Finite element model updating is the process of ensuring that
finite element analysis results in
models that better reflect the measured data than the initial models. It is part of
verification and validation
Verification and validation (also abbreviated as V&V) are independent procedures that are used together for checking that a product, service, or system meets requirements and specifications and that it fulfills its intended purpose. These are ...
of numerical models.
The process
The process is conducted by first choosing the
domain in which data is presented. The domains used include
time domain
Time domain refers to the analysis of mathematical functions, physical signals or time series of economic or environmental data, with respect to time. In the time domain, the signal or function's value is known for all real numbers, for the c ...
,
frequency domain
In physics, electronics, control systems engineering, and statistics, the frequency domain refers to the analysis of mathematical functions or signals with respect to frequency, rather than time. Put simply, a time-domain graph shows how a s ...
, modal domain, and time-frequency domain.
The second step is to determine which parts of the initial models are thought to have been modeled incorrectly.
The third task is to formulate a
function
Function or functionality may refer to:
Computing
* Function key, a type of key on computer keyboards
* Function model, a structured representation of processes in a system
* Function object or functor or functionoid, a concept of object-oriente ...
which has the parameters that are expected to be design variables, and which represents the distance between the ''measured'' data and the finite element model ''predicted'' data.
The fourth step is to implement the
optimization
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfi ...
method to identify parameters that
minimize this function. In most cases, a gradient-based optimization strategy will be used. For
nonlinear
In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many othe ...
analysis, more specific methods like
response surface modeling,
particle swarm optimization,
Monte Carlo optimization, and
genetic algorithms can be used. Recently, finite element model updating has been conducted using
Bayesian statistics
Bayesian statistics is a theory in the field of statistics based on the Bayesian interpretation of probability where probability expresses a ''degree of belief'' in an event. The degree of belief may be based on prior knowledge about the event, ...
which gives a probabilistic interpretation of model updating.
References
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*Marwala, T., and Heyns, P.S., "A multiple criterion method for detecting damage on structures" AIAA Journal, 195(2), 1998, pp. 1494-1501.
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External links
FEMtools : Software for finite element model updating in static and dynamic structural analysis
{{DEFAULTSORT:Finite Element Model Updating
Finite element method