Quantitative Analysis of the Social Value of Silk Road Flower Rain Dunhuang Music and Dance Drama

1. Introduction

Dunhuang music and dance culture is a major component of Dunhuangology, Dunhuang music and dance drama Silk Road Flower Rain integrates musical and dance elements from both the Central Plains and the Western Regions, showcasing cultural fusion along the ancient Silk Road. It absorbs musical and dance imagery depicted in the Dunhuang murals, such as the Reverse Pipa (playing the pipa behind the back) Dance, the Hu Xuan Dance, and the Scatter Flower Dance, and not only possesses high artistic value but also carries rich historical and cultural significance.

In 1979, the successful performance of Silk Road Flower Rain was a historically significant event that sparked a research boom among scholars on Dunhuang music and dance, setting off an upsurge in Dunhuang studies in the 1980s, resulting in numerous research achievements. Numerous scholars have elaborated on the formation and development of the Dunhuang music and dance genre from aspects such as its generative mechanism, cultural connotation, inheritance system, philosophical thought, aesthetic dimension, and the artistic value of Dunhuang music and dance. At the same time, they have made positive explorations in innovating the theory and practice of Dunhuang music and dance education. More musicians, dancers, and educators have affirmed its cultural and artistic characteristics, undertaking work in professional development, textbook compilation, and talent cultivation for Dunhuang music and dance (Dong, 1979,1982; Ye, 1982, 1985; Chen 1983, 1985, 1988a, 1988b; Xi, 1983, 1992a, 1992b; Zhuang, 1984, 2002; Niu, 1991; Zheng ,1997, 2002; Gao, 2000, 2002, 2008; Wang &Chai, 2007).

Dunhuang music and dance culture is a treasure in the ancient art heritage of China. Artists and scholars in China's educational circles keenly realized significant that build unique music and dance professional school, integrating this unique cultural heritage into university arts education helps broaden students' artistic perspectives, cultivate their aesthetic taste, and foster a sense of national pride. As an essential part of Chinese traditional arts, inheriting and promoting the value of Dunhuang music and dance culture in university arts education management plays a significant role in enhancing students' artistic literacy and promoting national culture. Professors He Yanyun and Shi Min from the Beijing Dance Academy are the dance performers of the early Silk Road Flower Rain. Subsequent research mainly focuses on the teaching of Dunhuang music and dance and has achieved much educational results. He Yanyun (2009) compiled Dunhuang Dance Training and Performance Tutorial, and Shi Min (2012, 2023) compiled respectively Dunhuang Dance Tutorial: Presentation of Musician Dancer Images and Dunhuang Dance Tutorial: Presentation of Male Musician Dancer Images and carried out the teaching of Dunhuang music and dance in the undergraduate and postgraduate teaching of the Beijing Dance Academy. To inherit and develop Dunhuang dance, Lanzhou University of Arts and Science specially established the Dunhuang Dance Inheritance and Development Research Center, and Northwest Normal University established the Dunhuang Institute, developing Dunhuang music and dance as a characteristic of the school's art education.

However, the current research on Dunhuang music and dance in China is mainly focused on the research stage of Dunhuang dance, in the current university arts education management system, the inheritance and development of Dunhuang music and dance culture still face many challenges:

First, the inheritance of Dunhuang music and dance requires specialized talent. The musical and dance terminology used by artists of the past era is wrapped in Dunhuang scriptures, making musical notation more difficult to interpret than transformation texts, lyrics, an arduous task indeed.

Second, in the construction of the university arts education system, many veteran artists and scholars have departed, leaving the teaching resources, faculty, and practice platforms for Dunhuang music and dance culture needing further improvement.

Third, under the impact of modern culture, the influence of traditional music and dance culture among young people is gradually weakening. From the 1980s to the end of the last century, after musicians Ye Dong (1982, 1985), Xi Zhenguan (1983, 1992a, 1992b), and Chen Yingshi (1983,1985,1988a,1988b) no young generation has been found to continue the inheritance and research of ancient Dunhuang music and dance scores.

Against this backdrop, to address these challenges, foster cultural confidence, and effectively inherit and develop Dunhuang music and dance culture, this study takes Silk Road Flower Rain, a representative work of Dunhuang music and dance, as the core research object. On the one hand, it explores the rich cultural significance of Dunhuang music and dance (a vital component of Dunhuangology) and empirically analyzes the impact of social cultural identity and social participation on its social value using questionnaire surveys and ridge regression models, to clarify the key driving factors of the social value of Dunhuang music and dance. On the other hand, it further seeks to optimize the development model of Dunhuang music and dance culture through targeted strategies: strengthening regional cultural exchanges, organizing community activities to boost social engagement, and providing education and training to encourage participation; utilizing modern technologies like artificial intelligence and virtual reality to innovate cultural outreach methods; integrating Dunhuang music and dance courses into educational systems to improve cultural education for younger generations; and promoting the global influence of Dunhuang culture in the context of the Belt and Road Initiative through policy support and international collaboration. Ultimately, this study aims to provide valuable references for scholars and managers in the field of Dunhuangology research and offer practical guidance for the modernization, and enhancement of social value in the inheritance of traditional Dunhuang music and dance culture.

Previous studies have mostly focused on art history and dance forms, while lacking quantitative research on social value, Therefore, this study attempts to quantitatively analyze the impact of social and cultural identity and social participation on the social value of Silk Road Flower Rain through questionnaires and ridge regression models.

Alternative approaches for Likert-scale outcomes include ordinal regression and structural equation modeling. We adopt a penalized linear specification for two reasons: (i) the composite outcome is approximately continuous with acceptable distributional diagnostics, and (ii) ridge penalization mitigates multicollinearity among conceptually related indicators without discarding information.

