Unsupervised Domain Adaptation Damage Identification Approach of High Arch Dams after Earthquakes

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Introduction
Hydraulic structures are among the primary infrastructure afecting national economy. Te destruction or collapse of these structures due to events, such as strong earthquakes, can result in mass death, injuries, and extremely severe property losses. Accordingly, the formulation of an accurate, efcient, and intelligent damage warning and identifcation model for concrete arch dams is necessary to ensure infrastructure safety.
Structural damage identifcation within the feld of structural health monitoring (SHM) has been garnering increasing attention. Vision-based damage identifcation methods, primarily using image processing techniques (IPTs), have been proposed to redeem the complexities [1][2][3][4][5]. However, hydraulic structures are bulky and a considerable portion of the area is located underwater, making it difcult for vision-based methods to comprehensively detect the structure in a short period of time. Te data-driven damage identifcation method can efectively solve this problem. Te data-driven damage identifcation method focuses on the exploration of monitoring data through statistical pattern recognition [6][7][8][9] (i.e., the search for correlations, not causality). Fundamentally, the method identifes diferent state patterns of the structure according to the probability distribution and evolution law of monitoring data [10][11][12][13]. Presently, the exploration of damage identifcation based on such methods is mainly implemented using small-scale monitoring data. However, performance considering large-scale monitoring data requires further exploration [14]. In terms of statistical process control, damage identifcation methods can be classifed into techniques based on univariate control charts [15] and those that refer to multivariate statistical analysis [16,17]. Under the action of variable coupling environmental loads, the monitoring signals of diferent parts of the arch dam typically have cross-correlations. Hence, a method based on multivariate statistical analysis is more suitable for actual engineering scenarios. With the rapid development of sensing technology and data acquisition systems in recent years, the theory of damage identifcation based on big data has fourished. Moreover, various damage identifcation methods based on deep learning have emerged [18][19][20][21][22][23]. Te foregoing type of damage identifcation typically involves two steps: feature extraction and pattern matching [24]. Damage identifcation methods based on supervised learning have been proven to have satisfactory damage identifcation ability [25,26]. However, such methods cannot derive the monitoring information of structures under various damage modes [27]. Terefore, research in this feld has gradually shifted from diagnoses based on supervised learning to those built on semisupervised and unsupervised learning. Sarmadi and Yuen [28] proposed an unsupervised singular value diagnosis method based on the Foley-Sammon transform of kernel null space that can reduce misdiagnosis in an environment with varying load conditions. Soleimani Babakamali et al. [29] proposed an unsupervised damage identifcation method that is robust to diferent sensor placement schemes. Te method uses previous data obtained by the structural health monitoring system for feature extraction; hence, the training data are deemed as a type of "prior information." Cha and Wang [30] proposed an unsupervised novelty detection-based density peak-based fast clustering algorithm and verifed the advantages of unsupervised learning in the feld of damage identifcation through a laboratory-scale steel structure. Cao et al. [31] proposed a feature extraction method based on unsupervised deep learning and a fast postearthquake damage identifcation model. Tis model solves the problems of low measurement accuracy and poor recognition robustness of manually designed damage sensitive features in actual arch dam engineering. However, for the damage identifcation of arch dams, the "prior information" provided by monitoring data is insufcient.
From a statistical perspective, the measurement threshold for feature classifcation is determined by analyzing the diferences in measurements (such as probability distribution) among multiple sets of data samples. However, due to the limitations of the monitoring system for arch dam, the efectiveness of selecting the measurement threshold may vary in diferent scenarios. In terms of engineering applications, these methods heavily rely on two requirements: highly accurate numerical models and diverse training scenarios. Regarding the frst requirement, it is worth noting that an unsupervised learning model only needs to collect the vibration signal from the intact structure during normal operation. Tis approach avoids the challenges of gathering sufcient training data from various damage scenarios. However, this method is constrained by the lack of damage information in the training data, which makes it difcult to accurately identify the extent of damage. As for the second requirement, when a large hydraulic structure is afected by an earthquake, the emergency department lowers the water level to mitigate the risk of secondary disasters, such as aftershocks and dam swells. However, this change in water level renders the damage identifcation model, based on the normal water level of the intact structure, inefective. In theory, the unsupervised damage detection model constructed using vibration data from the intact structure can only handle a single test scenario. Nevertheless, in practice, there are countless potential test scenarios. Terefore, the unsupervised damage detection model based on the response signal of an intact structure needs to adapt to emerging scenarios.
Tis study combines knowledge-driven and data-driven methods to obtain features that only refect the structure. In terms of feature design, the combination is unafected by the environment. Inspired by transfer learning, the idea of domain adaptation is introduced into the feld of structural health monitoring. Accordingly, a common feature extraction model, the denoising contractive sparse deep autoencoder (DCS-DAE) based on domain adaptation, is proposed.
First, the concept of maximum mean discrepancy (MMD) for constraining the data probability distribution of feature spaces in the source and target domains is fused with the DCS-DAE model under the same framework. Te fusion enables the newly constructed model to exhibit the feature extraction capability of the DCS-DAE model. Moreover, it resolves the problem in which the objective function cannot be applied to other similar scenarios because of the lack of consistency constraints of feature spaces between the source and target domains. Ten, according to the actual operation of the arch dam, four acquisition models of the target domain data are designed with model material error and water level interference considered as uncertain factors. Subsequently, the test results are compared and discussed. Te proposed approach enhances the generalization performance of the unsupervised anomaly detection model in terms of feature design. Te damage identifcation requisites are also extended such that the constructed detection model has the ability to "infer from others." Te confguration of the computer is 16.0 GB RAM and Intel Core i9 CPU@ 3.60 GHz.

