State projection via minimization of error energy
AssigneeThe MathWorks, Inc.
InventorsVictor Chudnovsky, Jeff Wendlandt
Life of this patent
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Abstract
The present invention improves in one aspect the accuracy, efficiency, and robustness of fixed-step solvers when simulating a physical system that does not change in energy at the critical event. The present invention uses the energy of the error as the figure of merit in finding the first state of the system under the new constraints. The present invention enables a fixed-step solver to be more robust even when the critical event falls between two time samples. The present invention may also be applied to variable-step solvers. Moreover, the present invention may also be used to simulate a physical system when the energy changes at the critical event in the physical system.
Claims27
A method comprising:
- calculating, using a processor, a first state of a system under a first set of constraints at a first time sample in a simulation of the system;
- calculating, using a processor, a second state of the system under the first set of constraints at a second time sample in the simulation of the system;
- detecting, using a processor, an event signaling a change from the first set of constraints to a second set of constraints, the event occurring between the first time sample and the second time sample;
- and
- calculating, using a processor, a new state of the system under the second set of constraints at the second time sample, the new state being calculated based at least in part on an energy of error function, the energy of error function being a mathematical composition of:
- an error function that finds a difference between a third state of the system under the second set of constraints and the second state of the system, and
- an energy function for the system as dictated by one or more equations that represent one or more dynamics of the system.
A non-transitory computer-readable medium storing instructions, the instructions comprising instructions for:
- calculating a first state of a system under a first set of constraints at a first time sample in a simulation of the system;
- calculating a second state of the system under the first set of constraints at a second time sample in the simulation of the system;
- detecting an event signaling a change from the first set of constraints to a second set of constraints, the event occurring between the first time sample and the second time sample;
- and
- calculating a new state of the system under the second set of constraints at the second time sample, the new state being calculated based at least in part on an energy of error function, the energy of error function being a mathematical composition of:
- an error function that finds a difference between a third state of the system under the second set of constraints and the second state of the system, and
- an energy function for the system as dictated by one or more equations that represent one or more dynamics of the system.
An apparatus comprising:
- a processor for executing instructions stored in a memory;
- said memory storing instructions for:
- calculating a first state of a system under a first set of constraints at a first time sample in a simulation of the system,
- calculating a second state of the system under the first set of constraints at a second time sample in the simulation of the system,
- detecting an event signaling a change from the first set of constraints to a second set of constraints, the event occurring between the first time sample and the second time sample, and
- calculating a new state of the system under the second set of constraints at the second time sample, the new state being calculated based at least in part on an energy of error function, the energy of error function being a mathematical composition of:
- an error function that finds a difference between a third state of the system under the second set of constraints and the second state of the system, and
- an energy function for the system as dictated by one or more equations that represent one or more dynamics of the system.
Dependencies are inferred from the claim text.