Structural deformation reconstruction by the Penrose–Moore pseudo-inverse and singular value decomposition–estimated equivalent force

2020 ◽  
pp. 147592172095233
Author(s):  
Yixian Li ◽  
Limin Sun
Keyword(s):  
Finite Element ◽  
Singular Value Decomposition ◽  
Finite Element Model ◽  
Singular Values ◽  
Element Model ◽  
Singular Value ◽  
Structural Deformation ◽  
Nodal Force ◽  
Influence Line ◽  
Value Decomposition

For structural health monitoring, estimating the external load is a typical ill-posed problem but significant. Because with the external force and the structural finite element model, any required response can be calculated, which is advantageous for further structural health monitoring works. This article first defines an underdetermined equation using a limited number of in-field measurements and the finite element model–calculated influence line matrix, and it proposes a load estimation method using the Penrose–Moore pseudo-inverse (generalized inverse). The objective of the proposed method is to obtain the equivalent nodal force vector with minimum length among all possible force vectors satisfying the deformation constraints. The estimated force is an equivalent nodal force, since it only satisfies limited deformation constraints. With the estimated nodal force, full structure static response can be easily calculated by multiplying the influence line matrix and the equivalent force vector. Besides, the truncated singular value decomposition is used to process the finite element model–calculated influence line matrix to avoid the over-fitting effect due to the measurement noise. The singular values of singular value decomposition represent the significance of the structural deformation modes, and the decreasing rate of the singular values is a good complexity indicator for a structure. The proposed frame can involve any types of static measurements, and it can realize real-time computation because it merely involves the matrix multiplying calculation. Finally, the sensitivity analysis is conducted by numerical simulation, and a large-scale model-based experiment has demonstrated that the algorithm is appropriate for in-field applications.

Estimation of Distributed Unbalance of Rotors

2001 ◽  
Author(s):  
Tachung Yang ◽  
Chunyi Lin
Keyword(s):  
Finite Element ◽  
Singular Value Decomposition ◽  
Element Model ◽  
Singular Value ◽  
Lumped Mass ◽  
Piecewise Polynomials ◽  
Mass Unbalance ◽  
Thick Disks ◽  
Value Decomposition ◽  
Thin Disks

Mass unbalance commonly causes vibration of rotor-bearing systems. Lumped mass modeling of unbalance was adapted in most previous research. The lumped unbalance assumption is adequate for thin disks or impellers, but not for thick disks or shafts. Lee et al. (1993) proposed that the unbalance of shafts should be continuously distributed. Balancing methods based on discrete unbalance models may not be very appropriate for rotors with distributed unbalance. A better alternative is to identify the distributed unbalance of shafts before balancing. In this study, the eccentricity distribution of the shaft is assumed in piecewise polynomials. A finite element model for the distributed unbalance is provided. Singular value decomposition is used to identify the eccentricity curves of the rotor. Numerical validation of this method is presented and examples are given to show the effectiveness of the identification method.

scholarly journals Through-Wall Image Enhancement Based on Singular Value Decomposition

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Muhammad Mohsin Riaz ◽  
Abdul Ghafoor
Keyword(s):  
Singular Value Decomposition ◽  
Image Enhancement ◽  
Visual Inspection ◽  
Signal To Noise Ratio ◽  
Singular Values ◽  
Singular Value ◽  
Information Theoretic ◽  
Value Decomposition ◽  
Suppress Noise ◽  
Wall Imaging

Singular value decomposition and information theoretic criterion-based image enhancement is proposed for through-wall imaging. The scheme is capable of discriminating target, clutter, and noise subspaces. Information theoretic criterion is used with conventional singular value decomposition to find number of target singular values. Furthermore, wavelet transform-based denoising is performed (to further suppress noise signals) by estimating noise variance. Proposed scheme works also for extracting multiple targets in heavy cluttered through-wall images. Simulation results are compared on the basis of mean square error, peak signal to noise ratio, and visual inspection.

scholarly journals Toward efficacy of piecewise polynomial truncated singular value decomposition algorithm in moving force identification

2019 ◽  
Vol 22 (12) ◽  
pp. 2687-2698 ◽  
Author(s):  
Zhen Chen ◽  
Lifeng Qin ◽  
Shunbo Zhao ◽  
Tommy HT Chan ◽  
Andy Nguyen
Keyword(s):  
Singular Value Decomposition ◽  
Singular Values ◽  
Singular Value ◽  
Decomposition Algorithm ◽  
Identification Accuracy ◽  
Piecewise Polynomial ◽  
Truncated Singular Value Decomposition ◽  
Force Identification ◽  
Moving Force ◽  
Value Decomposition

