- Email: [email protected]
Lifecycle Based User Value Analysis of Rail - Road Level Crossings: Probabilistic Approach Using Monte Carlo Simulation
Available online at www.sciencedirect.com
ScienceDirect Procedia Engineering 178 (2017) 409 – 418
16th Conference on Reliability and Statistics in Transportation and Communication, RelStat’2016, 19-22 October 2016, Riga, Latvia
Lifecycle Based User Value Analysis of Rail - Road Level Crossings: Probabilistic Approach Using Monte Carlo Simulation Hirut Grossbergera*, Christoph Maulerb, Frank Michelbergera a
Carl Ritter von Ghega Institute for Integrated Mobility Research, St. Poelten University of Applied Sciences Matthias Corvinus-Straße 1, St. Poelten, Austria b Wiener Lokalbahnen AG, Eichenstraße 1, 1120, Vienna, Austria
Abstract Railway operators are in continuous pressure to minimize maintenance and rehabilitation costs of infrastructures; at the same time they are expected to provide a reliable service by optimum allocation of natural and economical resources. Railway tracks and level crossings are long-lived assets where their service life stretch 30 to 100 years. This paper aims to show an approach that serve as a decision support whereby expert’s knowledge can directly be integrated by using a delphiround. A proposed methodology is illustrated by application examples using level crossings commonly used in Austria by Wiener Lokalbahnen. Lifecycle based user – product performance – expectations and economic imperatives could be incorporated through the development of key performance metrics. Assessment criteria are set by allocation percentages for value criteria under these criteria are the sub value – contingencies where Monte Carlo simulation is used for probabilistic scenario analysis. The approach facilitates the first step for a detailed lifecycle cost analysis of infrastructures by supporting experts and non-expert decision makers to get a quicker overview on system benefits as well as serve as a bridge to the practical application of more robust datadriven lifecycle cost analysis. © 2017 2017The TheAuthors. Authors. Published by Elsevier Ltd. is an open access article under the CC BY-NC-ND license © Published by Elsevier Ltd. This (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the 16th International Conference on Reliability and Statistics in Peer-review underand responsibility of the scientific committee of the International Conference on Reliability and Statistics in Transportation Communication. Transportation and Communication Keywords: maintenance, Lifcycle cost, probabilistic analysis, integrated lifecycle assessment
* Corresponding author. E-mail address: [email protected]
1877-7058 © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the International Conference on Reliability and Statistics in Transportation and Communication
doi:10.1016/j.proeng.2017.01.079
410
Hirut Grossberger et al. / Procedia Engineering 178 (2017) 409 – 418
1. Introduction The big challenge in the railway sector today is that the increasing amount of transport of goods, wagons with larger axel loads and at the same time increasing speeds that demand the modernization of the system (Olofsson et al., 2005; SB – LRA, 2007). Therefore, railway companies continuously strive to modernize rail routes in order to guarantee improvements for the users. As an essential goal of modernization of rail road; increasing number of routs are being modernized for more number of trains, passengers, freight trains and more frequent trains. The possible increase of speed increases the availability of the infrastructure and enhance attractivity of the rail transport that in turn improve sustainability. The routes that are modernized for more number of trains, passengers and freight transport need optimum measures for rail-road crossings that are safe. The challenge for the infrastructure owner lies on selection of level crossings with longer service life at minimum lifecycle costs, at the same time ensuring the societal demand for safe infrastructural system network authors. Railway tracks and level crossings are long-lived assets where their service life stretch 30 to 100 years. Hence efforts are being done by various researchers and practitioners in the sector to fulfil the Reliability, Availability, Maintainability and Safety (RAMS) demands during the whole lifecycle. Given that level crossings have long service life, they will be exposed to increasing axel loads, speeds and traffic volumes for longer times. The new modernized routes demand new plan, design and dimensioning with corresponding level of EU guidelines (EN 2004/50 EC) and according to the technical specifications for interoperability (TSI). For rail operators, these components with their different demands and lifespans are important framework for the construction and maintenance and can massively influence the performance and the lifecycle costs of the whole system. Rail operators need therefore, decision processes with which the performance and lifecycle cost analysis (LCCA)can be compared. So far, there exist barely studies that assess the whole lifecycle cost of level crossing systems. The performance of a railway infrastructures depend on, (i) a reliable design; (ii) optimal maintenance strategies supported by inspection monitoring methods (iii) reliable performance assessment approaches, (iv) suitable prediction techniques (Lichtberger, 2007; Quiroga, 2012). Hence, defining and planning the nature and frequency of maintenance play major role to sustain the quality of existing tracks at the most possible minimum lifecycle costs. In this regard, modelling of track deterioration is the basis for prediction and maintenance optimization processes (Yousefikia et al., 2014). The type of deterioration models, currently available and being used, are either deterministic or probabilistic models. Deterministic models describe the condition by a functional correlation between structural condition attributes. These deterministic models are either polynomial (Jovanovic, 2004) or exponential (Veit, 2007). The practical implementation of such models requires detailed information about their variables and do not express uncertainties. Railway operators continuously endeavour to apply artificial intelligent based maintenance planning methods. These maintenance planning methods are dependent on numerous factors, track degradation model is among them (Quiroga, 2011; Quiroga and Schneider, 2012). Maintenance planning algorithms (Koza, 1992) based on; degradation models and stochastic variables were performed by (Michalewicz and Fogel, 2002; Lake and Ferreira, 2002) among others. Monte Carlo simulation is implemented in random sampling from probabilistic distributions of each function parameter with long simulation runs. Monte Carlo approach is proven to be useful in simulation modeling many realizations. The typical uses of Monte Carlo modelling are (i) sampling; where information are gathered about a random object by observing many realizations; (ii) estimation, in which certain numerical quantities related to simulation are estimated and (iii) optimization, where randomness is introduced artificially to search the domain of the objective function more efficiently (Kroese et al., 2014). Monte Carlo simulations have proven to be useful in design optimization, reliability analysis and optimization of multiple processes. Furthermore, because of its effectiveness in the field of lifecycle costing by solving problems that acquire different sources of uncertainty, Monte Carlo method plays a critical role in risk analysis (Wang et al., 2012). In the Lifecycle assessment Monte Carlo method appears to be most popular method incorporating uncertainties in lifecycle assessment components (McCleese and LaPuma, 2002; Baker and Michael, 2009; Hung and Ma, 2009) among others. Lifecycle cost (LCC), which is generally modelled in the design phase changes when the system enters into the operation and maintenance phase due to changes in stakeholder requirement that make the costs incurred during the operation and maintenance phase predominant. For complex assets such as track infrastructure, the cost of maintenance plays an important role in the LCC analysis, this is because the operation and maintenance phase
