Machine learning-based strain response prediction method for structural members of a building using ground motion data and intensity measures

Abstract

This study presents a strain response prediction method for structural members of a building using ground motion (GM) data. The relationship between the strain response and the GM data is determined by a convolutional neural network (CNN), which is a machine learning technique. A CNN model with the time history GM data set as input and the strain response of structural members to earthquakes set as output is trained using the measurement data. The constructed CNN model is used to predict strain based on the recorded GM data when a seismic event occurs afterwards. In the proposed method, three seismic intensity measures such as singular value matrix, Arias Intensity, and cumulative absolute velocity extracted from the GM data are used as input data for the CNN in addition to time history GM data. Each seismic intensity measure with the GM data is employed in each CNN. Thus, a total four CNN models are presented. A comparison of strain prediction performance when subjected to seismic loads is made between the presented CNN models. The CNN model’s prediction performance is examined using the measured strain of structural members obtained from a shaking table test of a 3-story reinforced concrete frame specimen. Through the experimental study, intensity measures that are effective at predicting strain are discussed in detail.

Keywords

structural health monitoring strain estimation building structure ground motion intensity measure of ground motion convolutional neural network

Introduction

Structural Health Monitoring (SHM) technologies have been developed to evaluate structural safety against heavy loads such as strong earthquakes that can cause considerable damage. These technologies are also designed to identify structural damages and conditions after seismic events using a rational and scientific basis (Mahmoudi et al., 2023; Pan et al., 2022). In the SHM field, the safety of a building is evaluated using structural responses measured from various types of sensors installed on the structure before and after strong loads, or maintained at all times (Seon Park et al., 2022). Among the various sensors, the strain sensor installed inside or on the surface of the structural member measures the strain that occurs in the structural member to calculate the stress, constituting a direct approach to evaluating structural safety (Cheng et al., 2023). However, since the installed strain sensors have a significantly shorter lifespan than the buildings, sensor failure occurs frequently during the life cycle of the structures. This poses limitations in terms of long-term structural safety evaluation (Lu et al., 2017b). In particular, the strain sensor installed inside the concrete structural member cannot be replaced once it fails. The loss of structural response due to temporary instability in power supply during the transmission and reception of measured structural response is also pointed out as a limitation of sensing-based SHM technology (Avci et al., 2018).

Consequently, structural response prediction methods or data recovery techniques have been developed for structural safety evaluation when sensor failure or measurement data loss occurs. Research on structural response prediction has been undertaken to evaluate the safety of structural members in case of sensor fails. The data correlation between sensor data (Lu et al., 2017a; Chen et al., 2019), compressive sensing technique (O’Connor et al., 2014; Yu et al., 2015), and Kalman filter (Akintunde et al., 2023) have been applied for this purpose. Machine learning techniques have also been applied to predict the structural responses. Liao et al. (Liao et al., 2023) proposed machine learning-based seismic response prediction method for structures. To this end, two machine learning techniques, recurrent neural networks (RNN) and long short-term memory (LSTM), were employed in the method. A number of recorded ground motion (GM) data were set in the input layers of RNN and LSTM. Seismic responses of target structures were considered as the output information and predicted by the trained machine learnings. Ning et al. (2023) employed several deep learning models such as LSTM, WaveNet, and convolutional neural network (CNN) for predicting seismic responses of structures. The multiple GM data were utilized as the input information of the models. The time series of seismic responses were set as the prediction targets. These models applied to the seismic response prediction of three example structures and the prediction capacities of them were compared. Zhang et al. (2024a) introduced a new deep learning algorithm which is Transformer architecture combined with LSTM to predict seismic responses of structures. To train the deep learning, 300 recorded GM data were employed and utilized in the input information. The time series of the inter-story drift subjected seismic loads were selected as prediction target. The model was applied to seismic predictions of several structures and their prediction performances were verified. Hu et al. (2024) introduced a physics-informed neural network in the seismic response prediction. In the study, to improve accuracy of the method with sufficient datasets, pseudo-labelling data were generated by limited labelled data. The prediction target was selected as seismic displacement responses and the method showed outstanding prediction performances. Zhang et al. (2024b) utilized various seismic intensity measures such as peak ground acceleration, Arias Intensity, spectral acceleration, and Housner intensity for seismic response prediction. Using established intensity measures, many machine learning techniques were trained and their prediction performances were compared. In the study, the time series of seismic displacement responses was set as the output variable and predicted. As observed in the above recent studies, most machine leaning-based approaches focused on displacement prediction subjected to seismic loads.

Machine learning techniques have been employed in the strain response monitoring researches. Studies on machine learning-based strain prediction are listed in Table 1, where machine learning types and input and output responses in machine learning are also summarized. Kromanis and Kripakaran (2013) have focused on the strong correlation between temperature and response of concrete structures. The relationship between temperature and strain was defined through support vector regression (SVR), while the strain of the concrete girder was predicted using only temperature measurements. Oh et al. (2019) introduced the CNN as a machine learning technique to predict the wind-induced response of high-rise buildings susceptible to wind loads. The relationship among the wind load acting on the building, the wind-induced top displacement of the building and the strain of the column in the building was defined using the CNN. The constructed CNN was used to predict the strain of structural members using only wind information and wind-induced displacement measurements. Oh et al. (2020) focused on the relationship among strain responses measured from multiple strain sensors installed in structures. The strong correlation between strain responses at adjacent locations was identified using the CNN. The strain response to be measured in the faulty sensor was predicted using only the strain response measured at the adjacent location in the event a specific sensor fails. Seon Park et al. (2020) investigated the relationship between the dynamic structural responses such as acceleration and displacement measured in the building and the strain response of structural members in the building using the CNN. Gulgec et al. (2020) focused on the relationship between the strain and the acceleration response of a beam-like structure. The relationship between these responses was examined using LSTM technique, and was subsequently used for strain prediction. The input and output responses in the above studies on strain response prediction are summarized in Table 1.

