A deep neural network based surrogate model for damage identification in full-scale structures with incomplete noisy measurements

Abstract

The paper introduces a novel approach for detecting structural damage in full-scale structures using surrogate models generated from incomplete modal data and deep neural networks (DNNs). A significant challenge in this field is the limited availability of measurement data for full-scale structures, which is addressed in this paper by generating data sets using a reduced finite element (FE) model constructed by SAP2000 software and the MATLAB programming loop. The surrogate models are trained using response data obtained from the monitored structure through a limited number of measurement devices. The proposed approach involves training a single surrogate model that can quickly predict the location and severity of damage for all potential scenarios. To achieve the most generalized surrogate model, the study explores different types of layers and hyperparameters of the training algorithm and employs state-of-the-art techniques to avoid overfitting and to accelerate the training process. The approach’s effectiveness, efficiency, and applicability are demonstrated by two numerical examples. The study also verifies the robustness of the proposed approach on data sets with sparse and noisy measured data. Overall, the proposed approach is a promising alternative to traditional approaches that rely on FE model updating and optimization algorithms, which can be computationally intensive. This approach also shows potential for broader applications in structural damage detection.

Graphical abstract

Keywords

vibration-based damage detection / deep neural network / full-scale structures / finite element model updating / noisy incomplete modal data

1 Introduction

In recent years, vibration-based damage detection (VBDD) approaches have grown in popularity in structural engineering [1–3]. These methods identify damage by exploiting the relationship between a structure’s dynamic characteristics, such as mode shapes and natural frequencies, and its stiffness. The VBDD model-based approach involves minimizing the difference between a theoretical model, developed using the finite element (FE) method, and experimental measurements. Various techniques and optimization methods are used to achieve this. Once the FE model accurately reflects the stiffness, the adjusted parameters serve as damage indicators. FE model updating is classified as an inverse problem in classical mechanics [4–6] and there is a significant body of related research [7–14]. Gundes et al. [15] employed a sensitivity-based method to identify damage in complex reinforced concrete frame structures, while Zheng et al. [10] combined FE model updating with energy spectral density analysis of dynamic responses to identify damage in frame structures. Recently, Du et al. [13] studied the effectiveness of the Jaya algorithm, even in the presence of relatively high levels of noise, for addressing optimization-based structural damage diagnosis problems, using a hybrid objective function. More recently, Zhang et al. [14] presented a two-step procedure for detecting damage in offshore wind turbines by updating the FE model. Although these approaches have shown promising results for structural damage assessment, they have various restrictions affecting their performance and practicality. These restrictions include: 1) the high computational cost of the FE procedure and the loop optimization methods required to achieve optimal results for each damage scenario; 2) the difficulty and complexity of modeling the behavior of large and complex structures using computer programs such as MATLAB or FORTRAN; 3) the need for a complex optimization framework, including the optimization algorithm, problem statement, objective function, boundary constraints, constraint function, and design variables.

Machine learning (ML) and deep learning (DL) have become popular mathematical tools in various fields, including structural engineering [16–21]. In particular, artificial neural networks (ANNs) have been widely used to identify damage in different types of structures such as bridges, steel frame structures, beam structures, and trusses [22–27]. However, shallow ANNs with limited hidden layers may not be suitable for complex structures and high-dimensional data, leading to poor performance and long computation times [28]. To overcome these limitations, DL techniques, which involve multiple hidden layers, have been developed [29]. Deep neural networks (DNNs) have been employed to model complex nonlinear relationships in structural behavior, achieving promising results in damage detection [30–36]. For example, Pathirage et al. [30] used a DL-based sparse autoencoder framework to identify damage in a steel frame and in a prestressed concrete bridge. Wang et al. [32] suggested approaches, using mobile DL, to automatic damage detection in historic masonry buildings. Bokaeian et al. [34] developed the DNNs-coupled sparse coding classification ensemble method to detect damage in plates.

Despite the success of DNNs in detecting damage, much of the research has focused on small and simple structures or has relied solely on experimental data. Therefore, future research needs to address the application of DL to larger and more complex structures and should integrate numerical simulations with experimental data to enhance the performance and practicality of damage detection [37–40].

