Flexibility-Based Objective Functions for Constrained Optimization Problems on Structural Damage Detection

2011 ◽  
Vol 186 ◽  
pp. 383-387 ◽  
Author(s):  
Xi Chen ◽  
Ling Yu
Keyword(s):  
Damage Detection ◽  
Constrained Optimization ◽  
Objective Function ◽  
Structural Damage ◽  
Optimization Problems ◽  
Objective Functions ◽  
Structural Damage Detection ◽  
Constrained Optimization Problems ◽  
Modal Assurance Criterion ◽  
Damage Scenarios

Based on concepts of structural modal flexibility and modal assurance criterion (MAC), a new objective function is defined and studied for constrained optimization problems (COP) on structural damage detection (SDD) in this paper. Compared with traditionally objective function, which is defined based on natural frequencies and MAC, effect of objective functions on robustness of SDD calculation is evaluated through numerical simulation of a 2-storey rigid frame. Structural damages are identified by solving the COP on SDD based on an improved particle swarm optimization (IPSO) algorithm. Weak and multiple damage scenarios are mainly considered in various noise conditions. Some illustrated results show that the newly defined objective function is better than the traditional ones. It can be used to identify the damage locations but also to quantify the severity of weak and multiple damages in measurement noise conditions.

scholarly journals Analisis Karakteristik Fungsi Lagrange Dalam Menyelesaikan Permasalahan Optimasi Berkendala

2018 ◽  
Vol 1 (1) ◽  
pp. 037-043
Author(s):  
Theresia Mehwani Manik ◽  
Parapat Gultom ◽  
Esther Nababan
Keyword(s):  
Constrained Optimization ◽  
Objective Function ◽  
Lagrange Multiplier ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Quadratic Function ◽  
Lagrange Multiplier Method ◽  
Multiplier Method ◽  
Objective Functions ◽  
Constrained Optimization Problems

Optimasi adalah suatu aktivitas untuk mendapatkan hasil terbaik di dalam suatu keadaan yang diberikan. Tujuan akhir dari aktivitas tersebut adalah meminimumkan usaha (effort) atau memaksimumkan manfaat (benefit) yang diinginkan. Metode pengali Lagrange merupakan metode yang digunakan untuk menangani permasalahan optimasi berkendala. Pada penelitian ini dianalisis karakteristik dari metode pengali Lagrange sehingga metode ini dapat menyelesaikan permasalahan optimasi berkendala. Metode tersebut diaplikasikan pada salah satu contoh optimasi berkendala untuk meminimumkan fungsi objektif kuadrat sehingga diperolehlah nilai minimum dari fungsi objektif kuadrat adalah -0.0403. Banyak masalah optimasi tidak dapat diselesaikan dikarenakan kendala yang membatasi fungsi objektif. Salah satu karakteristik dari metode pengali Lagrange adalah dapat mentransformasi persoalan optimasi berkendala menjadi persoalan optimasi tanpa kendala. Dengan demikian persoalan optimasi dapat diselesaikan.   Optimization is an activity to get the best results in a given situation. The ultimate goal of the activity is to minimize the effort or maximize the desired benefits. The Lagrange multiplier method is a method used to handle constrained optimization problems. This study analyzed the characteristics of the Lagrange multiplier method with the aim of solving constrained optimization problems. The method was applied to one sample of constrained optimization to minimize the objective function of squares and resulted -0.0403 as the minimum value of the objective quadratic function. Many optimization problems could not be solved due to constraints that limited objective functions. One of the characteristics of the Lagrange multiplier method was that it could transform constrained optimization problems into non-constrained ones. Thus the optimization problem could be resolved. 

Numerical experiments on stochastic block proximal-gradient type method for convex constrained optimization involving coordinatewise separable problems

2019 ◽  
Vol 35 (3) ◽  
pp. 371-378
Author(s):  
PORNTIP PROMSINCHAI ◽  
NARIN PETROT ◽  
◽  
◽  
Keyword(s):  
Constrained Optimization ◽  
Optimization Problems ◽  
Gradient Algorithm ◽  
Objective Functions ◽  
Constrained Optimization Problems ◽  
Type Method ◽  
Coordinate Descent Algorithm ◽  
Proximal Gradient Algorithm ◽  
Separable Problems ◽  
Gradient Type

In this paper, we consider convex constrained optimization problems with composite objective functions over the set of a minimizer of another function. The main aim is to test numerically a new algorithm, namely a stochastic block coordinate proximal-gradient algorithm with penalization, by comparing both the number of iterations and CPU times between this introduced algorithm and the other well-known types of block coordinate descent algorithm for finding solutions of the randomly generated optimization problems with regularization term.