Table 1.

Input and output data for machine learning in existing literature on strain response prediction.

	Input response	Output response	Type of machine learning
Kromanis and Kripakaran (2013)	Temperature (measured in member)	Strain	SVR
Oh et al. (2019)	Top displacement + wind speed	Strain	CNN
Oh et al. (2020)	Strain of adjacent locations	Strain	CNN
Seon Park et al. (2020)	1) Acceleration	Strain	CNN
Seon Park et al. (2020)	2) Displacement	Strain	CNN
Gulgec et al. (2020)	Acceleration	Strain	LSTM

The above research on strain prediction based on machine learning effectively predicted the strain of a structure attributed to the application of an appropriate machine learning technique, but this method has several limitations. One of the above literatures (Kromanis and Kripakaran, 2013) used temperature data as the input information of the machine learning to predict strain response. When a concrete structure, such as a concrete bridge structure, whose deformation is affected by temperature and is exposed to the outside air, it is possible to predict the strain using only the temperature. On the other hand, most building structures in which concrete is covered with a finishing material do not respond sensitively according to the variations in air temperature. Oh et al. (2019) and Seon Park et al. (2020) set the time series of displacement responses as the input data of the neural networks for predicting strain responses. With the progress in research on displacement measurement of building structures, displacement measuring devices such as GPS are installed in high-rise buildings, but these are costly. The research (Oh et al., 2020) used multiple strain sensors for the input of the CNN to recover the strain response of adjacent sensor locations in the structures. The installation of multiple strain sensors in large and complex buildings are also costly and difficult to maintain. Seon Park et al. (2020) and Gulgec et al. (2020) utilized acceleration responses in the input information of the neural networks for predicting strain responses. Compared to other sensors, it is relatively easy to measure acceleration responses on a building. In addition, if the accelerometers are well installed by anchoring them in the concrete slab of the building, the acceleration responses can be stably measured (Yun et al., 2023). Nevertheless, the robustness of measurement can be negatively affected in cases of inappropriate sensor layout, low sensor specification, and improper sensor installation during extreme loading events specifically strong earthquakes (Liao et al., 2022; Rainieri et al., 2018). Thus, to overcome the previous studies on strain prediction, approaches using information that can be obtained more reliably and easily during earthquake events such as ground acceleration data are needed to be developed. To predict structural responses, the presented method uses ground motion data. Similar to previous methods (Gulgec et al., 2020; Kromanis and Kripakaran, 2013; Oh et al., 2019, 2020; Seon Park et al., 2020), stain is the prediction target in the presented method. In addition, to establish the relationship between strain responses and ground acceleration data, a machine learning technique is employed like previous methods. Especially, the CNN used in several methods (Oh et al., 2019, 2020; Seon Park et al., 2020) is selected as the machine learning in the method. Structural responses or temperature data that can be obtained from structural members or structures were utilized in the input data for machine learning trainings and required to predict strain responses after trainings in the previous methods (Gulgec et al., 2020; Kromanis and Kripakaran, 2013; Oh et al., 2019, 2020; Seon Park et al., 2020). On the other hand, only recorded ground motion data, that can be more easily obtained compared with structural responses such as displacement, acceleration, and strain, is required to train the CNN and predict strain responses, which is the major difference between previous methods (Gulgec et al., 2020; Kromanis and Kripakaran, 2013; Oh et al., 2019, 2020; Seon Park et al., 2020) and this work.

This study seeks to propose a method of predicting the strain of structural members in buildings using GM data. Compared with other strain prediction techniques, the method only requires GM data, which is relatively easy to measure compared to other types of signals. Even if GMs are very weak motions resulting low amplitude, they can be reliably detected with wide-bandwidth and high-precision accelerometers (Liao et al., 2022). The proposed method determines the relationship between time history ground acceleration data and time history strain measurements using the CNN. To construct the CNN, recorded GM data and strain responses reliably measured in advance are used and then the trained CNN is utilized to predict strain responses in case of strain sensor defect. The structural status of the member under seismic loading events can be evaluated by analyzing the predicted strain with the yield strain of the member. In addition to GM data, seismic intensity measures quantified from GM characteristics are also introduced to examine the applicability of strain prediction in this study. The intensity measures used are a singular value matrix representing the frequency characteristics of GM as well as Arias Intensity and cumulative absolute velocity (CAV) that indicate the characteristics of the radiation of the seismic energy with changes in time during the earthquake. Multiple CNN models using GM data and intensity measures as input data are proposed, and strain prediction performance is compared between the proposed CNN models. The GM data and strain measurements from the structural members of the specimen obtained from a shaking table test of a 3-story reinforced concrete (RC) frame structure are used to confirm the performance of the proposed models. The effects of intensity measures on strain prediction as well as the strain prediction performance of time history GM data are investigated.

