PSI - Issue 19

A. Halfpenny et al. / Procedia Structural Integrity 19 (2019) 150–167 Author name / Structural Integrity Procedia 00 (2019) 000–000

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- Epistemic uncertainties are reduceable through better knowledge; for example, better characterisation of the target loading environment, or measurement of residual stresses, etc. Where epistemic uncertainties prevail, a cost benefit study will reveal whether it is prudent to invest more money in measurement and simulation, or absorb the costs through over-design. - Aleatoric uncertainties are attributable to the inherent variability in a system and cannot be reduced. Examples include the inherent scatter in a material fatigue curve. However, it is important that aleatoric uncertainties are accurately characterised in order to reduce excessive safety margins. In the case of material fatigue test data, for example, increasing the number of tests will narrow the confidence bounds and reduce the safety margin necessitated by small sample sizes. Stochastic fatigue simulation Stochastic simulation is performed using a Monte Carlo approach. The requirement for a ‘Reduced Order FEA Model (ROM)’ (or ‘Surrogate Model’) is discussed in the paper. Statistical sampling techniques, known as ‘Design of Experiments (DOE)’, are also discussed for optimizing the size of the design space matrix. Two broad areas are covered: - Design for reliability – exploring the statistical variability of design space - Design for robustness – exploring the extremities of design space Reliability simulation Reliability simulation offers the following design advantages : - Optimize the design to achieve the target reliability with a specified confidence interval - Identify potential cost savings by identifying the most influential uncertainties - Simulate the reliability of the entire mechanical system by considering all the sub-systems - Validate the simulation against physical durability and reliability test data. Validation will include both the mean time to failure and the expected statistical scatter in observed life - Provide an optimized maintenance schedule in order to achieve the target reliability - Refine the simulation model by using in-service maintenance and failure data, and provide improved uncertainty parameters for future designs 2. Stochastic fatigue simulation Traditional fatigue analyses are performed through a deterministic calculation process where input parameters are assigned constant values. The same process can be implemented stochastically by embedding the deterministic process inside a Monte Carlo wrapper as illustrated in Fig. 2. The wrapper runs the deterministic process repeatedly. The input parameters are varied statistically with every run. The variations follow user-defined probability distributions. This creates a sample of simulated fatigue life results which are processed using the reliability analysis methods discussed later.  

Fig. 2. Schematic of a probabilistic design analysis