Gaussian Process‐Based Response Surface Method for Slope Reliability Analysis Article Swipe

PDF

Bin Hu , Guoshao Su , Jianqing Jiang , Yilong Xiao ·

YOU? · · 2019 · Open Access · · DOI: https://doi.org/10.1155/2019/9185756

A new response surface method (RSM) for slope reliability analysis was proposed based on Gaussian process (GP) machine learning technology. The method involves the approximation of limit state function by the trained GP model and estimation of failure probability using the first‐order reliability method (FORM). A small amount of training samples were firstly built by the limited equilibrium method for training the GP model. Then, the implicit limit state function of slope was approximated by the trained GP model. Thus, the implicit limit state function and its derivatives for slope stability analysis were approximated by the GP model with the explicit formulation. Furthermore, an iterative algorithm was presented to improve the precision of approximation of the limit state function at the region near the design point which contributes significantly to the failure probability. Results of four case studies including one nonslope and three slope problems indicate that the proposed method is more efficient to achieve reasonable accuracy for slope reliability analysis than the traditional RSM.

Related Topics

Gaussian Function

Response Surface Methodology

Mathematics

Slope Stability Analysis

Mathematical Analysis

Structural Engineering

Geometry

Engineering

Geotechnical Engineering

Evolutionary Biology

Quantum Mechanics

Concepts

Reliability (semiconductor) Limit (mathematics) Gaussian Response surface methodology Function (biology) Mathematics Slope stability Limit state design Stability (learning theory) Applied mathematics Gaussian process Surface (topology) Process (computing) Computer science Algorithm Mathematical optimization Statistics Machine learning Mathematical analysis Structural engineering Geometry Power (physics) Engineering Geotechnical engineering Evolutionary biology Operating system Quantum mechanics Biology Physics

Metadata

Type: article
Language: en
Landing Page: https://doi.org/10.1155/2019/9185756
PDF: https://downloads.hindawi.com/journals/ace/2019/9185756.pdf
OA Status: gold
Cited By: 11
References: 33
Related Works: 10
OpenAlex ID: https://openalex.org/W2923871099

All OpenAlex metadata

Raw OpenAlex JSON

OpenAlex ID: https://openalex.org/W2923871099

Canonical identifier for this work in OpenAlex
DOI: https://doi.org/10.1155/2019/9185756

Digital Object Identifier
Title: Gaussian Process‐Based Response Surface Method for Slope Reliability Analysis

Work title
Type: article

OpenAlex work type
Language: en

Primary language
Publication year: 2019

Year of publication
Publication date: 2019-01-01

Full publication date if available
Authors: Bin Hu, Guoshao Su, Jianqing Jiang, Yilong Xiao

List of authors in order
Landing page: https://doi.org/10.1155/2019/9185756

Publisher landing page
PDF URL: https://downloads.hindawi.com/journals/ace/2019/9185756.pdf

Direct link to full text PDF
Open access: Yes

Whether a free full text is available
OA status: gold

Open access status per OpenAlex
OA URL: https://downloads.hindawi.com/journals/ace/2019/9185756.pdf

Direct OA link when available
Concepts: Reliability (semiconductor), Limit (mathematics), Gaussian, Response surface methodology, Function (biology), Mathematics, Slope stability, Limit state design, Stability (learning theory), Applied mathematics, Gaussian process, Surface (topology), Process (computing), Computer science, Algorithm, Mathematical optimization, Statistics, Machine learning, Mathematical analysis, Structural engineering, Geometry, Power (physics), Engineering, Geotechnical engineering, Evolutionary biology, Operating system, Quantum mechanics, Biology, Physics

Top concepts (fields/topics) attached by OpenAlex
Cited by: 11

Total citation count in OpenAlex
Citations by year (recent): 2025: 2, 2024: 2, 2023: 1, 2022: 2, 2021: 1

