Safety Assessment of Ancient Buildings under Adjacent Subway Blasting Construction Based on the Optimized Fuzzy Optimal Method

Fragile ancient buildings are recognized as an eloquent testimony to human civilization, and their safety should arouse more attention. According to the special case of adjacent blasting construction, the assessment model should be essentially built to assess the effect of tunnel blasting on the safety of the ancient buildings. To analyze the structural safety of ancient buildings under blasting vibration and to protect the precious ancient buildings, a risk assessment model of ancient buildings with 20 relevant assessment indexes was initiatively built in this study. To be specific, the relative factors of blasting, the factors of ancient buildings, and other factors (e.g., religion) were comprehensively considered in the model. Subsequently, the risk level and weight were calculated more systematically and quantitatively by adopting the optimized optimal comprehensive method integrating the G1 method and the entropy method. Lastly, the overall risk value was determined by applying the fuzzy gray method. Afterward, the value was adopted to assess the safety of the Asoka Temple, the only existing temple named after the Indian King Asoka in China, as an attempt to verify the feasibility of this model. Besides, the Asoka tunnel was around it. As demonstrated from the results, the age of the buildings maximally impacted the safety of ancient buildings, and the safety level of the Asoka Temple was “relatively safe.” *e present study built an effective model to assess the safety of ancient buildings under adjacent subway blasting construction, which could help improve the efficiency and accuracy of assessments.


Introduction
Ancient buildings are an eloquent testimony to the countries' history and the embodiment of the countries' culture. However, the safety and durability of the structures as well as the sensitivity to blasting of tunnel construction are decreasing with the aging of the buildings [1][2][3]. A reasonable safety assessment model should be built to assess the safety of ancient buildings and protect the ancient buildings from destruction. In this study, its own factors, the effect of vibration, and other factors (e.g., religion) were all considered to define the safety of ancient buildings to be no longer limited to safety of the structure, whereas a comprehensive safety assessment was conducted.
Over the past few years, the analysis of ancient building structures has aroused huge attention from numerous researchers. Structural damage correlated with ancient buildings [4][5][6][7][8][9][10] has been extensively investigated, and ancient buildings [11][12][13] have been monitored and measured. Moreover, Xue et al. built an earthquake damage assessment model for Chinese ancient wooden structures to reveal the influences exerted by the vibration on the ancient building [14]. Qiu et al. examined the effect of vibration attributed to Xi'an subway during the tunnel excavation on Xi'an ancient circumvallation [15]. us, the architectural factor should be considered in the risk assessment. Wang et al. built a prioritization model for historic building conservation by complying with object element theory and then proposed a novel assessment decision method for subsequent heritage impacts following the metro lines [4].
ough the building structure has been extensively studied, most of the existing studies had certain limitations. To be specific, the safety of ancient buildings was only studied from a single perspective (e.g., vibration or structure). As indicated from the literature review, other factors (e.g., the public religious sentiment) should be considered when assessing the safety of ancient buildings [16]. Accordingly, a novel and comprehensive assessment model should be built given the factors of ancient buildings and the effect of other disciplines.
According to engineering, risks are estimated by adopting some methods. Lu et al. [17] exploited the fuzzy COPRAS (complex proportional assessment) method to select the optimal green suppliers. Besides, the cross-entropy optimization model was adopted to objectively determine the weight vector, and a mathematical programming model of dual-objective probabilistic neural network was built to obtain the comprehensive attribute weights of two inconsistent indicators. e model was verified to be effective by conducting an example study.
e entropy method was generally adopted for decision making. Furthermore, the G1 method is considered an optimized AHP method without the requirement for a consistency test.
ough various studies have long been conducted on the risk analysis of ancient buildings, few researchers have comprehensively considered the factors and built an assessment model in numerous aspects. Accordingly, the optimal combination weighting method of entropy value method integrated with the G1 method could make the assessment more accurate and more effectively control the risk of ancient buildings as a whole.
It is noteworthy that the Asoka Temple was taken as an example to verify and practically implement the model built by using the optimal weighting method, and the results were consistent with the relevant engineering practice. e mentioned assessment system based on the optimized fuzzy optimal method could effectively identify and reasonably assess the safety of ancient buildings, which showed the guiding significance to the subsequent protection of the ancient buildings.

Methodology
e steps shown in Figure 1 were followed to assess the safety of the ancient building and optimize the risk assessment [18].
According to the mentioned steps, the safety assessment can be presented in Figure 2. e specific risk assessment is illustrated in Figure 3.

