Measurement
Date: 31 May 2024
Article: 114528
Volume: Volume 231

Published by: Elsevier

Published by

Elsevier
Review article
Get rights and content

Missing measurement data recovery methods in structural health monitoring: The statechallenges and case study

Author links open overlay panel
Access through your organizationPurchase PDF

Abstract

In the field of structural health monitoring (SHM)the sensor measurement signals collected from the structure are the foundation and key of the SHM system. Howeverthe loss of sensor measurement signals can affect the accurate assessment of structural health. The restoration of missing measurement signals in SHM is a multidisciplinary research field. Thereforeanalyzing the features of the measurement signals from multiple perspectivesestablishing appropriate mathematical modelsand selecting efficient algorithms is crucial to solving this problem. This article briefly reviews the latest research progress on restoring missing sensor measurement signals in SHMusing mathematical models as classification criteriaincluding finite element methodssparse representation methodsstatistical inference methodsand machine learning algorithms. At the end of this articlea study is conducted on an engineering caseand the development trend and challenges of restoring missing measurement sensor signals in SHM are presented from multiple perspectives in-depth.

Keywords

Missing measurement data recovery
;
Structural health monitoring
;
Sensor science
;
Algorithms
;
Deep learning
;
Case study

Introduction

With the rapid development of industrialization and urbanizationthe safety and reliability of structures have become an increasingly important issue. Structural health monitoring (SHM) technology as an effective means can provide real-time monitoring and evaluation of structures to ensure structures safety and reliability. Howeverthere are often signal losses in monitoring data due to sensor agingcircuit faultsunstable power supplyand other reasons in practical applications. These losses may be randomperiodicor continuous. The measurement data acquisition system is often the foundation and most important part of SHM. The data loss may cause the damage identification system to be unable to accurately determine the health status of various parts of the structure. If the missing signal involves structures critical partsit may even affect structures overall health assessment. Thereforeto ensure the accuracy and effectiveness of SHMit is necessary to solve the problem of sensor measurement signal lossreconstruct the missing measurement signals to obtain complete and accurate monitoring data.
In recent yearsmany SHM measurement signal restoration techniques have emerged and have been applied to various structures such as buildings [1]TV towers [2]bridges [3]dams [4]swimming pools [5]and shield tunnel concrete segments [6]. These techniques can recover missing measurement signals from existing monitoring datathereby improving the completeness and accuracy of monitoring data. Before establishing a signal recovery modelit is essential to have a sufficient understanding of the basic characteristics of the measurement signals to be restored. In SHMthe types of signals collected by sensors involve structural response signals (acceleration [7]displacement [8]stress [2]strain [9]crack width [4]) and environmental parameter signals (temperature [10] and wind speed [11]). Different data types have different characteristics: acceleration data has time-varying; stress data has randomnessnonlinearityand high-dimensionality; earthquake wave measurement data has high-frequency randomnessinstantaneous variabilityand time-varying; temperature data has periodic; humidity data typically changes with the season; crack width measurement data has periodic and time-evolving; stress measurement data typically have random processes and nonlinearity; wind speed data usually exhibit non-stationary sequences. In additionthe data distribution of the same signal type is also different in different scenarios. Thereforeit is necessary to fully understand the spatial and temporal distribution of the missing measurement signals and select appropriate restoration methods accordingly.
Establishing an accurate mathematical model and selecting appropriate algorithms are critical to solving the problem of reconstructing missing sensors signals in SHM. In current researchSHM signal restoration methods can be classified from the perspective of mathematical model types and divided into numerical analysis methodoptimization methodprobability estimationand end-to-end regression model:
  • (a)
    Finite element-based methods as an indirect numeric analysis means of SHM measurement signal restoration aim to transform the structure's response recovery problem into an estimation problem of unknown inputs. The estimated input is applied to structure finite element modeland the structure complete response is calculated through finite element. Hong et al. [12] use the acceleration measured at high sampling rates and the displacement measured at very low sampling rates. The reconstructed control equations and boundary conditions are derived using variational formulations for inverse problems to minimize the error between the measured responses and reconstructed responses. Li et al. [13] proposed two multiscale finite element models for reconstructing structural responses.
  • (b)
