Sewer Pipelines Inspection Scheduling Using Optimization

Statistical models can be used to establish an optimum cost-based inspection plan and monitoring (Kim et al. 2013). The optimum inspection and maintenance alternatives and periods are obtained through formulating an optimization problem to maximize the expected service life

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and minimize the expected total life-cycle cost consisting of inspection and maintenance costs. Figure 2.8 shows the different approaches used to solve optimization problems to schedule inspection of assets.

Figure 2.8: Approaches Adopted in Literature for Optimizing Inspection Scheduling Plevris et al. (2010) presented a decision support system related to inspecting and repairing damaged infrastructures by unpredictable natural disasters such as earthquakes and flooding. Particle Swarm and Ant Colony Optimization based framework was presented to reach an optimal infrastructure condition assessment. Based on the condition of deteriorated infrastructures, the different inspection groups were assigned to elements that needed inspection. The other part of the formulated optimization problem was to select the optimal route for each group of workers to minimize the distance that each inspection group has to cover. Samrout et al. (2009) used ant colony system in optimizing the system component inspection period. The cost in the optimization problem was set equal to the sum of action costs applied during the preventative maintenance, as well as the costs caused by system unavailability.

Berardi et al. (2009) presented a model for selecting pipes to be inspected by formulating a multi-objective optimization problem to develop an inspection program by using Genetic Algorithms (GA) aiming to minimize the total cost of the inspection program and then the prioritization strategy based on repair costs resulting from emergency repairs due to blockages and collapses in sewer pipelines. GA was used to identify a set of Pareto-optimal inspection programs

Inspection Scheduling using Optimization

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by proposing a prioritization process, based on the pipe rankings. The objective functions formulated represent the sum of the cost of inspection for all pipes in the inspection set using Closed Circuit Television (CCTV) inspection. The indirect costs as a result of sewer blockage and collapses were calculated to include types of buildings affected, pollution, and traffic disruption costs. Blockage and collapse models were developed to determine the optimal inspection scheme for which objective functions could be minimized over both the cost of inspection and the emergency repairs due to the blockages and collapses.

Emergency repairs were represented by the cost of Cured in Place Pipes (CIPP) rehabilitation technique per linear meter of pipe. To develop the blockage model; pipe blockage rate, diameter and length were the pipe characteristics considered in the model. As for the collapse model, the depth, and age were used in the development of that model. An optimum decision is made on whether to inspect the sewer pipelines which are more prone to collapses and/or blockages while taking into consideration the adverse economic effects of these pipe failures by minimizing the developed objective functions.

GA was used in another study for solving a multi-objective optimization problem for allocating budgets for condition assessment of water and sewer networks (Osman et al. 2012). The developed methodology employed partially observable Markov decision process and GA to determine the most appropriate condition assessment technology and interval between inspections from which the condition of the pipelines could be assessed. This methodology addressed the pipes on the individual level to determine the suitable condition assessment technology and inspection interval; in addition, it addressed the asset level by determining where to allocate the budget used in condition assessment. The objective function formulated in this research aimed to reduce costs spent as a result of imperfect inspections which could be translated into reducing the risk of failure

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of the pipeline. The formulated objective function was solved by employing GA, where a random time interval was generated at which the condition assessment technique and value of information were calculated. This step was performed several times from which the solution (i.e. time) with the highest fitness in the population was chosen representing the optimal inspection interval yielding minimum cost as a result of pipe failure and within the available budget allocated for inspection.

Hegazy et al. (2012) presented two techniques to support the inspection and fund-allocation decision for assets. The two techniques could be implemented, individually or combined, into any asset management system. The multiple optimization and segmentation technique formulated large scale optimization problems involving thousands of assets simultaneously, maximizing the return value of money invested. Ugarelli and Federico (2009) presented a cost-based model to schedule the replacement year of deteriorating assets which are subject to operational and maintenance cycles, such as buried pipes in urban water and wastewater systems. The developed model used risk cost as a framework to define the optimal replacement time prediction value, based on the balance between investment for replacing and expenditures for maintaining the asset. The model was based on a conceptual framework to estimate the costs arising from the operation, maintenance, and management of single pipes. The total cost function included all the annual costs involved to maintain the appropriate level of service.

Maji and Jha (2007) presented a mathematical model for condition assessment of elements in highways that can be used while considering budget constraints to determine the optimal maintenance schedule over a specified period of time using genetic algorithm. The rehabilitation costs, threshold values for deterioration, and budget, were used as input for this model. The output for the model was the optimum maintenance schedule of an element. In order to determine the

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optimum schedule for maintenance, total maintenance costs in the design period were optimized to minimum while taking into consideration the budget limitation in a given year.

Chung et al. (2006) presented an approach using statistical models for selecting the most suitable nondestructive inspection techniques and optimal schedule for inspection of fracture critical members on steel bridges. The probability of detection function was combined together with numerical Monte Carlo Simulation of the crack propagation of the fracture-critical detail. A cost function was formulated that included the expected cost of inspections and failure resulting from the chosen Non Destructive Inspection (NDI) technique and alternative inspection schedules. The formulated optimization problem aimed to select the NDI technique with associated inspection schedule for fracture-critical inspections to get a minimum total cost. The inspection frequency was determined as part of the optimization problem with constraints on inspection intervals and a minimum acceptable structural safety level.

The above studies addressed inspection intervals from a multi-objective optimization perspective with the intent of reducing the cost or maximizing the value of condition assessment achieved for the inspected assets. The common attribute between the formulated objective functions is the huge global search space which made choosing GA suitable for the nature of the problem. However, additional computational effort is required to ensure that convergence of population is achieved but without locating the global maximum in the process which is also known as “slow finishing” (Kapelan, 2002). The problem of difficulty in converging towards the Pareto optimal frontier is usually due to the absence in gradient in the fitness function which can be solved by considering additional objectives to increase the pressure of fitness function to push the population towards an optimal frontier.

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In addition, there is usually a sacrifice in one or more objectives to achieve the rest of the objectives when moving from one Pareto solution to another, and to overcome this, the Pareto optimal sets can be increased with the increase of number of objectives (Deb 2001). Therefore, GA might seem an appropriate technique to be used in multi-objective optimization problems, but care should be given because of the computational effort and the sacrifice required when determining the solution for different objectives especially in large scale problems. As such other techniques that outperform GA, such as other evolutionary algorithms like Particle Swarm Optimization (PSO) and more advanced approaches like the general algebraic modeling systems, can be used to solve similar optimization problems.