• Structural Engineering and Mechanics
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• v.15 no.3
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• pp.299-314
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• 2003

This investigation presents an efficient method for identifying modal characteristics from the measured displacement, velocity and acceleration signals of multiple channels on structural systems. A Vector Backward Auto-Regressive model (VBAR) that describes the relationship between the output information in different time steps is used to establish a backward state equation. Generally, the accuracy of the identified dynamic characteristics can be improved by increasing the order of the Auto-Regressive model (AR) in cases of measurement of data under noisy circumstances. However, a higher-order AR model also induces more numerical modes, only some of which are the system modes. The proposed VBAR model provides a clear characteristic boundary to separate the system modes from the spurious modes. A numerical example of a lumped-mass model with three DOFs was established to verify the applicability and effectiveness of the proposed method. Finally, an offshore platform model was experimentally employed as an application case to confirm the proposed VBAR method can be applied to real-world structures.

• Structural Engineering and Mechanics
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• v.62 no.6
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• pp.709-717
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• 2017

This paper develops a two-stage method for structural damage identification by using modal data. First, the Residual Force Vector (RFV) is introduced to detect any potentially damaged elements of structures. Second, data of the frequency domain are used to build up the objective function, and then the Imperialist Competitive Algorithm (ICA) is utilized to estimate damaged extents. ICA is a heuristic algorithm with simple structure, which is easy to be implemented and it is effective to deal with high-dimension nonlinear optimization problem. The advantages of this present method are: (1) Calculation complexity can be decreased greatly after eliminating many intact elements in the first step. (2) Robustness, ICA ensures the robustness of the proposed method. Various damaged cases and different structures are investigated in numerical simulations. From these results, anyone can point out that the present algorithm is effective and robust for structural damage identification and is also better than many other heuristic algorithms.

• Coupled systems mechanics
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• v.9 no.1
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• pp.77-89
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• 2020

This study is dedicated to the dynamic elasticity problem for a semi-strip. The semi-strip is loaded by the dynamic load at the center of its short edge. The conditions of fixing are given on the lateral sides of the semi-strip. The initial problem is reduced to one-dimensional problem with the help of Laplace's and Fourier's integral transforms. The one-dimensional boundary problem is formulated as the vector boundary problem in the transform's domain. Its solution is constructed as the superposition of the general solution for the homogeneous vector equation and the partial solution for the inhomogeneous vector equation. The matrix differential calculation is used for the deriving of the general solution. The partial solution is constructed with the help of Green's matrix-function, which is searched as the bilinear expansion. The case of steady-state oscillations is considered. The problem is reduced to the solving of the singular integral equation. The orthogonalization method is applied for the calculations. The stress state of the semi-strip is investigated for the different values of the frequency.

• Structural Engineering and Mechanics
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• v.13 no.2
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• pp.135-154
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• 2002

This paper presents the convected material frame approach to study the nonlinear behavior of inelastic frame structures. The convected material frame approach is a modification of the co-rotational approximation by incorporating an adaptive convected material frame in the basic definition of the displacement vector and strain tensor. In the formulation, each discrete element is associated with a local coordinate system that rotates and translates with the element. For each load increment, the corresponding strain-displacement and nodal force-stress relationships are defined in the updated local coordinates, and based on the updated element geometry. The rigid body motion and deformation displacements are decoupled for each increment. This modified approach incorporates the geometrical nonlinearities through the continuous updating of the material frame geometry. A generalized nonlinear function is used to derive the inelastic constitutive relation and the kinematic hardening is considered. The equation of motion is integrated by an explicit procedure and it involves only vector assemblage and vector storage in the analysis by assuming a lumped mass matrix of diagonal form. Several numerical examples are demonstrated in close agreement with the solutions obtained by the ANSYS code. Numerical studies show that the proposed approach is capable of investigating large deflection of inelastic planar structures and providing an excellent numerical performance.

• Geomechanics and Engineering
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• v.25 no.1
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• pp.17-30
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• 2021

This paper develops a convenient approach for deterministic and probabilistic evaluations of tunnel face stability using support vector machine classifiers. The proposed method is comprised of two major steps, i.e., construction of the training dataset and determination of instance-based classifiers. In step one, the orthogonal design is utilized to produce representative samples after the ranges and levels of the factors that influence tunnel face stability are specified. The training dataset is then labeled by two-dimensional strength reduction analyses embedded within OptumG2. For any unknown instance, the second step applies the training dataset for classification, which is achieved by an ad hoc Python program. The classification of unknown samples starts with selection of instance-based training samples using the k-nearest neighbors algorithm, followed by the construction of an instance-based SVM-KNN classifier. It eventually provides labels of the unknown instances, avoiding calculate its corresponding performance function. Probabilistic evaluations are performed by Monte Carlo simulation based on the SVM-KNN classifier. The ratio of the number of unstable samples to the total number of simulated samples is computed and is taken as the failure probability, which is validated and compared with the response surface method.

