Identification of isolated structural damage from incomplete spectrum information using l1-norm minimization

Hernández, Eduardo

doi:10.1016/j.ymssp.2013.12.009

Cited by 63 publications

(61 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To provide a simple example of multitask learning, we use a simplified model involving linearization that follows Hernandez (). This sensitivity‐based method uses an approximate linear relationship between small changes in eigenvalues

ω^{2}

to small changes in the stiffness scaling parameter vector

θ = {[θ_{1}, \dots, θ_{N_{θ}}]}^{T} \in {double-struckR}^{N_{θ} \times 1}

Δ ω^{2} = S Δ θ

where

Δ θ = θ - θ_{u} \in {double-struckR}^{N_{θ} \times 1}

is the potential change in the stiffness scaling parameter vector

θ

of the current possibly damaged state compared with

θ_{u}

of the undamaged state;

Δ ω^{2} \in {double-struckR}^{N_{m} \times 1}

is the corresponding change in the eigenvalues due to

Δ θ

;

S \in {double-struckR}^{N_{m} \times N_{θ}}

is a sensitivity matrix and has entries

S_{i j}

involving eigenvectors

ϕ_{i}

and substructural stiffness matrices

K_{j}

(Hernandez, ).…”

Section: Applications In Shmmentioning

confidence: 99%

“…To provide a simple example of multitask learning, we use a simplified model involving linearization that follows Hernandez (2014). This sensitivity-based method uses an approximate linear relationship between small changes in eigenvalues ω 2 to small changes in the stiffness scaling parameter vector θ = [θ 1 , .…”

Section: Structural Damage Detection By Employing Multitask Sblmentioning

confidence: 99%

“…As one of the effective strategies to alleviate ill-conditioning and ill-posedness in inverse problems, sparse approximation techniques (Adeli and Sarma, 1995;Tibshirani, 1996;Sarma and Adeli, 1996;Tropp et al, 2006;Hastie et al, 2015) have attracted considerable interest in recent years, especially with the explosion in compressive sensing or compressive sampling (CS) techniques in the last decade (Candès, 2006), which have wide applications in many fields: for example, communications (Gilbert and Tropp, 2005), biology (Studer et al, 2012), physics (Krzakala et al, 2012), and so on. In the SHM community, sparse approximation techniques have also gained increasing attention in the last few years (Huang and Beck, 2015, Huang et al, 2014, 2016Huang et al, 2017a;Hernandez, 2014;Cao et al, 2018).…”

Section: Introductionmentioning

confidence: 99%

“…Although they are somewhat simplified examples, they provide some intuition about the utilization of informative relationships between multiple tasks to get better sparse inversion performance. These applications of multitask SBL are the first in the SHM community, to the best of the authors' knowledge, although there are an increasing number of recent publications that explore sparse approximation techniques in SHM (Huang and Beck, 2015;Huang et al, 2014Huang et al, , 2016Huang et al 2017a;Hernandez, 2014;Cao et al, 2018), including several on single-task SBL algorithms for SHM (Huang and Beck, 2015;Huang et al, 2014Huang et al, , 2016Huang et al 2017a). Huang et al (2017b) presented a preliminary study for multitask SBL for damage detection problems using simulated data.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Multitask Sparse Bayesian Learning with Applications in Structural Health Monitoring

Huang

Beck

2018

Computer aided Civil Eng

View full text Add to dashboard Cite

We focus on a Bayesian approach to learn sparse models by simultaneously utilizing multiple groups of measurements that are marked by a similar sparseness profile. Joint learning of sparse representations for multiple models has been mostly overlooked, although it is a useful tool for exploiting data redundancy by modeling informative relationships within groups of measurements. To this end, two hierarchical Bayesian models are introduced and associated algorithms are proposed for multitask sparse Bayesian learning (SBL). It is shown that the data correlations for different tasks are taken into account more effectively by using the hierarchical model with a common prediction‐error precision parameter across all related tasks, which leads to a better learning performance. Numerical experiments verify that exploiting common information among multiple related tasks leads to better performance, for both models that are highly and approximately sparse. Then, we examine two applications of multitask SBL in structural health monitoring: identifying structural stiffness losses and recovering missing data occurring during wireless transmission, which exploit information about relationships in the temporal and spatial domains, respectively. These illustrative examples demonstrate the potential of multitask SBL for solving a wide range of sparse approximation problems in science and technology.