Per-year citation counts (last 5 years)
References (count): 33

Number of works referenced by this work
Related works (count): 10

Other works algorithmically related by OpenAlex

Full payload

id	https://openalex.org/W2923871099
doi	https://doi.org/10.1155/2019/9185756
ids.doi	https://doi.org/10.1155/2019/9185756
ids.mag	2923871099
ids.openalex	https://openalex.org/W2923871099
fwci	1.36989886
type	article
title	Gaussian Process‐Based Response Surface Method for Slope Reliability Analysis
awards[0].id	https://openalex.org/G8441308767
awards[0].funder_id	https://openalex.org/F4320321001
awards[0].display_name
awards[0].funder_award_id	51369007
awards[0].funder_display_name	National Natural Science Foundation of China
biblio.issue	1
biblio.volume	2019
biblio.last_page
biblio.first_page
topics[0].id	https://openalex.org/T11046
topics[0].field.id	https://openalex.org/fields/22
topics[0].field.display_name	Engineering
topics[0].score	0.9998000264167786
topics[0].domain.id	https://openalex.org/domains/3
topics[0].domain.display_name	Physical Sciences
topics[0].subfield.id	https://openalex.org/subfields/2213
topics[0].subfield.display_name	Safety, Risk, Reliability and Quality
topics[0].display_name	Geotechnical Engineering and Analysis
topics[1].id	https://openalex.org/T10716
topics[1].field.id	https://openalex.org/fields/22
topics[1].field.display_name	Engineering
topics[1].score	0.9970999956130981
topics[1].domain.id	https://openalex.org/domains/3
topics[1].domain.display_name	Physical Sciences
topics[1].subfield.id	https://openalex.org/subfields/2205
topics[1].subfield.display_name	Civil and Structural Engineering
topics[1].display_name	Soil and Unsaturated Flow
topics[2].id	https://openalex.org/T10535
topics[2].field.id	https://openalex.org/fields/23
topics[2].field.display_name	Environmental Science
topics[2].score	0.9901000261306763
topics[2].domain.id	https://openalex.org/domains/3
topics[2].domain.display_name	Physical Sciences
topics[2].subfield.id	https://openalex.org/subfields/2308
topics[2].subfield.display_name	Management, Monitoring, Policy and Law
topics[2].display_name	Landslides and related hazards
funders[0].id	https://openalex.org/F4320321001
funders[0].ror	https://ror.org/01h0zpd94
funders[0].display_name	National Natural Science Foundation of China
is_xpac	False
apc_list.value	2400
apc_list.currency	USD
apc_list.value_usd	2400
apc_paid.value	2400
apc_paid.currency	USD
apc_paid.value_usd	2400
concepts[0].id	https://openalex.org/C43214815
concepts[0].level	3
concepts[0].score	0.7339383363723755
concepts[0].wikidata	https://www.wikidata.org/wiki/Q7310987
concepts[0].display_name	Reliability (semiconductor)
concepts[1].id	https://openalex.org/C151201525
concepts[1].level	2
concepts[1].score	0.6349048614501953
concepts[1].wikidata	https://www.wikidata.org/wiki/Q177239
concepts[1].display_name	Limit (mathematics)
concepts[2].id	https://openalex.org/C163716315
concepts[2].level	2
concepts[2].score	0.5708248615264893
concepts[2].wikidata	https://www.wikidata.org/wiki/Q901177
concepts[2].display_name	Gaussian
concepts[3].id	https://openalex.org/C150077022
concepts[3].level	2
concepts[3].score	0.534047544002533
concepts[3].wikidata	https://www.wikidata.org/wiki/Q3136137
concepts[3].display_name	Response surface methodology
concepts[4].id	https://openalex.org/C14036430
concepts[4].level	2
concepts[4].score	0.5191261172294617
concepts[4].wikidata	https://www.wikidata.org/wiki/Q3736076
concepts[4].display_name	Function (biology)
concepts[5].id	https://openalex.org/C33923547
concepts[5].level	0
concepts[5].score	0.5075422525405884
concepts[5].wikidata	https://www.wikidata.org/wiki/Q395
concepts[5].display_name	Mathematics
concepts[6].id	https://openalex.org/C110069353
concepts[6].level	2
concepts[6].score	0.5006248950958252
concepts[6].wikidata	https://www.wikidata.org/wiki/Q961278
concepts[6].display_name	Slope stability
concepts[7].id	https://openalex.org/C16995789
concepts[7].level	2
concepts[7].score	0.4838513433933258
concepts[7].wikidata	https://www.wikidata.org/wiki/Q2564634
concepts[7].display_name	Limit state design