Hirut Grossberger et al. / Procedia Engineering 178 (2017) 409 – 418
comprises a major share of the system’s lifecycle (Patra et al., 2008). Hence, for these measures optimum lifecycle activity profiles are crucial. (Adey and Mirzaei, 2014). Lifecycle assessment of these infrastructures is important for decision support. To improve the quality of decision making, lifecycle assessment incorporates; (i) the lifecycle performance assessment, (ii) the lifecycle cost by considering the direct and indirect consequences. The direct costs are based on the total cost associated with the lifetime of infrastructure starting with its construction to its replacement or final demolition. Numerous sources indicate a progress in the lifecycle cost analysis, in particular the importance of incorporating indirect costs such as user cost, societal and environmental costs (Sheils et al., 2006; Thoft Christenson, 2006; Noponen and Jutila, 2008; Frangopol, 2011; Frangopol et al., 2015) among others. However, companies face several challenges and barriers in implementation of a genuine data driven lifecycle cost. There are still many challenges to creating and expanding the use of LCCA in transportation. Beyond its applications in the pavement design process, broader use of LCCA on infrastructure projects has been limited (Eno and ASCE report, 2014). In case of maintenance and replacement costs, infrastructure owner staffs have years of experience amount of knowledge about the costs, frequency of maintenance required during the service life, system performance related to sustainability issues for example the effect of maintenance duration on the user, limitation on operation services and environment related issues. Since these experience and knowledge are not formalized and not necessarily datadriven, the decision makers are challenged (i) in the implementation and direct flow of such knowledge in the decision process from the experienced staff members, (ii) a holistic LCCA approach seem complicated and difficult to become a routine approach in practice. The aim of this paper is to contribute to decision support systems whereby expert’s knowledge can directly be integrated by using a delphiround. The approach shown in this paper facilitates the first step for the detailed LCCA of infrastructures and helps experts and non-expert decision makers to get a quicker overview on system benefits. The paper furthermore indicates the practical application of Monte Carlo simulation for scenario analysis and serve as a decision support for practitioners. 1.1. Level crossings Track bed support structures of railway level crossings are characterized by their design and construction types as well as materials used. As a result, every system has advantages and disadvantages related to construction and maintenance. Direct decision-parameters for system choice like average daily traffic volume and the rank of the railway line are further enhanced at: (i) construction costs and time, (ii) corrective maintenance effort, time and rate, (iii) feasibility of superstructure maintenance, (iv) drainability as well as (v) restrictions to road traffic and rail traffic during construction and maintenance times. The interaction between road and railways on the level crossings represent a critical point. The main functions of the level crossings is to guarantee a smooth and safe crossing of motorized transport over the railway tracks. In the area of railway crossings, settlements because of loads from rail and road transport are much more than that of the subsequent road itself. The reason here are the inadequate stiffness of the ballasted track, which are on one hand advantageous for rail transport and disadvantageous for motorized road transport (Rose and Anderson, 2006). For instance decreasing the maximum axel load of freight trains decreases the deterioration rate whereas increasing the allowed speed and maximum allowable axel loads favor fatigue damages (Caglayan et al., 2009). Rail- road crossings interlink the demands of the road and rail transport. The subsystems “road” and “rail” interact each other. It is essential, both subsystems and their components are kept in good and safe conditions corresponding to the demand of safety of the whole system. This is extended by the objective of attaining maximum service life with minimum maintenance direct and indirect costs. The service life of the level crossings depends on the technical and economic factors that are directly or indirectly affect the whole system. The selection of the level crossing systems are recommended according to Austrian federal railways, ÖBB B50 (2009) based on the average daily traffic volume individual and the route rank of the rail traffic.
411
412
Hirut Grossberger et al. / Procedia Engineering 178 (2017) 409 – 418
Table 1. An overview of different level crossing types and their corresponding places applications according to ÖBB B50-1 S.51 (The Austrian federal railway corporation guideline). Type
Route class
Average daily traffic
Wooden
3G
ADT < 500
Asphalt
2, 3 and 3G
500 < ADT < 2000
Concretesmallslabs
S, 1
ADT > 2000
Concreteslabtracks
S, 1
ADT > 4000
*because of their minor scale of application, wooden level crossings are not further considered in this paper
a
b
c
Fig. 1. Different types of level crossings commonly used in Austria (a) Asphalt pavement with protective rails / middle plate to keep wheel ruts free; (b) STRAIL- (left) und Bodan-pavemnt (right); (c) Concrete slabs.
2. Methods 2.1. Lifecycle user value analysis and probabilistic approach User value analysis based on long years of experience can support decision-making. This can be achieved through the development of key performance metrics to compare different scenarios. The key performance indicators should incorporate both the planned and expected values of actions for evaluated scenarios. The range of values across scenarios based on experts’ practical knowledge is the most useful information in this approach. The engineer is familiar with the coefficient of variation of each variable. In addition, scenario analysis serves in determining the inputs that have the most effect on value. The purpose of such strategic analysis is to provide decision makers with an improved overview to the system performance, expected cost, and value implication of their decisions. Strategic analysis that allows probabilistic modeling provides a better understanding of the system’s range of behavior due to various modeled uncertainties (Merrill et al, 2008). The probabilistic analysis incorporates uncertainty in a given scenario. Results from probabilistic analysis provide decision makers with additional data regarding the range of the parameters in a given scenario and the robustness of the scenario. In case of deterministic approach, decision makers use only nominal performance metrics without considering uncertainties. Probabilistic analysis allows illustrating lifecycle management actions to be optimized and can demonstrate the ultimate values of these actions to decision makers. This provides added value in investigation and comparison of different scenarios.
