Vulnerability Assessment Method for Immovable Cultural Relics Based on Artificial Neural Networks—An Example of a Heavy Rainfall Event in Henan Province

Cultural relic conservation capability is an important issue in cultural relic conservation research, and it is critical to decrease the vulnerability of immovable cultural relics to rainfall hazards. Commonly used vulnerability assessment methods are subjective, are mostly applied to regional conditions, and cannot accurately assess the vulnerability of cultural relics. In addition, it is impossible to predict the future vulnerability of cultural relics. Therefore, this study proposed a machine learning-based vulnerability assessment method that not only can assess cultural relics individually but also predict the vulnerability of cultural relics under different rainfall hazard intensities. An extreme rainfall event in Henan Province in 2021 was selected as an example, with a survey report on the damage to cultural relics as a database. The results imply that the back propagation (BP) neural network-based method of assessing the vulnerability of immovable cultural relics is reliable, with an accuracy rate higher than 92%. Based on this model to predict the vulnerability of Zhengzhou City’s cultural relics, the vulnerability levels of cultural relics under different recurrence periods of heavy rainfall were obtained. Among them, the vulnerability of ancient sites is higher than those of other cultural relic types. The assessment model used in this study is suitable for predicting the vulnerability of immovable cultural relics to heavy rainfall hazards and can provide a technical means for cultural relic conservation studies.


Introduction
China is among the countries with the greatest number of cultural relics. According to a report produced by the Third National Cultural Relics Census Project, China has more than 766,700 immovable cultural relics, including 5,058 National Key Cultural Relic Protection Units and 55 World Cultural Relics (Li 2022). Immovable cultural relics are extremely important, both in terms of their significant share in cultural relics and their uniqueness, representativeness, and cultural values (Lv 2013). In the past few decades, the frequency of major hazard occurrences and their associated losses have increased globally. Washouts caused by heavy rainfall have caused different degrees of impacts on various types of immovable cultural relics, which seriously threaten the protection and heritage of cultural relics. Some important cultural relics have been damaged or destroyed, resulting in partial damage or complete loss of their historical, artistic, and cultural values. Therefore, quantitative assessments of the vulnerability of cultural relics will enable conservation authorities to conduct efficient and timely conservation measures for vulnerable cultural relics.
The historical hazard-based approach has high requirements for historical hazard data in each study area and can be used only for comparative analysis between regions from the results. This approach is usually used in largescale study areas, and it is difficult to assess individual objects.
The indicator system method is simple to use and does not require much data, but the method is highly subjective, while the determination of weights is the most subjective aspect of the whole assessment process (Goyal et al. 2021). Commonly used weight determination methods, such as the expert scoring method (Liang et al. 2021) and the analytic hierarchy process (AHP) method (Huang et al. 2019;Moghadas et al. 2019;Zhang, Shen et al. 2021), are subjective and can lead to large errors in the final assessment results.
Hazard damage curves, also known as vulnerability curves, assess the relationship between the intensity of a hazard and the degree of damage to the hazard-affected elements (Zhang, Wang et al. 2021). This method can infer vulnerability results for an entire region by assessing the degree of damage to individual features but is not applicable for assessing objects such as cultural relics, which are different from each other.
Vulnerability to disasters refers to the magnitude of potential damage caused by disasters to socioeconomic systems. In previous studies, machine learning methods have often been used directly to assess the disaster vulnerability. It has the ability to provide good vulnerability predictions by training with large amounts of data, but related studies are still relatively preliminary, and there is no precedent in previous studies for using cultural relics as the assessment objects.
In summary, these vulnerability assessment methods have the following problems: (1) Most methods are suitable for vulnerability assessments of large-scale regional conditions but are not applicable to single objects such as cultural relics. The regional vulnerability does not accurately represent the vulnerability of cultural relics.
(2) The weights used in most of these methods are generally based on expert scoring or AHP methods, which are subjective.
(3) Most of these assessment methods cannot predict the future vulnerability of cultural relics and cannot simulate the vulnerability of cultural relics under different hazard intensities.
(4) Machine learning methods have not been applied to cultural relics.
To fill the gap in the quantitative research of cultural relic vulnerability and to solve the problem that the four listed methods are subjective, not applicable to single objects, and not predictive, this study proposed a vulnerability assessment method based on a back propagation (BP) neural network for cultural relics and provides new ideas for the conservation of immovable cultural relics.

