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A novel semi-convex function for simultaneous identification of moving vehicle loads and bridge damage

MECHANICAL SYSTEMS AND SIGNAL PROCESSING 2025年 223卷

作者： Hou, Zhilong Liang, Yi Yu, Ling Jinan Univ Sch Mech & Construct Engn MOE Key Lab Disaster Forecast & Control Engn Guangzhou 510632 Peoples R China

For the simultaneous identification (SI) problem on the moving vehicle loads and bridge damage, the existing methods fail to appropriately consider the sparse characteristics of structural damage and ignore the prior information of vehicle loads, which make them suffering from challenges such as prolonged computation cost, poor noise robustness, and limited identification accuracy. To address this issue, a novel semi-convex function is proposed to construct a theoretical framework for the SI problem using the bridge dynamic responses subjected to moving vehicles in this study. Firstly, the bridge damage-induced virtual forces are conceptualized as a new form of moving residual forces characterized by block sparsity properties, and the damage location is then determined by the frequency characteristics with the largest fundamental frequency amplitude of moving residual forces. Secondly, a semi-convex function model encompassing moving forces and moving residual forces is defined. Combined with sparse regularization strategy, an improved alternating direction method of multipliers algorithm is proposed and applied to simultaneously solve for both moving vehicle loads and damage degrees. To assess the effectiveness and feasibility of the proposed method, extensive numerical validations are conducted in various bridge damage scenarios. Additionally, a series of truss bridge experiments are performed in laboratory under multiple damage and vehicle axle-weight conditions. The results show that compared with the existing outstanding methods, the proposed semi-convex function method can significantly reduce the identification cost, enhance robustness to noise, and demonstrate notable improvements in accuracy for the SI problem, which provides an innovative and more efficient solution to the SI problem in bridge engineering.

关键词： Bridge structural health monitoring semi-convex function Moving vehicle loads Bridge damage Sparse regularization

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A semi-convex function for both constant and time-varying moving force identification

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MECHANICAL SYSTEMS AND SIGNAL PROCESSING 2021年 146卷 107062-107062页

作者： Liu, Huanlin Luo, Ziwei Yu, Ling Jinan Univ Sch Mech & Construct Engn MOE Key Lab Disaster Forecast & Control Engn Guangzhou 510632 Peoples R China

In recent years, many moving force identification (MFI) methods have been proposed to monitor moving forces indirectly from structural responses. However, the prior knowledge about moving forces has not been reasonably considered in the existing methods, so the identified moving forces are not accurate enough. To improve the accuracy of MFI results, a novel MFI method is proposed based on a semi-convex function in this study. Firstly, a model of a simply-supported beam subjected to moving forces is taken as an example to establish the relationship between moving forces and structural responses. Then, the prior knowledge that time-varying force component of a moving force usually fluctuates around its static weight in the time domain is adopted. Thus, the moving force is decomposed into constant and time-varying force components. The constant force component is unchanged over time and the time-varying force component is changed over time. Based on this prior knowledge, a semi-convex function is defined for MFI, which is inspired by an alternating iterative method (AIM) and regularization techniques. As a result, the semi-convex function is solved by the AIM, so the constant and time-varying force components can be respectively obtained through iterations, and the moving forces are identified from structural responses. Finally, to evaluate the effectiveness of the proposed method, both numerical simulations and experimental verifications are carried out. The identified results show that the proposed method can further improve the MFI results by comparing with the L-2 regularization and the moving average Tikhonov regularization. The characteristics of the identified moving forces are consistent with that described in the given prior knowledge. Moreover, the proposed method can provide a good ability to estimate the total weight of the model car. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： Moving force identification (MFI) Alternating iterative method (AIM) semi-convex function Regularization technique

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CURRENTS CARRIED BY THE SUBGRADIENT GRAPHS OF semi-convex functionS AND APPLICATIONS TO HESSIAN MEASURES

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Acta Mathematica Scientia 2018年第1期38卷 315-332页

作者：涂强陈文艺 Faculty of Mathematics and Statistics Hubei University School of Mathematics and Statistics Wuhan University

In this paper we study integer multiplicity rectifiable currents carried by the subgradient （subdifferential） graphs of semi-convex functions on an n-dimensional convex domain, and show a weak continuity theorem with respect to pointwise convergence for such currents. As an application, the structure theorem of the Lagrangian currents for semi-convex functions is given and the k-Hessian measures are calculated by a different method in terms of currents.

