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<p>To investigate the sustainable relationship between industrial structure (INS) and water utilization structure (WUS) in social change, Shannon entropy is employed to analyze their internal evolution characteristics. Meanwhile, cointegration theory and Granger causality test are applied to explore the quantitative relationship between industrial structure and water utilization structure (RISWS) with structural breaks. Then, a case study is conducted in Baoding City, China. The results show that (1) there is a strong RISWS, and industrial structure entropy (ISE) and water utilization structure entropy (WUSE) exhibit synchronous changes. The continuous evolutions of INS and WUS lead to an initial decrease in entropy values followed by an increase. (2) A policy-induced structural break is observed in ISE and WUSE in 2012, and their cointegration relationship improves significantly when accounting for this break. Moreover, there is a one-way predictive effect from ISE to WUSE, indicating that changes in INS lead to adjustments in WUS. (3) The constructed model 3 exhibits the largest correlation coefficient of 0.908, with greatly improved simulation accuracy for WUSE and a relative error of 4.26%, effectively reflecting the short-term fluctuation characteristics and long-term sustainable RISWS. The integrated framework developed in this study provides an effective technology for quantifying the sustainable RISWS with structural breaks in social change.</p>

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Analysis of Sustainable Relationship Between Industrial Structure and Water Utilization Structure in Social Change Based on the Quantitative Model

  • 期刊论文

  • 发表日期：

    2026年4月7日

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  • Honglin Xiao,
  • Jinping Zhang,
  • Yuhao Wang

摘要

To investigate the sustainable relationship between industrial structure (INS) and water utilization structure (WUS) in social change, Shannon entropy is employed to analyze their internal evolution characteristics. Meanwhile, cointegration theory and Granger causality test are applied to explore the quantitative relationship between industrial structure and water utilization structure (RISWS) with structural breaks. Then, a case study is conducted in Baoding City, China. The results show that (1) there is a strong RISWS, and industrial structure entropy (ISE) and water utilization structure entropy (WUSE) exhibit synchronous changes. The continuous evolutions of INS and WUS lead to an initial decrease in entropy values followed by an increase. (2) A policy-induced structural break is observed in ISE and WUSE in 2012, and their cointegration relationship improves significantly when accounting for this break. Moreover, there is a one-way predictive effect from ISE to WUSE, indicating that changes in INS lead to adjustments in WUS. (3) The constructed model 3 exhibits the largest correlation coefficient of 0.908, with greatly improved simulation accuracy for WUSE and a relative error of 4.26%, effectively reflecting the short-term fluctuation characteristics and long-term sustainable RISWS. The integrated framework developed in this study provides an effective technology for quantifying the sustainable RISWS with structural breaks in social change.