Study Area and Data
Henan Province is located in central China, with a total area of 167,000 km 2 . The terrain is high in the west and low in the east, and mountains and hills account for more than 40% of the total area of the province (Zhao et al. 2010). According to the Third National Cultural Relics Census, there are 65,519 immovable cultural relics in Henan Province, accounting for about 10% of the national total, including 14,607 ancient sites, 23,921 ancient buildings, and 693 caves and stone inscriptions (Zhu 2017). Among them, there are 417 immovable cultural relics at the national protection level.
Most areas of Henan Province have a warm temperate climate, and the southern part of the province straddles the subtropical zone, which has a continental monsoon climate from the northern subtropical zone to the warm temperate zone. There are four distinct seasons, with rain and heat at the same time and complex, diverse, and frequent meteorological hazards.
From 17 to 23 July 2021, Henan Province was subjected to historically rare and extraordinarily heavy rainfall, which triggered serious flooding in the north-central part of the province. This heavy rainfall covered numerous areas and caused damage to 150 counties and 1663 townships. Zhengzhou City is the capital of Henan Province. It is located in the north-central region of the province and accounted for 95.5% of the deaths and missing people in the province due to this heavy rainfall event. In addition to museums and unclassified immovable cultural relics, 563 cultural relics in Henan were affected by this heavy rainfall. Among the affected cultural relics were 470 cultural relic buildings (ancient buildings and important historical sites and representative buildings in modern times), 60 ancient sites and burial sites, 14 cave temples and stone carvings, and 19 museums. The location of the state-protected immovable cultural relics and the 18-21 July 2021 storm rainfall distribution in Henan are shown in Fig. 1. Most of the nationally protected immovable cultural relics are located in the central and northern regions of Henan, with fewer relics in the southern and eastern and western regions. In terms of rainfall, the north-central areas, such as Zhengzhou and Jiaozuo, experienced the most severe rainfall that overlapped with the areas where cultural relics are concentrated.
The rainfall data used in this study were obtained from the hourly precipitation data of the China Meteorological Station Network, and the average daily rainfall was derived by averaging the total daily rainfall from 18 to 21 July 2021. Basic information regarding the immovable cultural relics and damage information were mainly obtained from the survey and assessment report of the Chinese Academy of Cultural Relics for this rainfall event. This report was based on a survey conducted by professionals of ancient architecture, cave temples and rock carvings, ancient sites, and archaeology. The survey covered cultural relics in the central and northern regions of Henan Province. According to the survey result, there are 417 affected, nationally protected cultural relics, including ancient buildings, ancient sites, ancient tombs, cave temples and stone carvings, and important historical sites and representative buildings in modern times. Detailed records of their names, locations, types, protection levels, and specific damage are included in the survey report. The data used in this study are listed in Table 1.

Back Propagation (BP) Neural Network and Verification
Before using BP neural network for vulnerability assessment, the indicators need to be selected first to determine the training data of the assessment model. In this section, the process of vulnerability assessment using BP neural network and the computational principles of this neural network are introduced.

Research Framework
The vulnerability assessment method for immovable cultural relics using machine learning is divided into three parts: (1) index selection; (2) model construction and training; and (3) vulnerability assessment. The technical process is shown in Fig. 2.

Factors of Vulnerability
The vulnerability of cultural relics, which refers to the tolerance of cultural relics to damage caused to their structures, materials, and the environments in which they are located, indicates their state under hazard threats (Chen et al. 2009;Zhang et al. 2015). Considering the characteristics of immovable cultural relics and computational feasibility, we analyzed the vulnerability of cultural relics when affected by the following factors.

Materials used in Cultural Relics
Immovable cultural relics include ancient buildings, ancient sites, ancient tombs, cave temples, stone carvings, and important historical sites and representative buildings in modern times. Different materials are used in the  construction of different cultural relics-for example, most stone carvings and bridges are made of stone, some towers and houses are made of brick, and some temples are made of wood. Different materials have different degrees and probabilities of damage after being impacted by heavy rainfall, so the materials of cultural relics are taken as an influencing factor in the vulnerability assessment. Immovable cultural relics were classified into nine categories based on the construction materials used: earth, wood, brick, stone, wood and stone, earth and stone, earth and wood, brick and wood, brick and stone, and brick and earth. Individual relics with mixed and complex materials were classified into the group that represented the predominant material used in their construction.

