Biblio
Filters: Keyword is fault diagnosis [Clear All Filters]
An Early Warning Analysis Model of Metering Equipment Based on Federated Hybrid Expert System. 2022 15th International Symposium on Computational Intelligence and Design (ISCID). :217—220.
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2022. The smooth operation of metering equipment is inseparable from the monitoring and analysis of equipment alarm events by automated metering systems. With the generation of big data in power metering and the increasing demand for information security of metering systems in the power industry, how to use big data and protect data security at the same time has become a hot research field. In this paper, we propose a hybrid expert model based on federated learning to deal with the problem of alarm information analysis and identification. The hybrid expert system can divide the metering warning problem into multiple sub-problems for processing, which greatly improves the recognition and prediction accuracy. The experimental results show that our model has high accuracy in judging and identifying equipment faults.
Rolling Bearing Fault Diagnosis based on Deep Belief Network. 2022 IEEE International Conference on Advances in Electrical Engineering and Computer Applications (AEECA). :685–688.
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2022. In view of the characteristics that rolling bearing is prone to failure under actual working conditions, and it is difficult to classify the fault category and fault degree, the deep belief network is introduced to diagnose the rolling bearing fault. Firstly, principal component analysis is used to reduce the dimension of original input data and delete redundant input information. Then, the dimension reduced data are input into the deep belief network to extract the low dimensional fault feature representation, and the extracted features are input into the classifier for rolling bearing fault pattern recognition. Finally, the diagnosis effect of the proposed network is compared with the existing common shallow neural network. The simulation experiment is carried out through the bearing data in the United States.
Research on Mechanical Fault Diagnosis of Vacuum Circuit Breaker Based on Deep Belief Network. 2022 2nd International Conference on Electrical Engineering and Mechatronics Technology (ICEEMT). :259–263.
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2022. VCB is an important component to ensure the safe and smooth operation of the power system. As an important driving part of the vacuum circuit breaker, the operating mechanism is prone to mechanical failure, which leads to power grid accidents. This paper offers an in-depth analysis of the mechanical faults of the operating mechanism of vacuum circuit breaker and their causes, extracts the current signal of the opening and closing coil strongly correlated with the mechanical faults of the operating mechanism as the characteristic information to build a Deep Belief Network (DBN) model, trains each data set via Restricted Boltzmann Machine(RBM) and updates the model parameters. The number of hidden layer nodes, the structure of the network layer, and the learning rate are determined, and the mechanical fault diagnosis system of vacuum circuit breaker based on the Deep Belief Network is established. The results show that when the network structure is 8-110-110-6 and the learning rate is 0.01, the recognition accuracy of the DBN model is the highest, which is 0.990871. Compared with BP neural network, DBN has a smaller cross-entropy error and higher accuracy. This method can accurately diagnose the mechanical fault of the vacuum circuit breaker, which lays a foundation for the smooth operation of the power system.
Alarm Correlation Method Using Bayesian Network in Telecommunications Networks. 2022 23rd Asia-Pacific Network Operations and Management Symposium (APNOMS). :1–4.
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2022. In the operation of information technology (IT) services, operators monitor the equipment-issued alarms, to locate the cause of a failure and take action. Alarms generate simultaneously from multiple devices with physical/logical connections. Therefore, if the time and location of the alarms are close to each other, it can be judged that the alarms are likely to be caused by the same event. In this paper, we propose a method that takes a novel approach by correlating alarms considering event units using a Bayesian network based on alarm generation time, generation place, and alarm type. The topology information becomes a critical decision element when doing the alarm correlation. However, errors may occur when topology information updates manually during failures or construction. Therefore, we show that event-by-event correlation with 100% accuracy is possible even if the topology information is 25% wrong by taking into location information other than topology information.
ISSN: 2576-8565
SIMulation: Demystifying (Insecure) Cellular Network based One-Tap Authentication Services. 2022 52nd Annual IEEE/IFIP International Conference on Dependable Systems and Networks (DSN). :534–546.