    Sparse representation methods can be regarded as a type of optimization model. Bao et al. [5] explored a new compressed sensing method for wireless sensor networks in SHM. Sawant et al. [14] presented an orthogonal matching pursuit algorithm to recover lost data in ultrasound-based SHM applications. Yang et al. [15] used prior knowledge of data structures (intra-channel sparsity or inter-channel low-rank) to propose a method that minimizes sparse recovery and nuclear norm for low-rank matrix completion. This method can recover structurally random loss or damaged vibration response measurement data.
  • (c)
    Statistical inference methods can be regarded as a type of probability estimation model. Zhang et al. [9] brought forward a Bayesian dynamic regression method to reconstruct missing SHM measurement data. Niu et al. [16] designed a state and input estimator based on the Kalman filtering schemewhich can estimate unknown inputs and system states within one sampling time. Lin et al. [17] designed a data reconstruction method based on Kriging sequential interpolation combined with probability distribution correction.
  • (d)
    Machine learning-based data reconstruction methods can be regarded as a type of end-to-end regression model. Oh et al. [1] puts forward a structural response restoration method based on Convolutional neural network. Jiang et al. [18] studied a new data-driven Generative adversarial network for recovering missing strain measurement responses. In additionChen et al. [19] researched a strain reconstruction method that combines a nonlinear deep learning module with a linear autoregressive module.
Furthermoremeasurement noise (sensor noisemeasurement system-induced noiseand noise caused by environmental factors) is one of the unavoidable issues in SHM. Measurement noise can greatly affect the accuracy of SHM signal recoverymaking the signal contain parts that are unrelated to the desired signal. Peng et al. [20] proposed a modal Kalman filtering method based on excitation identification Kalman filteringwhich uses noisy acceleration and measured strain for structure response reconstruction and excitation estimation.
The other parts of this article are organized as follows: Section 2 provides a review of indirect methods for SHM missing measurement data recovery based on the finite element method. Section 3 summarizes and investigates the application of sparse representation methods in SHM missing measurement data recovery. It is divided into two parts: compressed sensing algorithm and matrix analysis method according to their respective implementation principles. Section 4 introduces statistical inference methods for signal recovery modelswhich is subdivided into three sub-sections based on the degree of assumption about the model data distribution (parameter modelnon-parametric modeland hybrid model). It elaborates on three commonly used signal recovery methods in parameter models (Bayesian methodsKalman filteringand other parameter model methods). Non-parametric methods are further divided into two parts (principal component analysis and other non-parametric methods). In Section 5a review of recovery models based on machine learning algorithms are presented. As machine learning algorithms are currently a hot research topic in this fieldthis section focuses on 6 types of machine learning methods (traditional machine learning algorithmConvolutional neural networksGenerative adversarial networksRecurrent neural networksAutoencoderand Graph neural networks) with specific network types as the classification indicator. In Section 6the practical application of missing measurement data recovery methods in SHM is demonstrated using a kilometer-scale suspension bridge as the research background. Furthermoreat the end of each sectionthe advantages and drawbacks of various algorithms are compared in the form of text descriptions or tables. In the conclusion section (Section 7)this article presents the development trend and challenges of SHM missing signal recovery from various perspectives based on an in-depth analysis of existing research. The missing measurement signal recovery methods for SHM are summarized in Fig. 1. In additionFig. 2 presents the keywords cloud of SHM missing data recovery methodsproviding a visual representation of the popularity of the main methods discussed in this study.

Organizational access

Get full-text access by signing in with your organisationAccess through your organization

Other access options

Purchase PDF
Need help with access?

Section snippets

Finite element-based methods

Finite element-based methods (FEM) as an indirect numeric analysis means of SHM signal restoration aim to transform the structure's response recovery problem into an estimation problem of unknown inputs. The estimated input is applied to the finite element model of the structureand the structure complete response is calculated through finite element. Fig. 3 shows the technical route of SHM missing measurement signal recovery based on finite element method. Hong et al. [12] proposed a

Compressed sensing algorithms

Compressed sensing (CS) is a method for efficient data compression and reconstruction by representing signals sparsely. It was first introduced by D.L. Donoho in 2006 [22]. In CSthe measurement signal can be sampled at a lower sampling rate. The mathematical model of CS considering noise effects can be represented as follows:y⌢=Φx⌢+ewhere y⌢ represents the measured signal; Φ is the measurement matrix; x⌢ is the original signaland e is the noise vector.
CS algorithm are commonly used to

