A Systematic Analysis of Influencing Factors on Wind Resilience in a Coastal Historical District of China

Abstract

Historical districts are the mark of the continuity of urban history and are non-renewable. Typhoon disasters rank among the most serious and frequent natural threats to China’s coastal regions. Improving the wind resilience of China’s coastal historical districts is of great significance for their protection and inheritance. Accurately analyzing the different characteristics of the influencing factors of wind resilience in China’s coastal historical districts can provide a theoretical basis for alleviating the damage caused by typhoons and formulating disaster prevention measures. This paper accurately identifies the main influencing factors of wind resilience in China’s coastal historical districts and constructs an influencing factor system from four aspects: block level, building level, typhoon characteristics, and emergency management. An IIM model for the systematic analysis of influencing factors of wind resilience in China’s coastal historical districts based on the Improved Decision Making Trial and Evaluation Laboratory (IDEMATEL), Interpretive Structural Modeling (ISM), and Matrices Impacts Croises-Multiplication Appliance Classement (MICMAC) methods is established. This allows us to explore the mechanism of action of internal influencing factors of typhoon disasters and construct an influencing factor system, in order to propose prevention measures from the perspective of typhoon disaster characteristics and the overall perspective of China’s coastal historical districts. The results show that the driving force of a building’s windproof design in China’s coastal historical districts is low, but its dependence is strong; the driving forces of block morphology, typhoon level, and emergency plan are strong, but their dependence is low. A building’s windproof design is a direct influencing factor of the wind resilience of China’s coastal historical districts; block morphology, typhoon level, and emergency plan are the most fundamental and key influencing factors of the wind resilience of China’s coastal historical districts.

1. Introduction

Historical districts are historical areas of a certain size in a city. They not only have precious cultural relics and historical buildings but can also more realistically reflect the traditional patterns and historical features of the local characteristics and inherit the cultural context of the city [1]. Historical districts in different regions face different challenges in the process of their protection, such as natural disasters and human destruction. Historical districts in China’s coastal areas are more frequently attacked by typhoons than inland areas [2,3]. Typhoons affect China’s coastal areas to varying degrees for three quarters of the year, especially from July to September, which is a typhoon-prone period. Hainan, located on the southeast coast of China, is situated in a low-latitude region where the surrounding sea temperatures are relatively high. This creates favorable thermal conditions for the formation of typhoons [4]. This warm marine environment is the basis for the formation of typhoons and is also one of the areas where typhoon disasters are prone to occur and are most severely affected. Especially in the coastal areas of Hainan, typhoons usually cause serious damage to the buildings and facilities in historical districts. Thus, studying the factors that influence the wind resilience of historical districts in Hainan’s coastal areas, which are susceptible to typhoons, holds significant theoretical and practical value for their protection.

In recent years, scholars have increasingly focused on disaster resilience, making notable progress in this field of study. However, much of the existing research focuses on theoretical frameworks and resilience evaluation, with few studies delving into the root causes of resilience and the pathways through which influencing factors interact. For instance, You et al. [5]. utilized the entropy method to examine urban resilience and its influencing factors. Similarly, Yu et al. [6] used the Analytic Hierarchy Process (AHP) and Criteria Importance Through Inter-criteria Correlation (CRITIC) method to evaluate the fire resilience of ancient buildings. Croce et al. [7] analyzed the systematic approach of sustainable urban response to climate from the perspective of urban planning, thereby improving urban resilience, while Jiao et al. [8] identified the key influencing factors for station resilience against heavy rain disasters using the Interpretive Structural Model method (ISM) with the Social Network Analysis method (SNA).The ISM method can make up for the shortcomings of the above research and give full consideration to the interaction between various factors, but it ignores the determination of key factors. Most research methods on influencing factors in the existing literature struggle to effectively identify key factors and their pathways of influence. Currently, limited research has addressed wind resilience specifically in the context of historical districts. Existing studies tend to focus on the impacts of typhoons on individual historical buildings, communities, or villages in coastal regions, rather than on integrated historical blocks. Jin et al. [9] examined historical villages and dwellings in the Leizhou Peninsula, one of mainland China’s most typhoon-prone regions, to explore adaptive design strategies for coping with typhoon climates. Their study proposed practical measures to enhance the wind resilience of historical settlements in coastal areas vulnerable to such extreme weather events. Taleb et al. [10] assessed the vulnerability of traditional wooden houses in Madagascar’s eastern coastal regions to extreme wind events and developed a model to evaluate their wind-related structural weaknesses. Mazumder et al. [11] developed a comprehensive framework to assess the resilience of coastal communities under various hurricane scenarios, considering both social and physical dimensions. By simulating potential damage and economic losses to community infrastructure, the framework supports decision-makers in formulating strategies to enhance the resilience of these vulnerable areas. Because of the complex interplay of factors influencing wind resilience in coastal historical districts, few studies have adopted a systematic, integrated approach to analyze these elements. As a result, the depth and focus of existing research in this area remain limited [12,13,14,15,16,17,18,19,20,21,22,23,24,25]. In view of this, in order to effectively clarify the influencing factors and action paths of wind resilience of China’s coastal historical districts, this study evaluated the impact intensity of the factors affecting wind resilience of China’s coastal historical districts, and clarified the internal connections and hierarchical structures among the factors, so as to provide corresponding suggestions in order to improve the wind resilience of China’s coastal historical districts.

In order to accurately identify the main influencing factors of the wind resilience of China’s coastal historical districts, this study proposed the IDEMATEL method based on the Decision Experimentation and Evaluation Laboratory (DEMATEL) method. DEMATEL is a method used to solve system factor analysis. The principle of this method is to combine graph theory with matrix theory to judge the importance of each factor in the system [26]. The core of improving the DEMATEL method is to select more reasonable research indicators to establish a more convincing set of influencing factors. The process for the method improvement is as follows: First, preliminary indicator data is collected through the Web of Science and Science Direct databases, and the indicators that appear frequently in related studies are summarized. Then, a two-round expert questionnaire survey method is used to score the indicators, and the reliability and validity tests of the expert scoring results are performed to screen the indicators and determine the final set of influencing factors. In this way, the dominance (centrality) of each influencing factor in the wind resilience of historical districts is explored, and the influencing factors are divided into two categories: causal factors and result factors. Then, the hierarchical structure diagram between the factors is drawn using the ISM method, and the dependency and driving force of each factor are analyzed using the MICMAC method. The influence relationship between the factors and between the factors and the system is visualized, and the results are compared with those obtained by the traditional DEMATEL method and cluster analysis method to verify the reliability and accuracy of the model.

