Stochastics

Who

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Stochastics Ltd. develop The Stochastics Solver which is an advanced risk and reliability analysis program for the engineering and scientific industries.

Stochastics Ltd. was founded in 2021. The mission of the company is to develop rapid and accurate software for engineering reliability analyses and to incorporate this technology into the finite element analysis method.

Why

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Being able to quantify the uncertainty in the scientific and engineering disciplines takes the guesswork out of the decision making process.

The Stochastics Solver uses machine learning to rapidly and accurately model various analytical and design states and scenarios and calculate their probability of occurance. Such information is invaluable when critical decisions have to be made as this information gives a critical insight into the uncertainty associated with decisions.

In some engineering industries, such as the Oil & Gas industry, performing extremely sensitive reliability analyses on subsea pipelines is a codified requirement.

What

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The Stochastics Solver uses machine learning to solve probabilistic multi variate equations which are fundemental when modelling engineering and scientific estimation, risk and reliability scenarios.

Methods, such as the Monte Carlo technique, which are used to solve multi variate equations, developed almost 100 years ago, are slow, approximate and gives limited output data.

In contrast The Stochastic Solver can solve any multi variate equation to a high precision in a fraction of the time the Monte Carlo method takes. In addition to detailed estimation, risk and reliability output data The Stochastics Solver gives the probability density and cumulative distribution functions of the resulting multivariate equation hence providing a complete mathematical description of the uncertainity if further probabilistic modelling is required. In terms of speed and accuracy the figures speak from themselves.

For independent screening checks The Stochastics Solver has a Monte Carlo random sampler to solve multivariate equations. The screenshot below shows the probability density function (red line) and the histogram (blue line) as calculated by The Stochastics Solver by machine learning and random sampling, respectively. The theoretical mean of the equation is 343 MPa. Machine learning and random sampling calculates (to six decimal places) 343.000000 MPa and 342.863784 MPa (100000 trials), respectively. The machine learning solve time is 20 milli-seconds which is over 400 times faster than the random sampling solution.

Chart: Comparison of the machine learning and random sampling traces for the Yield Stress parameter used in Challenge 2 of the NAFEMS Stochastics Working Group challange problems 2019.

The Beta, Binomial, Chi Squared, Exponential, F, Gamma, Hypergeometric, Log Normal, Negative Binomial, Normal, Poisson, T, Triangular, Uniform, User Defined and Weibull probability distributions are supported by The Stochastics Solver in the calculation of the probabilistic multi variate equations. The operations supported include unary positive, unary negative, addition, subtraction, multiplication, division and exponentiation.

For example the probabilistic multi variate equations for Challenge 2 of the NAFEMS Stochastics Working Group challange problems 2019 which The Stochastics Solver solves to calculate the probability of failure (reliability) are:

Load = ((normal(2.4,0.12)+uniform(1.9,2.3))*1000)/normal(17.2,1.7)

Resistance = lognormal(343,17)