A new cumulative damage model for time-dependent reliability analysis of deteriorating structures

In this paper, we consider a component exhibiting a continuous monotone degradation modeled as a Gamma process. The maintenance policy is of condition‐based type with periodic inspections. It follows the two threshold control limit policy with a preventive maintenance limit, a switching limit, and a given failure limit. Our interest is to minimize the annual expected maintenance cost subject to a constraint on the average availability. The decision variables are the preventive limit, the switching limit, and the inspections schedule. We derive exact results for the key performance indicators, but since they are numerically involved, we propose a simple, that is, involving necessary spreadsheet calculations, accurate approximation. We apply our model to a case from the process industry, namely, a carbon steel hydrogen dryer consisting of a cylindrical pressure vessel. This vessel suffers from corrosion with thickness growth modeled as a Gamma process. The optimization results show that although the annual maintenance cost increases with the mean and the coefficient of variation of the yearly corrosion thickness, its mean has a higher impact on cost. Based on the cost sensitivity analysis, we find that the impact of a vast increase of the corrective maintenance cost for the same inspection and preventive costs can be mitigated by appropriately reducing the corrective maintenance probability. Finally, we empirically show that the two threshold policy achieves an annual cost savings up to 12.3%$12.3\%$ compared to the single threshold policy.

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“…The Gamma process has been widely applied in maintenance, see Refs. 6 and 50. In this section, we give new exact results on the Gamma process.…”

Section: Renewal Gamma Processmentioning

confidence: 99%

Two‐threshold control limit policy in condition‐based maintenance

Hanbali

Saleh

Ullah

2022

Quality & Reliability Eng

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“…under two-level loadings, several studies have reported that the following relationship exists between the damage D e (n 1 ) under the first-level loading and its corresponding equivalent damage D e (n 2 0 ), 34,35…”

Section: The Improved Y-w Modelmentioning

confidence: 99%

“…Combining Equations ( 33) and (34), Equation ( 32) is then solved to obtain p GΘ (g, θ, n). Then the PDF of G(n) at n can be obtained by integrating on the random variable space Ω Θ as…”

Section: Probability Density Evolution Equationmentioning

confidence: 99%

Nonlinear time‐varying fatigue reliability analysis based on the improved toughness exhaustion model

Gao

Liu

2021

Fatigue Fract Eng Mat Struct

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The state function based on fatigue accumulation model has a great influence on accuracy of fatigue reliability analysis of components. A nonlinear fatigue accumulation model considering the interaction of loads is proposed in this paper. The square ratio of front and back loads is presented as a new load interaction factor and embedded into the conventional toughness exhaustion model; thus, this improved model can reflect the load sequence and interaction effect simultaneously. Moreover, the fatigue state function using the improved model is constructed and analyzed by the probability density evolution method. Then experimental data of four materials are used to verify the proposed model, and results show that the residual life fraction predicted by the proposed model is accurate. Furthermore, accuracy and efficiency of the timevarying fatigue reliability analysis using the proposed model is validated using experimental data from a carbon steel test and a helical compression spring test.

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“…9,10,24,25 Some uncertainties may be time-dependent, such as structural resistance degradation, load history, etc. 26–28 And other uncertainties may be related to space, such as concrete cover depth, surface chloride concentration, etc. 29–31 Therefore, the performance of RC structures will have temporal variability and spatial variability.…”

Section: Introductionmentioning

confidence: 99%

Temporal-spatial reliability analysis of RC bridges with corroded steel reinforcement bars

Chen

Wei

et al. 2022

Proceedings of the Institution of Mechanical Engineers, Part C:

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Corrosion of steel bars is one of the most significant causes of deterioration of reinforced concrete (RC) structures. The performance of RC structures is affected by many factors such as materials, environments, and load conditions, which usually possess uncertain features. Some of uncertainties may be time- and space-dependent, and the corresponding reliability problems become more challenging. To address these issues, this paper studies the temporal-spatial reliability analysis of RC bridges with corroded steel reinforcement bars. At first, a compound corrosion model is developed in which the combined effects of carbonation (general corrosion) and chloride penetration (pitting corrosion) are considered. In the reliability analysis, both the temporal and spatial variability are accounted through a stochastic process and a random field, respectively. An extended instantaneous response surface (t-IRS) method is then proposed to evaluate the temporal-spatial reliability. Unlike the original t-IRS method, in addition to the original variables, the random variables transformed from the random fields and the space variable are also used as the input variables of the extended surrogate model. When generating sample points, both the time variable and the space variable are treated as uniformly distributed random variables within given intervals. Finally, the proposed method is applied to a RC bridge example with corroded steel reinforcement bars and the results are compared with that of Monte Carlo simulation (MCS) method, demonstrating the effectiveness of the extended t-IRS method.

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A new cumulative damage model for time-dependent reliability analysis of deteriorating structures

Cited by 9 publications

References 43 publications

Two‐threshold control limit policy in condition‐based maintenance

Two‐threshold control limit policy in condition‐based maintenance

Nonlinear time‐varying fatigue reliability analysis based on the improved toughness exhaustion model

Temporal-spatial reliability analysis of RC bridges with corroded steel reinforcement bars

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