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Accurate force evaluation in prestressed cable-strut structures: A robust sparse Bayesian learning method with feedback-driven error optimization

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ENGINEERING STRUCTURES 2025年 330卷

作者： Chen, Yao Zhou, Haodong Gao, Jiangjun Shen, Zhengliang Xie, Tianyu Sareh, Pooya Southeast Univ Key Lab Concrete & Prestressed Concrete Struct Minist Educ Nanjing 211189 Peoples R China Southeast Univ Sch Civil Engn Wuxi Campus Wuxi 214082 Peoples R China China Construct Fifth Engn Bur Co Ltd Changsha 410004 Peoples R China Newcastle Univ Sch Engn Creat Design Engn Lab Cdel Newcastle Upon Tyne NE1 7RU England Univ Politecn Madrid UPM Escuela Tecn Super Ingn & Diseno Ind Madrid 28012 Spain

Force evaluation is critical to ensuring the safety of cable-strut structures during service. This study employs dynamic testing to assess the internal forces resulting from cable relaxation in prestressed cable-strut structures. A cross-model cross-mode algorithm is utilized to establish a cable force evaluation model. This approach broadens the range of available modes and addresses mismatches between modes before and after cable force loss. To enhance the accuracy and reliability of the force evaluation, a robust sparse Bayesian learning method is proposed. Measurement noise is modeled as a mixture of Gaussian distributions rather than a single Gaussian distribution, enabling a more precise representation of uncertainties in force evaluation. Furthermore, a feedback-driven error optimization process is introduced to minimize residuals through multiple linear iterations. Numerical simulations demonstrate that the proposed method achieves greater evaluation accuracy compared to existing sparse Bayesian approaches. Comparative analyses under varying noise levels reveal that the proposed method is robust and effectively reduces the impact of measurement noise.

关键词： Force evaluation Prestressed cable-strut structure Sparse Bayesian learning expectation-maximization algorithm Uncertainty quantification

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A numerically efficient implementation of the expectation maximization algorithm for state space models

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APPLIED MATHEMATICS AND COMPUTATION 2014年 241卷 222-232页

作者： Mader, Wolfgang Linke, Yannick Mader, Malenka Sommerlade, Linda Timmer, Jens Schelter, Bjoern Univ Freiburg Inst Phys Freiburg Germany Univ Freiburg Freiburg Ctr Data Anal & Modeling FDM Freiburg Germany Univ Med Ctr Freiburg Dept Neuropediat & Muscular Dis Freiburg Germany Univ Aberdeen Inst Complex Syst & Math Biol Aberdeen AB9 1FX Scotland

Empirical time series are subject to observational noise. Naive approaches that estimate parameters in stochastic models for such time series are likely to fail due to the error-in-variables challenge. State space models (SSM) explicitly include observational noise. Applying the expectation maximization (EM) algorithm together with the Kalman filter constitute a robust iterative procedure to estimate model parameters in the SSM as well as an approach to denoise the signal. The EM algorithm provides maximum likelihood parameter estimates at convergence. The drawback of this approach is its high computational demand. Here, we present an optimized implementation and demonstrate its superior performance to naive algorithms or implementations. (C) 2014 Elsevier Inc. All rights reserved.

关键词： Kalman filter expectation-maximization algorithm Parameter estimation State-space model

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DTSFormer: Decoupled temporal-spatial diffusion transformer for enhanced long-term time series forecasting

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KNOWLEDGE-BASED SYSTEMS 2025年 309卷

作者： Zhu, Jiaming Liu, Dezhi Chen, Huayou Liu, Jinpei Tao, Zhifu Anhui Univ Sch Internet Hefei 230039 Anhui Peoples R China Natl Engn Res Ctr Agroecol Big Data Anal & Applica Hefei 230601 Anhui Peoples R China Anhui Univ Sch Big Data & Stat Hefei 230601 Anhui Peoples R China Anhui Univ Sch Business Hefei 230601 Anhui Peoples R China

