Method for structural optimization of a design and cost of a physical object

1. A method of manufacturing a physical object by for optimizing a design of the physical object using a topology optimization algorithm, wherein the physical object is a structural part of a vehicle body of a land vehicle, sea vehicle, or air vehicle, the method comprising:

performing, by a computer, steps of:

obtaining, for topology optimization, a data representation of the design of the physical object, the data representation including a plurality of elements;

performing image processing on the data representation of the design of the physical object to determine plural element clusters, wherein each element cluster comprises a plurality of the elements with varied material densities;

converting the data representation of the design of the physical object to a converted design comprising elements with full material and elements without material;

performing image feature extraction on the converted design to extract geometric features of the physical object;

estimating a cost model for the physical object based on the extracted geometric features of the physical object and a manufacturing process for the physical object, wherein the manufacturing process comprises at least one of a stamping process, a casting process, a 3D printing process, a milling process, and an extruding process;

performing a numerical estimation to determine derivatives of the cost model with respect to a material density of each element cluster of the data representation;

computing at least one analytical derivative of a structural performance metric of the design, wherein the structural performance metric is based on at least one of a structural performance of the physical object, comprising a stiffness parameter or a stress parameter, and a characteristic property of the physical object, comprising a mass parameter, a geometric parameter or a volume parameter;

optimizing the design of the physical object by automatically optimizing at least one of a topology, a topometry, a topography, a shape and a size of the physical object using the topology optimization algorithm, wherein optimizing the design of the physical object uses manufacturing cost of the determined cost model directly as an objective function of the topology optimization algorithm in combination with constraints determined based on the structural performance metric, by iteratively performing:

varying the material density of at least one of the plurality of elements of at least one element cluster based on the analytical derivative of the structural performance metric, and further based on the estimated derivatives of the cost model,

estimating a cost using the cost model for the design based on the data representation including the plurality of elements with the varied material density,

determining whether at least one termination criterion is met;

generating and outputting, to at least one manufacturing machine, a signal comprising the data representation including the plurality of elements with the varied material density of the design for which the estimated cost is optimized in case the termination criterion has been met; and

performing, by the at least one manufacturing machine, a step of:

performing the manufacturing process comprising at least one of the stamping process, the casting process, the 3D printing process, the milling process, and the extruding process for manufacturing the physical object based on the optimized design of the physical object indicated in the signal.

2. The method according to claim 1 , wherein the method further comprises, by the computer,

determining the manufacturing process for manufacturing the physical object;

estimating the cost model as a manufacturing cost model for the physical object based on the determined manufacturing process.

3. The method according to claim 2 , wherein

estimating the manufacturing cost model comprises, for estimating a manufacturing cost of the physical object, using at least one of a custom model, empirical data, image or geometry processing libraries, cost estimators based on machine learning models, and analytical models.

4. The method according to claim 1 , wherein

performing the numerical estimation to determine the derivatives of the cost model with respect to the material density of each element cluster of the data representation uses direct numerical estimation based on a finite difference method for calculating the finite differences.

5. The method according to claim 4 , wherein

performing the numerical estimation to determine the derivatives of the cost model with respect to the material density of each element cluster further comprises mapping the calculated finite differences for each element cluster to individual elements of the element cluster.

6. The method according to claim 5 , wherein

mapping the calculated finite differences for each element cluster to individual elements is based on weighting an average finite difference for the cluster with a difference in density of the individual elements.

7. The method according to claim 1 , wherein

determining the plural element clusters comprises grid-based clustering or state-based clustering.

8. The method according to claim 1 , wherein

the method comprises randomizing a cluster size of the element cluster by using a different grid size in each iteration.

9. The method according to claim 1 , wherein

varying the material density of at least one of the plurality of elements of at least one element cluster includes varying the material density based on an update signal,

wherein the update signal is generated based on the derivatives of the cost model estimated via the cluster-based finite difference and on the at least one analytical derivative computed using an analytical formula for the structural performance metric based on finite element simulations.

