Local projection and global interpolation-based nonlinear model reduction method

Abstract

The invention belongs to the technical field of integrated circuits and relates to a local projection and global interpolation-based nonlinear model reduction method. The method comprises the steps of reading a circuit network list file, and performing writing in a state-space equation form; obtaining a system state track by utilizing "training input", selecting an expansion point on the state track, and performing piecewise linearization on a nonlinear system; generating a proper local projection matrix for each linear system in piecewise linear systems; transforming the local projection matrix to enable coordinate systems of local projection reduced-order subsystems to be consistent; and for each piecewise linear system, performing projection on the system by utilizing the transformed local projection matrix, and performing global interpolation on a projection reduced-order system to obtain a reduced-order system. According to the method, the transformation from local coordinates to global coordinates in a conventional method is avoided; and the global interpolation is adopted, so that the scale of required local reduced-order systems is remarkably reduced.

Description

technical field [0001] The invention belongs to the technical field of integrated circuits and relates to a nonlinear model order reduction method based on local projection and global interpolation. Background technique [0002] In the prior art, in order to shorten the circuit simulation time, the model order reduction method is widely used in fast circuit simulation and modeling. With the maturity of the model reduction methods for linear time-invariant systems, the model reduction of nonlinear systems has gradually attracted attention. For the weakly nonlinear system, the model reduction method is mainly to expand the nonlinear system to a linear system near a certain equilibrium point, and then use the Krylov subspace projection method to generate the projection matrix of the linearized system, and obtain step-down system. Since the nonlinear system in this method is only approximated near an equilibrium point, these methods are only applicable to weakly nonlinear syst...

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Problems solved by technology

[0004] One problem with the trajectory-based nonlinear model reduction method is that it relies on the global projection matrix to construct the reduced-order system; its global projection matrix is ​​generally constructed by combining the projection matrices of all expansion points; when there are many expansion points, the global The size of the projection matrix will be very large, so the scale of the reduced-order system cannot be significantly reduced; in order to solve this problem, a nonlinear model reduction method based on local projection is disclosed in the literature. For a certain state point in the state space, the method uses its The nearest k points are used to construct a local projection matrix, and the local nonlinear reduction system is obtained by interpolation after the local projection matrix is ​​reduced; the projection matrix of this method only depends on the adjacent k points, and its scale is much smaller than the original one based on The global projection matrix in the nonlinear model reduction method of the trajectory; however, there are still some problems with this method: first, during simulation, this method still needs a global projection matrix, and the solution of the local coordinate system needs to be projected back to the global projection matrix The coordinate system where the state point is located is used to determine the neighboring points of the state point and determine the local projection reduction system; on the other hand, because the interpolation of this method is performed locally, in order to ensure the accuracy of the interpolation, it must be guaranteed for each state point Ability to find 5-10 neighboring local reduced order systems for interpolation; this means that the method needs to store a large number of local reduced order systems

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