Transformer-based models have significantly advanced long-term time series forecasting by leveraging self- attention mechanisms to capture long-term dependencies. However, these models face high computational costs, slow inference speeds, and limitations in utilizing information from longer lookback windows. Additionally, existing methods often neglect implicit spatial dependencies between variables, and struggle with semantic misalignment and insufficient diffusion of spatial information. To address these challenges, we propose DTSFormer, a D ecoupled T emporal-Spatial Diffusion Transformer designed specifically for long-term time series forecasting: (1) DTSFormer effectively integrates temporal features with implicit spatial attributes, ensuring comprehensive utilization of both temporal and spatial information. (2) DTSFormer introduce a Mix- hop Diffusion layer to effectively propagate and aggregate spatial information while preserving the original graph structure, significantly improving the accuracy of spatial information dissemination. (3) we develop a cross-diffusion attention mechanism based on the expectation-maximization algorithm, which integrates graph structure information with varying semantics under a seasonal trend decomposition framework. This approach enhances the fusion of semantic information from different graph structures and reduces computational complexity. Our extensive experiments on multiple benchmark datasets across different domains demonstrate that DTSFormer consistently achieves state-of-the-art performance in both accuracy and efficiency. These results validate DTSFormer as a robust and scalable solution for advanced long-term time series forecasting tasks.

关键词： Long-term series forecasting Transformer-based model expectation-maximization algorithm Diffusion Temporal-Spatial features

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On Classical Inference of a Flexible Semi-Parametric Class of Distributions Under a Joint Balanced Progressive Censoring Scheme

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APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY 2025年第1期41卷

作者： Bhattacharyya, Dhrubasish Kundu, Debasis Rajiv Gandhi Inst Petr Technol Dept Math Sci Amethi India Indian Inst Technol Kanpur Dept Math & Stat Kanpur India

The paper deals with the estimation procedures for the proportional hazard class of distributions under a two-sample balanced joint progressive censoring scheme. The baseline hazard function is assumed to be piecewise constant, instead of any specific form. This adds flexibility to the proposed model, and the shape of the underlying hazard function is completely data-driven. Since the complicated form of the likelihood function does not yield closed-form estimators, we propose a variant of the expectation-maximization algorithm, known as the expectation Conditional maximization (ECM) algorithm, for obtaining maximum likelihood estimates of the model parameters. This leads to explicit expressions for the iterative constrained maximization steps of the algorithm. An extension to the case when the cut points are unknown has also been considered for dealing with problems involving real data. Simulation results and illustrations using real data have also been presented.

关键词： bootstrap confidence interval expectation conditional maximization algorithm expectation-maximization algorithm maximum likelihood estimators

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Restoration after deterioration in interdependent infrastructure networks: A two-stage hybrid method with minimum network performance loss

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INFORMATION SCIENCES 2025年 693卷

作者： Li, Yulong Su, Han Yang, Baisong Lin, Jie Shen, Yinghua Wu, Guobin Cent Univ Finance & Econ Sch Management Sci & Engn Beijing 100081 Peoples R China Chongqing Univ Sch Econ & Business Adm Chongqing 400044 Peoples R China

Restoration of interdependent infrastructure networks (IINs) relies on the information from deterioration, which is of great significance because IINs support the normal functioning of social productivity and life. However, existing research has not fully addressed the restoration after deterioration in IINs, which is not conducive to the timely elimination of the adverse effects of infrastructure deterioration. First, a unified model for IINs is innovatively devised by considering both functional and operational interdependencies between infrastructures. Second, a two-stage hybrid method that generates the optimal restoration strategies after deterioration in IINs is proposed. Specifically, in the first stage, a hidden Markov chain model for deterioration prediction is constructed, which is solved by the expectation-maximization (EM) algorithm. In the second stage, an objective programming model with minimum network performance loss for restoration optimization is developed, and the optimal strategy is obtained by the ant colony algorithm. Finally, a real-world case is used to validate the feasibility and effectiveness of the proposed method. The results show that this method is efficient and effective in finding optimal restoration strategy after deterioration in IINs. We also investigate the effects of initial restoration time and restoration resource grouping, which provide helpful decision guidance for real cases.