关键词： semi-convex function subgradient Cartesian current Hessian measure

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Simultaneous robot-world and hand-eye calibration by the alternative linear programming

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PATTERN RECOGNITION LETTERS 2019年 127卷 174-180页

作者： Zhao, Zijian Shandong Univ Sch Control Sci & Engn 17923 Jingshi Rd Jinan 250061 Shandong Peoples R China

A typical hand-eye robot system has two related kinematic loops, which proper functioning requires the accurate determination of robot-world (RW) and hand-eye (HY) transformations in them. Insofar as HY calibration can resolve only the issues related to HY transformation, this study is focused on the joint treatment of the RW&HY transformations, which process is referred to as simultaneous RW&HY calibration. An alternative linear programming is adopted for the construction of semi-convex objective functions via two algorithms. These involve the homogeneous matrix and dual quaternion parameterizations, respectively. Their feasibility was further tested using simulated and real experimental datasets and compared to the results obtained via two available methods (NL and LMI). The results obtained strongly suggest that the homogeneous matrix parametrization (ALP1) had better performance than the dual quaternion one (ALP2). Meanwhile, both of them yielded the good optimal calibration solutions instead of local minima ones. Therefore, both formulations provide new insights into the behavior and complexity of the simultaneous RW&HY calibration. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Robot-world calibration Hand-eye calibration Alternative linear programming semi-convex function

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An Alternating Iterative Method and Its Application in Statistical Inference

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Acta Mathematica Sinica,English Series 2008年第5期24卷 843-856页

作者： Ning Zhong SHI Guo Rong HU Qing CUI Key Laboratory for Applied Statistics of MOE and School of Mathematics and Statistics Northeast No~nal University Changchun 130024 P. R. China Department of Basic Courses Shijiazhuang Railway Institute Shijiazhuang 050043 P. R. China

This paper studies non-convex programming problems. It is known that, in statistical inference, many constrained estimation problems may be expressed as convex programming problems. However, in many practical problems, the objective functions are not convex. In this paper, we give a definition of a semi-convex objective function and discuss the corresponding non-convex programming problems. A two-step iterative algorithm called the alternating iterative method is proposed for finding solutions for such problems. The method is illustrated by three examples in constrained estimation problems given in Sasabuchi et al. （Biometrika, 72, 465472 （1983））, Shi N. Z. （J. Multivariate Anal., 50, 282-293 （1994）） and El Barmi H. and Dykstra R. （Ann. Statist., 26, 1878 1893 （1998））.

关键词： semi-convex function alternating iterative method accumulation point maximum likelihood estimation order restriction

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Steiner type formulae and weighted measures of singularities for semi-convex functions

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TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY 2000年第7期352卷 3239-3263页

作者： Colesanti, A Hug, D Univ Florence Dipartimento Matemat U Dini I-50134 Florence Italy Univ Freiburg Math Inst D-79104 Freiburg Germany

For a given convex (semi-convex) function u, defined on a nonempty open convex set Omega subset of R-n, we establish a local Steiner type formula, the coefficients of which are nonnegative (signed) Borel measures. We also determine explicit integral representations for these coefficient measures, which are similar to the integral representations for the curvature measures of convex bodies (and, more generally, of sets with positive reach). We prove that, for r is an element of {0,...,n}, the r-th coefficient measure of the local Steiner formula for u, restricted to the set of r-singular points of u, is absolutely continuous with respect to the r-dimensional Hausdorff measure, and that its density is the (n-r)-dimensional Hausdorff measure of the subgradient of u. As an application, under the assumptions that u is convex and Lipschitz, and Omega is bounded, we get sharp estimates for certain weighted Hausdorff measures of the sets of r-singular points of u. Such estimates depend on the Lipschitz constant of u and on the quermassintegrals of the topological closure of Omega.

关键词： Steiner formula convex function semi-convex function singularities weighted Hausdorff measures subgradient map unit normal bundle non-smooth analysis

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