Age of Cultural Relics
The ages of the immovable cultural relics vary. Therefore, the length of time they have survived to date varies. Most immovable cultural relics are located in open air environments-the older they are, the more storms and hazards they have experienced and the more problems they may have with their materials and structures due to age and disrepair. The immovable cultural relics in Henan Province come from many eras, including the Xia (2070-1600 BCE), Shang (1600-1046 BCE), Ming (1368-1644), and Qing (1636-1912) Dynasties and the Neolithic period (ca. 7000-1700 BCE). It is important to use the relic ages as an indicator in their vulnerability assessment.

Stability of Cultural Relics
The stability of cultural relics is an indicator used to determine whether there is a risk of collapse and loss. This indicator has a strong connection to the location, environment, structure, hazard, and other important factors of each relic. Some of the cultural relics that are affected by heavy rainfall have sinking foundations, building tilt, and cliff instability. Because structural or carrier instability greatly affects the level of vulnerability of cultural relics, we chose the stability of cultural relics as an important indicator to assess their vulnerability.

Affected Parts of Cultural Relics
Cultural relics have special properties, and different categories of cultural relics are built in different ways. Many cultural relics, such as cave temples and stone inscriptions, are built on cliff walls, and their carriers are the cliff walls. As another example, some cultural relics have annexes established around them. When these carriers and ancillary facilities are affected by hazards, they also have a certain impact on the cultural relics. Thus, the affected parts are divided into six categories depending on the affected structure: body, body and carrier, body and ancillary facilities, all three (body, carrier, and ancillary facilities), carrier, and ancillary facilities.

Hazard Intensity
When assessing the vulnerability of immovable cultural relics during natural hazard occurrences, their vulnerability and the intensity degree of the hazard have a strong link. For the extreme rainfall event of 2021 in Henan Province, the average daily rainfall in Henan from 18 to 21 July was selected as an indicator to assess the intensity of the damage. An average rainfall amount greater than 100 mm is considered severely impactful, 50−100 mm is generally impactful, and less than 50 mm is slightly impactful.

Back Propagation (BP) Neural Network
A BP neural network uses an error back propagation algorithm, a multilayer structured mapping model, which is the most widely used among neural network algorithms (Hu 1994). A BP neural network has strong nonlinear mapping abilities, the numbers of layers and neurons can be arbitrarily set, and its application in function approximation is also suitable for the training of immovable cultural relic vulnerability. Therefore, a BP neural network method using a sigmoid function in the Python language was chosen to assess the vulnerability of immovable artifacts.

Basic Principle of the Back Propagation (BP) Neural Network
The BP neural network model contains an input layer, a hidden layer, and an output layer with corresponding weights between each node called connection weights (Jiao 1992).
The principle consists of calculating the value of each node according to the given functional relationship when training the network and to continuously update the weights to cause the results to be infinitesimally close to the expected values according to the error analysis between the results of each training run and the expected results (Hu 1992).

Training Process of the Back Propagation (BP) Neural Network Training Process
The learning process for the BP neural network is divided into forward propagation and backward propagation. The output is calculated by forward propagation, and the error signal is connected and returned by backward propagation, which is continuously iterated to minimize the errors. Let the neural network input values be X (x 1 , x 2 , x 3 ......x i ) and the number of neurons in every layer be l, m, n. The activation function of each layer uses the sigmoid function, and the errors are calculated as follows (Hu 1992;Jiao 1992;Hu 1994): (1) Input layer error: where f(net j ) is the activation function of the neurons in the input layer, w jk is the connection weight of the (1) 2 output layer to the hidden layer, v ij is the connection weight of the input layer to the hidden layer, and x i is the input value.
(2) Hidden layer error: where f(net k ) is the activation function of the neuron in the hidden layer, w jk is the connection power between the output layer and hidden layer, and y j is the output value of the input layer.
(3) Output layer error: where d is the actual value of the output layer, O is the predicted value of the output layer, and l is the number of nodes in the output layer.
The connection weights of each layer are updated by calculating the obtained errors, which means using the back propagation process. The input layer, hidden layer, and output layer each has many layers. We use "out" to represent the output value of each part, "net" to represent the input value of each part, subscript "o" to represent the part of the output layer, subscript "h" to represent the part of the hidden layer, and subscript "n" to represent the number of layers in each part. For example, "out o1 " represents the first output value of the output layer, and "out h1 " represents the first output value of the hidden layer.
Suppose that out on (n = 1,2, …) is an output value with an error of E on . Its corresponding weight to be updated is the weight, w, between the hidden layer and the output layer. The output layer input value is net on . Then, we have where net on is the result of the implicit linear calculation, out on is the predicted value of the output, E = E o1 + ⋯ + E on , out hn is the implicit output value, and d is the actual value. Then, Therefore, the updated error, w , is calculated as where η is the learning rate. (2)

Back Propagation (BP) Neural Network-Based Vulnerability Assessment of Cultural Relics
The training of a machine learning model requires parameter adjustment and verification. The type of data used in the model must be in digital form. This section introduces the value assignment criteria of each indicator and the process of model training and verification.

