Multi-mode process monitoring based on a novel weighted local standardization strategy and support vector data description

There are multiple operating modes in the real industrial process, and the collected data follow the complex multimodal distribution, so most traditional process monitoring methods are no longer applicable because their presumptions are that sampled-data should obey the single Gaussian distribution or non-Gaussian distribution. In order to solve these problems, a novel weighted local standardization(WLS) strategy is proposed to standardize the multimodal data, which can eliminate the multi-mode characteristics of the collected data, and normalize them into unimodal data distribution. After detailed analysis of the raised data preprocessing strategy, a new algorithm using WLS strategy with support vector data description(SVDD) is put forward to apply for multi-mode monitoring process. Unlike the strategy of building multiple local models, the developed method only contains a model without the prior knowledge of multi-mode process. To demonstrate the proposed method's validity, it is applied to a numerical example and a Tennessee Eastman(TE) process. Finally, the simulation results show that the WLS strategy is very effective to standardize multimodal data, and the WLS-SVDD monitoring method has great advantages over the traditional SVDD and PCA combined with a local standardization strategy(LNS-PCA) in multi-mode process monitoring.

Multi-Fault Diagnosis for Autonomous Underwater Vehicle Based on Fuzzy Weighted Support Vector Domain Description

This paper addresses the multi-fault diagnosis problem of thrusters and sensors for autonomous underwater vehicles (AUVs). Traditional support vector domain description (SVDD) has low classification accuracy in the process of AUV multi-fault pattern classification because of the effect of sample sparse density and the uneven distribution of samples, and so on. Thus, a fuzzy weighted support vector domain description (FWSVDD) method based on positive and negative class samples is proposed. In this method, the negative class sample is introduced during classifier training, and the local density and the class weight are introduced for each sample. To improve the multi-fault pattern classifier training speed and fault diagnosis accuracy of FWSVDD, a multi-fault mode classification method based on a hierarchical strategy is proposed. This method adds fault contain detection surface for each thruster and sensor to isolate fault components during fault diagnosis. By considering the problem of pattern classification for a fuzzy sample, which may be located in the overlapping area of hyper-spheres or may not belong to any hyper-sphere in the process of multi-fault classification based on FWSVDD, a relative distance judgment method is given. The effectiveness of the proposed multi-fault diagnosis approach is demonstrated through water tank experiments with an experimental AUV prototype.

Confidence support vector domain description

To accelerate the training of support vector domain description （SVDD）, confidence support vector domain description （CSVDD） is proposed based on the observation that the description boundary is determined by a small subset of training data called support vectors. Namely, the number of training samples in the userdefined sphere is calculated and taken as the confidence measure, according to which the training samples are ranked in ascending order. Those former ranked ones are selected as the boundary targets for the SVDD training. Simulations on UCI data demonstrate the effectiveness and superiority of CSVDD： the number of training targets and the training time are reduced without any loss of accuracy.

Natural Numbers and the Strong Goldbach Conjecture

This study introduces the representation of natural number sets as row vectors and pretends to offer a new perspective on the strong Goldbach conjecture. The natural numbers are restructured and expanded with the inclusion of the zero element as the source of a strong Goldbach conjecture reformulation. A prime Boolean vector is defined, pinpointing the positions of prime numbers within the odd number sequence. The natural unit primality is discussed in this context and transformed into a source of quantum-like indetermination. This approach allows for rephrasing the strong Goldbach conjecture, framed within a Boolean scalar product between the prime Boolean vector and its reverse. Throughout the discussion, other intriguing topics emerge and are thoroughly analyzed. A final description of two empirical algorithms is provided to prove the strong Goldbach conjecture.

A Dual-Task Learning Approach for Bearing Anomaly Detection and State Evaluation of Safe Region

Predictive maintenance has emerged as an effective tool for curbing maintenance costs,yet prevailing research predominantly concentrates on the abnormal phases.Within the ostensibly stable healthy phase,the reliance on anomaly detection to preempt equipment malfunctions faces the challenge of sudden anomaly discernment.To address this challenge,this paper proposes a dual-task learning approach for bearing anomaly detection and state evaluation of safe regions.The proposed method transforms the execution of the two tasks into an optimization issue of the hypersphere center.By leveraging the monotonicity and distinguishability pertinent to the tasks as the foundation for optimization,it reconstructs the SVDD model to ensure equilibrium in the model’s performance across the two tasks.Subsequent experiments verify the proposed method’s effectiveness,which is interpreted from the perspectives of parameter adjustment and enveloping trade-offs.In the meantime,experimental results also show two deficiencies in anomaly detection accuracy and state evaluation metrics.Their theoretical analysis inspires us to focus on feature extraction and data collection to achieve improvements.The proposed method lays the foundation for realizing predictive maintenance in a healthy stage by improving condition awareness in safe regions.