Basic Principle
2.1.1. G1 Method and Its Improvement. In fact, the G1 method (order relation analysis method) [19] refers to a type of order relation analysis method without the requirement for a consistency test, thereby leading to a decrease in the computational complexity and an increase in the computation efficiency. e steps of the G1method (Figure 2) are as follows [19]: (1) Determine the order relationship between the assessment indexes X m : (2) Judge the relative significance between the adjacent index: where r k denotes the coefficient of significance of X k−1 to X k . (3) e calculation of the weighting number: e weight matrix of the index X � X 1 , X 2 , . . . , X m : As impacted by the limitation of human cognition and the complexity of the risk problem, experts failed to accurately determine the specific order of the weight while providing the exact degree of the significance coefficient.
us, the redefinition of the weight calculation coefficient was adopted during the calculation. Since the significance score recommended in the Guidelines [20] optimizes the significance comparison method, a significance assessment standard for the G1 method was proposed in this study, and experts were invited to compare the materiality of the respective risk indicator on a case-by-case basis. e novel expert scoring criteria [21] are listed in Table 1.

Entropy Weight Method.
To avoid the subjectivity of the results, an objective weighting method should be comprehensively selected.
e entropy weight method [22,23] has been extensively applied in problem decision making and exhibits strong objectivity. e entropy weight method was applied to the weight calculation to reduce the subjectivity brought by expert grading according to the G1 method. It could determine the weight of relevant factors by analyzing the amount of the information entropy of the respective indicator value [24,25]. e smaller the information entropy is, the greater the weight of the indicator would be. However, the subjective intention of the decision maker could be easy to ignore. e risk fell to five levels based on ISO 31000 [20]. e risk scale is illustrated in Figure 4.
Risk assessment criteria were formulated in accordance with the relevant codes [20,[26][27][28][29][30][31] and in consultation with experts in special fields. e experts invited consisted of researchers in the protection of ancient buildings, architectural protection engineers, government regulators, tunnel engineers, and tunnel technicians, who had high professional levels and huge engineering experiences and were in expert assessment teams. Subsequently, experts rated risk factors by complying with the criteria and actual situation of ancient buildings. e resulting risk scores were regarded as the entropy of each factor. In this study, the node value of risk classification and the data under the assessment of object indicators could jointly constitute the original indicator data. Afterward, the entropy value method could process the data to determine the ranking of the significance of the indicators. e specific steps are illustrated in Figure 2.

Establishment of the System.
In the present study, the factors (e.g., ancient buildings and blasting vibration) were considered with the references of Chinese regulations on ancient buildings and relevant literature to build the safety  Given the literature review [5,7,[11][12][13], this study subdivided the risk of ancient buildings into three target floors. U 1 contained nine subfactors, U 2 consisted of seven subfactors, and U 3 covered four subfactors. e system is presented in Figure 5. Table 2 lists the risk assessment criteria of the ancient buildings corresponding to risk factors in Figure 5. U 11 (foundation type), U 12 (age of the buildings), U 13 (significance), and U 14 (materials) represent the durability of the foundation of ancient buildings, the time of building the buildings, the protection level of the buildings in accordance with the national cultural relic classification standard, and the materials adopted to construct ancient buildings, respectively. U 15 (durability), U 16 (height), and U 17 (size), respectively, denote the durability of ancient buildings, the height of the buildings, and the floor space of the ancient buildings. U 18 (structure safety level) refers to the safety level of the ancient buildings assessed by the code [29]. Besides, U 19 (velocity response) represents the gap between the velocity response and permissible velocity of vibration [30]. U 21 (vibration source type), U 22 (frequency range), U 23 (source distribution), U 24 (blasting methods), U 25 (propagation velocity of an elastic wave), U 26 (position between buildings and source), and U 27 (distance between buildings and source), respectively, denote the cause of the vibration, the frequency exhibited by the blast, the type of blasting source distribution, the method rationality, the propagation velocity of an elastic wave, the position between buildings and source, and the distance between buildings and source. Furthermore, U 31 (construction personnel management), U 32 (public religious sentiment), U 33 (engineering geological condition), and U 34 (engineering hydrologic condition), respectively, represent the management during the construction, the public awareness and the degree of piety, the engineering geological condition, and the engineering hydrologic condition. A hierarchical assessment system was established, and the model fell to three levels. e correlation between the upper and lower levels was summarized and listed.

