processes. It is also clear that, under certain conditions, disorders are not associated with functionality. Several examples in which overcoming, suppressing, or combining both randomness and non-randomness is required are drawn from various fields. However, the need to suppress or overcome randomness does not negate its importance under certain conditions and its significance in valid processes and organ functions. Randomness should be acknowledged rather than ignored or suppressed; it can be viewed, at worst, as a disturbing disorder that may be treated to produce order, or, at best, as a 'beneficial disorder' that can be considered as a higher level of functionality.

An Improved Belief Entropy to Measure Uncertainty of Basic Probability Assignments Based on Deng Entropy and Belief Interval

It is still an open issue to measure uncertainty of the basic probability assignment function under Dempster-Shafer theory framework, which is the foundation and preliminary work for conflict degree measurement and combination of evidences. This paper proposes an improved belief entropy to measure uncertainty of the basic probability assignment based on Deng entropy and the belief interval, which takes the belief function and the plausibility function as the lower bound and the upper bound, respectively. Specifically, the center and the span of the belief interval are employed to define the total uncertainty degree. It can be proved that the improved belief entropy will be degenerated to Shannon entropy when the the basic probability assignment is Bayesian. The results of numerical examples and a case study show that its efficiency and flexibility are better compared with previous uncertainty measures.

Positive and Negative Evidence Accumulation Clustering for Sensor Fusion: An Application to Heartbeat Clustering

In this work, a new clustering algorithm especially geared towards merging data arising from multiple sensors is presented. The algorithm, called PN-EAC, is based on the ensemble clustering paradigm and it introduces the novel concept of negative evidence. PN-EAC combines both positive evidence, to gather information about the elements that should be grouped together in the final partition, and negative evidence, which has information about the elements that should not be grouped together. The algorithm has been validated in the electrocardiographic domain for heartbeat clustering, extracting positive evidence from the heartbeat morphology and negative evidence from the distances between heartbeats. The best result obtained on the MIT-BIH Arrhythmia database yielded an error of 1.44%. In the St. Petersburg Institute of Cardiological Technics 12-Lead Arrhythmia Database database (INCARTDB), an error of 0.601% was obtained when using two electrocardiogram (ECG) leads. When increasing the number of leads to 4, 6, 8, 10 and 12, the algorithm obtains better results (statistically significant) than with the previous number of leads, reaching an error of 0.338%. To the best of our knowledge, this is the first clustering algorithm that is able to process simultaneously any number of ECG leads. Our results support the use of PN-EAC to combine different sources of information and the value of the negative evidence.

Bearing Fault Diagnosis Based on a Hybrid Classifier Ensemble Approach and the Improved Dempster-Shafer Theory

Bearing fault diagnosis of a rotating machine plays an important role in reliable operation. A novel intelligent fault diagnosis method for roller bearings has been developed based on a proposed hybrid classifier ensemble approach and the improved Dempster-Shafer theory. The improved Dempster-Shafer theory well considered the combination of unreliable evidence sources, the uncertainty information of basic probability assignment, and the relative credibility of the evidence on the weights in the process of decision making under the framework of fuzzy preference relations, which can effectively deal with conflicts of the evidences and then well improve the diagnostic accuracy for the hybrid classifier ensemble. The effectiveness of the improved Dempster-Shafer theory has been verified via a numerical example. In addition, deep neural networks, a support vector machine, and extreme learning machine techniques have been utilized in the single-stage classification based on singular spectrum entropy, power spectrum entropy, time-frequency entropy, and wavelet packet energy spectrum entropy in this work. Performances of the proposed hybrid ensemble classifier has been demonstrated on a bearing test-rig, compared with the original Dempster-Shafer theory. It can be found that the overall error rate can be greatly reduced with the hybrid ensemble classifier and the improved Dempster-Shafer theory.

