scholarly journals Research on Fault Evolution Feature Extraction and Identification of Sun Gear Cracks in Planetary Gearbox Based on Volterra High-Order Kernel Generalized Frequency Response Graphic Analysis

2018 ◽  
Vol 2018 ◽  
pp. 1-18
Author(s):  
Haitao Wang ◽  
Zhenya Kang ◽  
Lichen Shi ◽  
Kun Wang ◽  
Kun Li
Keyword(s):  
Frequency Response ◽  
Kernel Function ◽  
Reproducing Kernel ◽  
Volterra Series ◽  
Reproducing Kernel Hilbert Space ◽  
High Order ◽  
Volterra Model ◽  
Third Order ◽  
The Third ◽  
Order Kernel

In this paper, relying on the Volterra series nonlinear system model and the high-order kernel Hilbert’s reconstructed kernel fast solved algorithm, a fault feature frequency domain identification method based on Volterra high-order kernel generalized frequency response graph analysis is proposed. Firstly, the method uses the system input and output vibration signals to determine the Volterra model. Then, the Volterra high-order kernel function is solved quickly by reproducing kernel Hilbert space method, and the generalized frequency response function is used to identify the model. Finally, multidimensional high-order spectral pattern analysis is used to separate and extract the fault and degree characteristic information implied by frequency and phase coupling in the third-order kernel function. Following the theoretical approach, in the experimental part, this paper uses the planetary gearbox fault loading test rig to complete the data collection and establishes the Volterra experimental model through the measured data. The generalized frequency responses of each order kernel function are compared and analyzed and the capability of distinguishing and the adaptability of different order kernel functions for the degree of crack failure are discussed. The effects of changing the memory length of the Volterra model and the order of the kernel function on the recognition result are verified. The final experimental results show that the use of reproducing kernel Hilbert space can effectively avoid the dimension disaster problem that occurs in the high-order kernel solution process. Moreover, the third-order kernel can describe more intuitively the nonlinear system model under multifactor coupling than the second-order kernel. Finally, Volterra series model the third-order kernel’s generalized frequency response can effectively distinguish between nondefective and faulty gears, and its resolution is enough to distinguish the degree of failure of gear cracks.

scholarly journals Numerical Algorithm for the Third-Order Partial Differential Equation with Three-Point Boundary Value Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Jing Niu ◽  
Ping Li
Keyword(s):  
Boundary Value Problem ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Boundary Value ◽  
Integral Condition ◽  
Order Partial Differential Equation ◽  
Point Boundary ◽  
Third Order ◽  
The Third ◽  
In Series

A numerical method based on the reproducing kernel theorem is presented for the numerical solution of a three-point boundary value problem with an integral condition. Using the reproducing property and the existence of orthogonal basis in a new reproducing kernel Hilbert space, we obtain a representation of exact solution in series form and its approximate solution by truncating the series. Moreover, the uniform convergency is proved and the effectiveness of the proposed method is illustrated with some examples.

scholarly journals Bipartite Consensus of High-Order Edge Dynamics on Coopetition Multiagent Systems

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Yilong Yang ◽  
Zhijian Ji ◽  
Lei Tian ◽  
Huizi Ma ◽  
Qingyuan Qi
Keyword(s):  
Multiagent Systems ◽  
Line Graph ◽  
Sufficient Conditions ◽  
High Order ◽  
Third Order ◽  
Positive Weight ◽  
The Third ◽  
Initial Graph ◽  
Strongly Connected ◽  
Bipartite Consensus

The bipartite consensus of high-order edge dynamics is investigated for coopetition multiagent systems, in which the cooperative and competitive relationships among agents are characterized by positive weight and negative weight, respectively. By mapping the initial graph to a line graph, the distributed control protocol is proposed for the strongly connected, digon sign-symmetric structurally balanced line graph; and then we give sufficient conditions for the third-order multi-gent system to achieve both the bipartite consensus of edge dynamics and the final value of bipartite consensus. By transforming the coefficients of characteristic polynomial from complex domain to real number domain, the sufficient conditions for the bipartite consensus of high-order edge dynamics are also proposed, and the final values of the high-order edge dynamics on multiagent systems are obtained.

