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Dynamic analysis of deployable structures using independent displacement modes based on Moore-Penrose generalized inverse matrix

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STRUCTURAL ENGINEERING AND MECHANICS 2015年第6期54卷 1153-1174页

作者： Xiang, Ping Wu, Minger Zhou, Rui Q. Waseda Univ Dept Architecture Tokyo 1698555 Japan Tongji Univ Dept Bldg Engn Shanghai 200092 Peoples R China Shanghai Inst Mech & Elect Engn Co Ltd Shanghai 200040 Peoples R China

Deployable structures have gained more and more applications in space and civil structures, while it takes a large amount of computational resources to analyze this kind of multibody systems using common analysis methods. This paper presents a new approach for dynamic analysis of multibody systems consisting of both rigid bars and arbitrarily shaped rigid bodies. The bars and rigid bodies are connected through their nodes by ideal pin joints, which are usually fundamental components of deployable structures. Utilizing the Moore-Penrose generalized inverse matrix, equations of motion and constraint equations of the bars and rigid bodies are formulated with nodal Cartesian coordinates as unknowns. Based on the constraint equations, the nodal displacements are expressed as linear combination of the independent modes of the rigid body displacements, i.e., the null space orthogonal basis of the constraint matrix. The proposed method has less unknowns and a simple formulation compared with common multibody dynamic methods. An analysis program for the proposed method is developed, and its validity and efficiency are investigated by analyses of several representative numerical examples, where good accuracy and efficiency are demonstrated through comparison with commercial software package ADAMS.

关键词： multibody system deployable structure dynamic analysis constraint equations equations of motion generalized inverse matrix

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A shape-finding approach of tree-like structure based on grouping strategy and generalized inverse matrix theory

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STRUCTURES 2021年 29卷 1960-1966页

作者： Tu, Guigang Chen, Chen Jilin Univ Coll Construct Engn Changchun 130012 Peoples R China

Unstable link models in equilibrium transfer their loads only through axial forces and the generalized inverse matrix theory can be used in the shape-finding analysis of unstable link structures. According to this principle and the generalized inverse matrix theory, a shape-finding approach for tree-like structure is proposed, which forms a progressive process to update the shape of branching model until the potential energy of the model reaches minimum. In the proposed approach, members of the branching model are grouped and the total length of the members in the same group are constrained. The total length can be redistributed among the members in the same group in the shape-finding process. The redistribution of length is particularly useful for the shape-finding of tree-like structure as it can avoid the generation of inefficient members in the shape-found structure. Changing the grouping mode of members is a way to generate multiple schemes of structural shapes. Numerical examples illustrate the features of the approach and validate its effectiveness.

关键词： Shape-finding Tree-like structure generalized inverse matrix Grouping mode

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generalized inverse matrix-recurrent neural network data processing algorithm for multiwavelength pyrometer

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OPTICAL ENGINEERING 2022年第12期61卷 124109-124109页

作者： Xing, Jian Yan, Pengyu Cui, Shuanglong Northeast Forestry Univ Coll Informat & Comp Engn Harbin Peoples R China

A generalized inverse matrix-recurrent neural network (GIM-RNN) data processing algorithm for unknown emissivity was proposed to measure high-temperature by multiwavelength pyrometer (MWP). First, emissivity classification was realized quickly according to a solution from generalized inverse algorithm to underdetermined multiwavelength equation group. According to the relationship between the emissivity of 2 adjacent channels of the 6 channel thermometer used in this paper, 243 emissivity models (1 * 3 * 3 * 3 * 3 * 3) were designed for classification. Twelve of them were shown on the schematic diagram in the text. To make the figure clear and easy to observe, the prediction results of six common emissivity models were listed as the experimental results. Then, it was input into the corresponding RNN subnetwork to inverse temperature precisely. Simulation results showed that in the range of 1500 to 3000 K temperature, the relative error of the test set was within 1.0% for the network trained after classification by GIM, whereas the relative error of the test set was within 1.2% for the network trained without GIM classification. After 5.0% random noise was added to the inputting data, the relative error still was controlled within 1.5%, which reflected the good antinoise performance of the algorithm. Multispectral measurement data of rocket engine plumes is processed by the proposed algorithm in this manuscript. The inversion results are consistent with the theoretical results. It is indicated that the proposed algorithm has good adaptability to different materials. It is expected to become a general data processing algorithm for MWP. (c) 2022 Society of Photo-Optical Instrumentation Engineers (SPIE)

关键词： multiwavelength pyrometer generalized inverse matrix recurrent neural network

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DYNAMIC ANALYSIS OF DEPLOYABLE STRUCTURES USING MOORE-PENROSE generalized inverse matrix METHOD

DYNAMIC ANALYSIS OF DEPLOYABLE STRUCTURES USING MOORE-PENROS...