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2022. A recently emerged cellular network based One-Tap Authentication (OTAuth) scheme allows app users to quickly sign up or log in to their accounts conveniently: Mobile Network Operator (MNO) provided tokens instead of user passwords are used as identity credentials. After conducting a first in-depth security analysis, however, we have revealed several fundamental design flaws among popular OTAuth services, which allow an adversary to easily (1) perform unauthorized login and register new accounts as the victim, (2) illegally obtain identities of victims, and (3) interfere OTAuth services of legitimate apps. To further evaluate the impact of our identified issues, we propose a pipeline that integrates both static and dynamic analysis. We examined 1,025/894 Android/iOS apps, each app holding more than 100 million installations. We confirmed 396/398 Android/iOS apps are affected. Our research systematically reveals the threats against OTAuth services. Finally, we provide suggestions on how to mitigate these threats accordingly.
ISSN: 2158-3927
IoT Based Smart Grid Communication with Transmission Line Fault Identification. 2022 International Conference on Intelligent Controller and Computing for Smart Power (ICICCSP). :1—5.
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2022. The electrical grid connects all the generating stations to supply uninterruptible power to the consumers. With the advent of technology, smart sensors and communication are integrated with the existing grid to behave like a smart system. This smart grid is a two-way communication that connects the consumers and producers. It is a connected smart network that integrates electricity generation, transmission, substation, distribution, etc. In this smart grid, clean, reliable power with a high-efficiency rate of transmission is available. In this paper, a highly efficient smart management system of a smart grid with overall protection is proposed. This management system checks and monitors the parameters periodically. This future technology also develops a smart transformer with ac and dc compatibility, for self-protection and for the healing process.
Research on GIS Isolating Switch Mechanical Fault Diagnosis based on Cross-Validation Parameter Optimization Support Vector Machine. 2022 IEEE International Conference on High Voltage Engineering and Applications (ICHVE). :1—4.
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2022. GIS equipment is an important component of power system, and mechanical failure often occurs in the process of equipment operation. In order to realize GIS equipment mechanical fault intelligent detection, this paper presents a mechanical fault diagnosis model for GIS equipment based on cross-validation parameter optimization support vector machine (CV-SVM). Firstly, vibration experiment of isolating switch was carried out based on true 110 kV GIS vibration simulation experiment platform. Vibration signals were sampled under three conditions: normal, plum finger angle change fault, plum finger abrasion fault. Then, the c and G parameters of SVM are optimized by cross validation method and grid search method. A CV-SVM model for mechanical fault diagnosis was established. Finally, training and verification are carried out by using the training set and test set models in different states. The results show that the optimization of cross-validation parameters can effectively improve the accuracy of SVM classification model. It can realize the accurate identification of GIS equipment mechanical fault. This method has higher diagnostic efficiency and performance stability than traditional machine learning. This study can provide reference for on-line monitoring and intelligent fault diagnosis analysis of GIS equipment mechanical vibration.
On Valuing the Impact of Machine Learning Faults to Cyber-Physical Production Systems. 2022 IEEE International Conference on Omni-layer Intelligent Systems (COINS). :1—6.
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2022. Machine learning (ML) has been applied in prognostics and health management (PHM) to monitor and predict the health of industrial machinery. The use of PHM in production systems creates a cyber-physical, omni-layer system. While ML offers statistical improvements over previous methods, and brings statistical models to bear on new systems and PHM tasks, it is susceptible to performance degradation when the behavior of the systems that ML is receiving its inputs from changes. Natural changes such as physical wear and engineered changes such as maintenance and rebuild procedures are catalysts for performance degradation, and are both inherent to production systems. Drawing from data on the impact of maintenance procedures on ML performance in hydraulic actuators, this paper presents a simulation study that investigates how long it takes for ML performance degradation to create a difference in the throughput of serial production system. In particular, this investigation considers the performance of an ML model learned on data collected before a rebuild procedure is conducted on a hydraulic actuator and an ML model transfer learned on data collected after the rebuild procedure. Transfer learning is able to mitigate performance degradation, but there is still a significant impact on throughput. The conclusion is drawn that ML faults can have drastic, non-linear effects on the throughput of production systems.
Intelligent fault diagnosis technology of power transformer based on Artificial Intelligence. 2022 IEEE 6th Information Technology and Mechatronics Engineering Conference (ITOEC). 6:1968—1971.