Drawing on the distribution patterns of typhoon disasters affecting China’s coastal historical districts and a statistical analysis of contributing factors, this study develops an IIM model. The Yazhou Qilou Historical District in Sanya City, Hainan Province, serves as the case study. The operation process of the IIM model established in this study is as follows: the relationship matrix between the factors in the system is established by the IDEMATEL method, and then the centrality and causality between the factors are calculated to judge the importance of each factor in the system. Then the ISM method is used to obtain the relationship between the factors, and it is used as the basis for the relationship judgment of the MICMAC method, and finally the influencing factors of wind resilience in China’s coastal historical districts can be obtained. This follows the idea of “key influencing factor identification/construction of influencing factor analysis model/analysis of influencing factors and preventive measures”, as shown in Figure 1. This study uses the IIM model to identify the relationship between the influencing factors of wind resilience in China’s coastal historical districts and the mechanism of action of each factor on the wind resilience of China’s coastal historical districts; finally, the preventive measures for typhoon disasters in China’s coastal historical districts are analyzed.

2. Methodology

2.1. IDEMATEL Method

2.1.1. Establish a Set of System Influencing Factors

By entering the research-related keywords in the Web of Science database and the Science Direct database to search for the literature, we can understand the current research hotspots and research status in the academic community. After in-depth reading, the indicators were initially screened, and the indicators that appeared frequently in the research were summarized. A two-round questionnaire survey method was used to determine the research-related indicators. First, several experts engaged in related research were invited to “merge”, “delete”, and “supplement” in the form of a questionnaire, and the expert semantics were informatized. Then, the second round of questionnaires was designed based on the feedback results of the first round of questionnaires, and experts were invited to score using a Likert five-level scale. Finally, the reliability and validity of the questionnaire scoring results were tested to screen indicators and establish a set of influencing factors.

The scoring results of the second round of questionnaires play a vital role in establishing a reasonable and credible set of influencing factors. Therefore, it is necessary to test the reliability and validity of the questionnaire data. The reliability of a questionnaire is a key factor in measuring the quality of questionnaire data. It refers to the reliability of the measurement results, that is, the reliability of the questionnaire data. All factors that may interact between the selected and the unselected are fully considered. This study uses Cronbach’s alpha (α) to verify and uses Formula (1) to calculate the reliability of all indicators. If the reliability coefficients of all indicators are greater than 0.7, the results indicate that the reliability of the questionnaire is good. The reliability range and reference standard of Cronbach’s alpha are shown in

Table 1. Reliability range and reference standard of Cronbach’s alpha.

Reliability Range	Reference Standards
0.9 ≤ Cronbach’s alpha.	Very high intrinsic credibility, credible
0.8 ≤ Cronbach’s alpha < 0.9	High intrinsic credibility and trustworthiness
0.7 ≤ Cronbach’s alpha < 0.8	Intrinsic credibility is acceptable and reliable
0.6 ≤ Cronbach’s alpha < 0.7	The scale has some problems, but it is of reference value and reliable
Cronbach’s alpha < 0.6	The scale has big problems and needs to be redesigned

[27].

$$\mathsf{\alpha }={\displaystyle \frac{g}{g-1}}\left(1-{\displaystyle \frac{{\sum }_{i=1}^g{\sigma }_i^2}{{\sigma }_{\mathit{total}}^2}}\right)$$

(1)

g is the number of indicators in the questionnaire, ${\sigma }_{total}^2$ is the variance of the questionnaire data, and ${\sigma }_i^2$ is the method of collecting data for the i-th question.

The validity analysis of questionnaire data can be tested by calculating Kendall’s coefficient of concordance, asymptotic significance, and coefficient of variation (CV). Kendall’s coefficient of concordance can measure the consistency level and distribution dispersion of expert scoring data. It tests the coordination of experts’ opinions on the importance of evaluation indicators. The Kendall coefficient p value is between 0 and 1. The larger the value, the higher the consistency of expert opinions. It can be calculated using Formula (2).

$$P={\displaystyle \frac{12}{m^2\left(n^3-n\right)}}\sum _{i=1}^n{\left(L_i-{\displaystyle \frac{m\left(n+1\right)}{2}}\right)}^2$$

(2)

m and n represent the number of experts and indicators, respectively, and L_i represents the sum of the orders of the i-th indicator.

The asymptotic significance of the questionnaire results can reflect that the experts’ judgment on the suitability of the indicators in the questionnaire has passed the consistency test. If the asymptotic significance X of the questionnaire results is less than 0.01, it proves that the experts’ judgment on the suitability of the indicators in the questionnaire has passed the consistency test. Calculate according to Formula (3).

X = H(J − 1)P

(3)

H represents the number of groups of evaluation indicators, J represents the frequency of each group of evaluation indicators, and P represents the Kendall harmony coefficient.

The coefficient of variation (CV) indicates the degree of coordination of experts on each specific indicator. The smaller the value, the higher the degree of coordination of experts on each specific indicator, but its value is generally less than 0.25. The coefficient of variation (CV) is calculated according to Formula (4).

$$CV={\displaystyle \frac{z}{\mu }}$$

(4)

In the formula, z is the standard deviation of the expert scores, and μ is the mean of the expert scores.

Summarize the index scores of the second round of the expert survey, and use the calculated coefficient of variation and average as the basis for index screening. Use the indexes screened out after verification calculation as the elements of the research, and construct the element set S according to Formula (5).

S = {S₁, S₂,…, S_n}

(5)

In Formula (5), S_i (i = 1, 2,…, n) represents the i-th influencing factor in the system.

2.1.2. Construct a Comprehensive Impact Matrix

Many elements of the system in the direct impact relationship matrix are organically linked together and are generally based on the direct impact between two elements, and the elements cannot directly affect themselves. The direct impact matrix represents the square matrix of the degree of direct impact between system elements (row elements affect column elements and do not consider their own impact). Based on the influence relationships among the different factors in the set S of wind resilience factors for coastal historical districts, corresponding scales are established. The Delphi method is used to determine the direct influence relationship matrix W, which preliminarily identifies the impact of these factors.

$$W=\left[\begin{array}{ccccc}{W}_{11}& W_{12}& \dots & W_{1(j-1)}& W_{1j}\\ W_{21}& W_{22}& \dots & W_{2(j-1)}& W_{2j}\\ \dots & \dots & \ddots & \dots & \dots \\ W_{(i-1)1}& W_{(i-1)2}& \dots & W_{(i-1)(j-1)}& W_{(i-1)j}\\ W_{i1}& W_{i2}& \dots & W_{i(j-1)}& W_{ij}\end{array}\right]$$

(6)

In Formula (6), if i = j, then W_ij = 0.