关键词： Interdependent infrastructure networks Deterioration prediction Restoration optimization expectation-maximization algorithm Ant colony algorithm

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Factor-augmented transformation models for interval-censored failure time data

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BIOMETRICS 2024年第3期80卷 ujae078页

作者： Li, Hongxi Li, Shuwei Sun, Liuquan Song, Xinyuan Guangzhou Univ Sch Econ & Stat Guangzhou 510006 Peoples R China Chinese Acad Sci Acad Math & Syst Sci Beijing 100190 Peoples R China Univ Chinese Acad Sci Sch Math Sci Beijing 100190 Peoples R China Chinese Univ Hong Kong Dept Stat Hong Kong 999077 Peoples R China

Interval-censored failure time data frequently arise in various scientific studies where each subject experiences periodical examinations for the occurrence of the failure event of interest, and the failure time is only known to lie in a specific time interval. In addition, collected data may include multiple observed variables with a certain degree of correlation, leading to severe multicollinearity issues. This work proposes a factor-augmented transformation model to analyze interval-censored failure time data while reducing model dimensionality and avoiding multicollinearity elicited by multiple correlated covariates. We provide a joint modeling framework by comprising a factor analysis model to group multiple observed variables into a few latent factors and a class of semiparametric transformation models with the augmented factors to examine their and other covariate effects on the failure event. Furthermore, we propose a nonparametric maximum likelihood estimation approach and develop a computationally stable and reliable expectation-maximization algorithm for its implementation. We establish the asymptotic properties of the proposed estimators and conduct simulation studies to assess the empirical performance of the proposed method. An application to the Alzheimer's Disease Neuroimaging Initiative (ADNI) study is provided. An R package ICTransCFA is also available for practitioners. Data used in preparation of this article were obtained from the ADNI database.

关键词： expectation-maximization algorithm factor analysis interval censoring joint model nonparametric maximum likelihood estimation

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Estimating parameters from the generalized inverse Lindley distribution under hybrid censoring scheme

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2024年第7期53卷 2483-2515页

作者： Sarkar, Mojammel Haque Tripathy, Manas Ranjan Kundu, Debasis Natl Inst Technol Rourkela Dept Math Rourkela India Indian Inst Technol Kanpur Dept Math & Stat Kanpur India Natl Inst Technol Rourkela Dept Math Rourkela 769008 India

Estimation of parameters of the generalized inverse Lindley (GIL) distribution is considered under a hybrid censoring scheme. The point estimators, such as the maximum likelihood estimators using the expectation-maximization (E-M) algorithm, have been derived. The two approximate Bayes estimators using Tierney and Kadane's method and Gibbs sampling procedure, using the gamma prior and the general entropy loss (GEL) function, have been obtained. Several confidence intervals are proposed, such as the asymptotic confidence intervals (ACIs), bootstrap confidence intervals, and the highest posterior density (HPD) credible intervals. The prediction for future observations has been considered under one and two-sample Bayesian prediction methods using the type-i hybrid censoring scheme. An extensive simulation study has been conducted to numerically evaluate all the estimators' performances. The point estimators are compared through their biases and mean squared errors (MSEs). The performances of confidence intervals are evaluated using coverage probability (CP), average length (AL), and probability coverage density (PCD). Two real-life datasets have been considered for illustrative purposes.

关键词： Approximate Bayes estimator asymptotic confidence interval Bayesian prediction bootstrap confidence interval expectation-maximization algorithm Gibbs sampling maximum likelihood estimator numerical comparison

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On algorithms and Approximations for Progressively Type-I Censoring Schemes

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STATISTICAL ANALYSIS AND DATA MINING-AN ASA DATA SCIENCE JOURNAL 2024年第6期17卷

作者： El-Saeed, Ahmed R. Almetwally, Ehab M. Imam Mohammad Ibn Saud Islamic Univ IMSIU Fac Sci Dept Math & Stat Riyadh Saudi Arabia Obour High Inst Management & Informat Dept Basic Sci Al Qalyubia Egypt Delta Univ Sci & Technol Fac Business Adm Gamasa Egypt

This research aims to study the estimation of parameters for a Burr-XII distribution and to investigate optimal sampling plans under progressive Type-I censoring (PTIC). For point estimation, we employed the maximum-likelihood estimation (MLE) method using two numerical approaches: Newton-Raphson and the expectation-maximization algorithm. We also utilized Bayesian estimation with squared error loss and linear exponential loss functions. Specifically, two approximate Bayesian methods, the Lindley and Tierney-Kadane methods were examined. Additionally, Bayesian numerical estimation was performed using Markov Chain Monte Carlo with the Metropolis-Hastings (MH) algorithm. For interval estimation, we constructed asymptotic confidence intervals for MLE and the highest posterior density method within the Bayesian framework. The practical study involved Monte Carlo simulations to assess the efficiency and accuracy of the proposed estimation methods across different PTIC schemes. A real data analysis is also provided to illustrate the practical application of these methodologies in analyzing a clinical trial dataset. Data from a clinical trial using a PTIC scheme reveals patterns in pain relief, aiding in evaluating the antibiotic ointment's effectiveness. The study further investigates optimal sampling plans for the Burr-XII distribution under PTIC.