Methodology

Ground motion and intensity measure

The proposed research method focuses on the relationship between GM and the strain response of structural members subjected to GM in order to predict strain responses of structural members of a building subjected to seismic loads. Numerous structural members in the building exhibit different behaviors according to the earthquake intensity and frequency characteristics of GM. Those seismic behaviors appear in the strain responses of structural members which are displayed via the strain responses. Figure 1 shows the ground acceleration and strain response of a column in a structure in response to ground acceleration data. As shown in the figure, the amplification characteristics of the ground motion that change with time are roughly reflected in the strain response. Nevertheless, it is rather difficult to clearly analyze and predict response characteristics such as the point at which the strain response reaches its peak and the trend of the decrease of the strain response after a peak of the strain response using GM data only. Given the possibility of an earthquake with varying conditions, the characteristics of each structure and the functional diversity of several structural members within a single structure, the relationship between GM data and strain response need to be analyzed from various angles in order to identify how structural members will respond to earthquakes.

Figure 1.

(a) Ground acceleration and (b) strain response of structural member subjected to ground motion.

In order to analyze the possibility of structural damage due to earthquakes and seismic responses, the characteristics of GM data have been studied in various aspects (Yakhchalian and Yakhchalian, 2022). The characteristics of time history change of GM data, frequency characteristics and energy characteristics were quantified by seismic intensity measures and displayed as vector or scalar values to analyze the effect on the structure (Yan et al., 2022). In this regard, this study seeks to examine the relationship between the seismic intensity measures and the strain responses in addition to the relationship between the time history of GM data and structural responses. There are spectrum-related intensities to represent the frequency characteristics of GM data (Bradley, 2010, 2011), and the effects of these indicators on damage and response to structures have been analyzed (Yakhchalian and Yakhchalian, 2022). The frequency characteristics of GM data are linked to the modal characteristics of the target structure and affect the amplification and damping of the structural responses. Therefore, in this study, a frequency domain decomposition (FDD) technique which indicates basic equations represented in (Brincker et al., 2001) for investigating the frequency characteristics of time history vibration data is introduced to identify the frequency characteristics of GM data. Generally, data correlation is addressed in the FDD process with data measured from multiple locations in structures. In this study, as only one type of data which is the time series of ground acceleration is applied to the FDD technique, data correlation is not considered. When the time history GM data is substituted into the FDD technique, a singular value matrix can be extracted using the following equations (1)–(3).

A (t) = \int_{- \infty}^{\infty} {\ddot{u}}_{g} (τ) {\ddot{u}}_{g} (t + τ) d τ

(1)

S (w) = \int_{- \infty}^{\infty} e^{- i w t} A (t) d t

(2)

S (w) = U (w) \times S V (w) \times V (w)

(3)

where

{\ddot{u}}_{g} (t)

is the time series of ground acceleration and

A (t)

denote the autocorrelation function of

{\ddot{u}}_{g} (t)

, respectively.

S (w)

indicates power spectrum density function of the autocorrelation function,

A (t)

S V (w)

is a rectangular diagonal matrix representing a singular value, and

U (w)

and

V (w)

are complex unitary matrices indicating singular vectors.

S V (w)

U (w)

, and

V (w)

are obtained from singular value decomposition of the power spectrum density function,

S (w)

. The singular value matrix is regarded as one intensity measure of GM data. The relationship between the index and the strain response of structural members subjected to seismic loads is examined in this study. The singular value of GM data given in Figure 1(a) is calculated using equations (1)–(3) and represented in Figure 2(a).

Figure 2.

Intensity measure of GM: (a) singular value by FDD, (b) normalized arias intensity, and (c) normalized CAV.

The intensity measure of the seismic energy radiation characteristics with time is also considered in this study. One of them is Arias Intensity (Arias, 1970), which is represented by equation (4).

I_{A} = \frac{π}{2 g} \int_{0}^{T} {({\ddot{u}}_{g} (t))}^{2} d t

(4)

where g denotes the gravitational acceleration, and T denotes the duration of ground motion. The Arias Intensity of GM data given in Figure 1(a) is calculated using equation (4) and represented in Figure 2(b). As shown in Figure 2(b), the Arias Intensity values used in this study are normalized by the maximum value. The effect of Arias Intensity extracted from GM data on the prediction of strain response of structural members is also examined in this study.

In addition, the CAV of ground motion (Benjamin, 1988) is considered and represented by equation (5) as another seismic intensity measure.

C A V = \int_{0}^{T} | {\ddot{u}}_{g} (t) | d t

(5)

The CAV of GM data in Figure 1(a) represented in Figure 2(c). As shown in Figure 2(c), the CAV used in this study are values normalized by the maximum value. The relationship between CAV and strain is examined for the strain response prediction of structural members.

CNN models using GM and its intensity measure

The presented method corresponds to data-driven approach with measurements by sensors. In the method, the recorded GM data is used to predict the strain of structural members in a building. Thus, to employ the proposed method, a sensing framework including accelerometers to record the GM and strain sensors to measure strain responses of members in the structure is required. The relationship between the GM data and the strain response is determined via the CNN, one of the machine learning techniques, and utilized for strain prediction. As the relationship is identified by a neural network model based on measurements, the presented method does not require any system model such as numerical models determined by mass, stiffness, and damping to represent the target structure.

In this method, GM data and the seismic intensity measure extracted are used as input data for the CNN. Strain that occurs in the structural members is used as output data for the CNN. Depending on whether the intensity measure is used in the CNN input layer mentioned in Ground motion and intensity measure section, and the type of the intensity measure, various CNN models are proposed. Each intensity measure is employed to each CNN model. The prediction performance of the models having different intensity measures were compared. From the comparison, it will be examined what types of intensity measures are effective for the strain response prediction.

