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Journal ArticleDOI

A compressive MUSIC spectral approach for identification of closely-spaced structural natural frequencies and post-earthquake damage detection

07 Feb 2020-Probabilistic Engineering Mechanics (Elsevier)-Vol. 60, pp 103030

TL;DR: Results suggest that the adopted approach for identifying resonant frequencies of white-noise excited structures using acceleration measurements acquired at rates significantly below the Nyquist rate is robust and noise-immune while it can reduce data transmission requirements in acceleration wireless sensors for natural frequency identification and damage detection in engineering structures.

AbstractMotivated by practical needs to reduce data transmission payloads in wireless sensors for vibration-based monitoring of engineering structures, this paper proposes a novel approach for identifying resonant frequencies of white-noise excited structures using acceleration measurements acquired at rates significantly below the Nyquist rate. The approach adopts the deterministic co-prime sub-Nyquist sampling scheme, originally developed to facilitate telecommunication applications, to estimate the autocorrelation function of response acceleration time-histories of low-amplitude white-noise excited structures treated as realizations of a stationary stochastic process. Next, the standard multiple signal classification (MUSIC) spectral estimator is applied to the estimated autocorrelation function enabling the identification of structural natural frequencies with high resolution by simple peak picking in the frequency domain without posing any sparsity conditions to the signals. This is achieved by processing autocorrelation estimates without undertaking any (typically computationally expensive) signal reconstruction step in the time-domain, as required by various recently proposed in the literature sub-Nyquist compressive sensing-based approaches for structural health monitoring, while filtering out any broadband noise added during data acquisition. The accuracy and applicability of the proposed approach is first numerically assessed using computer-generated noise-corrupted acceleration time–history data obtained by a simulation-based framework examining white-noise excited structural systems with two closely-spaced modes of vibration carrying the same amount of energy, and a third isolated weakly excited vibrating mode. Further, damage detection potential of the developed method is numerically illustrated using a white-noise excited reinforced concrete 3-storey frame in a healthy and two damaged states caused by ground motions of increased intensity. The damage assessment relies on shifts in natural frequencies between the pre-earthquake and post-earthquake state. Overall, numerical results demonstrate that the considered approach can accurately identify structural resonances and detect structural damage associated with changes to natural frequencies as minor as 1% by sampling up to 78% below Nyquist rate for signal to noise ratio as low as 10dB. These results suggest that the adopted approach is robust and noise-immune while it can reduce data transmission requirements in acceleration wireless sensors for natural frequency identification and damage detection in engineering structures.

Topics: Sampling (signal processing) (55%), Frequency domain (55%), Structural health monitoring (55%), Autocorrelation (55%), Nyquist rate (54%)

Summary (3 min read)

1 Introduction and motivation

  • Moreover, over the past two decades, wireless sensors/accelerometers have been heavily explored to further support the considered aim within the OMA framework as they enable rapidly deployable and low up-front cost field instrumentation compared to arrays of wired sensors [11- 12].
  • Along these lines, herein, a sparse-free structural system identification approach is put forth to estimate natural frequencies of existing linearly vibrating structures exposed to unmeasured broadband/white noise, within the OMA framework, from response acceleration measurements sampled at rates significantly below the nominal Nyquist rate.

2 Mathematical Background of Proposed Method

  • 1 Co-prime sampling and auto-correlation estimation of stationary stochastic processes Let x(t) be a real-valued wide-sense stationary band-limited stochastic process assuming a spectral representation by a superposition of R sinusoidal functions with frequencies fr, real amplitudes Br, and uncorrelated random phases θr uniformly distributed in the interval [0, 2π].
  • This signal model is motivated by the fact that response time-histories of linear vibrating structures under low-amplitude ambient excitation have well-localized energy in the frequency domain centered at the structural natural frequencies (e.g., [34]) and, in this respect, the model proved to be adequate for CS-based modal analysis in a previous study [14].
  • Co-prime sampling assumes that the process x(t) is simultaneously acquired by two sampling units, operating at different (sub-Nyquist) sampling rates, 1/(N1Ts) and 1/(N2Ts), where N1, N2 are coprime numbers (N1 < N2), and 1/Ts= 2fmax is the Nyquist sampling rate with fmax being the highest frequency component in Eq. (1) [24].
  • In the following section, the latter matrix is used as input to the MUSIC super-resolution spectral estimator to detect the R frequencies fr, (r= 1,2,…,R), of the considered stochastic process x(t).
  • The first term in Eq. (8) represents the signal sub-space with R eigenvalues 2( )i + , i=1,…,R, and R principal eigenvectors spanning the same subspace with the signal vector in Eq. (5).

