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Sensitivity analysis is the study of how the uncertainty in the output of a mathematical model or system (numerical or otherwise) can be divided and allocated to different sources of uncertainty in its inputs. [1] [2] This involves estimating sensitivity indices that quantify the influence of an input or group of inputs on the output.
Variance-based sensitivity analysis (often referred to as the Sobol’ method or Sobol’ indices, after Ilya M. Sobol’) is a form of global sensitivity analysis. [1] [2] Working within a probabilistic framework, it decomposes the variance of the output of the model or system into fractions which can be attributed to inputs or sets of inputs.
FAST is more efficient to calculate sensitivities than other variance-based global sensitivity analysis methods via Monte Carlo integration. However the calculation by FAST is usually limited to sensitivities referred to as “main effects” or “first-order effects” due to the computational complexity in computing higher-order effects.
EE is applied to identify non-influential inputs for a computationally costly mathematical model or for a model with a large number of inputs, where the costs of estimating other sensitivity analysis measures such as the variance-based measures is not affordable. Like all screening, the EE method provides qualitative sensitivity analysis ...
Sensitivity analysis identifies how uncertainties in input parameters affect important measures of building performance, such as cost, indoor thermal comfort, or CO 2 emissions. Input parameters for buildings fall into roughly three categories: Discrete design alternatives, e.g. different glazing options, number of storeys, etc.
Condition numbers can also be defined for nonlinear functions, and can be computed using calculus.The condition number varies with the point; in some cases one can use the maximum (or supremum) condition number over the domain of the function or domain of the question as an overall condition number, while in other cases the condition number at a particular point is of more interest.
A sensitivity analysis method widely used to screen factors in models of large dimensionality is the design proposed by Morris. [3] The Morris method deals efficiently with models containing hundreds of input factors without relying on strict assumptions about the model, such as for instance additivity or monotonicity of the model input-output ...
This type of analysis was popularized by Lord Rayleigh, in his investigation of harmonic vibrations of a string perturbed by small inhomogeneities. [ 1 ] The derivations in this article are essentially self-contained and can be found in many texts on numerical linear algebra or numerical functional analysis.