ESSENTIAL RELATIONSHIP BETWEEN DOMAIN-BASED ONE-CLASS CLASSIFIERS AND DENSITY ESTIMATION

One-class support vector machine （OCSVM） and support vector data description （SVDD） are two main domain-based one-class （kernel） classifiers. To reveal their relationship with density estimation in the case of the Gaussian kernel, OCSVM and SVDD are firstly unified into the framework of kernel density estimation, and the essential relationship between them is explicitly revealed. Then the result proves that the density estimation induced by OCSVM or SVDD is in agreement with the true density. Meanwhile, it can also reduce the integrated squared error （ISE）. Finally, experiments on several simulated datasets verify the revealed relationships.

Interactive early warning technique based on SVDD

After reviewing current researches on early warning, it is found that “bad”data of some systems is not easy to obtain, which makes methods proposed by these researches unsuitable for monitored systems. An interactive early warning technique based on SVDD （support vector data description） is proposed to adopt “good” data as samples to overcome the difficulty in obtaining the “bad” data. The process consists of two parts： （1） A hypersphere is fitted on “good” data using SVDD. If the data object are outside the hypersphere, it would be taken as “suspicious”; （2） A group of experts would decide whether the suspicious data is “bad” or “good”, early warning messages would be issued according to the decisions. And the detailed process of implementation is proposed. At last, an experiment based on data of a macroeconomic system is conducted to verify the proposed technique.

Rolling bearing performance degradation evaluation by VMD and embedding selection-based NPE

In order to improve the incipient fault sensitivity and stability of degradation index in the rolling bearing performance degradation evaluation process,an embedding selection-based neighborhood preserving embedding(ESNPE)method is proposed.Firstly,the acquired vibration signals are decomposed by variational mode decomposition(VMD),and the singular value and relative energy of each intrinsic mode function(IMF)are extracted to form a high-dimensional feature set.Then,the NPE manifold learning method is used to extract the embedded features in the feature space.Considering the problem that useful embedding information is easily suppressed in NPE,an embedding selection strategy is built based on the Spearman correlation coefficient.The effectiveness of embeddings is measured by the coefficient absolute value,and useful embeddings are preserved in the early stage of bearing degradation by using the first-order difference method.Finally,the degradation index is established using the support vector data description(SVDD)model and bearing performance degradation evaluation is achieved.The proposed method was tested with the whole life experiment data of a rolling bearing,and the result was compared with the feature extraction methods of traditional principal component analysis(PCA)and NPE.The results show that the proposed method is superior in improving the incipient fault sensitivity and stability of the degradation index.

Life prediction of ZPW-2000A track circuit equipment based on SVDD and gray prediction

Evaluation of the health state and prediction of the remaining life of the track circuit are important for the safe operation of the equipment of railway signal system.Based on support vector data description(SVDD)and gray prediction,this paper illustrates a method of life prediction for ZPW-2000A track circuit,which combines entropy weight method,SVDD,Mahalanobis distance and negative conversion function to set up a health state assessment model.The model transforms multiple factors affecting the health state into a health index named H to reflect the health state of the equipment.According to H,the life prediction model of ZPW-2000A track circuit equipment is established by means of gray prediction so as to predict the trend of health state of the equipment.The certification of the example shows that the method can visually reflect the health state and effectively predict the remaining life of the equipment.It also provides a theoretical basis to further improve the maintenance and management for ZPW-2000A track circuit.

A Method of Shield Attitude Working Condition Classification

Aiming at solving shield attitude rectification failure problem,a method of shield working condition classification based on support vector data description( SVDD) was introduced. Shield attitude mechanics model containing priori knowledge was helpful to feature selection. SVDD handled the one class classification problem and a decision function for attitude rectification was proposed. Experimental results indicate that the method is able to accomplish the shield attitude working condition classification.

Progressive transductive learning pattern classification via single sphere

In many machine learning problems, a large amount of data is available but only a few of them can be labeled easily. This provides a research branch to effectively combine unlabeled and labeled data to infer the labels of unlabeled ones, that is, to develop transductive learning. In this article, based on Pattern classification via single sphere （SSPC）, which seeks a hypersphere to separate data with the maximum separation ratio, a progressive transductive pattern classification method via single sphere （PTSSPC） is proposed to construct the classifier using both the labeled and unlabeled data. PTSSPC utilize the additional information of the unlabeled samples and obtain better classification performance than SSPC when insufficient labeled data information is available. Experiment results show the algorithm can yields better performance.

Power transmission risk assessment considering component condition

This paper proposes a new method for power transmission risk assessment considering historical failure statistics of transmission systems and operation failure risks of system components.Component failure risks are integrated into the new method based on operational condition assessment of components using the support vector data description(SVDD)approach.The traditional outage probability model of transmission lines has been modified to build a new framework for power transmission system risk assessment.The proposed SVDD approach can provide a suitable mechanism to map component assessment grades to failure risks based on probabilistic behaviors of power system failures.Under the new method,both up-todate component failure risks and traditional system risk indices can be processed with the proposed outage model.As a result,component failure probabilities are not only related to historical statistic data but also operational data of components,and derived risk indices can reflect current operational conditions of components.In simulation studies,the SVDD approach is employed to evaluate component conditions and link such conditions to failure rates using up-to-date component operational data,including both on-line and off-line data of components.The IEEE 24-bus RTS-1979 system is used to demonstrate that component operational conditions can greatly affect the overall transmission system failure risks.