3 Identification of closely-spaced natural frequencies from noisy acceleration data

  • The proposed co-prime sampling with MUSIC spectral estimator approach is numerically assessed to estimate closely-spaced resonant frequencies of white-noise excited structures modelled as multi-degree-of-freedom (MDOF) dynamic systems.
  • The derived noisy acceleration response signals, x[q], are then and co-prime sampled as detailed in section 2.1 and the full-rank autocorrelation matrix in Eq. (7) is constructed.
  • For the other sub-Nyquist sampling cases in Table 1 the pertinent coprime sampling parameters and correlation estimators are defined in a similar manner as above.
  • MUSIC pseudo-spectra of structure 2 in Fig.2(b) obtained for co-prime sampling specifications of Table 1 and for 5 different SNR values, also known as Figure 4.

4 Application for natural frequency-based post-earthquake damage detection

  • An additional numerical study is undertaken to demonstrate the applicability and usefulness of the proposed system identification method in detecting relatively light structural damage induced to buildings by earthquakes.
  • Herein, much more flexible structural systems than those examined in the previous section (Fig.2) are considered being representative of large-scale engineering structures for which wireless-sensor assisted OMA is practically mostly relevant [11].
  • To this aim, the proposed approach is applied to estimate natural frequencies before (healthy state) and after (potentially damaged state) a seismic event within the standard OMA context (i.e., stationary excitation and linear structural response assumptions apply).
  • Notably, in this setting, the consideration of wireless sensors in conjunction with the proposed co-prime sampling plus MUSIC approach leading to reduced sensor energy consumption is practically quite beneficial as long-term/permanent structural monitoring deployments are required for the purpose.
  • In such deployments reducing battery replacement frequency, and thus maintenance costs, becomes critical and may be a main criterion for installing a monitoring system in the first place (e.g., [13]).

4.1 Adopted structure and seismic action

  • The planar 3-storey single-bay reinforced concrete (r/c) frame in Figure 5 is considered as a case-study structure with beams and columns longitudinal and transverse reinforcement as indicated in the figure.
  • Lo is the shear span taken herein as half the structural member length, dbl is the diameter of the longitudinal reinforcement, and fyk, fuk/fuk are the steel strength and strain hardening ratio, respectively, given in the previous sub-section.
  • Specifically, two equivalent linear FE models are defined, corresponding to the two different damage states, in which the earthquake-induced damage is represented by means of the flexural stiffness reduction factors of Table 3.
  • Further, the pre-eartquake/“healthy” state of the considered structure is modelled by a linear FE model with the secant flexural rigidities at yield presented in Table 2 assigned to the full length of structural members.

4.3 Post-earthquake damage detection

  • Linear RHA is undertaken for the three FE models defined in the previous sub-section (healthy plus two damaged states), using the same low amplitude white noise base excitation of 80s duration.
  • It is noted that a certain level of overlapping between the considered time blocks occurs, given that the structural response acceleration signals are only 8000 Nyquist samples long.
  • Compared to Fourier-based spectral estimators, MUSIC yields a pseudo-spectrum with sharp peaks corresponding to the natural frequencies of the white-noise excited 3-storey frame (following standard OMA and linear random vibrations considerations), while filtering out additive broadband noise.
  • In all plots, a shift of the natural frequencies towards smaller values is seen indicating structural damage.