Construction of a Neural Network for Vulnerability Assessment
Based on the above-analyzed factors that influence the vulnerability of immovable cultural relics, materials used in cultural relics, ages of cultural relics, stability of cultural relics, affected parts of cultural relics, and hazard intensity are used as the assessment indicators of vulnerability. Through qualitative analysis of the storm damage reports of cultural relics, the vulnerability was classified into five levels: highest, high, medium, low, and lowest. The assessment criteria for each grade are listed in Table 2. Furthermore, experts from the Chinese Academy of Cultural Relics conducted a field survey of the affected cultural relics in Henan Province, and graded the vulnerability of the affected cultural relics in the province according to the grading criteria ( Table 2). The grading results are shown in Fig. 3, and we use them as output data in the subsequent model training.
Among the five indicators of vulnerability, the age of cultural relics and the intensity of the hazard are numerical indicators, which can be used for direct training after normalization. The normalization method is shown in Eq. 7.
where x ij and y ij are the original and standard values of the indicators, respectively; max(x ij ) refers to the maximum value of the indicator and min(x ij ) refers to the minimum value of the indicator.
Relic material, relic stability, and affected parts of the relic are text-based indicators and their values are assigned. To ensure correctness of the calculation results, the range of the assigned values was set to between 0 and 1. According to the ability to withstand rain, relic materials of stone, brick and stone, wood and stone, earth and stone, brick, brick and wood, brick and earth, earth and wood, wood, and earth were assigned values of 0.1−1 with an interval of 0.1. For the affected parts indicator, the body, body and carrier, body and ancillary facilities, all three (body, carrier, and ancillary facilities), carrier, and ancillary facilities were assigned values of 1, 0.8, 0.6, 0.4, 0.2, and 0.1, respectively. To train the neural network, the above indicators were used as the input to the neural network. The results of the qualitative The building structure is intact, with partial roof leakage, and a few cracks in the walls Less than 10% of the site proper is affected; important structures are slightly affected The body of the artifact is relatively well preserved with minor local damage that does not affect the overall stability

Lowest
The building as a whole is well preserved, with only localized leaks and minor cracks in individual walls Part of the structure is slightly damaged; an important structure is not damaged The body of the artifact is preserved intact, part of the carrier is slightly damaged, which does not affect the structural stability of cultural relics vulnerability assessment (Fig. 3) were used as the output of the network, with 1, 0.8, 0.6, 0.4, and 0.2 representing the levels of vulnerability: highest, high, medium, low and lowest, respectively. The vulnerability neural network model for immovable cultural relics is shown in Fig. 4.

Neural Network Model Training and Testing for Vulnerability Assessment
A dataset of 417 nationally preserved immovable cultural relics affected by the extreme rainfall event in July 2021 was selected as the sample set. We used the HOLD OUT method (Wang et al. 2016;Simonis et al. 2021;Sowell and Sengupta 2021) to divide them; 250 immovable cultural relics were used as the training set, 84 immovable cultural relics were used as the validation set to tune the model parameters, and the remaining 83 relics were used as the testing set to evaluate the performance of the trained model. We chose a simple random sampling method to sample the data and ran the assessment model on Jupyter using the Python language. To obtain the most accurate assessment results, we continuously adjusted the parameters, and the model parameters were finally determined as follows. The training process adopted a 5 × 8 × 1 network structure. Using the gradient descent method to update the weights and thresholds, the learning speed was set to 0.1, the initial iteration number was set to 1,000, and training ended when the mean square error value was less than 0.1e-6. The confusion matrix of the training model is shown in Fig. 5. The diagonal of the confusion matrix represents the number of cultural relics for which the vulnerability prediction was the same as the actual value. We can see that among the 84 immovable cultural relics in the validation set, the vulnerability level was correctly predicted for 78 of them, with an accuracy of 92.85%. For the six incorrect predictions, the predicted grades and actual grades differed by no more than one grade. The vulnerability assessment model based on the BP neural network is reliable, and the prediction results are accurate.
To further determine the above-unbiased estimates for evaluating the performance of the model, the testing set is necessary. The testing set selected in this study contains 83 immovable cultural relics, and the values of their vulnerability indicators are input into the trained assessment model as input data to obtain the vulnerability assessment results. Of the 83 immovable cultural relics in the testing set, a total of 77 have the same predicted vulnerability levels as the actual levels. This means that the accuracy of the assessment model reached 92.77%. It indicates that the above vulnerability assessment model based on the BP neural network produces accurate results, and we can use it in the vulnerability assessment of immovable cultural relics.

