Parallel Jacobi Transformation Algorithm for Generalized Eigen-Solution With Improved Damage Detection of Truss/Bridge-Type Structures

Serial Jacobi transformation algorithm for the solution of “standard eigen-problems” is re-visited to facilitate the explanation of the proposed parallel transformation algorithm, for which computational efficiency can be realized in this study through “pattern recognition” for the development and explanation of “explicit formulas” to avoid costly matrix time matrix operations. The proposed parallel Jacobi transformation for the solution of “generalized eigen-problems” has also been incorporated into the “improved damage detection” algorithm. Computational efficiency and robust behaviors for the entire proposed procedures (eigen-solution, damage detection and damage quantification) can be validated through several academic and real-life numerical examples. Numerical results obtained from this study have indicated that our proposed generalized Jacobi transformation is more robust/reliable as compared to MATLAB eigen-solver. Furthermore, our proposed simple rule of thumb for damage detection of aging bridge structures also give better results than existing algorithms