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CUSTOM MATHEMATICAL MODELIZATION

 AND OPTIMIZATION

OF PRODUCTS, EQUIPMENTS, UNIT OPERATIONS, ETC.

 

                          

Pragmathic offers a very pertinent mix of expertise that can be used to customize solutions to your situation. We can help you optimizing many aspects of your industrial activities and increasing your plant's profitability and competitiveness.

Whether you need to optimize a product (weight, volume, performance, cost, temperature rise, ...), improve a unit operation or equipment, troubleshoot your process or identify variability controlling factors, our knowledge in fundamental engineering sciences, mathematics and statistics can deliver cost-effective high fidelity models and solutions.

In some cases, our work has led to patents. If you need to simulate and optimize something unusual, we can help you!

 

Fundamental engineering sciences
 
Transport phenomena (momentum, heat, mass, diffusion)
Thermodynamics
Chemical and biochemical reaction kinetics

Physic
Rheology 

Simulation numerical methods
 

Analytical developments
Finite elements, volumes and differences (ex.: CFD)
Statistical multivariate analysis
Dimensional analysis

Surface response methodology

Data acquisition methods
 
Lab + design of experiments
Process + DOE
Operation databases

Optimization methods
 
Marquardt
Generalized reduced gradient
LP, QP, MILP, MINLP
Dynamic programming

Examples of tailored applications

(1) Thermodynamic model of the solid Lithium-Polymer battery technology (download here)

(2) Finite volume heat, mass and momentum transfer in a steam reboiler (capacity maximization)

 

 

 

 

(3) Computer simulation aided design of a calorimeter able to measure heat rates of 0.5 to 10 W within 0.1W.

 

 

csfmodel.gif (19977 octets)

 

(4) Statistical prediction model (PLS) of a TMP pulp freeness

 
(5)
Stress in a pressed Lithium-Polymer cell (MSC Nastran for Windows)

 

 

  

 

Application example: design optimization of a new automatic door operator
 
Step 1: Using design of experiments, find design weaknesses vs life span and noise. Factors respectively found: bearing and chain sizes.
 
Step 2: Develop a life span model to meet design specs (100,000 cycles), minimize components costs and support manufacturing process quality control. Ex.: model predicted a reject rate of X% at 95% confidence level with no change on the original components selection.

 | Design of experiments (DOE)

We design custom experimental programs using two different approaches as required:

the extensive Montgomery's Response Surface Methodology, in which the Taguchi methods are a special case,
 

the Dorian Shainin techniques especially developped to solve quality problems in manufacturing processes. 

   

   


 

 | Multivariate Multivariate statistical analysis
 
Many multivariate analysis methods are available: partial least squares (PLS), principal component analysis and regression, general linear or non-linear (Marquardt) multiple regression analysis, and dimensional analysis (an often neglected approach).

We have developped special tools to handle cases where non-linear effects and variable time lags happen. We have also developped means to check the level of information losses in compressed archived data.  Go here for more information.

   

 

Main commercial softwares used: Umetri Simca-p and Modde (multivariate statistical analysis and DOE), Visual basic, Matlab, MSC Nastran for Windows (finite element analysis).

   
 

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Copyright 2014 Pragmathic Inc.
Updated Feb 19, 2014

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