2. Literature and Research Hypothesis

The great work on the study of Dunhuang Grotto art, Complete Collection of the Dunhuang Grottoes (Dunhuang Academy, 2016), was compiled and published by the Dunhuang Academy, the content covers art, religion, archaeology, documents, cultural relics protection, etc., and can be used by researchers in related fields. The mural music and dance art in the Dunhuang caves is not only a unique form of art but also provides a comprehensive window for people to understand ancient culture and art. It embodies the integration of multiple academic disciplines. Apart from clearly displaying aesthetics, costume studies, musicology, dance, and painting, it also encompasses elements from architecture (Sun &Sun, 2001; Fan &Chai et al, 2011; Fan,2014; Peng, 2018),material science (Su &Zhang, 2018; Yin &Sun, 2019; Zhang et al, 2022), mechanics (Li &Du, 2016; Wang &Yan, 2016; Yuan &Shi, 2000; Zhang, 2022; Hu & Brimblecombe, 2023; Zhang &Tang et al, 2024), archaeology (Fan, 2014; Chai & Liu, 2019; Rong, 2024), history (Ning, 2020; Rong, 2024), sociology (Fan, 2014; Rong, 2024), and Buddhism (Ning, 2004; Rong, 2024), reflecting the profound knowledge and skills of ancient laborers. When people admire the mural music and dance art in Dunhuang caves, they are first presented with the beauty of cave architectural structures and the application of mechanical principles, the ingenious use of techniques for pigment preparation, the sophisticated painting skills, and the comprehensive application of aesthetics and dance studies in the murals, all of which are impressive. The meticulous representation of characters' costumes and dance details reveals different clothing styles and dance poses, offering a rich visual feast. This detailed portrait not only shows the artists' skills but also provides insight into the social features and aesthetics of that time.

Culture social identity theory, proposed by Tajfel and Turner (1979) and Tajfel (1982), defines social cultural identity as the sense of belonging and recognition individuals or groups have toward their societal culture, while social participation refers to individuals actively engaging in social activities and assuming social responsibilities. When people strongly identify with their social culture, they are more likely to participate in cultural inheritance and social welfare activities. These two elements play a key role in cultural heritage preservation and the realization of social values.

Cultural identity is the core driving force behind cultural heritage preservation, with stronger cultural identity enhancing public enthusiasm for participating in cultural protection efforts (Smith 2006). In addition, researchers (Putnam 2000) also emphasized the importance of social participation in accumulating social capital and realizing cultural value. He also discussed ways to rebuild community involvement, including encouraging people to return to social activities and strengthening economic and public policy support for communities.

In intangible cultural heritage and cultural identity, stating that the establishment of an intangible cultural heritage identity system requires the combined efforts of governments, experts, scholars, heritage inheritors, and the general public (Ma 2021).

Fan (2024) researched the relationship between university music and dance performances and social cultural inheritance, emphasizing that staging music and dance dramas on university campuses function not only as an engaging performance but also as a crucial vehicle for social cultural inheritance. It contributes to the preservation and promotion of cultural values, historical memory, and social sentiment. Research findings on the positive impact of social participation in traditional cultural inheritance reveal that active social engagement can enhance the social influence and recognition of traditional culture.

However, cultural identity is the most profound form of identity in the context of globalization. Citizenship theory emphasizes the importance of individual participation in public affairs, arguing that active social participation helps strengthen social cohesion and public welfare. Participating in cultural activities and heritage preservation is an essential form of civic engagement, facilitating cultural heritage and innovation. The mechanism by which individual cultural identity forms serve as an engine for cultural-identity-education. Cultural experience vividly interprets and embodies cultural identity, acting as a refueling station in the localization of cultural exploration pedagogy (Yan, 2023).

Social value inheritance preserves cultural uniqueness and provides market demand for the cultural creative industry. To achieve mutual benefits, the government can fund creative projects and encourage collaboration, while educational institutions can train talents with both inheritance and innovation abilities. This promotes cultural inheritance and innovation, bringing more cultural value to society. As an essential component of Chinese cultural heritage, Dunhuang music and dance carry both profound historical and rich social value.

Social cultural identity can enhance public understanding and recognition of the social value of Silk Road Flower Rain. When people have a deep recognition of the cultural connotations and social significance represented by Silk Road Flower Rain, they are more willing to support and participate in its inheritance activities. This sense of identity can also promote cultural exchanges among different groups, strengthening social cohesion.

Lin (2024) explored the relationship between digital preservation of museum artifacts and social participation through a dedicated study on the former. The research analyzed the role and significance of social participation in digital artifact preservation, revealing that social engagement not only facilitates the smooth implementation of digital preservation initiatives for artifacts but also enables the sharing and dissemination of cultural resources. Furthermore, it contributes to raising public awareness of historical culture and advancing both societal development and cultural heritage inheritance.

Social participation offers a broad platform for the inheritance of Silk Road Flower Rain. Through participation in various cultural activities, community projects, and volunteer services, the public and organizations can directly contribute to the promotion and development of Dunhuang music and dance. For instance, organizing cross-regional performances of Silk Road Flower Rain, conducting related educational training, and participating in cultural heritage preservation projects all play a role.

By enhancing social cultural identity and promoting social participation, the social influence and public recognition of Silk Road Flower Rain will be increased. This not only helps attract more resources and policy support but also promotes the inheritance and development of Silk Road Flower Rain on a broader societal level. In modern society, with the development of economic globalization and cultural diversity, people’s awareness of cultural identity and social participation has profoundly changed. For Silk Road Flower Rain strengthening social cultural identity and encouraging social participation aids in fully realizing and passing on its social value. This actively promotes exchanges and cooperation among different countries and ethnic groups, fostering mutual understanding and trust.

However, existing literature seldom integrates social capital theory and cultural identity theory into empirical modeling of cultural heritage value, this study proposes empirical analysis of the social value of Dunhuang Music and Dance Drama Silk Road Flower Rain. To deeply preserve traditional cultural content and innovate cultural dissemination methods can enhance cultural value. By delving into cultural depth, the spiritual richness of the work is elevated, and innovative dissemination methods expand its influence. We will put forward the following 2 research hypotheses.

H1: Social cultural identity has a significant positive impact on the social value of Silk Road Flower Rain.

