Abstract
Cave murals are vital to cultural heritage, but they face an escalating risk of deterioration due to environmental and anthropogenic factors. Current assessments that rely on expert judgment lack objectivity and comprehensiveness. This study proposes an innovative health assessment framework that combines the analytic hierarchy process (AHP) with entropy weighting to objectively assign indicator weights, calculate hazard scores, and classify health levels. Combined with a common cloud model, it analyzes the dynamic sensitivity of murals to deterioration through digital features and cloud mapping. The method enables multidimensional quantitative analysis from historical, current, and prognostic perspectives, providing data-driven support for prioritizing preventive conservation. By minimizing subjective bias and combining assessment with predictive power, this approach improves the accuracy of degradation management and advances the digital preservation of mural heritage. This study aims to provide a mural health assessment system that prioritizes method validation over case-specific findings.
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Introduction
Murals, as repositories of human knowledge and centers for the transmission of ideas, embody invaluable historical, artistic, and cultural treasures. They represent irreplaceable gems of human civilization and serve as fundamental pillars of global cultural heritage. In recent decades, the study and preservation of murals have gradually become focal points in academic research and the field of cultural conservation. This study utilizes the Web of Science database, including the Science Citation Index Expanded and the Social Sciences Citation Index, to examine the annual publication trends since 20001. The data indicate a marked growth in research outputs related to murals, wall murals, and cave murals, reflecting the global academic community’s increasing commitment to the preservation of such cultural heritage.
In recent years, researchers around the world have employed various techniques to explore multiple facets of murals. He et al.2,3 explored bacterial, fungal, and microbial communities in grotto and tomb murals, providing valuable data for preventing and mitigating microbial damage to murals. Bomin et al.4 conducted scientific studies on polymer materials used in mural restoration, providing theoretical and technical foundations for addressing aging, ineffective material removal, and secondary protection of the Dunhuang murals. Liu et al.5. Similarly, Sakr et al.6 employed a multidisciplinary approach to study the murals in the Kubitt Havasettka tomb in Aswan, Upper Egypt, assessing the factors contributing to mural degradation. Due to the different expansion coefficients of the attachment layer and the surface material of the mural, humidity changes can easily lead to stratification, which will reduce the bonding strength of the mural and increase the risk of peeling7,8,9,10. Salt crystallized inside the mural (salt expansion) will increase local stress, destroy the mural structure, and cause flaking or cracking11,12,13. While these findings contribute to managing deterioration, the growing global consensus on preventive conservation policies emphasizes the importance of health assessments in the preservation of cultural heritage14. Such assessments effectively decelerate aging and degradation processes, ensuring the long-term preservation of these invaluable historical treasures for future generations15.
Using the Analytic Hierarchy Process (AHP), various intervention plans can be compared based on predetermined evaluation standards, calculating preference indices to guide decision-makers toward scientifically grounded and rational choices16. It offers a straightforward yet effective approach for addressing multi-objective, multi-criteria, or unstructured decision-making problems17. By decomposing complex problems into manageable components, AHP offers a clear representation of the problem structure. Furthermore, it is especially suitable for evaluation scenarios that account for both quantitative and qualitative factors18. The Entropy Weight Method (EWM): The objective weighting mechanism of information entropy effectively mitigates issues of excessive subjectivity and unreasonable weight allocation in multi-criteria decision-making. Some scholars have weighted indicators at spatial scales based on an indicator system including physiological, ecological, and environmental factors. They have also evaluated indicators through linear weighting and corresponding calculations by improving ecosystem services or establishing a comprehensive evaluation model of MOCC19,20,21,22,23. These studies underscore the efficacy of the EWM in determining indicator weights, minimizing the influence of human subjectivity in analytical and evaluative processes. Consequently, the assessment outcomes are more reliable and possess greater referential value. The cloud model finds broad applications in fields such as uncertainty reasoning, fuzzy control, and intelligent information processing. It bridges the divide between qualitative and quantitative analysis, reflecting the inherent uncertainty of concepts24. The cloud model resolves uncertainty issues that traditional fuzzy mathematics cannot address, particularly in systems exhibiting both fuzziness and random fluctuations. It offers a method for bridging qualitative and quantitative analysis, making it particularly suited for multi-criteria decision analysis, risk assessment, and other scenarios requiring the handling of complex uncertainty, as demonstrated in the research presented in this study.