5 Concluding Remarks

  • A novel natural frequency identification and damage detection approach has been established utilizing response acceleration measurements of white-noise excited structures sampled at rates significantly below the Nyquist rate supporting reduced data transmission in wireless sensors for vibration-based structural monitoring.
  • Acceleration time-histories are treated as realizations of a stationary stochastic process without posing any sparse structure requirements.
  • It was shown that the adopted co-prime MUSIC-based strategy is a potent tool for natural frequency identification within the operational modal analysis context, capable to efficiently address the structural modal coupling effect even by treating response signals buried in noise.
  • The effectiveness and applicability of the proposed approach was numerically evaluated using a white-noise excited linear reinforced concrete 3-storey frame in a healthy and two damaged states caused by two ground motions of increased intensity.
  • The numerical results demonstrate that the considered approach is capable to detect very small structural damage directly from the compressed measurements even for high noise levels at SNR=10dB.

Acknowledgments

  • This work has been partly funded by EPSRC in UK, under grant No EP/K023047/1: the second author is indebted to this support.
  • The first author further acknowledges the support of City, University of London through a PhD studentship.

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Citation: Gkoktsi, K. and Giaralis, A. ORCID: 0000-0002-2952-1171 (2020). A
compressive MUSIC spectral approach for identification of closely-spaced structural natural
frequencies and post-earthquake damage detection. Probabilistic Engineering Mechanics,
103030.. doi: 10.1016/j.probengmech.2020.103030
This is the accepted version of the paper.
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Permanent repository link: https://openaccess.city.ac.uk/id/eprint/23628/
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Gkoktsi K and Giaralis A (2020) A compressive MUSIC spectral approach for identification of
closely-spaced structural natural frequencies and post-earthquake damage detection. Probabilistic
Engineering Mechanics, accepted.
1
A compressive MUSIC spectral approach for identification of closely-
spaced structural natural frequencies and post-earthquake damage
detection
KYRIAKI GKOKTSI
1
and AGATHOKLIS GIARALIS
1
1
Department of Civil Engineering, City, University of London, UK.
E-mail: agathoklis@city.ac.uk
Abstract
Motivated by practical needs to reduce data transmission payloads in wireless sensors for
vibration-based monitoring of engineering structures, this paper proposes a novel approach
for identifying resonant frequencies of white-noise excited structures using acceleration
measurements acquired at rates significantly below the Nyquist rate. The approach adopts the
deterministic co-prime sub-Nyquist sampling scheme, originally developed to facilitate
telecommunication applications, to estimate the autocorrelation function of response
acceleration time-histories of low-amplitude white-noise excited structures treated as
realizations of a stationary stochastic process. Next, the standard multiple signal
classification (MUSIC) spectral estimator is applied to the estimated autocorrelation function
enabling the identification of structural natural frequencies with high resolution by simple
peak picking in the frequency domain without posing any sparsity conditions to the signals.
This is achieved by processing autocorrelation estimates without undertaking any (typically
computationally expensive) signal reconstruction step in the time-domain, as required by
various recently proposed in the literature sub-Nyquist compressive sensing-based

Gkoktsi K and Giaralis A (2020) A compressive MUSIC spectral approach for identification of
closely-spaced structural natural frequencies and post-earthquake damage detection. Probabilistic
Engineering Mechanics, accepted.
2
approaches for structural health monitoring, while filtering out any broadband noise added
during data acquisition. The accuracy and applicability of the proposed approach is first
numerically assessed using computer-generated noise-corrupted acceleration time-history
data obtained by a simulation-based framework examining white-noise excited structural
systems with two closely-spaced modes of vibration carrying the same amount of energy,
and a third isolated weakly excited vibrating mode. Further, damage detection potential of
the developed method is numerically illustrated using a white-noise excited reinforced
concrete 3-storey frame in a healthy and two damaged states caused by ground motions of
increased intensity. The damage assessment relies on shifts in natural frequencies between
the pre-earthquake and post-earthquake state. Overall, numerical results demonstrate that the
considered approach can accurately identify structural resonances and detect structural
damage associated with changes to natural frequencies as minor as 1% by sampling up to
78% below Nyquist rate for signal to noise ratio as low as 10dB. These results suggest that
the adopted approach is robust and noise-immune while it can reduce data transmission
requirements in acceleration wireless sensors for natural frequency identification and damage
detection in engineering structures.
Keywords: co-prime sampling, MUSIC pseudo-spectrum, compressive sensing, spectral
estimation, system identification, closely-spaced modes.