10. The method according to claim 9 , wherein

generating the update signal is based on using a predetermined gradient-based optimization method, in particular a generalized optimality criteria method.

11. The computer-implemented method according to claim 1 , wherein

the physical object is a part of an autonomous device.

12. The method according to claim 1 , wherein

the physical object is a structural part of a car body, in particular a car hood frame, a car door frame, a car pillar, a side sill, a bumper, a front rail, a crashbox, a floor panel, or a crossmember.

13. The method according to claim 1 , wherein

the method is performing the numerical estimation exclusively to determine derivatives of the cost model with respect to the material density of each element cluster individually.

14. The method according to claim 1 , wherein

the method is performing the numerical estimation to determine derivatives of the cost model with respect to the material density at least partially in parallel to estimating at least one physical performance parameter of the physical object used as criterion in the topological optimization algorithm.

15. The method according to claim 1 , wherein

the cost model further comprises at least one of

an environmental cost model, a greenhouse gas emission model, a CO 2 gas emission model, a renewable resource energy model, a natural resource model, a toxicity model,

a social cost model, a model describing compliance with human right standards or labor right standards, and

a logistic cost model.

16. The method according to claim 1 , wherein

performing the numerical estimation to determine derivatives of the cost model with respect to the material density of each element uses finite differencing or automatic differentiation.

17. The method according to claim 1 , wherein

the topology optimization algorithm is

a gradient-based topology optimization algorithm, or

a non-gradient based topology optimization algorithm, in particular an evolutionary level set method, or

a heuristic non-gradient topology optimization algorithm, in particular an evolutionary structural optimization method, a hybrid cellular automata by integrating cost sensitivities via energy scaling method.

18. A method of manufacturing a physical object by optimizing a design of the physical object using a topology optimization algorithm, wherein the physical object is a structural part of a building, a civil engineering device or a medical engineering device, the method comprising:

performing, by a computer, steps of:

obtaining, for topology optimization, a data representation of the design of the physical object, the data representation including a plurality of elements;

performing image processing on the data representation of the design of the physical object to determine plural element clusters, wherein each element cluster comprises a plurality of the elements with varied material densities;

converting the data representation of the design of the physical object to a converted design comprising elements with full material and elements without material;

performing image feature extraction on the converted design to extract geometric features of the physical object;

estimating a cost model for the physical object based on the extracted geometric features of the physical object and a manufacturing process for the physical object, wherein the manufacturing process comprises at least one of a stamping process, a casting process, a 3D printing process, a milling process, and an extruding process;

performing a numerical estimation to determine derivatives of the cost model with respect to a material density of each element cluster of the data representation;

computing at least one analytical derivative of a structural performance metric of the design, the structural performance metric is based on at least one of a structural performance of the physical object, comprising a stiffness parameter or a stress parameter, and a characteristic property of the physical object, comprising a mass parameter, a geometric parameter or a volume parameter;

optimizing the design of the physical object by automatically optimizing at least one of a topology, a topometry, a topography, a shape and a size of the physical object using the topology optimization algorithm, wherein optimizing the design of the physical object uses manufacturing cost of the determined cost model directly as an objective function of the topology optimization algorithm in combination with constraints determined based on the structural performance metric, by iteratively performing:

varying the material density of at least one of the plurality of elements of at least one element cluster based on the analytical derivative of the structural performance metric, and further based on the estimated derivatives of the cost model,

estimating a cost using the cost model for the design based on the data representation including the plurality of elements with the varied material density,

determining whether at least one termination criterion is met;

generating and outputting, to at least one manufacturing machine, a signal comprising the data representation including the plurality of elements with the varied material density of the design for which the estimated cost is optimized in case the termination criterion has been met; and

performing, by the at least one manufacturing machine, a step of:

performing the manufacturing process comprising at least one of the stamping process, the casting process, the 3D printing process, the milling process, and the extruding process for manufacturing the physical object based on the optimized design of the physical object indicated in the signal.