concepts[8].id	https://openalex.org/C112972136
concepts[8].level	2
concepts[8].score	0.47917333245277405
concepts[8].wikidata	https://www.wikidata.org/wiki/Q7595718
concepts[8].display_name	Stability (learning theory)
concepts[9].id	https://openalex.org/C28826006
concepts[9].level	1
concepts[9].score	0.45919692516326904
concepts[9].wikidata	https://www.wikidata.org/wiki/Q33521
concepts[9].display_name	Applied mathematics
concepts[10].id	https://openalex.org/C61326573
concepts[10].level	3
concepts[10].score	0.4482552707195282
concepts[10].wikidata	https://www.wikidata.org/wiki/Q1496376
concepts[10].display_name	Gaussian process
concepts[11].id	https://openalex.org/C2776799497
concepts[11].level	2
concepts[11].score	0.43218719959259033
concepts[11].wikidata	https://www.wikidata.org/wiki/Q484298
concepts[11].display_name	Surface (topology)
concepts[12].id	https://openalex.org/C98045186
concepts[12].level	2
concepts[12].score	0.4227762222290039
concepts[12].wikidata	https://www.wikidata.org/wiki/Q205663
concepts[12].display_name	Process (computing)
concepts[13].id	https://openalex.org/C41008148
concepts[13].level	0
concepts[13].score	0.42274874448776245
concepts[13].wikidata	https://www.wikidata.org/wiki/Q21198
concepts[13].display_name	Computer science
concepts[14].id	https://openalex.org/C11413529
concepts[14].level	1
concepts[14].score	0.3949855864048004
concepts[14].wikidata	https://www.wikidata.org/wiki/Q8366
concepts[14].display_name	Algorithm
concepts[15].id	https://openalex.org/C126255220
concepts[15].level	1
concepts[15].score	0.3743633031845093
concepts[15].wikidata	https://www.wikidata.org/wiki/Q141495
concepts[15].display_name	Mathematical optimization
concepts[16].id	https://openalex.org/C105795698
concepts[16].level	1
concepts[16].score	0.2036069929599762
concepts[16].wikidata	https://www.wikidata.org/wiki/Q12483
concepts[16].display_name	Statistics
concepts[17].id	https://openalex.org/C119857082
concepts[17].level	1
concepts[17].score	0.1287541687488556
concepts[17].wikidata	https://www.wikidata.org/wiki/Q2539
concepts[17].display_name	Machine learning
concepts[18].id	https://openalex.org/C134306372
concepts[18].level	1
concepts[18].score	0.12378808856010437
concepts[18].wikidata	https://www.wikidata.org/wiki/Q7754
concepts[18].display_name	Mathematical analysis
concepts[19].id	https://openalex.org/C66938386
concepts[19].level	1
concepts[19].score	0.11539214849472046
concepts[19].wikidata	https://www.wikidata.org/wiki/Q633538
concepts[19].display_name	Structural engineering
concepts[20].id	https://openalex.org/C2524010
concepts[20].level	1
concepts[20].score	0.09196904301643372
concepts[20].wikidata	https://www.wikidata.org/wiki/Q8087
concepts[20].display_name	Geometry
concepts[21].id	https://openalex.org/C163258240
concepts[21].level	2
concepts[21].score	0.09189093112945557
concepts[21].wikidata	https://www.wikidata.org/wiki/Q25342
concepts[21].display_name	Power (physics)
concepts[22].id	https://openalex.org/C127413603
concepts[22].level	0
concepts[22].score	0.0902734100818634
concepts[22].wikidata	https://www.wikidata.org/wiki/Q11023
concepts[22].display_name	Engineering
concepts[23].id	https://openalex.org/C187320778
concepts[23].level	1
concepts[23].score	0.08925190567970276
concepts[23].wikidata	https://www.wikidata.org/wiki/Q1349130
concepts[23].display_name	Geotechnical engineering
concepts[24].id	https://openalex.org/C78458016
concepts[24].level	1
concepts[24].score	0.0
concepts[24].wikidata	https://www.wikidata.org/wiki/Q840400
concepts[24].display_name	Evolutionary biology
concepts[25].id	https://openalex.org/C111919701
concepts[25].level	1
concepts[25].score	0.0
concepts[25].wikidata	https://www.wikidata.org/wiki/Q9135
concepts[25].display_name	Operating system
concepts[26].id	https://openalex.org/C62520636
concepts[26].level	1
concepts[26].score	0.0
concepts[26].wikidata	https://www.wikidata.org/wiki/Q944
concepts[26].display_name	Quantum mechanics
concepts[27].id	https://openalex.org/C86803240
concepts[27].level	0
concepts[27].score	0.0
concepts[27].wikidata	https://www.wikidata.org/wiki/Q420
