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Global morphological analysis method for high-dimensional nonlinear system

A nonlinear system and morphological analysis technology, applied in complex mathematical operations, geometric CAD, instruments, etc., can solve the problems of large memory consumption and low calculation efficiency, and achieve the effect of avoiding repeated calculations

Pending Publication Date: 2022-07-22
NAVAL UNIV OF ENG PLA
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  • Summary
  • Abstract
  • Description
  • Claims
  • Application Information

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Problems solved by technology

For the global analysis of high-dimensional nonlinear energy well systems, there are problems of large memory consumption and low computational efficiency

Method used

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  • Global morphological analysis method for high-dimensional nonlinear system
  • Global morphological analysis method for high-dimensional nonlinear system
  • Global morphological analysis method for high-dimensional nonlinear system

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Experimental program
Comparison scheme
Effect test

Embodiment 1

[0139] Select f = 0.68, at this time, there are two stable period 1 attractors in the system response, and the phase trajectories of different attractors are as follows Figure 8 shown, where A 1 The attractor amplitude is greater than A 2 Attractor amplitude. According to the PMDCM method, if the analysis plane is selected -2≤z 1 ≤2, -2≤y 1 ≤2, fixed variable z 2 , y 2 The initial conditions are all 0, the analysis plane is divided into discrete cells of 100 × 100, a total of 10,000 original cells, and the number of parallel calculations N is set. s =100, the calculation result is as follows Figure 9 (a). The blue star in the picture is A 1 The position of the attractor, the red area is the corresponding attraction area, and the red star is A 2 Attractor position, the blue area is the corresponding attraction domain, as can be seen from the figure, A 1 The area occupied by the attractor attraction domain is 86.39% of the entire analysis plane, while A 2 The attrac...

Embodiment 2

[0141] Select f = 11.3, at this time, there is a stable period 1 attractor and a stable quasi-periodic attractor in the system response. Different attractor phase trajectories are as follows Figure 10 shown. If the analysis plane is selected -5≤z 1 ≤5, -5≤y 1 ≤5, fixed variable z 2 =0, y 2 =0, the calculation result is as follows Figure 11 As shown in (a), if the analysis plane is selected -8≤z 2 ≤8, -10≤y 2 ≤10, fixed variable z 1 =0, y 1 =0, the calculation result is as follows Figure 11 (b). The red star in the figure is the position of the period 1 attractor, while the green ring is the position of the quasi-periodic attractor, and the blue and red areas correspond to the attraction domains of the periodic attractor and the quasi-periodic attractor, respectively. from Figure 11 From (a), it can be seen that in z 1 -y 1 In the analysis plane, the periodic 1 attractor is located in its own domain of attraction, while the quasi-periodic attractor connects the...

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Abstract

The invention discloses a global morphological analysis method for a high-dimensional nonlinear system. The method comprises the following steps: 1) establishing a dynamic system model of mechanical equipment to be subjected to vibration reduction; 2) discretizing a continuous space of the dynamic system into a cellular space, selecting an analysis plane, and establishing a cellular matrix Z; 3) performing parameter initialization processing; 4) screening unprocessed cells from the cell matrix Z in sequence according to the progressive increase sequence of the line mark index r to be used for filling null lines of the identification matrix Zs; 5) carrying out parallel numerical calculation on the filled identification matrix Zs to obtain cell mapping image cells, and assigning values to the identification matrix Zs again; 6) carrying out scanning judgment on the identification matrix Zs subjected to image cell processing; and 7) post-processing the mapping sequence. The method is used for qualitatively analyzing different response mechanisms such as periodicity, quasi-periodicity or chaos, the cross mapping sequences can be combined, and the cells are prevented from being repeatedly calculated.

Description

technical field [0001] The invention relates to the technical field of dynamic analysis of mechanical equipment, in particular to a global morphological analysis method of a high-dimensional nonlinear system. Background technique [0002] Due to its advantages of small additional mass, directional energy transfer, and vibration absorption frequency bandwidth, nonlinear energy wells have been a research hotspot in the field of passive control technology in the past two decades, and have been successively used in mechanical engineering, civil engineering, aerospace engineering, acoustic control, Vibration energy harvesting and many other fields have been applied. Nonlinear energy well systems belong to the category of high-dimensional strong nonlinearity, in which there are abundant nonlinear dynamical behaviors. However, most of the current research work on nonlinear energy trap systems is carried out within the scope of deterministic system theory. In fact, when nonlinear e...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F30/17G06F30/20G06F17/13G06F119/14
CPCG06F30/17G06F30/20G06F17/13G06F2119/14
Inventor 杨庆超楼京俊李爽刘树勇柴凯
Owner NAVAL UNIV OF ENG PLA