Hirut Grossberger et al. / Procedia Engineering 178 (2017) 409 – 418
The user value analysis consists of modelling uncertainty as contingencies with specific probabilities of occurrence. The reason for this is that the times and conditions for the evaluation parameters are complex that they cannot be predicted with fair degree of accuracy. Therefore, it was decided to use Monte Carlo simulation to estimate uncertainty. This, in contrast to sensitivity analysis, supported the identification of parameters that are influential on the value estimation and its variability by considering uncertainties in all parameters simultaneously. Exhaustive and mutually exclusive contingencies were specified based on expert’s knowledge. These contingencies capture the full range of likely variation in user values and represent the range of possible outcomes and extremes. This is performed by assigning probabilities to each of them. The probabilities are non-negative and sum to one. Table 2 illustrates the classification of the different level crossing systems according to their lifecycle expenses from the practitioner’s point of view. Table 2. Summary of system lifecycle performance. Evaluation parameters
System characteristics
Construction
Construction cost (per m)
Asphalt pavement _protectiverails = € 466 Asphalt pavement _middle plate = € 526 Large paving slabs_concrete = € 695 System Bodan/STRAIL = € 3006 Concrete slabs = € 4273
Maintenance
Construction time
System Bodan/STRAIL more time demanding than the asphalt and large paving slabs; concrete slabs demand considerably longer time of construction than the other
Extent of maintenance works
Maintenance works on concrete slabs means complete replacement
Maintenance time
Asphalt curing time is considered, slab systems are accessible immediately after replacement; renovation of concrete slabs are equated to construction duration
Frequency of maintenance
Operational restrictions∗
Large paving slabs because of the demand of slabs regulation during their service life exhibit the most maintenance frequency than the rest of the systems
Maintenance of rail track/superstructure
Asphalt and large paving slabs should be constructed completely, the reinstallation is done with new construction. In case of Bodan/STRAIL, the plates can be constructed in easier way
Drainage
Asphalt pavements lead to drainage in the periphery-impurities and vegetation Large paving plates in relation to grit lead to increased bedding resistance under moisture conditions/ salt (stay current)
Service restriction on railway
Construction/renovation of concrete slabs demand lock-up, because the superstructure should be removed as a whole
Service restriction on road
Asphalt pavements cannot be used during their curing time; Bodan/STRAIL demand lock-up during the installation of support stones and concrete plates
2.1 Application examples Scenario definition The lifecycle user value analysis is computed under a number of different scenarios. The definition of the scenarios is performed by (i) determination of the factors the scenarios to be built around, (ii) determining the
∗
service limitation for users during maintenance and/or renovation actions
413
414
Hirut Grossberger et al. / Procedia Engineering 178 (2017) 409 – 418
number of scenarios to analyze for each factor, (iii) estimation of the weighting factors under each scenario. This was performed by giving focuses on critical parameters important for the decision body, (IV) assignment of probabilities to each scenario as well as the weighting factors. The scenarios are defined as strategies depending on priorities of the decision makers, this paper illustrates three approaches that can be varied depending on the objective function of the decision makers. The assignment of the weighting factors can be varied depending on the local and regional priorities. Assessment criteria are set by allocation percentages for value criteria under these criteria are the sub value – contingencies. These value criteria are defined by allocating weighting factors for construction, maintenance and sustainability (considering maintenance related operation limitations) respectively. Calculating expected value of benefits was performed by considering different weighting parameters in probabilistic manner and then multiply by that contingency's probability of occurrence. Then the sum of all points for the given assessment criteria.
,
(1)
where Pi = value, Ni = value assigned for the contingencies, Gi = weighting of each parameter. Tables 3, 4 and 5 illustrate the weighting factors assigned to each user value parameters in case of each analysis scenario. Table 3. Balanced weighting factors in reference to the whole lifecycle. Construction
Maintenance
Operational restriction
Parameter/weighting
Cost
0.20
Duration
0.05 Extent of maintenance works
0.15
Maintenance duration
0.05
Frequency of maintenance
0.25
Maintenance of rail track
0.15
Drainage
0.05 Railway
0.25
0.65
0.05
Road
0.05
0.10
1.00
As it can be seen from the summary of the different systems in table 2 above, each system has its own advantages and disadvantages. It is illustrated that for instance asphalt and large paving slabs have disadvantages in relation to maintenance relative to the other systems. These decision parameters are absolutely based on loads per time which the track and / or the level crossing should accommodate. By the selection of the level crossings, if all the boundary conditions are not considered the maintenance expenses will be very high. Besides the technical performance and maintenance demand during the whole service life, the challenges such as inaccessibility of level crossed railways for maintenance action lead to declining quality of the whole system. Further challenges such as missing maintenance possibilities of covered rail roads and settlements as well as insufficient drainage and unpleasant interruptions of the road and rail transport are also important factors for sustainability. Hence road and rail service expenses that are important during the renovation and maintenance of various level crossing systems are considered as well. Monte Carlo simulations are performed to generate inputs from random variables modeled by their corresponding probability distribution functions, which in this case are lognormal distributions. The initial estimation of the coefficients of variations in each weighting factors were done based on historical data on the cost, maintenance expenses and expert’s practical knowledge and judgment. In the Monte Carlo simulation Pseudo random numbers in
415
Hirut Grossberger et al. / Procedia Engineering 178 (2017) 409 – 418
a value between 0 and 1 are generated by pseudo random number functions. Then a vast amount of simulated the input values are generated from their corresponding cumulative probability distribution function by inverse transformation process. The generated inputs are used for computation in the models. This procedure is repeated for all simulations, where at the end the results of all computations are aggregated and described by statistical characteristics as a result. Table 4. Scenario 2: weighting factors with more focus on maintenance. Construction
Maintenance
Operational restriction
Cost
Parameter/weighting 0.05
Duration
0.10
0.05 Extent of maintenance works
0.05
Maintenance duration
0.05
Frequency of maintenance
0.50
Maintenance of rail track
0.10
Drainage
0.10
0.80
Railway
0.05
Road
0.05
0.10
1.00
Table 5. Scenario 3: weighting factors more on maintenance and sustainability related additional impact on the society – service for the users balanced weighting factors in reference to the whole lifecycle. Construction
Maintenance
Operational restriction
Parameter/weighting
Cost
0.05
Duration
0.05 Extent of maintenance works
0.05
Maintenance duration
0.05
Frequency of maintenance
0.50
Maintenance of rail track
0.10
Drainage
0.10 Railway
0.10
0.65 a
b
0.05
Road
0.05
0.10
1.00
416
Hirut Grossberger et al. / Procedia Engineering 178 (2017) 409 – 418 c
Fig. 2. Graphical representation of the considered scenarios after the Monte Carlo simulation.
The value assigned to the contingencies (N) is allocated as 5, 3 and 1 based on discussions with experts. From the experts point of view when the system showed a perfect target achievement for the allocated assessment parameter has 5 points, if it is moderate 3 and if the goal achievement is inadequate 1. Then each of these values was multiplied by the weighting factors (G) as shown in equation 1. Pi was calculated for construction, maintenance and operational service restriction. The sum of Pi is the total user value. Figure 3 illustrates the total user values of different systems after Monte Carlo simulation. a
b
Fig. 3. Illustration of the Lifecycle user value (total user value) of the different systems after the Monte Carlo simulation: (a) Scenario 1, (b) Scenario 2.
