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SOERP3

Second Order Error Propagation for Python

Overview

soerp3 is the Python implementation of the original Fortran code SOERP by N. D. Cox to apply a second-order analysis to error propagation (or uncertainty analysis). The package allows you to easily and transparently track the effects of uncertainty through mathematical calculations. Advanced mathematical functions, similar to those in the standard math module, can also be evaluated directly.

To use soerp3, the first eight statistical moments of the underlying distribution are required: mean, variance, and the standardized third through eighth moments. These can be input manually as an array, or generated using the provided constructors or directly from scipy.stats distributions. The result of all calculations generates a mean, variance, and standardized skewness and kurtosis coefficients.

Requirements

Example Usage

from soerp3 import uv, N, U, Exp, umath

# Normal distribution, mean=10, std=1
x = uv([10, 1, 0, 3, 0, 15, 0, 105])
# x = uv(rv=ss.norm(loc=10, scale=1))
x = N(10, 1)

# Three-part assembly
x1 = N(24, 1)
x2 = N(37, 4)
x3 = Exp(2)
Z = (x1 * x2**2) / (15 * (1.5 + x3))
print(Z)
Z.describe()

# Moments
print(x1.moments())
print(Z.moments())

# Correlations
print(x1 - x1)
square = x1**2
print(square - x1 * x1)

# Derivatives
print(Z.d(x1))
print(Z.d2(x2))
print(Z.d2c(x1, x3))
print(Z.gradient([x1, x2, x3]))
print(Z.hessian([x1, x2, x3]))
Z.error_components(pprint=True)

# Orifice flow example
H = N(64, 0.5)
M = N(16, 0.1)
P = N(361, 2)
t = N(165, 0.5)
C = 38.4
Q = C * umath.sqrt((520 * H * P) / (M * (t + 460)))
Q.describe()

Main Features

  1. Transparent calculations with automatic derivatives.
  2. Basic NumPy support.
  3. Nearly all standard math module functions supported via soerp3.umath.
  4. Analytical derivatives up to second order.
  5. Easy continuous distribution constructors:
    • N(mu, sigma) : Normal
    • U(a, b) : Uniform
    • Exp(lamda, [mu]) : Exponential
    • Gamma(k, theta) : Gamma
    • Beta(alpha, beta, [a, b]) : Beta
    • LogN(mu, sigma) : Log-normal
    • Chi2(k) : Chi-squared
    • F(d1, d2) : F-distribution
    • Tri(a, b, c) : Triangular
    • T(v) : T-distribution
    • Weib(lamda, k) : Weibull

See Also

  • uncertainties: First-order error propagation
  • mcerp: Real-time latin-hypercube sampling-based Monte Carlo error propagation

Acknowledgements

The author thanks Eric O. LEBIGOT for the original uncertainties package, which inspired many ideas reused or evolved here. If you only need first-order uncertainty analysis, his package is an excellent alternative.

References

  • N.D. Cox, 1979, Tolerance Analysis by Computer, Journal of Quality Technology, Vol. 11, No. 2, pp. 80-87