Analytical consistent sensitivities for external intervening between two sequential equilibriums
Embodiments provide methods and systems for optimizing a physical system. One such example embodiment begins by defining, in memory of a processor, a model comprising a plurality of design variables where the defined model represents a real-world physical system where behavior of the model is given by an equation that includes corresponding sensitivity equations for the plurality of design variables. The example method continues by iteratively optimizing the model with respect to a given design variable of the plurality, using the equation. In an example embodiment, the optimizing includes the processor accounting for a given external intervention event between equilibriums by adding a term for design response sensitivity of the given one of the plurality of design variables to the corresponding sensitivity equation of the given design variable. Such optimizing results in an improved optimization of the real-world physical model.
1. A computer-implemented method of optimizing a real-world physical system, the method comprising:
defining, in a memory of a processor, a model comprising a plurality of design variables, including loading conditions and boundary conditions for at least a first and a second sequential equilibrium of a behavior of interest in a respective optimization iteration, the defined model representing a real-world physical system where behavior of the defined model is given by an equation stored in the memory, the equation including corresponding sensitivity equations for the plurality of design variables; and
by the processor, iteratively optimizing the defined model with respect to a first one of the plurality of design variables and a second one of the plurality of design variables using the equation, the optimizing including the processor accounting for a given external intervention event between sequential equilibriums of the respective optimization iteration by:
(1) adding a term for design response sensitivity of the first one of the plurality of design variables to a corresponding sensitivity equation of the second one of the plurality of design variables, and
(2) adding a term for design response sensitivity of the second one of the plurality of design variables to a corresponding sensitivity equation of the first one of the plurality of design variables, the processor iteratively optimizing the defined model resulting in an improved optimization of the real-world physical system.
2. The method of claim 1 wherein iteratively optimizing the defined model further comprises:
modifying the defined model based upon a sensitivity solution of the design response sensitivity of the first one of the plurality of design variables and the second one of the plurality of design variables.
3. The method of claim 2 wherein modifying the defined model comprises:
modifying at least one of the first one of the plurality of design variables and the second one of the plurality of design variables in a direction indicated by the sensitivity solution of the design response sensitivity.
4. The method of claim 1 wherein the plurality of design variables further include at least one of: a dimension, a thickness, a width, a radius, a composite material angle, a sizing variable, a material interpolation variable for topology, a shape variable, and a bead variable.
5. The method of claim 1 wherein iteratively optimizing the defined model optimizes at least one of: a structural, a computational fluid dynamics (CFD), a thermo-mechanical, an electro-mechanical, an electromagnetic, an acoustic, and a fluid-structural response of the defined model.
6. The method of claim 1 wherein the adding the term for design response sensitivity of the first one of the plurality of design variables and the second one of the plurality of design variables results in consistently including the given external intervention event in the corresponding sensitivity equation of the first one of the plurality of design variables and the second one of the plurality of design variables for the iterative optimizing.
7. The method of claim 1 wherein adding the term for design response sensitivity of the first one of the plurality of design variables and the second one of the plurality of design variables is performed using an adjoint or a direct method.
8. The method of claim 1 wherein the iteratively optimizing determines a parameter value for the first one of the plurality of design variables and the second one of the plurality of design variables.
9. A system for optimizing a real-world physical system, the system comprising:
a processor; and
a memory with computer code instructions stored thereon, the processor and the memory with the computer code instructions being configured to cause the system to:
define, in the memory, a model comprising a plurality of design variables, including loading conditions and boundary conditions for at least a first and a second sequential equilibrium of a behavior of interest in a respective optimization iteration, the defined model representing the real-world physical system where behavior of the defined model is given by an equation stored in the memory, the equation including corresponding sensitivity equations for the plurality of design variables; and
by the processor, iteratively optimize the defined model with respect to a first one of the plurality of design variables and a second one of the plurality of design variables using the equation, the optimizing including the processor accounting for a given external intervention event between sequential equilibriums of the respective optimization iteration by:
(1) adding a term for design response sensitivity of the first one of the plurality of design variables to a corresponding sensitivity equation of the second one of the plurality of design variables, and
(2) adding a term for design response sensitivity of the second one of the plurality of design variables to a corresponding sensitivity equation of the first one of the plurality of design variables, the processor iteratively optimizing the defined model resulting in an improved optimization of the real-world physical system.
10. The system of claim 9 wherein the processor and the memory with the computer code instructions are further configured to cause the system to:
modify the defined model based upon a sensitivity solution of the design response sensitivity of the first one of the plurality of design variables and the second one of the plurality of design variables.
11. The system of claim 10 wherein the processor and the memory with the computer code instructions are further configured to cause the system to:
modify the first one of the plurality of design variables and the second one of the plurality of design variables in a direction indicated by the sensitivity solution of the design response sensitivity.
12. The system of claim 9 wherein the plurality of design variables further include at least one of: a dimension, a thickness, a width, a radius, a composite material angle, a sizing variable, a material interpolation variable for topology, a shape variable, and a bead variable.
13. The system of claim 9 wherein iteratively optimizing the defined model optimizes at least one of: a structural, a computational fluid dynamics (CFD), a thermo-mechanical, an electro-mechanical, an electromagnetic, an acoustic, and a fluid-structural response of the defined model.
14. The system of claim 9 wherein the adding the term for design response sensitivity of the first one of the plurality of design variables and the second one of the plurality of design variables results in consistently including the given external intervention event in the corresponding sensitivity equation of the first one of the plurality of design variables and the second one of the plurality of design variables for the iterative optimizing.
15. The system of claim 9 wherein adding the term for design response sensitivity of the first one of the plurality of design variables and the second one of the plurality of design variables is performed using an adjoint or a direct method.
16. The system of claim 9 wherein the iteratively optimizing determines a parameter value for the first one of the plurality of design variables and the second one of the plurality of design variables.
17. A non-transitory computer program product for optimizing a real-world physical system, the non-transitory computer program product executed by a server in communication across a network with one or more clients and comprising:
a computer readable medium, the computer readable medium comprising program instructions which, when executed by a processor, causes the processor to:
define, in memory of the processor, a model comprising a plurality of design variables, including loading conditions and boundary conditions for at least a first and a second sequential equilibrium of a behavior of interest in a respective optimization iteration, the defined model representing the real-world physical system where behavior of the defined model is given by an equation stored in the memory, the equation including corresponding sensitivity equations for the plurality of design variables; and
iteratively optimize the defined model with respect to a first one of the plurality of design variables and a second one of the plurality of design variables using the equation, the optimizing including the processor accounting for a given external intervention event between sequential equilibriums of the respective optimization iteration by:
(1) adding a term for design response sensitivity of the first one of the plurality of design variables to a corresponding sensitivity equation of the second one of the plurality of design variables, and
(2) adding a term for design response sensitivity of the second one of the plurality of design variables to a corresponding sensitivity equation of the first one of the plurality of design variables, the processor iteratively optimizing the defined model resulting in an improved optimization of the real-world physical system.