Vulnerability Prediction of Immovable Cultural Relics under Different Rainfall Recurrence Periods
The recurrence period is the average interval between the occurrence of rainfall equal to or greater than a certain storm intensity within a certain, long statistical period (Wei et al. 2018), which usually uses years as the unit of measure. To predict the vulnerability of immovable cultural relics during future rainfall events to improve the protection of highly vulnerable cultural relics in a targeted manner and to facilitate the reduction of the loss of cultural relics under rainfall hazards, this study predicted the vulnerability of immovable cultural relics under different rainfall recurrence periods based on the above vulnerability assessment model. Since Zhengzhou City was the area most severely affected by this rainfall event in Henan Province, this study took the immovable cultural relics in Zhengzhou as an example to provide vulnerability predictions for different rainfall recurrence periods. The rainfall intensities for different recurrence periods of heavy rainfall in Zhengzhou have been studied by Wang et al. (2022), who obtained the rainfall intensities at Zhengzhou meteorological station by fitting the P-III distribution for different recurrence periods based on the year-by-year maximum daily precipitation series at the station from 1951 to 2020. Therefore, we do not elaborate on the calculation process for rainfall intensities with different recurrence periods here. The intensities of heavy rainfall for different recurrence periods at Zhengzhou is shown in Table 3.
We replaced the hazard intensity in the vulnerability assessment with the rainfall intensity for each of the 10 recurrence periods, and used the trained assessment model to predict the vulnerability of immovable cultural relics in Zhengzhou. The results are shown in Fig. 6.
There are 82 immovable cultural relics in Zhengzhou City. From the vulnerability prediction results (Fig. 6), we can see that for a 5-year recurrence period, 19 cultural relics have a vulnerability rating of "High," and 5 cultural relics have a vulnerability rating of "Medium," accounting for 29.27% of all cultural relics. For a 10-year recurrence period, 19 cultural relics have a vulnerability rating of "High," and 9 cultural relics have a vulnerability rating of "Medium," accounting for 34.15% of all cultural relics. For a 20-year recurrence period, 20 cultural relics have a vulnerability rating of "High," and 9 cultural relics have a vulnerability rating of "Medium," accounting for 35.36% of all cultural relics. For a 30-year recurrence period, 20 cultural relics have a vulnerability rating of "High," and 12 cultural relics have a vulnerability rating of "Medium," accounting for 39.02% of all cultural relics. For a 50-year recurrence period, 25 cultural relics have a vulnerability rating of "High," and 8 cultural relics have a vulnerability rating of "Medium," accounting for 40.24% of all cultural relics. For a 100-year recurrence period, 29 cultural relics have a vulnerability rating of "High," and 7 cultural relics have a vulnerability rating of "Medium," accounting for 43.90% of all cultural relics.
There are no immovable cultural relics in Zhengzhou with a vulnerability rating of "Highest" for 5-to 100-year recurrence periods and the percentage of highly vulnerable cultural relics does not exceed 50%. When the recurrence period of a rainstorm is 200 years, there are 3 cultural relics with a vulnerability level "Highest," 30 with vulnerability level "High," and 6 with vulnerability level "Medium," accounting for 47.56% of all cultural relics. When the recurrence period of the rainstorm is 300 years, there are 4 cultural relics with vulnerability level "Highest," 32 with vulnerability level "High," and 5 with vulnerability level "Medium," accounting for 50% of all cultural relics. When the recurrence period of the rainstorm is 500 years, there are 4 cultural relics with vulnerability level "Highest," 34 with vulnerability level "High," and 4 with vulnerability level "Medium," accounting for 51.22% of all cultural relics. When the recurrence period of the rainstorm reaches 1,000 years, which was the hazard intensity of the July 2021 rainstorm event in Henan Province, there are 6 cultural relics with vulnerability level "Highest," 33 with vulnerability level "High," and 5 with vulnerability level "Medium," accounting for 53.66% of all cultural relics.
In summary, the number of cultural relics with high vulnerability increases as the storm recurrence period increases, and Fig. 6 shows that the vulnerability of cultural relics is generally higher in the central and northern areas of Zhengzhou and lower in the western areas. In addition, we found that even when the storm recurrence period reached 1000 years, there were still cultural relics with a vulnerability level of "lowest." This is because we changed only the hazard intensity indicator in our predictions, while the 1 3 vulnerability of cultural relics is related to factors in addition to the intensity of the hazard-their properties cannot be ignored. From the perspective of immovable cultural relic types, the vulnerability of ancient sites is generally higher, and the vulnerability of cave temples and stone carvings is lowest in comparison. For each recurrence period, most of the highvulnerability cultural relics are ancient buildings.

