{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,25]],"date-time":"2026-06-25T15:43:47Z","timestamp":1782402227767,"version":"3.54.5"},"reference-count":57,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2025,5,2]],"date-time":"2025-05-02T00:00:00Z","timestamp":1746144000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key R&amp;D Program of China","award":["2023YFC3007400"],"award-info":[{"award-number":["2023YFC3007400"]}]},{"name":"National Key R&amp;D Program of China","award":["22dz1200200"],"award-info":[{"award-number":["22dz1200200"]}]},{"name":"National Key R&amp;D Program of China","award":["22dz1201400"],"award-info":[{"award-number":["22dz1201400"]}]},{"name":"Shanghai Science and Technology Plan Project, China","award":["2023YFC3007400"],"award-info":[{"award-number":["2023YFC3007400"]}]},{"name":"Shanghai Science and Technology Plan Project, China","award":["22dz1200200"],"award-info":[{"award-number":["22dz1200200"]}]},{"name":"Shanghai Science and Technology Plan Project, China","award":["22dz1201400"],"award-info":[{"award-number":["22dz1201400"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>A significant challenge in probabilistic seismic demand analysis lies in selecting appropriate intensity measures and investigating their relationships with demand parameters to ensure accurate seismic fragility predictions. A single ground motion intensity measure is insufficient to capture the complex characteristics of ground motion, leading researchers to focus on compound intensity measures. It is essential to investigate the selection of ground motion features and the number of features included in the construction of compound intensity measures, as these measures cannot comprise an unlimited set of ground motion features. This study focused on machine learning feature selection methods to select ground motion features for compound intensity measures, utilizing mutual information for feature selection. Considering the symmetry and asymmetry requirements of this process, optimized features were selected. Based on the selected features, the compound ground motion intensity measure was constructed to evaluate structural seismic fragility. The compound ground motion intensity measure was evaluated against scalar intensity measure in terms of correlation, efficiency, practicality, proficiency, and sufficiency. A comprehensive comparative analysis demonstrates the applicability of the compound intensity measure. The study\u2019s findings support fragility analysis and performance evaluation using compound intensity measures. The corresponding results can be applied in the risk analysis aspect of performance-based earthquake engineering.<\/jats:p>","DOI":"10.3390\/sym17050699","type":"journal-article","created":{"date-parts":[[2025,5,4]],"date-time":"2025-05-04T20:42:37Z","timestamp":1746391357000},"page":"699","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Construction Method of Compound Ground Motion Intensity Measure Based on Mutual Information Asymmetry for Engineering Seismic Fragility Analysis"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9406-0965","authenticated-orcid":false,"given":"Zhuo","family":"Song","sequence":"first","affiliation":[{"name":"State Key Laboratory of Bridge Engineering Safety and Resilience, Beijing University of Technology, Beijing 100124, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7526-0558","authenticated-orcid":false,"given":"Xiaojun","family":"Li","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Bridge Engineering Safety and Resilience, Beijing University of Technology, Beijing 100124, China"},{"name":"Key Laboratory of Building Collapse Mechanism and Disaster Prevention, Institute of Disaster Prevention, Langfang 065201, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yushi","family":"Wang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Bridge Engineering Safety and Resilience, Beijing University of Technology, Beijing 100124, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bochang","family":"Zhou","sequence":"additional","affiliation":[{"name":"Shanghai Earthquake Administration, Shanghai 200062, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,5,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2829","DOI":"10.1007\/s10518-024-01885-1","article-title":"Relationships between ground motion parameters and energy demands for regular low-rise RC frame buildings","volume":"22","author":"Meral","year":"2024","journal-title":"Bull. Earthq. Eng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1002\/eqe.141","article-title":"Incremental dynamic analysis","volume":"31","author":"Vamvatsikos","year":"2002","journal-title":"Earthq. Eng. Struct. Dyn."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1193\/021113EQS025M","article-title":"Efficient Analytical Fragility Function Fitting Using Dynamic Structural Analysis","volume":"31","author":"Baker","year":"2015","journal-title":"Earthq. Spectra"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"107657","DOI":"10.1016\/j.soildyn.2022.107657","article-title":"Seismic energy demands and optimal intensity measures for continuous concrete box-girder bridges","volume":"165","author":"Eslamnia","year":"2023","journal-title":"Soil Dyn. Earthq. Eng."