H2: Social participation has a significant positive impact on the social value of Silk Road Flower Rain

In the following contents, this study will empirically test this hypothesis through data analysis, aiming to provide scientific evidence and strategic recommendations for the inheritance and realization of the social value of Silk Road Flower Rain.

3. Research Methodology

3.1. Questionnaire Design and Survey

To comprehensively evaluate the social value of Silk Road Flower Rain, we designed a detailed multi-value assessment questionnaire that encompasses various specific indicators. This questionnaire provides data support for the quantitative analysis of these indicators. Table 1 is the structure of the questionnaire and the survey indicators for each value dimension; the questionnaire is also divided into five levels: 1, 2, 3, 4, and 5, respondents only need to select the level they agree with.

The selection of the four core indicators in the questionnaire was based on two key considerations to ensure their scientific rigor and validity. First, it referenced mature scales in existing Dunhuang culture research. For example, Fan Xueqin (2024) used cultural exchange effectiveness and community cultural participation as core indicators in the study of the correlation between university music and dance performances and social cultural inheritance; this questionnaire drew on such indicator frameworks to align with academic consensus. Second, a pre-survey was conducted with 30 respondents (including 10 university teachers, 10 students, and 10 cultural workers) before the formal survey. The pre-survey data were subjected to reliability and validity tests: the Cronbach's α coefficient of the questionnaire was 0.87, indicating good internal consistency; the Kaiser-Meyer-Olkin (KMO) test value was 0.82, and the Bartlett spherical test result was significant (p < 0.001), confirming that the indicators were suitable for factor analysis. Based on the feedback from the pre-survey, the expression of individual items was optimized (e.g., revising influences Dunhuang culture to influences the public's sense of belonging and recognition toward Dunhuang culture to enhance clarity), and the final four indicators were determined.

We distributed this survey questionnaire to 150 respondents, including 50 university teachers and social scholars, 50 university students, and 50 artists and general workers, to ensure the representativeness of the sample. After collecting the questionnaires, we first conducted validity screening of the 123 returned questionnaires (with an effective recovery rate of 82%) based on the following criteria: (1) excluding questionnaires with incomplete answers (e.g., missing more than 2 items); (2) excluding questionnaires with obvious response biases (e.g., selecting the same scale option for all items); (3) excluding questionnaires with logical contradictions (e.g., rating promotion of cross-regional cultural exchanges as extremely effective but rating social cultural identity as no influence at all, which was judged irrational through cross-validation). After screening, we obtained 100 valid responses after quality control (attention checks and completion-time thresholds).

All analyses use the sample (n =100). Normality diagnostics are reported as robustness evidence rather than an inclusion criterion, this sample size meets the minimum requirement of sample size≥10 times the number of independent variables (Hastie et al., 2009) for ridge regression (with 6 independent variables in this study), ensuring the reliability of the model analysis. The descriptive statistics of the 100 final samples are shown in Table 2.

3.2. Data Processing and Variables Definition

Data Collection and Standardization: We collected scores from 100 respondents for the four questions outlined in the social value survey (Table 1). To eliminate the influence of different indicator dimensions (e.g., influence degree and importance degree) on the model results, all independent variables (the scores for Questions 1–4, as well as social participation and social recognition) were standardized using the Z-score method. The selection of the Z-score method instead of other standardization methods (e.g., Min-Max) was based on the following theoretical and practical considerations: First, Z-score standardization, as a data normalization technique, can be applied to any numerical data while preserving the relative distribution. In this study, because the Shapiro–Wilk test indicated the survey data did not significantly deviate from a normal distribution, the use of Z-score standardization is particularly appropriate. In this case, the standardized data not only retain their relative ordering but also follows a standard normal distribution, allowing us to fully leverage its statistical properties (for example, applying the empirical rule or conducting parametric tests). (Wooldridge, 2021). Second, the Z-score transforms each feature to have a mean of 0 and a standard deviation of 1, which can eliminate the influence of different dimensions (e.g., the difference between 1 to 5 points for influence degree and 1 to 5 points for importance degree) and ensure that the regression coefficients of each independent variable are comparable. Third, it is a common practice to approximate reliable Likert aggregated quantities as continuous quantities. The Z-score does not change the measurement level but unifies the dimension/stabilizes the estimation, while the Min-Max method may compress the data range and reduce the differences between variables. The specific formula for the Z-score method is as follows:

$$Z={\displaystyle \frac{X-\mu }{\sigma }}$$

(1)

where: X is the original value of a feature. μ is the mean of the feature across all data points. σ is the standard deviation of the feature across all data points. Z is the standardized score.

Measures and scaling. All predictors (X₁–X₆) were Z-standardized (mean=0, standard deviation =1) to harmonize scales and stabilize penalized estimation. Z-standardization does not change the measurement level of Likert items. Treating aggregated Likert-type scales as approximately continuous is common when reliability is adequate and distributions are not severely skewed, the outcome Y remains on the original 1–5 scale; under this scaling, the intercept approximates mean(Y) when predictors are at their means.

Variables Definition: In the social value survey that we conducted for Silk Road Flower Rain, the dependent variable (DV) is social value, denoted as Y. This variable reflects our overall assessment of Silk Road Flower Rain's impact on society. The independent variables (IVs) include social cultural values related to Questions 1, 2, 3, and 4, which we denote as X₁, X₂, X₃, and X₄. We also include two additional variables: Social Participation, denoted as X₅, which indicates the level of involvement of respondents in social and cultural activities. We calculate this score as the average of the scores for Questions 2 and 3 (X₂ and X₃). Additionally, Social Recognition, denoted as X₆, reflects respondents' level of approval of Silk Road Flower Rain, and we calculate this score as the average of the scores for Questions 1 and 4 (X₁ and X₄).

3.3. Theoretical Basis and Dimensional Rationality for Cultural Identity and Cultural Education for Younger Generations

The integration of Sociocultural Identity (X₁) and Cultural Education for Younger Generations (X₄) into the composite Social Recognition (X₆) draws on Smith’s heritage theory and the intergenerational transmission perspective (Smith, 2006). Smith emphasizes that the social value of heritage is dynamic: it depends on the current recognition of cultural meanings and on their future continuity through education-mediated transmission.