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2022. Transformer is the key equipment of power system, and its stable operation is very important to the security of power system In practical application, with the progress of technology, the performance of transformer becomes more and more important, but faults also occur from time to time in practical application, and the traditional manual fault diagnosis needs to consume a lot of time and energy. At present, the rapid development of artificial intelligence technology provides a new research direction for timely and accurate detection and treatment of transformer faults. In this paper, a method of transformer fault diagnosis using artificial neural network is proposed. The neural network algorithm is used for off-line learning and training of the operation state data of normal and fault states. By adjusting the relationship between neuron nodes, the mapping relationship between fault characteristics and fault location is established by using network layer learning, Finally, the reasoning process from fault feature to fault location is realized to realize intelligent fault diagnosis.
Forensic Analysis of Automotive Controller Area Network Emissions for Problem Resolution. 2021 IEEE International Joint EMC/SI/PI and EMC Europe Symposium. :619–623.
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2021. Electromagnetic emissions associated with the transmission of automotive controller area network (CAN) messages within a passenger car have been analysed and used to reconstruct the original CAN messages. Concurrent monitoring of the CAN traffic via a wired connection to the vehicle OBD-II port was used to validate the effectiveness of the reconstruction process. These results confirm the feasibility of reconstructing in-vehicle network data for forensic purposes, without the need for wired access, at distances of up to 1 m from the vehicle by using magnetic field measurements, and up to 3 m using electric field measurements. This capability has applications in the identification and resolution of EMI issues in vehicle data network, as well as possible implications for automotive cybersecurity.
Research on fault diagnosis in early stage of software development based on Object-oriented Bayesian Networks. 2021 IEEE 21st International Conference on Software Quality, Reliability and Security Companion (QRS-C). :161–168.
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2021. Continuous development of Internet of Things, big data and other emerging technologies has brought new challenges to the reliability of security-critical system products in various industries. Fault detection and evaluation in the early stage of software plays an important role in improving the reliability of software. However, fault prediction and evaluation, which are currently focused on the early stage of software, hardly provide high guidance for actual project development. In this study, a fault diagnosis method based on object-oriented Bayesian network (OOBN) is proposed. Starting from the time dimension and internal logic, a two-dimensional metric fault propagation model is established to calculate the failure rate of each early stage of software respectively, and the fault relationship of each stage is analyzed to find out the key fault units. In particular, it explores and validates the relationship between the failure rate of code phase and the failure caused by faults in requirement analysis stage and design stage in a train control system, to alert the developer strictly accordance with the industry development standards for software requirements analysis, design and coding, so as to reduce potential faults in the early stage. There is evidence that the study plays a crucial role to optimize the cost of software development and avoid catastrophic consequences.
Efficient Binary Static Code Data Flow Analysis Using Unsupervised Learning. 2021 4th International Conference on Artificial Intelligence for Industries (AI4I). :89—90.
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2021. The ever increasing need to ensure that code is reliably, efficiently and safely constructed has fueled the evolution of popular static binary code analysis tools. In identifying potential coding flaws in binaries, tools such as IDA Pro are used to disassemble the binaries into an opcode/assembly language format in support of manual static code analysis. Because of the highly manual and resource intensive nature involved with analyzing large binaries, the probability of overlooking potential coding irregularities and inefficiencies is quite high. In this paper, a light-weight, unsupervised data flow methodology is described which uses highly-correlated data flow graph (CDFGs) to identify coding irregularities such that analysis time and required computing resources are minimized. Such analysis accuracy and efficiency gains are achieved by using a combination of graph analysis and unsupervised machine learning techniques which allows an analyst to focus on the most statistically significant flow patterns while performing binary static code analysis.
Comparison of Active Vulnerability Scanning vs. Passive Vulnerability Detection. 2021 International Conference on Information Security and Cryptology (ISCTURKEY). :87–92.
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2021. Vulnerability analysis is an integral part of an overall security program. Through identifying known security flaws and weaknesses, vulnerability identification tools help security practitioners to remediate the existing vulnerabilities on the networks. Thus, it is crucial that the results of such tools are complete, accurate, timely and they produce vulnerability results with minimum or no side-effects on the networks. To achieve these goals, Active Vulnerability Scanning (AVS) or Passive Vulnerability Detection (PVD) approaches can be used by network-based vulnerability scanners. In this work, we evaluate these two approaches with respect to efficiency and effectiveness. For the effectiveness analysis, we compare these two approaches empirically on a test environment and evaluate their outcomes. According to total amount of accuracy and precision, the PVD results are higher than AVS. As a result of our analysis, we conclude that PVD returns more complete and accurate results with considerably shorter scanning periods and with no side-effects on networks, compared to the AVS.