This article introduces and evaluates the piecewise polynomial truncated singular value decomposition algorithm toward an effective use for moving force identification. Suffering from numerical non-uniqueness and noise disturbance, the moving force identification is known to be associated with ill-posedness. An important method for solving this problem is the truncated singular value decomposition algorithm, but the truncated small singular values removed by truncated singular value decomposition may contain some useful information. The piecewise polynomial truncated singular value decomposition algorithm extracts the useful responses from truncated small singular values and superposes it into the solution of truncated singular value decomposition, which can be useful in moving force identification. In this article, a comprehensive numerical simulation is set up to evaluate piecewise polynomial truncated singular value decomposition, and compare this technique against truncated singular value decomposition and singular value decomposition. Numerically simulated data are processed to validate the novel method, which show that regularization matrix [Formula: see text] and truncating point [Formula: see text] are the two most important governing factors affecting identification accuracy and ill-posedness immunity of piecewise polynomial truncated singular value decomposition.

Singular value decomposition for cross‐well tomography

Geophysics ◽  
1993 ◽  
Vol 58 (11) ◽  
pp. 1655-1661 ◽  
Author(s):  
Reinaldo J. Michelena
Keyword(s):  
Singular Value Decomposition ◽  
Null Space ◽  
Vertical Component ◽  
Singular Values ◽  
Singular Value ◽  
Velocity Estimation ◽  
One Dimensional ◽  
Anisotropic Models ◽  
Value Decomposition ◽  
Frequency Variations

I perform singular value decomposition (SVD) on the matrices that result in tomographic velocity estimation from cross‐well traveltimes in isotropic and anisotropic media. The slowness model is parameterized in four ways: One‐dimensional (1-D) isotropic, 1-D anisotropic, two‐dimensional (2-D) isotropic, and 2-D anisotropic. The singular value distribution is different for the different parameterizations. One‐dimensional isotropic models can be resolved well but the resolution of the data is poor. One‐dimensional anisotropic models can also be resolved well except for some variations in the vertical component of the slowness that are not sensitive to the data. In 2-D isotropic models, “pure” lateral variations are not sensitive to the data, and when anisotropy is introduced, the result is that the horizontal and vertical component of the slowness cannot be estimated with the same spatial resolution because the null space is mostly related to horizontal and high frequency variations in the vertical component of the slowness. Since the distribution of singular values varies depending on the parametrization used, the effect of conventional regularization procedures in the final solution may also vary. When the model is isotropic, regularization translates into smoothness, and when the model is anisotropic regularization not only smooths but may also alter the anisotropy in the solution.

ROBUST REFERENCE-WATERMARKING SCHEME USING WAVELET PACKET TRANSFORM AND BIDIAGONAL-SINGULAR VALUE DECOMPOSITION

2009 ◽  
Vol 09 (03) ◽  
pp. 449-477 ◽  
Author(s):  
GAURAV BHATNAGAR ◽  
BALASUBRAMANIAN RAMAN
Keyword(s):  
Singular Value Decomposition ◽  
Gaussian Noise ◽  
Copyright Protection ◽  
Wavelet Packet ◽  
Singular Values ◽  
Wavelet Packet Transform ◽  
Singular Value ◽  
Noise Type ◽  
Value Decomposition ◽  
Watermarking Scheme

This paper presents a new robust reference watermarking scheme based on wavelet packet transform (WPT) and bidiagonal singular value decomposition (bSVD) for copyright protection and authenticity. A small gray scale logo is used as watermark instead of randomly generated Gaussian noise type watermark. A reference watermark is generated by original watermark and the process of embedding is done in wavelet packet domain by modifying the bidiagonal singular values. For the robustness and imperceptibly, watermark is embedded in the selected sub-bands, which are selected by taking into account the variance of the sub-bands, which serves as a measure of the watermark magnitude that could be imperceptibly embedded in each block. For this purpose, the variance is calculated in a small moving square window of size Sp× Sp(typically 3 × 3 or 5 × 5 window) centered at the pixel. A reliable watermark extraction is developed, in which the watermark bidiagonal singular values are extracted by considering the distortion caused by the attacks in neighboring bidiagonal singular values. Experimental evaluation demonstrates that the proposed scheme is able to withstand a variety of attacks and the superiority of the proposed method is carried out by the comparison which is made by us with the existing methods.