The direct impact matrix is normalized to obtain the normalized impact matrix F, which is calculated as shown in Formulas (7) and (8).

$$f_{ij}=\left\{\begin{array}{c}{\displaystyle \frac{w_{ij}}{W_{max}}}(i=1,2,\dots ,k)\\ W\max =\max \left\{\sum _{j=1}^k{w}_{ij}\right\}\end{array}\right.$$

(7)

$$F=\left[\begin{array}{ccccc}{f}_{11}& f_{12}& \dots & f_{1(j-1)}& f_{1j}\\ f_{21}& f_{22}& \dots & f_{2(j-1)}& f_{2j}\\ \dots & \dots & \ddots & \dots & \dots \\ f_{(i-1)1}& f_{(i-1)2}& \dots & f_{(i-1)(j-1)}& f_{(i-1)j}\\ f_{i1}& f_{i2}& \dots & f_{i(j-1)}& f_{ij}\end{array}\right]$$

(8)

In this context, k represents the total number of columns that directly affect the matrix. $\sum _{j=1}^k{w}_{ij}$ signifies the sum of all elements in the f-th row, and Wmax represents the maximum value among the sum of all row elements.

The comprehensive influence matrix T is calculated from the normalized influence matrix F, as shown in Formula (9).

$$T={\displaystyle {\sum }_{k=1}^{\infty }}{F}^k={F(I-F)}^{-1}$$

(9)

In Formula (9), I represents the identity matrix. (I − F)⁻¹ is the inverse matrix of (I − F).

2.1.3. Calculate the Centrality Degree and Causation Degree

The influence degree (D) represents the comprehensive influence of a factor on all other factors, that is, the sum of the elements in each row of the comprehensive influence matrix T. The affected degree (E) refers to the comprehensive influence of a factor on all other factors, which can be obtained by calculating the sum of the columns of the T matrix, as shown in Formula (10).

$$\left\{\begin{array}{c}{D}_i={\sum }_{\mathrm{j}=1}^{\mathrm{n}}{T}_{ij}(i=1,2,\dots ,\mathrm{n})\\ E_i={\sum }_{\mathrm{j}=1}^{\mathrm{n}}{T}_{ij}(i=1,2,\dots ,\mathrm{n})\end{array}\right.$$

(10)

Centrality (B) can measure the importance of a factor in the system. The larger the centrality value, the greater the position and role of the factor in the factor system [28]. Causality (C) is a judgment indicator of causal factors. Causality C_i > 0 indicates that factor i is a causal factor, and C_i < 0 indicates that the factor is a result factor [28]. The calculation is shown in Formula (11).

$$\left\{\begin{array}{c}{B}_i=D_i+E_i(i=1,2,\dots ,n)\\ C_i=D_i-E_i(i=1,2,\dots ,n)\end{array}\right.$$

(11)

2.2. ISM Method

2.2.1. Determine the Reachable Matrix

Based on the comprehensive matrix T obtained by the IDEMATEL method, the overall influence matrix N of the system is obtained by adding it to the unit matrix. The calculation is shown in Formula (12).

N = I + T

(12)

The calculation of the reachable matrix M (M = [M_ij]_n×n) is shown in Formula (13).

$$M_{ij}=\left\{\begin{array}{c}\begin{array}{ccc}1,& N_{ij}& \begin{array}{cc}\ge & \lambda \end{array}\end{array}\\ \begin{array}{ccc}0,& N_{ij}& \begin{array}{cc}<& \lambda \end{array}\end{array}\end{array}\right.$$

(13)

where λ = $\overline{X}$ + σ, and $\overline{X}$ and σ are the mean and standard deviation of the comprehensive influence matrix T, respectively.

2.2.2. Hierarchical Division

Solve the reachable set (R), the antecedent set (A), and the common set (G); then filter the set factors to divide the influencing factor levels [29]. The reachable set R refers to the set consisting of all columns containing “1” factors (r_ij = 1) in the j-th column corresponding to the i-th row in the reachable matrix M. The antecedent set A refers to the collection of all rows in the reachable matrix M that contain “1” in the corresponding column j and row i (r_ji = 1).The common set G is the intersection of R and A, as shown in Formula (14).

$$\left\{\begin{array}{l}R\left(Mi\right)=\left\{M_jϵ\left.M\right|r_{ij}=1\right\}\\ A\left(Mi\right)=\left\{M_jϵ\left.M\right|r_{ji}=1\right\}\\ G\left(Mi\right)=R\left(Mi\right)\cap A\left(Mi\right)\end{array}\right.$$

(14)

The hierarchical classification results of the influencing factors are simplified and organized into levels. A multi-layer hierarchical directed topological diagram of the system’s influencing factors is drawn.

2.3. MICMAC Model

Based on the reachability matrix of the influencing factors, the dependency and driving force values of each factor are determined, the position and relationship of each factor in the system are analyzed [30], and the influence relationship between each factor and the system is further visualized using the quadrant diagram.

2.3.1. Calculate the Dependency and Driving Force

The dependence degree Y and driving force Q are the sums of the number of elements corresponding to “1” in the columns and rows of the reachability matrix M for each factor, calculated as shown in Formula (15).

$$\left\{\begin{array}{c}{Q}_i={\displaystyle \sum _{j=1}^n}{m}_{ij},(i,j=1,2,\dots \mathrm{n})\\ Y_j={\displaystyle \sum _{i=1}^n}{m}_{ij},(i,j=1,2,\dots \mathrm{n})\end{array}\right.$$

(15)

2.3.2. Draw Dependency and Driving Force Analysis Diagrams

The four quadrants of the coordinate axis classify the influencing factors as autonomous, dependent, associated, and independent, and graphs are created based on the analysis of each factor’s dependence degree Y and driving force Q.