Contradiction in Data Volume Gap among Diferent
Scenarios. Te increase in the number of newly devised machine learning-based feature extraction methods relies on a considerable amount of available training data. For general supervised learning, sufcient labeled data are required 2 Structural Control and Health Monitoring [32][33][34]; for general unsupervised learning, sufcient data from the same scene are necessary [35][36][37]. However, in actual large-scale water conservation projects, high-quality data are missing. In some data centers, only training data on a certain scenario (such as the state of structural loss) are available, whereas those on other scenarios (e.g., the state of structural damage) are insufcient. Te damage identifcation method based on unsupervised learning presents an innovative solution to this problem of training data insufciency. However, the output signal characteristics of the structure depend not only on system properties (i.e., state of the structure) but also on system input (i.e., state of the load). Specifcally, for arch dams under normal reservoir operations, the water impounded by the dam is typically stored at a normal water level to proft from dam operation as designed. Moreover, at this water level, the amount of dam vibration data is abundant; the information can be utilized to adjust runof and increase the output of the hydropower station. When the water height is between the constant and dead water levels, the amount of vibration data is large. Under normal reservoir operations, the lowest water level allowed for the reservoir is the dead water level. In particular scenarios, such as during dry years or periods of combat readiness, the lowest water level allowed is the limit dead water level. Tese two types of scenarios are special; hence, the data associated with these two water levels are scarce. Overall, leveraging the vibration data of the structure when the water height is close to the normal level yields greater advantages compared to utilizing data from a diferent water level.

Contradiction between Big Data and Weak Computing.
Te level of water impounded by the reservoir is infnite, and the vibration data of the structure corresponding to other water levels are extremely scarce. Variations in the amount of data under diferent scenarios may be ignored, and the vibration data of the structure at diferent water levels may be assumed sufcient. Nevertheless, constructing multiple anomaly detection models considering variable water levels after an earthquake is unrealistic. Big data require highperformance computing equipment for storage and calculation. However, not every water conservancy project is worth the cost of purchasing expensive computing equipment. Consequently, a contradiction between big data and weak computing exists. In other words, when highperformance computers are not available, the use of massive data to train a model is a hardware problem. An efective approach to solve this problem is the implementation of transfer learning.

