Estimating noise characteristics in physical system simulations

A computing system comprising:

• one or more processors configured to:
• analyze model elements of an executable model to partition the model elements into one or more linear portions of the executable model and one or more nonlinear portions of the executable model, the executable model representing a physical system comprising a hydraulic system, an electrical system, a mechanical system, or a pneumatic system;
• execute the executable model to simulate behavior of the physical system, the simulating including, for each of multiple time intervals of the simulation:
• for a first nonlinear portion, computing a correlation matrix characterizing noise associated with one or more ports of the executable model, the computing comprising (1) determining a scattering matrix that corresponds to a portion of the physical system represented by the first nonlinear portion without accounting for any noise within the portion of the physical system, and (2) based on noise within the portion of the physical system, deriving the correlation matrix from the scattering matrix,
• identifying noise sources representing noise within the portion of the physical system based on the correlation matrix, and
• computing at least one characteristic of noise associated with each noise source;
• and
• output noise characteristics at selected ports of the executable model;
• wherein the simulating further includes
• linearizing the first nonlinear portion at a first operating point during a first of the time intervals of the simulation, and computing the correlation matrix based on a linear representation of the first nonlinear portion, and
• repeating the linearizing of the first nonlinear portion at a second operating point, where the second operating point occurs during a second of the time intervals of the simulation, and the repeating occurs after a time duration between the second operating point and the first operating point exceeds a tolerance.

One or more non-transitory computer-readable media, having stored thereon instructions that, when executed by a computing system, cause the computing system to perform operations comprising:

• analyzing model elements of an executable model to partition the model elements into one or more linear portions of the executable model and one or more nonlinear portions of the executable model, the executable model representing a physical system comprising a hydraulic system, an electrical system, a mechanical system, or a pneumatic system;
• executing the executable model to simulate behavior of the physical system, the simulating including, for each of multiple time intervals of the simulation:
• for a first nonlinear portion, computing a correlation matrix characterizing noise associated with one or more ports of the executable model, the computing comprising (1) determining a scattering matrix that corresponds to a portion of the physical system represented by the first nonlinear portion without accounting for any noise within the portion of the physical system, and (2) based on noise within the portion of the physical system, deriving the correlation matrix from the scattering matrix,
• identifying noise sources representing noise within the portion of the physical system based on the correlation matrix, and
• computing at least one characteristic of noise associated with each noise source;
• and
• outputting noise characteristics at selected ports of the executable model;
• wherein the simulating further includes
• linearizing the first nonlinear portion at a first operating point during a first of the time intervals of the simulation, and computing the correlation matrix based on a linear representation of the first nonlinear portion, and
• repeating the linearizing of the first nonlinear portion at a second operating point, where the second operating point occurs during a second of the time intervals of the simulation, and the repeating occurs after a time duration between the second operating point and the first operating point exceeds a tolerance.

A method comprising:

• analyzing, by one or more processors, model elements of an executable model to partition the model elements into one or more linear portions of the executable model and one or more nonlinear portions of the executable model, the executable model representing a physical system comprising a hydraulic system, an electrical system, a mechanical system, or a pneumatic system;
• executing the executable model to simulate behavior of the physical system, the simulating including, for each of multiple time intervals of the simulation:
• for a first nonlinear portion, computing a correlation matrix characterizing noise associated with one or more ports of the executable model, the computing comprising (1) determining a scattering matrix that corresponds to a portion of the physical system represented by the first nonlinear portion without accounting for any noise within the portion of the physical system, and (2) based on noise within the portion of the physical system, deriving the correlation matrix from the scattering matrix,
• identifying noise sources representing noise within the portion of the physical system based on the correlation matrix, and
• computing at least one characteristic of noise associated with each noise source;
• and
• outputting noise characteristics at selected ports of the executable model;
• wherein the partitioning includes sorting representations of equations corresponding to the model elements, and the sorting is based at least in part on a comparison between:
• (1) a magnitude of a time derivative of a variable in a first equation corresponding to a first model element, and (2) a magnitude of a nonlinear effect due to a presence of nonlinearity in the first equation.

One or more non-transitory computer-readable media, having stored thereon instructions that, when executed by a computing system, cause the computing system to perform operations comprising:

• analyzing model elements of an executable model to partition the model elements into one or more linear portions of the executable model and one or more nonlinear portions of the executable model, the executable model representing a physical system comprising a hydraulic system, an electrical system, a mechanical system, or a pneumatic system;
• executing the executable model to simulate behavior of the physical system, the simulating including, for each of multiple time intervals of the simulation:
• for a first nonlinear portion, computing a correlation matrix characterizing noise associated with one or more ports of the executable model, the computing comprising (1) determining a scattering matrix that corresponds to a portion of the physical system represented by the first nonlinear portion without accounting for any noise within the portion of the physical system, and (2) based on noise within the portion of the physical system, deriving the correlation matrix from the scattering matrix,
• identifying noise sources representing noise within the portion of the physical system based on the correlation matrix, and
• computing at least one characteristic of noise associated with each noise source;
• and
• outputting noise characteristics at selected ports of the executable model;
• wherein the partitioning includes sorting representations of equations corresponding to the model elements, and the sorting is based at least in part on a comparison between:
• (1) a magnitude of a time derivative of a variable in a first equation corresponding to a first model element, and (2) a magnitude of a nonlinear effect due to a presence of nonlinearity in the first equation.