Parameter selection

groundhog.standards.eurocode7.parameter_selection.constant_value(data, mode='Low', cov=nan, confidence=0.95, **kwargs)

Selects the characteristic value from a set of measurements using Eurocode 7 rules. For a local low value, the 5% fractile is taken. For a mean value, a 95% confidence value or the mean is taken. The selection process assumes that the parameter under consideration is stationary and is normally distributed. For lognormally distributed parameters a transformation to the logarithm is required.

Parameters:

• data – List or numpy array with the measurements. The number of measurements is derived from the length.

• mode – Determines whether a local low value "Low" or mean vaue "Mean" needs to be taken

• cov – Coefficient of variation (\(V_x = \sigma / \mu\)) (given as the ratio of standard deviation to the mean, not in percent). If CoV is unknown, leave blank.

• confidence – Confidence level used for calculations (default = 95%)

\[ \begin{align}\begin{aligned}X_k = X_{mean} \cdot \left( 1 - k_n \cdot V_x \right)\\V_x \text{unknown}: k_{n,mean} = t_{n-1}^{0.95} \sqrt{ \frac{1}{n} }, \ k_{n,low} = t_{n-1}^{0.95} \sqrt{ \frac{1}{n} + 1}\\V_x \text{known}: k_{n,mean} = 1.64 \sqrt{ \frac{1}{n} }, \ k_{n,low} = 1.64 \sqrt{ \frac{1}{n} + 1}\end{aligned}\end{align} \]

Returns:

Dictionary with the following keys: - ‘n’: Number of datapoints - ‘t_nminus1’: Student-t factor - ‘kn’: kn value - ‘Xk’: Characteristic value of the parameter under consideration

groundhog.standards.eurocode7.parameter_selection.linear_trend(data, depths, requested_depths, mode='Low', confidence=0.95, **kwargs)

Selects the characteristic value from a set of measurements using Eurocode 7 rules. A linear trend is assumed in the data. For a local low value, the 5% fractile is taken. For a mean value, a 95% confidence value or the mean is taken. The selection process assumes that the parameter under consideration is stationary and, when de-trended, is normally distributed. For lognormally distributed parameters a transformation to the logarithm is required.

Parameters:

• data – List or numpy array with the measurements. The number of measurements is derived from the length.

• depths – List or numpy array with the depths. The number of depths needs to be identical to the number of measurements.

• requested_depths – List or numpy array with the depths where the characteristic value is requested.

• mode – Determines whether a local low value "Low" or mean vaue "Mean" needs to be taken

• confidence – Confidence level used for calculations (default = 95%)

\[ \begin{align}\begin{aligned}x^{*} = \bar{x} + b ( z - \bar{z} )\\\bar{x} = \frac{1}{n} \left( x_1 + x_2 + ... + x_n \right)\\\bar{z} = \frac{1}{n} \left( z_1 + z_2 + ... + z_n \right)\\b = \frac{\sum_{i=1}^n (x_i - \bar{x}) (z_i - \bar{z})}{\sum_{i=1}^n (z_i - \bar{z})^2}\\\text{Mean value}\\s_1 = \sqrt{ \frac{1}{n-2} \left( \frac{1}{n} + \frac{(z- \bar{z})^2}{\sum_{i=1}^{n} (z_i - \bar{z})^2} \right) \sum_{i=1}^n \left[ (x_i - \bar{x}) - b (z_i - \bar{z}) \right]^2 }\\X_k = \left[ \bar{x} + b (z - \bar{z}) \right] - t_{n-2}^{0.95} s_1\\\text{Local low value}\\s_2 = \sqrt{ \frac{1}{n-2} \left(1+ \frac{1}{n} + \frac{(z- \bar{z})^2}{\sum_{i=1}^{n} (z_i - \bar{z})^2} \right) \sum_{i=1}^n \left[ (x_i - \bar{x}) - b (z_i - \bar{z}) \right]^2 }\\X_k = \left[ \bar{x} + b (z - \bar{z}) \right] - t_{n-2}^{0.95} s_2\end{aligned}\end{align} \]

Returns:

Dictionary with the following keys: - ‘n’: Number of datapoints - ‘t_nminus1’: Student-t factor - ‘kn’: kn value - ‘Xk’: Characteristic values (Numpy array) of the parameter under consideration at the requested depths