Decision making in rehabilitation strategy forecasts

Introduction

The first step is the utilization of an ageing model that represents the individual deterioration behaviour of the analyzed network. That way the upcoming changes due to the continuous wear of the network can be predicted with a model like the semi-Markovchains.

To turn the prediction of the ongoing deterioration from a pure forecasting tool into an instrument for strategic and sustainable planning, the different decisions and the linked rehabilitation actions need to be a part of the forecasting procedure. That way it is not only possible to forecast the future ageing of the network but also how the ageing behaviour would change if certain rehabilitation decisions were applied, modified, postponed or renounced. The forecast of multiple possible but different rehabilitation strategies offers the chance of virtually rehabilitating the network, monitoring the effects, analyzing the results and selecting the most appropriate rehabilitation strategy according to the network operator’s predefined demands or iteratively forming an optimized strategy. This ex-ante check of the future rehabilitation strategy could lead to more sustainable rehabilitation planning but it definitely gives long-ranging planning security.

The crucial point of the strategy forecasts is the transparent, comprehensive and correct inclusion of the individual decision criteria in the analytical model of the ageing forecast.

Modeling of the Decision Process

A strategy prognosis generally consists of two main parts: the ageing forecast itself and the processing of the rehabilitation decision criteria with the related virtual rehabilitation of the selected candidates. This two-step-cycle repeats for each year of the strategy forecast. That way the consequences of the rehabilitation decision influence the ageing forecast of the subsequent year of the strategy forecast. Within the STATUS solution presented here the processing of the rehabilitation decision criteria is subdivided into three sub-processes

• preliminary decision space
• priority ranking
• final rehabilitation decision

which are closely related to the engineering approaches in the daily rehabilitation planning routine.

Ageing

Figure 1: Visualization of the process of semi-Markovchains (Source: S & P Consult GmbH)

A suitable mathematical model for dividing the deterioration process of sewers into inferior condition grades is the semi-Markov process. Within this process different states or classes are distinguished which the pipes are assigned to. For each discrete point in time a pipe remains in exactly one of the defined classes. Between the classes transition probabilities are given. Within STATUS, a Weibull distribution is assumed for the transition functions. These are calibrated by applying the least square method to empirical inspection results of sewer pipes, considering their weighted length in a particular substance value or condition grade. The functions describe the probability of a pipe of a particular condition grade and construction year entering the next worse condition grade.

The forecast of the priority as well as the forecast of the wear reserve bases on the calibrated transition functions and time discrete Markovchains. Within the mathematical model of Markovchains, deterioration is modelled as a stochastic process in the long term by forecasting future developments. Transition, as well as residual, probabilities are assigned to each condition state. Thus, future development is a function of the present state only and not of the pipe’s history.

The deterioration process is considered to be unidirectional, i.e. the deterioration process is without intervention (renovation or replacement), which would indicate the end of the pipe’s service life or failure of the old pipe in the statistical sense. This means the forecasted values can only decrease (if no rehabilitation measure is applied), and the useful service life comes to its end when a pipe reaches the worst class in both priority and wear reserve. The figure above illustrates the semi-Markov-process. As not only the final state is forecasted but the individual values for priority and wear reserve are also determined by the process at each point in time (yearly intervals), it is possible to interact with the decision model at any point with individual rehabilitation measures. This gives the chance of beside replacement measures also having renovation and repair measures in the arsenal of possible interactions; each with its individual impact on the ageing behaviour of the particular object. This way, the analytical rehabilitation approach comes much closer to the daily rehabilitation procedure in the real world.

Preliminary decision space

The very first decision within daily rehabilitation planning is the alteration or calibration of the classification values coming from a formalized assessment system according to the individual viewpoint of the network operator. The formalized assessment systems like the one defined in DWA-guidelines and standards can not consider all possible ancillary conditions which may be important for the particular network operator. There is therefore a difference between the viewpoint of the standards and the viewpoint of the network operator which needs to be determined.

Within STATUS the task is settled by the use of decision cubes which form a general decision space for priority and wear reserve. Each axis of the cubes stands for one of the rehabilitation targets, stability, tightness and operation safety. The decision cubes are built according to several rehabilitation decisions of the network operator on potential rehab candidates from the particular network.

In this way the difference in the viewpoints of the particular network operators can be processed analytically – making STATUS decision making similar to that of the particular rehabilitation engineers.

Individual ranking

Having assigned individual values for priority and wear reserve, the rehabilitation candidates are ranked according to specifications of the network operator. This ranking can be as individual as the ranking is in the daily routine of the network operator. At this point additional parameters are added to the initial ranking parameters priority and wear reserve. Ancillary conditions like ground water level, population density, traffic load, functional or even political issues may be considered important by the network operator. The preference of large diameter sewers over smaller ones or postponement of younger sewers (standard in case of equal priority and wear reserve) are examples of such individual settings.

