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Grid-moving equivalent source method in a probability framework for the transformer discharge fault localization

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MEASUREMENT 2022年 191卷 110800-110800页

作者： Yu, Liang Zhang, Chenyu Wang, Ran Yuan, Guogang Wang, Xiao Shanghai Jiao Tong Univ Inst Vibrat Shock & Noise State Key Lab Mech Syst & Vibrat Shanghai 200240 Peoples R China Shanghai Maritime Univ Coll Logist Engn Shanghai 201306 Peoples R China Shanghai Rhythm Elect Technol Ltd Co Shanghai 201108 Peoples R China

The transformer discharge fault localization is important for the power supply reliability. The audible sound radiated by the transformer can reflect the extensive operation information. Thus, discharge faults can be localized by high spatial resolution acoustic imaging techniques to facilitate the inspection and maintenance of power equipment. In this paper, the grid-moving equivalent source method (GMESM) is proposed to visualize the discharge fault on a transformer, where the equivalent source grids can approach the discharge fault position adaptively. A probability framework is established in GMESM. The noise power can be firstly estimated by the Bayes rule to avoid an additional measurement of the background noise. Then, the expectation maximization algorithm is used to optimize the proposed model. Two experiment cases are used to validate the proposed method. It turns out that the proposed GMESM can visualize the discharge fault on the transformer with high spatial resolution and accuracy.

关键词： Acoustic imaging Transformer discharge fault expectation maximization algorithm Noise power estimation Bayes rule

An approach to operational modal analysis using the expectation maximization algorithm

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MECHANICAL SYSTEMS AND SIGNAL PROCESSING 2012年 31卷 109-129页

作者： Cara, F. Javier Carpio, Jaime Juan, Jesus Alarcon, Enrique Univ Politecn Madrid Stat Lab ETS Ingenieros Ind E-28006 Madrid Spain Univ Politecn Madrid Dept Struct Mech ETS Ingenieros Ind E-28006 Madrid Spain

This paper presents the expectation maximization algorithm (EM) applied to operational modal analysis of structures. The EM algorithm is a general-purpose method for maximum likelihood estimation (MLE) that in this work is used to estimate state space models. As it is well known, the MLE enjoys some optimal properties from a statistical point of view, which make it very attractive in practice. However, the EM algorithm has two main drawbacks: its slow convergence and the dependence of the solution on the initial values used. This paper proposes two different strategies to choose initial values for the EM algorithm when used for operational modal analysis: to begin with the parameters estimated by Stochastic Subspace Identification method (SSI) and to start using random points. The effectiveness of the proposed identification method has been evaluated through numerical simulation and measured vibration data in the context of a benchmark problem. Modal parameters (natural frequencies, damping ratios and mode shapes) of the benchmark structure have been estimated using SSI and the EM algorithm. On the whole, the results show that the application of the EM algorithm starting from the solution given by SSI is very useful to identify the vibration modes of a structure, discarding the spurious modes that appear in high order models and discovering other hidden modes. Similar results are obtained using random starting values, although this strategy allows us to analyze the solution of several starting points what overcome the dependence on the initial values used. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Structural dynamics Operational modal analysis System identification Stochastic subspace identification method Maximum likelihood estimation expectation maximization algorithm

Estimation of finite population proportions for small areas – a statistical data integration approach

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arXiv 2023年

作者： Sen, Aditi Lahiri, Partha University of Maryland College Park United States The Joint Program in Survey Methodology Department of Mathematics University of Maryland College ParkMD20742 United States

Empirical best prediction (EBP) is a well-known method for producing reliable proportion estimates when the primary data source provides only small or no sample from finite populations. There are potential challenges in implementing existing EBP methodology such as limited auxiliary variables in the frame (not adequate for building a reasonable working predictive model) or unable to accurately link the sample to the finite population frame due to absence of identifiers. In this paper, we propose a new data linkage approach where the finite population frame is replaced by a big probability sample, having a large set of auxiliary variables but not the outcome binary variable of interest. We fit an assumed model on the small probability sample and then impute the outcome variable for all units of the big sample to obtain standard weighted proportions. We develop a new adjusted maximum likelihood (ML) method so that the estimate of model variance doesn’t fall on the boundary, which is otherwise encountered in commonly used ML method. We also propose an estimator of the mean squared prediction error using a parametric bootstrap method and address computational issues by developing an efficient expectation maximization algorithm. The proposed methodology is illustrated in the context of election projection for small areas. © 2023, CC BY.

