Cepstrum Coefficients for Earthquake Damage Assessment of Bridges Leveraging Deep Learning-0629

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Cepstral Coefficients for Earthquake Damage Assessment of Bridges

Leveraging Deep Learning

Seyedomid Sajedi, Ph.D. Candidate,1 Xiao Liang, Ph.D., M.ASCE2

1206 Ketter Hall, Department of Civil, Structural and Environmental Engineering, University at

Buffalo SUNY, 14260-4300, Buffalo; e-mail: ssajedi@buffalo.edu

2242 Ketter Hall, Department of Civil, Structural and Environmental Engineering, University at

Buffalo SUNY, 14260-4300, Buffalo; e-mail: liangx@buffalo.edu

ABSTRACT

Bridges are indispensable elements in resilient communities as essential parts of the lifeline

transportation systems. Knowledge about the functionality of bridge structures is crucial,

especially after a major earthquake event. In this study, we propose signal processing approaches

for automated AI-equipped damage detection of bridges. Mel-scaled filter banks and cepstral

coefficients are utilized for training a deep learning architecture equipped with Gated Recurrent

Unit (GRU) layers that consider the temporal variations in a signal. The proposed framework has

been validated on an RC bridge structure in California. The bridge is subjected to 180 bi-

directional ground motion records with sampled scale factors and six different intercept angles.

Compared with the benchmark cumulative intensity features, the Mel filter banks resulted in

15.5% accuracy in predicting critical drift ratios. The developed strategy for spatio-temporal

analysis of signals enhances the robustness of damage diagnosis frameworks that utilize deep

learning for monitoring lifeline structures.

INTRODUCTION

Continuous operation of bridges contributes to minimizing the impacts of natural disasters, given

their key role in lifeline transportation systems. Access to reliable and timely information on the

structural integrity of bridges is a critical step for effective emergency management and

minimum downtime in densely populated areas. Human-based inspections have been the primary

means of Structural Health Monitoring (SHM) in form of reconnaissance teams comprised of

experts. Such a process can be time and resource-consuming since structural engineers are often

required to visit the same structure a few times to complete an inspection. Moreover, the

outcome of an inspection on the same structure may not be consistent if done by different

engineering teams, making the process subjective. Due to the limitations of human-based

inspections, obtaining reliable data rapidly after disasters such as earthquakes can be challenging,

which further highlights the importance of automation in SHM.

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The recent advances of AI have had an enormous effect on automated engineering

systems’ capabilities, with SHM being no exception. Many studies have been focused on visual

inspections and image processing techniques that benefit from deep/machine learning algorithms

(Dong and Catbas 2020; Liang 2019; Sajedi and Liang 2021). Images are valuable sources of

information but face certain limits when it comes to near real-time damage diagnosis. For

example, visual data might not be readily available after an earthquake, and it might only

represent surface damage in concrete bridges (Kashif Ur Rehman et al. 2016). Another limitation

is that quantifying structural damage is challenging or, in cases impossible, using pixel data.

Vibration-based SHM is an alternative damage diagnosis of civil infrastructure that has

the potential to address these problems. Some studies have focused on using data-driven models

solely relying on ground motion signals in seismic assessments (Tamhidi et al. 2020; Xu et al.

2020). However, Bridges can be instrumented with an array of accelerometers where the

vibration data is uploaded into remote servers in near real-time. Instrumented structures have the

potential to provide more accurate and robust information about structural damage. Vibration

patterns can be utilized to obtain quantifiable measures of structural damage as they reflect

dynamic structural characteristics.

The mappings between acceleration time-series and structural damage can be

complicated. Data-driven SHM models have shown promising performance to find such robust

mappings using the state-of-the-art deep/machine learning. Some studies have used the raw

acceleration records as the input (Abdeljaber et al. 2018). Others have proposed methods to

preprocess time-series before feeding them to a data-driven model (Azimi and Pekcan 2020;

Mangalathu and Jeon 2020; Sajedi and Liang 2020). There have been limited studies in the

literature that consider the temporal variations of input acceleration data as a part of the learning

process.

