A new fast convergent iteration regularization method

Wang, Linjun; Xie, Youxiang; Wu, Zhengjia; Du, Yi; He, Kongde

doi:10.1007/s00366-018-0588-4

Cited by 15 publications

(4 citation statements)

References 21 publications

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“…In addition, the HT, HHT, and VMD methods can only provide empirical information [11] and lack strict mathematical derivation. Considering that only timedomain methods can be applied for online identifcation due to their recursive characteristics, while basic frequency domain methods are generally nonrecursive [12], timedomain methods such as least squares estimation (LSE), extended Kalman flter (EKF), unscented Kalman flter (UKF), Monte Carlo flter (MCF), and others [13][14][15][16][17][18][19][20][21] have received signifcant attention.…”

Section: Introductionmentioning

confidence: 99%

A Novel Adaptive Square Root UKF with Forgetting Factor for the Time-Variant Parameter Identification

Zhang,

Ding,

et al. 2023

Structural Control and Health Monitoring

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The unscented Kalman filter (UKF) serves as an efficient estimator widely utilized for the recursive identification of parameters. However, the UKF is not well suited for tracking time-variant parameters. Moreover, the unscented transformation (UT) used in the UKF typically relies on Cholesky decomposition to perform the square root operation of the covariance matrix. This method necessitates the matrix to maintain symmetry and positive definiteness. Due to the adverse influence of rounding error and noise, it becomes challenging to guarantee the positive definiteness of the matrix in each recursive step for practical engineering. The square root UKF (SRUKF) eliminates the need for the square root operation in the UT by directly updating the square root of the covariance matrix during each recursion. However, the SRUKF still relies on the rank 1 update to the Cholesky factorization to perform the recursive process, which also necessitates the matrix to be positive definite. Furthermore, the SRUKF is ineffective in the identification of time-variant parameters. Therefore, this paper proposes a modification to the SRUKF that ensures unconditional numerical stability by utilizing QR decomposition. Subsequently, the modified square root UKF (MSRUKF) method is enhanced by incorporating an adaptive forgetting factor that can be adjusted based on the residual information from each recursive step. This adaptation leads to the development of the adaptive SRUKF with forgetting factor (ASRUKF-FF) method, which significantly improves the tracking capability for time-variant parameters. To validate the effectiveness of the proposed method, this paper demonstrates its application in identifying the time-variant stiffness and damping parameters of a three-story frame structure. In addition, the method is employed to estimate the time-variant stiffness of the bridge excited by vehicles. The simulation results show that the proposed method has the superiority of high accuracy, strong robustness, and widespread applicability, even with incomplete measurements and inappropriate parameter settings.

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Section: Introductionmentioning

confidence: 99%

A Novel Adaptive Square Root UKF with Forgetting Factor for the Time-Variant Parameter Identification

Zhang,

Ding,

et al. 2023

Structural Control and Health Monitoring

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“…In recent years, force identification in structural dynamics has attracted lots of interest of many scholars. [1][2][3][4][5][6][7] The inverse force identification by structural vibration data such as displacement responses is particularly suitable for structural mechanics and structural health monitoring in the field of mechanical engineering. However, for a great many practical engineering problems, we have to try our best to know the corresponding information of external loads.…”

Section: Introductionmentioning

confidence: 99%

A New Conjugate Gradient Method and Application to Dynamic Load Identification Problems

Wang¹,

Gao²,

Xie³

et al. 2021

The International Journal of Acoustics and Vibration

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In this paper, a modified conjugate gradient (MCG) algorithm is proposed for solving the force reconstruction problems in practical engineering. This new method is derived from a stable regularization operator and is also strictly proved using the mathematical theory. Moreover, we also prove the sufficient descent and global convergence characteristic of the newly developed algorithm. Finally, the proposed algorithm is applied to force reconstruction for the airfoil structure and composite laminated cylindrical shell. Numerical simulations show that the proposed method is highly efficient and has robust convergence performances. Additionally, the accuracy of the proposed algorithm in identifying the expected loads is satisfactory and acceptable in practical engineering.

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“…Regularization method is the most common technique for solving such ill-posed inverse problem [11]- [13]. A set of neighboring well-posed questions is used to approximate the original ill-posed problem, and the solution of the wellposed question can be viewed as the approximate solution of the original problem.…”

Section: Introductionmentioning

confidence: 99%

Regularized Cubic B-Spline Collocation Method With Modified L-Curve Criterion for Impact Force Identification

Liu

Xie

et al. 2020

IEEE Access

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The time history of the impact force, especially for the peak force, is vital to monitor the performance of mechanical products over the lifetime. However, considering the limitation of sensing technology and inaccessibility of installing, it is always difficult or even impossible to measure the force directly in engineering practice. Therefore, a regularized cubic B-spline collocation (RCBSC) method combined with the modified L-curve criterion (RCBSC-ML) is presented to identify the impact force by easily measurable dynamic response. Because the profile of cubic B-spline is close to that of impact force, a linear combination of cubic B-spline functions is used to approximate the unknown impact force. Then the force identification equation is reformed, wherein the unknown variable changes from impact force vector to weight coefficient vector. Furthermore, the modified L-curve criterion is developed to select the optimal number of collocation points which is the regularization parameter of RCBSC method. Rich simulation studies on a five degree-of-freedoms structure and experimental studies on a simplified artillery test-bed are performed to validate the performance of RCBSC-ML method. The results illustrate that RCBSC-ML method can be used to accurately identify the unknown impact force, and compared with modified generalized cross validation criterion, the presented modified L-curve criterion is more suitable to determine the optimal regularization parameter of RCBSC method. Furthermore, compared with classical Tikhonov regularization method, RCBSC-ML method is more efficient and accurate in impact force identification. INDEX TERMS Cubic B-spline, impact force identification, ill-posed inverse problem, modified L-curve criterion.

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A new fast convergent iteration regularization method

Cited by 15 publications

References 21 publications

A Novel Adaptive Square Root UKF with Forgetting Factor for the Time-Variant Parameter Identification

A Novel Adaptive Square Root UKF with Forgetting Factor for the Time-Variant Parameter Identification

A New Conjugate Gradient Method and Application to Dynamic Load Identification Problems

Regularized Cubic B-Spline Collocation Method With Modified L-Curve Criterion for Impact Force Identification

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