1. Introduction
Earthquakes in the proximity of structurally vulnerable buildings could cause damage of varying intensities. Damage of different risk levels is often difficult to classify rapidly, making it difficult to accurately determine the structural safety of a building. For example, according to the National Institute of Civil Defense of Peru, during the Pisco earthquake on 15 August 2007, in the five main regions of Peru (Lima is included, which is the capital of Peru), 136,149 dwellings, 1278 educational buildings, and 126 health buildings collapsed or were damaged, and their use was classified as restricted or unsafe [
1]. However, this report was released almost two months after the earthquake, during which time, all activities in the affected areas of the main regions had to be suspended, including the construction of temporary dwellings.
Resilient cities are goals that countries are building towards to increase the capacity for learning from past disasters for better future protection and to improve risk reduction measures [
2]. In particular, as part of this concept, there is a need to develop modern structures for which we can quickly obtain the structural safety information after an earthquake for resuming economic and social activities in order to minimize social disruption and mitigate the effects of future earthquakes [
3]. In order to promote and disseminate knowledge to increase social resilience and reduce earthquake risk, experts from academia and industry gathered in 2019 for a workshop focused on state-of-the-art risk-reduction strategies. It identified a need for research in the area of structural health monitoring (SHM) to assess the integrity and performance of engineering structures in order to quickly detect damage after an earthquake and enable decision making [
4]. SHM is a field where it is possible to obtain the real-time structural responses and successful fast post-earthquake damage detection of monitored buildings, bridges, cultural heritage structures, dams, base-isolated buildings, etc. [
5,
6]. For instance, Goulet et al. proposed a methodology that updates the prediction of the damage state of uninspected monitored buildings as the model learns from collected data of the damage state of inspected buildings [
7]. This proposal was validated in a city with 1000 buildings. Furthermore, Sivasuriyan et al. reviewed a large number of studies on the practical implementation and operations of SHM in multi-story buildings, as well as damage evaluation of monitored buildings, and discussed the structural response by considering static and dynamic analysis using numerical simulations such as finite element analysis (FEA) [
8].
In the field of SHM, there are several types of sensors to measure and diagnose the static and dynamic properties of the monitored buildings. Antunez et al. demonstrated that optical fiber sensors can be useful in the static and dynamic monitoring of large raw earth masonry structures common in cultural, historical, and architecturally recognized buildings around the world [
9]. Piezoelectric sensors are another type of monitoring device, and Roghaei et al. proposed a method to identify stress and deformation using an array of sensors mounted in certain locations [
10]. They verified the proposed method using a three-story steel building and confirmed that continuous monitoring and analysis of sensor signals can help the building manager to apply warning alarms and call for evacuation. However, the most common monitoring control sensor is the accelerometer. For instance, Wang et al. developed a method to evaluate the story damage index (SDI) based on the modal frequency and mode shape obtained from the records of earthquake response of a building [
11]. Furthermore, an approximate story damage index (ASDI) was developed without considering the information of the floor mass to identify the extent of damage to the story. Although it was possible to verify the damage index by some numerical simulations and the experimental data analysis established previously, it was necessary to calculate the modal frequency and mode shapes from the post-earthquake structural responses of each story and to compare with the values of the building before the earthquake. It is worth pointing out that a large number of sensors will require a high investment. For this reason, Xu et al. estimated the maximum drift and time histories of relative displacement in all stories of multi-degree-of-freedom (MDOF) structures considering only one accelerometer, verifying the effectiveness of the method by taking into account the robustness, installation location, and truncation error [
12].
The machine learning method, which predicts the structural responses using a learning model specific to the structure, may provide higher accuracy by updating the model after each earthquake. According to study [
13], there are two approaches for damage identification: model-driven methods and data-driven methods. In a model-driven approach, usually, a high-fidelity physical model of the structure is used to establish a comparison metric between the model and the measured data from the real structure to distinguish the damage condition from the normal condition. In a data-driven approach, a structural model is used as a statistical representation of the system, and the main algorithms developed for this purpose are those in the field of pattern recognition or, more broadly, machine learning. A convolutional neural network (CNN) is a tool for solving the problem of pattern recognition related to image and video recognition, classification, natural language processing, and others. Oh et al. studied a method of predicting the time histories of displacement of building structures from the measured acceleration responses on each floor based on a CNN, considering that the time series of acceleration structural response is similar to pixel-based image data (every acceleration value corresponds to one pixel), which is the basic input data in CNN [
14]. The validation of their proposed method was from a numerical process using the ASCE benchmark model and an experimental test on a reinforced concrete (RC) frame structure. However, the structural model and dynamic responses used in the studies exhibited linear behavior. Tsuchimoto et al. proposed a rapid safety evaluation of multi-story buildings using sparse acceleration measurements [
15]. Their proposed method predicts the maximum story drift ratio, and ultimately classifies the damage into three classes, namely “Safe”, “Restricted Use”, and “Unsafe” from a damage-sensitive feature (comparison between linear and nonlinear acceleration measurement responses) and ground acceleration as input data. Subsequently, Tsuchimoto et al. modified the previous method for high-rise buildings and validated considering an experimental test of a large-scale structure (1/3-scale 18-story steel building tested on the shaking table at E-Defense in Japan) [
16].