The first model used only the time history of ground acceleration as input for the CNN, and it is labeled CNN_G in this study. In the CNN_G model, the acceleration data of a specific time band (or range) among GM data is set as the input map of CNN for one dataset to train the CNN as shown in Figure 3(a), while the time history strain data generated in the structural member at the same time window is used as the CNN’s output vector of CNN as shown in Figure 3(b). In this study, the specific time band for one dataset was set as 1.56 s. As the sampling frequency was set as 256.41 Hz, a total of 400 data points was insulted to one dataset. In addition, to consider the accumulative effect of the data, data overlap was implemented in the constitution of datasets. The overlap time was set as 0.195 s. Thus, the start point of the next dataset was moved to 50 data points after the start point of the current dataset. In addition to CNN_G, the same data overlap method was employed to the constitutions of the datasets in other three CNN models.

Figure 3.

Description of CNN_G model: (a) input data – time series of GM and (b) output data – time series of strain response.

Generally, there are multiple convolutional and pooling layers in pairs between the input map and the output vector. In all the presented models, two pairs of convolutional and pooling layers exist between the input map and the output vector. Data in the input map in the CNN_G model that consists of time series of ground acceleration are normalized. As the sigmoid function is employed as the activation function in the output layer, the normalized value is set to be between 0 and 1. Normalization is conducted using the below equation (6).

X = \frac{x - \min {x}}{\max {x} - \min {x}}

(6)

where, X denotes normalized values and x indicates data in the input map. Normalized input map is filtered by the first kernel presented in Table 2 and the first convolutional layer is extracted. The convolutional operator used in this study can be expressed as below:

Y = X \otimes h + b

(7)

where, h and b indicate kernel matrix and bias vector, respectively. Y denotes a matrix consists of the convolutional layer.

\otimes

is the convolutional operator. Then, the pooling layer is generated by subsampling of the convolutional layer. In the subsampling, the maximum values are extracted. The same processes are proceeded to generate the second convolutional and pooling layers using operators presented in Table 2. A fully connected layer connects between the second pooling layer and the output vector. The output layer is extracted by applying the activation function to FC layer. The desired value extracted from the output vector of the CNN consists of the loss function. The loss function, E, in this study can be presented by equation (8).

E = \frac{1}{2 N} \sum_{i = 1}^{N} {(y_{d} - y_{r})}^{2}

(8)

where,

y_{d}

and

y_{r}

indicate desired output from the output vector of the CNN and reference data, respectively. N denotes a total length of data. While minimizing the loss function, the weights in the CNN are updated by the back propagation. In the back propagation, the steepest descent method is employed. In the training, a constant value of learning rate is used. Using all training datasets constituted by aforementioned data, the CNN is trained until the given epoch.

Table 2.

CNN architecture parameter.

Layer	Size/depth	Operator	Size/stride
Input layer	20 × 20	Kernel 1	7 × 7/1
Convolutional layer 1	14 × 14/10	Subsampling 1	2 × 2/2
Pooling layer 1	7 × 7/10	Kernel 2	5 × 5/1
Convolutional layer 2	3 × 3/20	Subsampling 2	1 × 1/1
Pooling layer 2	3 × 3/20
Fully connected layer	180
Output layer	400

CNN architecture is illustrated in Figure 4 and Detailed information of selected parameters of the CNN architecture of CNN is listed in Table 2. CNN architecture and its prediction performance are determined and affected by parameters in CNN. The sizes of layers are determined by the sizes of kernels and subsampling. The performance of the CNN was evaluated according to the variations in the size of the first kerel. In this examination, other conditions are identical to the information in Table 2. Figure 5(a) shows the results of the examination. The smallest and largest sizes of kernel worsened the prediction performances. Some median values such as five and seven yielded relatively smaller errors than other cases. In addition, the effect of the depth in the CNN was investigated and the results are shown in Figure 5(b). The values in x-axis of Figure 5(b) means the depth of the first convolutional layer. The depth of the second convolutional layer is set as twice of the value in Figure 5(b). Results shows the increase of depth worsened the prediction performance of the CNN. 10 and 20 of the depth in the first and second convolutional layers showed the best performance. Thus, it was found that the parameters selected in this study as shown in Figure 4 and Table 2 are appropriate in terms of the prediction performance.

Figure 4.

CNN architecture.

Figure 5.

Effect of CNN parameters on prediction error: (a) kernel and (b) depth.

In addition to CNN_G, the models presented in this study used the seismic intensity measure described in section 2.1 along with the time history of GM data as the input data for the CNN. The second CNN model is a CNN_F model in which the singular value matrix extracted through the GM data is used together with the time history of ground acceleration as the input data. The input data configuration of CNN_F is given in Figure 6(a). All singular value matrix extracted from a specific time domain (or range) of GM data are set as input for CNN_F, and used to configure the input map of CNN_F together with time history of GM data. In this study, the input size was set as 625. The input constitution includes 400 of the time series of GM data, 200 of singular value data, and the rest of zero padding. As the singular values are extracted as half of the original time domain data, the lengths of time and frequency domain data in the input of CNN_F are different. Thus, as those two data cannot be matched with the same size of the input map, they are arranged in one input layer as shown in Figure 6(a) instead of three-dimensional input constitution. In the input constitutions of rest two CNN models such as CNN_A and CNN_C, time domain data and intensity measure data are set in one input layer to compare prediction performance with CNN_F under the same condition for the input constitution. The strain response of the structural member corresponding to this specific time domain is configured as the output vector of the CNN model as in CNN_G. The architecture between the input map and output vector of CNN_F is configured in the same manner as in CNN_G described earlier.

Figure 6.

Description of CNN_F model: (a) input data – time series of GM with singular values of GM and (b) output data – time series of strain response.