关键词： expectation maximization algorithm

Adaptive maximization of social welfare

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arXiv 2023年

作者： Cesa-Bianchi, Nicolò Colomboni, Roberto Kasy, Maximilian Università degli Studi di Milano Politecnico di Milano Italy Department of Economics University of Oxford United Kingdom

We consider the problem of repeatedly choosing policies to maximize social welfare. Welfare is a weighted sum of private utility and public revenue. Earlier outcomes inform later policies. Utility is not observed, but indirectly inferred. Response functions are learned through experimentation. We derive a lower bound on regret, and a matching adversarial upper bound for a variant of the Exp3 algorithm. Cumulative regret grows at a rate of T2/3. This implies that (i) welfare maximization is harder than the multi-armed bandit problem (with a rate of T1/2 for finite policy sets), and (ii) our algorithm achieves the optimal rate. For the stochastic setting, if social welfare is concave, we can achieve a rate of T1/2 (for continuous policy sets), using a dyadic search algorithm. We analyze an extension to nonlinear income taxation, and sketch an extension to commodity taxation. We compare our setting to monopoly pricing (which is easier), and price setting for bilateral trade (which is harder). © 2023, CC BY-NC-SA.

关键词： expectation maximization algorithm

Deep Out-of-Distribution Uncertainty Quantification via Weight Entropy maximization

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arXiv 2023年

作者： de Mathelin, Antoine Deheeger, François Mougeot, Mathilde Vayatis, Nicolas Manufacture Française des pneumatiques Michelin Clermont-Ferrand63000 France Centre Borelli Université Paris-Saclay CNRS ENS Paris-Saclay Gif-sur-Yvette91190 France

This paper deals with uncertainty quantification and out-of-distribution detection in deep learning using Bayesian and ensemble methods. It proposes a practical solution to the lack of prediction diversity observed recently for standard approaches when used out-of-distribution (Ovadia et al., 2019;Liu et al., 2021). Considering that this issue is mainly related to a lack of weight diversity, we claim that standard methods sample in "over-restricted" regions of the weight space due to the use of "over-regularization" processes, such as weight decay and zero-mean centered Gaussian priors. We propose to solve the problem by adopting the maximum entropy principle for the weight distribution, with the underlying idea to maximize the weight diversity. Under this paradigm, the epistemic uncertainty is described by the weight distribution of maximal entropy that produces neural networks "consistent" with the training observations. Considering stochastic neural networks, a practical optimization is derived to build such a distribution, defined as a trade-off between the average empirical risk and the weight distribution entropy. We provide both theoretical and numerical results to assess the efficiency of the approach. In particular, the proposed algorithm appears in the top three best methods in all configurations of an extensive out-of-distribution detection benchmark including more than thirty competitors. © 2023, CC BY.

关键词： expectation maximization algorithm

Distinctiveness maximization in Datasets Assemblage

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arXiv 2023年

作者： Wang, Tingting Huang, Shixun Bao, Zhifeng Culpepper, J. Shane Dedeoglu, Volkan Arablouei, Reza RMIT University MelbourneVIC Australia The University of Wollongong WollongongNSW Australia The University of Queensland St LuciaQLD Australia CSIRO’s Data61 PullenvaleQLD Australia

In this paper, given a user’s query set and budget, we aim to use the limited budget to help users assemble a set of datasets that can enrich a base dataset by introducing the maximum number of distinct tuples (i.e., maximizing distinctiveness). We prove this problem to be NP-hard. A greedy algorithm using exact distinctiveness computation attains an approximation ratio of (1 − e−1)/2, but it lacks efficiency and scalability due to its frequent computation of the exact distinctiveness marginal gain of any candidate dataset for selection. This requires scanning through every tuple in candidate datasets and thus is unaffordable in practice. To overcome this limitation, we propose an efficient machine learning (ML)-based method for estimating the distinctiveness marginal gain of any candidate dataset. This effectively eliminates the need to test each tuple individually. Estimating the distinctiveness marginal gain of a dataset involves estimating the number of distinct tuples in the tuple sets returned by each query in a query set across multiple datasets. This can be viewed as the cardinality estimation for a query set on a set of datasets, and the proposed method is the first to tackle this cardinality estimation problem. This is a significant advancement over prior methods that were limited to single-query cardinality estimation on a single dataset and struggled with identifying overlaps among tuple sets returned by each query in a query set across multiple datasets. Extensive experiments using five real-world data pools demonstrate that our algorithm, which utilizes ML-based distinctiveness estimation, outperforms all relevant baselines in effectiveness, efficiency, and scalability. A case study on two downstream ML tasks also highlights its potential to find datasets with more useful tuples to enhance the performance of ML tasks. Copyright © 2023, The Authors. All rights reserved.

