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Gaussian process metamodel and Markov chain Monte Carlo-based bayesian inference framework for stochastic nonlinear model updating with uncertainties

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PROBABILISTIC ENGINEERING MECHANICS 2024年 75卷

作者： Ding, Ya-Jie Wang, Zuo-Cai Xin, Yu Hefei Univ Dept Urban Construct & Transportat Hefei 230601 Anhui Peoples R China Hefei Univ Anhui Prov Key Lab Urban Rail Transit Safety & Eme Hefei 230601 Anhui Peoples R China Hefei Univ Technol Dept Civil Engn Hefei 230601 Anhui Peoples R China Anhui Engn Technol Res Ctr Civil Engn Disaster Pre Hefei 230009 Anhui Peoples R China 99 Jinxiu Rd Hefei 230000 Anhui Peoples R China

The estimation of the posterior probability density function (PDF) of unknown parameters remains a challenge in stochastic nonlinear model updating with uncertainties;thus, a novel bayesian inference framework based on the Gaussian process metamodel (GPM) and the advanced Markov chain Monte Carlo (MCMC) method is proposed in this paper. The instantaneous characteristics (ICs) of the decomposed measurement response, calculated using the Hilbert transform and the discrete analytical mode decomposition methodology, are extracted as nonlinear indices and further used to construct the likelihood function. Then, the posterior PDFs of structural nonlinear model parameters are derived based on the bayesian theorem. To precisely calculate the posterior PDF, an advanced MCMC approach, i.e., delayed rejection adaptive Metropolis-Hastings (DRAM) algorithm, is adopted with the advantages of a high acceptance ratio and strong robustness. However, as a common shortage in most MCMC methods, the resampling technology is still applied, and numerous iterations of nonlinear simulations are conducted to ensure accuracy, thus directly reducing the computational efficiency of the DRAM. To address the abovementioned issue, a mathematical regression metamodel of the GPM with a polynomial kernel function is adopted in this paper instead of the traditional finite element model (FEM) to simulate a nonlinear response for the reduction of computational cost, and the hyperparameters are further estimated using the conjugate gradient optimization methodology. Finally, numerical simulations concerning a Giuffre '-Menegotto-Pinto modeled steelframe structure and a seven-storey base-isolated structure are conducted. Furthermore, a shake-table experimental test of a nonlinear steel framework is investigated to validate the accuracy of the bayesian inference method. Both simulations and experiment demonstrate that the proposed GPM and DRAM-based bayesian method effectively estimates the posterior PDF o

关键词： Nonlinear model updating Uncertainty quantification bayesian inference framework Markov chain Monte Carlo Instantaneous characteristics

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Object tracking using discriminative sparse appearance model

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SIGNAL PROCESSING-IMAGE COMMUNICATION 2015年 37卷 1-18页

作者： Huang, Dandan Sun, Yi Dalian Univ Technol Dept Elect Engn Dalian 116024 Liaoning Peoples R China

Object tracking based on sparse representation formulates tracking as searching the candidate with minimal reconstruction error in target template subspace. The key problem lies in modeling the target robustly to vary appearances. The appearance model in most sparsity-based trackers has two main problems. The first is that global structural information and local features are insufficiently combined because the appearance is modeled separately by holistic and local sparse representations. The second problem is that the discriminative information between the target and the background is not fully utilized because the background is rarely considered in modeling. In this study, we develop a robust visual tracking algorithm by modeling the target as a model for discriminative sparse appearance. A discriminative dictionary is trained from the local target patches and the background. The patches display the local features while their position distribution implies the global structure of the target. Thus, the learned dictionary can fully represent the target. The incorporation of the background into dictionary learning also enhances its discriminative capability. Upon modeling the target as a sparse coding histogram based on this learned dictionary, our tracker is embedded into a bayesian state inference framework to locate a target. We also present a model update scheme in which the update rate is adjusted automatically. In conjunction with the update strategy, the proposed tracker can handle occlusion and alleviate drifting. Comparative results on challenging benchmark image sequences show that the tracking method performs favorably against several state-of-the-art algorithms. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Visual tracking Sparse representation Dictionary learning Adaptive update bayesian inference framework

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Black Hole Entropic Fuzzy Clustering

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IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS 2018年第9期48卷 1622-1636页

作者： Liu, Jiefang Chung, Fu-Lai Wang, Shitong Jiangnan Univ Sch Digital Media Wuxi 214122 Peoples R China Hubei Commun Tech Coll Sch Traff Informat Wuhan 430079 Hubei Peoples R China Hong Kong Polytech Univ Dept Comp Hong Kong Hong Kong Peoples R China

