{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T15:07:21Z","timestamp":1785424041954,"version":"3.56.0"},"reference-count":97,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T00:00:00Z","timestamp":1777334400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["51979109"],"award-info":[{"award-number":["51979109"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["72271091"],"award-info":[{"award-number":["72271091"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"award":["51979109"],"award-info":[{"award-number":["51979109"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"publisher"}]},{"award":["72271091"],"award-info":[{"award-number":["72271091"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"publisher"}]},{"name":"the Natural Science Foundation of Henan","award":["252300420469"],"award-info":[{"award-number":["252300420469"]}]},{"name":"the High-level Talent Research Start-up Project of North China University of Water Resources and Electric Power","award":["202310024"],"award-info":[{"award-number":["202310024"]}]},{"name":"the Training Programme for Young Backbone Teachers of Higher Education Institutions in Henan Province","award":["2024GGJS061"],"award-info":[{"award-number":["2024GGJS061"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Systems"],"abstract":"<jats:p>Inter-basin water transfer projects (IBWTPs) play a pivotal role in alleviating the spatiotemporal imbalances of water resources. However, their operation is exposed to multiple, highly interdependent safety risks that can significantly undermine system stability and water supply reliability. Existing studies predominantly focus on isolated risk factors or rely heavily on subjective data, which limits their ability to capture the complex interrelationships among risks and reveal their underlying propagation mechanisms. To address these limitations, this study proposes a novel risk correlation analysis framework that integrates Interpretive Structural Modeling (ISM) with copula functions. ISM is first employed as a preprocessing tool to structure expert knowledge and develop an initial risk correlation framework. It is then used to hierarchically organize the complex interrelationships among risks. Subsequently, copula functions are utilized to model nonlinear dependencies and tail behaviors among risk variables. This enables a quantitative assessment of correlation strengths and facilitates the construction of a risk topological network. An empirical case study is conducted based on the Middle Route of the South-to-North Water Diversion Project. The results reveal 13 significant correlations among six second-level risk categories. Natural risks (e.g., floods and geological hazards) are identified as the primary driving factors. They exhibit a strong positive correlation (0.6155) with engineering risks and serve as the most critical nodes for proactive risk prevention and control. Engineering risks function as central intermediary hubs in the risk transmission process, whereas water quality and economic risks are characterized as terminal endpoints. Furthermore, three principal risk propagation pathways are identified: (1) natural risks \u2192 engineering risks \u2192 economic risks; (2) natural risks \u2192 operational scheduling risks \u2192 social risks; and (3) engineering risks \u2192 water quality risks \u2192 economic risks. The resulting risk topological network demonstrates significant small-world properties, indicating highly efficient risk transmission within the system. Ultimately, this study provides a robust quantitative approach for analyzing risk interactions in complex engineering systems and enriches the theoretical framework of engineering risk management. It also identifies critical nodes and key transmission pathways for risk prevention and control in IBWTPs, thereby offering significant practical implications for operational safety.<\/jats:p>","DOI":"10.3390\/systems14050477","type":"journal-article","created":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:43:51Z","timestamp":1777448631000},"page":"477","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Correlation Analysis of Operational Safety Risks in Inter-Basin Water Transfer Projects Based on ISM-Copula"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-1568-4695","authenticated-orcid":false,"given":"Tianyu","family":"Fan","sequence":"first","affiliation":[{"name":"School of Water Conservancy, North China University of Water Resources and Electric Power, Zhengzhou 450046, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhiyong","family":"Li","sequence":"additional","affiliation":[{"name":"School of Water Conservancy, North China