In conclusion, this study focuses on the murals of the Cave temple complexes in Gansu Province and aims to develop a novel and objective method for mural health assessment. This study introduces the combination of the AHP with the EWM. The EWM is employed to assign weights to the evaluation indicators, effectively reducing the subjectivity inherent in the weighting process. This system guarantees the objectivity and scientific validity of weight allocation, thereby enhancing the adaptability and precision of decision-making while mitigating the influence of human biases on evaluation outcomes. Simultaneously, the Normal cloud model is utilized to establish the relationship between qualitative and quantitative factors, capturing the inherent uncertainty of the murals. The cloud diagram visually represents this uncertainty. In this study, AHP is employed to analyze the degree of mural deterioration, with subjective influence mitigated through its combination with EWM for objective weight allocation. Finally, the cloud model is applied to establish the relationship between qualitative and quantitative factors, effectively capturing the murals’ inherent uncertainty. Moreover, this method optimizes the decision-making process, enabling decision-makers to comprehensively consider both the importance and uncertainty of various factors in analyzing complex issues. By employing this integrated approach, decision quality is assured while effectively managing and utilizing available information, thereby optimizing the decision-making process. In conclusion, the combination of AHP and EWM offers a structured and flexible decision analysis framework, laying the foundation for scientific, objective, and detailed decision-making. Additionally, the cloud model’s prediction of mural uncertainty facilitates a comprehensive and objective evaluation, thereby improving the rationality, objectivity, and precision of decision-making.
Method
Study object
The Cave temple complexes in Gansu Province are widely recognized as one of the most invaluable cultural heritage sites globally (Fig. 1). The grottoes are renowned for their vibrant murals, sculptures, and cave temples. They represent an extraordinary repository of ancient Chinese civilization, bearing testament to the dialog and exchange between diverse cultures along the ancient Silk Road. The site features a grand scale, rich content, and a long history, ranking as the foremost cave complex in China and one of the largest and most well-preserved cave art treasures globally. The preservation of the grottoes can largely be attributed to their remote, arid climate and the relatively confined cave environment25. The site showcases an impressive integration of architecture, sculpture, and mural art (http://dh.dha.ac.cn/AllResource/List?table=Ebook2_METADATA). The murals vividly portray scenes of production, labor, social life, architecture, music, and dance from ancient ethnic groups and social classes. However, over time, the murals have been impacted by changes in the natural environment, leading to various forms of salt-induced deterioration, including peeling, bubbling, hollows, and encrustations26. Among these, mural salt deterioration is intimately connected to environmental changes within the caves27,28. The murals consist of a gypsum layer, a white powder layer, and a pigment layer. The salts in the gypsum layer primarily include NaCl and Na2SO429. When fluctuations in temperature and humidity surpass a critical threshold, NaCl undergoes a dissolution-crystallization transformation, while Na2SO4 undergoes a hydration-dehydration phase change. These salts generate stress during crystallization and hydration-dehydration, leading to structural damage to the gypsum layer of the murals30. Rainfall is also a significant factor contributing to increased cave humidity31. In the region where the Cave Temple is situated, rainfall is concentrated between June and August, with high intensity over short durations. On rainy days, the humidity inside the caves increases significantly, and once it surpasses a critical threshold, salt deterioration is triggered32. Therefore, the primary factors contributing to the deterioration of the Cave Temple murals include changes in the natural environment, alterations in the cave environment, and human activities that adversely impact the murals. This paper aims to develop a systematic analytical method for health assessment based on the aforementioned factors, considering both the current deterioration of mural surfaces and the impact of adhesion layers, thereby providing valuable data for scientific conservation efforts.
Technology roadmap.
The subject of this study is the murals of the Cave temple complexes in Gansu Province (Fig. 2). The on-site picture in Fig. 2 was taken by our group when collecting data on-site.
Study area and site map.
The murals at the Cave Temple are relatively well-preserved and cover a wide range of themes, including narrative paintings, landscapes, and architectural scenes, all of which are outstanding representations of Tang Dynasty art, a, b, c, d are the east, west, south, and north of the grotto temple respectively. (Fig. 3). Figure 3 shows the murals on different walls obtained by modeling, spliced together according to their orientation. For ease of reference, the murals in this study have been given names, using the capitalized initials of their pinyin transliterations as identifiers. For example, the east wall is marked as “EW,” and the top of the east wall is denoted as “EW-U.”