show abstract

ω^{2}

to small changes in the stiffness scaling parameter vector

θ = {[θ_{1}, \dots, θ_{N_{θ}}]}^{T} \in {double-struckR}^{N_{θ} \times 1}

Δ ω^{2} = S Δ θ

where

Δ θ = θ - θ_{u} \in {double-struckR}^{N_{θ} \times 1}

is the potential change in the stiffness scaling parameter vector

θ

of the current possibly damaged state compared with

θ_{u}

of the undamaged state;

Δ ω^{2} \in {double-struckR}^{N_{m} \times 1}

is the corresponding change in the eigenvalues due to

Δ θ

;

S \in {double-struckR}^{N_{m} \times N_{θ}}

is a sensitivity matrix and has entries

S_{i j}

involving eigenvectors

ϕ_{i}

and substructural stiffness matrices

K_{j}

(Hernandez, ).…”

Section: Applications In Shmmentioning

confidence: 99%

Section: Structural Damage Detection By Employing Multitask Sblmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Multitask Sparse Bayesian Learning with Applications in Structural Health Monitoring

Huang

Beck

2018

Computer aided Civil Eng

View full text Add to dashboard Cite

show abstract

“…Thus, the damage parameter vector is a sparse vector because most of the damage parameters have a zero value. Consequently, the l 1 regularization has begun to be applied in structural damage identification to improve the identification accuracy by considering the damage sparsity . For example, Hou et al proposed a damage detection method based on a model updating and l 1 regularization technique, two experimental examples demonstrated the effectiveness and superiority of the method.…”

Section: Introductionmentioning

confidence: 99%

Improved Kalman filter damage detection approach based on l _p regularization

Huang

Chun

et al. 2019

Struct Control Health Monit

View full text Add to dashboard Cite

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.

show abstract

Comparative studies on damage identification with Tikhonov regularization and sparse regularization

Zhang

2015

Struct. Control Health Monit.

View full text Add to dashboard Cite

SUMMARYStructural damage identification is essentially an inverse problem. Ill-posedness is a common obstacle encountered in solving such an inverse problem, especially in the context of a sensitivity-based model updating for damage identification. Tikhonov regularization, also termed as ℓ 2 -norm regularization, is a common approach to handle the illposedness problem and yields an acceptable and smooth solution. Tikhonov regularization enjoys a more popular application as its explicit solution, computational efficiency, and convenience for implementation. However, as the ℓ 2 -norm term promotes smoothness, the solution is sometimes over smoothed, especially in the case that the sensor number is limited. On the other side, the solution of the inverse problem bears sparse properties because typically, only a small number of components of the structure are damaged in comparison with the whole structure. In this regard, this paper proposes an alternative way, sparse regularization, or specifically ℓ 1 -norm regularization, to handle the ill-posedness problem in response sensitivity-based damage identification. The motivation and implementation of sparse regularization are firstly introduced, and the differences with Tikhonov regularization are highlighted. Reweighting sparse regularization is adopted to enhance the sparsity in the solution. Simulation studies on a planar frame and a simply supported overhanging beam show that the sparse regularization exhibits certain superiority over Tikhonov regularization as less false-positive errors exist in damage identification results. The experimental result of the overhanging beam further demonstrates the effectiveness and superiorities of the sparse regularization in response sensitivity-based damage identification.

show abstract

Identification of isolated structural damage from incomplete spectrum information using l1-norm minimization

Cited by 63 publications

References 24 publications

Multitask Sparse Bayesian Learning with Applications in Structural Health Monitoring

Multitask Sparse Bayesian Learning with Applications in Structural Health Monitoring

Improved Kalman filter damage detection approach based on l _p regularization

Comparative studies on damage identification with Tikhonov regularization and sparse regularization

Contact Info

Product

Resources

About

Identification of isolated structural damage from incomplete spectrum information using l1-norm minimization

Cited by 63 publications

References 24 publications

Multitask Sparse Bayesian Learning with Applications in Structural Health Monitoring

Multitask Sparse Bayesian Learning with Applications in Structural Health Monitoring

Improved Kalman filter damage detection approach based on l p regularization

Comparative studies on damage identification with Tikhonov regularization and sparse regularization

Contact Info

Product

Resources

About

Improved Kalman filter damage detection approach based on l _p regularization