University of Water Resources and Electric Power, Zhengzhou 450046, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-2004-5788","authenticated-orcid":false,"given":"Qikai","family":"Li","sequence":"additional","affiliation":[{"name":"School of Management and Economics, North China University of Water Resources and Electric Power, Zhengzhou 450046, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0789-1964","authenticated-orcid":false,"given":"Bo","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Water Conservancy, North China University of Water Resources and Electric Power, Zhengzhou 450046, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiangtian","family":"Nie","sequence":"additional","affiliation":[{"name":"School of Water Conservancy, North China University of Water Resources and Electric Power, Zhengzhou 450046, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,4,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"134543","DOI":"10.1016\/j.scitotenv.2019.134543","article-title":"Eutrophication and heavy metal pollution patterns in the water suppling lakes of China\u2019s south-to-north water diversion project","volume":"711","author":"Guo","year":"2020","journal-title":"Sci. Total Environ."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1080\/00049182.2019.1684625","article-title":"A review of the impacts of pumped hydro energy storage construction on subalpine and alpine biodiversity: Lessons for the Snowy Mountains pumped hydro expansion project","volume":"51","author":"Normyle","year":"2019","journal-title":"Aust. Geogr."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1093\/aepp\/ppw013","article-title":"Drought index insurance for the Central Valley Project in California","volume":"38","author":"Maestro","year":"2016","journal-title":"Appl. Econ. Perspect. Policy"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"12867","DOI":"10.1007\/s11356-016-6854-3","article-title":"Eco-environmental impact of inter-basin water transfer projects: A review","volume":"23","author":"Zhuang","year":"2016","journal-title":"Environ. Sci. Pollut. Res."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"109251","DOI":"10.1016\/j.jenvman.2019.07.022","article-title":"Predicting hydrological impacts of the Yangtze-to-Huaihe Water Diversion Project on habitat availability for wintering waterbirds at Caizi Lake","volume":"249","author":"Li","year":"2019","journal-title":"J. Environ. Manag."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Fan, T., Li, Q., Wang, B., Li, Z., and Nie, X. (2025). Evolutionary Modeling of Risk Transfer for Safe Operation of Inter-Basin Water Transfer Projects Using Dempster-Shafer and Bayesian Network. Systems, 13.","DOI":"10.3390\/systems13121064"},{"key":"ref_7","first-page":"100305","article-title":"Establishment risk of invasive golden mussel in a water diversion project: An assessment framework","volume":"17","author":"Yang","year":"2024","journal-title":"Environ. Sci. Ecotech"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"20233","DOI":"10.1007\/s10668-023-03468-7","article-title":"Emergency risk assessment of sudden water pollution in South-to-North Water Diversion Project in China based on driving force-pressure-state-impact-response (DPSIR) model and variable fuzzy set","volume":"26","author":"Zhang","year":"2023","journal-title":"Environ. Dev. Sustain."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Nong, X., Zeng, J., Ma, Y., Chen, L., Zhang, C., Behzadian, K., and Campos, L.C. (2023). Algal proliferation risk assessment using Vine Copula-based coupling methods in the South-to-North Water Diversion Project of China. Front. Ecol. Evol., 11.","DOI":"10.3389\/fevo.2023.1193163"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"669176","DOI":"10.1155\/2020\/6691764","article-title":"Operational Safety Risk Assessment for the Water Channels of the South-to-North Water Diversion Project Based on TODIM-FMEA","volume":"2020","author":"Li","year":"2020","journal-title":"Complexity"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Gao, W., Zeng, Y., Liu, Y., and Wu, B. (2019). Human Activity Intensity Assessment by Remote Sensing in the Water Source Area of the Middle Route of the South-to-North Water Diversion Project in China. Sustainability, 11.","DOI":"10.3390\/su11205670"},{"key":"ref_12","first-page":"5021004","article-title":"Risk Response of Complex Projects: Risk Association Network Method","volume":"37","author":"Yang","year":"2021","journal-title":"J. Manag. Eng."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"819","DOI":"10.1016\/j.ijproman.2016.03.001","article-title":"Selecting risk response strategies considering project risk interdependence","volume":"34","author":"Zhang","year":"2016","journal-title":"Int. J. Proj. Manag."