In case of scenario 1, where assessment parameters such as maintenance followed by construction expenses are given 25, 65 percent respectively and the sustainability criteria such as operational restriction are assigned by 10 percent importance: for example the system Bodan showed lower total user value than the Asphalt pavement, large paving slabs concrete slabs (Figure 3(a)). on the other hand, in the second scenario where maintenance expenses have got larger weighting factor 0.8 (80%); the system Bodan is found to possess larger user value as compared to
Hirut Grossberger et al. / Procedia Engineering 178 (2017) 409 – 418
for example to large paving slabs. In scenario, 3 (Figure 3(c)) concrete slabs show significant total user value than most of the systems. c
Fig. 4. Illustration of the Lifecycle user value (total user value) of the different systems after the Monte Carlo simulation: (c) Scenario 3.
3. Conclusion The probabilistic scenario analysis using Monte Carlo simulation allows decision-makers to optimize the scenario selection and develop contingency planning, ensuring the final implemented scenario will provide as much value to infrastructure management. The use of probabilistic approaches for infrastructural decision making is infant. A proposed methodology illustrated by application examples serves as a prior step to the practical application of a detailed data-driven LCCA. It also supports experts and non-expert decision makers to get a quicker overview on system benefits and comparison of system performance based on defined value criteria. The method can further be applied in the lifecycle management of other railway infrastructure components. Acknowledgements We gratefully acknowledge the financial support of the Austrian Research Funding Agency (FFG) through the Project ILCA-Sondierung. References Adey, B.T. and Mirzaei, Z. (2014) An investigation of two methodologies to determine optimal life cycle activity profiles for bridges, 4th international symposium on life-cycle engineering, Tokyo, Japan, November 16–19 (Keynote lecture). Baker, Jack W. and Michael D. Lepech (2009) Treatment of uncertainties in life cycle assessment. Proceedings of the ICOSSAR. Caglayan B.O., Ozakgul K. and Tezer O. (2009) Fatigue life evaluation of a through-girder steel railway bridge. Engineering Failure Analysis. 01/2009; 16, 765–774. DOI:10.1016-/j.engfailanal.2008.06.018. Eno and ASCE report. (2014) Maximizing the value of investment using lifecycle cost analysis. American Society of Civil Engineers, Eno Center for Transportation. http://www.asce.org/-uploadedFiles/Issues_and_AdvocacyOur_Initiatives/Infrastructure/Content_Pieces/asce-enolifecycle-report.pdf Frangopol D.M (2011) Life-cycle performance, management, and optimisation of structural systems under uncertainty: accomplishments and challenges. Structure and Infrastructure Engineering, 7(6): 389–413.
417
418
Hirut Grossberger et al. / Procedia Engineering 178 (2017) 409 – 418 Frangopol D.M, Sabatino, S. and Soliman M. (2015) Maintenance and safety of deteriorating system: a lifecycle perspective. http://plse2015.org/cms/USB/pdf/full-paper_4180.pdf. Jovanovic, (2004) Railway track quality assessment and related decision-making. In: Proceedings IEEE systems. Man and cybernetics conference, pp 5038–5043. Hung, M. and Ma, H. (2009) Quantifying system uncertainty of life cycle assessment based on Monte Carlo simulation. Int. J. Life Cycle Assess, 14: 19. DOI:10.1007/s11367-008-0034-8. Kroese, D.P., Brereton, T., Taimre, T. and Botev, Z.I. Why the Monte Carlo Method is so Important Today. Comput. Stat. 2014, 6, 386−392 Lake, M. and Ferreira, L. (2002) Towards A Methodology To Evaluate Public Transport Projects. Physical Infrastructure Centre Research Report 02-03, School of Civil Engineering, Queensland University of Technology, Brisbane. Lichtberger B. (2007) Das System Gleis und seine Instandhaltung. EI Der Eisenbahn-ingenieur. ISSN: 0013-2810 Jg.58, Nr.1, 2007, S.10-19. Merrill R. G, Andraschko M., Stromgren C. Cirillo B. Earle K. and Goodlift K. (2008) A comparison of probabilistic and deterministic analysis for human space exploration. American Institute of Aerodynamics and Astronautics. Ntrs.nasa,gov.pdf accessed 05.03.2016. Michalewicz, Z. and Fogel, D. (2002) How to solve it: Modern heuristics. New York: Sp. Noponen S. and Jutila A. (2008) LCC case studies for bridges in different design phases. In: Proceedings of the international Symposium on Lifecycle Civil Engineering. June 11–14, 2008. IALCCE’08, Vrenna, lake Como Italy. Olofsson I., L. Elfgren, B. Bells, B. Paulsson, E. Niederleithinger, J. S. Jensen, G. Feltrin, B. Taljsten, C. Cremona, R. Kiviluoma and J. Bien. (2005) Assessment of European railway bridges for future traffic demands and longer lives – EC project 239, ‘’Sustainable Bridges’’. Structure & Infrastructure Engineering: Maintenance, Management, Life-Cycle Design & Performance, 1(2), 93–100. Patra A. P, Söderholm P. and Kumar U. (2008) Uncertainty estimation in railway track lifecycle cost: a case study from Swedish national Rail Administration. In: Proceedings of IMechE Vol. 222 Part F:J. Rail and Rapid Transit. Quiroga (2011) Ganzheitliche Optimierung des Instandhaltungsprozesses der Gleisgeometrie. Diss. Fakltät für Maschinenbau der technischen Universität Carolo-Wilhelmina zu Brauenschweig. Quiroga L. M. and Schneider E. (2012) Monte Carlo simulation of railway track geometry deterioration and restoration. In: Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, June 2012 226(3), 274–282. Rose J.G and Anderson J. S. (2006) Long-term performance of asphalt underlayment track beds for special track bed applications. The American Railway Engineering and Maintenance-of-Way Association, 2006 Annual Conference and Exposition, September 17–20, 2006, Louisville, Kentucky. ÖBB: B50-1 Oberbauformen, 2009. SB – LRA (2007) Guidelines for Load and Resistance Assessment of Existing European railway bridges. Advices on the use of advanced methods. COWI A/S 2007. Sheils E., O’Connor A., Breysse D. (2006) Reliability based maintenance management of structures. Report no. 9.2, Maintenance; MEDACHS _interreg IIB Atlantic Space- project no. 197. Thoft-Christensen P. (1998) Assessment of reliability profiles for concrete bridges. J. Engineering structures, 20(11), 1004–1009. Veit P. (2007) Track quality-Luxury or necessity? RTR special: maintenance & renewal, Railway technical review, pp. 8–12. Springer-Verlag. Wang N., Chang Y-C. andEl-Sheikh A. A (2012). Monte Carlo simulation approach to life cycle cost management. Structure and Infrastructure Engineering: Maintenance, Management, Life-Cycle Design and Performance. Pages 739–746. DOI:10.1080/15732479.2010.481304 Yousefikia M., Moridpour S. Setunge S. and Mazloumi. E. (2014) Modeling Degradation of Tracks for Maintenance Planning on a Tram Line. Journal of Traffic and Logistics Engineering Vol. 2.
