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2016 | OriginalPaper | Chapter

4. Stochastic Models

Authors : Ana Silva, Jorge de Brito, Pedro Lima Gaspar

Published in: Methodologies for Service Life Prediction of Buildings

Publisher: Springer International Publishing

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Abstract

This chapter proposes the formulation of stochastic models (logistic regression analysis and Markov chains model), which allow analysing the claddings’ service life based on probabilistic distribution functions. These models allow assessing: i) the probability of each façade with a given degradation condition according to its age, its characteristics, and the environmental exposure condition; ii) the period of time with maximum probability of transition from a degradation condition to the next one (more severe); iii) the probability of each case study reaching the end of its service life over a given period of time.

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previous chapter Deterministic Models
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Literature
Agresti A (1986) Applying R2 type measures to ordered categorical data. Technometrics 28(2):133–138
Aikivuori AM (1999) Critical loss of performance—what fails before durability. In: 8th international conference on durability of buildings materials and components, DBMC, Vancouver, Canada, pp 1369–1376
Ash A, Shwartz M (1999) R2: a useful measure of model performance when predicting a dichotomous outcome. Stat Med 18(4):375–384CrossRef
Augenbroe GLM, Park C-S (2002) Towards a maintenance performance toolkit for GSA. Interim Report submitted to GSA, Georgia Institute of Technology, Atlanta, USA
Baik HS, Jeong HS, Abraham DM (2006) Estimating transition probabilities in Markov chain-based deterioration models for management of wastewater systems. J Water Resour Plan Manage 132(1):15–24CrossRef
Balaras A, Droutsa K, Dascalaki E, Kontoyiannidis S (2005) Deterioration of European apartment buildings. Energy Build 37(5):515–527CrossRef
Baum LE, Petrie T (1966) Statistical inference for probabilistic functions of finite state Markov chains. Ann Math Stat 37(6):1554–1563MathSciNetCrossRefMATH
Bayaga A (2010) Multinomial logistic regression: usage and application in risk analysis. J Appl Quant Methods 5(2):288–297
Bladty M, Sorensen M (2009) Efficient estimation of transition rates between credit ratings from observations at discrete time points. Quant Finance 9(2):147–160MathSciNetCrossRef
Bocchini P, Saydam D, Frangopol DM (2013) Efficient, accurate, and simple Markov chain model for the life-cycle analysis of bridge groups. Struct Saf 40:51–64CrossRef
Bogdanoff JL (1978) A new cumulative damage model- Part 1. J Appl Mech 45(2):246–250CrossRef
Brandt E, Rasmussen M (2002) Assessment of building conditions. Energy Build 34(2):121–125CrossRef
Carrington PJ, Scott J, Wasserman S (eds) (2005) Models and methods in social network analysis, 1st edn. Cambridge University Press, New York
Chew M (2005) Defect analysis in wet areas of buildings. Constr Build Mater 19(3):165–173CrossRef
Choi EC (1999) Wind driven rain on building facades and the driving rain index. Wind Eng Ind Aeronaut 79(1–2):105–122CrossRef
Choi M, Lee G (2010) Decision tree for selecting retaining wall systems based on logistic regression analysis. Autom Construct 19(7):917–928MathSciNetCrossRef
Cox DR, Miller HD (1965) The theory of stochastic processes, 1st edn. Chapman and Hall, LondonMATH
Cox DR, Snell EJ (1989) The analysis of binary data, 2nd edn. Chapman and Hall, LondonMATH
Cox DR, Wermuch N (1992) A comment on the coefficient of determination for binary responses. Am Stat 46(1):1–4
Das PC (1998) New developments in bridge management methodology. Struct Eng Int 8(4):299–302
Dekker R, Nicolai RP, Kallenberg LCM (2008) Maintenance and Markov decision models. Encyclopedia of statistics in quality and reliability. Wiley, London
Ellingwood BR (2005) Risk-informed condition assessment of civil infrastructure: state of practice and research issues. Struct Infrastruct Eng Maintenance Manage Life-Cycle Des Perform 1(1):7–18CrossRef
Frangopol DM, Neves LC (2004) Probabilistic maintenance and optimization strategies for deteriorating civil infrastructures. In: Topping BHV, Mota Soares CA (eds) Progress in computational structures technology. Saxe-Coburg Publishers, Stirling, pp 353–377