Cave temple complexes in Gansu Province.
This paper constructs a scientifically rigorous, rational, and standardized comprehensive evaluation system based on hierarchical analysis of the index weight distribution, utilizing the EWM combined with normal cloud model prediction. Initially, the paper determines the index system using the hierarchical analysis method; then, it calculates the weight vector through hierarchical single sorting, and after satisfying the consistency test, the EWM is employed in place of hierarchical total sorting to assign weights to the evaluation indicators. Subsequently, the weight of each indicator, as well as the weight of each indicator relative to each mural, is utilized to calculate the hazard scores for each mural; finally, the health score of each mural is calculated based on the hazard scores, and the health status is assessed. Furthermore, the digital features of each mural’s cloud model are computed using the vector data of each evaluation indicator, and generate their respective cloud maps to analyze the Deterioration Dynamic Susceptibility of the murals. The evaluation results of the system are then obtained. The technical route is depicted in the figure below, with the methods for each part of the technical route introduced thereafter.
Elements of the mural health assessment
In evaluating the health condition of the murals, it is crucial to consider a range of factors comprehensively to ensure the scientific accuracy and reliability of the results. These factors can be broadly categorized into three primary categories: the mural’s environmental context, surface deterioration, and the properties of the mural’s adhesion surface. The environmental context encompasses factors such as temperature, humidity, and lighting. Surface deterioration, as outlined in the “GB/T 30237-2013 Ancient Mural Deterioration and Illustration” standard, includes 28 distinct types of damage. Various murals may exhibit different forms of deterioration, with the specific conditions of the murals studied in this research illustrated in Fig. 4. The properties of the adhesion surface include surface hardness, moisture content, and salt concentration. This study comprehensively considers the selection of evaluation indicators in mural health assessments, ensuring that the resulting evaluation is both accurate and reliable, thereby providing valuable insights for mural conservation practitioners.
Factors affecting the health of murals.
This study focuses on the murals of the Cave temple complexes in Gansu Province. Due to the consistent environmental conditions (temperature, humidity, lighting) at the site, these factors were excluded from the evaluation indicator system. However, they are listed here for reference, in case future scholars conduct mural health assessments under different environmental conditions33. The extraction of surface deterioration is elaborated in the experimental section. For the assessment of adhesion surface properties, the average value of multiple points within the mural area was selected as the hardness indicator. This approach accounts for local variations, resulting in more comprehensive and representative hardness data. To ensure the effective evaluation of moisture and salt content without damaging the mural, a micro-damage analysis method was employed. This technique involves extracting small samples from the mural for chemical analysis, without compromising the mural’s integrity.
Entropy weight determination AHP
The principle of the AHP is to decompose a phenomenon or problem into relevant factors based on their nature prior to analysis. These factors are then classified into a multi-level hierarchical model based on their relationships. Subsequently, experts or empirical data are used to assess and measure the relative importance of lower-level factors to higher-level ones, and weight rankings are determined based on the degree of importance, facilitating quantitative analysis and comparison. The EWM is a weighting technique that calculates the entropy value of each indicator based on the extent to which the values of the indicators influence the overall system, thereby determining the weight34. In information theory, entropy refers to the degree of disorder or uncertainty in a system (entropy is a quantitative measure of uncertainty). The larger the entropy value of an indicator, the lower its weight.
AHP transforms decision-making problems into multi-level, single-objective issues, yielding clear results through straightforward mathematical calculations. The advantage of AHP lies in its foundation in the evaluator’s profound understanding of the problem’s nature, emphasizing the importance of qualitative analysis. However, because AHP necessitates the human construction of judgment matrices for each evaluation indicator during the hierarchical ranking process, it introduces a substantial amount of subjective error. To mitigate this, this study employs the EWM (entropy weighting) to assign weights to the evaluation indicators, thereby reducing human bias. This method effectively combines qualitative and quantitative analysis, rendering the decomposition process of complex systems mathematical and systematic, thereby enhancing decision-makers’ understanding. AHP simulates human decision-making thought by quantifying the impact of each factor at different levels, ensuring transparency and precision in the decision-making process35. With the reasonable weight distribution provided by the entropy method, the judgment of the importance of evaluation indicators is simplified into an intuitive weight calculation, enabling it to address practical problems that traditional optimization techniques struggle to solve.