In the third CNN model, Arias Intensity is set as the input data for the CNN. As shown in Figure 7(a), the time history of GM data of a specific time domain and the normalized Arias Intensity of the same time domain are set together in the input data for the CNN, and is referred to as CNN_A model in this study. The time history of strain response of the structural member corresponding to the time history of GM data set in the input layer is set in the output layer of CNN_A as in the preceding models. The architecture of CNN_A is also the same as the models described earlier.

Figure 7.

Description of CNN_A model: (a) input data – time series of GM with normalized arias intensity and (b) output data – time series of strain response.

The fourth model is a CNN_C model using time history of GM data and CAV values extracted from GM data as the input data for the CNN. As shown in Figure 8(a), the GM data of a specific time zone and the normalized CAV value of the corresponding time zone are used as the input map of CNN_C. The strain response of the structural member subjected to the seismic load in the same time zone as the GM data used in the input map is set as the output vector of CNN_C. The four CNN models are trained using measured GM data and strain data measured from structural members in the target building. The strain prediction performances of the four constructed CNN models subjected to earthquakes not used in the CNN training are subsequently investigated and compared.

Figure 8.

Description of CNN_C model: (a) input data – time series of GM with normalized CAV and (b) output data – time series of strain response.

Application

Descriptions of the experiment

The structural responses of building structures subjected to earthquakes are needed to examine the performance of the CNN models for strain prediction using GM data presented in this study and to confirm the validity of the intensity measure used. A shaking table test was performed on a specimen in order to obtain the strain response of the structural member to GM. The target structure is a 3-story RC frame structure with a single span as shown in Figure 9. The story height is 1.2 m, while the total height of the structure is 3.6 m. The sizes of the girder and column constituting the specimen, and the reinforcement details are given in Figure 9(d). Figure 9(a) and (b) show sensor layout including LVDT, accelerometer, and strain sensors. Strain sensors were installed on the main bar and hoop reinforcement in columns of the specimen in order to measure the strain of structural members during seismic loading through a shaking table. Among measured responses from many strain sensors, strain responses from a strain sensor installed in a main rebar of the lowest column were used to construct the CNN models in the experimental study. The location of the used strain sensor is shown in Figure 9(b)–(d). Ground accelerations were automatically extracted from shaking table system. Numerous earthquake simulations were prepared to train the CNN models. A total of 20 GM data were prepared and applied in a shaking table test. Detailed information on the earthquake data used are listed in the Table 3. Ground motion data in Table 3 were scaled down and 0.2 scaled ground acceleration data were used in the experiment.

Figure 9.

Experimental specimen: (a) photo of specimen, (b) front view with sensor layout, (c), side view with sensor layout, and (d) reinforcement details of column and girder (Seon Park et al., 2020).

Table 3.

Information on input ground motion (Seon Park et al., 2020).

No.	GM	Record	PGA (g)	Duration (sec.)	Use
1	1993 Kuril Island	Hokkaido Coast SW (LG)	0.3291	40.00	Train
2	1994 Kuril Island	Hokkaido East Coast SW (LG)	0.4472	60.00	Train
3	1995 Kobe	Hyougoken South (N12 W)	0.6027	50.00	Train
4	1968 Hyuganada	Hyuganada Coast (TR)	0.3925	40.00	Train
5	1995 Kobe	Hyougoken South (NS)	0.7955	30.00	Train
6	1995 Kobe	Hyougoken South (NS)	0.7004	40.00	Train
7	1995 Kobe	Hyougoken South (NS)	0.5685	50.00	Train
8	1968 Hyuganada	Hyuganada Coast (LG)	0.3698	40.00	Train
9	1978 Miyagi	Miyagi Coast (LG)	0.3251	30.00	Train
10	1983 Nihonkai-Chubu	Nihonkai Central (TR)	0.4419	60.00	Train
11	2011 Tohoku	Tohoku Coast (EW)	0.8105	240.00	Train
12	2011 Tohoku	Tohoku Coast (EW)	0.6882	240.00	Train
13	2011 Tohoku	Tohoku Coast (NS)	0.7042	240.00	Train
14	2003 Tokachi-oki	Tokachi Coast (EW)	0.5484	120.00	Train
15	2003 Tokachi-oki	Tokachi Coast (EW)	0.6313	120.00	Train
16	2003 Tokachi-oki	Tokachi Coast (EW)	0.5160	120.00	Train
17	1995 Kobe	Hyougoken South (EW)	0.6859	40.00	Train
18	1995 Kobe	Hyougoken South (EW)	0.6314	50.00	Train
19	1978 Miyagi	Miyagi Coast (TR)	0.3262	30.00	Test
20	1983 Nihonkai-Chubu	Nihonkai Central (LG)	0.4324	60.00	Test

Many methods for ground motion selections have been developed using seismic intensity measures including frequency-content parameters (Yaghmaei-Sabegh, 2017; Yaghmaei-Sabegh and Jodat-Saeidabad, 2023), time domain characteristics (Arias, 1970), and energy accumulative indicators (Benjamin, 1988). To apply the seismic response prediction method to future earthquakes, the neural network-based prediction models are needed to be trained by data with various ground motion characteristics. In this regard, characteristics of 20 GM data were examined using seismic intensity measures. Of many intensity measures, five types of seismic intensity measures such as peak ground acceleration, mean period, significant duration, the maximum value of cumulative absolute velocity, and the maximum value of Arias intensity were selected and listed in Table 4. For those 20 earthquakes in Table 3, five seismic intensity measures were calculated and the relationships of PGA and remaining four intensity measures were presented in Figure 10. One circle in each figure of Figure 10 corresponds one earthquake listed in Table 3. As shown in Figure 10, data were mostly scattered and widely distributed. From the results, it was confirmed that 20 GM data in Table 3 have relatively various seismic characteristics. As those GM data have various characteristics and show unbiased distributions, it is expected that the relationships of those GM characteristics and corresponding responses can be reflected in the trainings of the models. Thus, 20 GM data listed in Table 3 were employed to CNN model training and testing in this study.