concepts[27].display_name	Biology
concepts[28].id	https://openalex.org/C121332964
concepts[28].level	0
concepts[28].score	0.0
concepts[28].wikidata	https://www.wikidata.org/wiki/Q413
concepts[28].display_name	Physics
keywords[0].id	https://openalex.org/keywords/reliability
keywords[0].score	0.7339383363723755
keywords[0].display_name	Reliability (semiconductor)
keywords[1].id	https://openalex.org/keywords/limit
keywords[1].score	0.6349048614501953
keywords[1].display_name	Limit (mathematics)
keywords[2].id	https://openalex.org/keywords/gaussian
keywords[2].score	0.5708248615264893
keywords[2].display_name	Gaussian
keywords[3].id	https://openalex.org/keywords/response-surface-methodology
keywords[3].score	0.534047544002533
keywords[3].display_name	Response surface methodology
keywords[4].id	https://openalex.org/keywords/function
keywords[4].score	0.5191261172294617
keywords[4].display_name	Function (biology)
keywords[5].id	https://openalex.org/keywords/mathematics
keywords[5].score	0.5075422525405884
keywords[5].display_name	Mathematics
keywords[6].id	https://openalex.org/keywords/slope-stability
keywords[6].score	0.5006248950958252
keywords[6].display_name	Slope stability
keywords[7].id	https://openalex.org/keywords/limit-state-design
keywords[7].score	0.4838513433933258
keywords[7].display_name	Limit state design
keywords[8].id	https://openalex.org/keywords/stability
keywords[8].score	0.47917333245277405
keywords[8].display_name	Stability (learning theory)
keywords[9].id	https://openalex.org/keywords/applied-mathematics
keywords[9].score	0.45919692516326904
keywords[9].display_name	Applied mathematics
keywords[10].id	https://openalex.org/keywords/gaussian-process
keywords[10].score	0.4482552707195282
keywords[10].display_name	Gaussian process
keywords[11].id	https://openalex.org/keywords/surface
keywords[11].score	0.43218719959259033
keywords[11].display_name	Surface (topology)
keywords[12].id	https://openalex.org/keywords/process
keywords[12].score	0.4227762222290039
keywords[12].display_name	Process (computing)
keywords[13].id	https://openalex.org/keywords/computer-science
keywords[13].score	0.42274874448776245
keywords[13].display_name	Computer science
keywords[14].id	https://openalex.org/keywords/algorithm
keywords[14].score	0.3949855864048004
keywords[14].display_name	Algorithm
keywords[15].id	https://openalex.org/keywords/mathematical-optimization
keywords[15].score	0.3743633031845093
keywords[15].display_name	Mathematical optimization
keywords[16].id	https://openalex.org/keywords/statistics
keywords[16].score	0.2036069929599762
keywords[16].display_name	Statistics
keywords[17].id	https://openalex.org/keywords/machine-learning
keywords[17].score	0.1287541687488556
keywords[17].display_name	Machine learning
keywords[18].id	https://openalex.org/keywords/mathematical-analysis
keywords[18].score	0.12378808856010437
keywords[18].display_name	Mathematical analysis
keywords[19].id	https://openalex.org/keywords/structural-engineering
keywords[19].score	0.11539214849472046
keywords[19].display_name	Structural engineering
keywords[20].id	https://openalex.org/keywords/geometry
keywords[20].score	0.09196904301643372
keywords[20].display_name	Geometry
keywords[21].id	https://openalex.org/keywords/power
keywords[21].score	0.09189093112945557
keywords[21].display_name	Power (physics)
keywords[22].id	https://openalex.org/keywords/engineering
keywords[22].score	0.0902734100818634
keywords[22].display_name	Engineering
keywords[23].id	https://openalex.org/keywords/geotechnical-engineering
keywords[23].score	0.08925190567970276
keywords[23].display_name	Geotechnical engineering
language	en
locations[0].id	doi:10.1155/2019/9185756
locations[0].is_oa	True
locations[0].source.id	https://openalex.org/S86499044
locations[0].source.issn	1687-8086, 1687-8094
locations[0].source.type	journal
locations[0].source.is_oa	True
locations[0].source.issn_l	1687-8086
locations[0].source.is_core	True
locations[0].source.is_in_doaj	True
locations[0].source.display_name	Advances in Civil Engineering
locations[0].source.host_organization	https://openalex.org/P4310319869