2.4. Case Study

Yazhou in Sanya is one of the four ancient states on Hainan Island in China, boasting a history of over two thousand years. The arcade district is the earliest architectural complex in this historic city, integrating commerce and residence with a blend of Chinese and Western styles. These arcade buildings are over a hundred years old and hold significant historical and academic value for studying the extension of arcade architecture in southern China and the economic status of commercial trade in the Qiong Nan region during the Republic of China period. The arcades in Yazhou, Sanya are built along the walls on both sides of the street market, with arcade colonnades in the front and shops in the back. The width of the building is generally 3.5–4 m, the depth is 15–25 m, and the height is about 13–15 m. Among them are guild halls, businesses, and houses. The architectural style is unique, complicated and smooth, dignified and elegant. It is a perfect combination of Nanyang architecture and arcade buildings in southern China. The part of the building that extends outward on the sidewalk seems to be riding on the road, so this style of building is named arcade. And this architectural style has the function of sunshade and rain shelter for Sanya, which has a tropical marine monsoon climate. Yazhou arcade buildings are imported buildings. Yazhou is close to the sea. Generations of Sanya people went overseas to do business and brought the arcade building style of Southeast Asia back to their hometown during these exchanges. It also integrates local characteristics, using Hainan eucalyptus wood as beams, lime as building materials, mineral raw materials for painting, and blue bricks and tiles with a unique style.

Yazhou arcade districts absorb the architectural concept of northern courtyard houses, with one bright room and two dark rooms, and three connected rooms. The colors of the Yazhou arcade in Sanya are mainly beige, milky white, and light yellow, which is the most authentic and detailed embodiment of the multicultural Yazhou. It has a strong ancient Chinese traditional architectural style. In 2015, it was designated as one of the third batch of cultural relic protection units by the People’s Government of Hainan Province, China.

The arcade district in Yazhou, Sanya is unique in the local area, and its historical value is precious. Now the brick walls are mottled, and moss is all over the walls. The precious historical relics of the arcade are in urgent need of protection. The IDEMATEL-ISM-MICMAC analysis model is utilized to identify the interaction mechanisms among various factors and their impact on the wind resilience of the Yazhou arcade historical district in Sanya. Finally, targeted measures to improve the wind resilience are proposed [31,32,33,34,35]. Efforts should be made to maintain the historical style of the arcade street in the past and let the classic culture of the ancient buildings in the arcade street be integrated into the soft power of creating a national civilized city, as depicted in Figure 2.

3. Results

3.1. Results of IDEMATEL

3.1.1. Results of Constructing the Influencing Factor Set

This paper uses “coastal historical districts”, “block wind resistance”, “typhoon disasters”, “wind resilience”, and “disaster prevention management” as keywords to search for literature in the Web of Science database and Science Direct database, screen out the influencing factors of wind resilience of coastal historical districts, and summarize the influencing factor indicators that appear frequently in the research, as shown in

Table 2. High-frequency influencing factor indicators.

Number	Indicator	Frequency	Number	Indicator	Frequency
1	Windproof design	103	11	Block direction	52
2	Block form	98	12	Hidden danger identification	51
3	Building Structure	87	13	Resilience Concept	44
4	Typhoon level	80	14	Safety Education	35
5	Emergency Plan	76	15	Impact intensity	29
6	Typhoon wind speed	72	16	Preventive protection	26
7	Architectural composition	63	17	Risk assessment	23
8	Typhoon direction	61	18	Protection and renewal	21
9	Strong typhoon	57	19	Hazard investigation	19
10	Block density	55	20	Coastal cities	15

.

Based on the preliminary selection of 20 indicators of factors affecting the wind resilience of coastal historical districts, 100 experts in the field of historical district protection and disaster prevention and reduction were invited to “merge”, “delete”, and “supplement” in the form of questionnaires, and the expert semantics were informatized, as shown in Appendix A. A total of 100 questionnaires were distributed, and 95 were finally collected. According to the experts’ suggestions, the four indicators of “resilience concept”, “coastal city”, “protection and renewal”, and “risk assessment” with a negligible impact on the wind resilience of coastal historical districts were eliminated. At the same time, to avoid the same meaning as other existing indicators, the experts suggested deleting the four indicators with repeated concepts, “impact intensity”, “strong typhoon”, “preventive protection”, and “hazard investigation”.

The second round of questionnaires was designed based on the feedback from the first round of questionnaires. A Likert five-level scale was used to evaluate the importance of the evaluation indicators of the wind resilience influencing factors of coastal historical districts determined in the second round of questionnaires (1–5 importance rating), as shown in Appendix B. A total of 95 questionnaires were distributed, and 89 were effectively collected, with an efficiency of 93.7%. Invalid questionnaires included four questionnaires with serious missing items and two questionnaires with careless filling.

The reliability analysis of the measurement was performed using SPSS 27.0, according to Formula (1), and the overall Cronbach’s α coefficient was 0.798. The reliability coefficients of all indicators were greater than 0.7. By comparing the standards in

Table 3. Kendall synergy coefficient of expert opinions.

Test Statistics	Kendall	Asymptotic Significance
Evaluation indicators	0.634	0.001

, it can be seen that the reliability of the questionnaire results is good. According to Formulas (2) and (3), the Kendall synergy coefficient and asymptotic significance of expert opinions were calculated, as shown in Table 3.

Since the asymptotic significance of the questionnaire results is far less than 0.01, it proves that the experts’ judgment on the suitability of the indicators passed the consistency test. We summarized the indicator scores and used the calculated coefficient of variation and average as the basis for indicator screening. The average and coefficient of variation are calculated according to Formula (4). The results are shown in

Table 4. Average values and coefficients of variation of indicators.

Indicator	Average Values	Coefficients of Variation	Indicator	Average Values	Coefficients of Variation
Windproof design	4.9438	0.0468	Architectural composition	4.9663	0.0365
Block form	4.0449	0.2004	Typhoon direction	4.0562	0.1979
Building Structure	4.9775	0.0299	Block density	4.9888	0.0212
Typhoon level	3.8764	0.2124	Block direction	3.8202	0.2109
Emergency Plan	4.9663	0.0365	Hazard investigation	4.9551	0.0420
Typhoon wind speed	3.9438	0.2036	Safety Education	3.9101	0.2027

, showing that the consistency of the experts’ scores is high.

From the results verified in Table 4, we can see that there are 12 effective indicators that can be used as the research factors affecting the wind resilience of China’s coastal historical districts. In order to ensure the rationality of this study, it was finally determined to summarize the 12 influencing factors into four aspects, block level, building level, typhoon characteristics, and emergency management, to establish a system of influencing factors for the wind resilience of China’s coastal historical districts, as shown in

Table 5. System of factors affecting wind resilience of China’s coastal historical districts.