Contradiction between Generalized Model and Requisites
of Specifc Scenarios. With rapid developments in sensing, storage, and signal processing technologies, the long-term tracking and processing of the dam body response are no longer a problem. For example, strong-motion seismometers are widely used for monitoring large dams. In the feld of monitoring the health of large hydraulic structures, damage identifcation based on machine learning is a prerequisite because considerable amounts of dam response data are available. First, rapid model building must be possible to satisfy emergency requirements after an earthquake. Second, the model must have strong generalization capability, that is, although the built models may be few, they can be applied to as many scenarios as possible. For traditional machine learning methods, the typical assumption is that newly acquired data follow the same distribution as the original data. However, in structural health monitoring, this assumption is difcult to sustain. In view of this, a well-ftted model is adapted and transformed according to a small amount of data obtained from diferent scenarios. Te model strives to be "unchangeable and adapts to all changes," such that it can be efective for anomaly detection tasks in specifc scenarios.

Domain Adaptation Techniques.
Domain D is the subject of transfer learning and consists of two parts: feature space, X (data), and marginal probability distribution (P (X)). Here, X � x 1 , x 2 , . . . , x n ∈ X represents feld data; it is a type of matrix, where x i represents the i th sample or feature [38]. Te marginal probability distribution, P (X), is a logical concept, and diferent felds can be considered to have varied probability distributions. Because transfer learning is involved, two fundamental domains are considered: source domain (D s ) and target domain (D t ). Transfer is achieved when knowledge propagates from D s to D t .
Correspondingly, task T is the learning target, which also consists of two parts: label space Y and learning function f(•). Te label space of the source and target domains can be expressed as Y s and Y t , respectively, and the class labels of actual samples in the source and target domains can be expressed as y s and y t , respectively. In fact, in most real production activities, the data labels of the target domain are not available, and unsupervised methods are easily extended to supervised methods. Consequently, a key research area in current transfer learning is unsupervised transfer learning. Unless otherwise specifed, the following discussion concerns unsupervised transfer learning. Specifcally, D s � x s i , y s i n s i�1 represents the labeled data of the source domain, where x s i ∈ X s and y s i ∈ Y s . Similarly, D t � x t i n t i�1 represents the unlabeled target domain data, where Consider a given labeled source domain, D s � x s i , y s i n s i�1 (n s is the number of samples in the source domain), and an unlabeled target domain, D t � x t i n t i�1 (n t is the number of samples in the target domain). Te marginal probability distributions for the two domains difer, that is, P s (x s ) ≠ P t (x t ). Te goal of transfer learning is to learn a classifer, f: x t ⟶ y t , by virtue of D s to predict the label (y t ∈ Y t ) [39]. Consider a given labeled source domain, D s � x s i , y s i n s i�1 , and an unlabeled target domain, If the feature spaces of the two felds are the same (X s � X t ), then the label space and conditional probability distribution are also the same, i.e., Y s � Y t and Q s (x s | y s ) � Q t (x t | y t ), respectively. However, the two Structural Control and Health Monitoring domains have diferent marginal probability distributions (P s (x s ) ≠ P t (x t )). Te purpose of the domain adaptation method is to learn a classifer, f: x t ⟶ y t , using the source domain, D s , to predict the label, y t ∈ Y t , of the target domain, D t . Similar to the domain adaptation method, the core of the deep domain adaptation method is to learn a deep neural network, f: x t ⟶ y t , to predict the label, y t ∈ Y t , of the target domain, D t , using the source domain, D s .