locations[0].source.host_organization_name	Hindawi Publishing Corporation
locations[0].source.host_organization_lineage	https://openalex.org/P4310319869
locations[0].source.host_organization_lineage_names	Hindawi Publishing Corporation
locations[0].license	cc-by
locations[0].pdf_url	https://downloads.hindawi.com/journals/ace/2019/9185756.pdf
locations[0].version	publishedVersion
locations[0].raw_type	journal-article
locations[0].license_id	https://openalex.org/licenses/cc-by
locations[0].is_accepted	True
locations[0].is_published	True
locations[0].raw_source_name	Advances in Civil Engineering
locations[0].landing_page_url	https://doi.org/10.1155/2019/9185756
locations[1].id	pmh:oai:doaj.org/article:f9bac3cd8bc94772b39322fb279c7250
locations[1].is_oa	False
locations[1].source.id	https://openalex.org/S4306401280
locations[1].source.issn
locations[1].source.type	repository
locations[1].source.is_oa	False
locations[1].source.issn_l
locations[1].source.is_core	False
locations[1].source.is_in_doaj	False
locations[1].source.display_name	DOAJ (DOAJ: Directory of Open Access Journals)
locations[1].source.host_organization
locations[1].source.host_organization_name
locations[1].license
locations[1].pdf_url
locations[1].version	submittedVersion
locations[1].raw_type	article
locations[1].license_id
locations[1].is_accepted	False
locations[1].is_published	False
locations[1].raw_source_name	Advances in Civil Engineering, Vol 2019 (2019)
locations[1].landing_page_url	https://doaj.org/article/f9bac3cd8bc94772b39322fb279c7250
indexed_in	crossref, doaj
authorships[0].author.id	https://openalex.org/A5033080517
authorships[0].author.orcid	https://orcid.org/0000-0002-1938-1857
authorships[0].author.display_name	Bin Hu
authorships[0].countries	CN
authorships[0].affiliations[0].institution_ids	https://openalex.org/I43922553
authorships[0].affiliations[0].raw_affiliation_string	School of Resource and Environmental Engineering, Wuhan University of Science and Technology, P.O. Box 430081, Wuhan
authorships[0].institutions[0].id	https://openalex.org/I43922553
authorships[0].institutions[0].ror	https://ror.org/00e4hrk88
authorships[0].institutions[0].type	education
authorships[0].institutions[0].lineage	https://openalex.org/I43922553
authorships[0].institutions[0].country_code	CN
authorships[0].institutions[0].display_name	Wuhan University of Science and Technology
authorships[0].author_position	first
authorships[0].raw_author_name	Bin Hu
authorships[0].is_corresponding	False
authorships[0].raw_affiliation_strings	School of Resource and Environmental Engineering, Wuhan University of Science and Technology, P.O. Box 430081, Wuhan
authorships[1].author.id	https://openalex.org/A5039750959
authorships[1].author.orcid	https://orcid.org/0000-0001-9506-6827
authorships[1].author.display_name	Guoshao Su
authorships[1].countries	CN
authorships[1].affiliations[0].institution_ids	https://openalex.org/I150807315
authorships[1].affiliations[0].raw_affiliation_string	Key Laboratory of Disaster Prevention and Structural Safety of Ministry of Education, School of Civil and Architecture Engineering, Guangxi University, Nanning, Guangxi 530004
authorships[1].institutions[0].id	https://openalex.org/I150807315
authorships[1].institutions[0].ror	https://ror.org/02c9qn167
authorships[1].institutions[0].type	education
authorships[1].institutions[0].lineage	https://openalex.org/I150807315
authorships[1].institutions[0].country_code	CN
authorships[1].institutions[0].display_name	Guangxi University
authorships[1].author_position	middle
authorships[1].raw_author_name	Guo-shao Su
authorships[1].is_corresponding	False
authorships[1].raw_affiliation_strings	Key Laboratory of Disaster Prevention and Structural Safety of Ministry of Education, School of Civil and Architecture Engineering, Guangxi University, Nanning, Guangxi 530004
authorships[2].author.id	https://openalex.org/A5102956653
authorships[2].author.orcid	https://orcid.org/0000-0001-6090-697X
authorships[2].author.display_name	Jianqing Jiang
authorships[2].countries	CN