},{"key":"ref_14","first-page":"3","article-title":"Research on Operational Risk Assessment of Urban Typical Lifeline in the Context of Complex Interdependence","volume":"26","author":"Suo","year":"2014","journal-title":"Manag. Rev."},{"key":"ref_15","first-page":"130","article-title":"Study on Identification Method for Risk Factors of Urban Typical Lifeline Operation Considering a Complex Interdependent Context","volume":"22","author":"Suo","year":"2014","journal-title":"Chin. J. Manag. Sci."},{"key":"ref_16","first-page":"209","article-title":"Risk Transmission Mechanism of Complex Engineering Project","volume":"41","author":"Yang","year":"2021","journal-title":"Sci. Technol. Manag. Res."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"129434","DOI":"10.1016\/j.jhydrol.2023.129434","article-title":"Coupling Bayesian Network and copula theory for water shortage assessment: A case study in source area of the South-to-North Water Division Project (SNWDP)","volume":"620","author":"Zha","year":"2023","journal-title":"J. Hydrol."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"841","DOI":"10.1007\/s00477-015-1113-6","article-title":"Bayesian network-based risk assessment for hazmat transportation on the Middle Route of the South-to-North Water Transfer Project in China","volume":"30","author":"Wang","year":"2015","journal-title":"Stoch. Environ. Res. Risk A"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"635","DOI":"10.1109\/TSE.2010.108","article-title":"A Risk Management Methodology for Project Risk Dependencies","volume":"37","author":"Kwan","year":"2011","journal-title":"IEEE Trans. Softw. Eng."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Hu, Q., Kou, Y., Liu, J., Liu, W., Yang, J., Li, S., He, P., Liu, X., Ma, K., and Li, Y. (2023). TerraSAR-X and GNSS Data for Deformation Detection and Mechanism Analysis of a Deep Excavation Channel Section of the China South-North Water-Diversion Project. Remote Sens., 15.","DOI":"10.3390\/rs15153777"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Xu, X., Xu, W., Xie, C., and Khan, M.Y.A. (2021). Prediction of the long-term performance based on the seepage-stress-damage coupling theory: A case in south-to-north water diversion project in China. Appl. Sci., 11.","DOI":"10.3390\/app112311413"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"121450","DOI":"10.1016\/j.jenvman.2024.121450","article-title":"Traceability of gushing water in the Middle Route of the South-to-North Water Diversion (Beijing section) through the river area","volume":"364","author":"Bi","year":"2024","journal-title":"J. Environ. Manag."},{"key":"ref_23","first-page":"1264","article-title":"Aqueducts under high seismic intensity and complex geological conditions","volume":"64","author":"Zhang","year":"2024","journal-title":"J. Tsinghua Univ. (Sci. Technol.)"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2731","DOI":"10.1007\/s11269-024-03777-0","article-title":"Impact of Climate Change on Water Diversion Risk of Inter-Basin Water Diversion Project","volume":"38","author":"Mu","year":"2024","journal-title":"Water Resour. Manag."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2505","DOI":"10.1007\/s11269-022-03387-8","article-title":"Impact of Climate Change on Water Transfer Scale of Inter-basin Water Diversion Project","volume":"37","author":"Bai","year":"2022","journal-title":"Water Resour. Manag."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"125649","DOI":"10.1016\/j.jenvman.2025.125649","article-title":"Inter-basin water transfer will face greater drought risk in the future","volume":"385","author":"Wang","year":"2025","journal-title":"J. Environ. Manag."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"130437","DOI":"10.1016\/j.jhydrol.2023.130437","article-title":"Challenges of typical inter-basin water transfer projects in China: Anticipated impacts of climate change on streamflow and hydrological drought under CMIP6","volume":"627","author":"Wu","year":"2023","journal-title":"J. Hydrol."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"8424","DOI":"10.1002\/2015GL065904","article-title":"Investigation of the probability of concurrent drought events between the water source and destination regions of China\u2019s water diversion project","volume":"42","author":"Liu","year":"2015","journal-title":"Geophys. Res. Lett."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1998","DOI":"10.1007\/s11442-022-2033-2","article-title":"Increasing probability of concurrent drought between the water intake and receiving regions of the Hanjiang to Weihe River Water Diversion Project, China","volume":"32","author":"Wang","year":"2022","journal-title":"J. Geogr. Sci."