Frangopol DM, Kallen M-J, Noortwijk JMV (2004) Probabilistic models for life-cycle performance of deteriorating structures: review and future directions. Prog Struct Mat Eng 6(4):197–212CrossRef
Freitas VP, Sousa M, Abrantes V (1999) Survey of the durability of facades of 4000 dwellings in northern Portugal. In: 8th DBMC, international conference on the durability of building materials and components; Ottawa, Canada, pp 1040–1050
Gao S, Shen J (2007) Asymptotic properties of a double penalized maximum likelihood estimator in logistic regression. Stat Probab Lett 77(9):925–930MathSciNetCrossRefMATH
Garavaglia E, Gianni A, Molina C (2004) Reliability of porous materials: two stochastic approaches. J Mater Civ Eng 16(5):419–426CrossRef
Gaspar P (2009) Service life of constructions: development of a method to estimate the durability of construction elements. Application to renderings of current buildings (in Portuguese). Doctor thesis in sciences of engineering, Instituto Superior Técnico, University of Lisbon, Portugal
Gu MG, Kong FH (1998) A stochastic approximation algorithm with Markov chain Monte Carlo method for incomplete data estimation problems. Nat Acad Sci USA 95(13):7270–7274MathSciNetCrossRefMATH
Hair JF, Black WC, Babin B, Anderson RE, Tatham RL (2007) Multivariate data analysis, 6th edn. Prentice-Hall Publishers, Englewood Cliffs
Handel RV (2008) Hidden Markov models. Lecture Notes, Princeton University, New Jersey, USA
Henry NW (1971) The retention model: a Markov chain with variable transition probabilities. J Am Stat Assoc 66(334):264–267CrossRef
Higham D, Higham N (2005) MATLAB guide, 2nd edn. Society for Industrial Mathematics, PhiladelphiaCrossRefMATH
Horn R, Johnson C (1985) Matrix analysis. Cambridge University Press, Cambridge
Hosmer DW, Lemeshow S (1980) Goodness of fit tests for the multiple logistic regression model. Commun Stat Part A Theory Methods 9(10):1043–1069CrossRefMATH
Hosmer DW, Hjort NL (2002) Goodness-of-fit processes for logistic regression: simulation results. Stat Med 21(18):2723–2738CrossRef
Hossain KMA, Lachemi M, Şahmaran M (2009) Performance of cementitious building renders incorporating natural and industrial pozzolans under aggressive airborne marine salts. Cement Concr Compos 31(6):358–368CrossRef
Howell DC (2002) Statistical methods for psychology, 5th edn. Wadsworth Publishing, Pacific Grove
Hu B, Shao J, Palta M (2006) Pseudo-R2 in logistic regression model. Statistica Sinica 16(3):847–860MathSciNetMATH
Kallen MJ (2009) A comparison of statistical models for visual inspection data. Safety, reliability and risk structures, infrastructures and engineering systems. In: Tenth international conference on structural safety and reliability (ICOSSAR), Osaka, Japan, pp 3235–3242
Kobayashi K, Do M, Han D (2010) Estimation of Markovian transition probabilities for pavement deterioration forecasting. KSCE J Civil Eng 14(3):343–351CrossRef
Koch A, Siegesmund S (2004) The combined effect of moisture and temperature on the anomalous expansion behaviour of marble. Environ Geol 46(3–4):350–363
Kus H, Nygren K (2000) Long-term exposure of rendered autoclaved aerated concrete: measuring and testing programme. In: RILEM/CIB/ISO international symposium—integrated life-cycle design of materials and structures, Helsinki, Finland, pp 415–420
Kus H, Nygren K (2002) Microenvironmental characterization of rendered autoclaved aerated concrete. Build Res Inf 30(1):25–34CrossRef
Kus H, Nygren K, Norberg P (2004) In-use performance assessment of rendered autoclaved concrete walls by long-term moisture monitoring. Build Environ 39(6):677–687CrossRef
Kuss O (2002) Global goodness-of-fit tests in logistic regression with sparse data. Stat Med 21(24):3789–3801CrossRef
Lacasse MA, Kyle BR, Talon A, Boissier D, Hilly T, Abdulghani K (2008) Optimization of the building maintenance management process using a markovian model. In: 11th international conference on the durability of building materials and components, Istanbul, Turkey, pp 1–9 (T72)
Lee S, Hershberger S (1990) A simple rule for generating equivalent models in covariance structure modeling. Multivar Behav Res 25(3):313–334CrossRef
Lethanh N, Adey B (2012) A hidden Markov model for modeling pavement deterioration under incomplete monitoring data. In: International conference on mathematical, computational and statistical sciences, and engineering 2012, Stockholm, Sweden, pp 722–729
Lewis KN, Heckman BD, Himawan L (2011) Multinomial logistic regression analysis for differentiating 3 treatment outcome trajectory groups for headache-associated disability. Pain 152(8):1718–1726CrossRef