Structural Damage Detection Using Linear Matrix Inequality Methods

2000 ◽  
Vol 122 (4) ◽  
pp. 448-455 ◽  
Author(s):  
M. O. Abdalla ◽  
K. M. Grigoriadis ◽  
D. C. Zimmerman
Keyword(s):  
Experimental Data ◽  
Linear Matrix Inequality ◽  
Damage Detection ◽  
Structural Damage ◽  
Optimization Problems ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Structural Damage Detection ◽  
Test Bed ◽  
Stiffness Reduction

In this work, linear matrix inequality (LMI) methods are proposed for computationally efficient solution of damage detection problems in structures. The structural damage detection problem that is considered consists of estimating the existence, location, and extent of stiffness reduction in structures using experimental modal data. This problem is formulated as a convex optimization problem involving LMI constraints on the unknown structural stiffness parameters. LMI optimization problems have low computational complexity and can be solved efficiently using recently developed interior-point methods. Both a matrix update and a parameter update formulation of the damage detection is provided in terms of LMIs. The presence of noise in the experimental data is taken explicitly into account in these formulations. The proposed techniques are applied to detect damage in simulation examples and in a cantilevered beam test-bed using experimental data obtained from modal tests. [S0739-3717(00)00104-5]

A hybrid ant lion optimizer with improved Nelder–Mead algorithm for structural damage detection by improving weighted trace lasso regularization

2019 ◽  
Vol 23 (3) ◽  
pp. 468-484 ◽  
Author(s):  
Chengbin Chen ◽  
Ling Yu
Keyword(s):  
Damage Detection ◽  
Objective Function ◽  
Hybrid Algorithm ◽  
Structural Damage ◽  
Heuristic Algorithms ◽  
Structural Damage Detection ◽  
Ant Lion Optimizer ◽  
Computing Performance ◽  
Ant Lion ◽  
Nelder Mead Algorithm

Structural damage detection is the kernel technique in deploying structural health monitoring. The structural damage–detection technique using heuristic algorithms has been developed at an astounding pace over the past years. However, some existing structural damage–detection methods are prone to easily fall into the local optimum and to be unstable when they are applied to complex structures. In order to make full use of advantages of heuristic algorithms and overcome abovementioned shortcomings, a hybrid algorithm, which combines the ant lion optimizer with an improved Nelder–Mead algorithm, is proposed to solve the constrained optimization problem of complex structural damage detection. First, an objective function is established for damage identification using structural modal parameters, that is, frequencies and mode shapes. The solution to the objective function is accurately attained by a newly improved weighted trace lasso which can improve the computing performance and stability of procedure and reduce randomness of weighted coefficients. After assessing the computing performance of the proposed hybrid algorithm using three classical mathematical benchmark functions, two structural damage–detection numerical simulations and a laboratory verification are then conducted to fully assess the structural damage–detection capability of the proposed method. Meanwhile, the equivalent element stiffness-reduction model is introduced to estimate the real damage severities of cracks which are created in laboratory structures and to compare with the structural damage–detection results by the proposed method. The illustrated results show that the proposed hybrid algorithm can locate damage and quantify damage severity more accurately and stably with a good robustness to noise.

Structural Damage Detection Using Signal Pattern-Recognition

2008 ◽  
Vol 400-402 ◽  
pp. 465-470 ◽  
Author(s):  
Long Qiao ◽  
Asad Esmaeily ◽  
Hani G. Melhem
Keyword(s):  
Pattern Recognition ◽  
Damage Detection ◽  
Structural Damage ◽  
Experimental Studies ◽  
Least Square ◽  
Structural Damage Detection ◽  
Damage Scenario ◽  
Damage Pattern ◽  
Damage Scenarios ◽  
Unknown Damage

Deterioration significantly affects the structure performance and safety. A signal-based pattern-recognition procedure is applied for structural damage detection with a limited number of input/output signals. The method is based on extracting and selecting the sensitive features of the structure response to form a unique pattern for any particular damage scenario, and recognizing the unknown damage pattern against the known database to identify the damage location and level (severity). In this study, two types of transformation algorithms are implemented separately for feature extraction: (1) Continuous Wavelet Transform (CWT); and (2) Wavelet Packet Transform (WPT). Three pattern-matching algorithms are also implemented separately for pattern recognition: (1) correlation, (2) least square distance, and (3) Cosh spectral distance. To demonstrate the validity and accuracy of the procedure, experimental studies are conducted on a simple three-story steel structure. The results show that the features of the signal for different damage scenarios can be uniquely identified by these transformations, and correlation algorithms can best perform pattern recognition to identify the unknown damage pattern. The proposed method can also be used to possibly detect the type of damage. It is suitable for structural health monitoring, especially for online monitoring applications.

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