The Mural hazard scores is a comprehensive metric used to quantitatively assess mural health. It involves scoring various forms of damage, degradation, and environmental impacts, followed by weighting and aggregating these scores to yield a final value reflecting the overall deterioration of the mural. This index assists in evaluating the extent of damage, the degradation trend, and the potential restoration measures required.
This study classifies the health status according to the mural hazard scores. The average value of all hazard scores data is calculated, and this average is treated as the median of the hazard scores. The maximum upper limit of all data is then determined, and the data is processed to derive the mural health score. The conversion factor, \(M=\frac{{Maximum\; upper\; limit}}{10}\), is obtained from the maximum upper limit of the mural hazard scores. Subsequently, the mural health score is calculated using Formula (1)36.
Among them, Z is the mural health score, Y is the mural hazard scores, and M is the conversion multiple.
The health grade of the murals is based on a 10-point system, with a lower limit of 0, an upper limit of 10, four groups, and a group interval of 2.5. The health grading table is presented in Table 1. The grading system consists of four levels: Grade I, Grade II, Grade III, and Grade IV. The higher the grade, the healthier the murals. Murals are assigned a health grade based on the grading table. A higher health score indicates better mural health and a higher grade, while greater damage corresponds to a lower health grade.
Degradation dynamic sensitivity analysis
The cloud model is a mathematical tool designed to handle fuzziness and uncertainty. It integrates the principles of fuzzy mathematics and probability statistics, enabling the transformation of qualitative concepts into quantitative analysis. The Degraded Dynamic Sensitivity of the mural is quantified using three numerical values: expectation (Ex), entropy (En), and super entropy (He). Ex reflects the “central stability” of the data; the smaller En, the more stable and less volatile the data. He represents the cloud’s thickness, with a smaller He indicating better mural Degraded Dynamic Sensitivity. As illustrated in Fig. 5.
Schematic diagram of the three digital features of the cloud model.
The entropy-weighted AHP can assess the health status of murals and provide an intuitive display of their current condition. This study also used a cloud model to analyze the dynamic sensitivity of the murals to degradation. The extracted mural surface damage and attachment surface attribute data serve as the input for the cloud model, which is then processed through the forward cloud generator to generate the digital features of the cloud and the mural cloud map. By comparing the results from the forward cloud generator, to analyze the Deterioration Dynamic Susceptibility of the mural. The health assessment system developed in this study overcomes the limitations of a single assessment approach, enhances the reliability of the evaluation results, and provides robust decision-making support for mural conservation and restoration (Table 2).
Method innovation and suitability for mural assessment
The AHP-entropy weight transfer was established for the first time. The cloud model hyperentropy (He) was mapped to the rescue priority index, breaking through the traditional static evaluation.
Results
Acquisition of experimental data
For the health assessment of murals in a cave at the Cave temple complexes in Gansu Province, this study utilized several evaluation indicators, including surface loss rate (paint layer detachment, ground layer detachment, scratches, and animal damage), cracks, moisture content, salt content, and hardness. First, the calculation of the surface loss rate provides not only a direct indication of the extent of damage but also a critical indicator for evaluating the effectiveness of restoration efforts. This data is derived from a detailed surface analysis, which accurately reflects the mural’s degradation over time. Secondly, hardness, as a significant physical property of the mural, is directly related to its durability and resistance to external physical impacts. In the hardness assessment, the average value of multiple points within the mural area was used as the hardness indicator. This method balances the influence of local variations on the overall assessment, yielding more comprehensive and representative hardness data. Finally, moisture content and salt content are two crucial chemical indicators affecting the preservation state of the mural, and their measurement is essential for understanding the mural’s condition and for formulating future conservation measures. By applying the aforementioned methods, this study conducted data analysis, weight distribution of different evaluation indicators, calculation of the mural hazard scores, and an intuitive presentation of the mural’s Deterioration Dynamic Susceptibility. The process and results of this study are presented below in detail.
Disease extraction
In the process of protecting and restoring ancient murals, accurately assessing their disease status is a crucial step. This paper uses our research platform to extract vectors of different diseases on the surface of murals, including surface diseases (peeling of the pigment layer, peeling of the ground layer, scratches, and animal damage) and linear diseases (cracks).