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"103527","DOI":"10.1016\/j.pce.2023.103527","article-title":"Reliability of stream flow in inter-basin water transfer under different climatic conditions using remote sensing in the Upper Tana basin","volume":"134","author":"Nyingi","year":"2024","journal-title":"Phys. Chem. Earth Parts A\/B\/C"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Fu, X., Wang, G., Ren, M., Ding, L., Jiang, X., He, X., Zhao, L., and Wu, N. (2021). Flood Control Risk Identification and Quantitative Assessment of a Large-Scale Water Transfer Project. Water, 13.","DOI":"10.3390\/w13131770"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"134053","DOI":"10.1016\/j.jhydrol.2025.134053","article-title":"The risk assessment model for water diversion projects based on a fuzzy Bayesian network","volume":"662","author":"Long","year":"2025","journal-title":"J. Hydrol."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/j.ecoleng.2016.02.021","article-title":"Assessing the eutrophication risk of the Danjiangkou Reservoir based on the EFDC model","volume":"96","author":"Chen","year":"2016","journal-title":"Ecol. Eng."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1016\/j.scitotenv.2016.03.069","article-title":"Risk assessment of water pollution sources based on an integrated k-means clustering and set pair analysis method in the region of Shiyan, China","volume":"557\u2013558","author":"Li","year":"2016","journal-title":"Sci. Total Environ."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/j.ecoleng.2015.11.024","article-title":"Risk forecasting of pollution accidents based on an integrated Bayesian Network and water quality model for the South to North Water Transfer Project","volume":"96","author":"Tang","year":"2016","journal-title":"Ecol. Eng."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/j.ecolind.2017.06.044","article-title":"Effect of inter-basin water transfer on water quality in an urban lake: A combined water quality index algorithm and biophysical modelling approach","volume":"92","author":"Feng","year":"2018","journal-title":"Ecol. Indic."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"115781","DOI":"10.1016\/j.watres.2020.115781","article-title":"Evaluation of water quality in the South-to-North Water Diversion Project of China using the water quality index (WQI) method","volume":"178","author":"Nong","year":"2020","journal-title":"Water Res."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"110530","DOI":"10.1016\/j.ress.2024.110530","article-title":"Increasing the available water diversion volume of water source project through flood resource utilization: A case study of the middle route of the South-to-North water diversion project in China","volume":"253","author":"Zhang","year":"2025","journal-title":"Reliab. Eng. Syst. Safe"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"160500","DOI":"10.1016\/j.scitotenv.2022.160500","article-title":"Sustainability of water transfer projects: A systematic review","volume":"860","author":"Faundez","year":"2023","journal-title":"Sci. Total Environ."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"263","DOI":"10.52547\/jwmr.11.22.263","article-title":"Investigating of the Positive and Negative Consequences of Inter-basin Water Transfer Plans","volume":"11","author":"Amirnejad","year":"2020","journal-title":"J. Watershed Manag. Res."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"137646","DOI":"10.1016\/j.scitotenv.2020.137646","article-title":"A new framework for integrated, holistic, and transparent evaluation of inter-basin water transfer schemes","volume":"721","author":"Sinha","year":"2020","journal-title":"Sci. Total Environ."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"13369","DOI":"10.1080\/10106049.2022.2076926","article-title":"Increased artificiality trend driven by an inter-basin water transfer on the Zayandeh-rud River floodplain in Iran","volume":"37","author":"Fazelpoor","year":"2022","journal-title":"Geocarto Int."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"100940","DOI":"10.1016\/j.envdev.2023.100940","article-title":"Policy and regulatory context for self-supplied drinking water services in two cities in Indonesia: Priorities for managing risks","volume":"49","author":"Priadi","year":"2024","journal-title":"Environ. Dev."