Computational technologies have significantly improved commercial FE modeling software, thereby creating powerful tools for engineering applications. These software packages enable accurate and efficient analysis of complex structural systems and can be integrated with third-party software, such as MATLAB [41]. Consequently, researchers have utilized optimization-based FE model updating techniques for damage identification, frequently in combination with commercially available FE software. For instance, Sanayei and Rohela [42] created a platform for automatic FE model updating in full-scale buildings, which included a four-story building made of shell/frame elements. Nozari et al. [43] provided a framework for FE model updating that incorporated a gradient-based optimization method, using SAP2000 software, for damage assessment in a ten-story building. Recently, Dinh-Cong et al. [44] suggested a FE model update approach for full-scale structure damage assessment, using the software SAP2000 integrated with an enhanced symbiotic organism search method.

However, despite these advancements, research on model-based damage identification techniques for the full-scale structures has been relatively limited, and the application of DL techniques to this problem remains little studied. Moreover, there is a dearth of research on effective frameworks for collecting data sets with large and complex structures. To date, no study has investigated DL techniques for damage detection in full-scale structures using data sets that feature incomplete modal data and noise. These research gaps highlight the urgent need for further exploration of advanced techniques, including DL, for damage detection in full-scale structures.

This study is therefore conducted to propose a novel approach to address the aforementioned research gaps within the field of damage assessment of engineering structures. To achieve this, a generalized approach based on DNNs is presented for constructing surrogate models. The proposed approach involves a framework for collecting data sets by a reduced FE model using commercial SAP2000 software, which is integrated with MATLAB code via the SAP2000-OAPI feature. This framework enables the extraction of response data, such as vibration characteristics (including mode shapes and natural frequencies), from the monitored structure, which serves as input to the surrogate model. By utilizing a single surrogate model trained on this data, the proposed approach can quickly predict the severity and location of damage in the structure, for all damage scenarios. To construct the most generalized surrogate model, we investigate two distinct layer types and the hyperparameters of the training algorithm and adopt state-of-the-art methods to prevent overfitting and improve the training process. The accuracy, efficiency, and application of the approach are illustrated using numerical examples involving an industrial steel frame and a three-dimensional (3D) three-story building. The study also validates the proposed approach’s robustness on data sets with noise-polluted and incomplete measurement data.

2 Damage identification using deep neural networks

2.1 Damage identification

The dynamic properties of structures are described by the equation below [33]:

(1)\left(\left[K\right]-{\lambda }^2\left[M\right]\right)\mathrm{\Delta }=0,

where \left[K\right] and \left[M\right] represent the stiffness and mass matrices, respectively; {\lambda }^2 denotes the eigenvalue; and Δ is the corresponding eigenvector.

When using FE analysis for damage simulation, a crucial consideration is the characterization of material damage behavior. One such method relies on the strain equivalence hypothesis, which involves measuring changes in the material’s elastic modulus before and after damage. This approach is widely applicable and straightforward to implement [45]. The hypothesis states that the deformed damaged material is equivalent to a virtual undamaged material deformed under an effective stress, with both having equal effective bearing areas. The mathematical representation in the one-dimensional (1D) space is as follows:

(2)\epsilon =\frac{{\sigma }^{\prime }}{E^{\mathrm{u}\mathrm{d}}}=\frac{\sigma }{E^{\mathrm{d}}},

where E^{\mathrm{u}\mathrm{d}} indicates the original elasticity modulus; E^{\mathrm{d}} defines the elasticity modulus of the damaged element; \sigma indicates nominal stress; {\sigma }^{\prime } defines effective stress. The following is an expression relating effective stress to nominal stress:

(3){\sigma }^{\prime }=\frac{\sigma }{1-d};\frac{\sigma }{E^{\mathrm{u}\mathrm{d}}(1-d)}=\frac{\sigma }{E^{\mathrm{d}}},

where d represents the damage factor. Now, the stiffness change caused by the damage is the decrease in the elasticity modulus, as follows:

(4)E_j^{\mathrm{d}}=E_j^{\mathrm{u}\mathrm{d}}\left(1-d_j\right),(j=1,\dots ,n)

where E_j^{\mathrm{u}\mathrm{d}} indicates the original elasticity modulus of the jth element; E_j^{\mathrm{d}} defines the elasticity modulus of the damaged jth element; d_j is the damage index of the jth element, the index ranges between \left[0,1\right]; n defines the number of elements.