Bayesian methods

In the task of SHM measurement signal recoveryan unknown data value can be inferred using a Bayesian modelwhich utilizes known data and prior knowledge. Firstlya prior probability distribution needs to be established to describe the distribution of unknown data. Thenthe prior probability distribution is updated by observing known data to obtain the posterior probability distributionwhich can be used to estimate and predict unknown data. Sun et al. [45] established a hierarchical

Traditional machine learning algorithms

In SHMa large amount of sensor data is usually collectedand significant achievements have been made in resolving the issue of sensor signal miss based on machine learning methods [65]. Machine learning algorithms have the ability to process large amounts of data and adaptively learn from itand this method can also infer and estimate missing data patterns and rules based on known datathereby filling in missing data. The process of recovering missing measurement data in SHM based on

Case study

In order to demonstrate the practical application of missing measurement data recovery methods in SHMthis section focuses on the Hardanger Bridge in Norwaya kilometer-scale suspension bridge. The description of the structure and datasetintroduction of data preprocessing methodsConvolutional neural network data recovery approachpresentation of resultsand model evaluation are discussed in this case study.
The Hardanger Bridge spans the Hardangerfjord on the west coast of Norway. It is

Conclusions

In SHMmissing sensor measurement signals may have a significant impact on the accuracy of damage identification and health assessment of structures. Thereforeaccurately recovering missing SHM sensor signals has significant practical significance and engineering application value. This article reviews the research progress in the recovery of missing measurement signals in SHM.Currentlythe methods used for missing data recovery in SHM can be classified into four categories: finite element

CRediT authorship contribution statement

Jianwei Zhang: ConceptualizationMethodologySoftwareFormal analysisWriting - Original DraftFunding acquisition. Minshui Huang: SupervisionFunding acquisitionWriting - Review & EditingResources. Neng Wan: Funding acquisition. Zhihang Deng: Visualization. Zhongao He: Writing - Review & Editing. Jin Luo: Writing - Review & Editing.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

This work was supported by the National Natural Science Foundation of China [grant numbers 52178300]Wuhan Municipal Urban-Rural Development Bureau Scientifc and Technological Project [grant numbers 202358] and Graduate Innovative Fund of Wuhan Institute of Technology [grant numbers CX2022175CX2023358].

References (110)

  • V.S.G. Thadikemalla et al.

    A data loss recovery technique using compressive sensing for structural health monitoring applications

    KSCE J. Civ. Eng.

    (2018)
  • S. Sabeti et al.

    Spatio-temporal undersampling: Recovering ultrasonic guided wavefields from incomplete data with compressive sensing

    Mech. Syst. Signal Process.

    (2020)
  • S. Sawant et al.

    Performance evaluation of compressive sensing based lost data recovery using OMP for damage index estimation in ultrasonic SHM

    Ultrasonics.

    (2021)
  • M. Zhao et al.

    Missing value recovery for encoder signals using improved low-rank approximation

    Mech. Syst. Signal Process.

    (2020)
  • Z. Zhu et al.

    Structural dynamic response reconstruction with multi-type sensorsunknown inputand rank deficient feedthrough matrix

    Mech. Syst. Signal Process.

    (2023)
  • P. Ren et al.

    Incremental Bayesian matrix/tensor learning for structural monitoring data imputation and response forecasting

    Mech. Syst. Signal Process.

    (2021)
  • P. Ni et al.

    Bayesian model updating of civil structures with likelihood-free inference approach and response reconstruction technique

    Mech. Syst. Signal Process.

    (2022)
  • X. Zhang et al.

    Adaptive mode selection integrating kalman filter for dynamic response reconstruction

    J. Sound. Vib.

    (2021)
  • Z. Zhang et al.

    Restoring method for missing data of spatial structural stress monitoring based on correlation

    Mech. Syst. Signal Process.

    (2017)
  • L. Li et al.

    Missing data estimation method for time series data in structure health monitoring systems by probability principal component analysis

    Adv. Eng. Softw.

    (2020)
  • Z. Chen et al.

    LQD-RKHS-based distribution-to-distribution regression methodology for restoring the probability distributions of missing SHM data

    Mech. Syst. Signal Process.

    (2019)
  • Y. Ma et al.

    Probabilistic reconstruction for spatio-temporal sensor data integrated with Gaussian process regression

    Probabilist. Eng. Mech.

    (2022)
  • Y. Bao et al.

    The state of the art of data science and engineering in structural health monitoring

    Engineering.

    (2019)
  • S. Kuok et al.