},{"key":"ref_44","first-page":"7787","article-title":"Optimization of operation safety risk indicator based on grey relational and sensitivity analysis of the south-to-north water diversion project","volume":"38","author":"Nie","year":"2020","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"817","DOI":"10.1016\/j.ijproman.2012.11.012","article-title":"An empirical investigation on how portfolio risk management influences project portfolio success","volume":"31","author":"Teller","year":"2013","journal-title":"Int. J. Proj. Manag."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"1426139","DOI":"10.1155\/2019\/1426139","article-title":"Governance of Relationship Risks in Megaprojects: A Social Network Analysis","volume":"2019","author":"Xie","year":"2019","journal-title":"Adv. Civ. Eng."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"8897196","DOI":"10.1155\/2020\/8897196","article-title":"Stakeholder-Associated Risks and Their Interactions in PPP Projects: Social Network Analysis of a Water Purification and Sewage Treatment Project in China","volume":"2020","author":"Yang","year":"2020","journal-title":"Adv. Civ. Eng."},{"key":"ref_48","first-page":"170","article-title":"Relation of accident statistics to industrial accident prevention","volume":"33\u201334","author":"Heinrich","year":"1930","journal-title":"Process Causality Actuar. Soc."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"768","DOI":"10.1136\/bmj.320.7237.768","article-title":"Human error: Models and management","volume":"320","author":"Reason","year":"2000","journal-title":"Br. Med. J."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1109\/TR.1985.5222114","article-title":"Fault Tree Analysis, Methods, and Applications \u07dd A Review","volume":"34","author":"Lee","year":"1985","journal-title":"IEEE Trans. Reliab."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/S0304-3894(02)00244-3","article-title":"Master Logic Diagram: Method for hazard and initiating event identification in process plants","volume":"97","author":"Papazoglou","year":"2003","journal-title":"J. Hazard. Mater."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"830","DOI":"10.1016\/j.jhazmat.2016.09.074","article-title":"Dynamic safety assessment of natural gas stations using Bayesian network","volume":"321","author":"Zarei","year":"2017","journal-title":"J. Hazard. Mater."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1016\/j.ijpe.2010.11.022","article-title":"Interactions-based risk clustering methodologies and algorithms for complex project management","volume":"142","author":"Marle","year":"2013","journal-title":"Int. J. Prod. Econ."},{"key":"ref_54","first-page":"1465","article-title":"Method of selecting project risk response strategies considering risk interdependence","volume":"32","author":"Guan","year":"2017","journal-title":"Control Decis."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"101706","DOI":"10.1016\/j.frl.2020.101706","article-title":"The dependency measures of commercial bank risks: Using an optimal copula selection method based on non-parametric kernel density","volume":"37","author":"Jin","year":"2020","journal-title":"Financ. Res. Lett."},{"key":"ref_56","first-page":"61","article-title":"Research on Country Risk Assessment for Overseas Investment Considering Risk Interdependence and Decision Makers\u2019 Preference","volume":"30","author":"Meng","year":"2022","journal-title":"Chin. J. Manag. Sci."},{"key":"ref_57","first-page":"225","article-title":"Research on operational risk probability assessment for urbancritical infrastructures considering multi-interdependency anddynamic stochasticity","volume":"35","author":"Suo","year":"2021","journal-title":"J. Ind. Eng.\/Eng. Manag."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1142\/S0219622019410013","article-title":"A Multiobjective Optimization Approach for Selecting Risk Response Strategies of Software Project: From the Perspective of Risk Correlations","volume":"18","author":"Wu","year":"2019","journal-title":"Int. J. Inf. Tech. Decis."},{"key":"ref_59","first-page":"45","article-title":"Research on Risk Assessment Method for Transport Infrastructure Construction Considering the Interdependency and Stochasticity of Risks","volume":"32","author":"Zhang","year":"2020","journal-title":"Manag. Rev."},{"key":"ref_60","first-page":"2391","article-title":"Evolutionary game model of risk-sharing of rail transit PPP projects considering risk correlation","volume":"40","author":"Wang","year":"2020","journal-title":"Syst. Eng. Theory Pract."},{"key":"ref_61","first-page":"32","article-title":"Method of Selecting Project Risk Response Strategies Considering Total Risk Interdependence","volume":"28","author":"Zhang","year":"2020","journal-title":"Chin. J. Manag. Sci."