Li P (2007) Hypothesis testing in finite mixture models. Doctoral thesis in Statistics, University of Waterloo, Ontario, Canada
Li Z, Wang W (2006) Computer aided solving the high-order transition probability matrix of the finite Markov chain. Appl Math Comput 172(1):267–285MathSciNetMATH
Liu T (2010) Application of Markov chains to analyze and predict the time series. Mod Appl Sci 4(5):162–166CrossRefMATH
Ljung L (1987) System identification—theory for the user. Prentice-Hall, Englewood Cliffs
Lounis Z, Vanier DJ (2000) A multi-objective and stochastic system for building maintenance management. Comput Aided Civil Infrastruct Eng 15(5):320–329CrossRef
Lounis Z, Lacasse MA, Siemes AJM, Moser K (1998) Further steps towards a quantitative approach to durability design. Materials and technologies for sustainable construction, construction & environment. CIB World Building Congress, Gävle, Sweden, pp 315–324
Madanat S, Mishalani R, Ibrahim WHW (1995) Estimation of infrastructure transition probabilities from condition rating data. J Infrastruct Syst 1(2):120–125CrossRef
Maroco J (2007) Statistical analysis using SPSS. (in Portuguese), 3rd edn. Sílabo Editions, Lisbon
Marteinsson B, Jónsson B (1999) Overall survey of buildings—performance and maintenance. In: 8th DBMC, international conference on the durability of building materials and components, Ottawa, Canada, pp 1634–1654
Mc Duling JJ (2006) Towards the development of transition probability matrices in the Markovian model for the predicted service life of buildings. PhD thesis in civil engineering, Faculty of Engineering, Built Environment and Information Technology, University of Pretoria, Pretoria
McFadden D (1973) Conditional logit analysis of qualitative choice behavior. In: Zarembka P (ed) Frontiers of econometrics. Academic Press, New York, pp 105–142
Menard S (2000) Coefficients of determination for multiple logistic regression analysis. Am Stat 54(1):17–24
Mitchell DS (2007) The use of lime & cement in traditional buildings. Technical Conservation, Research and Education Group, Historic Scotland, Longmore House, Salisbury Place, Edinburgh, Scotland, 8p
Mittlbock M, Schemper M (1996) Explained variation for logistic regression. Stat Med 15(19):1987–1997CrossRef
Monika SO (2005) Statistical inference and hypothesis testing for Markov chains with interval censoring—application to bridge condition data in the Netherlands. Master thesis in civil engineering, Delft University of Technology, Delft
Morcous G (2006) Performance prediction of bridge deck systems using Markov chains. J Perform Construct Facil 20(2):146–155CrossRef
Morcous G, Lounis Z, Mirza MS (2003) Identification of environmental categories for Markovian deterioration models of bridge decks. J Bridge Eng 8(6):353–361CrossRef
Moser K (2003) Engineering design methods for service life planning—state of the art. In: WMDBP 2003, international workshop on management of durability in the building process, Politecnico di Milano, Milan, Italy, paper 40
Neves LC, Frangopol DM, Cruz PJS (2006) Lifetime multi-objective optimization of maintenance of existing steel structures. In: 6th international symposium steel bridges, European Convention for Construction Steelwork, Prague, Czech Republic, pp 206–215
Newsom JT (2011) Logistic regression. Course of Data analysis II, Institute on Aging, School of Community Health, Portland State University
Ng S, Moses F (1996) Prediction of bridge service life using time-dependent reliability analysis. In: 3rd International conference on bridge management, University of Surrey, Guildford, UK, pp 26–33
Parnham P (1997) Prevention of premature staining of new buildings. E & FN Spon, LondonCrossRef
Parzen E (1962) Stochastic processes. Holden Day, San FranciscoMATH
Robelin C-A (2006) Facility-level and system-level stochastic optimization of bridge maintenance policies for Markovian management systems. PhD thesis in civil and environmental engineering, University of California, California, USA
Robelin CA, Madanat S (2007) History-dependent bridge deck maintenance and replacement optimization with Markov decision process. J Infrastruct Syst 13(3):195–201CrossRef
Roh Y-S, Xi Y (2000) A general A general formulation for transition probabilities of Markov model and the application to fracture of composite materials. Probab Eng Mech 15(3):241–250CrossRef