Primary Indicator	Secondary Indicator	Indicator Definition	Coding
Block level	Block density	Block density is the ratio of building area to land area	S1
	Block form	The space between the road surface and the buildings on either side, along with the wind field characteristics around the block, significantly influences how wind impacts the buildings	S2
	Block direction	The varying angles between the blocks and the wind direction result in different distributions of wind load across the building surfaces	S3
Building level	Architectural composition	The different organizational forms of buildings significantly affect the wind field	S4
	Building Structure	The extent of damage to various building structures will also differ	S5
	Windproof design	Selecting suitable building forms and materials can enhance a building’s wind resistance	S6
Typhoon characteristics	Typhoon level	Tropical cyclones are primarily classified into six categories based on the wind speed near their center	S7
	Typhoon direction	In the northern hemisphere, typhoons rotate counterclockwise. However, the relationship between various locations and typhoons differs, resulting in varying wind directions at each site	S8
	Typhoon wind speed	Wind speed is a crucial parameter for numerically simulating the wind load characteristics of buildings	S9
Emergency Management	Emergency Plan	Integrating local conditions with scientific data is essential for developing effective response plans	S10
	Hazard investigation	Identifying areas vulnerable to typhoons can enhance wind resilience	S11
	Safety Education	Enhancing the public’s ability to prevent, withstand, and respond to disasters can be achieved through educational initiatives and practical drills	S12

.

The influencing factor indexes can be determined from Table 5, and the system influencing factor set S is constructed according to Formula (5).

S = {S₁, S₂, S₃, S₄, S₅, S₆, S₇, S₈, S₉, S₁₀, S₁₁, S₁₂}

3.1.2. Calculate the Comprehensive Influence Matrix

The Delphi method is used to preliminarily determine the correlation between the influencing factors, and the direct influence relationship matrix W is determined according to Formula (6).

$$W=\left[\begin{array}{cccccccccccc}0& 0& 0& 0& 0& 2& 0& 1& 1& 1& 2& 0\\ 0& 0& 0& 3& 0& 4& 0& 3& 1& 0& 0& 0\\ 0& 0& 0& 2& 0& 2& 0& 3& 2& 0& 0& 0\\ 2& 2& 2& 0& 0& 1& 0& 3& 1& 0& 2& 0\\ 0& 0& 0& 0& 0& 3& 0& 0& 0& 0& 0& 0\\ 0& 1& 0& 1& 2& 0& 0& 2& 1& 1& 1& 0\\ 0& 0& 0& 0& 4& 3& 0& 1& 3& 2& 4& 3\\ 0& 1& 1& 1& 1& 3& 0& 0& 0& 0& 2& 0\\ 0& 1& 0& 0& 3& 2& 1& 0& 0& 1& 3& 0\\ 1& 1& 1& 1& 0& 3& 0& 0& 0& 0& 4& 3\\ 1& 1& 0& 0& 3& 3& 0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 0& 2& 0& 0& 0& 1& 3& 0\end{array}\right]$$

After determining the direct influence relationship matrix, the normalization is performed using Formulas (7) and (8). The row sum maximum method is employed to normalize and calculate the normalized influence matrix F.

$$F=\left[\begin{array}{cccccccccccc}0.000& 0.000& 0.000& 0.000& 0.000& 0.100& 0.000& 0.050& 0.050& 0.050& 0.100& 0.000\\ 0.000& 0.000& 0.000& 0.150& 0.000& 0.200& 0.000& 0.150& 0.050& 0.000& 0.000& 0.000\\ 0.000& 0.000& 0.000& 0.100& 0.000& 0.100& 0.000& 0.150& 0.100& 0.000& 0.000& 0.000\\ 0.100& 0.100& 0.100& 0.000& 0.000& 0.050& 0.000& 0.150& 0.050& 0.000& 0.100& 0.000\\ 0.000& 0.000& 0.000& 0.000& 0.000& 0.150& 0.000& 0.000& 0.000& 0.000& 0.000& 0.000\\ 0.000& 0.050& 0.000& 0.050& 0.100& 0.000& 0.000& 0.100& 0.050& 0.050& 0.050& 0.000\\ 0.000& 0.000& 0.000& 0.000& 0.200& 0.150& 0.000& 0.050& 0.150& 0.100& 0.200& 0.150\\ 0.000& 0.050& 0.050& 0.050& 0.050& 0.150& 0.000& 0.000& 0.000& 0.000& 0.100& 0.000\\ 0.000& 0.050& 0.000& 0.000& 0.150& 0.100& 0.050& 0.000& 0.000& 0.050& 0.150& 0.000\\ 0.050& 0.050& 0.050& 0.050& 0.000& 0.150& 0.000& 0.000& 0.000& 0.000& 0.200& 0.150\\ 0.050& 0.050& 0.000& 0.000& 0.150& 0.150& 0.000& 0.000& 0.000& 0.000& 0.000& 0.050\\ 0.000& 0.000& 0.000& 0.000& 0.000& 0.100& 0.000& 0.000& 0.000& 0.050& 0.150& 0.000\end{array}\right]$$

First, sum the rows and columns of the initial direct influence matrix S and compare their sizes. Based on Formula (9), calculate the normalized influence matrix [36]. Finally, the comprehensive influence matrix T can be computed.

$$T=\left[\begin{array}{cccccccccccc}0.012& 0.028& 0.009& 0.020& 0.052& 0.168& 0.003& 0.076& 0.063& 0.063& 0.145& 0.017\\ 0.024& 0.053& 0.031& 0.188& 0.065& 0.293& 0.004& 0.221& 0.082& 0.021& 0.076& 0.008\\ 0.017& 0.042& 0.024& 0.129& 0.058& 0.184& 0.006& 0.199& 0.122& 0.017& 0.068& 0.007\\ 0.115& 0.140& 0.117& 0.054& 0.069& 0.186& 0.004& 0.221& 0.087& 0.020& 0.168& 0.012\\ 0.002& 0.012& 0.003& 0.012& 0.021& 0.165& 0.001& 0.021& 0.010& 0.009& 0.015& 0.002\\ 0.016& 0.081& 0.018& 0.079& 0.143& 0.099& 0.003& 0.137& 0.066& 0.060& 0.103& 0.105\\ 0.027& 0.057& 0.016& 0.039& 0.314& 0.336& 0.009& 0.102& 0.176& 0.137& 0.317& 0.188\\ 0.016& 0.081& 0.062& 0.083& 0.100& 0.228& 0.001& 0.058& 0.027& 0.014& 0.136& 0.009\\ 0.016& 0.080& 0.008& 0.029& 0.218& 0.213& 0.051& 0.042& 0.025& 0.069& 0.202& 0.028\\ 0.074& 0.093& 0.064& 0.089& 0.077& 0.274& 0.002& 0.068& 0.033& 0.028& 0.273& 0.168\\ 0.055& 0.069& 0.005& 0.025& 0.183& 0.220& 0.001& 0.040& 0.019& 0.018& 0.038& 0.055\\ 0.014& 0.023& 0.006& 0.016& 0.046& 0.157& 0.001& 0.023& 0.011& 0.060& 0.180& 0.018\end{array}\right]$$

3.1.3. The Results of the Centrality and Causation Degree

The influence degree set (D) and the affected degree set (E) can be calculated according to Formula (10). The centrality set (B) and the causation degree set (C) can be calculated according to Formula (11) [37,38,39]. The results are shown in

Table 6. Results of influencing factor analysis.

