Confidence level in peak results computation

Statistics are used to assess both the input and output analysis quantities. Typically, you want to know the probability that these quantities will lie in a certain range. For a Gaussian distribution, which is most common form shown in the following figure, this range is usually expressed as a scalar multiple of the standard deviation:

				where:p(x) is the Gaussian probability density function of quantity x.σx is one standard deviation of this quantity from the mean. It is equal to the root mean square (RMS) when the mean is zero.μx is the mean.

A commonly used confidence level is 99.73% which, for a Gaussian distribution, is achieved when the magnitude of the response exceeds 3 times the standard deviation (3σ).

All input and output quantities that are computed by the Laminate Dynamics solution process follow a Gaussian distribution, except for Von Mises stresses, some ply failure indices, some ply strength ratios, and some ply margins of safety, depending on the selected ply failure theory. Results that follow Gaussian distributions yield identical peak values, whether you define a confidence level or enter the equivalent number of standard deviations. For such results, the RMS value, multiplied by the number of standard deviations, is called a peak value. The number of standard deviations is sometimes referred to as the “peak-to-RMS” ratio.

Typical values for the number of standard deviations, along with their corresponding confidence level, are shown in the following table.

Number of standard deviations	Confidence Level (%)
1.0	68.2689
2.0	95.4500
3.0	99.7300
4.0	99.9937
5.0	99.9999

For results that do not follow Gaussian distribution, the number of standard deviations is not directly meaningful since the probability density function is unknown. Hence, the confidence level is used to determine a peak value.

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Confidence level in peak results computation, Simcenter 3D 2021.1 Series

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