Table 4.

Descriptions on intensity measures.

Intensity measure	Expression
Peak ground acceleration	$P G A = \max \| {\ddot{u}}_{g} (t) \|$
Mean period (Yaghmaei-Sabegh, 2020, 2021)	$T_{m} = \frac{\sum_{i}^{N} C_{i}^{2} \times \frac{1}{f_{i}}}{\sum_{i}^{N} C_{i}^{2}}$
Significant duration (Arias, 1970)	Time domain with Arias intensity from 5% to 95% ( ${D u r}_{s i g}$ )
Peak of cumulative absolute velocity (Benjamin, 1988)	${C A V}_{\max} = \max (\int_{0}^{T_{\max}} \| {\ddot{u}}_{g} (t) \| d t)$
Peak of Arias intensity (Arias, 1970)	${A r i a s}_{\max} = \max (\frac{π}{2 g} \int_{0}^{T_{\max}} {\ddot{u}}_{g}^{2} (t) d t)$

Figure 10.

Ground motion characteristics: (a) Tm versus PGA, (b) ${D u r}_{s i g}$ versus PGA, (c) ${C A V}_{\max}$ versus PGA, and (d) ${A r i a s}_{\max}$ versus PGA.

In an experiment, when the prepared earthquake simulation was applied to the specimen, the strain response of the column of the specimen was measured. For the measured strain responses, the preprocessing was performed. At first, to adjust the starting point of strain measurement to around zero, offset was conducted using an average value of the initial 100 data points. The strain responses with offset were generated by subtracting the average value from raw data of strain measurements. And then, the offset strain responses were filtered by band pass filtering with a frequency range of 0.5–40 Hz considering the natural frequencies of the specimen for the first three translational modes. Finally, the filtered offset strain data were employed to the CNN training. In the test for the trained CNN, the filtered offset strain data were set as prediction target responses. The CNN models presented in section 2 were trained using the GM data and the corresponding strain data. Among a total of 20 earthquake simulations, 18 were used in the training, and the trained CNN models were verified using the measurement data for the remaining two earthquake simulations.

Results

Based on the recorded GM data and the measured strain data, the four CNN models presented in section 2 were trained under the same conditions. All CNN models converged stably with a rapid reduction in loss function at the beginning of training, and the convergence curves are shown in Figure 11. The convergence patterns in the initial stage of training were similar for all models, and the final loss function value of CNN_F and CNN_G was smaller than other models. At the end of training, CNN_F showed slightly lower value of loss function than CNN_G. Even if CNN_A and CNN_C have more parameters such as Arias Intensity and CAV with GM data than CNN_G having only GM data, they showed worse results than CNN_G in CNN training. On the other hand, CNN_F which has also more parameter such as singular value matrix with GM data exhibits better training result than CNN_G. In this regard, it is regarded that reflecting FDD results in the CNN input data has positive effects on CNN training. It is fact that more manual computation is needed to use CNN_F compared with CNN_G. Nevertheless, this computation for FDD is simple and fast process. Thus, to improve CNN training performance, it is necessary to construct datasets for CNN_F.

Figure 11.

Convergence curves of loss function in the training of CNN models.

The test earthquake data not used for training and the strain measurement response subjected to the test earthquake were used to examine the strain prediction performance of the trained CNN models. Figure 12 shows the estimated strain and reference strain values of the CNN models for the test datasets. The estimated strain and reference strain values are distributed in a relatively linear manner, which indicates that the strain prediction of CNN models is possible. In the figures, values for coefficient of determination between estimation and reference are provided. CNN_F showed the highest value compared with other models which can be regarded as showing the best performance for strain response prediction. Nevertheless, the values of coefficient of determination provided in Figure 12 were below 0.5. As shown in reference values (gray) of Figures 14 and 17, ±10 με of noise data were observed in fairly long periods especially initial stage before earthquake events and last stage after earthquake events during shaking table tests. For these periods, CNN models predicted strains with very small values compared with noise levels. Discrepancies between predicted strain and noise data in these periods may negatively affected the calculations of coefficient of determinations. Indeed, significant periods were between initial and last stages during earthquake events as shown in blue dotted boxes in Figures 14 and 17. Thus, prediction performances of the CNN models for the periods during earthquakes events were examined. The effective ranges of no. 19 earthquakes were selected from 6 s to 26 s as shown in blue dotted boxes in Figure 17. Those of no. 20 earthquakes were selected from 13 s to 60 s as shown in blue dotted boxed in Figure 14. The prediction results and coefficient of determinations for the reduced ranges were presented in Figure 13. The values of coefficient of determinations for the reduced ranges were increased as 0.08 to 0.09 compared with those for the whole ranges. Nevertheless, those values were still low. That came from lacks of datasets and technical limitation only using ground motion data in this method.

Figure 12.

Strain estimation results of CNN models for test datasets: (a) CNN_G, (b) CNN_F, (c) CNN_A, and (d) CNN_C.

Figure 13.

Strain estimation results of CNN models for the reduced range of test datasets: (a) CNN_G, (b) CNN_F, (c) CNN_A, and (d) CNN_C.