Gkoktsi K and Giaralis A (2020) A compressive MUSIC spectral approach for identification of
closely-spaced structural natural frequencies and post-earthquake damage detection. Probabilistic
Engineering Mechanics, accepted: 27/12/2019.
3
1 Introduction and motivation
Accurate identification of the natural frequencies of large-scale (civil) engineering structures
and structural components is key to several important practical applications such as: the design
verification of structural systems sensitive to resonance with external loading frequencies [1,2]; the
detection of structural damage [3-5]; the tuning/designing of resonant vibration absorbers [6],
meta-structures [7], and dynamic energy harvesters [8] for suppressing structural vibrations; the
performance assessment of structures equipped with dynamic vibration absorbers [9]. In this
regard, there is scope in developing cost-efficient modalities for on-site estimation of natural
frequencies in existing/as-built engineering structures. This aim is widely pursued in practice via
linear system identification techniques relying on measuring solely response acceleration time-
histories collected from vibrating structures under operational/ambient unmonitored low-amplitude
broadband excitations within the so-called operational modal analysis (OMA) framework [10].
Moreover, over the past two decades, wireless sensors/accelerometers have been heavily explored
to further support the considered aim within the OMA framework as they enable rapidly
deployable and low up-front cost field instrumentation compared to arrays of wired sensors [11-
12].
Still, wireless sensors are constrained by frequent battery replacement requirements leading to
increase maintenance costs while their bandwidth transmission limitations pose restrictions to the
amount of acceleration measurements that can be reliably transmitted. To this end, it has been
recently established that the above disadvantages of wireless sensors may be alleviated by
developing compressive system identification approaches using acceleration measurements
sampled at rates significantly below the nominal application-dependent Nyquist rate [13-22].
However, no particular provision is taken by any of the developed approaches for accurately
resolving structural natural frequencies from the low-rate (sub-Nyquist) sampled acceleration
measurements. Specifically, some of the approaches focus on estimating vibrational mode shapes

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References
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Journal ArticleDOI
TL;DR: This lecture note presents a new method to capture and represent compressible signals at a rate significantly below the Nyquist rate, called compressive sensing, which employs nonadaptive linear projections that preserve the structure of the signal.
Abstract: This lecture note presents a new method to capture and represent compressible signals at a rate significantly below the Nyquist rate. This method, called compressive sensing, employs nonadaptive linear projections that preserve the structure of the signal; the signal is then reconstructed from these projections using an optimization process.

3,226 citations


"A compressive MUSIC spectral approa..." refers background or methods in this paper

  • ...In this regard, note that, with the exception of the approach in [21], all sub-Nyquist system identification techniques rely on the compressive sensing (CS) paradigm [23] involving randomly sampled in time measurements whose (sub-Nyquist) sampling rate for faithful time/frequency domain information recovery or modal properties extraction depends on the acceleration signals sparsity....

    [...]

  • ...2007) in Japan: (a) Time-history, (b) Squared amplitude of Fourier spectrum [23]...

    [...]


Book
01 Nov 1998

2,406 citations


"A compressive MUSIC spectral approa..." refers background in this paper

  • ...These systems represent cases of structures for which resolving natural frequencies with high accuracy from response acceleration signals is a rather challenging task, especially in noisy environments [35]....

    [...]

  • ...where H(f) is the frequency response function (FRF) of the MDOF system termed as accelerance in the field of modal testing [35]....

    [...]


Journal ArticleDOI
Abstract: The use of natural frequency as a diagnostic parameter in structural assessment procedures using vibration monitoring is discussed in the paper. The approach is based on the fact that natural frequencies are sensitive indicators of structural integrity. Thus, an analysis of periodical frequency measurements can be used to monitor structural condition. Since frequency measurements can be cheaply acquired, the approach could provide an inexpensive structural assessment technique. The relationships between frequency changes and structural damage are discussed. Various methods proposed for detecting damage using natural frequencies are reviewed. Factors which could limit successful application of vibration monitoring to damage detection and structural assessment are also discussed.

1,710 citations


"A compressive MUSIC spectral approa..." refers background in this paper

  • ...Accurate identification of the natural frequencies of large-scale (civil) engineering structures and structural components is key to several important practical applications such as: the design verification of structural systems sensitive to resonance with external loading frequencies [1,2]; the detection of structural damage [3-5]; the tuning/designing of resonant vibration absorbers [6], meta-structures [7], and dynamic energy harvesters [8] for suppressing structural vibrations; the performance assessment of structures equipped with dynamic vibration absorbers [9]....