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"118838","DOI":"10.1016\/j.oceaneng.2024.118838","article-title":"Development of the compound intensity measure and seismic performance assessment for aqueduct structures considering fluid-structure interaction","volume":"311","author":"Du","year":"2024","journal-title":"Ocean. Eng."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"106961","DOI":"10.1016\/j.soildyn.2021.106961","article-title":"Optimal selection of scalar and vector-valued seismic intensity measures based on Gaussian Process Regression","volume":"152","author":"Yan","year":"2022","journal-title":"Soil Dyn. Earthq. Eng."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"107201","DOI":"10.1016\/j.soildyn.2022.107201","article-title":"Effectiveness of vector intensity measures in probabilistic seismic demand assessment","volume":"155","author":"Li","year":"2022","journal-title":"Soil Dyn. Earthq. Eng."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1016\/j.soildyn.2019.01.036","article-title":"The importance of non-spectral intensity measures on the risk-based structural responses","volume":"120","author":"Kiani","year":"2019","journal-title":"Soil Dyn. Earthq. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"698","DOI":"10.1016\/S0141-0296(00)00074-2","article-title":"Correlation study between seismic acceleration parameters and damage indices of structures","volume":"23","author":"Elenas","year":"2001","journal-title":"Eng. Struct."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1551","DOI":"10.1002\/eqe.492","article-title":"Effect of peak ground velocity on deformation demands for SDOF systems","volume":"34","author":"Akkar","year":"2005","journal-title":"Earthq. Eng. Struct. Dyn."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"104857","DOI":"10.1016\/j.tust.2022.104857","article-title":"Optimal selection of scalar and vector-valued intensity measures for improved fragility analysis in cross-fault hydraulic tunnels","volume":"132","author":"Sun","year":"2023","journal-title":"Tunn. Undergr. Space Technol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1193\/1.1586011","article-title":"Earthquakes, Records, and Nonlinear Responses","volume":"14","author":"Shome","year":"1998","journal-title":"Earthq. Spectra"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1193\/1.2723158","article-title":"Structure-specific scalar intensity measures for near-source and ordinary earthquake ground motions","volume":"23","author":"Luco","year":"2007","journal-title":"Earthq. Spectra"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2057","DOI":"10.1002\/eqe.2575","article-title":"Average spectral acceleration as an intensity measure for collapse risk assessment","volume":"44","author":"Eads","year":"2015","journal-title":"Earthq. Eng. Struct. Dyn."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1189","DOI":"10.1080\/13632469.2016.1210059","article-title":"Optimal Spectral Acceleration-based Intensity Measure for Seismic Collapse Assessment of P-Delta Vulnerable Frame Structures","volume":"21","author":"Adam","year":"2017","journal-title":"J. Earthq. Eng."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1861","DOI":"10.1002\/eqe.700","article-title":"Probabilistic structural response assessment using vector-valued intensity measures","volume":"36","author":"Baker","year":"2007","journal-title":"Earthq. Eng. Struct. Dyn."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1573","DOI":"10.1002\/eqe.496","article-title":"Developing efficient scalar and vector intensity measures for IDA capacity estimation by incorporating elastic spectral shape information","volume":"34","author":"Vamvatsikos","year":"2005","journal-title":"Earthq. Eng. Struct. Dyn."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2329","DOI":"10.1007\/s10518-021-01283-x","article-title":"New insights into the relationship between seismic intensity measures and nonlinear structural response","volume":"20","author":"Hurtado","year":"2022","journal-title":"Bull. Earthq. Eng."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1193","DOI":"10.1002\/eqe.474","article-title":"A vector-valued ground motion intensity measure consisting of spectral acceleration and epsilon","volume":"34","author":"Baker","year":"2005","journal-title":"Earthq. Eng. Struct. Dyn."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1725","DOI":"10.1007\/s10518-013-9571-z","article-title":"Vector fragility surfaces for reinforced concrete frames in Europe","volume":"12","author":"Modica","year":"2014","journal-title":"Bull. Earthq. Eng."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/j.strusafe.2013.04.002","article-title":"Probabilistic seismic response analysis of a 3-D reinforced concrete building","volume":"44","author":"Marco","year":"2013","journal-title":"Struct. Saf."