An Exploration of Microprocessor Self-Test Optimisation Based On Safe Faults. 2021 IEEE International Symposium on Defect and Fault Tolerance in VLSI and Nanotechnology Systems (DFT). :1—6.
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2021. Microprocessor software test libraries (STLs) must provide maximum fault coverage with minimum overhead. Pruning safe faults, which cannot cause errors in the output of the processor, from the fault list can increase fault coverage without adding test overhead. Applying more application-specific constraints can lead to the identification of more safe faults, and some such constraints are yet to be explored. This work explores the use of signal combination-based constraints alongside well-known constant signal-based constraints for identifying safe faults. Also, for the first time, information on safe faults is utilised during test compaction in order to further minimise test overhead. Results for an OpenRISC processor design show up to 2.33% improvement in fault coverage with the use of the proposed constraints. In one test program, a code segment contributing only to the coverage of safe faults is identified, with its removal providing a 1.09 % code size reduction on top of existing compaction techniques. The results may vary for a larger and more complex commercial design with greater scope for redundant logic. This work explores the use of signal combination-based constraints alongside well-known constant signal-based constraints for identifying safe faults. Also, for the first time, information on safe faults is utilised during test compaction in order to further minimise test overhead. Results for an OpenRISC processor design show up to 2.33% improvement in fault coverage with the use of the proposed constraints. In one test program, a code segment contributing only to the coverage of safe faults is identified, with its removal providing a 1.09 % code size reduction on top of existing compaction techniques. The results may vary for a larger and more complex commercial design with greater scope for redundant logic.
A Sensor Fault Diagnosis Algorithm for UAV Based on Neural Network. 2021 International Conference on Intelligent Transportation, Big Data Smart City (ICITBS). :260–265.
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2021. To improve the security and reliability of the system in case of sensor failure, a fault diagnosis algorithm based on neural network is proposed to locate the fault quickly and reconstruct the control system in this paper. Firstly, the typical airborne sensors are introduced and their common failure modes are analyzed. Then, a new method of complex feature extraction using wavelet packet is put forward to extract the fault characteristics of UAV sensors. Finally, the observer method based on BP neural network is adopted to train and acquire data offline, and to detect and process single or multiple sensor faults online. Matlab simulation results show that the algorithm has good diagnostic accuracy and strong generalization ability, which also has certain practicability in engineering.
Convolutional Compaction-Based MRAM Fault Diagnosis. 2021 IEEE European Test Symposium (ETS). :1–6.
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2021. Spin-transfer torque magnetoresistive random-access memories (STT-MRAMs) are gradually superseding conventional SRAMs as last-level cache in System-on-Chip designs. Their manufacturing process includes trimming a reference resistance in STT-MRAM modules to reliably determine the logic values of 0 and 1 during read operations. Typically, an on-chip trimming routine consists of multiple runs of a test algorithm with different settings of a trimming port. It may inherently produce a large number of mismatches. Diagnosis of such a sizeable volume of errors by means of existing memory built-in self-test (MBIST) schemes is either infeasible or a time-consuming and expensive process. In this paper, we propose a new memory fault diagnosis scheme capable of handling STT-MRAM-specific error rates in an efficient manner. It relies on a convolutional reduction of memory outputs and continuous shifting of the resultant data to a tester through a few output channels that are typically available in designs using an on-chip test compression technology, such as the embedded deterministic test. It is shown that processing the STT-MRAM output by using a convolutional compactor is a preferable solution for this type of applications, as it provides a high diagnostic resolution while incurring a low hardware overhead over traditional MBIST logic.
Multiple Open-Switch Fault Diagnosis Using ANNs for Three-Phase PWM Converters. 2021 24th International Conference on Electrical Machines and Systems (ICEMS). :2436–2439.