Bearing Fault Diagnosis Method Based on Deep Convolutional Neural Network and Random Forest Ensemble Learning

Recently, research on data-driven bearing fault diagnosis methods has attracted increasing attention due to the availability of massive condition monitoring data. However, most existing methods still have difficulties in learning representative features from the raw data. In addition, they assume that the feature distribution of training data in source domain is the same as that of testing data in target domain, which is invalid in many real-world bearing fault diagnosis problems. Since deep learning has the automatic feature extraction ability and ensemble learning can improve the accuracy and generalization performance of classifiers, this paper proposes a novel bearing fault diagnosis method based on deep convolutional neural network (CNN) and random forest (RF) ensemble learning. Firstly, time domain vibration signals are converted into two dimensional (2D) gray-scale images containing abundant fault information by continuous wavelet transform (CWT). Secondly, a CNN model based on LeNet-5 is built to automatically extract multi-level features that are sensitive to the detection of faults from the images. Finally, the multi-level features containing both local and global information are utilized to diagnose bearing faults by the ensemble of multiple RF classifiers. In particular, low-level features containing local characteristics and accurate details in the hidden layers are combined to improve the diagnostic performance. The effectiveness of the proposed method is validated by two sets of bearing data collected from reliance electric motor and rolling mill, respectively. The experimental results indicate that the proposed method achieves high accuracy in bearing fault diagnosis under complex operational conditions and is superior to traditional methods and standard deep learning methods.

An Extension to Deng's Entropy in the Open World Assumption with an Application in Sensor Data Fusion

Quantification of uncertain degree in the Dempster-Shafer evidence theory (DST) framework with belief entropy is still an open issue, even a blank field for the open world assumption. Currently, the existed uncertainty measures in the DST framework are limited to the closed world where the frame of discernment (FOD) is assumed to be complete. To address this issue, this paper focuses on extending a belief entropy to the open world by considering the uncertain information represented as the FOD and the nonzero mass function of the empty set simultaneously. An extension to Deng’s entropy in the open world assumption (EDEOW) is proposed as a generalization of the Deng’s entropy and it can be degenerated to the Deng entropy in the closed world wherever necessary. In order to test the reasonability and effectiveness of the extended belief entropy, an EDEOW-based information fusion approach is proposed and applied to sensor data fusion under uncertainty circumstance. The experimental results verify the usefulness and applicability of the extended measure as well as the modified sensor data fusion method. In addition, a few open issues still exist in the current work: the necessary properties for a belief entropy in the open world assumption, whether there exists a belief entropy that satisfies all the existed properties, and what is the most proper fusion frame for sensor data fusion under uncertainty.

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.

Feature Fusion of ICP-AES, UV-Vis and FT-MIR for Origin Traceability of Boletus edulis Mushrooms in Combination with Chemometrics

Origin traceability is an important step to control the nutritional and pharmacological quality of food products. Boletus edulis mushroom is a well-known food resource in the world. Its nutritional and medicinal properties are drastically varied depending on geographical origins. In this study, three sensor systems (inductively coupled plasma atomic emission spectrophotometer (ICP-AES), ultraviolet-visible (UV-Vis) and Fourier transform mid-infrared spectroscopy (FT-MIR)) were applied for the origin traceability of 192 mushroom samples (caps and stipes) in combination with chemometrics. The difference between cap and stipe was clearly illustrated based on a single sensor technique, respectively. Feature variables from three instruments were used for origin traceability. Two supervised classification methods, partial least square discriminant analysis (FLS-DA) and grid search support vector machine (GS-SVM), were applied to develop mathematical models. Two steps (internal cross-validation and external prediction for unknown samples) were used to evaluate the performance of a classification model. The result is satisfactory with high accuracies ranging from 90.625% to 100%. These models also have an excellent generalization ability with the optimal parameters. Based on the combination of three sensory systems, our study provides a multi-sensory and comprehensive origin traceability of B. edulis mushrooms.

