Dynamics & Vibration Research Group

In many industries there is a need to quantitatively assess the reliability of an engineering structure. For example the aircraft industry has for many years relied on the use of factors of safety, but there is an increasing requirement to assess the probability of failure that underlies these safety factors, in the interests of both safety and efficiency of design.

The probability of failure of a complex structure can be estimated directly by using Monte Carlo techniques in combination with a finite element model of the structure. However this approach is computationally intensive and for several decades research has been directed at the development of alternative, more efficient, methods. A widely used approach is FORM (the First Order Reliability Method) which is based on an asymptotic approach to the reliability integral: in brief, the safety margin is expressed in terms of uncorrelated standardised normal variables and linearised about the design point. While this approach works well for static problems (where the safety margin is a smooth and often monotonic function of the random variables) it is problematic for dynamic problems, where the safety margin is typically multiply connected and non monotonic. This project is directed at reliability methods for dynamic problems.

Project Details

The project, which is leading to a PhD, will have the following primary objective and work program.

Objective:
To develop a robust method of predicting the reliability of a complex structure subjected to dynamic loading.

Task Program:


As illustrated in the above figure, the project will have the following sequential methods/tasks:

1. Screening Test (with limited finite element runs): A first order RS model with a saturated design scheme will be used to identify the important factors (variables), while others can be 'eliminated' (substituted with their mean values) in the subsequent analysis. The dimension of the variable set will be reduced from n to m.
2. Safety margin curve construction procedure:
   1. Transformation procedure: for dynamic systems, a new set of parameters will be developed. A new safety margin curve will be defined in terms of the new m random variables.
   2. Higher order RS model fitting procedure: for other systems (or even for dynamic systems, to compare with the transformation procedure), second order RS models will be fit to provide a better approximated safety margin.
3. Reliability analysis procedure: FORM/SORM, Monte Carlo simulation methods, etc., will be employed to work on the simplified safety margin. Safety index and probability of failure will be delivered.

Relevant/Recent Publications

1. Bin Wu, An Investigation of Response Surface Methodology (RSM) for Structural Reliability Analysis, First Year Report, Engineering Department, University of Cambridge, February 2003

Principal Investigator & Researchers

• Professor R. S. Langley
• Mr Bin Wu

Collaborators

• QinetiQ Ltd

Funding Body

• EPSRC/MOD, 2002-2004