To challenge the surrogate models, and to evaluate the proposed approach’s robustness, we introduce multiple noise levels into the input data. The modeling of the influence of noise levels on input data are as follows [46]:

(5){\theta }_{\text{noise}}=\theta +\alpha \left(2\text{rand}\left(\right)-1\right)\theta ,

where {\theta }_{\text{noise}} denotes the mode shape vectors or natural frequencies contaminated by noise; \theta represents the original mode shape vectors or natural frequency; rand() generates a random number [0,1]; \alpha defines the noise level.

2.2 Deep neural network architectures

To deal with input data contaminated by high levels of noise, CNN-layers with the 1D convolutions, activation functions, and pooling are added to deep feed-forward neural network architectures to improve the performance of the surrogate model [47]. It consists mainly of convolutional layers, pooling layers, and fully connected layers at the end. Convolutional neural networks [48] are inspired by biological processes that can learn to refine the filters (or kernels) through automated learning. 1D-CNNs are well-suited for applications with limited labeled data or high signal variations, as they have low computational requirements. In the following sections, each major component of deep architectures is introduced briefly, with more information available in Ref. [49].

2.2.1 Convolutional layer

A convolutional layer is typically the first layer in a CNN architecture. It acts as a filter, with a receptive field that can be adjusted to optimize feature extraction. The convolutional layer helps create a more robust feature space using learning filters that are sensitive to specific features in the input signal. The parameters of these filters and biases are learned in the training process of the CNN. The following is how 1D forward propagation is described in each layer.

(6)x_k^l= b_k^l+ {\sum }_{i=1}^{N_{l-1}}\mathit{c}\mathit{o}\mathit{n}\mathit{v}1D\left(w_{ik}^{l-1},s_i^{l-1}\right),

where x_k^l indicates the input; b_k^l defines the bias of the kth neuron of lth layer; w_{ik}^{l-1} denotes the kernel of the ith neuron at the (l-1)th layer; \mathit{c}\mathit{o}\mathit{n}\mathit{v}1D(. ,.) is used to carry out “in-valid” 1D convolution without zero-padding.

2.2.2 Pooling layer

The pooling layers’ goal is to reduce the spatial dimension of the convolutional layer output. This helps to reduce the computational cost of the models by decreasing the parameter number and also helps to control overfitting by reducing the number of parameters that the model has to learn. The pooling layer performs a summarizing operation, such as taking the mean, maximum, or minimum of a group of values, to reduce the spatial size of the output. This helps extract the main features of the input signal and makes the model more efficient during training.

2.2.3 Fully connected layer

Finally, at the end of the CNN architecture, the fully connected layer is utilized to transfer the high-level information extracted by the convolutional layers to the model’s final output. The hidden layers have the task of receiving and processing input information, extracting the feature representations from the previous layer, and providing high-precision decision results for the surrogate model. The information is transmitted from the previous layers to the output layer by the hidden layer. A neuron only receives input from the preceding neuron and transmits output to the succeeding neuron; there is no back-propagation [50]. Assuming that the fully connected layer consists of N layers then the output signal z^l_j of lth layer can be written as:

(7){\mathit{\text{z}}}_j^l=f\left(w_j^T{a}_j^{l-1}+b_j\right),l=1,2,3,\dots ,N,

where f represents the activation function; w_j^T denotes the weight vector; a_j^{l-1} defines the \left(l-1\right)th layer’s output signal; b_j defines the bias value of the jth neuron in the lth layer.