Automatic speech recognition (ASR) is one area where deep learning has shown

impressive success (Chan et al. 2016). Inspired by this progress, this paper investigates the

potential application of Mel Filter Banks (MFBs) and Mel Frequency Cepstral Coefficients

(MFCCs) for vibration-based damage diagnosis. The remainder of the paper first discusses the

steps required to obtain these features. Later, a reinforced concrete bridge in California is

considered to validate the potential use of the proposed signal preprocessing approach for AI-

equipped vibration-based SHM.

FEATURE EXTRACTION WITH MEL FILTER BANKS

Acceleration records due to seismic events are commonly recorded in thousands of time steps.

Using the raw vibration records as the direct input to a machine/deep learning algorithm is often

challenging concerning computational costs. The Recurrent Neural Networks (RNNs) and their

more advanced successors, including the Long Short-Term Memory (LSTM) and Gated

Recurrent Unit (GRU), are the proper models to learn from the temporal signal variations. Given

the raw vibration input size, these models could be ineffective in processing relatively long

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sequences. As a general rule of thumb, increasing the input tensor's complexity and size often

dictates an increase in the number of learnable parameters in the data-driven model. For

example, a deeper neural network architecture might be necessary. Even with unlimited

computational capacities, this increase is likely to promote overfitting because the datasets for

structural damage might be relatively small to calibrate millions of network weights.

An alternative approach is to preprocess the acceleration records into a new

representation that A) is more compressed, B) maintains the time-variant nature of a sequence,

and C) contains target sensitive features. In the following, we will explain that utilizing Mel filter

banks, a representation of such characteristics can be obtained for vibration-based damage

diagnosis. This process is initially described for a single record. We will later explain how to

consider the information from several sensors with multiple channels.

The first step is to break the acceleration signal into a series of overlapping time frames

(Figure 1.a and 1b). Frame’s length and stride are the two hyperparameters selected based on the

signal characteristics such as Sampling Rate (SR). These values are often in the scale of

milliseconds for speech signals given substantially higher SR. We noticed that tensors

representing human voices are often much larger than the existing earthquake records. For

example, an audio signal typically has sampling rates in the order 8-16 kHz. However, ground

motions in the PEER NGA West 2 database (Ancheta et al. 2014) are often recorded with

approximately 50-500 Hz sampling rates (i.e., times steps varying between 0.002-0.02s). Based

on such observations, a window length of 1 s with the stride of 0.4 s is selected to discretize the

signal. The number of frames or windows (Nw) will depend on the ground motion duration and is

variable for each earthquake realization.

Each time frame includes the acceleration amplitudes in the time domain. A better

representation can be obtained by creating the periodogram of the frames (Figure 1c). This is

possible by taking the Fast Fourier Transform (FFT) and extracting NFFT coefficients for each

frame. NFFT =512 is considered, and a signal will be padded with zeros if the number of data

points in a frame is less than NFFT depending on an earthquake record’s SR. The periodogram of

a frame is obtained by considering the magnitude of these complex coefficients (

( )

FFT a

). The

following equation is used to obtain points that construct this spectrum (Xf):

( )

FFT

FFT a

. (Eq. 1)

Similar to the accelerations series, the periodogram includes a substantial amount of Xf’s for each

frame in the frequency domain. The cepstral coefficients are a compressed representation of the

periodogram where instead of individual values, different intervals of frequencies are considered.

To this end, the Mel scale is proposed to define such intervals (Davis and Mermelstein 1980).

Each Hertz point (fi) can be converted into an equivalent Mel value (Mi), using the following

equation:

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–1–CepstralCoefficientsforEarthquakeDamageAssessmentofBridgesLeveragingDeepLearningSeyedomidSajedi,Ph.D.Candidate,1XiaoLiang,Ph.D.,M.ASCE21206KetterHall,DepartmentofCivil,StructuralandEnvironmentalEngineering,UniversityatBuffaloSUNY,14260-4300,Buffalo;e-mail:ssajedi@buffalo.edu2242KetterHall,Departm...

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Cepstrum Coefficients for Earthquake Damage Assessment of Bridges Leveraging Deep Learning-0629

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