The different ranking criteria can be applied in parallel like in figure 3, adding a weighting component to the ranking, consecutively or as a mixture of both. In figure 3 the process is visualized for the three criteria priority, wear reserve and system relevance which are applied in parallel and change the ranking of the rehabilitation candidates. With this flexibility the ranking can be adjusted to any ranking approach by the network operators or enable them to extend their way of ranking.

Individual decision tree

The last step, before the next year in the forecast is carried out, is the processing of an extensive individual decision tree which considers all different ancillary conditions, restrictions and guidelines that are relevant from the viewpoint of the network operator. This decision tree reflects all questions, an engineer answers in order to justify or change a rehabilitation decision. Budget and amortization issues are most common, as well as special defect issues which may change the pre-selected rehabilitation method (no renovation if major deformation or displacement defects) or ancillary conditions like traffic loads above.

Decision trees are an appropriate method for analytically defining decision processes and decision rules within strategy forecasts as realistically as possible. They grant flexible and transparent definition and linking of hierarchic decision rules. Thus they suit the need for a tool that forms formal decision rules from empiric knowledge. Especially in the field of rehabilitation engineering in sewer networks, many of the rehabilitation decisions are based to a significant share on experience and specific, local knowledge that is of no use elsewhere. Standardized decision procedures often can not consider such individual knowledge and decision criteria.

With the use of decision trees for strategic forecasts all information which is linked to single network objects (e.g. DN for sewers) or network parts (e.g. flow for catchment areas) or object groups (e.g. corrosion protection for concrete manholes) or any way to the network itself (e.g. tariff constraints) can become decision criteria. Especially the possibility to include very individual information pieces coming from other information sources (e.g. flow-time from hydraulic analysis, condition and rehab probability for other infrastructures such as roads) into the decision tree is the primary strength of decision trees. This makes the strategy forecasts not only a tool to mirror and analyze the present rehabilitation preferences but also a tool to find an optimized rehabilitation path towards a sustainable network infrastructure. The decisions tree can not only fork on standard rehab decision criteria (e.g. defect types, defect severity, budget availability) but as well in time. This means that decision patterns can be designed as changing over time for example to reach a specific target in a certain predefined time.

The flexibility of such decision trees is at the same time their Achilles' heel as the complexity increases according to the number of decision rules represented by decision nodes in the tree. Thus the consistent definition becomes increasingly difficult and consumes a significant share of the total effort of strategy building. A single decision node in the wrong place may cause a domination of subordinated criteria over urgent ones and will corrupt the whole rehabilitation decision. An example would be the postponement of a rehabilitation measure due to depleted or spent budget although that rehabilitation measure would switch to another, non-depleted budget area due to a decision rule which is misleadingly placed after the budget decision rules. Yet, although the utilization of decision trees is complex and has an inherent risk of failure, the effort pays off additionally via a collateral gain. Once built, the decision tree represents decision structure, decision background and empirical decision knowledge of a network operator which has usually not been systematically determined and documented before.

After the finalization of all steps, the rehabilitation candidates selected within the particular year of the strategy are “virtually” rehabilitated and the forecast continues with the next year of the strategy. This way the development of various key figures such as asset net value, fees and tariffs and average rehabilitation priority show the sustainability of the strategies analyzed thus giving way to the selection of the most appropriate solution.

Practical Experiences

The approach has been used in numerous strategic rehabilitation planning projects. Due to the possibility of personalization of different strategies to the specific needs and requirements of the particular network operator, the strategy analysis delivered important additional information essential for the long-term strategic rehabilitation planning of the network operators and the various stakeholders.

With the information from comparative strategy analysis the pros and cons of the different rehabilitation approaches defined in the strategies have become clearly visible even though the real effect of a deficient strategy often only becomes apparent after decades.

The different parts of figure 5 and figure 6 show statements resulting from such strategic forecasts from recently carried out long-term rehabilitation planning projects, which would not have been possible – or far less precise – if the decision model could not have reflected the intentions of the network operator that closely.

The figures show some interesting aspects, as the maximum rehabilitation strategy (blue) has the same rehabilitation budget as the conventional rehabilitation strategy (yellow) only the applied rehab methods vary. The latter strategy focuses on replacement and rarely uses renovation. The sustainable strategy (green) although less well funded than the previous mentioned strategies can keep pace regarding the rehabilitation effects on the sewer network.

Conclusion

In this paper, an approach for rehabilitation strategy modelling is introduced. The combination of an ageing forecast for the deterioration of single sewers by using Markovchains completed with a three-step decision model significantly improves long-term rehabilitation planning by pre-emptive analysis of various rehabilitation strategies regarding their suitability for the utility. Network demands and network operator decisions can be modelled close to the real decision process of the utility, and thus the different rehabilitation paths into the future can be compared and validated leading towards an optimized rehabilitation strategy and giving long-term planning safety.

Authors

Dr.-Ing. Robert Stein
S & P Consult GmbH Bochum
Tel. +49 234 5167-110
robert.stein@stein.de

Dipl.-Ing. Adrian Uhlenbroch
S & P Consult GmbH Bochum
Tel. +49 234 5167-164
adrian.uhlenbroch@stein.de

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