Design Exploration

Solve complex engineering problems with no specialized competence required: Design Exploration tools support the automatic selection of the best suitable technique.

Why do Design Exploration?

Design Exploration capabilities empower users to explore various design alternatives and easily find optimal solutions. pSeven tools allow users to fully set up Design of Experiments studies, combine Design Optimization strategies, run Uncertainty Quantification and switch between techniques while solving design problems on the fly.

Design Exploration allows engineers to:

  • Develop trust in their models
  • Explore design alternatives
  • Perform trade-off studies
  • Discover bottlenecks
  • Identify models
  • Set goals

“Design Exploration (or Design Space Exploration) is both a class of quantitative methods and a category of software tools for systematically and automatically exploring very large numbers of design alternatives and identifying optimal performance parameters.”

B. Jenkins, Ora Research


Create a workflow describing your product or process

Design Exploration

Apply Design Exploration tools


Make decisions based on numbers

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. DoE can be used to perform reliable Surrogate-Based Optimization (SBO) or to generate a training data sample for a building of an accurate predictive model.


Create a simulation model


Define design variables and responses

Design of Experiments

Run a series of model evaluations

Model behavior can be very different in dimensionality, size, smoothness, noisiness etc., and the available number of model evaluations is often limited. To explore such models faster and more effective pSeven offers a variety of techniques including well-known batch algorithms and in-house proprietary adaptive search.

Adaptive Design of Experiments

Adaptive Design of Experiments (ADoE) considers model behavior before adding new points and takes into account linear and non-linear constraints of the model. ADoE supports 3 scenarios:

ADoE Uniform

1. Uniform

Feasible domain sampling:

  • Setup: variables and bounds, linear and non-linear constraints
  • Result: uniform sample in feasible domain
ADoE Explore

2. Explore

Response surface improvement:

  • Setup: variables and bounds, linear and non-linear constraints, an objective function
  • Result: sample in a feasible domain for better objective function approximation
ADoE Contour

3. Contour

Search for designs with given objective function value:

  • Setup: variables and bounds, linear and non-linear constraints, objective function and its required value
  • Result: sample in a feasible domain with given value of the objective function

Design Optimization

Design optimization is a process of finding the values of input parameters, which lead to the best performance of analytical or simulation model of a product or a manufacturing process under investigation. Ultimately, it answers the following questions:

  • How to improve product or process characteristics?
  • Which combination of input parameters is the best?
  • How to decrease the effect of input parameters variability on the overall product or process behavior?
Simulation model

Create a simulation model


Define design variables and goals


Run optimization

pSeven offers a complete set of in-house developed methods and algorithms to conduct optimization of one or multiple model objective functions subject to various constraints. It allows to efficiently solve both design optimization problems with fast to evaluate analytical models and the problems where the key challenge is expensive in terms of computing resources simulations.


Instead of tedious tuning of optimization algorithms internal parameters, in pSeven the user has to simply set the basic properties of the model (if known), such as its evaluation expensiveness, smoothness of responses etc. After that automatic and adaptive choice of specific design optimization algorithms based on this information is provided by SmartSelection technique.

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Analytical and simulation models used in engineering have a set of specific aspects that often blocks the using of open-source or academic optimization tool. Such aspects can be easily taken into account during the design optimization process in pSeven:

Large dimensionality

pSeven allows to handle optimization problems with:

  • Hundreds of design variables
  • Dozens of constraints
  • Up to 10 objective functions

Advanced problem statements

pSeven supports any combination of:

  • Continuous and discrete variables
  • Linear and non-linear constraints
  • Noisy, multiextremal and non-differentiable objectives

Long evaluation time

pSeven supports parallel execution of optimization procedures allowing to reduce the computational time of resource-consuming problems solution drastically.

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 can’t be found directly, more advanced research is required.


Bad fit = model parameters unknown


Good fit = model parameters identified!

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 a 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.

Uncertainty Quantification (UQ)

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.

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.

Uncertainty Propagation

pSeven allows efficiently quantify and deal with uncertainties in design variables and responses:

  • Manual selection of input distribution types
  • Automatic fitting of input and output samples to the available distribution type
  • Creating non-parametric distributions
  • Running Sensitivity Analysis to estimate the influence of uncertainties on product behavior

Distributions of uncertain design variables




Estimate the influence of uncertainties

Reliability Analysis

Some realizations of the model with uncertainties may satisfy all the design criteria, but some may fail. pSeven allows to easily assess the reliability of the product:

  • Variety of methods for model sampling available (eg. Monte Carlo, LHS etc.)
  • Approximation is used to drastically reduce the number of heavy simulation runs
  • Estimation of failure probability (N failures / N of simulations)

Distributions of uncertain design variables




Introduce constraint, e.g. stress safety factor

Failure domain

Failure domain found

Results and external 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 correlation analysis

Parameters dependency analysis

Parameters dependency analysis

Design points in parallel coordinates

Design points in parallel coordinates

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