关键词： Bayesian estimation expectation-maximization algorithm Lindley approximation Markov chain Monte Carlo Newton-Raphson optimal sampling plans progressive Type-I censoring Tierney-Kadane approximation

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Logistic model for pattern inference of subway passenger flows based on fare collection and vehicle location data

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APPLIED MATHEMATICAL MODELLING 2024年 130卷 472-495页

作者： Li, Chunya Xiong, Shifeng Xiong, Hui Sun, Xuan Qin, Yong Shanghai Univ Engn Sci Sch Math Phys & Stat Shanghai 201620 Peoples R China Chinese Acad Sci Acad Math & Syst Sci NCMIS KLSC Beijing 100190 Peoples R China Univ Chinese Acad Sci Sch Math Sci Beijing 100049 Peoples R China Hainan Univ Sch Mech & Elect Engn Haikou 570228 Peoples R China Beijing Jiaotong Univ Sch Traff & Transportat Beijing 100044 Peoples R China Beijing Jiaotong Univ State Key Lab Rail Traff Control & Safety Beijing 100044 Peoples R China

With large volume of passengers boarding and alighting through subway platforms, the stations are getting crowded, resulting in drops in the level of service and safety concerns, especially for subway systems operating at capacity during peak hours. Thus, it is crucial for subway agencies to sense changes in travel demand and adjust their management schemes accordingly. In this paper we propose a statistical approach to estimate dynamic passenger flows with automated data. First, we develop a dynamic logistic model for calculating passenger tap -out times, which can be employed to infer passenger flow characteristics at the aggregate level. In addition, a new passenger -to -train assignment model for any subway route is derived based on the dynamic model. Subsequently, we apply an expectation -maximization algorithm to estimate the model parameters with automated fare collection and automated vehicle location data. Finally, a crossvalidation method is employed to validate our approach with data obtained from several routes in Beijing subway system in China. Results of 95% prediction intervals indicate the effectiveness of the models and the proposed estimation methods.

关键词： Boarding probability Travel time prediction Congestion evaluation Available safe egress time expectation-maximization algorithm Dynamic logistics model

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τ-Inflated Beta Regression Model for Estimating τ-Restricted Means and Event-Free Probabilities for Censored Time-to-Event Data

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BIOMETRICAL JOURNAL 2024年第8期66卷

作者： Wang, Yizhuo Murray, Susan Univ Michigan Dept Biostat Ann Arbor MI 48109 USA

In this research, we propose analysis of tau-restricted censored time-to-event data via a tau-inflated beta regression (tau-IBR) model. The outcome of interest is min(tau,T), where T and tau are the time-to-event and follow-up duration, respectively. Our analysis goals include estimation and inference related to tau-restricted mean survival time (tau-RMST) values and event-free probabilities at tau that address the censored nature of the data. In this setting, it is common to observe many individuals with min(tau,T)=tau, a point mass that is typically overlooked in tau-restricted event-time analyses. Our proposed tau-IBR model is based on a decomposition of min(tau,T) into tau[I(T >=tau)+(T/tau)I(Texpectation-maximization algorithm. An alternative multiple imputation (MI) algorithm for fitting the tau-IBR model has the additional advantage of producing uncensored datasets for analysis. Simulations indicate excellent performance of the tau-IBR model(s), and corresponding tau-RMST estimates, in independent and dependent censoring settings. We apply our method to the Azithromycin for Prevention of Chronic Obstructive Pulmonary Disease (COPD) Exacerbations Trial. In addition to tau-IBR model results providing a nuanced understanding of the treatment effect, visually appealing heatmaps of the tau-restricted event times based on our MI datasets are given, a visualization not typically available for censored time-to-event data.

关键词： expectation-maximization algorithm inflated beta regression multiple imputation of censored times-to-event restricted mean survival time

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