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1066","DOI":"10.1002\/eqe.3177","article-title":"Conditional spectrum bidirectional record selection for risk assessment of 3D structures using scalar and vector IMs","volume":"48","author":"Kohrangi","year":"2019","journal-title":"Earthq. Eng. Struct. Dyn."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"472","DOI":"10.1016\/j.engstruct.2012.07.002","article-title":"Comparing vector-valued intensity measures for fragility analysis of steel frames in the case of narrow-band ground motions","volume":"45","author":"Bojorquez","year":"2012","journal-title":"Eng. Struct."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1525","DOI":"10.1193\/053115EQS081M","article-title":"Vector and Scalar IMs in Structural Response Estimation: Part II\u2014Building Demand Assessment","volume":"32","author":"Kohrangi","year":"2016","journal-title":"Earthq. Spectra"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"106096","DOI":"10.1016\/j.soildyn.2020.106096","article-title":"A drift-correlated ground motion intensity measure: Application to steel frame buildings","volume":"132","author":"Luis","year":"2020","journal-title":"Soil Dyn. Earthq. Eng."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1747","DOI":"10.1080\/13632469.2018.1481157","article-title":"An Approach to Develop Compound Intensity Measures for Prediction of Damage Potential of Earthquake Records Using Canonical Correlation Analysis","volume":"24","author":"Liu","year":"2020","journal-title":"J. Earthq. Eng."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"7107","DOI":"10.1007\/s10518-022-01505-w","article-title":"Exploratory factor analysis-based method to develop compound intensity measures for predicting potential structural damage of ground motion","volume":"20","author":"Liu","year":"2022","journal-title":"Bull. Earthq. Eng."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"105725","DOI":"10.1016\/j.soildyn.2019.105725","article-title":"Development of a compound intensity measure using partial least-squares regression and its statistical evaluation based on probabilistic seismic demand analysis","volume":"125","author":"Liu","year":"2019","journal-title":"Soil Dyn. Earthq. Eng."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"104890","DOI":"10.1016\/j.tust.2022.104890","article-title":"Compound intensity measures for improved seismic performance assessment in cross-fault hydraulic tunnels using partial least-squares methodology","volume":"132","author":"Sun","year":"2023","journal-title":"Tunn. Undergr. Space Technol."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"107828","DOI":"10.1016\/j.soildyn.2023.107828","article-title":"Ranking method of the severest input ground motion for underground structures based on composite ground motion intensity measures","volume":"168","author":"Chen","year":"2023","journal-title":"Soil Dyn. Earthq. Eng."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"107966","DOI":"10.1016\/j.soildyn.2023.107966","article-title":"Machine learning-driven probabilistic seismic demand model with multiple intensity measures and applicability in seismic fragility analysis for nuclear power plants","volume":"171","author":"Yong","year":"2023","journal-title":"Soil Dyn. Earthq. Eng."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1080\/13632469909350343","article-title":"The effective duration of earthquake strong motion","volume":"3","author":"Bommer","year":"1999","journal-title":"J. Earthq. Eng."},{"key":"ref_33","unstructured":"Hansen, R.J. (1970). Seismic Design for Nuclear Power Plants, MIT Press."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/j.soildyn.2017.10.005","article-title":"Quantification of response spectra of pulse-like near-fault ground motions","volume":"104","author":"Pu","year":"2018","journal-title":"Soil Dyn. Earthq. Eng."},{"key":"ref_35","unstructured":"Kramer, S.L. (1996). Geotechnical Earthquake Engineering, Prentice Hall."},{"key":"ref_36","unstructured":"Mackie, K.R. (2004). Fragility-Based Seismic Decision Making for Highway Overpass Bridges. [Ph.D. Thesis, University of California, Berkeley]."},{"key":"ref_37","unstructured":"Applied Technology Council (1978). Tentative Provisions for the Development of Seismic Regulations for Buildings, Applied Technology Council. ATC-3-06."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1709","DOI":"10.1061\/(ASCE)0733-9445(1987)113:8(1709)","article-title":"Uncertainties in Establishing Design Earthquakes","volume":"113","author":"Anderson","year":"1987","journal-title":"J. Struct. Eng.-Asce"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"106917","DOI":"10.1016\/j.istruc.2024.106917","article-title":"Seismic intensity measure selection incorporating interaction effects for damage assessment across different structural sensitive regions","volume":"67","author":"Wu","year":"2024","journal-title":"Structures"},{"key":"ref_40","first-page":"463","article-title":"Earthquake ground motions for design and analysis of dams","volume":"20","author":"Thun","year":"1988","journal-title":"Geotech. Spec. Publ."