2.2.4 Activation function

The primary objective of an activation function is to add nonlinearity to the model. This is significant because the majority of real-world data are nonlinear, and a linear model cannot capture the complexity of such data. Recently, many activation functions have been proposed for DL models, which speed up the training process significantly [51]. Sigmoid, tanh, Rectified Linear Unit (ReLU), SELU, and Leaky ReLU are examples of typical activation functions. The activation function used is determined by the type of data being processed and the desired output of the model.

2.2.5 Loss function

The mean square error (MSE), which measures the precision of the prediction model, is frequently employed as a loss function in regression problems. The average of the squared differences between the true values and the predicted values is used to define the MSE loss function.

(8)E_{\mathrm{M}\mathrm{S}\mathrm{E}}=\frac{1}{n}{\sum }_{k=1}^n{\left(y_k-t_k\right)}^2,

where n indicates the data point number in the data set; y_k represents the true output; and t_k is the output value from the prediction model. To train the DNN model, the loss function should be minimized. The loss is calculated for each sample and then averaged over all samples. The smaller the MSE is, the better the model’s performance becomes.

3 Data collection and preprocessing

Our research utilizes a framework that combines the use of SAP2000v16 software and MATLAB programming loop to gather data sets from FE models. This framework, as depicted in Fig.1, allows us to effectively collect information from a limited sensor number located at specific nodes of the FE model to identify damage in full-scale structures modeled with a large number of degrees of freedom. In the measured modal data, the information of the measured frequencies is typically more precise than the mode shapes, but the mode shapes are sensitive to local damage. Thus, we use both frequencies and mode shapes of a limited number of sensor nodes as input data in the training set of the surrogate model. 80% of the collected data set is used for training, and the remaining 20% is used to evaluate performance. It should be noted that K-fold cross-validation is effective in certain cases and that our data set was randomly generated through simulations, with the data splitting process also being random. Consequently, using K-fold cross-validation may not be necessary in this context, as the random nature of the data already helps to reduce potential bias. Each data point includes an input-output pair generated randomly with regard to the damage element number, locations, and damage severity, with the damage level d in the range of [0,0.5]. To construct a single surrogate model capable of capturing a wide range of potential damage scenarios, we create random failure scenarios for data points using a uniform distribution, and the maximum damage element is set to 4. Furthermore, to replicate the effects of noise, as described in Eq. (5), random error is added to the input data. Before the training phase, the input data are normalized to guarantee an equal contribution among variables in the training model [52]. To collect a large amount of data quickly and efficiently, multiple applications of SAP2000/MATLAB can be executed simultaneously. In the examples, to collect 5000 data points from simulations using a combination of SAP2000 and MATLAB, it would typically take around 2943 s to run the task once. However, a more efficient approach is to run multiple data collection tasks simultaneously. By employing 10 tasks in parallel, each dedicated to collecting 5000 data points, we can gather a total of 50000 data points in a significantly reduced time frame. In optimization-based FE model updating techniques the optimization process loop would require sequential computing to reach an optimal solution and must be executed repeatedly for each scenario. In contrast, our approach uses only a single surrogate model that is trained to predict all potential damage scenarios.

4 Numerical examples

The performance and applicability of the proposed method for damage identification are demonstrated in this section through two numerical examples. To evaluate the accuracy and reliability of our approach, we compare the outcomes obtained using deep feedforward neural networks (DFNN-only fully connected layers) and 1D deep convolutional neural networks (DCNN-1D CNN layers, and fully connected layers) with the actual damage results. Additionally, we investigate the influence of various parameters on the performance of the DCNN model. These parameters include the number of mode shapes and frequencies, activation functions, optimization algorithms, CNN and fully connected architectures. Furthermore, different levels of noise are introduced into the input data to evaluate the capability and stability of models. All simulations are performed on a desktop PC with 16 GB RAM and a 6-core AMD Ryzen 3500 processor running at 3.6 GHz, ensuring a fair comparison. The following sub-sections present a detailed investigation and discussion of the numerical examples.