ScienceDirect Procedia Engineering 178 (2017) 409 – 418
16th Conference on Reliability and Statistics in Transportation and Communication, RelStat’2016, 19-22 October 2016, Riga, Latvia
Lifecycle Based User Value Analysis of Rail - Road Level Crossings: Probabilistic Approach Using Monte Carlo Simulation Hirut Grossbergera*, Christoph Maulerb, Frank Michelbergera a
Carl Ritter von Ghega Institute for Integrated Mobility Research, St. Poelten University of Applied Sciences Matthias Corvinus-Straße 1, St. Poelten, Austria b Wiener Lokalbahnen AG, Eichenstraße 1, 1120, Vienna, Austria
Abstract Railway operators are in continuous pressure to minimize maintenance and rehabilitation costs of infrastructures; at the same time they are expected to provide a reliable service by optimum allocation of natural and economical resources. Railway tracks and level crossings are long-lived assets where their service life stretch 30 to 100 years. This paper aims to show an approach that serve as a decision support whereby expert’s knowledge can directly be integrated by using a delphiround. A proposed methodology is illustrated by application examples using level crossings commonly used in Austria by Wiener Lokalbahnen. Lifecycle based user – product performance – expectations and economic imperatives could be incorporated through the development of key performance metrics. Assessment criteria are set by allocation percentages for value criteria under these criteria are the sub value – contingencies where Monte Carlo simulation is used for probabilistic scenario analysis. The approach facilitates the first step for a detailed lifecycle cost analysis of infrastructures by supporting experts and non-expert decision makers to get a quicker overview on system benefits as well as serve as a bridge to the practical application of more robust datadriven lifecycle cost analysis. © 2017 2017The TheAuthors. Authors. Published by Elsevier Ltd. is an open access article under the CC BY-NC-ND license © Published by Elsevier Ltd. This (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the 16th International Conference on Reliability and Statistics in Peer-review underand responsibility of the scientific committee of the International Conference on Reliability and Statistics in Transportation Communication. Transportation and Communication Keywords: maintenance, Lifcycle cost, probabilistic analysis, integrated lifecycle assessment
* Corresponding author. E-mail address: [email protected]
1877-7058 © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the International Conference on Reliability and Statistics in Transportation and Communication
doi:10.1016/j.proeng.2017.01.079
410
Hirut Grossberger et al. / Procedia Engineering 178 (2017) 409 – 418
1. Introduction The big challenge in the railway sector today is that the increasing amount of transport of goods, wagons with larger axel loads and at the same time increasing speeds that demand the modernization of the system (Olofsson et al., 2005; SB – LRA, 2007). Therefore, railway companies continuously strive to modernize rail routes in order to guarantee improvements for the users. As an essential goal of modernization of rail road; increasing number of routs are being modernized for more number of trains, passengers, freight trains and more frequent trains. The possible increase of speed increases the availability of the infrastructure and enhance attractivity of the rail transport that in turn improve sustainability. The routes that are modernized for more number of trains, passengers and freight transport need optimum measures for rail-road crossings that are safe. The challenge for the infrastructure owner lies on selection of level crossings with longer service life at minimum lifecycle costs, at the same time ensuring the societal demand for safe infrastructural system network authors. Railway tracks and level crossings are long-lived assets where their service life stretch 30 to 100 years. Hence efforts are being done by various researchers and practitioners in the sector to fulfil the Reliability, Availability, Maintainability and Safety (RAMS) demands during the whole lifecycle. Given that level crossings have long service life, they will be exposed to increasing axel loads, speeds and traffic volumes for longer times. The new modernized routes demand new plan, design and dimensioning with corresponding level of EU guidelines (EN 2004/50 EC) and according to the technical specifications for interoperability (TSI). For rail operators, these components with their different demands and lifespans are important framework for the construction and maintenance and can massively influence the performance and the lifecycle costs of the whole system. Rail operators need therefore, decision processes with which the performance and lifecycle cost analysis (LCCA)can be compared. So far, there exist barely studies that assess the whole lifecycle cost of level crossing systems. The performance of a railway infrastructures depend on, (i) a reliable design; (ii) optimal maintenance strategies supported by inspection monitoring methods (iii) reliable performance assessment approaches, (iv) suitable prediction techniques (Lichtberger, 2007; Quiroga, 2012). Hence, defining and planning the nature and frequency of maintenance play major role to sustain the quality of existing tracks at the most possible minimum lifecycle costs. In this regard, modelling of track deterioration is the basis for prediction and maintenance optimization processes (Yousefikia et al., 2014). The type of deterioration models, currently available and being used, are either deterministic or probabilistic models. Deterministic models describe the condition by a functional correlation between structural condition attributes. These deterministic models are either polynomial (Jovanovic, 2004) or exponential (Veit, 2007). The practical implementation of such models requires detailed information about their variables and do not express uncertainties. Railway operators continuously endeavour to apply artificial intelligent based maintenance planning methods. These maintenance planning methods are dependent on numerous factors, track degradation model is among them (Quiroga, 2011; Quiroga and Schneider, 2012). Maintenance planning algorithms (Koza, 1992) based on; degradation models and stochastic variables were performed by (Michalewicz and Fogel, 2002; Lake and Ferreira, 2002) among others. Monte Carlo simulation is implemented in random sampling from probabilistic distributions of each function parameter with long simulation runs. Monte Carlo approach is proven to be useful in simulation modeling many realizations. The typical uses of Monte Carlo modelling are (i) sampling; where information are gathered about a random object by observing many realizations; (ii) estimation, in which certain numerical quantities related to simulation are estimated and (iii) optimization, where randomness is introduced artificially to search the domain of the objective function more efficiently (Kroese et al., 2014). Monte Carlo simulations have proven to be useful in design optimization, reliability analysis and optimization of multiple processes. Furthermore, because of its effectiveness in the field of lifecycle costing by solving problems that acquire different sources of uncertainty, Monte Carlo method plays a critical role in risk analysis (Wang et al., 2012). In the Lifecycle assessment Monte Carlo method appears to be most popular method incorporating uncertainties in lifecycle assessment components (McCleese and LaPuma, 2002; Baker and Michael, 2009; Hung and Ma, 2009) among others. Lifecycle cost (LCC), which is generally modelled in the design phase changes when the system enters into the operation and maintenance phase due to changes in stakeholder requirement that make the costs incurred during the operation and maintenance phase predominant. For complex assets such as track infrastructure, the cost of maintenance plays an important role in the LCC analysis, this is because the operation and maintenance phase