There are two main characteristics observed on the ground motion records due to earthquakes. The first is the non-stationary characteristics in which the intensity of the ground motion varies with time; they are represented by the acceleration, velocity, and displacement. The second is the non-stationary characteristics in which the frequency content of the ground motion varies with time; they depend on several parameters such as magnitude, source and path effects, local site conditions, etc. [
17]. Time–frequency distribution analysis is a method of obtaining a two-dimensional spectral function (there are several types of functions according to resources and needs) from a one-dimensional signal (ground motion or time–history structural response) that reflects the time and frequency of the original signal and is suitable to analyze the changes in the linear and nonlinear structural responses with only one function. For instance, Tao et al. used the matching pursuit decomposition algorithm to analyze the time–frequency distribution of the ground motion and verify the effect on the dynamic response of a nonlinear structure, and finally, this method reveals the effect of the ground motion on the nonlinear structural response [
18]. Moreover, Cao et al. demonstrated the effect of energy concentration on the structural nonlinear response by using the wavelet transform to obtain a local spectrum and change the energy distribution over time for several earthquake records [
19]. Spanos et al. analyzed the undamaged and damaged condition of a 20-story steel frame building using the harmonic wavelet transform applied to structural responses to obtain the variation of the effective natural frequencies due to the influence of the nonlinearity developed during the seismic event [
20]. Balafas and Kiremidjian used the continuous wavelet transform of the input and output acceleration measurements to extract damage sensitive features for seismic damage estimation in civil structures [
21]. Noh et al. proposed an extraction method of three damage-sensitive features using wavelet transform spectrum for structural damage diagnosis and applied them to experimental data of a reinforced concrete bridge column and a four-story steel moment-resisting frame structure [
22]. In general, time–frequency distributions are two-dimensional spectral functions that can be used as input data for a CNN to predict dynamic issues related to structural engineering. For example, Xu et al. proposed a methodology to recognize and classify different types of vibrational events (digging, walking, vehicles passing, and damaging) [
23]. First, they denoise the unknown signal and use the short-time Fourier transform (STFT) to obtain the time–frequency spectra and input them to the CNN for automatic feature extraction and classification. The proposed method used the support vector machine method to compare the obtained recognition rates of vibration events over 90% with the previous soft-max classifier. Dokht et al. used a CNN and STFT to consider a dataset of over 4900 earthquakes recorded over 3 years in Canada to classify between earthquake and noise signals. They also used another CNN and wavelet spectrum to classify and separate P from S waves and estimate their approximate arrival times [
24]. Their results achieved an average accuracy of nearly 99% for both networks. Mousavi et al. proposed a detector based on a deep neural network (CNN belong to this field) called CNN-RNN Earthquake Detector (CRED), which is a network that combines a CNN and a recurrent neural network (RNN), specifically the bidirectional long-short-term-memory (LSTM) method, to learn the time-frequency characteristics of the dominant phases in an earthquake signal from three-component data recorded at a single station, having an accuracy of 99.95% [
25]. In addition, Liao et al. proposed an identification method for a structural seismic response using a wavelet spectrum as input data in a CNN to distinguish the responses during an earthquake event under serviceability conditions [
26]. Linear and nonlinear behaviors are considered in the research. According to previous studies, the CNN method in the SHM field has advantages over other methods in terms of higher accuracy by updating the model after each earthquake, flexibility to combine different methodologies, wide application areas, etc., however, it requires a large database of known data to train the model.