On the identity dimension (X₁), Silk Road Flower Rain embodies meanings such as intercultural dialogue and inclusiveness. Our questionnaire items (e.g., perceived accuracy in conveying Dunhuang’s inclusive spirit; strengthened pride in traditional culture) are designed to capture acceptance of these meanings. In the ridge specification reported in Section 4, the coefficient for Cultural Identity (X₁) is positive (≈0.17), indicating a positive association with perceived social value under our modeling assumptions (inference based on permutation + bootstrap with Holm adjustment).

On the education dimension (X₄), both formal curricula (e.g., Dunhuang dance modules in higher education; aesthetic education in primary and secondary schools) and interactive formats (e.g., youth versions of the production; digital practice tools) serve as channels through which meanings are internalized by younger audiences, the future subjects of identity in Smith’s terms. Descriptively, respondents who reported participation in Dunhuang-related educational activities assigned higher social-value ratings on average than non-participants (mean difference≈0.98 on a 1–5 scale; descriptive comparison, non-causal). Bringing X₁ (current recognition) together with X₄ (future-oriented cultivation) captures the full-cycle aspect of recognition emphasized by Smith.

3.4. Theoretical Basis and Empirical Connection for the Operational Indicators of Social Participation

The choice of community cultural activities (X₂) and cross-regional cultural exchanges (X₃) as the operational indicators for Social Participation (X₅) is grounded in social capital theory and cultural communication theory, aligns with Putnam’s framework on bonding and bridging social capital (Putnam, 2000). At the community level, frequent, accessible cultural activities (e.g., Dunhuang music-and-dance workshops and abridged performances of Silk Road Flower Rain in neighborhood venues) cultivate familiarity and attachment to cultural meanings in everyday settings. Such participation can support the diffusion of cultural symbols and strengthen local networks that carry social value.

Beyond local engagement, cross-regional exchanges function as boundary-spanning mechanisms that extend cultural reach and visibility. For a production whose narrative centers on the Silk Road, touring and interregional collaborations (e.g., performances in Xi’an, Beijing, and Shanghai; exchanges that juxtapose Dunhuang dance with local forms) represent natural opportunities for bridging ties. In our data, respondents who reported participating in activities associated with cross-regional exchange related to Silk Road Flower Rain rated social value higher on average than non-participants (mean difference≈1.23 on a 1–5 scale; descriptive comparison). This pattern is associated and consistent with the theoretical expectation that both localized participation and boundary-spanning exchanges contribute to perceived social value; it does not imply causality.

The integration of cultural identity and cultural education for younger generations into social recognition (X₆) also takes into account the complementarity between the two: Cultural identity is the current value foundation, and cultural education for younger generations is the future value guarantee. Only the combination of the two can fully reflect the full-cycle dimension of the social recognition of Silk Road Flower Rain. This design not only conforms to Smith’s (2006) dynamic perspective on cultural heritage protection but also makes the measurement of social recognition more comprehensive and theoretically in-depth, avoiding the short-sightedness of identity that may be caused by single-dimensional measurement. These theoretical insights justify the inclusion of X₂, X₃ as social participation indicators and X₁, X₄ as social recognition indicators.

3.5. Model Selection and Model Test

Model Selection. Ridge regression addresses strong correlations among conceptually related indicators and their composites while retaining all theoretically relevant predictors. We select the penalty λ by repeated 10-fold cross-validation (50 repetitions), minimizing mean cross-validated MAE (ties broken by the smallest λ). The optimal λ value is determined to be 0.15, which significantly alleviates multicollinearity (average VIF drops to 2.3 < 3).

Model performance. The model demonstrates strong out-of-sample explanatory power, with mean cross-validated R²≈0.905(SD≈0.055) and mean cross-validated RMSE≈0.22 on the 1–5 outcome scale (Table 2). These metrics were computed on held-out folds; we do not interpret MSE as a percentage of variance. Correlation diagnostics and the penalty path indicate that ridge regression stabilizes estimates in the presence of multicollinearity.

Validation and inference. We assessed generalization using repeated cross-validation and 100 iterations of a random 80/20 holdout. No artificial noise was added to Y in the primary analyses. Uncertainty was quantified with 10,000-sample permutation tests (labels shuffled, X held fixed) and 10,000-sample stratified bootstraps to construct two-sided 95% percentile confidence intervals, with Holm–Bonferroni correction applied for multiple slope comparisons. Adjusted p-values are reported to four decimal places (minimum reportable value = 0.0001).

4. Results and Discussions

Analyses were conducted in Python using scikit-learn for model fitting and cross-validation, NumPy/Pandas for data handling, and custom routines for permutation/bootstrapping.

4.1. Average Scores of Respondents

Average scores and standard deviation are reported in Table 3.

4.2. Ridge Regression Model Building

Ridge regression performed using Python software, the regression equation is obtained as follows:

Y=2.9238+0.1734X₁+0.2009X₂+0.1955X₃+0.1607X₄+0.2798X₅+0.2302X₆

(2)

where:Y represents social value. X₁, X₂, X₃, X₄ correspond to the scores for questions 1, 2, 3, and 4, respectively. X₅ represents social participation (average of questions 2 and 3). X₆ represents Social Recognition (average of questions 1 and 4).

A ridge regression model is used for predictions: Input standardized new data and use the trained ridge regression model to predict social value. Predicting social value (solid line) with 95% bootstrap confidence band (shaded) are shown in Figure 1. Estimates are from ridge regression with λ selected by repeated 10-fold cross-validated (50 repetitions). Predictors are Z-standardized; the outcome is on the original 1–5 scale. Bands are based on 10,000 stratified bootstrap resamples.

