Finite element updating
Encyclopedia
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
of numerical models.
, frequency domain
, 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
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
method to identify parameters that minimize
this function. In most cases, a gradient-based optimization strategy will be used. For nonlinear analysis, more specific methods like response surface
modeling, particle swarm optimization
, Monte Carlo optimization
, and genetic algorithm
s can be used.
Mathematical model
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used not only in the natural sciences and engineering disciplines A mathematical model is a...
that better reflect the measured data than the initial models. It is part of verification and validation
Verification and Validation
In software project management, software testing, and software engineering, verification and validation is the process of checking that a software system meets specifications and that it fulfills its intended purpose...
of numerical models.
The process
The process is conducted by first choosing the domain in which data is presented. The domains used include time domainTime domain
Time domain is a term used to describe 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 case of continuous time, or at various...
, frequency domain
Frequency domain
In electronics, control systems engineering, and statistics, frequency domain is a term used to describe the domain for analysis of mathematical functions or signals with respect to frequency, rather than time....
, 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 (mathematics)
In mathematics, a function associates one quantity, the argument of the function, also known as the input, with another quantity, the value of the function, also known as the output. A function assigns exactly one output to each input. The argument and the value may be real numbers, but they can...
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
Optimization (mathematics)
In mathematics, computational science, or management science, mathematical optimization refers to the selection of a best element from some set of available alternatives....
method to identify parameters that minimize
Maxima and minima
In mathematics, the maximum and minimum of a function, known collectively as extrema , are the largest and smallest value that the function takes at a point either within a given neighborhood or on the function domain in its entirety .More generally, the...
this function. In most cases, a gradient-based optimization strategy will be used. For nonlinear analysis, more specific methods like response surface
Response surface methodology
In statistics, response surface methodology explores the relationships between several explanatory variables and one or more response variables. The method was introduced by G. E. P. Box and K. B. Wilson in 1951. The main idea of RSM is to use a sequence of designed experiments to obtain an...
modeling, particle swarm optimization
Particle swarm optimization
In computer science, particle swarm optimization is a computational method that optimizes a problem by iteratively trying to improve a candidate solution with regard to a given measure of quality...
, Monte Carlo optimization
Monte Carlo method
Monte Carlo methods are a class of computational algorithms that rely on repeated random sampling to compute their results. Monte Carlo methods are often used in computer simulations of physical and mathematical systems...
, and genetic algorithm
Genetic algorithm
A genetic algorithm is a search heuristic that mimics the process of natural evolution. This heuristic is routinely used to generate useful solutions to optimization and search problems...
s can be used.