# Data & Model Analysis

## Data Analysis

pSeven provides full control over external data and rich post-processing capabilities. Visualize and reuse engineering results with a comprehensive set of interactive and customizable tools, including all kinds of tables and statistics, correlations, dependencies, parallel coordinates and 2D/3D visualization.

*Parameters correlation analysis*

*Parameters dependency analysis*

*Design points in parallel coordinates*

## Design of Experiments

Design of Experiments (DoE) is a selection of inputs at which outputs of the model are measured to explore design space or to get as much information as possible about the model behavior using a small number of observations as possible.

*Create model*

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*Define variables*

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*Run Design of Experiments*

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*Analyze results*

Model behavior can be very different in dimensionality, size, smoothness, noisiness, etc. and the available number of model computations is often limited. To explore such models faster and more effective pSeven offers a variety of techniques for Design of Experiments including batch, sequential and adaptive sampling. Sequential sampling is a uniform filling of white regions of the model step by step, while adaptive sampling considers model behavior before adding new points. Also, DoE can be used to perform reliable surrogate-based optimization or to generate a training data sample for a building of an accurate approximation model.

DoE techniques available in pSeven:

**Batch:**

- Latin Hypercube
- Optimized Latin Hypercube
- Full Factorial
- Fractional Factorial
- Parametric Study
- Orthogonal Array
- Box-Behnken Design
- D-Optimality, I-Optimality

**Sequential:**

- Random Sampling
- Halton Sequence
- Sobol Sequence
- Faure Sequence

**Adaptive:**

- Uniform
- Maximum Variance
- Integrated Mean Square Error Gain - Maximum Variance
- Adaptive Design

## Sensitivity Analysis

Sensitivity Analysis in pSeven allows studying the dependencies present in data, for instance, in series of input and output model parameters values. Ultimately, it answers the following question: What input parameters have small or no influence at all on the output and thus can be dropped in the further studies?

For example, during design optimization, when the number of allowed model computations (budget) is limited, knowing what features are less important allows dropping them in the optimization process. Reducing the number of input variables by not considering features that have little effect on the dependency, one can do more optimization iterations with the same budget, possibly acquiring a better solution.

*Provide data set of input and output values*

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*Run Sensitivity Analysis*

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*Qualify variables*

In the building of approximation models, it may also be beneficial to remove the least important features to create a denser sample for the same computation time that will provide a more accurate approximation. Also, many approximation techniques sometimes work better in smaller dimensions in terms of time/memory requirements.

## Uncertainty Quantification

Specialists from a wide spectrum of industries face the need to evaluate the influence of uncertain parameters of a product, like material properties or operating conditions, on its technical and operational characteristics. Uncertainty Quantification (UQ) in pSeven addresses this need and allows engineers to significantly improve quality and reliability of designed products and manage potential risks at early design, manufacturing and operating stages.

*Set input distributions*

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*Evaluate model responses*

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*Identify output distribution*

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*Estimate failure probability*

UQ is used to assess model design point taking into account all possible deviations of input parameters and their influence on the output. Uncertainties of the input parameters are described with distributions, based on experimental data, production constraints, best practices or engineering judgment. The most important part of UQ process is defining the model assessment criteria, for example, failure conditions. As a result of UQ user obtains a distribution of these criteria, including mean and dispersion values which allow to evaluate the model reliability and make better engineering decisions.

## Dimension Reduction

Complex geometries are described by a large number of parameters, and it is often desirable to reduce their dimensionality for easier parameterization, optimization or visualization. For example, if the geometry is represented as a set of multi-dimensional points, pSeven can approximate it with a smooth hypersurface and produce compression and decompression procedures which allow to:

- Automatically re-parameterize geometry with a smaller number of parameters.
- Quickly generate topologically similar geometries.

The number of parameters required to describe the geometry with the smallest error in pSeven is estimated automatically and may be manually changed.

*Provide input parameters for a set of profiles*

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*Run Dimension Reduction*

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*Reconstruct profiles with less input parameters*

## Model Identification

Sometimes model input parameters are hard or impossible to determine, for example, damping or scattering coefficient. Running an experiment may help, but if these parameters canâ€™t be found directly, a more advanced research is required.

*Create a model with unknown parameters*

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*Run a physical test and collect measurements*

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*Minimize residual with optimization*

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*Evaluate unknown input parameters*

In such cases, model identification (or data matching) in pSeven can be used. The idea is to collect output data of the experiment and create simulation or analytical model of the product or manufacturing process with unknown input parameters. After that, an optimization process with residual check between predicted and experimental data is set up to identify unknown input parameters. This approach provides less expensive research and grants more reliable simulation.