Discussion
The vulnerability assessment model proposed in this study addresses immovable cultural relics in response to the scarcity of vulnerability-related research on cultural relics. The application of machine learning to vulnerability assessment provides new ideas for vulnerability-related research. Vulnerability assessment research methods such as weighted synthesis, expert scoring, and AHP are subjective, and determination of weights or expert assessment results are often difficult to separate from human assessments. In contrast, in the BP neural network used in this study, the values of the weights are determined by an algorithm based on the training results of the data, which largely decreases errors caused by the influence of human subjectivity.
In previous studies (Sun 2021), data on cultural relics were mostly derived from survey data, and the damage states of cultural relics were generally determined based on the text form of the report. However, it is difficult to clearly represent the vulnerability of cultural relics in this way, and it is also more difficult to combine the results with disaster risk studies. Therefore, this study used survey reports to quantify the damage information obtained by researchers so that relevant calculations could be performed and clear results could be obtained to classify the vulnerability levels. In addition, the assessment model used in the study can make preliminary predictions for cultural relics with unknown damage. This not only reduces the manpower consumed by personnel to investigate relics one by one but also provides a reference for some studies where it is difficult to obtain data on damage to cultural relics. The vulnerability assessment model presented in this article is not limited to cultural relics in Henan Province but can be used for immovable cultural relics in other provinces and regions as well. If the field of cultural relic conservation uses our model as a reference, combined with weather forecast data, the model can determine in advance what the most vulnerable cultural relics are to prepare for timely protection. In addition, due to the climate, the amount of rainfall varies greatly from season to season, and rainfall is usually more frequent in summer, so the vulnerability of artifacts is higher in summer compared to other seasons. In terms of the types of cultural relics, most of the high-vulnerability cultural relics are ancient sites and buildings, while cave temples and stone carvings are relatively less vulnerable, so in the face Fig. 6 Prediction results for cultural relic vulnerability for different recurrence periods (5 years to 1000 years) of heavy rainfall in Zhengzhou City, Henan Province.
1 3 of heavy rainstorm hazards, ancient sites and ancient architectural relics need to be protected in a focused way.
There are still shortcomings in the methodology used in this study because the proportions of different types of cultural relics in Henan Province vary greatly-with more ancient buildings and sites and fewer cave temples and stone carvings-which can lead to a less balanced sample and ultimately greater errors in the assessments of cave temples and stone carvings. To obtain a more accurate assessment model, we will subsequently attempt to collect more data on the damage to cultural relics.

Conclusion
In this study, a vulnerability assessment model for immovable cultural relics was constructed based on the extreme rainstorm event that occurred in Henan Province in July 2021. A BP neural network was used to train the model used to assess the vulnerability of immovable cultural relics to rainstorm hazards. After verification, the accuracy of this model was high. Following this, immovable cultural relics in Zhengzhou City were used as examples, and the assessment model was used to predict their vulnerability for different rainstorm recurrence periods. The main findings are: (1) With the confusion matrix, we obtained an accuracy rate of 92.77% for this assessment model. This suggests that vulnerability assessments based on BP neural networks are more accurate than assessment based on other methods. (2) We found that the vulnerability of immovable cultural relics in Zhengzhou has a trend of high in the middle and low on both sides for all recurrence periods. The proportion of highly vulnerable relics increases with longer recurrence periods. (3) Under heavy rainstorm hazards, the vulnerability of ancient sites is generally higher, and the vulnerability of cave temples and stone carvings is lower.
For immovable cultural relics, the BP neural network model-based vulnerability assessment method is more accurate than other assessment methods but still has room for improvement. If we can obtain more data, more indicators related to cultural relics and hazards can be added to the indicator system so that assessments could be improved further.
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