Estimation of Distributed Unbalance of Rotors

2002 ◽  
Vol 124 (4) ◽  
pp. 976-983 ◽  
Author(s):  
T. Yang ◽  
C. Lin
Keyword(s):  
Finite Element ◽  
Element Model ◽  
Singular Value ◽  
Lumped Mass ◽  
Piecewise Polynomials ◽  
Mass Unbalance ◽  
Rotor Bearing ◽  
Thick Disks ◽  
Value Decomposition ◽  
Thin Disks

Mass unbalance commonly causes vibration of rotor-bearing systems. Lumped mass modeling of unbalance was adapted in most previous research. The lumped unbalance assumption is adequate for thin disks or impellers, but not for thick disks or shafts. Lee et al. (Lee, A. C., et al., 1993, “The Analysis of Linear Rotor-Bearing Systems: A General Transfer Matrix Method,” ASME J. Vib. Acoust., 115, pp. 490–497) proposed that the unbalance of shafts should be continuously distributed. Balancing methods based on discrete unbalance models may not be very appropriate for rotors with distributed unbalance. A better alternative is to identify the distributed unbalance of shafts before balancing. In this study, the eccentricity distribution of the shaft is assumed in piecewise polynomials. A finite element model for the distributed unbalance is provided. Singular value decomposition is used to identify the eccentricity curves of the rotor. Numerical validation of this method is presented and examples are given to show the effectiveness of the identification method.

scholarly journals Simple Correspondence Analysis of Nominal-Ordinal Contingency Tables

2008 ◽  
Vol 2008 ◽  
pp. 1-17 ◽  
Author(s):  
Eric J. Beh
Keyword(s):  
Singular Value Decomposition ◽  
Correspondence Analysis ◽  
Contingency Table ◽  
Singular Values ◽  
Singular Value ◽  
Ordered Categories ◽  
Nominal Structure ◽  
Classical Technique ◽  
Versatile Tool ◽  
Value Decomposition

The correspondence analysis of a two-way contingency table is now accepted as a very versatile tool for helping users to understand the structure of the association in their data. In cases where the variables consist of ordered categories, there are a number of approaches that can be employed and these generally involve an adaptation of singular value decomposition. Over the last few years, an alternative decomposition method has been used for cases where the row and column variables of a two-way contingency table have an ordinal structure. A version of this approach is also available for a two-way table where one variable has a nominal structure and the other variable has an ordinal structure. However, such an approach does not take into consideration the presence of the nominal variable. This paper explores an approach to correspondence analysis using an amalgamation of singular value decomposition and bivariate moment decomposition. A benefit of this technique is that it combines the classical technique with the ordinal analysis by determining the structure of the variables in terms of singular values and location, dispersion and higher-order moments.

A fast algorithm for regularized focused 3D inversion of gravity data using randomized singular-value decomposition

Geophysics ◽  
2018 ◽  
Vol 83 (4) ◽  
pp. G25-G34 ◽  
Author(s):  
Saeed Vatankhah ◽  
Rosemary Anne Renaut ◽  
Vahid Ebrahimzadeh Ardestani
Keyword(s):  
Linear System ◽  
Singular Value Decomposition ◽  
Fast Algorithm ◽  
Large Scale ◽  
Gravity Data ◽  
Singular Values ◽  
Singular Value ◽  
System Matrix ◽  
Large Scale System ◽  
Value Decomposition

We develop a fast algorithm for solving the under-determined 3D linear gravity inverse problem based on randomized singular-value decomposition (RSVD). The algorithm combines an iteratively reweighted approach for [Formula: see text]-norm regularization with the RSVD methodology in which the large-scale linear system at each iteration is replaced with a much smaller linear system. Although the optimal choice for the low-rank approximation of the system matrix with [Formula: see text] rows is [Formula: see text], acceptable results are achievable with [Formula: see text]. In contrast to the use of the iterative LSQR algorithm for the solution of linear systems at each iteration, the singular values generated using RSVD yield a good approximation of the dominant singular values of the large-scale system matrix. Thus, the regularization parameter found for the small system at each iteration is dependent on the dominant singular values of the large-scale system matrix and appropriately regularizes the dominant singular space of the large-scale problem. The results achieved are comparable with those obtained using the LSQR algorithm for solving each linear system, but they are obtained at a reduced computational cost. The method has been tested on synthetic models along with real gravity data from the Morro do Engenho complex in central Brazil.

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