Figure 1 presents the ridge regression fitting curve between standardized independent variables (X₁- X₆) and social value (Y), with a 95% bootstrap confidence band (shaded area). The fitting curve of social participation (X₅) has the steepest slope (0.28), consistent with its highest regression coefficient, while the curve of youth cultural education (X₄) has the gentlest slope (0.16), reflecting its weak driving effect. All curves are within the 95% confidence band, indicating stable predictive performance of the model.

4.3. Ridge Regression Model Test

Inference Under Penalization. Because ridge regression does not yield OLS-style closed-form standard errors, we quantify uncertainty via 10,000-sample permutation tests (labels shuffled; X fixed) and 10,000-sample stratified bootstrap to construct two-sided 95% percentile CIs. We control the family-wise error rate using Holm-Bonferroni and report adjusted p-values to four decimals (minimum reportable value p= 0.0001).

Overall Fitting Test: The results of the cross-validation show that the average Mean Squared Error (MSE) is 0.0491 with a standard deviation of 0.0093, and the average R² value is 0.9052 with a standard deviation of 0.0550. This indicates that the model still explains the variability of the target variable well, accounting for approximately 90% of its variability. The model performance remains quite good, and the small standard deviations of both the MSE and R² suggest that the model's performance is relatively stable across different folds.

The model exhibits high out-of-sample explanatory power and stable error metrics across repetitions, indicating reliable predictive associations but not causal effects.

4.4. Model Interpretation

The regression coefficients for X₁, X₂, X₃, X₄, X₅, and X₆ are 0.1734, 0.2009, 0.1955, 0.1607, 0.2798, and 0.2302 in equation 1, respectively. All these coefficients are positive, indicating a positive correlation between the independent variables and the dependent variable (social value Y). As these variables increase, social value also increases.

The coefficients for X₅ and X₆ are relatively large (0.2798 and 0.2302, respectively), suggesting that social participation (the average of questions 2 and 3) and social recognition (the average of questions 1 and 4) have a more significant impact on social value.

The size and direction of the regression coefficients are reasonable and align with expectations. Particularly, the larger impacts of social participation (X₅) and social recognition (X₆) on social value are consistent with reality, as social participation generally has a greater influence on social value.

Although X₅ and X₆ are derived from other independent variables, ridge regression effectively addresses the multicollinearity issue by introducing a penalty term (L2 regularization), preventing overfitting. The model performs excellently in this regard, with very stable prediction performance. Ridge regression is highly suitable for this scenario.

The model exhibits high out-of-sample explanatory power (mean cross-validated R²≈0.90, SD≈0.05) with stable error metrics across repetitions. Coefficients are directionally positive; after Holm adjustment, X₅ and X₆ remain statistically significant (adjusted p<0.0001), and the 95% CIs for these predictors exclude 0. Due to the model's high prediction accuracy, it can provide reliable decision support in practical applications.

To check the robustness of the research findings, we compared the standardized coefficients from the ordinal logistic regression (adopted to address the ordinal nature of Likert-scale data) with those from the ridge regression. The results show that the direction and relative magnitude of the coefficients are highly consistent across the two models (Table 4). Additionally, the ordinal regression passed the Brant test (all p-values > 0.05), confirming the proportional odds assumption holds. These results collectively verify that the main findings of this study are robust, and treating aggregated Likert-scale data as approximately continuous variables in the ridge regression does not introduce significant bias.

All coefficients in ordinal regression are statistically significant (p < 0.01), consistent with the ridge regression’s significance results. The ordinal regression model fit (McFadden’s pseudo-R² = 0.89) is also close to the ridge regression’s R²=0.905, further verifying robustness.

4.5. Impact Analysis of Each Factor on Social Value

The regression coefficient analysis reveals the heterogeneous influence of different dimensions on the social value of Silk Road Flower Rain, and interpreting these coefficients through specific cultural practices and realistic contexts can further clarify the internal logic of social value generation.

Question 1 (Impact of Social Cultural Identity, X₁): With a coefficient of 0.1734, this indicator exerts a moderately positive effect on social value. A one-unit increase in the score for social cultural identity leads to a 0.1734-unit rise in social value, reflecting that the public’s sense of belonging to Dunhuang culture, shaped by Silk Road Flower Rain, lays a foundational emotional foundation for recognizing its social value. For instance, audience feedback from domestic tour performances shows that 68% of respondents who reported strong identification with Dunhuang’s cultural connotation in the drama also rated its contribution to promoting national culture as extremely significant, verifying the role of cultural identity as a value perception precursor.

Question 2 (Role in Enhancing Community Cultural Activities, X₂): The coefficient of 0.2009 indicates that enhancing community cultural activities effectively boosts social value. A one-unit increase in this indicator’s score corresponds to a 0.2009-unit increase in social value, suggesting that enhancing community cultural activities promotes social value and that Silk Road Flower Rain plays a positive role in community events.

Question 3 (Effectiveness in Promoting Cultural Exchanges between Different Regions, X₃): With a coefficient of 0.1955, the highest among the four single indicators, this dimension has the most prominent impact on social value. A one-unit increase in its score leads to a 0.1955-unit increase in social value, which is strongly supported by the drama’s cross-regional and cross-border performance practices.

Since its debut in 1979, Silk Road Flower Rain has staged more than 40,000 performances in over 40 countries and regions, including Hong Kong, China, North Korea, Japan, Italy, Thailand, France, and the United States etc. Over more than four decades of artistic continuity, Silk Road Flower Rain has shared Dunhuang’s rich historical and cultural heritage with audiences around the world. In 2022, the production premiered online for a global audience, drawing over 200,000 live viewers and forming part of the cultural exchange program of the Belt and Road Initiative(Ding, 2024; Sheng, 2024). Such cross-regional cultural interaction not only expands the drama’s influence but also transforms single performance dissemination into two-way cultural co-creation, thereby amplifying its social value in promoting intercultural understanding, exactly explaining why this indicator ranks highest in coefficient among the four single questions.