scholarly journals Multi-robot formation control based on high-order bilateral consensus

2020 ◽  
Vol 53 (5-6) ◽  
pp. 983-993
Author(s):  
Dejian Liu ◽  
Chengguo Zong ◽  
Detang Wang ◽  
Wenbin Zhao ◽  
Yuehua Wang ◽  
...  
Keyword(s):  
Information Exchange ◽  
Formation Control ◽  
Sufficient Conditions ◽  
Higher Order ◽  
High Order ◽  
Third Order ◽  
Control Protocol ◽  
The Third ◽  
Multi Agent ◽  
Multi Robot

A high-order bilateral consensus robot formation control protocol for multi-agent systems is proposed in this paper. Considering the relationship between the state of the information exchange topology and derivatives, a third-order bilateral consistency protocol is presented and is extended it to a higher order bilateral consensus protocol. First, sufficient conditions for the third-order multi-agent system are given to achieve the bilateral consensus control protocol, and the system’s asymptotical stability is also achieved by adjusting the feedback system gain parameters. Then, by further studying the cohesive relationship between each state variable of the third-order protocol and the gauge transformation, the sufficient conditions of the higher order system are also provided. Finally, by applying the third-order control protocol to the control of multi-robot formation, the general control scheme of robot formation is given and the control of robot formation is successfully achieved.

A NOVEL APPROACH FOR CONSTRUCTING HIGH-ORDER CHUA'S CIRCUIT WITH MULTI-DIRECTIONAL MULTI-SCROLL CHAOTIC ATTRACTORS

2013 ◽  
Vol 23 (02) ◽  
pp. 1350022 ◽  
Author(s):  
CHUN HUA WANG ◽  
HAO XU ◽  
FEI YU
Keyword(s):  
High Order ◽  
Chaotic Attractors ◽  
Chua’S Circuit ◽  
Nonlinear Functions ◽  
Third Order ◽  
Chua's Circuit ◽  
Controlled Source ◽  
The Third ◽  
Novel Approach ◽  
Rc Structure

A novel approach for constructing a high-order Chua's circuit is proposed. Based on a dual-port RCL network, a high-order Chua's circuit which can generate multi-directional multi-scroll (MDMS) chaotic attractors can be realized by introducing a RC structure and suitable nonlinear functions. First, a fourth-order Chua's circuit is achieved by adding a capacitor, a resistance and a controlled-source constituted by stair functions in the third-order Chua's circuit. And then, this recursive method can be adopted in higher-order Chua's circuit which can generate multi-scroll chaotic attractors in more directions. Finally, a sixth-order Chua's circuit is designed and its experimental results demonstrate the feasibility of this method.

scholarly journals Consensus Conditions for High-Order Multiagent Systems with Nonuniform Delays

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Mengji Shi ◽  
Kaiyu Qin ◽  
Ping Li ◽  
Jun Liu
Keyword(s):  
Multiagent Systems ◽  
Time Delays ◽  
Second Order ◽  
High Order ◽  
Sixth Order ◽  
Multiple Time ◽  
State Variables ◽  
Third Order ◽  
First Order ◽  
The Third

Consensus of first-order and second-order multiagent systems has been wildly studied. However, the convergence of high-order (especially the third-order to the sixth-order) state variables is also ubiquitous in various fields. The paper handles consensus problems of high-order multiagent systems in the presence of multiple time delays. Obtained by a novel frequency domain approach which properly resolves the challenges associated with nonuniform time delays, the consensus conditions for the first-order and second-order systems are proven to be nonconservative, and those for the third-order to the sixth-order systems are provided in the form of simple inequalities. The method revealed in this article is applicable to arbitrary-order systems, and the results are less conservative than those based on Lyapunov approaches, because it roots in sufficient and necessary criteria of stabilities. Simulations are carried out to validate the theoretical results.