Figure 14 shows the time history of strain predictions of the trained CNN models for one test earthquake which is no. 20 earthquake presented in Table 3. Except for CNN_C, all the remaining CNN models predict the time history of strain responses subjected to test earthquake relatively accurately. Figure 15 shows enlarged plots of prediction of the time history of strain response. Plot shows a range with high amplitude between 15 s and 17 s. It is observed that three models except for CNN_C show a good agreement between estimation and reference for the range with high amplitude strain response. From this, in the presented approach, it was clearly found that CAV used in CNN_C worsens the strain response prediction capacity of the CNN. Although those three models predict fairly well one of the highest strain values around 16.8 s, they show a little gap between reference and estimation another highest strain value around 15.2 s. That comes from lack of datasets. As the models were trained by datasets from only 18 earthquakes, it is regarded that various characteristics of seismic waves were not reflected in the training resulting a discrepancy between estimation and reference in the prediction result. If sufficient datasets including various characteristics of many earthquakes are employed to the training, it is expected that the prediction capacities of the models are improved.

Figure 14.

Estimation results of the time series of strain response subjected to no. 20 earthquake: (a) CNN_G, (b) CNN_F, (c) CNN_A, and (d) CNN_C.

Figure 15.

Enlarged plot of prediction of time series of strain response subjected to no. 20 earthquake: (a) CNN_G, (b) CNN_F, (c) CNN_A, and (d) CNN_C.

A quantitative comparison of strain prediction performance was made between the four CNN models. The root mean square error (RMSE) of the four CNN models for training and test datasets were calculated and compared as shown in Figure 16. The RMSE of the four models showed similar patterns for both the training datasets and the test datasets. It was confirmed that CNN_F with the lowest RMSE showed the highest strain prediction performance. The RMSE for the test datasets of CNN_G using only the time history of GM data as input for the CNN was 4.1629, which was slightly higher than the RMSE of CNN_F, 4.1183. Accordingly, it was confirmed that the singular value matrix used as input for CNN_F in addition to the time history of GM data is regarded as an intensity measure that improves the CNN’s strain prediction performance. The RMSE of CNN_A and CNN_C was 4.300 and 4.6975, respectively, showing lower strain prediction performance when compared to CNN_G. In particular, CNN_C failed to predict the time history strain as shown in Figure 14(d). As Arias Intensity and CAV in addition to the GM data were utilized as input for CNN_A and CNN_C, it was thus confirmed that the addition of these two seismic intensity measures reduces the strain prediction performance.

Figure 16.

RMSE of CNN models for strain estimation.

Figure 17 shows the time history of strain prediction results of the trained CNN models for another test earthquake which is no. 19 earthquake in Table 3. In this prediction, CNN_C still fails to predict strain responses. In addition, different to the case with no. 20 earthquake, CNN_A shows worse prediction results for no. 19 earthquake. CNN_G and CNN_F show relatively accurate prediction performances especially the response range with high amplitude approximately around 10 s.

Figure 17.

Estimation results of the time series of strain response subjected to no. 19 earthquake: (a) CNN_G, (b) CNN_F, (c) CNN_A, and (d) CNN_C.

The training conditions that are able to affect prediction capacities for CNN_F and CNN_G which showed better performance than other models were examined more detailed. The size of the input in CNN_G was set as 400 that are all time series of GM data. On the other hand, the input size of CNN_F was 625 including 400 of time series of GM data, 200 of singular value matrix, and the rest of zero padding. As the size of CNN_F is a little larger than that of CNN_G, this is not same training condition. Under the identical input size of CNN_G with zero padding to that of CNN_F, CNN_G was trained and validated. In this examination, CNN_G having the identical input size to CNN_F showed higher RMSE by 1.63% than above CNN_G with the 400 of the input sizes. It was confirmed that, under the same input constitution condition, CNN_G showed worse performance than CNN_F.

As shown in Figure 6(a), the magnitude of data in the input of CNN_F was quite different. Time series data is unit’s place while singular value is around hundred’s place. Even if the levels of the magnitudes of two data were significantly different, the same kernel was used to extract features. To examine the effect of the difference of the magnitude of data on prediction performance, CNN training was conducted with the data adjusting the magnitude of singular value to almost unit’s place. In this case, CNN_F trained with modified data showed the exactly same prediction performance to the case using different levels of the magnitudes of the data. It was regarded that the features can be extracted regardless of the difference of the magnitudes of the data in one input map. Another case using singular value data normalized by the maximum value of singular values was examined. In this case, a little higher RMSE by 2.19% was shown than the case using unnormalized singular values. From this, it was found that the use of unmodified singular value data in the input of the CNN_F is advantageous to the better prediction performance.

To confirm the repeatability of the presented method, additional CNN training and validation with a different set of data was conducted. In the newly constituted datasets, no. 2 and no. 7 earthquakes presented in Table 3 were selected for the test datasets. Remaining 18 earthquakes were set as the training datasets. In the selection of test earthquakes, the median values for PGA and duration were considered. By using data for 18 earthquakes, the presented four CNN models were trained under the identical conditions for data constitution and training condition. The trained CNN models were validated for the test datasets derived from no. 2 and no. 7 earthquakes.