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

The multi-sensor data fusion technique plays a significant role in fault diagnosis and in a variety of such applications, and the Dempster–Shafer evidence theory is employed to improve the system performance; whereas, it may generate a counter-intuitive result when the pieces of evidence highly conflict with each other. To handle this problem, a novel multi-sensor data fusion approach on the basis of the distance of evidence, belief entropy and fuzzy preference relation analysis is proposed. A function of evidence distance is first leveraged to measure the conflict degree among the pieces of evidence; thus, the support degree can be obtained to represent the reliability of the evidence. Next, the uncertainty of each piece of evidence is measured by means of the belief entropy. Based on the quantitative uncertainty measured above, the fuzzy preference relations are applied to represent the relative credibility preference of the evidence. Afterwards, the support degree of each piece of evidence is adjusted by taking advantage of the relative credibility preference of the evidence that can be utilized to generate an appropriate weight with respect to each piece of evidence. Finally, the modified weights of the evidence are adopted to adjust the bodies of the evidence in the advance of utilizing Dempster’s combination rule. A numerical example and a practical application in fault diagnosis are used as illustrations to demonstrate that the proposal is reasonable and efficient in the management of conflict and fault diagnosis.

An Improved Evidential-IOWA Sensor Data Fusion Approach in Fault Diagnosis

As an important tool of information fusion, Dempster-Shafer evidence theory is widely applied in handling the uncertain information in fault diagnosis. However, an incorrect result may be obtained if the combined evidence is highly conflicting, which may leads to failure in locating the fault. To deal with the problem, an improved evidential-Induced Ordered Weighted Averaging (IOWA) sensor data fusion approach is proposed in the frame of Dempster-Shafer evidence theory. In the new method, the IOWA operator is used to determine the weight of different sensor data source, while determining the parameter of the IOWA, both the distance of evidence and the belief entropy are taken into consideration. First, based on the global distance of evidence and the global belief entropy, the α value of IOWA is obtained. Simultaneously, a weight vector is given based on the maximum entropy method model. Then, according to IOWA operator, the evidence are modified before applying the Dempster's combination rule. The proposed method has a better performance in conflict management and fault diagnosis due to the fact that the information volume of each evidence is taken into consideration. A numerical example and a case study in fault diagnosis are presented to show the rationality and efficiency of the proposed method.

Fuzzy Risk Evaluation in Failure Mode and Effects Analysis Using a D Numbers Based Multi-Sensor Information Fusion Method

Failure mode and effect analysis (FMEA) is a useful tool to define, identify, and eliminate potential failures or errors so as to improve the reliability of systems, designs, and products. Risk evaluation is an important issue in FMEA to determine the risk priorities of failure modes. There are some shortcomings in the traditional risk priority number (RPN) approach for risk evaluation in FMEA, and fuzzy risk evaluation has become an important research direction that attracts increasing attention. In this paper, the fuzzy risk evaluation in FMEA is studied from a perspective of multi-sensor information fusion. By considering the non-exclusiveness between the evaluations of fuzzy linguistic variables to failure modes, a novel model called D numbers is used to model the non-exclusive fuzzy evaluations. A D numbers based multi-sensor information fusion method is proposed to establish a new model for fuzzy risk evaluation in FMEA. An illustrative example is provided and examined using the proposed model and other existing method to show the effectiveness of the proposed model.

A Time-Space Domain Information Fusion Method for Specific Emitter Identification Based on Dempster-Shafer Evidence Theory

Specific emitter identification plays an important role in contemporary military affairs. However, most of the existing specific emitter identification methods haven’t taken into account the processing of uncertain information. Therefore, this paper proposes a time–space domain information fusion method based on Dempster–Shafer evidence theory, which has the ability to deal with uncertain information in the process of specific emitter identification. In this paper, radars will generate a group of evidence respectively based on the information they obtained, and our main task is to fuse the multiple groups of evidence to get a reasonable result. Within the framework of recursive centralized fusion model, the proposed method incorporates a correlation coefficient, which measures the relevance between evidence and a quantum mechanical approach, which is based on the parameters of radar itself. The simulation results of an illustrative example demonstrate that the proposed method can effectively deal with uncertain information and get a reasonable recognition result.