Cross-Domain Feature Adaptation.
In this study, the core idea of cross-domain feature adaptation is to transform knowledge from the source domain (i.e., sufcient arch dam vibration data at normal water levels) to the target domain (i.e., insufcient arch dam vibration data at other water levels) for knowledge acquisition. Te structural information obtained from a structure at a certain water level is considered benefcial for acquiring knowledge of the structural state at another water level. In other words, the mechanical nature of damage to the structure at diferent water levels is similar.
Consistency constraints of feature spaces between the source and target domains in the objective function are lacking. Tus, when the data distributions of the source and target domains considerably difer, the feature extractor based on the DCS-DAE model is probably based on data with considerable distribution diferences. Consequently, more data features can be derived, increasing the variation in the original data distribution. As shown in Figure 1(a), reconstruction becomes more problematic [40]. By contrast, cross-domain feature adaptation can use metrics to constrain the data probability distribution of feature spaces in the source and target domains for extracting common features, as shown in Figure 1(b).

MMD in Reproducing Kernel Hilbert Space.
Suppose F is a set of functions (f: X ⟶ R), p and q conform to probability distributions, and two sets of data, X � (x 1 , x 2 , . . . , x m ) and Y � (y 1 , y 2 , . . . , y n ), are independent and identically distributed samples collected from p and q, respectively. Te MMD and its empirical estimation are defned as follows [41][42][43]: where sup f∈F (·) denotes supremum. To measure the difference between two sets of data efectively, the following two requirements are required for the function space, F. (1) When p and q have the same distribution, MMD [F, p, q] is equal to zero. (2) As the size of the observation set increases, MMD [F, p, q] can quickly converge to its expectation. Accordingly, Gretton et al. [44] elaborated on various function spaces and pointed out that when using a unit ball in reproducing kernel Hilbert space (RKHS) as the function space, efective trade-of can be achieved for the two foregoing requirements.
Using the RKHS, equation (1) can be expressed as follows: Tus far, the calculation method for the MMD in the RKHS has been derived. However, the problem is that the mapping, ϕ(x), is not determinable. As presented in the previous section, the kernel function can be imagined as obtained by multiplying the mapping. Te mapping can be determined by obtaining the square of equation (1) and applying the kernel technique to derive the following: If two sets of data, X � (x 1 , x 2 , . . . , x m ) and Y � (y 1 , y 2 , . . . , y n ), are independent and identically distributed samples collected from p and q, respectively, then the empirical estimate of equation (4) can be deduced as

Framework of Model and Objective Function.
Te DCS-DAE is an improved feature extractor based on unsupervised learning [25,31,45], which can realize anomaly diagnosis using reconstruction error and boxplot [46,47] as well as achieve anomaly localization through the weighted K-nearest neighbor algorithm [48]. To improve the abnormal recognition ability of the DCS-DAE model in different structural scenarios, a domain-adaptive DCS-DAE model is proposed. Te overall framework of the model is illustrated in Figure 2, where solid lines represent the training process of the unsupervised domain adaptation technique based on DCS-DAE, while dashed lines depict the testing process of vibration response signals under unknown structural conditions. Te specifc implementation process is shown in Figure 3. Te objective function of the model consists of two parts: the reconstruction error loss of DCS-DAE (J DCS−DAE ) and MMD-based probability of the source and target domains with respect to the consistency constraints (J MMD ) of feature space distribution. Accordingly, the optimization objective function of this model can be expressed as follows: where λ is used to weigh the contributions of J DCS−DAE and J MMD to the objective function.