Question 4 (Impact on Cultural Education of the Young Generation, X₄): Despite a positive coefficient of 0.1607 (indicating a promoting effect), this indicator has the weakest impact on social value among the four questions. A one-unit increase in its score only leads to a 0.1607-unit increase in social value, which is closely related to the current limitations of Dunhuang music and dance education for young people. First, in terms of educational coverage, Dunhuang music and dance courses remain marginalized in most educational institutions: only a handful of universities (e.g., Beijing dance academy, Dunhuang college of northwest normal university) offer specialized Dunhuang dance majors or electives, while primary and secondary schools rarely integrate related content into aesthetic education curricula. Second, in terms of dissemination channels, youth-oriented promotion still relies heavily on offline forms (e.g., campus tour performances, museum lectures), while digital content tailored to young people’s media usage habits (such as short videos, interactive games, or virtual reality experiences) is relatively scarce. These realistic constraints limit the depth and breadth of the drama’s influence on young people’s cultural education, resulting in its relatively low coefficient.

Social participation (average of questions 2 and 3, X₅): With the highest coefficient of 0.2798 among all variables, social participation exerts the strongest driving effect on social value. A one-unit increase in social participation leads to a 0.2798-unit increase in social value, confirming that community engagement combined with cross-regional exchange, the core connotation of social participation, is the key path to enhancing the Silk Road Flower Rain drama’s social value.

Social recognition (average of questions 1 and 4, X₆): The coefficient of 0.2302 indicates a significant promoting effect on social value. A one-unit increase in social recognition corresponds to a 0.2302-unit increase in social value, reflecting that the public’s comprehensive approval of the drama (integrating cultural identity and recognition of youth education) is an important guarantee for its long-term social value. For example, won the title of The best Chinese dance drama in the Guinness Book of world in the 2024 (Du, 2024), Silk Road Flower Rain ranked first in the social recognition category, with 81% of respondents citing its ability to connect social cultural identity (X₁) with youth cultural education (X₄) as the primary reason for their approval, this directly aligns with the definition of X₆ as the composite of X₁and X₄, verifying the rationality of X₆’s dimensional design and its significant promoting effect on social value.

In summary, social participation and social recognition: Both have a significant impact on social value, particularly social participation, which shows that active engagement by the audience is a key to enhancing social values.

Impact of the four questions: All coefficients are positive, indicating that Silk Road Flower Rain has a positive impact in all areas, especially in promoting cultural exchanges.

Comparison: Social participation and social recognition show stronger influence compared to the individual questions, suggesting that assessing social value across different dimensions can better reflect the overall effect.

From the above analysis, it can be seen that the Dunhuang music and dance drama Silk Road Flower Rain has a wide and positive impact on social value, especially in terms of social participation and cultural exchange. Through targeted promotion and optimization, its social value can be further enhanced.

The above analysis verifies the establishment of research hypothesis, that is, social and cultural identity and social participation have a significant impact on the social value of Silk Road Flower Rain.

5. Development Strategies for Social Value of Dunhuang Music and Dance

Based on the empirical findings that social participation (X₅) has the strongest impact on social value and youth cultural education (X₄) has the weakest impact, this section designs targeted optimization strategies in accordance with the priority of influence factors, forming a closed loop of empirical conclusion to problem diagnosis to strategy implementation to ensure that each measure directly responds to the results of the regression analysis.

5.1. Prioritizing the Enhancement of Social Participation: Building a Community-University-Theater Linkage Mechanism

As the core explanatory variable of social value, social participation (X₅) is operationally defined as the composite of community cultural activities (X₂) and cross-regional cultural exchanges (X₃). To maximize its driving effect, the optimization focuses on expanding the breadth of public engagement and deepening the depth of cultural participation, with the following specific pathways:

5.1.1. Leveraging the Flying Apsara Effect of Silk Road Flower Rain

To address the demand for accessible cultural participation at the grassroots level, this study proposes launching the Silk Road Flower Rain community promotion program, which operates in quarterly cycles centered on the performance-interaction-co-creation model. The program’s implementation framework includes three core links:

Low-Threshold Performance Outreach. The Gansu song and dance theater dispatches mobile performance teams to residential communities, focusing on 15-minute abridged versions of the drama’s classic segments (e.g., the flower scattering dance and market scene in Chang’an). This design reduces the time and space barriers for community residents, particularly middle-aged and elderly groups, to access Dunhuang culture.

Interactive Workshop-Driven Participation. After each performance, professional Dunhuang dancers host thematic workshops to teach foundational movements (e.g., cloud hands and Flying Apsaras postures) and guide residents in creating community-adapted micro-dance works based on local life scenarios. These co-created works are publicly displayed through community electronic screens and the theater’s official social media platforms, which not only enhances residents’ sense of cultural belonging but also transforms passive viewing into active cultural production.

Ambassador-Led Sustained Participation. From workshop participants, community cultural ambassadors are selected and trained in Dunhuang cultural history and promotional methods. These ambassadors organize regular small-scale cultural sharing sessions (e.g., Dunhuang mural storytelling and simplified dance practice) to maintain long-term cultural vitality in the community, avoiding the one-off participation dilemma common in traditional cultural outreach.

5.1.2. Cross-Regional Exchange Participation: Breaking Geographical Barriers to Cultural Dissemination

In order to amplify the spillover effects of Silk Road Flower Rain across regions, a national touring scheme, coupled with a regional co-creation mechanism, is established and implemented through two principal strategies:

Hierarchical tour layout. Annual cross-regional tour seasons will target first-tier cities with high cultural consumption (e.g., Beijing, Shanghai) alongside selected second- and third-tier cities in central and western China (e.g., Chengdu, Xi’an, Kunming) that offer rich cultural diversity. At each stop, collaborative activities will be launched with local cultural centers to create drama segments that incorporate regional traditions, for example, integrating Sichuan opera’s face-changing technique into Silk Road Flower Rain performances in Chengdu, and weaving the Banhu melodies of Shaanxi folk music into the score in Xi’an. These localized adaptations strengthen the production’s cultural resonance with regional audiences.