关键词： expectation maximization algorithm

Blind source separation with time series variational Bayes expectation maximization algorithm

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DIGITAL SIGNAL PROCESSING 2012年第1期22卷 17-33页

作者： Sun, Shijun Peng, Chenglin Hou, Wensheng Zheng, Jun Jiang, Yingtao Zheng, Xiaolin Zhanjiang Normal Coll Sch Phys Sci & Technol Zhanjiang 524048 Guangdong Peoples R China Chongqing Univ Bioengn Coll Chongqing 400030 Peoples R China New Mexico Inst Min & Technol Dept Comp Sci Socorro NM 87801 USA Univ Nevada Dept Elect & Comp Engn Las Vegas NV 89154 USA

This paper presents a variational Bayes expectation maximization algorithm for time series based on Attias' variational Bayesian theory. The proposed algorithm is applied in the blind source separation (BSS) problem to estimate both the source signals and the mixing matrix for the optimal model structure. The distribution of the mixing matrix is assumed to be a matrix Gaussian distribution due to the correlation of its elements and the inverse covariance of the sensor noise is assumed to be Wishart distributed for the correlation between sensor noises. The mixture of Gaussian model is used to approximate the distribution of each independent source. The rules to update the posterior hyperparameters and the posterior of the model structure are obtained. The optimal model structure is selected as the one with largest posterior. The source signals and mixing matrix are estimated by applying LMS and MAP estimators to the posterior distributions of the hidden variables and the model parameters respectively for the optimal structure. The proposed algorithm is tested with synthetic data. The results show that: (1) the logarithm posterior of the model structure increases with the accuracy of the posterior mixing matrix: (2) the accuracies of the prior mixing matrix, the estimated mixing matrix, and the estimated source signals increase with the logarithm posterior of the model structure. This algorithm is applied to Magnetoencephalograph data to localize the source of the equivalent current dipoles. (C) 2010 Elsevier Inc. All rights reserved.

关键词： Time series Variational Bayes expectation maximization algorithm Blind source separation

Learning Atom Probe Tomography time-of-flight peaks for mass-to-charge ratio spectrometry

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ULTRAMICROSCOPY 2022年 237卷 113521页

作者： Coakley, Kevin J. Sanford, Norman A. NIST 325 Broadway Boulder CO 80305 USA

In laser-assisted atom probe tomography, an important goal is to reconstruct the mass-to-charge ratio, (m/z), spectrum due to various ion species. In general, the probability mass function (pmf) associated with the time-of-flight (TOF) spectrum produced by each ion species is unknown and varies from species-to-species. Moreover, measuring pmfs for distinct ion species in calibration experiments is not practical. Here, we present a mixture model method to determine TOF pmfs that can vary from peak-to-peak. In this approach, we determine weights of candidate pmfs with a maximum likelihood method. In a proof-of-principle study, we apply our method to a TOF spectrum acquired from a silicon sample and determine intensity estimates of singly charged isotopes of silicon.

关键词： Atom Probe Tomography Cross-validation expectation maximization algorithm Machine learning Maximum likelihood Mixture model Silicon isotopes

On-line harmonic signal denoising from the measurement with non-stationary and non-Gaussian noise

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SIGNAL PROCESSING 2022年 201卷

作者： Yu, Liang Chen, Yanqi Zhang, Yongli Wang, Ran Zhang, Zhaodong Shanghai Jiao Tong Univ State Key Lab Mech Syst & Vibrat Inst Vibrat Shock & Noise Shanghai 200240 Peoples R China Hagong Intelligent Robot Co Ltd Shanghai 201100 Peoples R China Shanghai Maritime Univ Coll Logist Engn Shanghai 201306 Peoples R China

Harmonic denoising is one of the important preprocessing steps before extracting harmonic signal characteristics. Several signal processing techniques have been developed and applied for denoising the harmonics, which assume that the noise follows a Gaussian distribution and is stationary. However, the noise is often not so simple as a Gaussian distribution, and it could be non-Gaussian and non-stationary in most practical scenarios. A novel online denoising method for the harmonic signal with non-stationary complex noises based on the Bayesian Maximum a Posteriori (MAP) framework is proposed in this paper. The measured signal is divided equally into several frames. Then these frames are transformed into the time-frequency domain by the Short-Time Fourier transform (STFT) and are assumed to be the sum of a low-rank matrix and a noise matrix. The online model of the low-rank matrix and the noise matrix is then constructed between the frames. The online Gaussian mixture model (GMM) and low-rank matrix factorization are performed on the measurement matrix in the complex number domain to reconstruct the harmonic signal. The performance of the proposed method is validated in the simulations. The non-Gaussian and non-stationary noise can be removed more effectively, and the proposed algorithm can improve the frequency estimation accuracy. (C) 2022 Elsevier B.V. All rights reserved.

关键词： Harmonic denoising Gaussian mixture model Low-rank modeling Online algorithm expectation maximization algorithm