Training Process and Hyperparameter Settings.
Te cost function of the model is composed of J DCS−DAE and J MMD . First, the calculation and optimization of J DCS−DAE are discussed in this section. Te cost functions of the denoising, contractive, and sparse autoencoders are as follows:  where i and N represent the sample number and total number of samples, respectively; ‖·‖ 2 indicates the L2 norm; J f (x (i) ) represents the Jacobian penalty; ψ is the shrinkage coefcient; λ is the norm weight; β is the sparse rate; and ρ is the sparse target. In the training process, the sigmoid function is used as the activation function for each layer of the network.
Second, the calculation and optimization of J MMD are described. Assume that X s (which has m pieces of data), X t (which has n pieces of data), z l(i) s , and z l(i) t represent the source domain, target domain, output of the l th hidden layer of the i th sample in the source domain, and output of the l th hidden layer of the jth sample in the target domain, respectively.
Accordingly, the MMD-based probability distribution consistency constraint of the source and target domains in the l th hidden layer can be expressed as follows: where ‖·‖ H represents the normal RKHS form. Using the kernel trick, the above equation can be rewritten as     Structural Control and Health Monitoring Te kernel function uses a Gaussian kernel, which is expressed as where σ is set equal to ��� d/2 √ [49] and d is the dimension of the output vector. Note that when updating the parameters (W l E , b l E , W l D , and b l D ), only J l MMD is related to the encoding process. Terefore, In the current unsupervised domain adaptation problem, the selection of hyperparameters remains a difcult problem. Moreover, unifed and standard model parameter selection methods are not available. Terefore, in the model debugging process in this study, each parameter is selected within a certain range. Te parameter selection process for the submodel DCS-DAE can be found in the research results by Cao et al. [31].
As discussed in Section 3.4.1, the parameter λ in equation (6) plays a crucial role in balancing the classifcation loss term and the domain discrepancy term. However, determining the optimal value of λ through validation is not feasible due to the absence of labels in the target domain within the model's framework [50]. To address this, the sensitivity of the parameter λ is explored and a recent approach for parameter selection in unsupervised domain adaptation called deep embedded validation [51] is examined. Figure 4 depicts the target intersection over union (IoU) for Task 4 in the target domain, with varying parameter λ. λ falls within the range of {1, 5, 10, 50, 100, 300, 500, 800, 1000}, allowing for a comprehensive investigation of its infuence across a wide range of magnitudes. Te results show that the IoU follows a bell-shaped curve, where it initially increases with λ, reaches its maximum at λ � 1000, and then decreases as λ decreases. Tis observation can be reasonably explained by the fact that a small λ causes the network to disregard domain discrepancies and focus solely on damage localization in the source domain, resulting in reduced IoU in the target domain. On the other hand, an excessively large λ leads to an emphasis on domain discrepancy loss, which ultimately impairs the network's ability to identify damage. In conclusion, achieving optimal performance in the target domain requires selecting an appropriate value for λ (λ �1000), as both excessively small and excessively large values will result in a decrease in target IoU.

Design of Source and Target Domains.
In this study, to build the framework, a numerical model verifed by experiments is used. Tis verifcation ensures the reliability of the model and is efective in testing the recognition efect of the algorithm on various scenarios of the arch dam. Te Baihetan Dam is a large-span double-curvature arch dam that uses advanced technologies. Te dam has a height of 289 m and is the largest hydropower station in the world; accordingly, it is selected as the research object. In the dynamic calculation, hydrodynamic pressure is applied to the nodes located on the upstream surface of the dam using the additional mass method proposed by Westergaard [52]. Te concrete damaged plasticity (CDP) model proposed by Lee and Fenves [53] is adopted for the dam body. Te sensor layout scheme is designed using the normal cloud mutation-shufed frog leaping algorithm (NCM-SFLA) proposed by Cao et al. [54]. A sensor system consisting of 32 single-axis acceleration sensors (the test direction is along the river) is also integrated, as shown in Figure 5.

Structural Control and Health Monitoring
Four types of target domain models are designed by introducing random structural element stifness and load variation disturbances considering diferent water levels. Ten, diferent monitoring scenarios during the operation of the arch dam are reproduced. For the target domain data to be more consistent with the status of the actual project operation, the operation scenario of the Baihetan Arch Dam is described. Te reservoir starts to store water near the dead water level (765 m) in June until the food control limit level (785 m) is reached. Te food control limit water level was maintained from June to July. Every 10 d, the water level was controlled at 10 m from early August until the water level reached the normal water level (825 m) in early September. Te reservoir supplied water from December to the end of May of the following year with water approximating the dead water level (765 m). Accordingly, the vibration data of the arch dam when the water level was normal were considered as the source domain. Te vibration data when the water was at the food control limit and dead water levels were selected for the two target domains. Te number of samples in each target domain is half the number of samples in the source domain. Tis reproduces the state in which the amount of structural vibration data in some scenarios in actual engineering is low, as listed in Table 1. Te following describes the working conditions of the four target domains.