Influencing Factors	D	E	B	C	Factor Attributes
S1	0.657	0.388	1.045	0.269	Causal factors
S2	1.065	0.761	1.825	0.304	Causal factors
S3	0.872	0.363	1.235	0.510	Causal factors
S4	1.195	0.763	1.957	0.432	Causal factors
S5	0.273	1.346	1.619	−1.073	Resulting factors
S6	0.819	2.522	3.341	−1.702	Resulting factors
S7	1.718	0.086	1.804	1.632	Causal factors
S8	0.816	1.209	2.025	−0.393	Resulting factors
S9	0.983	0.721	1.704	0.262	Causal factors
S10	1.241	0.516	1.757	0.724	Causal factors
S11	0.728	1.720	2.447	−0.992	Resulting factors
S12	0.553	0.526	1.079	0.027	Causal factors

.

According to the results in Table 6, a causal relationship diagram of the factors affecting the wind resilience of China’s coastal historical districts was drawn with centrality B as the horizontal axis and causation C as the vertical axis, as shown in Figure 3.

The results in Table 6 and Figure 4 show the influence degree values for block form (S₂), architectural composition (S₄), typhoon level (S₇), and emergency plan (S₁₀) are relatively high, indicating that these four factors have a significant impact on other factors in the system. The influence values of building structure (S₅), windproof design (S₆), typhoon direction (S₈), and hazard investigation (S₁₁) are also considerable, suggesting that these factors are more significantly affected by others.

The results in Table 6 and Figure 5 show that, in terms of centrality, the centrality values of block form (S₂), architectural composition (S₄), windproof design (S₆), typhoon level (S₇), typhoon direction (S₈), and hazard investigation (S₁₁) are relatively large, indicating that these six factors play a dominant role in the influencing factor system of wind resilience of China’s coastal historical districts and are of high importance. In terms of degree of causation, the causation degree values of block direction (S₃), typhoon level (S₇), and emergency plan (S₁₀) are relatively large, which are causal factors, while the causal degree value of windproof design (S₆) is the lowest, which is a result factor.

3.2. Results of ISM

3.2.1. Calculate the Reachable Matrix

Set a reference threshold and use Formula (12) to determine the threshold λ and the overall influence matrix N [40]. To ensure that the introduced threshold λ effectively eliminates relationships with minimal influence among the factors, calculate the overall influence matrix N with λ = $+\mathsf{\sigma }=0.076+0.078=0.154$.

$$N=\left[\begin{array}{cccccccccccc}1.012& 0.028& 0.009& 0.020& 0.052& 0.168& 0.003& 0.076& 0.063& 0.063& 0.145& 0.017\\ 0.024& 1.053& 0.031& 0.188& 0.065& 0.293& 0.004& 0.221& 0.082& 0.021& 0.076& 0.008\\ 0.017& 0.042& 1.024& 0.129& 0.058& 0.184& 0.006& 0.199& 0.122& 0.017& 0.068& 0.007\\ 0.115& 0.140& 0.117& 1.054& 0.069& 0.186& 0.004& 0.221& 0.087& 0.020& 0.168& 0.012\\ 0.002& 0.012& 0.003& 0.012& 1.021& 0.165& 0.001& 0.021& 0.010& 0.009& 0.015& 0.002\\ 0.016& 0.081& 0.018& 0.079& 0.143& 1.099& 0.003& 0.137& 0.066& 0.060& 0.103& 0.015\\ 0.027& 0.057& 0.016& 0.039& 0.314& 0.336& 1.009& 0.102& 0.176& 0.137& 0.317& 0.188\\ 0.016& 0.081& 0.062& 0.083& 0.100& 0.228& 0.001& 1.058& 0.027& 0.014& 0.136& 0.009\\ 0.016& 0.080& 0.008& 0.029& 0.218& 0.213& 0.051& 0.042& 1.025& 0.069& 0.202& 0.208\\ 0.074& 0.093& 0.064& 0.089& 0.077& 0.274& 0.002& 0.068& 0.033& 1.028& 0.273& 0.168\\ 0.055& 0.069& 0.005& 0.025& 0.183& 0.220& 0.001& 0.040& 0.019& 0.018& 1.038& 0.055\\ 0.014& 0.023& 0.006& 0.016& 0.046& 0.157& 0.001& 0.023& 0.011& 0.060& 0.180& 1.018\end{array}\right]$$

Using the Boolean operation rules and substituting λ = 0.154 into Formula (13), we derived the reachable matrix M from the previously calculated relationships.

$$M=\left[\begin{array}{cccccccccccc}1& 0& 0& 0& 0& 1& 0& 0& 0& 0& 0& 0\\ 0& 1& 0& 1& 0& 1& 0& 1& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 1& 0& 1& 0& 0& 0& 0\\ 0& 0& 0& 1& 0& 1& 0& 1& 0& 0& 1& 0\\ 0& 0& 0& 0& 1& 1& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 1& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 1& 1& 1& 0& 1& 0& 1& 1\\ 0& 0& 0& 0& 0& 1& 0& 1& 0& 0& 0& 0\\ 0& 0& 0& 0& 1& 1& 0& 0& 1& 0& 1& 0\\ 0& 0& 0& 0& 0& 1& 0& 0& 0& 1& 1& 1\\ 0& 0& 0& 0& 1& 1& 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 1& 0& 0& 0& 0& 1& 1\end{array}\right]$$

3.2.2. Determine the Hierarchical Division

According to the reachable matrix M, the reachable set R, antecedent set A, and common set G of each influencing factor can be determined. This allows for hierarchical decomposition of the system factors. First, the initial level is processed, where factors in the reachable set R that are equal to those in the common set G are identified as top-level factors [41,42,43]. Then, the subsequent levels are divided according to this rule. The division is calculated according to Formula (14). Subsequently, following this rule, the lower levels are classified, with the results shown in

Table 7. Factor hierarchy classification.