authorships[2].affiliations[0].institution_ids	https://openalex.org/I9224756
authorships[2].affiliations[0].raw_affiliation_string	Key Laboratory of Ministry of Education on Safe Mining of Deep Metal Mines, Northeastern University, Shenyang 110819
authorships[2].affiliations[1].institution_ids	https://openalex.org/I150807315
authorships[2].affiliations[1].raw_affiliation_string	Key Laboratory of Disaster Prevention and Structural Safety of Ministry of Education, School of Civil and Architecture Engineering, Guangxi University, Nanning, Guangxi 530004
authorships[2].institutions[0].id	https://openalex.org/I150807315
authorships[2].institutions[0].ror	https://ror.org/02c9qn167
authorships[2].institutions[0].type	education
authorships[2].institutions[0].lineage	https://openalex.org/I150807315
authorships[2].institutions[0].country_code	CN
authorships[2].institutions[0].display_name	Guangxi University
authorships[2].institutions[1].id	https://openalex.org/I9224756
authorships[2].institutions[1].ror	https://ror.org/03awzbc87
authorships[2].institutions[1].type	education
authorships[2].institutions[1].lineage	https://openalex.org/I9224756
authorships[2].institutions[1].country_code	CN
authorships[2].institutions[1].display_name	Northeastern University
authorships[2].author_position	middle
authorships[2].raw_author_name	Jianqing Jiang
authorships[2].is_corresponding	True
authorships[2].raw_affiliation_strings	Key Laboratory of Disaster Prevention and Structural Safety of Ministry of Education, School of Civil and Architecture Engineering, Guangxi University, Nanning, Guangxi 530004, Key Laboratory of Ministry of Education on Safe Mining of Deep Metal Mines, Northeastern University, Shenyang 110819
authorships[3].author.id	https://openalex.org/A5102219299
authorships[3].author.orcid
authorships[3].author.display_name	Yilong Xiao
authorships[3].countries	CN
authorships[3].affiliations[0].institution_ids	https://openalex.org/I150807315
authorships[3].affiliations[0].raw_affiliation_string	Key Laboratory of Disaster Prevention and Structural Safety of Ministry of Education, School of Civil and Architecture Engineering, Guangxi University, Nanning, Guangxi 530004
authorships[3].institutions[0].id	https://openalex.org/I150807315
authorships[3].institutions[0].ror	https://ror.org/02c9qn167
authorships[3].institutions[0].type	education
authorships[3].institutions[0].lineage	https://openalex.org/I150807315
authorships[3].institutions[0].country_code	CN
authorships[3].institutions[0].display_name	Guangxi University
authorships[3].author_position	last
authorships[3].raw_author_name	Yilong Xiao
authorships[3].is_corresponding	False
authorships[3].raw_affiliation_strings	Key Laboratory of Disaster Prevention and Structural Safety of Ministry of Education, School of Civil and Architecture Engineering, Guangxi University, Nanning, Guangxi 530004
has_content.pdf	True
has_content.grobid_xml	True
is_paratext	False
open_access.is_oa	True
open_access.oa_url	https://downloads.hindawi.com/journals/ace/2019/9185756.pdf
open_access.oa_status	gold
open_access.any_repository_has_fulltext	False
created_date	2025-10-10T00:00:00
display_name	Gaussian Process‐Based Response Surface Method for Slope Reliability Analysis
has_fulltext	True
is_retracted	False
updated_date	2025-11-06T03:46:38.306776
primary_topic.id	https://openalex.org/T11046
primary_topic.field.id	https://openalex.org/fields/22
primary_topic.field.display_name	Engineering
primary_topic.score	0.9998000264167786
primary_topic.domain.id	https://openalex.org/domains/3
primary_topic.domain.display_name	Physical Sciences
primary_topic.subfield.id	https://openalex.org/subfields/2213
primary_topic.subfield.display_name	Safety, Risk, Reliability and Quality
primary_topic.display_name	Geotechnical Engineering and Analysis
related_works	https://openalex.org/W2073503281, https://openalex.org/W2384332569, https://openalex.org/W3006216983, https://openalex.org/W2907978266, https://openalex.org/W4288908364, https://openalex.org/W2313279086, https://openalex.org/W4323538665, https://openalex.org/W1964286703, https://openalex.org/W2169866437, https://openalex.org/W3056417032
