Methods and apparatus for designing a system using the tensor convolution block toeplitz-preconditioned conjugate gradient (TCBT-PCG) method
AssigneeBBNT Solutions LLC
InventorRobert D. Preuss
Life of this patent
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Abstract
Systems and methods for designing or determining parameters for a system are disclosed. These systems and methods exploit the Tensor Convolution Block Toeplitz (TCBT) structure involved in certain systems wherein a symmetric positive definite linear system of equations needs to be solved in the design or determination of the parameters for the system. Further, these methods and systems employ a TCBT-PCG process that uses a fast matrix-vector multiply in order to improve the computational efficiency in the design or determination of these system parameters.
Claims19
A process for computing a plurality of controllable parameters that affect the operation of a system, comprising:
- generating a sequence of matrices V(r) using a known system;
- generating a sequence of matrices S(t) using an input signal, wherein the sequence of matrices V(r) and the sequence of matrices S(t) correspond to a Tensor-Convolution Block-Toeplitz structure;
- generating a vector b using the input signal and the known system;
- and
- generating the plurality of controllable parameters using the sequence of matrices V(r), the sequence of matrices S(t), and the vector b by a process employing a fast matrix-vector multiply.
A system, wherein a plurality of controllable parameters that affect the operation of the system are expressible as a vector x, and wherein a constraint relationship related to the controllable parameters, is expressible in the form of a matrix A associated with the controllable parameters, and with a set of constraint limits, b, such that Ax=b, comprising:
- a memory for storing a sequence of matrices V(r), a sequence of matrices S(t), and a vector b, wherein the sequence of matrices V(r) and the sequence of matrices S(t) correspond to a Tensor Convolution Block Toeplitz structure, wherein the sequence of matrices V(r) is generated using a known system, and wherein the sequence of matrices S(t) is generated using an input signal;
- and
- a processor for determining a plurality of controllable parameters, x, using the sequence of matrices V(r), the sequence of matrices S(t), and the vector b, by a process employing a fast matrix-vector multiply, and wherein the vector b is generated using the input signal and the known system.
A system for computing a plurality of controllable parameters that affect the operation of a system, comprising:
- means for generating a sequence of matrices V(r) using a known system;
- means for generating a sequence of matrices S(t) using an input signal, wherein the sequence of matrices V(r) and the sequence of matrices S(t) correspond to a Tensor-Convolution Block-Toeplitz structure;
- means for generating a vector b using the input signal and the known system;
- and
- means for generating the plurality of controllable parameters using the sequence of matrices V(r), the sequence of matrices S(t), and the vector b by a process employing a fast matrix-vector multiply.
A computer-readable medium capable of causing a computer to perform the following steps for computing a plurality of controllable parameters that affect the operation of a system:
- generating a sequence of matrices V(r) using a known system;
- generating a sequence of matrices S(t) using an input signal, wherein the sequence of matrices V(r) and the sequence of matrices S(t) correspond to a Tensor-Convolution Block-Toeplitz structure;
- generating a vector b using the input signal and the known system;
- generating the plurality of controllable parameters using the sequence of matrices V(r), the sequence of matrices S(t), and the vector b by a process employing a fast matrix-vector multiply.
A process for reducing vibrations, comprising
- generating a sequence of matrices V(r) using a known system;
- generating a sequence of matrices S(t) using an input signal, wherein the sequence of matrices V(r) and the sequence of matrices S(t) correspond to a Tensor-Convolution Block-Toeplitz structure;
- generating a vector b using the input signal and the known system;
- and
- generating the plurality of controllable parameters using the sequence of matrices V(r), the sequence of matrices S(t), and the vector b by a process employing a fast matrix-vector multiply.
A process for determining a plurality of parameters for an unknown system given a known system, comprising
- generating a sequence of matrices V(r) using the known system;
- generating a sequence of matrices S(t) using an input signal, wherein the sequence of matrices V(r) and the sequence of matrices S(t) correspond to a Tensor-Convolution Block-Toeplitz structure;
- generating a vector b using the input signal and the known system;
- and
- generating the plurality of parameters using the sequence of matrices V(r), the sequence of matrices S(t), and the vector b by a process employing a fast matrix-vector multiply.
Dependencies are inferred from the claim text.