Transparent Rehearsal Mechanism. During the tour, an open rehearsal day system will be implemented, with 2–3 weekly rehearsal sessions open to the public. Local audiences can observe the creative process (for example, choreography adjustments and costume design), engage in dialogue with directors and performers, and offer suggestions for regional cultural adaptation. Feedback gathered from these sessions will be used to refine the production’s content, thereby improving its regional dissemination and audience acceptance.

5.1.3. Leveraging the Flying Apsara Brand Effect and Digital Technology Innovation

The Flying Apsara element in Silk Road Flower Rain has transcended its artistic connotation to form a global cultural brand, with its image adopted in trademarks such as Flying Apsara TV station and Flying Apsara grand hotel (Wang, 2009). This study proposes leveraging this brand effect to drive the comprehensive revival of Dunhuang music and dance, while integrating modern digital technologies to innovate cultural dissemination methods:

Brand Value Conversion. Promote integration of Dunhuang art with the cultural and creative industries. Examples include developing Flying Apsara–themed products and experimenting with arts-finance partnerships, for example, public-welfare performances co-sponsored by cultural institutions and enterprises. These measures will both expand economic support for Dunhuang culture and increase its public visibility.

Cross-Media Promotion. Incorporate the Flying Apsara brand into multi-media content (e.g., Silk Road Flower Rain’s youth-version posters, Dunhuang culture documentaries) to strengthen brand recognition among young groups, complementing the digital education efforts in Section 5.2.

5.2. Strengthening Youth Cultural Education: Building a Curriculum-Practice-Digital Integrated System

The empirical analysis indicates that youth cultural education (X₄) has the weakest impact on social value, primarily due to two bottlenecks: limited coverage of Dunhuang music and dance courses in the education system (only offered by a few institutions such as Beijing Dance Academy) and over-reliance on offline dissemination channels (e.g., campus tours). To address these issues, this study constructs a curriculum-practice-digital trinity education management system for Dunhuang music and dance:

5.2.1. Curriculum Integration: Embedding Dunhuang Culture into Formal Education

Professional Curriculum Development. Integrate Dunhuang music and dance into the professional training system of art colleges and universities. For example, set up specialized courses such as history of Dunhuang dance, basic movements of Dunhuang music and dance, and choreography of Dunhuang dance dramas in undergraduate and postgraduate programs. Teaching resources such as Gao Jinrong’s Teaching Outline for Basic Training in Dunhuang Dance and Shi Min’s Dunhuang dance tutorial: Presentation of Music and Dance Images of Heavenly Music are used to standardize teaching content and cultivate high-level professional talents.

General Education Electives. Launch practical elective courses on Dunhuang music and dance in non-art majors of universities and secondary schools. These courses include hands-on modules (e.g., practice of simplified Flying Apsara dance movements) and cultural cognition modules (e.g., field trips to Dunhuang mural exhibitions and attendance at Silk Road Flower Rain live performances), aiming to improve the general public’s cultural literacy in Dunhuang art.

5.2.2. Digital Education Expansion: Breaking the Constraints of Offline Channels

To address the issue of uneven educational resources across regions, this study proposes collaborating with internet platforms (NetEase, Bilibili) to develop a Dunhuang Music and Dance Digital Classroom.The platform includes two core components:

VR Interactive Teaching Resources. Develop VR courseware such as 3D Restoration of Dunhuang Mural Dance, students can scan virtual mural images to trigger dynamic demonstrations of dance movements, and participate in virtual cave tours to understand the historical context of Dunhuang music and dance. These resources are incorporated into the national primary and secondary school aesthetic education resource database, enabling students in remote areas (e.g., rural schools in Gansu) to access high-quality Dunhuang culture education.

Youth-Oriented Digital Content. Produce short video tutorials (e.g., 5-Minute Learning of Dunhuang Dance Basics) and interactive learning games (e.g., Dunhuang Dance Movement Matching) to adapt to the media usage habits of young people. The platform also sets up a Youth Creation Zone, where students can share their Dunhuang-themed works (e.g., dance covers, digital paintings) to stimulate their initiative in cultural inheritance.

5.2.3. University-Industry-Research Collaboration: Expanding the Boundaries of Education

Promote multi-stakeholder collaboration among universities (e.g., Dunhuang College of Northwest Normal University), research institutions (Dunhuang Academy), and cultural enterprises to form a synergistic mechanism for Dunhuang music and dance education:

Joint Research on Teaching Resources. Cooperate with the Dunhuang Academy to sort out and digitize ancient Dunhuang music and dance scores (e.g., Xi Zhenguan’s translated versions of Dunhuang musical notations) and develop targeted teaching materials for different age groups.

Practice Platform Construction. Collaborate with cultural performance enterprises to establish off-campus practice bases—students participate in the rehearsal and performance of Silk Road Flower Rain’s youth version, engage in the development of cultural and creative products (e.g., Dunhuang dance-themed costumes, accessories) to connect classroom learning with practical application.

5.3. Policy Support and International Promotion: Guaranteeing Long-Term Sustainable Development

5.3.1. Policy and Financial Guarantee for Cultural Industry Integration

Policy Incentives. Governments at all levels (especially Gansu Province) should formulate targeted policies, such as providing tax reductions for cultural enterprises engaged in Dunhuang music and dance creation with allocating special funds for the construction of rehearsal venues and performance spaces. Additionally, incorporate Dunhuang music and dance into the list of key protected intangible cultural heritage to strengthen institutional guarantees for its inheritance.

Cultural Tourism Integration. Incorporate Dunhuang music and dance into tourism development and creative economic initiatives, for example, establish a permanent Flying Apsara performance venue within the Dunhuang scenic area offering immersive shows and simplified participatory dance workshops for tourists. Encourage local businesses to create derivative cultural products (e.g., Dunhuang mural–themed merchandise and traditional dance costumes) to extend the cultural consumption chain and strengthen the economic sustainability of Dunhuang music and dance inheritance.

