Uncertainty Quantification

In some cases, common analysis tools and methods may not be sufficient for an engineer who wants to:

  • Validate the designed product robustness under various conditions or
  • Study the behavior and possible ways to improve these products as well as their describing models.

Let’s consider the situation where the goal is to design a building which is reliable with respect to a potential earthquake. The advanced design tools allow an engineer to build a model which predicts whether the building with the defined parameters (geometry, strength, and stiffness of the materials) will collapse or not in case of an earthquake with a certain magnitude, duration etc.  However, in reality, the values of this predictive model parameters (geometry, strength, magnitude etc) always contain some uncertainty. This uncertainty can be both caused by technological limitations on the accuracy (in the context of geometry) and by the natural variability of a parameter (in the context of magnitude). So, while designing the building, the behavior of the model under consideration should be analyzed with respect to these uncertainties.

Specialists from a wide spectrum of industries such as energy, chemical and many other face the need to evaluate the influence of uncertain parameters of a product (material properties, operating conditions etc.) on the technical and operational characteristics guaranteed. An easy to use tool to fill this need is available in pSeven software package with the OpenTURNS algorithmic library integrated. Uncertainty Quantification with pSeven allows to significantly improve the quality of products designed, manage potential risks at the design, manufacturing and operating stages and to guarantee product reliability.

Uncertainty Quantification in pSeven

In pSeven, Uncertainty Quantification is performed by means of a full range of industry-proven algorithms in an intuitive interface for users with no programming background, coupled with DATADVANCE’s proprietary optimization and approximation techniques of pSeven Core.

Uncertainty Quantification procedure in pSeven comprises three steps: 

 

Steps

Description

Methods in pSeven 

I. Computational model and criteria specification for further study As an option to fasten the solution process, pSeven Core Approximation tool allows to replace computationally expensive models with the fast and accurate approximation models (surrogate models)

To build an approximation model:

  • Choose the experimental design (Latin Hypercube Sampling, low-discrepancy sequences)
  • Run the computational model
  • Construct approximation model (Polynomial chaos expansions, Kriging, Support vector machines)
II. Constructing a probabilistic model, describing the uncertainties of computational model parameters (quantification of the uncertainty sources) There are two ways to construct a probabilistic model:
  • Based on experimental data
  • Based on engineering judgment or best practices from the literature
  • Probability model (non-parametric, e.g. Kernel Smoothing; parametric, e.g. Normal, Beta)
  • Auto-selection of distribution type for parameters sample
  • Goodness-of-fit tests for sample-based probability models (e.g. Kolmogorov-Smirnov test)
  • Dependencies of input parameters (e.g. Spearman correlation coefficient)
III. Uncertainty propagation and reliability analysis Identifying the characteristics of interest, assessment criteria (i.e. the distribution of the output of the computational model under uncertainties, the probability of failure).
  • Central dispersion, output distribution analysis (Monte Carlo)
  • Failure probability  (Reliability analysis): approximation (FORM), simulation (Monte Carlo, LHS, Directional sampling)
 IV.  Additional step: Sensitivity Analysis Identifying the influence of uncertainties of computational model parameters on the result of uncertainty propagation.

After this step is complete, the need to modify the probabilistic model may appear. 

  • Correlation of model response with the input parameters (e.g. Spearman correlation coefficient)
  • FORM importance factors
 V. Uncertainty Quantification results visualization Visualization of UM steps for performing preliminary data/model analysis and a better understanding of the obtained results A wide variety of plot types  available:
  • Histogram and Kernel Smoothing
  • Convergence plot with confidence intervals for failure probability
  • Multidimensional data visualization (Parallel coordinates plot, Pairwise correlation plot)

Uncertainty Quantification Workflow in pSeven

In pSeven the steps enumerated above are executed by the means of special blocks (workflow elements):

  • Distribution block allows constructing the probabilistic model that describes the uncertainties of the model parameters.
  • Physical model (PythonScript or an analog) implements the computational model. NB: in pSeven several block types are available in addition to PythonScript to represent various types of computational models.
  • UQ block implements the uncertainty propagation.

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