s. ah. esfehani

In this paper, an explicit family with higher-order of accuracy is proposed for dynamic analysis of structural and mechanical systems. By expanding the analytical amplification matrix into Taylor series, the Runge-Kutta family with  stages can be presented. The required coefficients ( ) for different stages are calculated through a solution of nonlinear algebraic equations. The contribution of the new family is the equality between its accuracy order, and the number of stages used in a single time step ( ). As a weak point, the stability of the proposed family is conditional, so that the stability domain for each of the first three orders ( 5, 6, and 7) is smaller than that for the classic fourth-order Runge-Kutta method. However, as a positive point, the accuracy of the family boosts as the order of the family increases. As another positive point, any arbitrary order of the family can be easily achieved by solving the nonlinear algebraic equations. The robustness and ability of the authors’ schemes are illustrated over several useful time integration methods, such as Newmark linear acceleration, generalized-𝛼, and explicit and implicit Runge-Kutta methods. Moreover, various numerical experiments are utilized to show higher performances of the explicit family over the other methods in accuracy and computation time. The results demonstrate the capability of the new family in analyzing nonlinear systems with many degrees of freedom. Further to this, the proposed family achieves accurate results in analyzing tall building structures, even if the structures are under realistic loads, such as ground motion loads.

Damage diagnosis of a high-dimensional structural signal is a complicated and time-consuming task. In the worse case, if the signal is measured under noisy ambient loads, the extracted features lead to unreliable results in damage diagnosis. In this study, a robust feature extraction method is presented by using time series analysis and correlation relationship generalized in the frequency domain. At first, a time-series model of the response signal is obtained, and the parameters of the model containing inherent and dynamic characteristics of the signal are separated from the model residual, which is influenced by the noise of ambient loads. Upon measuring the model parameters, the high-dimensional signal is transferred to a space with a lower value in size, and the issues due to high-dimensional data are addressed. By using the obtained parameters, the characteristic function of the signal is calculated in the frequency domain. By utilizing a generalized correlation coefficient relationship in the frequency domain, a 2D damage-sensitive feature being a complex value can be extracted from the characteristic function. Structural damage is detected by investigating the angle of the feature extracted. Moreover, by attending to the real part of the feature, the location of damage can be identified. To investigate the abilities of the new feature in damage diagnosis tasks, a real-world structure, S101 Bridge, is examined. To demonstrate the advantages of the new feature in structural damage diagnosis, the outcomes of this study in different levels of damage diagnosis, i.e., damage detection and damage localization, are compared to some state-of-the-art techniques in the field of Structural Health Monitoring (SHM). The achievements of this study clearly show the abilities of the proposed feature for damage diagnosis of real-world structures, especially in the case of high-dimensional data and noisy ambient excitations. Moreover, in comparison to other techniques, the proposed damage diagnosis algorithm in this paper can detect and localize structural damage with more accuracy.