5.3.2. Constructing an International Exchange Platform for Cultural Dissemination

As a representative work of Silk Road cultural exchange, Silk Road Flower Rain requires international collaboration to expand its global influence. This study proposes establishing an international Dunhuang music and dance exchange platform with three core functions:

Academic Exchange. Host annual international seminars on Dunhuang music and dance inheritance and innovation, inviting scholars and artists from countries along the Belt and Road (e.g., Iran, Kazakhstan) to discuss topics such as cross-cultural adaptation of Dunhuang art and digital preservation of dance heritage.

Performance Tour and Exhibition. Organize international tour performances of Silk Road Flower Rain (e.g., the 2019 Tehran performance that promoted Sino-Iranian dance fusion) and hold Dunhuang music and dance art exhibitions in major cultural centers (e.g., the Louvre in Paris), showcasing the artistic charm of Dunhuang culture to a global audience.

Global Dissemination Network. Collaborate with renowned international art schools (e.g., the Royal Academy of Dance in the UK) and media platforms (e.g., UNESCO’s cultural channels) to build a global dissemination network. Through this network, share Dunhuang music and dance teaching resources (e.g., digital versions of Dunhuang dance tutorial) and promote cross-cultural co-creation projects (e.g., joint dance works integrating Dunhuang and Western ballet elements).

5.4. Synergistic Optimization of Other Dimensions: Forming a Comprehensive Value Enhancement System

Based on the regression coefficient ranking of influencing factors X₅ > X₆ > X₂ > X₃ > X₁ > X₄, while prioritizing social participation and youth education, supplementary measures are implemented for other dimensions to ensure the comprehensiveness of the optimization system:

Enhancing Social Cultural Identity (X₁). Host monthly Dunhuang culture salons in major cities (Beijing, Shanghai, Lanzhou). The salons invite Dunhuang scholars, Silk Road Flower Rain performers, and intangible cultural heritage inheritors to share behind-the-scenes stories (e.g., the restoration process of Reverse Pipa Dance from murals) and organize immersive experiences (e.g., mural appreciation combined with dance practice). This aims to deepen the public’s emotional identification with Dunhuang culture.

Improving Strategy Implementation Efficiency. Develop an AI-driven personalized cultural recommendation system based on users’ historical data (e.g., participation in Silk Road Flower Rain performances, browsing Dunhuang culture content), the system pushes customized information (e.g., cross-regional tour schedules for users interested in cultural exchanges, youth digital courses for parents) to improve the precision and efficiency of strategy implementation.

5.5. Quantified Expected Outcomes

The outcomes map directly to the regression indicators (X₁–X₆) and therefore reflect targeted improvements in social-value drivers. Key expected outcomes by 2030 are:

• Socio-cultural identity (X₁): 85% public recognition of Dunhuang’s inclusive value and more than 10,000 young creators active on Bilibili.
• Youth education (X₄): university course coverage increase to 30%; 50% of young people familiar with Silk Road Flower Rain; and the X₄ coefficient rising to 0.22.
• Social participation (X₅): exceed 50,000 participants (300% of the 2025 baseline), with 60% engagement among local residents.
• International reach: tours in over 10 Belt-and-Road countries and a cumulative audience exceeding 1 million.

These benchmarks will be used for ongoing monitoring and dynamic adjustment of interventions, with the objective of increasing Silk Road Flower Rain’s overall social-value score by more than 40% by 2030.

5.6. Limitations and Future Directions

The sample in this study (100 copies) only covers the Northwest (45%), East China (23%), and South China (18%), lacking data from regions such as North China and Southwest China. From a statistical perspective, the small sample size leads to limited statistical power, such as the minimum detectable effect size for regression coefficients is 0.15, higher than the actual coefficient of X₄=0.1607, which may affect the precision of result inference. Future studies can expand the sample size to 300-500 copies, adopt stratified sampling (allocating samples according to the proportion of regional population), cover 6 major regions across the country, and include samples of overseas audiences (such as audiences from countries along the Belt and Road), so as to further verify the cross-regional and cross-cultural applicability of the model.

6. Conclusions

This study employs questionnaire surveys and ridge regression models to empirically analyze the social value of the Dunhuang music and dance drama Silk Road Flower Rain, yielding the following key findings:

First, ridge regression results confirm that all independent variables exert significantly positive effects on social value, with a high model goodness of fit (R²=0.905) and stable predictive performance—providing a reliable quantitative tool for evaluating the social value of Dunhuang music and dance culture. The regression coefficients of all independent variables are significantly positive at the p<0.05, according to the magnitude of the regression coefficients, the order of influence from strongest to weakest is: social participation(X₅=0.2798)>social recognition (X₆=0.2302)>community cultural activities (X₂=0.2009)>cross-regional cultural exchanges (X₃=0.1955) > social cultural identity (X₁=0.1734)>youth cultural education (X₄=0.1607). Among these, social participation emerges as the core driver, particularly excelling in promoting cross-regional exchanges and community engagement, while youth cultural education is identified as a critical area for addressing weak links.

Second, enhancing the social value of Silk Road Flower Rain and Dunhuang music and dance requires multi-dimensional synergy: integrating artificial intelligence (AI) and virtual reality (VR) to innovate cultural dissemination; optimizing the educational management system to expand youth cultural education coverage; and leveraging policy support and international collaboration (e.g., within the Belt and Road Initiative framework) to strengthen global cultural influence. Broader public participation and diversified dissemination channels, enabled by the fusion of culture and technology, are essential for achieving sustainable inheritance of Dunhuang culture.

Finally, this study makes several contributions. It operationalizes social value with a multi-indicator instrument and reports reliability (Cronbach’s α) and sampling adequacy (KMO), and it develops a quantitative analytical framework for the social value of Dunhuang music and dance culture—addressing a gap in the literature that has focused mainly on art history and dance forms while neglecting social value quantification. Methodologically, it employs penalized regression with resampling-based inference to ensure stable estimation under multicollinearity and offers transparent out-of-sample evaluation through repeated cross-validation and preregistered robustness checks. Together, the findings and proposed strategies provide practical guidance for modernizing traditional cultural inheritance and enhancing the social value of cultural heritage.