Hirut Grossberger et al. / Procedia Engineering 178 (2017) 409 – 418
comprises a major share of the system’s lifecycle (Patra et al., 2008). Hence, for these measures optimum lifecycle activity profiles are crucial. (Adey and Mirzaei, 2014). Lifecycle assessment of these infrastructures is important for decision support. To improve the quality of decision making, lifecycle assessment incorporates; (i) the lifecycle performance assessment, (ii) the lifecycle cost by considering the direct and indirect consequences. The direct costs are based on the total cost associated with the lifetime of infrastructure starting with its construction to its replacement or final demolition. Numerous sources indicate a progress in the lifecycle cost analysis, in particular the importance of incorporating indirect costs such as user cost, societal and environmental costs (Sheils et al., 2006; Thoft Christenson, 2006; Noponen and Jutila, 2008; Frangopol, 2011; Frangopol et al., 2015) among others. However, companies face several challenges and barriers in implementation of a genuine data driven lifecycle cost. There are still many challenges to creating and expanding the use of LCCA in transportation. Beyond its applications in the pavement design process, broader use of LCCA on infrastructure projects has been limited (Eno and ASCE report, 2014). In case of maintenance and replacement costs, infrastructure owner staffs have years of experience amount of knowledge about the costs, frequency of maintenance required during the service life, system performance related to sustainability issues for example the effect of maintenance duration on the user, limitation on operation services and environment related issues. Since these experience and knowledge are not formalized and not necessarily datadriven, the decision makers are challenged (i) in the implementation and direct flow of such knowledge in the decision process from the experienced staff members, (ii) a holistic LCCA approach seem complicated and difficult to become a routine approach in practice. The aim of this paper is to contribute to decision support systems whereby expert’s knowledge can directly be integrated by using a delphiround. The approach shown in this paper facilitates the first step for the detailed LCCA of infrastructures and helps experts and non-expert decision makers to get a quicker overview on system benefits. The paper furthermore indicates the practical application of Monte Carlo simulation for scenario analysis and serve as a decision support for practitioners. 1.1. Level crossings Track bed support structures of railway level crossings are characterized by their design and construction types as well as materials used. As a result, every system has advantages and disadvantages related to construction and maintenance. Direct decision-parameters for system choice like average daily traffic volume and the rank of the railway line are further enhanced at: (i) construction costs and time, (ii) corrective maintenance effort, time and rate, (iii) feasibility of superstructure maintenance, (iv) drainability as well as (v) restrictions to road traffic and rail traffic during construction and maintenance times. The interaction between road and railways on the level crossings represent a critical point. The main functions of the level crossings is to guarantee a smooth and safe crossing of motorized transport over the railway tracks. In the area of railway crossings, settlements because of loads from rail and road transport are much more than that of the subsequent road itself. The reason here are the inadequate stiffness of the ballasted track, which are on one hand advantageous for rail transport and disadvantageous for motorized road transport (Rose and Anderson, 2006). For instance decreasing the maximum axel load of freight trains decreases the deterioration rate whereas increasing the allowed speed and maximum allowable axel loads favor fatigue damages (Caglayan et al., 2009). Rail- road crossings interlink the demands of the road and rail transport. The subsystems “road” and “rail” interact each other. It is essential, both subsystems and their components are kept in good and safe conditions corresponding to the demand of safety of the whole system. This is extended by the objective of attaining maximum service life with minimum maintenance direct and indirect costs. The service life of the level crossings depends on the technical and economic factors that are directly or indirectly affect the whole system. The selection of the level crossing systems are recommended according to Austrian federal railways, ÖBB B50 (2009) based on the average daily traffic volume individual and the route rank of the rail traffic.
411
412
Hirut Grossberger et al. / Procedia Engineering 178 (2017) 409 – 418
Table 1. An overview of different level crossing types and their corresponding places applications according to ÖBB B50-1 S.51 (The Austrian federal railway corporation guideline). Type
Route class
Average daily traffic
Wooden
3G
ADT < 500
Asphalt
2, 3 and 3G
500 < ADT < 2000
Concretesmallslabs
S, 1
ADT > 2000
Concreteslabtracks
S, 1
ADT > 4000
*because of their minor scale of application, wooden level crossings are not further considered in this paper
a
b
c
Fig. 1. Different types of level crossings commonly used in Austria (a) Asphalt pavement with protective rails / middle plate to keep wheel ruts free; (b) STRAIL- (left) und Bodan-pavemnt (right); (c) Concrete slabs.
2. Methods 2.1. Lifecycle user value analysis and probabilistic approach User value analysis based on long years of experience can support decision-making. This can be achieved through the development of key performance metrics to compare different scenarios. The key performance indicators should incorporate both the planned and expected values of actions for evaluated scenarios. The range of values across scenarios based on experts’ practical knowledge is the most useful information in this approach. The engineer is familiar with the coefficient of variation of each variable. In addition, scenario analysis serves in determining the inputs that have the most effect on value. The purpose of such strategic analysis is to provide decision makers with an improved overview to the system performance, expected cost, and value implication of their decisions. Strategic analysis that allows probabilistic modeling provides a better understanding of the system’s range of behavior due to various modeled uncertainties (Merrill et al, 2008). The probabilistic analysis incorporates uncertainty in a given scenario. Results from probabilistic analysis provide decision makers with additional data regarding the range of the parameters in a given scenario and the robustness of the scenario. In case of deterministic approach, decision makers use only nominal performance metrics without considering uncertainties. Probabilistic analysis allows illustrating lifecycle management actions to be optimized and can demonstrate the ultimate values of these actions to decision makers. This provides added value in investigation and comparison of different scenarios.