Influencing Factors	R (Si)	A (Si)	G (Si)
S1	S1, S6	S1	S1
S2	S2, S4, S6, S8	S2	S2
S3	S3,S6,S8	S3	S3
S4	S4, S6, S8, S11	S2, S4	S4
S5	S5, S6	S5, S7, S9, S11	S5
S6	S6	S1, S2, S3, S4, S5, S6, S7, S8, S9, S10, S11, S12	S6
S7	S5, S6, S7, S9, S11, S12	S7	S7
S8	S6, S8	S2, S3, S4, S8	S8
S9	S5, S6, S9, S11	S7, S9	S9
S10	S6, S10, S11, S12	S10	S10
S11	S5, S6, S11	S4, S7, S9, S10, S11, S12	S11
S12	S6, S11, S12	S7, S10, S12	S12

.

The hierarchical classification results of each factor in Table 7 were processed hierarchically to construct a multi-layer hierarchical structural model of factors affecting the wind resilience of China’s coastal historical districts, as shown in Figure 6.

Figure 6 illustrates that the twelve influencing factors in the wind resilience system of China’s coastal historical districts are categorized into five levels. Factors positioned at lower levels are considered more fundamental to the influencing factor system. The first level factors belong to the surface direct influencing factors, the second to fourth level factors belong to the middle layer indirect influencing factors, and the fifth level factors belong to the bottom layer fundamental factors. In the first level, there is one factor (S₆), which represents the surface influencing factor for the wind resilience of China’s coastal historical districts. The second level includes three factors: block density (S₁), building structure (S₅), and typhoon direction (S₈). The third level contains two factors: block direction (S₃) and hazard investigation (S₁₁). Lastly, the fourth level comprises three factors: architectural composition (S₄), typhoon wind speed (S₉), and safety education (S₁₂). The three factors in the fourth level are considered middle-level influencing factors for the wind resilience of China’s coastal historical districts. These factors directly impact the first-level factor while also being influenced by the underlying fundamental factors. The bottom level consists of three factors: block form (S₂), typhoon level (S₇), and emergency plan (S₁₀). These three factors are the root influencing factors for the wind resilience of China’s coastal historical districts. They impact wind resilience by influencing both surface and middle-level factors.

3.3. MICMAC Results

3.3.1. Results of Dependence Degree and Driving Force

Using the reachable matrix M obtained from the ISM method, we counted the sum of “1” elements in the rows and columns for each influencing factor based on Formula (15). This allows for the computation of the dependence degree and driving force, with the results shown in

Table 8. Table of dependence degree and driving force values.

Influencing Factors	Q	Y	Influencing Factors	Q	Y
S1	1	2	S7	1	6
S2	1	4	S8	4	2
S3	1	3	S9	2	4
S4	2	4	S10	1	4
S5	4	2	S11	6	3
S6	12	1	S12	3	3

.

3.3.2. Dependence Degree–Driving Force Analysis Diagram

The X and Y axes represent dependence degree and driving force, with the average values of dependence degree and driving force serving as the quadrant dividing line [44], a dependence degree–driving analysis diagram is created based on the values of dependence degree and driving force for each influencing factor shown in Table 8, as illustrated in Figure 7.

Analyzing Figure 7 reveals the distribution of various influencing factors across the quadrants, illustrating their driving forces and dependencies. Each quadrant indicates the role and significance of the factors within the overall system of wind resilience.

The spontaneous factor group in the first quadrant includes block density (S₁), building structure (S₅), and typhoon direction (S₈). Factors in this quadrant exhibit low dependence and driving force, indicating simpler relationships among them. When addressing factors influencing the wind resilience of China’s coastal historical districts, those in this quadrant should be prioritized. These factors typically occupy the middle layer of the multi-layer hierarchical structure model and exhibit both correlation and mediation effects. These factors can influence those in the upper layer while also being constrained by factors in the lower layer. Consequently, they are not easily controlled indirectly by affecting other factors. Moreover, if a spontaneous factor is compromised, it can trigger a chain reaction throughout the system.

The second quadrant of dependent factors includes windproof design (S₆). The influencing factors in this quadrant depend on lower-level factors and are influenced by their driving forces, making it difficult for them to affect other factors. They are considered direct influencing factors. As shown in Figure 7, the factors in this quadrant are positioned in the first layer of the ISM model, which aligns with the actual structural model.

The third quadrant, representing the linkage factor group, includes hazard investigation (S₁₁). Factors in this quadrant exhibit both high dependence and high driving force, indicating their significant role in influencing other factors while also being heavily influenced by them. In the wind resilience influencing factor system of China’s coastal historical districts, hazard investigation (S₁₁) serves as a transitional influencing factor, facilitating the transmission of influence from lower factors to upper factors. This highlights its critical role in the overall dynamics of the system. As illustrated in Figure 7, the influencing factors in the third layer of the multi-layer hierarchical structure model can transmit the influence of lower factors to higher factors. They can also affect the wind resilience of China’s coastal historical districts through independent actions, aligning with the actual structural model.

The fourth quadrant, representing the independent factor group, includes block form (S₂), block direction (S₃), architectural composition (S₄), typhoon level (S₇), typhoon wind speed (S₉), emergency plan (S₁₀), and safety education (S₁₂). Factors in this quadrant exhibit low dependence and high driving force, indicating that they can influence other factors without being significantly affected themselves. The factors in this quadrant act as driving factors within the system, characterized by low dependence and high driving force. They continue to influence other factors while being relatively unaffected by the dynamics of the system. These factors represent the root influencing factors in the system affecting the wind resilience of China’s coastal historical districts. The quadrant includes both bottom-level and fourth-level factors, with the driving force of the bottom-level factors being stronger than that of the fourth-level factors, aligning with the actual structural model. Strengthening the management of factors in this quadrant can effectively control the likelihood of other factors emerging, thereby enhancing the wind resilience of China’s coastal historical districts.