Clustering is a common approach for finding the intrinsic pattern structure embedded in unlabeled data. In this paper, a new clustering algorithm, called black hole entropic fuzzy clustering (BHEFC), is presented to absorb the merits of three aspects: 1) black hole entropy (BHE)-based information theory;2) fuzzy clustering;and 3) bayesian inference model. First, through the link between clustering and the black hole phenomenon in astrophysics, the minimum BHE criterion for fuzzy clustering is proposed. Then, it is revealed that BHE-based fuzzy clustering can be realized by using a maximum-a-posteriori (MAP) framework, which in fact indicates that fuzziness and probability can co-jointly work in a collaborative rather than repulsive way. According to the proposed MAP framework for BHEFC, the fuzzifier m, which is limited to be less than 1 rather than bigger than 1 in fuzzy c-means, can be explained as the partition accuracy in the form of (1-m) for a dataset, and the fuzzy memberships and clustering centers can be determined in a probabilistic inference way, by means of iterative sampling with the assumption of the Dirichlet distribution of the fuzzy memberships. The incremental version of the proposed fuzzy clustering model is also developed here. Experimental results on synthetic and real datasets and images for segmentation demonstrate the improved clustering results of the proposed algorithms over the comparison algorithms.

关键词： bayesian inference framework black hole entropy (BHE) fuzzy clustering algorithms probabilistic clustering model

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Compact discriminative object representation via weakly supervised learning for real-time visual tracking

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IET COMPUTER VISION 2017年第7期11卷 585-595页

作者： Shen, Weichao Wu, Yuwei Jia, Yunde Beijing Inst Technol Sch Comp Sci Beijing Lab Intelligent Informat Technol Beijing 100081 Peoples R China

Object representations are of great importance for robust visual tracking. Although the high-dimensional representation can effectively encode the input data with more information, exploiting it in a real-time tracking system would be intractable and infeasible due to the high computational cost and memory requirements. In this study, the authors propose a compact discriminative object representation to achieve both good tracking accuracy and efficiency. An ensemble of weak training sets is generated based on the self-representative ability of tracking samples, which is applied to learn discriminative functions. Each candidate is represented by the concatenation of project values on all the weak training sets. Tracking is then carried out within a bayesian inference framework where the classification score of the support vector machine is used to construct the observation model. The evaluations on TB50 benchmark dataset demonstrate that the proposed algorithm is much more computationally efficient than the state-of-the-art methods with comparable accuracy.

关键词： learning (artificial intelligence) object tracking real-time systems Bayes methods inference mechanisms support vector machines image classification object representation learning weakly supervised learning real-time visual tracking real-time tracking system bayesian inference framework classification score support vector machine computational efficiency

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bayesian zero-order TSK fuzzy system modeling

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APPLIED SOFT COMPUTING 2017年 55卷 253-264页

作者： Liu, Jiefang Chung, Fu-lai Wang, Shitong Jiangnan Univ Sch Digital Media Wuxi Jiangsu Peoples R China Hong Kong Polytech Univ Dept Comp Hong Kong Hong Kong Peoples R China Hubei Commun Tech Coll Sch Transportat & Informat Wuhan Peoples R China

Different from the existing TSK fuzzy system modeling methods, a novel zero-order TSK fuzzy modeling method called bayesian zero-order TSK fuzzy system (B-ZTSK-FS) is proposed from the perspective of bayesian inference in this paper. The proposed method B-ZTSK-FS constructs zero-order TSK fuzzy system by using the maximum a posteriori (MAP) framework to maximize the corresponding posteriori probability. First, a joint likelihood model about zero-order TSK fuzzy system is defined to derive a new objective function which can assure that both antecedents and consequents of fuzzy rules rather than only their antecedents of the most existing TSK fuzzy systems become interpretable. The defined likelihood model is composed of three aspects: clustering on the training set for antecedents of fuzzy rules, the least squares (LS) error for consequent parameters of fuzzy rules, and a Dirichlet prior distribution for fuzzy cluster memberships which is considered to not only automatically match the "sum-to-one" constraints on fuzzy cluster memberships, but also make the proposed method B-ZTSK-FS scalable for large-scale datasets by appropriately setting the Dirichlet index. This likelihood model indeed indicates that antecedent and consequent parameters of fuzzy rules can be linguistically interpreted and simultaneously optimized by the proposed method B-ZTSK-FS which is based on the MAP framework with the iterative sampling algorithm, which in fact implies that fuzziness and probability can co-jointly work for TSK fuzzy system modeling in a collaborative rather than repulsive way. Finally, experimental results on 28 synthetic and real-world datasets are reported to demonstrate the effectiveness of the proposed method B-ZTSK-FS in the sense of approximation accuracy, interpretability and scalability. (c) 2017 Elsevier B.V. All rights reserved.