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2021. In this paper, a multiple switches open-fault diagnostic method using ANNs (Artificial Neural Networks) for three-phase PWM (Pulse Width Modulation) converters is proposed. When an open-fault occurs on switches in the converter, the stator currents can include dc and harmonic components. Since these abnormal currents cannot be easily cut off by protection circuits, secondary faults can occur in peripherals. Therefore, a method of diagnosing the open-fault is required. For open-faults for single switch and double switches, there are 21 types of fault modes depending on faulty switches. In this paper, these fault modes are localized by using the dc component and THD (Total Harmonics Distortion) in fault currents. For obtaining the dc component and THD in the currents, an ADALINE (Adaptive Linear Neuron) is used. For localizing fault modes, two ANNs are used in series; the 21 fault modes are categorized into six sectors by the first ANN of using the dc components, and then the second ANN localizes fault modes by using both the dc and THDs of the d-q axes current in each sector. Simulations and experiments confirm the validity of the proposed method.
A Reliable Open-Switch Fault Diagnosis Strategy for Grid-tied Photovoltaic Inverter Topology. 2021 International Conference on Automation, Control and Mechatronics for Industry 4.0 (ACMI). :1–4.
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2021. In order to increase the availability and reliability of photovoltaic (PV) systems, fault diagnosis and condition monitoring of inverters are of crucial means to meet the goals. Numerous methods are implemented for fault diagnosis of PV inverters, providing robust features and handling massive amount of data. However, existing methods rely on simplistic frameworks that are incapable of inspecting a wide range of intrinsic and explicit features, as well as being time-consuming. In this paper, a novel method based on a multilayer deep belief network (DBN) is suggested for fault diagnosis, which allows the framework to discover the probabilistic reconstruction across its inputs. This approach equips a robust hierarchical generative model for exploiting features associated with faults, interprets functions that are highly variable, and needs lesser prior information. Moreover, the method instantaneously categorizes the fault conditions, which eventually strengthens the adaptability of applying it on a variety of diagnostic problems in an inverter domain. The proposed method is evaluated using multiple input signals at different sampling frequencies. To evaluate the efficacy of DBN, a test model based on a three-phase 2-level grid-tied PV inverter was used. The results show that the method is capable of achieving precise diagnosis operations.
Collaboratively Diagnosing IGBT Open-circuit Faults in Photovoltaic Inverters: A Decentralized Federated Learning-based Method. IECON 2021 – 47th Annual Conference of the IEEE Industrial Electronics Society. :1–6.
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2021. In photovoltaic (PV) systems, machine learning-based methods have been used for fault detection and diagnosis in the past years, which require large amounts of data. However, fault types in a single PV station are usually insufficient in practice. Due to insufficient and non-identically distributed data, packet loss and privacy concerns, it is difficult to train a model for diagnosing all fault types. To address these issues, in this paper, we propose a decentralized federated learning (FL)-based fault diagnosis method for insulated gate bipolar transistor (IGBT) open-circuits in PV inverters. All PV stations use the convolutional neural network (CNN) to train local diagnosis models. By aggregating neighboring model parameters, each PV station benefits from the fault diagnosis knowledge learned from neighbors and achieves diagnosing all fault types without sharing original data. Extensive experiments are conducted in terms of non-identical data distributions, various transmission channel conditions and whether to use the FL framework. The results are as follows: 1) Using data with non-identical distributions, the collaboratively trained model diagnoses faults accurately and robustly; 2) The continuous transmission and aggregation of model parameters in multiple rounds make it possible to obtain ideal training results even in the presence of packet loss; 3) The proposed method allows each PV station to diagnose all fault types without original data sharing, which protects data privacy.
Multidimensional Reconstruction-Based Contribution for Multiple Faults Isolation with k-Nearest Neighbor Strategy. 2021 40th Chinese Control Conference (CCC). :4510–4515.
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2021. In the multivariable fault diagnosis of industrial process, due to the existence of correlation between variables, the result of fault diagnosis will inevitably appear "smearing" effect. Although the fault diagnosis method based on the contribution of multi-dimensional reconstruction is helpful when multiple faults occur. But in order to correctly isolate all the fault variables, this method will become very inefficient due to the combination of variables. In this paper, a fault diagnosis method based on kNN and MRBC is proposed to fundamentally avoid the corresponding influence of "smearing", and a fast variable selection strategy is designed to accelerate the process of fault isolation. Finally, simulation study on a benchmark process verifies the effectiveness of the method, in comparison with the traditional method represented by FDA-based method.
Optimal Solution Discrimination of an Analytic Model for Power Grid Fault Diagnosis Employing Electrical Criterion. 2021 4th International Conference on Energy, Electrical and Power Engineering (CEEPE). :744–750.
