System Identification

While ObjexxSISAME provides an excellent and efficient platform for simulation of lumped parameter systems, it is the system identification capability that makes it unique. We explore what that is and how ObjexxSISAME achieves it here.

Optimal Structures

System identification, or inverse modeling, of structures is essentially inverse simulation, where we start with the known behavior (such as from testing or finite element simulation) of a system and back out the optimal structure to match that behavior. This has many practical applications, such as:

• Finding the best model of modest complexity for a given structure so that a large matrix of simulations can be performed.
• Finding an optimal design/redesign of a structure to achieve a desired "improved" behavior, such as a safety-modified occupant compartment motion.
• Distilling a finite element model of an existing structure to an ObjexxSISAME model to optimize the design for safety or some other criterion or to tune the FEM model to better track test results.

Finite element modeling (FEM) of both small and large deformation events has revolutionized our ability to verify the behavior of complex structures before they are built. But FEM is a poor tool for design, being too difficult and expensive to use for refining a structure to improve the behavior. ObjexxSISAME is designed to complement FEM modeling and provide that missing high-level design capability that allows a direct leap to a better design.

The ObjexxSISAME Methodology

At its simplest, ObjexxSISAME performs a parametric simulation, accumulating a time-global matrix that expresses the contribution of the extracted parameters to the equations of motion, which can then be solved for the optimal parameters. ObjexxSISAME actually does more than this, such as optimizing the parameters to match a weighted combination of the acceleration, velocity, and displacement forms of the equations of motion so that the resulting model tracks well in all of these motion domains. Estimated parameter values can also be supplied, as can relationships between parameters. ObjexxSISAME also has the ability to simulate part of a model while extracting optimal parameters on other parts, and using a mix of fully and partially defined components along with components where all parameters are being extracted. Other "targets" for the solution, such as a cost-based function, could be used as well. By supporting this wide range of solution capabilities ObjexxSISAME serves as a design optimization workbench.

To read the full mathematical formulation behind ObjexxSISAME please contact Objexx.

Other Approaches

Many FEM and hybrid simulation tools have recently added so-called optimization capabilities that, in theory, provide an inverse modeling capability. A closer examination of these reveals that the main approach used is a search and local gradient descent over the full N-dimensional parameter space, which is extremely slow and not likely to find a global optimum, and provides no guarantee on the quality of the best solution found. An example of this is the LS-OPT add-on tool for the LS-DYNA FEM application or the Optimizer utility for MADYMO.

ObjexxSISAME was designed from the ground up as a parametric simulation and optimization tool, rather than having some optimization capability grafted on later. As a result ObjexxSISAME does a more direct optimization process with much less need for iteration and a much higher confidence that an optimal solution is produced.

Notes

For purely linear systems there are nice frequency domain methods for system identification. ObjexxSISAME is designed for the highly nonlinear large deformation impact events where such methods are not available.