cited_by_count	11
counts_by_year[0].year	2025
counts_by_year[0].cited_by_count	2
counts_by_year[1].year	2024
counts_by_year[1].cited_by_count	2
counts_by_year[2].year	2023
counts_by_year[2].cited_by_count	1
counts_by_year[3].year	2022
counts_by_year[3].cited_by_count	2
counts_by_year[4].year	2021
counts_by_year[4].cited_by_count	1
counts_by_year[5].year	2020
counts_by_year[5].cited_by_count	3
locations_count	2
best_oa_location.id	doi:10.1155/2019/9185756
best_oa_location.is_oa	True
best_oa_location.source.id	https://openalex.org/S86499044
best_oa_location.source.issn	1687-8086, 1687-8094
best_oa_location.source.type	journal
best_oa_location.source.is_oa	True
best_oa_location.source.issn_l	1687-8086
best_oa_location.source.is_core	True
best_oa_location.source.is_in_doaj	True
best_oa_location.source.display_name	Advances in Civil Engineering
best_oa_location.source.host_organization	https://openalex.org/P4310319869
best_oa_location.source.host_organization_name	Hindawi Publishing Corporation
best_oa_location.source.host_organization_lineage	https://openalex.org/P4310319869
best_oa_location.source.host_organization_lineage_names	Hindawi Publishing Corporation
best_oa_location.license	cc-by
best_oa_location.pdf_url	https://downloads.hindawi.com/journals/ace/2019/9185756.pdf
best_oa_location.version	publishedVersion
best_oa_location.raw_type	journal-article
best_oa_location.license_id	https://openalex.org/licenses/cc-by
best_oa_location.is_accepted	True
best_oa_location.is_published	True
best_oa_location.raw_source_name	Advances in Civil Engineering
best_oa_location.landing_page_url	https://doi.org/10.1155/2019/9185756
primary_location.id	doi:10.1155/2019/9185756
primary_location.is_oa	True
primary_location.source.id	https://openalex.org/S86499044
primary_location.source.issn	1687-8086, 1687-8094
primary_location.source.type	journal
primary_location.source.is_oa	True
primary_location.source.issn_l	1687-8086
primary_location.source.is_core	True
primary_location.source.is_in_doaj	True
primary_location.source.display_name	Advances in Civil Engineering
primary_location.source.host_organization	https://openalex.org/P4310319869
primary_location.source.host_organization_name	Hindawi Publishing Corporation
primary_location.source.host_organization_lineage	https://openalex.org/P4310319869
primary_location.source.host_organization_lineage_names	Hindawi Publishing Corporation
primary_location.license	cc-by
primary_location.pdf_url	https://downloads.hindawi.com/journals/ace/2019/9185756.pdf
primary_location.version	publishedVersion
primary_location.raw_type	journal-article
primary_location.license_id	https://openalex.org/licenses/cc-by
primary_location.is_accepted	True
primary_location.is_published	True
primary_location.raw_source_name	Advances in Civil Engineering
primary_location.landing_page_url	https://doi.org/10.1155/2019/9185756
publication_date	2019-01-01
publication_year	2019
referenced_works	https://openalex.org/W2069527243, https://openalex.org/W4235971626, https://openalex.org/W1482294348, https://openalex.org/W2116120504, https://openalex.org/W2003986068, https://openalex.org/W1992282017, https://openalex.org/W1975048675, https://openalex.org/W1991548802, https://openalex.org/W1978459922, https://openalex.org/W2014715727, https://openalex.org/W2087423781, https://openalex.org/W1972550919, https://openalex.org/W2156909104, https://openalex.org/W1983116803, https://openalex.org/W2404690789, https://openalex.org/W2732319205, https://openalex.org/W1657213141, https://openalex.org/W2047989844, https://openalex.org/W2070820628, https://openalex.org/W2019044917, https://openalex.org/W2046298174, https://openalex.org/W2040404518, https://openalex.org/W2008034786, https://openalex.org/W4376595430, https://openalex.org/W319904513, https://openalex.org/W2003035369, https://openalex.org/W2023261859, https://openalex.org/W2014773637, https://openalex.org/W4211049957, https://openalex.org/W2038726880, https://openalex.org/W2027751236, https://openalex.org/W2045514380, https://openalex.org/W2041398635