Hirut Grossberger et al. / Procedia Engineering 178 (2017) 409 – 418
The user value analysis consists of modelling uncertainty as contingencies with specific probabilities of occurrence. The reason for this is that the times and conditions for the evaluation parameters are complex that they cannot be predicted with fair degree of accuracy. Therefore, it was decided to use Monte Carlo simulation to estimate uncertainty. This, in contrast to sensitivity analysis, supported the identification of parameters that are influential on the value estimation and its variability by considering uncertainties in all parameters simultaneously. Exhaustive and mutually exclusive contingencies were specified based on expert’s knowledge. These contingencies capture the full range of likely variation in user values and represent the range of possible outcomes and extremes. This is performed by assigning probabilities to each of them. The probabilities are non-negative and sum to one. Table 2 illustrates the classification of the different level crossing systems according to their lifecycle expenses from the practitioner’s point of view. Table 2. Summary of system lifecycle performance. Evaluation parameters
System characteristics
Construction
Construction cost (per m)
Asphalt pavement _protectiverails = € 466 Asphalt pavement _middle plate = € 526 Large paving slabs_concrete = € 695 System Bodan/STRAIL = € 3006 Concrete slabs = € 4273
Maintenance
Construction time
System Bodan/STRAIL more time demanding than the asphalt and large paving slabs; concrete slabs demand considerably longer time of construction than the other
Extent of maintenance works
Maintenance works on concrete slabs means complete replacement
Maintenance time
Asphalt curing time is considered, slab systems are accessible immediately after replacement; renovation of concrete slabs are equated to construction duration
Frequency of maintenance
Operational restrictions∗
Large paving slabs because of the demand of slabs regulation during their service life exhibit the most maintenance frequency than the rest of the systems
Maintenance of rail track/superstructure
Asphalt and large paving slabs should be constructed completely, the reinstallation is done with new construction. In case of Bodan/STRAIL, the plates can be constructed in easier way
Drainage
Asphalt pavements lead to drainage in the periphery-impurities and vegetation Large paving plates in relation to grit lead to increased bedding resistance under moisture conditions/ salt (stay current)
Service restriction on railway
Construction/renovation of concrete slabs demand lock-up, because the superstructure should be removed as a whole
Service restriction on road
Asphalt pavements cannot be used during their curing time; Bodan/STRAIL demand lock-up during the installation of support stones and concrete plates
2.1 Application examples Scenario definition The lifecycle user value analysis is computed under a number of different scenarios. The definition of the scenarios is performed by (i) determination of the factors the scenarios to be built around, (ii) determining the
∗
service limitation for users during maintenance and/or renovation actions
413
414
Hirut Grossberger et al. / Procedia Engineering 178 (2017) 409 – 418
number of scenarios to analyze for each factor, (iii) estimation of the weighting factors under each scenario. This was performed by giving focuses on critical parameters important for the decision body, (IV) assignment of probabilities to each scenario as well as the weighting factors. The scenarios are defined as strategies depending on priorities of the decision makers, this paper illustrates three approaches that can be varied depending on the objective function of the decision makers. The assignment of the weighting factors can be varied depending on the local and regional priorities. Assessment criteria are set by allocation percentages for value criteria under these criteria are the sub value – contingencies. These value criteria are defined by allocating weighting factors for construction, maintenance and sustainability (considering maintenance related operation limitations) respectively. Calculating expected value of benefits was performed by considering different weighting parameters in probabilistic manner and then multiply by that contingency's probability of occurrence. Then the sum of all points for the given assessment criteria.
,
(1)
where Pi = value, Ni = value assigned for the contingencies, Gi = weighting of each parameter. Tables 3, 4 and 5 illustrate the weighting factors assigned to each user value parameters in case of each analysis scenario. Table 3. Balanced weighting factors in reference to the whole lifecycle. Construction
Maintenance
Operational restriction
Parameter/weighting
Cost
0.20
Duration
0.05 Extent of maintenance works
0.15
Maintenance duration
0.05
Frequency of maintenance
0.25
Maintenance of rail track
0.15
Drainage
0.05 Railway
0.25
0.65
0.05
Road
0.05
0.10
1.00
As it can be seen from the summary of the different systems in table 2 above, each system has its own advantages and disadvantages. It is illustrated that for instance asphalt and large paving slabs have disadvantages in relation to maintenance relative to the other systems. These decision parameters are absolutely based on loads per time which the track and / or the level crossing should accommodate. By the selection of the level crossings, if all the boundary conditions are not considered the maintenance expenses will be very high. Besides the technical performance and maintenance demand during the whole service life, the challenges such as inaccessibility of level crossed railways for maintenance action lead to declining quality of the whole system. Further challenges such as missing maintenance possibilities of covered rail roads and settlements as well as insufficient drainage and unpleasant interruptions of the road and rail transport are also important factors for sustainability. Hence road and rail service expenses that are important during the renovation and maintenance of various level crossing systems are considered as well. Monte Carlo simulations are performed to generate inputs from random variables modeled by their corresponding probability distribution functions, which in this case are lognormal distributions. The initial estimation of the coefficients of variations in each weighting factors were done based on historical data on the cost, maintenance expenses and expert’s practical knowledge and judgment. In the Monte Carlo simulation Pseudo random numbers in
415
Hirut Grossberger et al. / Procedia Engineering 178 (2017) 409 – 418
a value between 0 and 1 are generated by pseudo random number functions. Then a vast amount of simulated the input values are generated from their corresponding cumulative probability distribution function by inverse transformation process. The generated inputs are used for computation in the models. This procedure is repeated for all simulations, where at the end the results of all computations are aggregated and described by statistical characteristics as a result. Table 4. Scenario 2: weighting factors with more focus on maintenance. Construction
Maintenance
Operational restriction
Cost
Parameter/weighting 0.05
Duration
0.10
0.05 Extent of maintenance works
0.05
Maintenance duration
0.05
Frequency of maintenance
0.50
Maintenance of rail track
0.10
Drainage
0.10
0.80
Railway
0.05
Road
0.05
0.10
1.00
Table 5. Scenario 3: weighting factors more on maintenance and sustainability related additional impact on the society – service for the users balanced weighting factors in reference to the whole lifecycle. Construction
Maintenance
Operational restriction
Parameter/weighting
Cost
0.05
Duration
0.05 Extent of maintenance works
0.05
Maintenance duration
0.05
Frequency of maintenance
0.50
Maintenance of rail track
0.10
Drainage
0.10 Railway
0.10
0.65 a
b
0.05
Road
0.05
0.10
1.00
416
Hirut Grossberger et al. / Procedia Engineering 178 (2017) 409 – 418 c
Fig. 2. Graphical representation of the considered scenarios after the Monte Carlo simulation.
The value assigned to the contingencies (N) is allocated as 5, 3 and 1 based on discussions with experts. From the experts point of view when the system showed a perfect target achievement for the allocated assessment parameter has 5 points, if it is moderate 3 and if the goal achievement is inadequate 1. Then each of these values was multiplied by the weighting factors (G) as shown in equation 1. Pi was calculated for construction, maintenance and operational service restriction. The sum of Pi is the total user value. Figure 3 illustrates the total user values of different systems after Monte Carlo simulation. a
b
Fig. 3. Illustration of the Lifecycle user value (total user value) of the different systems after the Monte Carlo simulation: (a) Scenario 1, (b) Scenario 2.
In case of scenario 1, where assessment parameters such as maintenance followed by construction expenses are given 25, 65 percent respectively and the sustainability criteria such as operational restriction are assigned by 10 percent importance: for example the system Bodan showed lower total user value than the Asphalt pavement, large paving slabs concrete slabs (Figure 3(a)). on the other hand, in the second scenario where maintenance expenses have got larger weighting factor 0.8 (80%); the system Bodan is found to possess larger user value as compared to
Hirut Grossberger et al. / Procedia Engineering 178 (2017) 409 – 418
for example to large paving slabs. In scenario, 3 (Figure 3(c)) concrete slabs show significant total user value than most of the systems. c
Fig. 4. Illustration of the Lifecycle user value (total user value) of the different systems after the Monte Carlo simulation: (c) Scenario 3.
