PSI - Issue 19

Aaron Stenta et al. / Procedia Structural Integrity 19 (2019) 27–40 Stenta and Panzarella / Structural Integrity Procedia 00 (2019) 000–000

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is assumed to grow at an uncertain Crack Growth Rate described by a lognormal distribution with mean and variance that also depend on the type of material selected. The crack will grow until it reaches some Critical Crack Size at which point it fails. For the base case, failure is assumed to occur when the crack size reaches or exceeds 70% of the wall thickness. The optimal Run Time for these particular choices is determined by the decision network to be within the range of 180 to 190 cycles (ranges are used rather than using every possible value in order to reduce the complexity of the model and cut down on the time require to obtain a solution) for the most crack resistant material. Note that this is about one standard deviation below the mean number of permissible cycles of 200 for this material. The associated maximum expected relative return is 420 per cycle for this optimal run time. Note that this return is only about 42% of the maximum possible revenue of 1000 per cycle if there were no possible failure. If the less crack-resistant material were selected, the optimal Run Time reduces to between 120 and 130 cycles and the expected relative return per cycle drops to just 131 (only 10% of its maximum value). For this selection of relative costs, choosing a more crack resistant material is obviously the better choice. This example illustrates the benefit of using these sorts of decision networks to maximize expected revenue. While it might not be clear from intuition alone whether using a better material is warranted, when all costs and benefits are entered into a network like this, the best decision is quickly arrived at. It is important to point out that these decisions are possible without having perfect knowledge of any of the inputs. In fact, the uncertainty in the inputs is just another input. For example, if the uncertainty in the crack initiation cycles is increased by doubling the standard deviation of its distribution to 40, the optimal number of cycles for the case of a crack-resistant material is reduced to be within 150 to 160 cycles. This is a reduction of about 30 cycles of run time as a result of increased uncertainty about the parameters of the fatigue model, and the expected return reduces to 284 (from 420 before). This allows one to directly ascertain the value of knowledge in financial terms. The above example shows that if it were possible to cut in half the uncertainty in the cycles to crack initiation, this would lead to an increase in the expected financial return of about 50% for this particular case, resulting in a very significant increase in profits. An analysis like this can be used to justify further research into improved fatigue models if they can be shown to provide such a significant financial benefit. Any parameter in the decision network can be varied to see its effect. For example, if the failure crack size were reduced to be just 50% of the wall thickness, then the optimal number of cycles reduces to the 160 to 170 cycles range and the expected relative return per cycle drops to 376. The previous example found the optimal Run Time without permitting any inspections or repair. The component is operated up to this recommended time and then replaced, without any thought given to any intermediate inspections or repairs. This is always one possible operational strategy for any asset, but it is obviously not always the best choice. If performing inspection or repairs is beneficial, then they should be considered, along with their associated costs. If the expected revenue per cycle with inspections and repairs performed is higher than without them, then they are worth it and recommended. Such an extended decision network is shown in Figure 7. The possibility of performing a single inspection, followed by a repair if a crack is detected, is accounted for by breaking the total run time up into two intervals (before and after inspection). To accomplish this, the single run time decision node is now split into two, Run Time Before Inspection and Run Time After Inspection . It is assumed that the inspection would be performed at the time specified by the Run Time Before Inspection node. At the time of inspection, the crack is either detected or not, and if it is detected, a measurement of the crack size is taken. It is assumed that the crack can only be detected if it is greater than some minimal detectable crack size, which would normally depend on the technique being used, but here it is assumed to be equal to 10% of the wall thickness. More accurate techniques can detect smaller cracks but at an additional cost. Measurement error in the sizing of the crack is also accounted for, when the cracks are larger than the detectable limit. If a crack is detected, it can be repaired, but at some additional cost. For this model, the repair is assumed to reset the crack size back to its initial distribution (a perfect repair is assumed), and any accumulated fatigue damage is removed. The possibility of a second crack initiating and growing after the repair is permitted, but only after an additional time to initiation has passed. Both the Mean Cycles to Crack Initiation and the Crack Growth Rate are uncertain parameters described by discrete probability distributions. The additional costs of inspection and repair are assumed to be 10 and 100, respectively, in the same relative terms discussed before. Assuming all other parameters have the same values, it turns out that an inspection is indeed always recommended between 210 and 220 cycles for the more crack resistant material, and if a crack is