关键词： Fuzzy modeling Zero-order TSK fuzzy system bayesian inference framework Maximum a posteriori (MAP) principle Dirichlet distribution

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bayesian Takagi-Sugeno-Kang Fuzzy Classifier

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IEEE TRANSACTIONS ON FUZZY SYSTEMS 2017年第6期25卷 1655-1671页

作者： Gu, Xiaoqing Chung, Fu-Lai Wang, Shitong Jiangnan Univ Sch Digital Media Wuxi 214122 Peoples R China Changzhou Univ Sch Informat Sci & Engn Changzhou 213164 Peoples R China Hong Kong Polytech Univ Dept Comp Hong Kong Hong Kong Peoples R China

In this paper, the Takagi-Sugeno-Kang (TSK) fuzzy classifier is casted into the bayesian inference framework and a new fuzzy classifier called bayesian TSK fuzzy classifier (B-TSK-FC) is proposed accordingly. The proposed classifier can be constructed by learning both the antecedent and consequent parameters of the involved fuzzy rules simultaneously. As a result of the introduction of bayesian inference, the proposed B-TSK-FC can be distinguished as follows. 1) Unlike most existing TSK fuzzy classifiers where the antecedent and consequent parameters of fuzzy rules are learnt in a decoupled manner and the antecedent parameters are learnt only in the input space, the antecedent parameters of the fuzzy rules in B-TSK-FC are learnt by developing a fuzzy clustering method in the input-output space, and the consequent parameters of fuzzy rules are learnt in accordance with the maximum margin of separation principle, thereby resulting to form an intrinsic link between the input and output spaces to achieve improved classification performance and better interpretability. 2) With a Dirichlet prior assumption about fuzzy memberships in fuzzy clustering, a Markov-Chain Monte-Carlo technique is employed to estimate the parameters of the proposed classifier from a sampling perspective. 3) Rather than being rivals, fuzziness and probability in B-TSK-FC are collaboratively modeled to enhance the performance of TSK fuzzy classifier, in terms of classification and interpretability. Our experimental results in synthetic datasets as well as several real-world datasets confirm such merits of the proposed fuzzy classifier.

关键词： Antecedent and consequent parameter learning bayesian inference framework fuzzy clustering Markov-chain Monte-Carlo (MCMC) technique Takagi-Sugeno-Kang (TSK) fuzzy classifier

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Multi-frame blind deconvolution of atmospheric turbulence degraded images with mixed noise models

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ELECTRONICS LETTERS 2018年第4期54卷 206-208页

作者： Yang, Afeng Jiang, Xue Li, David Day-Uei Natl Univ Def Technol Coll Basic Educ Changsha Hunan Peoples R China Univ Strathclyde Dept Naval Architecture Ocean & Marine Engn Glasgow Lanark Scotland Univ Strathclyde Ctr Biophoton Glasgow Lanark Scotland

A mixed noise model is proposed and the multi-frame blind deconvolution is used to restore the images of space objects under the bayesian inference framework. To minimise the cost function, an algorithm based on iterative recursion was proposed. In addition, three limited bandwidth constraints of the point spread functions were imposed into the solution process to avoid converging to local minima. Experimental results show that the proposed algorithm can effectively restore the turbulence degraded images and alleviate the distortion caused by the noise.

关键词： deconvolution atmospheric turbulence image restoration Bayes methods inference mechanisms iterative methods multiframe blind deconvolution atmospheric turbulence mixed noise model space object image restoration bayesian inference framework cost function minimisation iterative recursion three limited bandwidth constraint point spread function

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Compressive Blind Source Separation

Compressive Blind Source Separation

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IEEE International Conference on Image Processing

作者： Wu, Yiyue Chi, Yuejie Calderbank, Robert Princeton Univ Dept Elect Engn Princeton NJ 08544 USA

ISBN: (纸本)9781424479948

The central goal of compressive sensing is to reconstruct a signal that is sparse or compressible in some basis using very few measurements. However reconstruction is often not the ultimate goal and it is of considerable interest to be able to deduce attributes of the signal from the measurements without explicitly reconstructing the full signal. This paper solves the blind source separation problem not in the high dimensional data domain, but in the low dimensional measurement domain. It develops a bayesian inference framework that integrates hidden Markov models for sources with compressive measurement. Posterior probabilities are calculated using a Markov Chain Monte Carlo (MCMC) algorithm. Simulation results are provided for one-dimensional signals and for two-dimensional images, where hidden Markov tree models of the wavelet coefficients are considered. The integrated bayesian framework is shown to outperform standard approaches where the mixtures are separated in the data domain.