Target Domain 1.
Te modeling error of the numerical model is reproduced considering the infuence of the heterogeneity of dam material parameters on the vibration response signal owing to factors, such as zonal pouring. Te Baihetan Arch Dam is partitioned according to the portioning method reported in [55], assigning diferent elastic moduli to various regions. Te elastic moduli of materials in the same area may not be uniform during the pouring process. Hence, a slight disturbance is introduced according to the mean value of the elastic modulus of each area to simulate the state of the arch dam in actual engineering. Based on the random feld simulation method of the spatial variability of structural materials [56,57], the dynamic elastic modulus of each area of the arch dam is assumed to conform to a log-normal distribution with a certain mean and coefcient of variation [58]. To simplify the simulation process, autocorrelation distance is ignored. Finally, each element in every area obeys the following material parameter settings: the elastic modulus has a slight disturbance in its interval, and the density is uniform, as shown in Figure 6.

Target Domains 2 and 3.
Te interference of water level loading conditions is considered in these domains. Target domains 2 and 3 are the operating scenarios of the intact structure with uniform material distribution when the water heights are under the food control limit (785 m) and dead water level (765 m) conditions, respectively.

Target Domain 4.
Te heterogeneity of material parameters and interference of water level load conditions are considered together to increase the gap between the source and target domains further. Terefore, target domain 4 represents the vibration data of the dam body at the dead

Test Case Design.
To simulate the damage to an arch dam, typically, the structure is frst divided into zones and then the elastic modulus of each zone is reduced to a fxed value. However, during an earthquake, the damage to each part of the dam is related, and the traditional damage simulation method conceals the actual damage state. Terefore, the equivalent damage model for high arch dams subjected to earthquakes proposed by Chen et al. [59] was adopted in this study. Te advantage of this model is that it can rapidly reverse damage without losing the damage correlation among various parts of the dam body. Te derivation and experimental verifcation of this model are discussed in detail in the literature [59,60], as shown in  Table 2; S-S indicates that the training set is only composed of the data generated by the benchmark model. Te training data, S-T1-S-T4, are composed of those generated by the benchmark model and four revised models. To obtain the vibration information of the arch dam in an actual engineering scene as soon as possible, a multifrequency sine wave with added noise is used as excitation load [23], as shown in Figure 8. Te sampling time for each calculation is 5 s, and the sampling frequency is 200 Hz. Each scene model of the arch dam is calculated 180 and 30 times under intact and damaged conditions, respectively.

Infuence of Model Error on Natural Frequency of
Structure. Wet modal analysis was performed on each domain case to explore the diferences among the four target domains relative to the source domain. Table 3 summarizes the frst fve natural frequencies corresponding to each wet mode of the target domain as well as the frequency diference between the target and source domain models. Te table indicates that the model gap between target domain 1 and the source domain is small. Tis is because the setting of target domain 1 does not consider the autocorrelation distance of material spatial diferences. Although the elastic mode of the material is spatially nonuniform, because the positive and negative disturbances nullify each other, the entire material conforms to the log-normal distribution. Te diference between the source domain and target domains 2 and 3 is considerable, indicating that the change in operating water level has a signifcant infuence on the dynamic response of the arch dam. Te gap between target domain 4 and the source domain model is the largest among all domain cases. Tis is because target domain 4 simultaneously considers the efects of material inhomogeneity and water level changes. Notably, the related results [31] indicate that the spatial randomness of the material has a negligible efect on the mean of the response of each area of the structure; however, the standard deviation of the spatial distribution is considerable. Terefore, the efect of material randomness on the structure cannot be accurately measured based merely on the mode shape. Tis efect can be more directly refected by the standard deviation of the responses.