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"416","DOI":"10.1016\/j.ress.2019.03.048","article-title":"Modeling risks in dependent systems: A Copula-Bayesian approach","volume":"188","author":"Pan","year":"2019","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"2:1","DOI":"10.1147\/JRD.2010.2042914","article-title":"Problems with scoring methods and ordinal scales in risk assessment","volume":"54","author":"Hubbard","year":"2010","journal-title":"Ibm J. Res. Dev."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"4668","DOI":"10.1007\/s10489-023-05153-8","article-title":"Conditional probability table limit-based quantization for Bayesian networks: Model quality, data fidelity and structure score","volume":"54","author":"Ribeiro","year":"2024","journal-title":"Appl. Intell."},{"key":"ref_65","doi-asserted-by":"crossref","unstructured":"Wang, W., and Wang, R. (2024). Measuring the Systemic Risk of Clean Energy Markets Based on the Dynamic Factor Copula Model. Systems, 12.","DOI":"10.3390\/systems12120584"},{"key":"ref_66","first-page":"2579","article-title":"Causal network topology analysis: Characterizing causal context for risk management","volume":"44","author":"Lin","year":"2024","journal-title":"Risk Anal. Off. Publ. Soc. Risk Anal."},{"key":"ref_67","first-page":"10","article-title":"The Delphi technique: Making sense of consensus","volume":"12","author":"Hsu","year":"2007","journal-title":"Pract. Assess. Res. Eval."},{"key":"ref_68","first-page":"10","article-title":"Research on Social Risk of Overseas Major InfrastructureInvestment Projects Based on ISM","volume":"34","author":"Xiang","year":"2020","journal-title":"J. Eng. Manag."},{"key":"ref_69","first-page":"92","article-title":"Virtual Sample Generation Method and Its application in Reforming Data Modeling","volume":"52","author":"He","year":"2021","journal-title":"Pet. Process. Petrochem."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"110270","DOI":"10.1016\/j.ress.2024.110270","article-title":"Multivariate copula-based framework for stochastic analysis of landslide runout distance","volume":"250","author":"Ma","year":"2024","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_71","doi-asserted-by":"crossref","unstructured":"Anghel, C.G., and Ianculescu, D. (2025). Application of the GEV Distribution in Flood Frequency Analysis in Romania: An In-Depth Analysis. Climate, 13.","DOI":"10.3390\/cli13070152"},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"1619","DOI":"10.1016\/j.ress.2011.09.003","article-title":"A study of Weibull shape parameter: Properties and significance","volume":"96","author":"Jiang","year":"2011","journal-title":"Reliab. Eng. Syst. Safe"},{"key":"ref_73","first-page":"83","article-title":"Joint probability distribution model of wind and wave with Vine Copula function","volume":"45","author":"Wang","year":"2023","journal-title":"J. Civil. Environ. Eng."},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/j.enggeo.2018.05.020","article-title":"Three-dimensional reliability analysis of seismic slopes using the copula-based sampling method","volume":"242","author":"Xu","year":"2018","journal-title":"Eng. Geol."},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"280","DOI":"10.1080\/00031305.1986.10475414","article-title":"The joy of copulas: Bivariate distributions with uniform marginals","volume":"40","author":"Genest","year":"1986","journal-title":"Am. Stat."},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1007\/s11269-025-04464-4","article-title":"Probabilistic Risk Assessment of Meteorological and Hydrological Droughts with Copula Functions: A Multivariate Framework","volume":"40","author":"Terzi","year":"2026","journal-title":"Water Resour. Manag."},{"key":"ref_77","doi-asserted-by":"crossref","unstructured":"Haddad, K. (2025). An Integrated Goodness-of-Fit and Vine Copula Framework for Windspeed Distribution Selection and Turbine Power-Curve Assessment in New South Wales and Southern East Queensland. Atmosphere, 16.","DOI":"10.3390\/atmos16091068"},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"735","DOI":"10.1175\/JHM-D-23-0102.1","article-title":"Compound Flooding Potential from the Joint Occurrence of Precipitation and Storm Surge in the Qiantang Estuary, China","volume":"25","author":"Wu","year":"2024","journal-title":"J. Hydrometeorol."},{"key":"ref_79","unstructured":"Nelsen, R.B. (2007). An Introduction to Copulas, Springer Science & Business Media."},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/s10687-006-0015-x","article-title":"Copulas: Tales and facts","volume":"9","author":"Mikosch","year":"2006","journal-title":"Extremes"},{"key":"ref_81","doi-asserted-by":"crossref","first-page":"1137","DOI":"10.1214\/aoms\/1177699260","article-title":"Some concepts of dependence","volume":"37","author":"Lehmann","year":"1966","journal-title":"Ann. Math. Stat."