Improved Kalman filter damage detection approach based on l _p regularization

Abstract

Summary The conventional extended Kalman filter (EKF) for detecting structural damage with measured responses is a dynamic inverse problem. With the increase in size of the extended state vector, EKF suffers from low accuracy and convergence difficulty due to the ill‐condition of the inverse problem and increased computational error. To overcome the aforementioned drawbacks, an improved EKF method based on lp regularization (EKF‐lp) is proposed in this paper. In the proposed method, the sparse characteristic on the distribution of local damage, as a priori information, is introduced into EKF by the lp regularization technique. Then, the unconstrained optimization problem of EKF becomes the optimization problem with the lp‐norm constraint. To obtain a recursive solution of the constrained optimization, a pseudo‐measurement equation is used to embed the lp‐norm constraint into the recursive EKF steps. In addition, a precise integration method is employed in the time update step to improve the accuracy of state prediction. To select an appropriate p value in the EKF‐lp method, a novel L‐surface approach is proposed. Finally, the proposed EKF‐lp method is compared with the existing EKF with Tikhonov regularization method and EKF with l1 regularization method on a beam example and an experiment of a three‐story shear building. It is shown that the proposed method is stable and reliable, and its identification precision is higher than the other methods. Moreover, it requires significant less measurements than conventional methods.

Multi-Sensor and Decision-Level Fusion-Based Structural Damage Detection Using a One-Dimensional Convolutional Neural Network

“…The results showed that the computational efficiency (Table 9) of the proposed decision-level fusion was about 60% of the data-level fusion, while the efficiency of the D-S evidence fusion strategy was lower than that of the proposed decision-level fusion. The eigen perturbation and Kalman-filter-based SDD methods can process the structural vibration response signals in real time and identify the structural parameters [10,44]. Figure 16 shows the observed, real, and Kalman filter values of a vibration signal; it shows that the Kalman filter could effectively reduce the noise interference.…”

Structural damage identification with unknown external inputs based on the sparse constraint

“…Assuming that the structural system is time-invariant, the parameter evolution is modeled as. (7) where w θ denotes parameter noise with zero mean Gaussian covariance Q θ . Accordingly, an augmented state vector is defined as…”

“…In this paper, the value of R ε will be determined using the L-curve. By plotting the summed mean squared values of the novelty term ∥ y k − ŷk ∥ 2 2 which is related to the regularized identification results of [7,43] can be obtained. The optimal value of R ε will be selected as the value at the corner of the L-curve, as shown in later figure 1.…”

“…Zhang et al [5] proposed an EKF with l 1 -norm regularization algorithm for structural damage identification, which can identify local damage more accurately than only using EFK. In [5][6][7][8], the EKF is approximated to nonlinear systems by first-order linearization method based on Taylor series expansion. However, large errors will be generated in the linearization process, due to the loss of higher order terms of the system.…”

Analysis of Stiffness of Clamped Joints versus Bolted Joints in Steel Structures by Means of Accelerometers and Shaking Table Tests

“…For real-time analysis and online damage identification techniques, Kalman filter solutions [ 36 , 37 , 38 ] and eigen perturbation [ 39 , 40 ] could be implemented. In particular, industries have introduced eigen perturbation and Kalman filter approaches along with spectral decomposition methods for condition monitoring.…”