Frequency‐dependent principal component analysis of multicomponent earthquake ground motions

Das, Sandip; Hazra, Budhaditya

doi:10.1002/eqe.3008

Cited by 7 publications

(11 citation statements)

References 13 publications

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“…The slow-varying envelope is a frequency-dependent amplitude modulation that evolves according to the Priestley process. 22,23 In general, the response of structure due to narrow band component contains a part of the excitation envelope embedded in it. This non-stationary envelope can mask the occurrence (time stamp) of damage in the vibrating system by introducing spurious peaks in the identification phase at regions where the system response has non-stationary spikes and/or modulation.…”

Section: Proposed Framework For Real-time Damage Detectionmentioning

confidence: 99%

Online damage detection of earthquake-excited structure based on near real-time envelope extraction

Panda

Tripura

Hazra

2021

Structural Health Monitoring

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A robust real-time damage detection technique of earthquake-excited structures based on a new demodulation technique for nonlinear and non-stationary vibration signals through the identification of signal envelopes in real time is presented. In the present work, the need for the detection of envelope in a vibration signal in real time is addressed by reformulating the concept of Hermitian interpolation functions to a recursive Hermitian polynomial, which is a key entitlement of the present work. Once, the near real-time demodulation is achieved, the proposed framework proceeds to the newly developed error-adapted framework by addressing the errors accrued between the standard and generalized eigen perturbation formulation in the context of real-time estimation of proper orthogonal modes and linear normal modes. In the adaptive framework, the error is modeled as a feedback, which is constructed to account for the truncation in the order of eigen perturbation. In addition to the improved accuracy due to the envelope extraction, the proposed error-adapted eigen perturbation further improves the detectability over the currently available eigen perturbation–based real-time algorithms. To ensure robustness of the proposed algorithm, a new real-time damage indicator based on the maximum of principal eigenvector of the evolving transformed covariance matrix is proposed. The proposed modules together not only improve the detectability of the damage detection in real-time but also enhance the overall performance in presence of non-stationary excitation, that often mask the damage information in the higher energy zones of the amplitude and frequency-modulated response. Simulations for the proposed framework is performed by considering a 5 degrees-of-freedom linear and base-isolated nonlinear structural system driven by non-stationary stochastic excitations with damage simulated at intermediate floor at a particular time instant. Evidence of the near real-time demodulation and/or envelope removal from the signal and improved damage identification is also provided. An examination of the proposed framework using experimental data further validates the robustness of the proposed scheme.

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Section: Proposed Framework For Real-time Damage Detectionmentioning

confidence: 99%

Online damage detection of earthquake-excited structure based on near real-time envelope extraction

Panda

Tripura

Hazra

2021

Structural Health Monitoring

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“…In Figure 2, we show a partition of a 4 × 4 image into four subfigures in the matrix form (in the top figure) and in the vector form (bottom figure) when the pixels of the image are ordered from the top to the bottom and from the left to the right. If we consider the original image as a vector in R 16 , then the subfigures are in four orthogonal subspaces of dimension 4 embedded in R 16 .…”

Section: Some Analysis Of the Ddpcamentioning

confidence: 99%

Summation pollution of principal component analysis and an improved algorithm for location sensitive data

Cai

2021

Numerical Linear Algebra App

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Principal component analysis (PCA) is widely used for dimensionality reduction and unsupervised learning. The reconstruction error is sometimes large even when a large number of eigenmode is used. In this paper, we show that this unexpected error source is the pollution effect of a summation operation in the objective function of the PCA algorithm. The summation operator brings together unrelated parts of the data into the same optimization and the result is the reduction of the accuracy of the overall algorithm. We introduce a domain decomposed PCA that improves the accuracy, and surprisingly also increases the parallelism of the algorithm. To demonstrate the accuracy and parallel efficiency of the proposed algorithm, we consider three applications including a face recognition problem, a brain tumor detection problem using two-and three-dimensional MRI images.

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“…It can be seen that the correlation coefficients and the principal directions for the simulated average cases are comparable with those quantities for the recorded motions. For the low correlation cases the matching is not very close for correlation coefficients because of sample to sample variation of temporal mean-square at the decomposed level (see Equation (22)). However, with larger number of samples (around 100) than 30, the values come close to the observed ones.…”

Section: Numerical Illustrations For Simulationmentioning

confidence: 99%

“…In fact, the period content and the ranges of 𝑗 remain same for bi-directional ground motion process as well because unidirectional process is one of the components, chosen arbitrarily, of the bi-directional process. Each decomposed motion, 𝑔 𝑗 (𝑡), can be obtained by using Fourier analysis as [22] 𝑔 𝑗…”

Section: Review Of Stochastic Simulation Of Unidirectional Ground Motionmentioning

confidence: 99%

“…Das and Hazra [ 22 ] have shown that the principal directions of a bi‐directional motion are in general frequency‐dependent and they may be significantly different from each other possibly because of frequency‐dependent anisotropy present in the path of wave propagation. Similar observations are found for the correlation coefficient between the pair of motions as well.…”

Section: Introductionmentioning

confidence: 99%

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Bi‐directional ground motions: Stochastic simulation and frequency‐dependent modal combination rule

Naskar

Das

2021

Earthq Engng Struct Dyn

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For direct statistical analysis of 3‐D structures against lateral earthquake shaking, stochastic simulation of fully nonstationary bi‐directional ground motions is essential. The recorded bi‐directional ground motions (or their projections) along the two orthogonal axes of a structure are usually correlated and their correlation influences the overall structural response. Further, the correlation is, in general, frequency‐dependent, that is, the correlation coefficients are different for different narrow frequency bands of the (composite) pair of motions. So it is important to have a method for stochastic simulation of bi‐directional motions that can maintain a target frequency‐dependent correlation. This type of simulated ensemble of bi‐directional motions for a recording process provides a sound basis for the statistical analysis of structural response vis‐à‐vis the observed/recorded correlation. In the present paper, a Priestley process based framework is proposed to simulate bi‐directional ground motions that can emulate the frequency‐dependent correlation structure of the parent recording process while maintaining the time–frequency characteristics of the recorded bi‐directional motion. Since principal directions are frequency‐dependent, it is imperative to develop a modal combination rule for multi‐directional ground motions which can address the frequency‐dependence of principal directions. For this purpose, a new ground motion frequency‐dependent modal combination rule is also proposed. It is found that the proposed frequency‐dependent combination rule performs better than the conventional frequency‐independent one, especially when the response is dominated by some frequency bands having different individual principal directions from each other or from those of the composite pair of motions.

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Frequency‐dependent principal component analysis of multicomponent earthquake ground motions

Cited by 7 publications

References 13 publications

Online damage detection of earthquake-excited structure based on near real-time envelope extraction

Online damage detection of earthquake-excited structure based on near real-time envelope extraction

Summation pollution of principal component analysis and an improved algorithm for location sensitive data

Bi‐directional ground motions: Stochastic simulation and frequency‐dependent modal combination rule

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