},{"key":"ref_82","unstructured":"Hollander, M., Wolfe, D.A., and Chicken, E. (2013). Nonparametric Statistical Methods, John Wiley & Sons."},{"key":"ref_83","doi-asserted-by":"crossref","first-page":"879","DOI":"10.1214\/aos\/1176345528","article-title":"On nonparametric measures of dependence for random variables","volume":"9","author":"Schweizer","year":"1981","journal-title":"Ann. Stat."},{"key":"ref_84","first-page":"907","article-title":"Modelfor Water Shortage Risk Econimic LossesBased on M-Copula and Its Application","volume":"30","author":"Qian","year":"2022","journal-title":"J. Basic. Sci. Eng."},{"key":"ref_85","unstructured":"(2002). Environmental Quality Standards for Surface Water (Standard No. GB 3838-2002)."},{"key":"ref_86","unstructured":"China South-to-North Water Diversion Yearbook Editorial Board (2025). China South-to-North Water Diversion Yearbook 2025, China Water & Power Press."},{"key":"ref_87","unstructured":"Ministry of Water Resources, South-to-North Water Diversion Project Management Department (2024). South-to-North Water Diversion Project Flying Inspection Report."},{"key":"ref_88","unstructured":"China South-to-North Water Diversion Co., Ltd (2024). The MRSNWDP Safety Risk Assessment Report, China South-to-North Water Diversion Co., Ltd.. Internal Report."},{"key":"ref_89","unstructured":"China South-to-North Water Diversion Group Central Route Co., Ltd (2024). The SNWDP Operational Safety Inspection Technology Research and Demonstration Project Report, China South-to-North Water Diversion Group Central Route Co., Ltd.. Internal Report."},{"key":"ref_90","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/j.ress.2012.04.002","article-title":"Risk-averse decision-making for civil infrastructure exposed to low-probability, high-consequence events","volume":"104","author":"Cha","year":"2012","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_91","doi-asserted-by":"crossref","unstructured":"Koryt\u00e1rov\u00e1, J., and Hrom\u00e1dka, V. (2020). Risk Assessment of Large-Scale Infrastructure Projects\u2014Assumptions and Context. Appl. Sci., 11.","DOI":"10.3390\/app11010109"},{"key":"ref_92","doi-asserted-by":"crossref","unstructured":"Li, P., Dong, F., Lv, G., Wang, Y., Sheng, Y., Cheng, F., and Wang, B. (2025). Multiple Correlation Analysis of Operational Safety of Long-Distance Water Diversion Project Based on Copula Bayesian Network. Water, 17.","DOI":"10.3390\/w17162389"},{"key":"ref_93","doi-asserted-by":"crossref","first-page":"110950","DOI":"10.1016\/j.ress.2025.110950","article-title":"Cascading failure analysis of interdependent water-power networks based on functional coupling","volume":"259","author":"Li","year":"2025","journal-title":"Reliab. Eng. Syst. Safe"},{"key":"ref_94","doi-asserted-by":"crossref","first-page":"120703","DOI":"10.1016\/j.jenvman.2024.120703","article-title":"Risk assessment of inter-basin water transfer plans through integration of Fault Tree Analysis and Bayesian Network modelling approaches","volume":"356","author":"Roozbahani","year":"2024","journal-title":"J. Environ. Manag."},{"key":"ref_95","doi-asserted-by":"crossref","first-page":"3139","DOI":"10.1007\/s11269-021-02865-9","article-title":"Development of multi-hazard risk assessment model for agricultural water supply and distribution systems using bayesian network","volume":"35","author":"Bozorgi","year":"2021","journal-title":"Water Resour. Manag."},{"key":"ref_96","doi-asserted-by":"crossref","unstructured":"Wei, S., Lin, K., Huang, L., Yao, Z., Bai, X., and Chen, Z. (2022). Assessing the vulnerability of water resources system using VSD-SD coupling model: A case of pearl river delta. Water, 14.","DOI":"10.3390\/w14071103"},{"key":"ref_97","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1016\/j.envsoft.2017.11.008","article-title":"Coupling infrastructure resilience and flood risk assessment via copulas analyses for a coastal green-grey-blue drainage system under extreme weather events","volume":"100","author":"Joyce","year":"2018","journal-title":"Environ. Model. Softw."}],"container-title":["Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-8954\/14\/5\/477\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T04:20:16Z","timestamp":1777522816000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-8954\/14\/5\/477"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4,28]]},"references-count":97,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2026,5]]}},"alternative-id":["systems14050477"],"URL":"https:\/\/doi.org\/10.3390\/systems14050477","relation":{},"ISSN":["2079-8954"],"issn-type":[{"value":"2079-8954","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4,28]]}}}