Previous studies have not fully investigated how to define the damage level of each floor of a structure from the time–frequency distribution of the observation data of a single sensor. The Japan Structural Consultants Association (JSCA), an organization of building structural engineers in Japan, uses three parameters of safety criteria used on the assessment of a building: absolute acceleration, ductility ratio, and story drift ratio [
27]. Acceleration is related to damage in nonstructural components, and ductility and story drift ratio are related to damage in structural components. It is worth pointing out that the use of only one sensor implies a low-cost investment. This study proposes a methodology to predict the absolute acceleration, ductility ratio, and story drift ratio on each floor under earthquake conditions using machine learning. In the beginning, the earthquake responses of a model building are calculated under the scaled earthquake records with several intensities (scale factors). The level of intensity is established to obtain a range of linear and nonlinear behavior of the building. Then, wavelet spectra are developed from the structural response accelerations on the upper floor of the building. The wavelet spectra are the input data of a CNN model to predict the absolute acceleration, ductility ratio, and story drift ratio on each floor, which correspond to the damage of the nonstructural and structural components of the building.
This paper contains sections as follows: In
Section 2, the basis and methods of the structural response prediction for damage identification are described, including the structural model of the case study, wavelet spectrum, convolutional neural network, input ground motion, and scale factor of records. Next, the application of the methodology is carried out by two processes: training and validation. The results and the comparison of the prediction and reference values of the case study are shown in
Section 3. In
Section 4, a summary and discussion of the research results are presented.
3. Prediction and Validation of the Case Study
An example of the analysis results is shown in
Figure 20.
Figure 20a shows the ductility ratio results under the scaled Petrolia California E–W records, comparing the prediction (horizontal axis) and the reference (vertical axis). In the figure, the straight line represents the perfect prediction. The points represent the results of each story and scale factor defined in
Section 2.1 and
Section 2.4. Additionally,
Figure 20a shows the regions that define the damage condition. The green, yellow, orange, and red regions represent the no damage, minor damage, significant damage, and severe damage conditions, respectively. The collapse condition is considered for any value greater than the severe damage condition. The dashed red rectangle encloses the region for any value that is greater than the minor damage condition and means that the use of the building is restricted or unsafe (condition for evacuating the building).
Figure 20b shows an example of the prediction and reference values of each story for a scale factor that produces Sa(T
1) = 900 gal.
Figure 21 shows the results of the ductility ratio, story drift ratio, and acceleration for the validation process under the scaled Petrolia California N–S records. The regions that define the damage condition are also shown in the figure. As seen in
Figure 21b, the story drift ratios do not reach the significant damage, severe damage, and collapse condition. Likewise, the restricted or unsafe use condition is not reached.
Figure 22 shows the prediction and reference values of the ductility ratio, story drift ratio, and acceleration on each floor considered under the same record for a scale factor that produces Sa(T
1) = 875 gal.
The coefficient of correlation (
r) is used to measure the accuracy of the CNN model in this study, and it is defined as shown in Equation (3):
where
ypred is the prediction output by the CNN model,
yref is the reference output by the structural analysis,
and
are the mean of
ypred and
yref, respectively, and
N is the number of samples.
Table 6 shows the
r-values for the validation process. The average values of the
r-values of the ductility ratio, story drift ratio, and acceleration are 0.905, 0.846, and 0.829, respectively. In particular, the accuracy of the estimation of the ductility ratio is the highest.
Two new ratios are introduced, the damage condition ratio (DCR) and the restricted or unsafe use ratio (RUUR), to examine the accuracy of the prediction of structural damage. The damage condition ratio (DCR) is defined as the ratio of the number of the predicted values and the number of reference values inside the damage condition region as shown in Equation (4). Likewise, the restricted or unsafe use ratio (RUUR) is defined as the number of the predicted values and the number of reference values inside the restricted or unsafe region as shown in Equation (5).
Figure 23 shows the comparison of the DCR and RUUR for the ductility ratio. In general, the DCR of no damage and collapse condition are larger and more accurate than others. In most cases, RUUR has high precision—greater than 80%. Notice that DCR and (or) RUUR for some records is not reached because the structural response is not over the limit for being measured.
Figure 24 shows the comparison of the DCR and RUUR for the story drift ratio. In general, the DCR of no damage and minor damage condition are larger and more accurate than other conditions. Few data reach DCR of severe damage and collapse conditions.
Figure 25 shows the comparison of the DCR and RUUR for the acceleration. In general, the DCR of significant damage condition is larger and more accurate than others. Few data reach DCR of severe damage and collapse conditions. In most cases, RUUR has high precision—greater than 90%.