Multi-model space-time modeling method based on finite Gaussian mixture model

A technology of Gaussian mixture model and modeling method, which is applied in the field of modeling of nonlinear distributed parameter system, can solve the problem of high model complexity, and the modeling method of nonlinear distributed parameter system cannot adapt to the strong nonlinear and time-varying dynamics of the system , Affecting the accuracy and efficiency of modeling and other issues

Active Publication Date: 2019-10-25
GUANGDONG UNIV OF TECH
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  • Claims
  • Application Information

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Problems solved by technology

[0004] The present invention solves the problem that the existing nonlinear distributed parameter system modeling method cannot adapt to the system's strong nonlinearity, time-varying dynamics and large working range with multiple wor

Method used

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  • Multi-model space-time modeling method based on finite Gaussian mixture model
  • Multi-model space-time modeling method based on finite Gaussian mixture model
  • Multi-model space-time modeling method based on finite Gaussian mixture model

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Embodiment 1

[0144] A multi-model spatio-temporal modeling approach based on finite Gaussian mixture models, applied to nonlinear distributed parameter systems such as figure 1 shown, including the following steps:

[0145] S1. Based on the finite Gaussian mixture model, the nonlinear space obtained by the nonlinear distributed parameter system is divided into multiple local operation subspaces. The specific steps include:

[0146] S11. Obtain spatio-temporal training data: collect data from a nonlinear distributed parameter system as a data set, where u(t)∈R is the input signal of the nonlinear distributed parameter system; y(x,t)∈R is the measured Spatio-temporal data, that is, the temperature of the i-th sensor’s spatial location point at the j-th moment; x is a spatial variable that changes in the spatial domain Ω, t is a time variable, L is the length of time, and N is the number of sensors; select N The temperature of the L moments of the spatial position points is used as the spati...

Embodiment 2

[0247] This embodiment 2 is based on the modeling method of the embodiment 1, applied to the curing heat process in the semiconductor back-end packaging process, and simulates and verifies the two-dimensional curing heat process.

[0248] First build the experimental model of the curing furnace: the curing furnace is used to cure the chip connected to the lead frame at a specific temperature, and four rectangular heaters (h1-h4) are provided on the lead frame to provide heat sources, such as figure 2 As shown, 16 sensors are evenly installed on the lead frame at the same time to collect the spatio-temporal data of the temperature distribution changing with time during the curing process.

[0249] For comparison, the following error metrics are set:

[0250] 1) Space-time error:

[0251] 2) Absolute relative error:

[0252] 3) Space normalized absolute error:

[0253] 4) Time normalized absolute error:

[0254] 5) root mean square error:

[0255] In the experime...

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Abstract

The invention discloses a multi-model space-time modeling method based on a finite Gaussian mixture model. The method is applied to a nonlinear distribution parameter system, a nonlinear space obtained by the nonlinear distribution parameter system is divided into a plurality of local operation subspaces based on a finite Gaussian mixture model, and an original complex nonlinear space-time dynamicequation is summarized into a plurality of simple nonlinear space-time dynamic equations, so that local modeling is carried out; when all the local space-time models are integrated, a principal component regression method is adopted to calculate the weight of each local space-time model, the existence of multiple colinearity is avoided, and a global space-time model of a large working area is reconstructed through multi-model modeling. The method provided by the invention has better performance for a large-scale, strong-nonlinearity and time-varying system.

Description

technical field [0001] The invention relates to the field of modeling of nonlinear distributed parameter systems, in particular to a multi-model space-time modeling method based on a finite Gaussian mixture model. Background technique [0002] Many industrial processes, such as thermal processing, fluid flow, chemical engineering, etc., are not only time-dependent but also space-dependent. These systems are typical nonlinear distributed parameter systems (DPSs), usually using partial differential equations (PDEs) and other The corresponding initial conditions and boundary conditions are described. Since the input, output, and even the parameters of the nonlinear distributed parameter system will change in the time and space directions, they are coupled in time and space, and have infinite-dimensional characteristics, which make the modeling, control and optimization of the system become very difficult. [0003] At present, there are a lot of research results on the modelin...

Claims

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Application Information

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IPC IPC(8): G06F17/50
CPCG06F30/20
Inventor 徐康康杨海东印四华朱成就
Owner GUANGDONG UNIV OF TECH
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