In the additional examination, the similar prediction results were derived compared with the above prediction results using datasets where test datasets were set as the data for no. 19 and no. 20 earthquakes. The results showed the presented CNN models accurately predicted strain responses except CNN_C. Figure 18(a) and (b) shows examples of the strain prediction results by CNN_F for no. 2 and no. 7 earthquakes, respectively. In these figures, it was observed that CNN_F fairly well predicted the time history of the strain responses. CNN_G and CNN_A also predicted the time history of the strain responses relatively accurately. Figure 19 shows RMSE of four CNN models for new datasets. CNN_F showed the lowest RMSE value, 3.3191, for test datasets that means the highest prediction performance. CNN_G, CNN_A, and CNN_C showed RMSE values of 3.4245, 3.3313, and 3.4892, for test datasets, respectively. Although CNN_G exhibited lower value of RMSE for training datasets than CNN_A, CNN_G showed higher value of RMSE for test dataset than CNN_A, which indicates that CNN_G was much better trained than CNN_A and CNN_A may be underfitted. After all, CNN_F showed the highest prediction performance for both training and test datasets which were similar trend above analysis using test datasets from no. 19 and no. 20 earthquakes.

Figure 18.

Estimation results of the time series of strain response for the new set of data subjected to: (a) no. 2 earthquake, (b) no. 7 earthquake.

Figure 19.

RMSE of CNN models for strain estimation for the new set of data.

To examine influences of long duration records on the CNN training, additional cases studies where ground motions with long durations were excluded in the training datasets and included in the testing datasets were conducted. Under the same conditions, types of input ground motions in the training and testing were altered in two case studies. In the first case study, data for no. 11 earthquake and no. 12 earthquake with the longest durations were used in the testing datasets and data for remaining 18 earthquakes were set as training datasets. In the second case study, data for no. 11 earthquake with the longest duration and no. 15 earthquake with the second longest duration were set as testing datasets and data for remaining 18 earthquakes were set as training datasets. Among several models, CNN_F model was employed in these case studies. The results showed that the prediction performances in these cases were lower than those in the aforementioned study where data for no. 19 and no. 20 earthquakes were set as the testing datasets and data for remaining 18 earthquakes including ground motions with long durations were set as the training datasets. RMSEs of the first and second cases for the testing datasets were 4.2447 and 4.2160, respectively. RMSE of the aforementioned study using CNN_F model for testing datasets was 4.1183. From the results, it was indirectly confirmed that the uses of ground motions with long durations can improve the prediction performances of the presented method.

Conclusions

This study aims to propose a method for predicting strain responses of structural members in buildings using GM data. Models capable of identifying the relationship between the strain response of structural members in a building and the GM data were presented. The comparative evaluation of strain prediction performance was made between CNN models using GM intensity measures including singular value matrix, Arias Intensity and CAV, in addition to the time history of GM data as input. The applicability of the proposed method was examined using the GM data and seismic response obtained using the shaking table test of a 3-story RC structure. The results obtained through the application are summarized as follows.

■ This study proposed a method for estimating the strain of structural members in a building using measured GM data and intensity measures extracted from the building. It was found that the strain of structural members subjected to seismic loading was estimated with relative accuracy using the proposed method.

■ In this study, one of the machine learning techniques, CNN, was introduced for strain response estimation. The CNN_G model using only the GM data, the CNN_F model using the GM data and the singular value of GM, the CNN_A model using the GM data and the Arias Intensity of GM, and the CNN_C model using the GM data and the CAV of GM were proposed and used for strain prediction.

■ The strain prediction performance of the proposed CNN models was subsequently examined, and the results showed that compared to the CNN_G model using only the time series of ground acceleration as input, the CNN_F model using the singular value extracted by FDD together with the time series of ground acceleration as input yielded higher strain prediction performance.

■ Specific GM intensity measures such as Arias Intensity and CAV used as input for the CNN model in addition to the time series of ground acceleration degrade the strain prediction performance compared to when only the time series of ground acceleration is used as input.

Basically, to apply the presented method to the real-world problem, a sensing system should be embedded in the target structure such as strain sensors. Thus, the presented method can be applied to various types of RC buildings that have strain sensing systems. If the type of the target structure is RC frames, strain sensors are needed to be installed in the reinforcement rebar of the structural members such as columns and beams before concrete pouring. Target members for monitoring can be selected based on structural analyses considering internal force distribution or combined stress distribution. During the earthquake events, strain responses should be measured and stored to train the presented CNN models. The ground accelerations data recorded during various earthquake events are also needed. With measured strain responses and recoded ground motion data subjected to various earthquake loads, CNN models should be constructed in advance. Constructed CNN models can be utilized to predict strain responses subjected to future earthquakes using only recorded ground motion data. To employ the recorded data in the trained CNN models, the time series of ground motion data should be rearranged and converted to the form of the input map described in Section 2.2. In addition, to construct accurate prediction models, it is important to retain a big data measured during seismic excitation. Nevertheless, relatively small data for only 20 earthquake loading events were measured and employed to CNN model trainings in this study due to the experimental test conditions which can be regarded as one of the limitations of this study. It is expected that more datasets subjected to GMs with various characteristics generate more reliable and robust neural networks.

The data used in the application of the presented method remain in the elastic range. Thus, the nonlinearity of the structural response in the prediction was not considered. It is necessary to consider the nonlinearity of the response for decision making to assess safety or re-occupancy of the structures after severe seismic loading events. Thus, in the further study, the nonlinear response prediction method will be developed through the studies with structural data from more severe loading tests (Yaghmaei-Sabegh, 2021).

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by a National Research Foundation of Korea (NRF) grant funded by the Korea government (Ministry of Science, ICT & Future Planning, MSIP) (NRF-2021R1A2C3008989, No. 2018R1A5A1025137, and NRF-2022R1C1C1009871). This research was supported by the Yonsei University Research Fund of 2023-22-0447.

ORCID iD

Byung Kwan Oh

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