3. Conclusion The probabilistic scenario analysis using Monte Carlo simulation allows decision-makers to optimize the scenario selection and develop contingency planning, ensuring the final implemented scenario will provide as much value to infrastructure management. The use of probabilistic approaches for infrastructural decision making is infant. A proposed methodology illustrated by application examples serves as a prior step to the practical application of a detailed data-driven LCCA. It also supports experts and non-expert decision makers to get a quicker overview on system benefits and comparison of system performance based on defined value criteria. The method can further be applied in the lifecycle management of other railway infrastructure components. Acknowledgements We gratefully acknowledge the financial support of the Austrian Research Funding Agency (FFG) through the Project ILCA-Sondierung. References Adey, B.T. and Mirzaei, Z. (2014) An investigation of two methodologies to determine optimal life cycle activity profiles for bridges, 4th international symposium on life-cycle engineering, Tokyo, Japan, November 16–19 (Keynote lecture). Baker, Jack W. and Michael D. Lepech (2009) Treatment of uncertainties in life cycle assessment. Proceedings of the ICOSSAR. Caglayan B.O., Ozakgul K. and Tezer O. (2009) Fatigue life evaluation of a through-girder steel railway bridge. Engineering Failure Analysis. 01/2009; 16, 765–774. DOI:10.1016-/j.engfailanal.2008.06.018. Eno and ASCE report. (2014) Maximizing the value of investment using lifecycle cost analysis. American Society of Civil Engineers, Eno Center for Transportation. http://www.asce.org/-uploadedFiles/Issues_and_AdvocacyOur_Initiatives/Infrastructure/Content_Pieces/asce-enolifecycle-report.pdf Frangopol D.M (2011) Life-cycle performance, management, and optimisation of structural systems under uncertainty: accomplishments and challenges. Structure and Infrastructure Engineering, 7(6): 389–413.
417
418
Hirut Grossberger et al. / Procedia Engineering 178 (2017) 409 – 418 Frangopol D.M, Sabatino, S. and Soliman M. (2015) Maintenance and safety of deteriorating system: a lifecycle perspective. http://plse2015.org/cms/USB/pdf/full-paper_4180.pdf. Jovanovic, (2004) Railway track quality assessment and related decision-making. In: Proceedings IEEE systems. Man and cybernetics conference, pp 5038–5043. Hung, M. and Ma, H. (2009) Quantifying system uncertainty of life cycle assessment based on Monte Carlo simulation. Int. J. Life Cycle Assess, 14: 19. DOI:10.1007/s11367-008-0034-8. Kroese, D.P., Brereton, T., Taimre, T. and Botev, Z.I. Why the Monte Carlo Method is so Important Today. Comput. Stat. 2014, 6, 386−392 Lake, M. and Ferreira, L. (2002) Towards A Methodology To Evaluate Public Transport Projects. Physical Infrastructure Centre Research Report 02-03, School of Civil Engineering, Queensland University of Technology, Brisbane. Lichtberger B. (2007) Das System Gleis und seine Instandhaltung. EI Der Eisenbahn-ingenieur. ISSN: 0013-2810 Jg.58, Nr.1, 2007, S.10-19. Merrill R. G, Andraschko M., Stromgren C. Cirillo B. Earle K. and Goodlift K. (2008) A comparison of probabilistic and deterministic analysis for human space exploration. American Institute of Aerodynamics and Astronautics. Ntrs.nasa,gov.pdf accessed 05.03.2016. Michalewicz, Z. and Fogel, D. (2002) How to solve it: Modern heuristics. New York: Sp. Noponen S. and Jutila A. (2008) LCC case studies for bridges in different design phases. In: Proceedings of the international Symposium on Lifecycle Civil Engineering. June 11–14, 2008. IALCCE’08, Vrenna, lake Como Italy. Olofsson I., L. Elfgren, B. Bells, B. Paulsson, E. Niederleithinger, J. S. Jensen, G. Feltrin, B. Taljsten, C. Cremona, R. Kiviluoma and J. Bien. (2005) Assessment of European railway bridges for future traffic demands and longer lives – EC project 239, ‘’Sustainable Bridges’’. Structure & Infrastructure Engineering: Maintenance, Management, Life-Cycle Design & Performance, 1(2), 93–100. Patra A. P, Söderholm P. and Kumar U. (2008) Uncertainty estimation in railway track lifecycle cost: a case study from Swedish national Rail Administration. In: Proceedings of IMechE Vol. 222 Part F:J. Rail and Rapid Transit. Quiroga (2011) Ganzheitliche Optimierung des Instandhaltungsprozesses der Gleisgeometrie. Diss. Fakltät für Maschinenbau der technischen Universität Carolo-Wilhelmina zu Brauenschweig. Quiroga L. M. and Schneider E. (2012) Monte Carlo simulation of railway track geometry deterioration and restoration. In: Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, June 2012 226(3), 274–282. Rose J.G and Anderson J. S. (2006) Long-term performance of asphalt underlayment track beds for special track bed applications. The American Railway Engineering and Maintenance-of-Way Association, 2006 Annual Conference and Exposition, September 17–20, 2006, Louisville, Kentucky. ÖBB: B50-1 Oberbauformen, 2009. SB – LRA (2007) Guidelines for Load and Resistance Assessment of Existing European railway bridges. Advices on the use of advanced methods. COWI A/S 2007. Sheils E., O’Connor A., Breysse D. (2006) Reliability based maintenance management of structures. Report no. 9.2, Maintenance; MEDACHS _interreg IIB Atlantic Space- project no. 197. Thoft-Christensen P. (1998) Assessment of reliability profiles for concrete bridges. J. Engineering structures, 20(11), 1004–1009. Veit P. (2007) Track quality-Luxury or necessity? RTR special: maintenance & renewal, Railway technical review, pp. 8–12. Springer-Verlag. Wang N., Chang Y-C. andEl-Sheikh A. A (2012). Monte Carlo simulation approach to life cycle cost management. Structure and Infrastructure Engineering: Maintenance, Management, Life-Cycle Design and Performance. Pages 739–746. DOI:10.1080/15732479.2010.481304 Yousefikia M., Moridpour S. Setunge S. and Mazloumi. E. (2014) Modeling Degradation of Tracks for Maintenance Planning on a Tram Line. Journal of Traffic and Logistics Engineering Vol. 2.