The disease types in the experimental data of this article are displayed (Table 3).
Disease vector data
In accordance with the “GB/T 30237-2013 Ancient Mural Deterioration and Illustration” standards, the experimental platform developed by this research group was employed to systematically extract data on mural deterioration. The actual surface area affected by surface diseases, the actual length of linear diseases, as well as the total surface area and perimeter of each mural, are presented in Table 4. Based on the surface area and perimeter of the selected mural sections, quantitative indicators such as the relative area percentage and relative length percentage of each type of disease were calculated. The results of these quantitative analyses are shown in Table 5.
Visual analysis of diseases
The surface damage to cave murals can be intuitively represented using radar charts, as shown in Fig. 6. A smaller radar chart area indicates fewer damages in the cave. Additionally, it reveals the relative severity of surface damage within a mural and allows for a comparative analysis of different murals. For example, paint loss occupies the largest area in the radar chart, indicating that this type of damage is the most severe; conversely, animal damage is the least significant.
Disease radar chart.
Data preprocessing
Based on the disease vector data obtained in Section 4.1.2, the surface loss rate of each mural is calculated as the sum of the relative area percentages of all surface diseases. The cracks are derived from the length percentages of linear diseases, and the moisture content, salt content, and hardness values are obtained as described in the section “Acquisition of experimental data.” The vector data for the obtained evaluation indicators are presented in Table 6. To facilitate a better understanding and analysis of these data and to prepare for the subsequent health assessment, the original data in Table 6 were averaged, with the processed results shown in Table 7. This data processing not only simplifies the interpretation of the results but also provides support for further statistical analysis and trend prediction, thereby enabling the formulation and adjustment of the protection strategy in a more scientific manner.
Visual analysis of mural health status
After averaging the raw data, the disease data of the cave murals are intuitively represented in the form of a radar chart, as shown in Fig. 7. A smaller area on the radar chart indicates better health of the mural. The closer the chart is to a specific indicator, the more pronounced the indicator’s status on the mural. For instance, as shown in Fig. 7, paint loss in WW-U is the most severe, while deep loss and cracks in EW are the most prominent. Additionally, the radar chart can display multiple indicators simultaneously, allowing for both the comparison of the same indicators across multiple murals and the identification of strong and weak relationships between various indicators of each mural.
Mural health radar chart.
Data analysis
According to the section “Data analysis,” the first step is to use Formula (2) to calculate the vector for each indicator. The core of this step is to transform qualitative comparisons into quantitative values for further analysis. These vectors are then standardized using Formula (3) to ensure that the sum of the weights of each indicator equals one. These weights represent the relative importance of each indicator in the overall decision-making process. Finally, using Formula (4), we construct a weight matrix and calculate its maximum eigenvalue. The calculation of the maximum eigenvalue not only helps verify the consistency of the judgment matrix but also serves as the core of the entire hierarchical analysis method. The closer its value is to the actual number of indicators, the more consistent the judgment matrix is, thereby increasing the reliability of the decision-making process and results. Finally, the consistency index (CI) is calculated using Formula (5). The results are presented in Table 8.
According to the obtained consistency index \({CI}\), combined with the \({RI}\) value in Table 3, the \({CR}\) value is calculated by Formula (6). \({CR} < 0.1\) indicates that the consistency test has passed. At this time, the eigenvector of A can be used to calculate the weight vector (Table 9).
The weights of the mural evaluation index after averaging are determined in Table 8.
As shown in Table 10, the most critical factor in the health assessment of murals is the surface loss rate, which has a weight score of 0.5491. The surface loss rate of murals is directly related to their visual and structural integrity, making it the most significant and immediate indicator for assessing their health. Subsequently, the EWM is employed to determine the relative weight of each evaluation indicator.
EWM to determine the relative weight of each evaluation index
The EWM is applied to determine the weight of each attribute from a quantitative perspective. By calculating the information entropy of each evaluation indicator, its contribution to the overall information is quantitatively evaluated. Indicators with larger information content play a more significant role in the overall evaluation process and are assigned higher weights accordingly. Furthermore, the EWM effectively quantifies the uncertainty of each indicator, Visualize degradation dynamic sensitivity through entropy value, highlights the differences between indicators, and assigns greater weight to those that play a decisive role in the evaluation. Therefore, the weight distribution derived from the EWM is highly reasonable and accurately reflects the true impact of each indicator in the comprehensive evaluation. It reduces the influence of subjective judgment in weight assignment, making the weight distribution more scientific and objective.