Data Preprocessing and Evaluation Criteria.
In a real environment, noise is typically caused by many diferent sources. Real noise is assumed to be a combination of many random variables with diferent probability distributions; each variable is presumed independent. Ten, according to   Stifness of damage center decreases by 0%, 20%, 50%, and 80% 30 T4-DS 3 30 the central limit theorem, their normalized sum tends toward a Gaussian distribution with an increase in the number of noise sources. Terefore, to test the resistance of the proposed method to noise, the acceleration signals collected under each test condition are polluted with Gaussian white noise with a signal-to-noise ratio of 4 dB. Before inputting the original acceleration response signal measured in the time dimension into the model for data reconstruction, the input data must be normalized. Tis ensures that the data of each indicator are of the same order of magnitude, thus eliminating the dimensional infuence on the indicators. In this study, the Z-score method was applied to normalize the acceleration response signals measured by each sensor, and 1.5 × IQR [61][62][63][64] was used as the threshold for abnormal warning. An appropriate discrimination index plays an important role in the reliability of model discrimination. Te confusion matrix can evaluate the model from diferent levels, as shown in Figure 9.
In order to comprehensively consider the evaluation efects of precision and recall, F-score is introduced as a model evaluation method. F-score is the harmonic mean of precision and recall, which can be given by Te damage identifcation method in this paper considers that precision and recall are equally important, so F1 score (β � 1) is chosen as the evaluation metric for the model's performance [65]. In addition, in order to comprehensively consider all false positives and false negatives, mean intersection over union (MIoU) is introduced as model evaluation index, which can be given by where k + 1 represents k foreground classes and 1 background class, p ii represents the number of pixels correctly classifed, p ij represents the number of pixels of class i predicted as class j, and p ji represents the number of pixels of class j predicted as class i. Te range of MIoU is from 0 to 1, and a higher value indicates better performance of the model. Note that the core of the proposed method is information reconstruction, and the cross-domain may lead to a reduction in the reconstruction ability of the model. In other words, the model, which is constructed using the source domain data only, considerably enhances the detection of abnormal samples in other domains but signifcantly weakens the model's ability to identify normal samples. To highlight the ability of the model to detect normal samples, the number of normal samples in each domain was designed to be twice the sum of the number of     Figure 10(a). Te F1 score obtained by DCS-DAE in the source domain model is as high as 95.51%. Hence, the model has good diagnostic ability under various damage conditions in this domain. However, the anomaly detection model constructed using source and target domain data also had a considerably high recall value for abnormal samples. In contrast, the recall value for the intact samples of other target domains signifcantly decreased.
In other words, if the data in the source and target domains are concurrently used as training samples, diferentiating between intact and abnormal samples can be easier; the network is constructed through the DCS-DAE model without introducing domain adaptation. Tus, the ability to identify diferent damage conditions in each domain cannot be used as the standard for the successful migration of the model; instead, the ability of the model to identify intact samples must be considered. Te use of F1 score can resolve this problem to a certain extent. As expected, the F1 score obtained by the DCS-DAE in the source domain model was as high as 95.51%; however, the F1 score decreased to varying degrees during anomaly detection in other domains.
Te current DCS-DAE model has a considerably high recall value for the diagnosis of abnormal samples in each domain; Figure 10(b) shows the degradation of the model performance caused by the cross-domain. In target domain 1, as a result of perturbing the stifness of the structural model, the F1 score and recall value for identifying intact samples are only attenuated by 2.38% and 4.44%, respectively. Tis shows that the complete randomness of material space within a certain range has negligible discreteness in the overall response.
In target domain 2, the level of water impounded by the dam is reduced to the food control limit (785 m), which is 40 m lower than that in the source domain. As expected, the F1 score of the DCS-DAE model for recognizing abnormal samples is only 68.44%. Te performance and recall values of recognizing normal samples decrease by 27.06% and 44.44%, respectively, compared with those of recognizing samples in the source domain. Tis phenomenon confrms that the structural features extracted by the DCS-DAE model are related to the water level. In target domain 3, water impounded by the dam is further reduced to the dead water level (765 m), which is 60 m lower than that in the source domain. Te F1 score of abnormal sample recognition and the recall value of normal sample recognition are further reduced. Te extent of attenuation is 36.09% and 66.67%, respectively, compared with that of the source domain. In target domain 4, the F1 score of abnormal samples identifed by the model is only 57.88%. Te attenuation degree of the F1 score for abnormal sample recognition and the recall value of normal sample recognition are 37.63% and 71.11%, respectively, compared with those of recognizing samples in the source domain. Moreover, the IoU of the DCS-DAE without domain adaptation model corresponding to source domain and target domain 1 to target domain 4 is 0.91, 0.87, 0.52, 0.42, and 0.40, respectively. Te MIoU of this model is only 0.55. Te foregoing discussion shows that the anomaly detection model using the DCS-DAE without domain adaptation has certain limitations. In other words, the training data must virtually be in the same scene, and the detection scene must be consistent with the training scene during application. To a certain extent, this restricts the implementation of damage identifcation based on feature extraction in practical engineering.
Te convergence curve of the MMD values of the DCS-DAE model with domain adaptation in the four target domains during the training process is shown in Figure 11. Te trend of the MMD value change curve is similar in each target domain. Specifcally, MMD values start from zero because at the beginning of training, the weights and ofsets in the network are randomly set, resulting in a random output. At this stage, the network cannot extract the characteristics of the source and target domains; consequently, the gap between the two cannot be refected. With an increase in training time, the corresponding MMD values of each target domain improve. Tis is because the main goal of the network at this stage is to extract features refecting the structural health state to the extent possible (i.e., in the trial learning stage). Next, the MMD value gradually decreased because the network gradually extracted the common domain features of the structure corresponding to diferent water levels. Tat is, a set of parameters that gradually render the characteristics of the source and target domain data sufciently similar to achieve the purpose of migration is found. In general, when the MMD value is stable, its convergence values, arranged from high to low, are those from target domains 4, 3, 2, and 1. Tis is consistent with the detection performance attenuation of DCS-DAE without adaptation in the target domain, as shown in Figure 10(b); the greater the model error, the higher the MMD value at the time of convergence.
Te diagnostic capability of the DCS-DAE model based on domain adaptation in the four target domains is shown in Figure 12(a). Te performance diference between the DCS-DAE model (with domain adaptation) and traditional DCS-DAE model (under various evaluation criteria) is presented in Figure 12(