    Model-free data reconstruction of structural response and excitation via sequential broad learning

    Mech. Syst. Signal Process.

    (2020)
  • Y. Ni et al.

    Wind pressure data reconstruction using neural network techniques: a comparison between BPNN and GRNN

    Measurement.

    (2016)
  • J. Huang et al.

    Recovery of missing field measured wind pressures on a supertall building based on correlation analysis and machine learning

    J. Wind. Eng. Ind. Aerod.

    (2022)
  • Q. Lin et al.

    Deep learning based missing data recovery of non-stationary wind velocity

    J. Wind. Eng. Ind. Aerod.

    (2022)
  • P. Ni et al.

    Traffic-induced bridge displacement reconstruction using a physics-informed convolutional neural network

    Comput. Struct.

    (2022)
  • B.K. Oh et al.

    Convolutional neural network-based wind-induced response estimation model for tall buildings

    Comput.-Aid. Civ. Inf.

    (2019)
  • K. Jiang et al.

    Lost data neural semantic recovery framework for structural health monitoring based on deep learning

    Comput.-Aid. Civ. Inf.

    (2022)
  • G. Fan et al.

    Data driven structural dynamic response reconstruction using segment based Generative adversarial networks

    Eng. Struct.

    (2021)
  • G. Fan et al.

    Structural dynamic response reconstruction using self-attention enhanced Generative adversarial networks

    Eng. Struct.

    (2023)
  • S. Jeong et al.

    Sensor data reconstruction using bidirectional recurrent neural network with application to bridge monitoring

    Adv. Eng. Inform.

    (2019)
  • K. Jiang et al.

    Structural dynamic response reconstruction and virtual sensing using a sequence to sequence modeling with attention mechanism

    Autom. Constr.

    (2021)
  • C. Chen et al.

    Temperature-induced response reconstruction method based on DL-AR model and attention mechanism

    Structures.

    (2023)
  • Y. Lu et al.

    Reconstruction of structural long-term acceleration response based on BiLSTM networks

    Eng. Struct.

    (2023)
  • J. Xin et al.

    A signal recovery method for bridge monitoring system using TVFEMD and encoder-decoder aided LSTM

    Measurement.

    (2023)
  • B.K. Oh et al.

    Convolutional neural network-based data recovery method for structural health monitoring

    Struct. Health. Monit.

    (2020)
  • H. Wan et al.

    Bayesian modeling approach for forecast of structural stress response using structural health monitoring data

    J. Struct. Eng.

    (2018)
  • L. Li et al.

    A hybrid method coupling empirical mode decomposition and a Long short-term memory network to predict missing measured signal data of SHM systems

    Struct. Health. Monit.

    (2021)
  • Y. Bao et al.

    Compressive sampling-based data loss recovery for wireless sensor networks used in civil structural health monitoring

    Struct. Health. Monit.

    (2013)
  • H. Li et al.

    Compressed sensing-based electromechanical admittance data loss recovery for concrete structural health monitoring

    Struct. Health. Monit.

    (2021)
  • X. Lei et al.

    Displacement response estimation of a cable-stayed bridge subjected to various loading conditions with one-dimensional residual convolutional autoencoder method

    Struct. Health. Monit.

    (2022)
  • Y. Zhang et al.

    Bayesian dynamic regression for reconstructing missing data in structural health monitoring

    Struct. Health. Monit.

    (2022)
  • H. Wan et al.

    Bayesian multi-task learning methodology for reconstruction of structural health monitoring data

    Struct. Health. Monit.

    (2019)
  • S. Sawant et al.

    Compressive sensing based data-loss recovery enables robust estimation of damage index in ultrasonic structural health monitoring

  • H. Jiang et al.

    Continuous missing data imputation with incomplete dataset by Generative adversarial networks-based unsupervised learning for long-term bridge health monitoring

    Struct. Health. Monit.

    (2022)
  • Z. Peng et al.

    A modal-based Kalman filter approach and Osp method for structural response reconstruction

    Shock. Vib.

    (2019)
  • D.L. Donoho

    Compressed sensing

    IEEE. t. Inform. Theory.

    (2006)
  • R. Klis et al.

    Data recovery via hybrid sensor networks for vibration monitoring of civil structures

    Int. J. Sustain. Mater. Struct. Syst.

    (2015)
    • View full text

    Cited by (85)

    View all citing articles on Scopus
    © 2024 Elsevier Ltd. All rights reserved.