    [...]


Book
01 Jan 2007
Abstract: The concept of designing structures to achieve a specified performance limit state defined by strain or drift limits was first introduced, in New Zealand, in 1993. Over the following years, and in particular the past five years, an intense coordinated research effort has been underway in Europe and the USA to develop the concept to the stage where it is a viable and logical alternative to current force-based code approaches. Different structural systems including frames, cantilever and coupled walls, dual systems, bridges, wharves, timber structures and seismically isolated structures have been considered in a series of coordinated research programs. Aspects relating to characterization of seismic input for displacement-based design, and to structural representation for design verification using time-history analysis have also received special attention. This paper summarizes the general design approach, the background research, and some of the more controversial issues identified in a book, currently in press, summarizing the design procedure. perceived in terms of simple mass-proportional lateral forces, resisted by elastic structural action. In the 1940's and 50's the influence of structural period in modifying the intensity of the inertia forces started to be incorporated into structural design, but structural analysis was still based on elastic structural response. Ductility considerations were introduced in the 1960's and 70's as a consequence of the experimental and empirical evidence that well- detailed structures could survive levels of ground shaking capable of inducing inertia forces many times larger than those predicted by elastic analysis. Predicted performance came to be assessed by ultimate strength considerations, using force levels reduced from the elastic values by somewhat arbitrary force-reduction factors, that differed markedly between the design codes of different seismically-active countries. Gradually this lead to a further realization, in the 1980's and 90's that strength was important, but only in that it helped to reduce displacements or strains, which can be directly related to damage potential, and that the proper definition of structural vulnerability should hence be related to deformations, not strength. This realization has lead to the development of a large number of alternative seismic design philosophies based more on deformation capacity than strength. These are generally termed " performance-based" design philosophies. The scope of these can vary from comparatively narrow structural design approaches, intended to produce safe structures with uniform risk of damage under specified seismicity levels, to more ambitious approaches that seek to also combine financial data associated with loss-of-usage, repair, and a client-based approach (rather than a code-specified approach) to acceptable risk. This paper does not attempt to provide such ambitious guidance as implied by the latter approach. In fact, it is our view that such a broad-based probability approach is more appropriate to assessment of designed structures than to the design of new structures. The

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Abstract: A new array geometry, which is capable of significantly increasing the degrees of freedom of linear arrays, is proposed. This structure is obtained by systematically nesting two or more uniform linear arrays and can provide O(N2) degrees of freedom using only N physical sensors when the second-order statistics of the received data is used. The concept of nesting is shown to be easily extensible to multiple stages and the structure of the optimally nested array is found analytically. It is possible to provide closed form expressions for the sensor locations and the exact degrees of freedom obtainable from the proposed array as a function of the total number of sensors. This cannot be done for existing classes of arrays like minimum redundancy arrays which have been used earlier for detecting more sources than the number of physical sensors. In minimum-input-minimum-output (MIMO) radar, the degrees of freedom are increased by constructing a longer virtual array through active sensing. The method proposed here, however, does not require active sensing and is capable of providing increased degrees of freedom in a completely passive setting. To utilize the degrees of freedom of the nested co-array, a novel spatial smoothing based approach to DOA estimation is also proposed, which does not require the inherent assumptions of the traditional techniques based on fourth-order cumulants or quasi stationary signals. As another potential application of the nested array, a new approach to beamforming based on a nonlinear preprocessing is also introduced, which can effectively utilize the degrees of freedom offered by the nested arrays. The usefulness of all the proposed methods is verified through extensive computer simulations.

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"A compressive MUSIC spectral approa..." refers background in this paper

  • ...(5), whose number increases with increasing N1 and/or N2, are systematically eliminated by extending the approach discussed in [26] for the case of spatial processes (direction of arrival problem), to treat the herein addressed problem of temporal frequency estimation....

    [...]

  • ...In this manner, the spectral estimation problem is cast in the time-domain rather than in the spatial domain pertaining to the direction of arrival problem in telecommunication applications [26] (i....

    [...]