4.1 Example 1: The large-span industrial steel frame

In this example, we consider a large-span industrial steel frame modeled using the SAP2000 v16 commercial software, as illustrated in Fig.2(a), and that has a 45-m width and an 8-m height. The structure includes 16 elements and 18 nodes as described in Fig.2(b). All elements have an I-shaped cross-section. However, for elements 3, 4, 7, and 8, the height of the section varies with the length of the beam (non-principal). The remaining elements are prismatic rigid beams and columns. The material properties and geometric details of the elements are presented in Tab.1. The first five natural frequencies of the frame, calculated by the SAP2000 v16 commercial software, are 3.482, 3.922, 7.201, 8.595, and 15.097 Hz. Five different damage scenarios are randomly chosen as described in Tab.2. To evaluate the robustness of the models, different noise levels (0%, 2%, and 5%) are introduced into the input data. The predicted outcomes of the DCNN model using noise-free and noisy input data sets are compared to those of the DFNN model and the actual damage for each scenario.

To achieve good performance from the surrogate model constructed by DNN architectures, the relevant hyperparameters are investigated in detail. There are two types of hyperparameters: model-specific and optimizer hyperparameters. The network architecture is designed with model-specific hyperparameters, and the training is handled by optimizer hyperparameters. Selecting appropriate values for these hyperparameters is crucial for achieving a highly accurate training model for any given model and learning algorithm. In addition, weight optimization in a network typically uses batch gradient descent, but model updates can be slow for large data sets. Mini-batch gradient descent, introduced by Hinton [53], can solve this issue by dividing the training set into smaller batches for more efficient error computation and model updates. Depending on the various applications, common mini-batch sizes include 32, 64, 128, 256, etc. The mini-batch size in this investigation is set to 64. The dropout technique is also adopted to prevent overfitting, where 20% of neurons are randomly dropped during training [54].

First, an investigation into two damaged scenarios in the steel-framed industrial structure is conducted in order to establish the appropriate number of measured frequencies and mode shapes. A data set of 20000 samples is collected to train the surrogate model to capture the behavior of the structure. Due to the limited number of measuring sensors, the data set consists of 95 input data points, which include the natural frequency and mode shape signals measured at five different nodes (4, 7, 11, 13, and 15), and 16 output data points, which comprise the signals of the random quantity, location, and severity of the 16 damaged elements. The surrogate model is then trained with default hyperparameters (95-500-16, an architecture with 95 inputs, a hidden layer of 500 neurons, and 16 outputs). Fig.3 demonstrates that to attain an acceptable level of accuracy for the first scenario with a single damaged element, at least the first two frequencies and mode shapes are needed. However, for the last scenario with multiple damaged elements, it can be observed from Fig.4 that the usage of the first 1, 2, 3, and 4 mode shapes in the input data are not sufficient to be able to correctly predict all four damaged elements. The prediction of damage severity is significantly different from the actual damage severity, and there are some false predictions relating to other elements. Only when the first five mode shapes are used, the surrogate model correctly predict all damaged elements (labels 3, 6, 9, 14) and provide the best accuracy for damage severity prediction. It can be determined that the number of first modes employed in the input data set has a significant impact on the precision of the model. To ensure accurate estimation of stiffness reduction damage, the monitored structure’s initial five natural frequencies and mode shapes must be measured.