To facilitate analysis, data from different ranges are converted into a unified standard form, and the evaluation indicators are standardized: Based on the original data, each value in the matrix X from Formula (7) is calculated using Formula (8), where surface loss rate, cracks, moisture content, and salt content are positive indicators, while hardness is a negative indicator. The corresponding formulas are applied, and the results are shown in Table 11. Next, Formula (9) is applied to calculate the numerical weights of all murals for different evaluation indicators, and the results are presented as follows.
The weights of the murals on the surface loss rate are:
The weights of the murals on the cracks are:
The weights of the murals on moisture content are:
The weights of the murals on the salt content are:
The weights of the murals on hardness are:
Calculation of mural hazard scores
The entropy-weighted AHP described above is used to calculate the overall weight of all evaluation indicators for the cave, as well as the weight of each mural relative to different indicators. The hazard scores of each mural are then calculated based on the AHP. The method involves multiplying the overall weight of each evaluation indicator (Table 10) by the weight of the mural for that indicator, summing the results of all indicators, and finally multiplying by 100 to enhance the data’s intuitiveness without affecting the results. The hazard scores for each mural are shown in Table 12.
Health level assessment
The conversion multiple \(M=\frac{{Maximum\; upper\; limit}}{10}=3\). According to the hazard scores of the mural, the health score of the mural is calculated using Formula (13), as shown in Table 13.
Based on the health grade table, the selected murals from the Cave Temple are categorized as follows: SW-U is level I, BQ and NQ are level II, and NW-U, EW-U, EW, and WW-U are level III. A higher mural health score corresponds to a better health grade, indicating better overall health of the mural. Through the application of the entropy-weighted AHP, these hazard scores are converted into an intuitive representation of the murals’ health status. This approach not only provides quantitative evaluation results but also effectively guides the prioritization of protection and restoration efforts. The application of the AHP, by establishing a multi-level structural model to quantitatively evaluate the influence of each factor, effectively integrates and analyzes multiple evaluation indicators, ensuring the scientific rigor and systematic nature of the evaluation results. The inclusion of the EWM addresses the limitations of the AHP and mitigates the influence of human subjectivity on the evaluation results. The combination of the AHP and the EWM enhances the reliability and value of the results for future reference.
Degradation dynamic sensitivity analysis based on the cloud model
Using the entropy-weighted hierarchical analysis method, we have classified the health status of the murals and evaluated their health levels. The murals will inevitably continue to deteriorate due to various factors. Therefore, we use cloud models to analyze the dynamic sensitivity of murals to degradation, integrating their current health status to provide a more scientifically grounded basis for their protection.
This paper uses the vector data of mural surface diseases and attachment surface attributes as input for the forward cloud generator. The original data is averaged to adjust the scale, ensuring that the mean of the data is zero, thus preventing any bias in its distribution. The results are presented in Table 14. These digital features capture the uncertainty and fuzziness of the attribute values. Utilizing these data through cloud maps effectively simulates the distribution and fluctuation of attribute values, Subsequently, the three digital features were fused to analyze the dynamic sensitivity of the mural to degradation, as illustrated in Table 15.
The advantage of the normal cloud model lies in its ability to facilitate the transition from theoretical analysis at the conceptual level to specific applications at the data level through simple mathematical transformations, thereby enabling the model to adapt to various analytical and processing needs. The normal cloud model is highly effective in representing and reasoning about various types of uncertain knowledge. In particular, it intuitively displays the uncertainty of the mural through a cloud map. This visual representation not only simplifies the understanding of complex data but also assists decision-makers in making more informed and rational judgments in the face of uncertainty. Figure 8 illustrates a cloud map of the mural.
Mural Cloud Map.
The cloud map of the murals reveals that the super entropy (He) of EW, WW-U, and SW-U is zero, while the entropy (En) of EW is the highest among the three murals, and the entropy (En) of SW-U is the lowest, indicating that SW-U exhibits the best stability. The entropy (En) and super entropy (He) of NW-U are the largest among the seven murals, indicating that NW-U demonstrates the worst stability.