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2nd International Postgraduate Conference on Infrastructure and Environment

作者： Xiang, P. Wu, M. Tongji Univ Dept Bldg Engn Shanghai Peoples R China

ISBN: (纸本)9789881731142

Deployable structures are structures which can be furled for transportation or storage, and remotely deployed. The applications of the deployable structures concept are expanded to many areas, especially in aerospace. To study the deployable structures, it is necessary to research the kinematics and dynamics of deployable structures. This paper presents a Moore-Penrose generalized inverse matrix method for dynamic analyses of hybrid deployable structures consisting of rigid bars and arbitrary shaped rigid bodies. In addition, a numerical example is given to verify the accuracy and effectivity of the mechanical analytical model and analytical method.

关键词： Deployable structures rigid body dynamic analysis generalized inverse matrix numerical analysis

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A Study of Dynamic Decoupling Fuzzy Control Systems by Means of generalized inverse matrix

A Study of Dynamic Decoupling Fuzzy Control Systems by Means...

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3rd International Conference on Artificial Intelligence and Computational Intelligence (AICI 2011)

作者： Fan, Qing-Min Taiyuan Univ Technol Dept Math Taiyuan 030024 Peoples R China

ISBN: (纸本)9783642242816

In the dynamic decoupling fuzzy control system, if singular or rectangle matrices are encountered in the state equation, the only way is to consider the decoupling control over partial states of the system. This paper presents a new conclusion with fewer parameters by virtue of generalized inverse matrix and realized decoupling fuzzy control over the system with multiple variables, which demonstrates good control effect.

关键词： Nonlinear dynamic inverse Decoupling control generalized inverse matrix Fuzzy controller

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Semi-blind hyperspectral and multispectral image fusion via generalized inverse matrix optimization

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INFRARED PHYSICS & TECHNOLOGY 2024年 139卷

作者： Lin, Hong Huang, Da Li, Jun Zhou, Tong Long, Jian Peng, Yuanxi Natl Univ Def Technol Coll Comp Sci State Key Lab High Performance Comp Chang Sha 410073 Peoples R China Natl Univ Def Technol Coll Elect Sci Chang Sha 410073 Peoples R China

Combining a low spatial resolution hyperspectral image (HSI) with a high spatial resolution multispectral image (MSI) is an economical way to obtain a high spatial resolution hyperspectral image (HR-HSI). However, existing fusion methods often rely on a critical variable, the point spread function (PSF), which is difficult to obtain in practice. Additionally, these methods often require a long fusion time and have many parameters that need re -debugging on different datasets to achieve satisfactory results. Many existing methods lack robustness in handling complex scenarios, such as complex PSF, changing spatial downsampling factors, and large-scale datasets. These issues can result in degraded performance or render the methods inapplicable to practical scenarios. Therefore, we propose an efficient and parameterless semi -blind fusion method based on generalized inverse matrix optimization (GIMO), which is robust for multiple complex situations. Our method uses the definition of generalized inverse matrix and the relationship among HSI, MSI, and HR-HSI to approximate the function module of PSF. Then, we calculate the generalized inverse matrix of the spectral response function (SRF). Finally, we optimize the generalized inverse matrix of SRF using the Sylvester equation and multiply it with MSI to obtain HR-HSI. This is the first proposed method to achieve hyperspectral image super -resolution by optimizing the inverse matrix of the spectral response function. Experiments on multiple simulated datasets and one real dataset have validated that our GIMO method outperforms existing state-of-the-art methods, especially regarding fusion time and robustness for various complex scenarios.