4. Discussion

Currently, there is limited research on the wind resilience of coastal historical districts [12,13,14,15,16,17,18,19,20,21,22,23,24,25]. Scholars have focused on in-depth studies regarding the wind resistance simulation of individual historical buildings, the quantification of a community’s overall capacity to withstand hurricanes, and subjective evaluations of historical district protection through field surveys. Yi et al. [45] conducted an on-site inspection of Lujiang Academy, a representative historical building in Guangzhou. They utilized computational fluid dynamics to simulate the wind pressure distribution on the building’s roof, leading to the proposal of preventive measures aimed at reducing typhoon-related disasters. Abdelhady et al. [46] developed a quantitative framework to assess a community’s ability to resist hurricanes. This framework is based on damage estimates derived from a vulnerability model and incorporates a probabilistic recovery model. Li et al. [47] analyzed the resilience of public spaces in historical districts during disasters from the perspective of public space transformation and governance. The study pointed out that existing research has rarely analyzed the factors affecting spontaneous disaster responses in historical districts, and put forward conclusions and suggestions for improving the resilience of historical districts in the future when responding to disasters. However, the protection of China’s coastal historical districts involves different factors compared to those affecting inland areas. For instance, historical districts in China’s coastal areas face typhoons significantly more frequently than those in inland regions. Consequently, it is essential to identify and clarify the specific factors influencing the wind resistance of historical districts in China’s coastal areas.

The influencing factors of wind resilience in China’s coastal historical districts are complex, affected not only by typhoon-related factors but also by numerous incidental factors. This leads to characteristics of randomness and ambiguity in both time and space. However, understanding wind resilience is essential in the process of protecting China’s coastal historical districts. Therefore, this study constructs a systematic analysis model of the influencing factors of wind resilience in China’s coastal historical districts for detailed exploration. First, the IDEMATEL method is used to identify the dominant factors, followed by the ISM method to reveal the hierarchical structure of the factors. Finally, the MICMAC method is applied to analyze the interaction mechanisms among the factors and validate the feasibility of the model. In the study, by combining the practical case of the Yazhou arcade historical district in Sanya, key core factors influencing wind resilience in China’s coastal historical districts were identified, along with the structural relationships and interaction mechanisms among these factors. It is evident that the comprehensive research method established in this study is a more holistic systematic analysis approach, which holds significant innovative value for improving the theoretical research of the influencing factors analysis model for wind resilience in China’s coastal historical districts.

This study also has certain limitations. Although the selection of influencing factors for wind resilience in China’s coastal historical districts has been combined through theoretical literature screening and practical investigation, it may still lack comprehensiveness. We hope that more scholars will join in the research on wind resilience in China’s coastal historical districts to establish a more scientific system of influencing factors. At the same time, the influencing factors at the block level, building level, typhoon characteristics, and emergency management for China’s coastal historical districts have been studied. The study analyzed the wind resilience of China’s coastal historical districts from a macro level. Future research can build on this model to develop a more specialized and detailed academic framework, enabling investigations at a micro level. The research findings can be effectively applied to real-world activities aimed at enhancing wind resilience in China’s coastal historical districts, thereby maximizing the value and impact of the study’s outcomes.

5. Conclusions

This paper focuses on the wind resilience of Yazhou arcade districts in Sanya, analyzing the influencing factors from four key aspects: block level, building level, typhoon characteristics, and emergency management. A system analysis model for the influencing factors of wind resilience in China’s coastal historical districts is constructed. The key findings of this paper are as follows.

(1)

The causal factors that rank high in centrality are primarily causal factors, with most falling under the categories of building level and typhoon characteristics. The centrality of windproof design (S₆) ranks first, indicating that this factor occupies a core position at the building level and exerts significant influence on the entire system. Therefore, the internal structure of the building should be periodically inspected and reinforced on a daily basis, and building materials with wind-resistant properties should be used when reinforcing and repairing the exterior of the building. The centrality of hazard investigation (S₁₁) ranks second, belonging to the emergency management level, which highlights its significant influence on the wind resilience influencing factor system of China’s coastal historical districts. Therefore, it is particularly important to establish a special patrol system for hidden dangers in historical districts. The centrality rankings of typhoon direction (S₈) and architectural composition (S₄) are third and fourth, respectively, indicating that both factors are significant influencers of the wind resilience in China’s coastal historical districts, with typhoon direction (S₈) belonging to typhoon characteristics and architectural composition (S₄) to the building level. The causal factors primarily include typhoon level (S₇), emergency plan (S₁₀), block direction (S₃), architectural composition (S₄), block form (S₂), block density (S₁), typhoon wind speed (S₉), and safety education (S₁₂). Among these, block direction (S₃), block form (S₂), and block density (S₁) fall under the block level, indicating that the block level significantly influences the wind resilience influencing factor system of China’s coastal historical districts. Therefore, wind tunnel experiments can be conducted for simulation at the block level, and the density and layout of the block can be optimized based on the simulation results to improve the wind resistance of the district.

(2)

The 12 influencing factors affecting the wind resilience of China’s coastal historical districts are categorized into five distinct layers. The lower-level influencing factors are typically independent factors, the middle-level factors are mainly spontaneous and linkage factors, while the upper-level factors are generally dependent factors. The influencing factors in the fifth layer are block form (S₂), typhoon level (S₇), and emergency plan (S₁₀). The three factors in the fifth layer exhibit greater driving force and are the most fundamental and important influencing factors in the system. The influencing factors in the fourth layer include architectural composition (S₄), typhoon wind speed (S₉), and safety education (S₁₂). The driving force of the factors in the fourth layer is slightly greater than their dependence, indicating their strong connecting role. The influencing factors in the third layer are block direction (S₃) and hazard investigation (S₁₁). The driving force of the factors in the third layer is slightly greater than their dependence, positioning them in the middle of the multi-layer hierarchical structure model. This allows them to effectively connect the relationships between the lower and upper influencing factors. The influencing factors in the second layer are block density (S₁), building structure (S₅), and typhoon direction (S₈). The driving force of the factors in the second layer is less than or equal to their dependence, meaning they directly influence the surface factors. The influencing factor in the first layer is windproof design (S₆), which has high dependence and is the most susceptible to external influences in the system.

(3)

The building level and typhoon characteristics play a crucial leading role in the wind-resilience-influencing factor system of China’s coastal historical districts. Additionally, the block level and emergency management exert a significant influence on this system. The key influencing factor at the block level is block form (S₂), at the building level is architectural composition (S₄), at the typhoon characteristics level is typhoon level (S₇), and at the emergency management level is emergency plan (S₁₀). To enhance the wind resilience of coastal historical districts, it is crucial to focus on the key influencing factors at the block level (block form), building level (architectural composition), typhoon characteristics (typhoon level), and emergency management (emergency plan).