referenced_works_count	33
abstract_inverted_index.A	0, 45
abstract_inverted_index.GP	32, 62, 77, 96
abstract_inverted_index.an	103
abstract_inverted_index.at	119
abstract_inverted_index.by	29, 54, 74, 94
abstract_inverted_index.is	150
abstract_inverted_index.of	25, 36, 48, 70, 112, 114, 134
abstract_inverted_index.on	13
abstract_inverted_index.to	108, 129, 153
abstract_inverted_index.The	20
abstract_inverted_index.and	34, 85, 141
abstract_inverted_index.for	6, 59, 88, 157
abstract_inverted_index.its	86
abstract_inverted_index.new	1
abstract_inverted_index.one	139
abstract_inverted_index.the	23, 30, 40, 55, 61, 65, 75, 80, 95, 99, 110, 115, 120, 123, 130, 147, 162
abstract_inverted_index.was	10, 72, 106
abstract_inverted_index.(GP)	16
abstract_inverted_index.RSM.	164
abstract_inverted_index.case	136
abstract_inverted_index.four	135
abstract_inverted_index.more	151
abstract_inverted_index.near	122
abstract_inverted_index.than	161
abstract_inverted_index.that	146
abstract_inverted_index.were	51, 92
abstract_inverted_index.with	98
abstract_inverted_index.(RSM)	5
abstract_inverted_index.Then,	64
abstract_inverted_index.Thus,	79
abstract_inverted_index.based	12
abstract_inverted_index.built	53
abstract_inverted_index.limit	26, 67, 82, 116
abstract_inverted_index.model	33, 97
abstract_inverted_index.point	125
abstract_inverted_index.slope	7, 71, 89, 143, 158
abstract_inverted_index.small	46
abstract_inverted_index.state	27, 68, 83, 117
abstract_inverted_index.three	142
abstract_inverted_index.using	39
abstract_inverted_index.which	126
abstract_inverted_index.amount	47
abstract_inverted_index.design	124
abstract_inverted_index.method	4, 21, 43, 58, 149
abstract_inverted_index.model.	63, 78
abstract_inverted_index.region	121
abstract_inverted_index.(FORM).	44
abstract_inverted_index.Results	133
abstract_inverted_index.achieve	154
abstract_inverted_index.failure	37, 131
abstract_inverted_index.firstly	52
abstract_inverted_index.improve	109
abstract_inverted_index.limited	56
abstract_inverted_index.machine	17
abstract_inverted_index.process	15
abstract_inverted_index.samples	50
abstract_inverted_index.studies	137
abstract_inverted_index.surface	3
abstract_inverted_index.trained	31, 76
abstract_inverted_index.Gaussian	14
abstract_inverted_index.accuracy	156
abstract_inverted_index.analysis	9, 91, 160
abstract_inverted_index.explicit	100
abstract_inverted_index.function	28, 69, 84, 118
abstract_inverted_index.implicit	66, 81
abstract_inverted_index.indicate	145
abstract_inverted_index.involves	22
abstract_inverted_index.learning	18
abstract_inverted_index.nonslope	140
abstract_inverted_index.problems	144
abstract_inverted_index.proposed	11, 148
abstract_inverted_index.response	2
abstract_inverted_index.training	49, 60
abstract_inverted_index.algorithm	105
abstract_inverted_index.efficient	152
abstract_inverted_index.including	138
abstract_inverted_index.iterative	104
abstract_inverted_index.precision	111
abstract_inverted_index.presented	107
abstract_inverted_index.stability	90
abstract_inverted_index.estimation	35
abstract_inverted_index.reasonable	155
abstract_inverted_index.contributes	127
abstract_inverted_index.derivatives	87
abstract_inverted_index.equilibrium	57
abstract_inverted_index.probability	38
abstract_inverted_index.reliability	8, 42, 159
abstract_inverted_index.technology.	19
abstract_inverted_index.traditional	163
abstract_inverted_index.Furthermore,	102
abstract_inverted_index.approximated	73, 93
abstract_inverted_index.formulation.	101
abstract_inverted_index.probability.	132
abstract_inverted_index.approximation	24, 113
abstract_inverted_index.first‐order	41
abstract_inverted_index.significantly	128
cited_by_percentile_year.max	97
cited_by_percentile_year.min	89
corresponding_author_ids	https://openalex.org/A5102956653
countries_distinct_count	1
institutions_distinct_count	4
corresponding_institution_ids	https://openalex.org/I150807315, https://openalex.org/I9224756
citation_normalized_percentile.value	0.78763501
citation_normalized_percentile.is_in_top_1_percent	False
citation_normalized_percentile.is_in_top_10_percent	False