Discussion and Conclusion
In this study, a DCS-DAE model based on domain adaptation is proposed considering the anomaly detection requirements of arch dams under diferent water level conditions in actual engineering scenarios. Te main fndings are as follows: (1) Te anomaly detection method based on the unsupervised learning model of DCS-DAE has a high limit on test conditions, restricting the application of this method to actual arch dam project scenarios. When the water level conditions in the test scenario difer from those in the training scenario, the anomaly detection capability in the test scenario is signifcantly reduced. Te greater the diference between the water level conditions of the test and training scenarios, the worse the anomaly detection performance of the DCS-DAE model.

Data Availability
No data were used to support this study.

Conflicts of Interest
Te authors declare that they have no conficts of interest.

Authors' Contributions
Xiangyu Cao was responsible for methodology, data curation, software, original draft preparation, and funding acquisition. Liang Chen was responsible for conceptualization, data curation, and draft revision. Jianyun Chen was responsible for conceptualization, supervision, funding acquisition, and project administration. Jing Li was responsible for investigation, methodology, and data curation. Wenyan   Lu was responsible for conceptualization, methodology, and software. Haixiang Liu was responsible for conceptualization, supervision, and review and editing. Pengfei Liu was responsible for methodology, software, and draft revision. Minyong Ke was responsible for formal analysis, visualization, and original draft preparation. Yunqing Tang was responsible for conceptualization, funding acquisition, and project administration.