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1061\/JMCEA3.0000102","article-title":"Behavior of Structures During Earthquakes","volume":"85","author":"Housner","year":"1959","journal-title":"J. Eng. Mech. Div."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1061\/(ASCE)1090-0241(1998)124:2(150)","article-title":"Simplified Frequency Content Estimates of Earthquake Ground Motions","volume":"124","author":"Rathje","year":"1998","journal-title":"J. Geotech. Geoenvironmental Eng."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"15087","DOI":"10.1109\/ACCESS.2018.2815606","article-title":"Supervised Feature Selection With a Stratified Feature Weighting Method","volume":"6","author":"Chen","year":"2018","journal-title":"IEEE Access"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"328","DOI":"10.1016\/j.patcog.2018.02.020","article-title":"Class-specific mutual information variation for feature selection","volume":"79","author":"Gao","year":"2018","journal-title":"Pattern Recognit."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1580","DOI":"10.1007\/s10489-018-1348-2","article-title":"Hybridization of feature selection and feature weighting for high dimensional data","volume":"49","author":"Singh","year":"2019","journal-title":"Appl. Intell."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"1272","DOI":"10.1007\/s10489-019-01597-z","article-title":"Feature redundancy term variation for mutual information-based feature selection","volume":"50","author":"Gao","year":"2020","journal-title":"Appl. Intell."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"5130","DOI":"10.1073\/pnas.1522586113","article-title":"Part mutual information for quantifying direct associations in networks","volume":"113","author":"Zhao","year":"2016","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"326","DOI":"10.1016\/j.physa.2004.06.144","article-title":"Mutual information: A measure of dependency for nonlinear time series","volume":"344","author":"Dionisio","year":"2004","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"1226","DOI":"10.1109\/TPAMI.2005.159","article-title":"Feature selection based on mutual information criteria of max-dependency, max-relevance, and min-redundancy","volume":"27","author":"Hanchuan","year":"2005","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Lin, D., and Tang, X. (2006, January 7\u201313). Conditional Infomax Learning: An Integrated Framework for Feature Extraction and Fusion. Proceedings of the Computer Vision\u2014ECCV 2006, Graz, Austria.","DOI":"10.1007\/11744023_6"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1016\/j.patrec.2018.06.005","article-title":"Feature selection considering the composition of feature relevancy","volume":"112","author":"Gao","year":"2018","journal-title":"Pattern Recognit. Lett."},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"Lai, Q.H., Hu, J.J., Xu, L.J., Xie, L.L., and Lin, S.B. (2022). Method for Ranking Pulse-like Ground Motions According to Damage Potential for Reinforced Concrete Frame Structures. Buildings, 12.","DOI":"10.3390\/buildings12060754"},{"key":"ref_53","doi-asserted-by":"crossref","unstructured":"Song, Z., Li, X., Wang, Y., and Zhou, B. (2025). Amplitude-Scaling Bias Analysis of Ground Motion Record Set in Strip Method for Structural Seismic Fragility Assessment. Buildings, 15.","DOI":"10.3390\/buildings15030401"},{"key":"ref_54","unstructured":"McKenna, F., Fenves, G., Scott, M., and Jeremic, B. (2000). Open System for Earthquake Engineering Simulation (OpenSees), Pacific Earthquake Engineering Research Center, University of California."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"526","DOI":"10.1061\/(ASCE)0733-9445(2002)128:4(526)","article-title":"Probabilistic basis for 2000 SAC Federal Emergency Management Agency steel moment frame guidelines","volume":"128","author":"Cornell","year":"2002","journal-title":"J. Struct. Eng."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"951","DOI":"10.1002\/eqe.386","article-title":"Comparing the adequacy of alternative ground motion intensity measures for the estimation of structural responses","volume":"33","author":"Giovenale","year":"2004","journal-title":"Earthq. Eng. Struct. Dyn."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"711","DOI":"10.1002\/eqe.782","article-title":"Selection of optimal intensity measures in probabilistic seismic demand models of highway bridge portfolios","volume":"37","author":"Padgett","year":"2008","journal-title":"Earthq. Eng. Struct. Dyn."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/5\/699\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:26:31Z","timestamp":1760030791000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/5\/699"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,5,2]]},"references-count":57,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2025,5]]}},"alternative-id":["sym17050699"],"URL":"https:\/\/doi.org\/10.3390\/sym17050699","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,5,2]]}}}