Schouenborg B, Grelk B, Malaga K (2007) Testing and assessment of marble and limestone (TEAM) - Important results from a large European research project on cladding panels. ASTM Int 4(5):10–22
Shohet I, Rosenfeld Y, Puterman M, Gilboa E (1999) Deterioration patterns for maintenance management—a methodological approach. In: 8th international conference on durability of building materials and components, Vancouver, Canada, pp 1666–1678
Shtatland ES, Kleinman K, Cain EM (2002) One more time about R2 measures of fit in logistic regression. In: 15th annual Nesug conference; statistics, data analysis and econometrics, Issue M, pp 1–6
Silva A, de Brito J, Gaspar PL (2012) Application of the factor method to maintenance decision support for stone cladding. Autom Constr 22(3):165–174CrossRef
Silva A, de Brito J, Gaspar P (2013) Probabilistic analysis of the degradation evolution of stone wall cladding (directly adhered to the substrate). J Mater Civil Eng 25(2): 227–235
Singer B (1981) Estimation of nonstationary Markov chains from panel data. Sociol Methodol 12:319–337CrossRef
Smyth GK (2003) Pearson’s goodness of fit statistic as a score test statistic. In: Goldstein DR (ed) Science and atatistics: a festschrift for terry speed. IMS lecture notes—monograph series, vol. 40. Institute of Mathematical Statistics, Hayward, California
Soroka I, Carmel D (1987) Durability of external renderings in a marine environment—durability of building materials. Elsevier Science Publishers, Amsterdam, pp 61–72
Stelzl I (1986) Changing causal relationships without changing the fit: some rules for generating equivalent LISREL models. Multivar Behav Res 21(3):309–331CrossRef
Straub A (2003) Using a condition-dependent approach to maintenance to control costs and performances. Facil Manage 1(4):380–395CrossRef
Suthar V, Tarmizi RA, Midi H, Adam MB (2010) Students’ beliefs on mathematics and achievement of university students: logistics regression analysis. In: International conference on mathematics education research (ICMER 2010). Procedia—Social and Behavioral Sciences, vol 8, pp 525–531
Thomasson F (1982) Les enduits monocouches à base de liants hydrauliques. UNITECNA, France, Paris, 129p
Trexler JC, Travis J (1993) Nontraditional regression analysis. Ecology 74(6):1629–1637CrossRef
Uchwat C, MacLeod D (2012) Case studies of regression and Markov chain models. In: Conference of the transportation Association of Canada, New Brunswick, Canada, Session: pavement performance case studies (SES), 19p
Veiga MR (2000) Methodology to evaluate the cracking susceptibility of mortars. Selection criteria of rendering and repointing mortars for ancient buildings. Seminar “Malte a vista com sabie locali nella conservazione degli edifici storici”, Torino, Italy, Politecnico di Torino, July, pp 1–16
Wald A (1943) Tests of statistical hypotheses concerning several parameters when the number of observations is large. Trans Am Math Soc 54(3):426–482MathSciNetCrossRefMATH
Wang Y (2005) A multinomial logistic regression modeling approach for anomaly intrusion detection. Comput Secur 24(8):662–674CrossRef
Westergren A, Karlsson S, Andersson P, Ohlsson O, Hallberg IR (2001) Eating difficulties, need for assisted eating, nutritional status and pressure ulcers in patients admitted for stroke rehabilitation. J Clin Nurs 10(2):257–269CrossRef
White JL (2013) Logistic regression model effectiveness: proportional chance criteria and proportional reduction in error. J Contemp Res Educ 2(1):4–10
Witten IH, Frank E (2005) Data mining: Practical machine learning tools and techniques, 2nd edn. Morgan Kaufman, BostonMATH
Wuensch KL (2011) Binary logistic regression. East Carolina University, Department of Psychology
Xie XJ, Pendergast J, Clarke W (2008) Increasing the power: a practical approach to goodness-of-fit test for logistic regression models with continuous predictors. Comput Stat Data Anal 52(5):2703–2713MathSciNetCrossRefMATH
Yokota H, Furuya K, Hashimoto K, Hanada S (2012) Reliability of deterioration prediction with Markov model for mooring facilities. In: IALCCE—International Association for Life-Cycle Civil Engineering, 3rd international symposium on life-cycle civil engineering, Vienna, Austria, pp 523–530, 3–6 Oct 2012
Metadata
Title
Stochastic Models
Authors
Ana Silva
Jorge de Brito
Pedro Lima Gaspar
Copyright Year
2016
Book
Methodologies for Service Life Prediction of Buildings

Print ISBN: 978-3-319-33288-8

Electronic ISBN: 978-3-319-33290-1

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-33290-1_4