A Theoretical Framework for Risk–Cost-Optimized Maintenance Strategy for Structures

Abstract

This paper presents a theoretical framework for developing a risk–cost optimised maintenance strategy for structures during their whole service life. A time-dependent reliability method is employed to determine the probability of structural failure and a generic form of stochastic model is developed for structural responses. To facilitate practical application of the proposed framework, a general algorithm is developed and programmed in a user-friendly manner. The merit of the proposed framework is that, in predicting when, where and what maintenance is required for the structure, all structural components and multi-failure modes are considered. It is found in the paper that, to ensure the safe and serviceable operation of the structure as a whole, some components need maintenance multiple times for different failure modes, whilst other components need “do nothing”. It is also found that ignorance of correlation amongst structural components and failure modes would underestimate the risk of structural failures in longer term and that the components with higher cost of structural failures require more maintenance actions. The paper concludes that the proposed framework can equip structural engineers, operators and asset managers with a tool for developing a risk–cost optimal maintenance strategy for structures under their management.

Appendix

According to the theory of stochastic processes (Papoulis and Pillai 2002), all variables in Eq. (9) can be determined, for a given Gaussian stochastic process with mean function μ_S(t), and auto-covariance function $C_{SS} (t_{i} ,t_{j} )$, as follows:

$$\mu_{{\dot{S}|S}} = E[\dot{S}|S = L] = \mu_{{\dot{S}}} + \rho \frac{{\sigma_{{\dot{S}}} }}{{\sigma_{S} }}(L - \mu_{S} ),$$

(30)

$$\sigma_{{\dot{S}|S}} = \left[ {\sigma_{{\dot{S}}}^{2} (1 - \rho^{2} )} \right]^{1/2} ,$$

(31)

where

$$\mu_{{\dot{S}}} = \frac{{{\text{d}}\mu_{S} (t)}}{{{\text{d}}t}},$$

(32)

$$\sigma_{{\dot{S}}} = \left[ {\frac{{\partial^{2} C_{\text{SS}} (t_{i} ,t_{j} )}}{{\partial t_{i} \partial t_{j} }}|_{i = j} } \right]^{1/2} ,$$

(33)

$$\rho = \frac{{C_{{S\dot{S}}} (t_{i} ,t_{j} )}}{{\left[ {C_{SS} (t_{i} ,t_{j} ) \cdot C_{{\dot{S}\dot{S}}} (t_{i} ,t_{j} )} \right]^{1/2} }},$$

(34)

and the cross-covariance function is

$$C_{{S\dot{S}}} (t_{i} ,t_{j} ) = \frac{{\partial C_{\text{SS}} (t_{i} ,t_{j} )}}{{\partial t_{j} }}.$$

(35)

Based on the above relationships, all the variables in Eq. (9) can be determined.