To determine the appropriate hidden unit number, layer types, and epochs for DNN architectures, this work investigates various combinations. In training DNNs, the MSE loss function serves as the objective. The impact of the hidden layer number and neuron number on the MSE of the surrogate model is demonstrated in Tab.3 and Tab.4. As shown in both tables, the architecture with four hidden layers and 500 neurons per layer (95-500-500-500-500-16) achieves the lowest MSE value compared to other architectures. To get the greatest training process performance, the combinations of activation functions and optimization methods are investigated. The choice of activation function can impact the optimization algorithm as it affects the nonlinearity of the model and can mitigate the vanishing gradient issue. As shown in Tab.5, the findings show that ReLU paired with SGD have the highest MSE value after 10,000 epochs, whereas SeLU combined with Adamax have the lowest MSE value. If only fully connected layers are utilized, the model is referred to as “DFNN” in comparisons. The study then evaluates the parameters of the 1D CNN layer added before the fully connected layers, including the convolution layer number, the size and the number of kernels, through trial and error. Tab.6–Tab.8 display the impact of these parameters on the MSE loss function. It can be seen that the best generalized surrogate model of “DCNN” is obtained with 1 convolution layer, 128 kernels, and a kernel size of 1 × 5. Additionally, the number of epochs also impacts the model’s accuracy, with a minimal number reducing training time but decreasing precision and stability. To examine this, we compare the effect of the epoch number on the surrogate models, as demonstrated in Fig.5 and Tab.7. The MSE convergence history of the prediction model is depicted in Fig.5. The findings show that the loss function value becomes stable as the number of epochs increases. Tab.9 indicates that while the MSE decreases and the training time increases with a higher number of epochs, a good prediction result can still be obtained with 10000 epochs, and the training time remains acceptable. Therefore, the DNN models are trained with 10000 epochs. Furthermore, to ensure these models are suitable for this task, we conduct a comparison between the DCNN and DFNN models with other ML approaches, XGBoost [55], and CatBoost [56]. Tab.10 shows that both the DCNN and DFNN models exhibit superior performance in detecting structural damage. This is attributed to the powerful capabilities of DNN architectures in capturing complex relationships within the signal data derived from structural responses and damage patterns.

The outcomes of damage prediction using the surrogate models with different levels of noise input data for five damage scenarios are presented in Tab.11 and Fig.6–Fig.20. Across all scenarios, the DCNN model outperforms the DFNN network in terms of damage location, quantity, and severity accuracy. This can be attributed to the ability of the CNN layers to effectively extract relevant features for the forecast model. The results in Fig.6 show that both the DCNN and DFNN models give predictions very close to the actual damage in the simple case of only single damage with non-noisy. However, as the noise level increases to 2% and 5%, the accuracy of the DCNN model is higher than the DFNN, as demonstrated in Fig.7 and Fig.8.

As illustrated in Fig.9, Fig.12, and 15 for scenarios 2, 3, and 4, respectively, the accuracy of the DFNN model is inferior to that of the DCNN model when using a noise-free data set. In particular, in Fig.9, the DFNN model performs poorly (18.5% for element 11 and generating wrong alarms at element 16 (15%)). On the other hand, the DCNN model predicts 42.7% damage in that element. Similar results are observed for noisy input data. For the most challenging scenario with four damaged elements (scenario 5), Fig.18–Fig.20 depict the results. The DCNN model accurately predicts the location and severity of all four damaged elements. The damage severity of elements is forecast with great accuracy, with only a relatively small error of 2% at element 6. For the cases of 2% and 5% noisy input data, as depicted in Fig.19 and Fig.20, the DCNN model still accurately locates the damage while closely estimating the severity of damages. In contrast, with 5% noise in the input data, the performance of the DFNN model is low. As seen in Fig.20, the DFNN model fails to detect damage in element 14. This result demonstrates that the DCNN model consistently outperforms the DFNN model in terms of damage quantity, location, and severity, even when various levels of noise are introduced into the input data. Furthermore, the surrogate model uses a very small amount of computation time (less than 1s) for each scenario, allowing a quick and efficient forecast of the location and severity of damage.