Third-Order Volterra Kernel Identification Technique in Aerodynamics

2011 ◽  
Vol 52-54 ◽  
pp. 618-623
Author(s):  
Yun Hai Wang ◽  
Jing Long Han ◽  
Wei Zhou
Keyword(s):  
Nonlinear System ◽  
Volterra Series ◽  
Volterra Kernel ◽  
Third Order ◽  
Volterra Kernels ◽  
Weakly Nonlinear ◽  
The Third ◽  
Identification Technique ◽  
Volterra Kernel Identification ◽  
Identification Techniques

In this paper, we will extend a Volterra identification technique of nonlinear systems. In reality there exists a large class of weakly Nonlinear System which can be well defined by the first few kernels of the Volterra series. In general, Engineers believe that identifying high-order Volterra kernels is a big problem and hope for the advent of better identification techniques. However, with the extensive development of the Volterra kernels’ identification technique, the situation may improve. The formulas used to calculate kernels up to the third-order are given.

scholarly journals High-Order Sequential Simulation via Statistical Learning in Reproducing Kernel Hilbert Space

2019 ◽  
Vol 52 (5) ◽  
pp. 693-723
Author(s):  
Lingqing Yao ◽  
Roussos Dimitrakopoulos ◽  
Michel Gamache
Keyword(s):  
Random Field ◽  
Statistical Learning ◽  
Spatial Statistics ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Training Image ◽  
High Order ◽  
Learning Framework ◽  
Sample Data ◽  
Legendre Moment

AbstractThe present work proposes a new high-order simulation framework based on statistical learning. The training data consist of the sample data together with a training image, and the learning target is the underlying random field model of spatial attributes of interest. The learning process attempts to find a model with expected high-order spatial statistics that coincide with those observed in the available data, while the learning problem is approached within the statistical learning framework in a reproducing kernel Hilbert space (RKHS). More specifically, the required RKHS is constructed via a spatial Legendre moment (SLM) reproducing kernel that systematically incorporates the high-order spatial statistics. The target distributions of the random field are mapped into the SLM-RKHS to start the learning process, where solutions of the random field model amount to solving a quadratic programming problem. Case studies with a known data set in different initial settings show that sequential simulation under the new framework reproduces the high-order spatial statistics of the available data and resolves the potential conflicts between the training image and the sample data. This is due to the characteristics of the spatial Legendre moment kernel and the generalization capability of the proposed statistical learning framework. A three-dimensional case study at a gold deposit shows practical aspects of the proposed method in real-life applications.

Design of Third-Order Non-Circular Planetary Gear

2012 ◽  
Vol 482-484 ◽  
pp. 305-308
Author(s):  
Ya Zhou Wang ◽  
Bo Chen ◽  
Chi Bing Hu ◽  
Shuo Tao Zhang ◽  
Te Li ◽  
...  
Keyword(s):  
Elliptic Curve ◽  
Planetary Gear ◽  
High Order ◽  
Third Order ◽  
The Third ◽  
Matlab Program ◽  
Gear Mechanism ◽  
Center Distance ◽  
Planetary Gear Mechanism ◽  
Circular Pitch

The design of the third-order non-circular planetary gear is presented. In order to design the third-order non-circular planetary gear, the pitch of those gears is needed. Firstly theory and composition of the third-order non-circular planetary gear mechanism is introduced. Then according to the two conditions that the pitch should meet, the non-circular pitch formulas of the third-order non-circular planetary gear mechanism is given. Finally an application case of the center distance 3-4 type planetary gear mechanism was calculated by using the designed MATLAB program and created high-order elliptic curve. The design of the third-order non-circular planetary gear is achieved.

Sign in / Sign up

Export Citation Format

Share Document