关键词： Bayes methods bayesian inference framework Markov Chain Monte Carlo algorithm Monte Carlo methods blind source separation compressive blind source separation hidden Markov models hidden Markov tree models low dimensional measurement domain one-dimensional signals posterior probabilities signal reconstruction signal reconstruction trees (mathematics) two-dimensional images wavelet coefficients wavelet transforms

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Gender-dependent and speaker-dependent speech enhancement

Gender-dependent and speaker-dependent speech enhancement

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IEEE International Conference on Acoustics, Speech, and Signal Processing

作者： Potamitis, I Fakotakis, N Kokkinakis, G Univ Patras Dept Elect & Comp Engn Wire Commun Lab GR-26110 Patras Greece

ISBN: (纸本)0780374029

Our work introduces a speech enhancement technique that can explicitly incorporate prior information about the gender or speaker time-frequency characteristics in its formalism. We approximate the multimodal, clean speech linear spectrum magnitude with a mixture of Gaussians pdfs using the Expectation-Maximization algorithm (EM). Subsequently, we apply the bayesian inference framework to the degraded spectral coefficients and by employing Minimum Mean Square Error Estimation (MMSE) we derive a closed form solution for the spectral magnitude estimation task adapted to the spectral characteristics and noise variance of each band. We suggest that 2-3 minutes of phonetically balanced non-degraded gender or speaker dependent speech is adequate to tune our algorithm. We demonstrate the benefit of using an enhancement technique tailored to a specific gender or speaker and propose its use in cases where message ambiguity is of critical importance. We evaluate of our algorithm using Lynx helicopter and White Gaussian noise on the task of improving the quality of speech and in combination with a speech coder and demonstrate its robustness at very low SNRs. Implementation code is available at: http://***/potamitis/***.

关键词： speech enhancement least mean squares methods white noise Gaussian noise acoustic noise iterative methods Bayes methods gender-dependent speech enhancement speaker-dependent speech enhancement prior information speaker time-frequency characteristics multimodal clean speech linear spectrum magnitude Gaussian pdfs expectation-maximization algorithm bayesian inference framework degraded spectral coefficients minimum mean square error estimation MMSE closed form solution spectral magnitude estimation task phonetically balanced nondegraded speech Lynx helicopter noise white Gaussian noise quality of speech speech coder

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bayesian Inversion of Soil Hydraulic Properties from Simplified Evaporation Experiments: Use of DREAM_(ZS) Algorithm

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WATER 2021年第19期13卷 2614页

作者： Wang, Xinghui Wang, Xu-sheng Li, Na Wan, Li China Univ Geosci Minist Educ Key Lab Groundwater Circulat & Environm Evolut Beijing 100083 Peoples R China China Univ Geosci Beijing Key Lab Water Resources & Environm Engn Beijing 100083 Peoples R China

There is an increasing interest in identifying soil hydraulic properties from simplified evaporation experiments. However, the conventional simplified evaporation method includes a deficit due to using the linear assumption and not accounting for uncertainty in parameters. A suggested alternative method is assessing the parameter uncertainties through inverse modeling. We examined the combination of a bayesian inverse method, namely, DREAM((ZS)), and a numerical simulation model, namely, HYDRUS-1D, for parameter inversion with data in simplified evaporation experiments. The likelihood function could be conditioned only on pressure head observations (single-objective (SO)), or on both pressure head and evaporation rate observations (multi-objective (MO)), with different treatments on the top boundary condition. Three synthetic numerical experiments were generated in terms of the soil types of sand, loam and clay to verify the inverse modeling method. The MO approach performed better than the SO approach and linear assumption when the stage 1 evaporation rate was kept constant. However, the SO inversion was more robust when oscillations existed in the potential evaporation rate. Then, the SO inverse modeling was adopted to investigate two real experiments on loamy-sand soils and compared with the linear assumption. The linear assumption could be reliable for wet conditions with stage 1 evaporation but was not always useable for a relatively dry condition, such as that with stage 2 evaporation. The inverse modeling could be more successful in capturing the whole evaporation process of soils when both stage 1 and stage 2 were involved.

关键词： simplified evaporation method soil hydraulic properties bayesian inference framework inverse modeling MCMC method DREAM((ZS)) algorithm

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