In mural conservation, salt content and hardness are key indicators with significant weights, reaching 0.2225 and 0.2442, respectively. This indicates that these two factors significantly impact the DDS and deterioration of the murals. The hardness of the mural’s substrate directly affects its stability and durability. The higher the hardness, the more stable the structure, effectively reducing the formation of cracks. Once cracks form, they provide channels for moisture and contaminants to penetrate the mural layer, thereby accelerating its deterioration. Walls with higher hardness exhibit greater resistance to external environmental influences, offering enhanced protection for murals. Simultaneously, the presence and migration of salts contribute to several issues. They absorb moisture from the environment, leading to fluctuations in the surface humidity of the mural. These humidity fluctuations can cause the mural material to expand and contract, leading to cracks and peeling. Certain salts may also react with pigments or chemical components in the mural, leading to color changes or damaging the chemical structure. Overall, most murals are affected by multiple diseases, with their health primarily influenced by surface diseases, while the properties of the mural’s substrate predominantly determine its stability.
Discussion
This paper proposes an evaluation system based on cave temple murals. Compared with the existing single-method evaluation, this paper combines the hierarchical analysis method with the entropy weight distribution method and the normal cloud model. The hierarchical analysis method is used for scientific analysis, and the EWM is combined to weight the evaluation indicators, avoiding the subjective error caused by the artificial construction of the judgment matrix of the hierarchical analysis method to determine the weight of the evaluation indicators. Finally, the cloud model is used to perform a dynamic sensitivity analysis of the murals. The mural evaluation system constructed in this paper comprehensively considers various risk factors affecting the health status of the murals and evaluates the health status of the murals. The influence of subjective human factors is effectively reduced, making the evaluation results more scientific. The results of this study show that although NW-U has the best health, its stability is poor; SW-U has the worst health, but its performance is the most stable. It can be seen that if the murals studied in this paper need to be maintained, it is recommended to give priority to NW-U, because NW-U has the best health, relatively fewer diseases, and is easier to repair. In addition, NW-U has poor stability, which means that the disease increases faster, so timely maintenance is required. Empirical research shows that this method is accurate and feasible in the health assessment of cave temple murals and can effectively overcome the limitations that may be caused by relying on a single method. The analysis results of this method provide us with a comprehensive, accurate, and objective assessment of the health status of murals. It not only improves work efficiency but also makes the assessment results more comprehensive and credible, providing a feasible idea for subsequent research, and is of great significance to the preventive protection of murals. In summary, through precise data analysis and advanced evaluation methods, we can not only clearly identify the current health status of each mural area but also formulate more targeted protection measures based on these data, thereby prolonging the preservation of these precious cultural assets and providing a solid scientific foundation for future conservation efforts.
Although the health assessment method proposed in this paper is highly reliable and objective in the assessment of ancient building murals, it still has certain limitations. First, although the existing health assessment system integrates disease and physical and chemical indicators, it has not fully considered the chemical kinetic properties of materials. In the future, molecular dynamics simulation and material aging database can be introduced to construct a three-dimensional coupled degradation prediction model of mural materials, environment, and time; secondly, with the development of science and technology, the extraction of evaluation indicators will be more accurate, thereby obtaining more detailed evaluation results. This paper aims to propose a practical mural health assessment method, verify its feasibility and rationality, and provide a certain reference for future related research.
Data availability
The data used in this study were not obtained from the Internet or other channels, but were authorized to be collected on-site in the scientific research projects in which this group participated.
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Acknowledgements
This research was supported by the National Natural Science Foundation of China (No. 42171416) and the National Natural Science Foundation of China (No. 41401536).
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C.H. and G.X. conceived the proposed ideas and proposed the experiments. Y.W. performed and improved the analysis system and wrote the manuscript. Y.H., X.M. and X.L. were responsible for commenting on the manuscript and interpreting the research significance of the paper. All authors approved the final manuscript.
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Hu, C., Wang, Y., Xia, G. et al. Health assessment method of cave murals based on entropy-weighted AHP-cloud model. npj Herit. Sci. 13, 279 (2025). https://doi.org/10.1038/s40494-025-01856-y
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DOI: https://doi.org/10.1038/s40494-025-01856-y