4.2 Example 2: The three-dimensional three-story full-scale building

In this example, we investigate a more complex structure, a 3D, three-story full-scale building (with a length of 8 m, a width of 4 m, and a height of 9 m) consisting of 34 frame elements, 78 nodes, and 45 shell elements, as depicted in Fig.21(a). This example assumes a random distribution of structural damage in terms of location and severity, reflecting real-world uncertainties. Additionally, the number of available sensors is limited and sparsely placed across the structure. A FE model is created using the SAP2000 v16 software, and its material and geometrical properties are listed in Tab.12. The first six vibration modes of the full-scale building structures under monitoring are shown in Fig.22. These modes represent the distinct patterns of vibration exhibited by the building under different excitation conditions. Given the exceptional performance demonstrated by the DCNN architecture in the first example, it is utilized as the surrogate model in this instance. For the full-scale 3D three-story building, 50000 samples are collected from 28 nodes (as highlighted in Fig.21(b)). The parameters of CNN-layers, hidden layers, neurons, and epochs are determined through a process similar to that used in the first example. In full connected layers, the architecture used is 6 hidden layers and 1200 hidden neurons in each layer (1200-1200-1200-1200-1200-1200), and the model is trained for 10,000 epochs. The effectiveness and reliability are demonstrated using 5% noisy input data. Five randomly selected damage scenarios are shown in Tab.13. The results predicted by the DCNN model are compared to the actual model in each scenario, both in the absence of noise and with 5% noise level.

The prediction results for each scenario are displayed in Fig.23–Fig.27 and Tab.14. In the first scenario (Fig.23), it is assumed that a structural column denoted as “28” has incurred 20% damage. The DCNN model predicts this damage with high accuracy, achieving results of 20.2% and 20.4% for the noise-free and 5% noise input data, respectively. Next, Fig.24 and Fig.25 display the second and third scenarios and accurate prediction of two damaged elements. Although the addition of 5% noise result in incorrect warnings for elements 11 and 76 at 1.6% and 2.7%, respectively, as shown in Fig.24, it is not a significant issue. In the fourth scenario, three damaged elements and their severity are correctly predicted, as demonstrated in Fig.26. Of particular note is the excellent prognosis of damage to element 31, even with 5% noise level. As depicted in Fig.27, the fifth scenario involves four damaged elements with varying levels of damage severity. The DCNN model performs excellently in identifying damage, both in the noise-free and 5% noisy data, with an acceptable error in estimating the damage severity. These results reveal that the number of damaged elements has an impact on the precision of the prediction model. Regarding the computational cost per scenario, the surrogate model requires more time than required in the case of Example 1, primarily because of the difference in neural network architecture. Nevertheless, the computational cost remains practical for real-world applications, allowing for near-real-time monitoring and decision-making processes.

In conclusion, the outcomes from the five scenarios demonstrate the good performance, applicability, and stability of the proposed method for detecting structural damage with 5% noise model data. A minor error in alarms is observed with an increase in the number of damaged elements and noise levels, highlighting that detecting damage in structures with higher noise levels remains a challenge and requires further research. Overall, this is a promising method for structural damage identification.

5 Conclusions

The study presents a novel approach for damage identification in full-scale frame structures, utilizing a surrogate model trained by noisy and incomplete modal data. The approach overcomes the challenge of limited measurement data for full-scale structures by developing a framework for collecting data sets from a FE model built on the SAP2000 v16 commercial software through a loop of MATLAB programming utilizing SAP2000-OAPI features. The responses from the monitored structures serve as the input for the surrogate model. The parameters of both the CNN layers and fully connected layers have been thoroughly studied to establish a generalized convolutional neural network architecture suitable for use as a surrogate model. The proposed approach is evaluated for its accuracy and reliability under various damaged scenarios and with different levels of noise in the measurement data. The results show that the approach is stable and capable of providing accurate and reliable outcomes under a variety of conditions.

Based on the outcomes, the following important conclusions can be drawn.

1) The proposed approach successfully develops a novel framework for quickly creating data sets, including dynamic responses collected from FE models built on the software SAP2000 version 16 and a MATLAB program through SAP2000-OAPI features.

2) A single surrogate model is used to predict the quantity, location, and severity of damage for all damage scenarios.

3) The number of measured modes has an impact on the efficiency and robustness of the proposed approach. To successfully predict the quantity, location, and severity of damage, the surrogate model requires at least the data of the first five measurement modes.

4) The results demonstrate that the performance of the DCNN models is superior to that of the DFNN models for both incomplete and noisy data.

5) The increase in noise levels of input data impacts the performance of the surrogate models, causing some incidence of false alarms and reducing the precision of damage severity. Further research is needed for high noise-level damage detection.

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