Model-Free Identification of Nonlinear Restoring Force with Modified Observation Equation

Abstract

Nonlinearity exists widely in civil engineering structures; for example, the initiation and growth of damage under dynamic loadings is a typical nonlinear process. To date, for the purpose of structural evaluation and a better understanding nonlinear characteristics of complicated structures, a number of parametric and nonparametric methods have been developed for the identification of nonlinear restoring force (NRF). However, due to the highly individualistic nature of nonlinear systems, it would be inefficient to attempt to express the structural NRF in a general parametric form. For many nonparametric techniques, their nonparametric models or approximations may result in undesirable results or oscillations around unsmooth points. In this paper, on the basis of extended Kalman filter (EKF), a model-free NRF identification approach is proposed to circumvent the limitations mentioned above. The NRF to be identified was treated as ‘unknown fictitious input’, and thus, no prior assumptions or approximations for the NRF model were required. With the aid of a projection matrix, a modified version of observation equation was obtained. Based on the principle of EKF, the recursive solution of the proposed approach was analytically derived. The NRFs provided by the nonlinear components were identified by means of least squares estimation (LSE) at each time step. Numerical examples, including building structures equipped with magnetorheological (MR) damper and shape memory alloy (SMA) damper, demonstrated that the proposed approach is capable of satisfactorily identifying NRF without knowledge or intuitive assumptions of any nonlinear model class in advance.

Output-Only Parameters Identification of Earthquake-Excited Building Structures with Least Squares and Input Modification Process

“…However, in some practical situations, for example an earthquake-excited building, the measurements of loadings are sometimes unavailable. Therefore, the parameters cannot be directly identified according to Equation (8) in this case. Additional information or supplementary equations are required for the identification.…”

“…To date, a number of vibration-based system identification and damage detection methods have been developed, and review articles with different emphases can be also found [2][3][4]. In general, structural parameters identification can be performed in three different paradigms: (i) time domain (e.g., [5][6][7][8][9][10]), (ii) frequency domain (e.g., [11][12][13][14]), and (iii) time-frequency domain (e.g., [15][16][17]).…”

Hysteresis and dynamic loading nonparametric identification for multi‐degree‐of‐freedom structures using an updated general extended Kalman filter and a Legendre polynomial model

“…In the nonlinear behavior identification approaches proposed in the above studies, a parametric mathematical model describing the nonlinear behavior of the structure to be identified should be assumed in advance. Considering the complexity and individuality of structural nonlinear behavior of engineering structures in practice that are made of different construction materials with different structure types, the development of nonparametric or mathematical model‐free identification methods for nonlinear systems has received significant attention and has shown their advantages in recent years 3,4,39,40 . A new technique called “Describing Surface Method” (DSM) was developed by Karaagacli and Ozguven 41 to identify local nonlinearity in a dynamic structure in an nonparametric way.…”

“…Considering the complexity and individuality of structural nonlinear behavior of engineering structures in practice that are made of different construction materials with different structure types, the development of nonparametric or mathematical model-free identification methods for nonlinear systems has received significant attention and has shown their advantages in recent years. 3,4,39,40 A new technique called "Describing Surface Method" (DSM) was developed by Karaagacli and Ozguven 41 to identify local nonlinearity in a dynamic structure in an nonparametric way. However, this method requires measuring the complete dynamic responses at each DOF of the structure.…”

Structural Damage Detection and Health Monitoring

“…Examples include the flexural testing of high-performance steel beams, steel bar corrosion [26], testing of bonding behavior in reinforced concrete [27], among others [28,29]. At a higher level, using the current understanding of system mechanical behaviors, investigators have developed methods to identify, extract features, and classify the health of different structures using minimal knowledge of system behavior [30][31][32][33][34][35]. Supporting such work are other researchers that specialize in the long-term monitoring of damage and help strategize everything from sensor placement to understanding what the key parameters that need to be monitored are.…”