• Structural Engineering and Mechanics
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• v.68 no.6
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• pp.691-700
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• 2018

Ground granulated blast furnace slag (GGBS) is a by product obtained from iron and steel industries, useful in the design and development of high quality cement paste/mortar and concrete. This paper investigates the applicability of relevance vector machine (RVM) based regression model to predict the compressive strength of various GGBS based concrete mixes. Compressive strength data for various GGBS based concrete mixes has been obtained by considering the effect of water binder ratio and steel fibres. RVM is a machine learning technique which employs Bayesian inference to obtain parsimonious solutions for regression and classification. The RVM is an extension of support vector machine which couples probabilistic classification and regression. RVM is established based on a Bayesian formulation of a linear model with an appropriate prior that results in a sparse representation. Compressive strength model has been developed by using MATLAB software for training and prediction. About 70% of the data has been used for development of RVM model and 30% of the data is used for validation. The predicted compressive strength for GGBS based concrete mixes is found to be in very good agreement with those of the corresponding experimental observations.

• Structural Engineering and Mechanics
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• v.84 no.1
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• pp.1-16
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• 2022

An efficient and accurate classification method for failure modes of reinforced concrete (RC) columns was proposed based on key characteristic parameters. The weight coefficients of seven characteristic parameters for failure modes of RC columns were determined first based on the support vector machine-recursive feature elimination. Then key characteristic parameters for classifying flexure, flexure-shear and shear failure modes of RC columns were selected respectively. Subsequently, a support vector machine with key characteristic parameters (SVM-K) was proposed to classify three types of failure modes of RC columns. The optimal parameters of SVM-K were determined by using the ten-fold cross-validation and the grid-search algorithm based on 270 sets of available experimental data. Results indicate that the proposed SVM-K has high overall accuracy, recall and precision (e.g., accuracy>95%, recall>90%, precision>90%), which means that the proposed SVM-K has superior performance for classification of failure modes of RC columns. Based on the selected key characteristic parameters for different types of failure modes of RC columns, the accuracy of SVM-K is improved and the decision function of SVM-K is simplified by reducing the dimensions and number of support vectors.

• Coupled systems mechanics
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• v.11 no.1
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• pp.33-41
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• 2022

Quite often we have a lot of measurement data and would like to find some relation between them. One common task is to see whether some measured data or a curve of known shape fit into the cumulative measured data. The problem can be visualized since data could generally be presented as curves or planes in Cartesian coordinates where each curve could be represented as a vector. In most cases we have measured the cumulative 'curve', we know shapes of other 'curves' and would like to determine unknown coefficients that multiply the known shapes in order to match the measured cumulative 'curve'. This problem could be presented in more complex variants, e.g., a constant could be added, some missing (unknown) data vector could be added to the measured summary vector, and instead of constant factors we could have polynomials, etc. All of them could be solved with slightly extended version of the procedure presented in the sequel. Solution procedure could be devised by reformulating the problem as a measurement problem and applying the generalized inverse of the measurement matrix. Measurement problem often has some errors involved in the measurement data but the least squares method that is comprised in the formulation quite successfully addresses the problem. Numerical examples illustrate the solution procedure.

• Structural Engineering and Mechanics
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• v.87 no.1
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• pp.19-28
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• 2023

This paper describes the experimental investigation of steel pallet rack beam-to-column connec-tions. Total behavior of moment-rotation (M-φ) curve and the effect of particular characteristics on the behavior of connection were studied and the associated load strain relationship and corre-sponding failure modes are presented. In this respect, an estimation of SPRBCCs moment and rotation are highly recommended in early stages of design and construction. In this study, a new approach based on Support Vector Machines (SVMs) coupled with discrete wavelet transform (DWT) is designed and adapted to estimate SPRBCCs moment and rotation according to four input parameters (column thickness, depth of connector and load, beam depth,). Results of SVM-WAVELET model was compared with genetic programming (GP) and artificial neural networks (ANNs) models. Following the results, SVM-WAVELET algorithm is helpful in order to enhance the accuracy compared to GP and ANN. It was conclusively observed that application of SVM-WAVELET is especially promising as an alternative approach to estimate the SPRBCCs moment and rotation.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.1123-1128
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• 1996

Let A be an (nonassociative) algebra with multiplication xy over a field F, and denote by $A^-$ the algebra with multiplication [x, y] = xy - yx$ defined on the vector space A. If $A^-$ is a Lie algebra, then A is called Lie-admissible. Lie-admissible algebras arise in various topics, including geometry of invariant affine connections on Lie groups and classical and quantum mechanics(see [2, 5, 6, 7] and references therein).