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2021. When a fault occurs in power grid, the analytic model for power grid fault diagnosis could generate multiple solutions under one or more protective relays (PRs) and/or circuit breakers (CBs) malfunctioning, and/or one or more their alarm information failing. Hence, this paper, calling the electrical quantities, presents an optimal solution discrimination method, which determines the optimal solution by constructing the electrical criteria of suspicious faulty components. Furthermore, combining the established electrical criteria with the existing analytic model, a hierarchical fault diagnosis mode is proposed. It uses the analytic model for the first level diagnosis based on the switching quantities. Thereafter, aiming at multiple solutions, it applies the electrical criteria for the second level diagnosis to determine the diagnostic result. Finally, the examples of fault diagnosis demonstrate the feasibility and effectiveness of the developed method.
A Novel Assessment Metric for Intelligent Fault Diagnosis of Rolling Bearings with Different Fault Severities and Orientations. 2021 7th International Conference on Condition Monitoring of Machinery in Non-Stationary Operations (CMMNO). :225–228.
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2021. The output of rolling bearings, as one of the most widely used support elements, has a significant impact on the equipment's stability and protection. Automatic and effective mining of features representing performance condition plays an important role in ensuring its reliability. However, in the actual process, there are often differences in the quality of features extracted from feature engineering, and this difference cannot be evaluated by commonly used methods, such as correlation metric and monotonicity metric. In order to accurately and automatically evaluate and select effective features, a novel assessment metric is established based on the attributes of the feature itself. Firstly, the features are extracted from different domains, which contain differential information, and a feature set is constructed. Secondly, the performances of the features are evaluated and selected based on internal distance and external distance, which is a novel feature evaluation model for classification task. Finally, an adaptive boosting strategy that combines multiple weak learners is adopted to achieve the fault identification at different severities and orientations. One experimental bearing dataset is adopted to analyze, and effectiveness and accuracy of proposed metric index is verified.
Multi-band Analysis for Enhancing Multiple Combined Fault Diagnosis. 2021 18th International Multi-Conference on Systems, Signals Devices (SSD). :116–123.
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2021. In this work, a novel approach to detect and diagnose single and combined faults in the Induction Motor (IM) is proposed. In Condition Monitoring Systems (CMS) based on the Motor Current Signature Analysis (MCSA), the simultaneous occurrence of multiple faults is a major challenge. An innovative technique called Multiple Windowed Harmonic Wavelet Packet Transform (MWHWPT) is used in order to discriminate between the faulty components of the IM, even during compound faults. Thus, each motor component is monitored by a specific Fault Index (FI) which allows the fault diagnosis without the need for a classifier. The tests carried on Rotor and Bearing faults show high fault diagnosis rate even during compound faults and proves the competitive performance of the proposed approach with literature works.
Comparison on Multiple Signal Analysis Method in Transformer Core Looseness Fault. 2021 IEEE Asia-Pacific Conference on Image Processing, Electronics and Computers (IPEC). :908–911.
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2021. The core looseness fault is an important part of transformer fault. The state of the core can be obtained by analyzing the vibration signal. Vibration analysis method has been used in transformer condition monitoring and fault diagnosis for many years, while different methods produce different results. In order to select the correct method in engineering application, five kinds of joint time-frequency analysis methods, such as short-time Fourier transform, Wigner-Ville distribution, S transform, wavelet transform and empirical mode decomposition are compared, and the advantages and disadvantages of these methods for dealing with the vibration signal of transformer core are analyzed in this paper. It indicates that wavelet transform and empirical mode decomposition have more advantages in the diagnosis of core looseness fault. The conclusions have referential significance for the diagnosis of transformer faults in engineering.
Application of multi-fault diagnosis based on discrete event system in industrial sensor network. 2021 4th International Conference on Advanced Electronic Materials, Computers and Software Engineering (AEMCSE). :1122–1126.
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2021. This paper presents a method to improve the diagnosability of power network under multiple faults. In this paper, the steps of fault diagnosis are as follows: first, constructing finite automata model of the diagnostic system; then, a fault diagnoser model is established through coupling operation and trajectory reasoning mechanism; finally, the diagnosis results are obtained through this model. In this paper, the judgment basis of diagnosability is defined. Then, based on the existing diagnosis results, the information available can be increased by adding sensor devices, to achieve the purpose of diagnosability in the case of multiple faults of the system.