Combination Weighting Method.
e combined weighting method [32] could indicate the opinions and preferences of decision makers, as well as the laws of objective data. Besides, the difference between subjective weight and objective weight complied with the difference   Figure 5: e risk assessment system. between their corresponding distribution coefficients. e combination coefficient of subjective factors and objective factors was determined by equations (5)-(10) to yield the combination weight. Subjective weighting was determined by consulting the opinions of relevant experts, followed by the entropy according to statistics. e optimal combination weighting model was built to address the unreasonable weight problem of single weighting. e steps to obtain the combined weight are illustrated in Figure 6. e combination weight method should determine the combination weight coefficient in accordance with the following two factors. e first was to ensure the minimum distance between the weighted score of each assessment object and the ideal generalized point in the following formula.
e second was Jaynes maximum entropy principle [7], capable of avoiding the contribution error of various weighting results to the combined weighting results to the maximal extent. e objective function built by the idea of minimizing the difference of the respective weighting result could simplify the calculation: where α denotes the balance coefficient between the two targets, 0 ≤ θ ≤ 1, θ � 0.5. Given the mentioned two factors, the Lagrange function could yield the combination weight coefficient and the value of α c : e combination weight w [32]: where w c represents the weight of the index obtained by a single method.

Gray Fuzzy Analysis
Method. By using the gray fuzzy assessment method to the risk assessment of ancient buildings, the cognitive differences attributed to evaluators could be avoided to a certain extent, and the scientific nature of the assessment results could be improved. e process of the gray theory [33,34] calculation (sample assessment matrix construction ⟶ determination of the whitening weight function ⟶ construction of gray assessment matrix), the whitening weight function, and gray assessment matrix were acquired by the following equations [35].
(1) Sample Assessment Matrix Construction. e risk assessment level vector can be acquired based on the established risk assessment indicators system: where t represents the number of risk levels. By using the Delphi method [21], p experts invited independently scored the respective indicator with the consideration of the assessment level vector V. Set the jth expert's assessment value of the jth secondary indicator of the first-level indicator U i of the criterion level as d (q) ij . e final sample assessment matrix D obtained is written as where i � 1, 2, 3, . . ., n; j � 1, 2, 3, . . ., n; i, q � 1, 2, . . ., p; (2) Determination of the Whitening Weight Function. e determination of the whitening function was different due to the different assessment objects. e function used in the gray assessment method was determined abiding by the literature and the practical assessment of this study. In the present study, the risk fell to five levels. us, we chose the five gray assessment model [36]. e functions that can be used to construct the gray assessment matrix in the gray statistical method are listed in Table 3. ij ). e following equations represent the gray statistics n (e) ij of the index U ij pertaining to the eth gray class and the total gray statistics n ij , respectively [36]: Based on the gray statistics and the total gray statistics, the gray assessment weight z (e) ij could be calculated by In the above equation, the value of z (e) ij indicates how strongly all experts advocate that U ij belongs to the eth gray class. e gray assessment weight vector Z i � (z (1) ij , z (2) ij , . . . , z (e) ij , . . . , z (E) ij ) of U ij for each assessment gray class can be obtained from z (e) ij . In turn, the gray assessment matrix Z of indicator U ij on each assessment gray class is expressed as   Shock and Vibration

Gray Relation Sensitivity Analysis.
e advantage of gray relational degree analysis is that it can be easy to calculate, and there will be no inconsistency between the quantitative results and the qualitative results. e calculated steps are represented as follows.
(1) Prioritization: m represents the number of assessment samples; n represents risk assessment index; x i is the mean value of the index set; and x 0 is the reference sample. We set it as the final risk in the gray fuzzy method in this article. e original assessment matrix x i ′ is [37] x i where i � 0, 1, 2, . . . , n. (2) Absolute difference Δ i (k) calculation: where k � 0, 1, 2, . . . , m.
where ρ � 0.5. (4) Gray correlation r i calculation: e greater the correlation is, the weaker the uncertainty and the less the sensitivity would be.

Comprehensive Assessment.
Based on the weight vector W and the gray assessment matrix Z obtained by the optimized combination method and the gray statistical method, respectively, their product was the comprehensive assessment vector H [24]: Under the combination of the integrated assessment vector H and the risk level vector V, the overall structural safety assessment value risk of the system was the product of the H and the risk level vector V: During the practical assessment process, the most intuitive way was to express the risk status of the system as quantitative assessment values. Risk denotes the final risk assessment value of the system. e safety risk level of the system could be determined through the combination with the risk assessment level vector V. It laid a scientific and effective reference basis for assessing the safety of ancient building structures.