关键词： Hyperspectral imaging super-resolution Multispectral Image fusion generalized inverse matrix

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An Exact Cholesky Decomposition and the generalized inverse of the Variance–Covariance matrix of the Multinomial Distribution, with Applications

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Journal of the Royal Statistical Society: Series B (Statistical Methodology) 1992年第1期54卷 211-219页

作者： Kunio Tanabe Masahiko Sagae Institute of Statistical Mathematics Tokyo Japan Science University of Tokyo Japan

A symbolic formula is given for the square-root-free Cholesky decomposition of the variance–covariance matrix of the multinomial distribution. The evaluation of the symbolic Cholesky factors requires much fewer arithmetic operations than does the general Cholesky algorithm. Since the symbolic formula is not affected by an ill-conditioned matrix, it is particularly useful when the elements of a probability vector are of quite different orders of magnitude. A simpler formula is obtained for Pederson's procedure of sampling from a multinomial population. An explicit formula of the Moore–Penrose inverse of the variance–covariance matrix is given as well as a symmetric representation of a multinomial density approximation to the multinomial distribution. These formulae facilitate symmetric manipulation of the matrix and are useful in statistical modelling and computation involving the logistic density transformation of the multinomial distribution and in computer simulations of dynamic models in population genetics. Each element of the Cholesky factors is given interesting probabilistic interpretations.

关键词： bayesian modelling cholesky decomposition condition number generalized inverse matrix genetic simulation logistic density transformation multinomial distribution multinormal approximation random number generator statistical computation subdeterminant symbolic decomposition variance–covariance matrix

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Resolution of matrix equations over arbitrary Brouwerian lattices

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FUZZY SETS AND SYSTEMS 2008年第1期159卷 40-46页

作者： Han, Song-Chol Li, Hong-Xing Wang, Ha-Yin Beijing Normal Univ Sch Math Sci Beijing 100875 Peoples R China Kim Il Sung Univ Dept Math & Mech Pyong Yang North Korea Dalian Univ Technol Sch Elect & Informat Engn Dalian 116023 Peoples R China

This paper studies the problem of solving a matrix equation over an arbitrary (not necessarily complete) Brouwerian lattice. A criterion for the solvability and a method for finding all solutions of the equation are obtained. Over an arbitrary self-dual Brouwerian lattice, an equivalent condition for the unique solution, a necessary and sufficient condition for the minimal solution and a procedure for constructing minimal solutions less than or equal to any given solution of the equation are presented. It is shown that the results of the paper can be applied to the determination of generalized inverses of a matrix over an arbitrary Brouwerian lattice. (c) 2007 Elsevier B.V. All rights reserved.

关键词： fuzzy relations algebra Brouwerian lattice matrix equation generalized inverse matrix

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Universal wind load distribution simultaneously reproducing largest load effects in all subject members on large-span cantilevered roof

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JOURNAL OF WIND ENGINEERING AND INDUSTRIAL AERODYNAMICS 2007年第9-11期95卷 1145-1165页

作者： Katsumura, A. Tamura, Y. Nakamura, O. Tokyo Polytech Univ Tokyo Japan

This paper discusses the equivalent static wind load that reproduces the largest load effects in structural member (hereafter referred to as the universal ESWL). In this study, the universal ESWL is shown by a combination of eigenmodes calculated by POD analysis of fluctuating wind pressure. Applying singular value decomposition to a matrix of eigenmodes by the influence function optimizes the universal ESWL combination. This method is applied to large cantilevered roof models. The largest load effects for bending moment (hereafter referred to as BM) and shear force (hereafter referred to as SF) are determined to estimate the universal ESWL. The largest load effects reproduced by the universal ESWL show good agreement with those directly estimated by time-domain response analyses. (C) 2007 Elsevier Ltd. All rights reserved.

关键词： equivalent static wind load cantilevered roof generalized inverse matrix POD analysis

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An Improved BP Algorithm and Its Application in Classification of Surface Defects of Steel Plate

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Journal of Iron and Steel Research International 2007年第2期14卷 52-55页

作者： ZHAO Xiang-yang LAI Kang-sheng DAI Dong-ming Research and Development Division Haler Group Qingdao 266101 Shandong China Department of Physics Dalian University of Technology Dalian 116024 Liaoning China

Artificial neural network is a new approach to pattern recognition and classification. The model of multilayer perceptron （MLP） and back-propagation （BP） is used to train the algorithm in the artificial neural network. An improved fast algorithm of the BP network was presented, which adopts a singular value decomposition （SVD） and a generalized inverse matrix. It not only increases the speed of network learning but also achieves a satisfying precision. The simulation and experiment results show the effect of improvement of BP algorithm on the classification of the surface defects of steel plate.

关键词： artificial neural network MLP BP algorithm SVD generalized inverse matrix

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