3.1.
e Study Area. e Asoka Temple was initially established in the third year of Taikang emperor of the Western Jin Dynasty (282 AD) with a history of over 1,700 years, located in Yinzhou District of Ningbo. e Asoka Temple is known as the "Southeast Buddhist country." It refers to famous 283 temples of Zen Buddhism and one of the Chinese Buddhism "five mountains." Moreover, it is the only existing thousand-year-old temple in China named after the Indian King Asoka. e temple is notable for its treasure of Sakyamuni Buddha and exquisite pagoda.
ere are numerous scenic spots and historical sites close to King Asoka Temple. e plan is presented in Figure 7. e Asoka Temple takes up a crucial position to inherit the favorable Buddhist cultural tradition and carry forward the Buddhist cultural thoughts in the history of Buddhism for its historical and cultural value.
Given the urban transportation planning, the Treasure House Station of the Ningbo rail transit 1st line 2nd phase 10] e second gray class Relatively [7,10] e third gray class Relatively Shock and Vibration 7 went through the Asoka Temple. e Asoka tunnel refers to the only tunnel project in Ningbo with drilling and blasting construction methods. e construction of the tunnel went through the fault fracture zone. Moreover, the surrounding environment of this tunnel is complex. e upper soil slope section exhibits poor stability. Several parts of the tunnel exit are made up of gravel silty clay, intensely weathered rhyolite porphyry, moderately weathered rhyolite porphyry, and fault fracture zone. e rock mass was relatively cracked and underwent strong weathering. is project exhibits poor self-steady ability. e core protection area of Asoka Temple, a national-level cultural relic protection unit, is approximately 98.6 m away from the tunnel. Figure 8 illustrates the relative position between the subway and the temple. us, blasting vibration is capable of easily affecting the safety of the Asoka Temple and the stability of the existing railways. A safety assessment is required for the Asoka Temple.

e Weight Results and Analysis
3.2.1. G1 Methods. Ten experts were invited to fill in the scoring form in Table 4. Experts scored the significance of risk indicators abiding by the criteria in Table 1. e weight obtained by the subjective assessment method of the first index and the secondary index is listed in Table 5.

Risk Factor Weight Values Determined Based on
Entropy Weighting Method. Ten experts scored the 20 indicators by using the safety assessment system, as listed in Table 2. e score ranged from 1 to 10, with the most significance when reaching 10 and the least significance when reaching 1. Moreover, the weight calculation of the risk factors was performed with the improved order relation analysis method, and the results are listed in Table 6.
e calculation brought the weights of the indicators in the safety assessment system and the combination coefficients into the formula of the combination weights to obtain the combination weights. e results of combined weights are provided in Table 7.

Risk Values and Analysis.
In fact, this study used the Delphi method and invited 10 experts to assess 18 risk indicators based on the score criteria in Table 1. Besides, the indicator matrix was constructed and then normalized. e results of experts' assessment of the risk indexes are shown in   Table 8, from which we can analyze the opinions of 10 experts on the mentioned indicators. Fuzzy assessment matrix: According to Table 3, the gray assessment matrix weight vector can be calculated, and the total calculation results are shown in Table 9.
e correlation coefficient and ranking of risk factors are represented in Table 10.
Form a gray assessment matrix from gray assessment weight vectors Z and obtain the comprehensive assessment vector according to formula (11): e overall tunnel safety assessment level of the system from the equation:

Results and Discussion
Given Table 7, the weight of each tertiary risk factor was ranked as follows: 12 . e weights of the secondary risk factors were ranked as U 1 > U 2 > U 3 . As indicated from the weighting, the indicators of the ancient building itself exerted a critical effect on its safety assessment. According to Figure 9, among the mentioned tertiary risk indicators, the age of ancient buildings gained the maximal weight since the older the ancient buildings in China are, the more likely they would be damaged. Moreover, previous protective measures may not be sufficiently effective due to the limitations of science and technology, thereby significantly impacting the safety of the mentioned buildings. e arrangement of the correlation degree in Table 10 revealed that the risk  6.8 6.5 6.6 6.1 6.8 6.7 6.6 6.9 7.2 6.8 U 17 6.1 6.2 6.1 6.0 6.1 6.5 6.1 6.5 6.3 6.4 U 18 6.5 6.8 6.6 7. assessment value was highly sensitive to the two factors U 23 and U 25 , and U 23 was the most sensitive. e weighting of risk indicators was calculated with the combined optimal method, which reduced subjectivity in the assessment process to some extent. In particular, the greater the weighting is, the more significant the effect of the method on the combined weight would be. According to the risk values of the individual risk factors obtained in Table 7 and the overall risk value acquired eventually, the risk level of the building was IV (relatively safe).
As indicated in Figure 10, most of the risk factors of this project were in IV (relatively safe)-V (safe) risk level. However, the risk level of U 14 , the structure type, was III (relatively dangerous). e structure type of the building referred to a masonry-timber building's structure. On the whole, its destruction factor included wood corrosion, moth, and building deformation.
e safety of ancient buildings in masonrytimber structures was reduced attributed to long-time physical action, chemical action, and seismic factors. Moreover, the main vibration frequency of field blasting earthquakes was largely distributed in the range of 10-70 Hz, as indicated from the field data of the project. e structural dynamic response and modal analysis of the masonry tower indicate that its natural frequency ranged from 1 to 10 Hz. us, the two might overlap in the low-frequency region. While the blasting vibration was attenuated with the distance, the frequency of vibration tended to be in a smaller range and even overlapped the natural frequency. Consequently, the structural resonance would be caused inevitably, and then the dynamic response would be amplified. us, the blasting method U 24 and the frequency range U 22 should be considered.
In Figure 11, the range of most indicators' risk value was between 6 and 8, the fourth range according to Figure 4. It was therefore suggested that the experts invited considered   that the risk level of the mentioned factors was relatively safe given the situation provided by the actual engineering information. According to the mentioned results, dynamic blasting construction was adopted to monitor blast vibration. Such a method could maintain the security and durability of ancient buildings. Moreover, the step method, short drilling ruler method, and small dosage method were employed to regulate the risk factors according to the topographic and geological conditions of the site and the existing tunneling technology.
In the present study, the mean square root error (RMSE) acted as a convenient method to measure the deviation between the observed value and the true value. e synthetic risk value was taken as the observational value while the experts' score was considered true. As revealed from the results in Table 11, all relative errors were less than 1, thereby demonstrating that the model could be effective, which could be referenced for construction protection. Given the risk score of the expert assessment, the engineer should write the construction plan of safety protection of ancient buildings, and the constructor should take different     protective measures in accordance with the risk plan and obtain assessment results to increase the construction efficiency.

Conclusions
In this study, a set of safety assessment systems considering the complexity and fragility of ancient buildings was developed and applied to the Asoka Temple close to the Treasure House Station of Ningbo Rail Transit Line 1 Phase II Project. Several conclusions were drawn as follows: (1) e present study improved the original G1 method and preprocessed the initial data obtained to comprehensively assess ancient buildings' safety. e method adopted here converted quantitative data into interval numbers. Compared with the conventional analytic hierarchy process, this method could be more reasonable and accurate. e results revealed the risk scores of the tunnel construction. Besides, the risk level of the respective risk factor was determined to target the risk factors in the construction and control the risk promptly. e algorithm could exert significant application effects on the risk assessment of ancient buildings through the calculation of an example.
(2) e safety assessment model exhibited generality and could be applied to other ancient buildings in the same situation. To a certain extent, this study could effectively protect the preservation of ancient buildings and facilitate the modernization of the country and the survival of ancient buildings. It is significant to maintain the historical culture and continuously develop the advanced multiculture. (3) e optimized combined optimal method was employed to determine the weight of risk indicators and rank them given their significance. e results were real and reliable. e method guided the construction personnel to take appropriate protective measures. ey could allocate protection resources timely and provide measures to construct target safety protection projects.
On the whole, this study expedited the optimization of the ancient building adjacent to the blasting safety assessment in China. It is noteworthy that this study still relied partially on the expert scoring method, so it was considered subjective. In the subsequent research, experts can exploit the fuzzy sets of images to assess the safety of ancient buildings qualitatively and quantitatively, achieve accurate and comprehensive assessment results, and then provide guidance opinions on the protection of the buildings. Furthermore, the combination of artificial neural networks and assessment methods can be employed to make the safety of buildings predictable.
Data Availability e datasets employed and analyzed in the present study are available from the corresponding author upon reasonable request.

Conflicts of Interest
e authors declare that they have no conflicts of interest.