Identification of the Nonlinear Vibration Characteristics Based on the Wiener Kernels

2012 ◽  
Vol 204-208 ◽  
pp. 4668-4672
Author(s):  
Yi Chun Ren ◽  
Yin Hua Yu
Keyword(s):  
Nonlinear System ◽  
White Noise ◽  
Input Signal ◽  
Correlation Functions ◽  
Nonlinear Response ◽  
Cross Correlation ◽  
Gaussian White Noise ◽  
Wiener Kernels ◽  
Input And Output ◽  
Order Kernel

Wiener series are the important functional series describing nonlinear system. If an input signal is the Gaussian white noise, the wiener kernels are estimated through calculating the cross-correlation functions of the input and output of a nonlinear system. In this paper, a single-DOF quadratic nonlinear system is identified by the Wiener series. The results show that the intensity of the nonlinear response can be expressed by the second-order kernel.

Artifacts in Wiener Kernels Estimated Using Gaussian White Noise

1984 ◽  
Vol BME-31 (6) ◽  
pp. 454-461 ◽  
Author(s):  
Robert E. Wickesberg ◽  
C. Daniel Geisler
Keyword(s):  
White Noise ◽  
Gaussian White Noise ◽  
Wiener Kernels

scholarly journals Nonlinear identification of the total baroreflex arc

2015 ◽  
Vol 309 (12) ◽  
pp. R1479-R1489 ◽  
Author(s):  
Mohsen Moslehpour ◽  
Toru Kawada ◽  
Kenji Sunagawa ◽  
Masaru Sugimachi ◽  
Ramakrishna Mukkamala
Keyword(s):  
Dynamic System ◽  
White Noise ◽  
Nonlinear Model ◽  
Carotid Sinus ◽  
Gaussian White Noise ◽  
Second Order ◽  
Linear Dynamic System ◽  
Linear Dynamic ◽  
Nonlinear Behaviors ◽  
Order Kernel

The total baroreflex arc [the open-loop system relating carotid sinus pressure (CSP) to arterial pressure (AP)] is known to exhibit nonlinear behaviors. However, few studies have quantitatively characterized its nonlinear dynamics. The aim of this study was to develop a nonlinear model of the sympathetically mediated total arc without assuming any model form. Normal rats were studied under anesthesia. The vagal and aortic depressor nerves were sectioned, the carotid sinus regions were isolated and attached to a servo-controlled piston pump, and the AP and sympathetic nerve activity (SNA) were measured. CSP was perturbed using a Gaussian white noise signal. A second-order Volterra model was developed by applying nonparametric identification to the measurements. The second-order kernel was mainly diagonal, but the diagonal differed in shape from the first-order kernel. Hence, a reduced second-order model was similarly developed comprising a linear dynamic system in parallel with a squaring system in cascade with a slower linear dynamic system. This “Uryson” model predicted AP changes 12% better ( P < 0.01) than a linear model in response to new Gaussian white noise CSP. The model also predicted nonlinear behaviors, including thresholding and mean responses to CSP changes about the mean. Models of the neural arc (the system relating CSP to SNA) and peripheral arc (the system relating SNA to AP) were likewise developed and tested. However, these models of subsystems of the total arc showed approximately linear behaviors. In conclusion, the validated nonlinear model of the total arc revealed that the system takes on an Uryson structure.

scholarly journals Identifying Odd/Even-Order Binary Kernel Slices for a Nonlinear System Using Inverse Repeat m-Sequences

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Jin-yan Hu ◽  
Gang Yan ◽  
Tao Wang
Keyword(s):  
Nonlinear System ◽  
Cross Correlation ◽  
Correlation Method ◽  
Kernel Functions ◽  
Third Order ◽  
Mathematical Properties ◽  
M Sequence ◽  
System Output ◽  
Even Order ◽  
Order Kernel

The study of various living complex systems by system identification method is important, and the identification of the problem is even more challenging when dealing with a dynamic nonlinear system of discrete time. A well-established model based on kernel functions for input of the maximum length sequence (m-sequence) can be used to estimate nonlinear binary kernel slices using cross-correlation method. In this study, we examine the relevant mathematical properties of kernel slices, particularly their shift-and-product property and overlap distortion problem caused by the irregular shifting of the estimated kernel slices in the cross-correlation function between the input m-sequence and the system output. We then derive the properties of the inverse repeat (IR) m-sequence and propose a method of using IR m-sequence as an input to separately estimate odd- and even-order kernel slices to reduce the chance of kernel-slice overlapping. An instance of third-order Wiener nonlinear model is simulated to justify the proposed method.

Synthesis of Cross-Correlation Functions of Partial Responses and the Extended Kalman Filter Approach for Structural Damage Detection Under Ambient Excitations

2018 ◽  
Vol 18 (08) ◽  
pp. 1840003 ◽  
Author(s):  
Y. Lei ◽  
D. D. Xia ◽  
F. Chen ◽  
Y. M. Deng
Keyword(s):  
Kalman Filter ◽  
Damage Detection ◽  
White Noise ◽  
Extended Kalman Filter ◽  
Correlation Functions ◽  
Structural Damage ◽  
Cross Correlation ◽  
Product Models ◽  
Structural Responses ◽  
Measurement Noises

It is still necessary to investigate the detection of structural damage under ambient excitations since the excitations are random and unmeasured while measurement noises are inevitable. In this paper, a method based on the synthesis of cross-correlation functions of partial structural responses and the extended Kalman filter (EKF) approach is proposed for the identification and damage detection of structures under ambient excitations, in which both independent stationary and non-stationary white noise excitations in the product models are discussed. First, the equations of cross-correlation functions of structural responses are established when the ambient excitations are independent stationary white noise processes. Then, the EKF approach is utilized to identify structural parameters and cross-correlation functions using partial measurements of structural acceleration responses. Structural damage is detected based on the degradations of the identified structural element stiffness parameters. Finally, the proposed method is extended to deal with independent non-stationary white noise excitations in the product models. The numerical simulation examples of the ASCE structural health monitoring benchmark building subject to ambient excitation, a moment resisting frame model under white noise excitation, and a cantilever beam model under multiple independent non-stationary excitations are used to validate the feasibility of the proposed method. It is shown that the method is not sensitive to measurement noises. Also, a lab experimental study of the identification of a multi-story shear structure is investigated to further illustrate the applicability of the proposed method.

Nonspiking and Spiking Proprioceptors in the Crab: White Noise Analysis of Spiking CB-Chordotonal Organ Afferents

2003 ◽  
Vol 89 (4) ◽  
pp. 1815-1825 ◽  
Author(s):  
E. Rolland Gamble ◽  
Ralph A. DiCaprio
Keyword(s):  
White Noise ◽  
Information Transfer ◽  
Noise Analysis ◽  
Second Order ◽  
Chordotonal Organ ◽  
White Noise Analysis ◽  
Response Component ◽  
First Order ◽  
Wiener Kernels ◽  
Order Kernel

The proprioceptors that signal the position and movement of the first two joints of crustacean legs provide an excellent system for comparison of spiking and nonspiking (graded) information transfer and processing in a simple motor system. The position, velocity, and acceleration of the first two joints of the crab leg are monitored by both nonspiking and spiking proprioceptors. The nonspiking thoracic-coxal muscle receptor organ (TCMRO) spans the TC joint, while the coxo-basal (CB) joint is monitored by the spiking CB chordotonal organ (CBCTO) and by nonspiking afferents arising from levator and depressor elastic strands. The response characteristics and nonlinear models of the input-output relationship for CB chordotonal afferents were determined using white noise analysis (Wiener kernel) methods. The first- and second-order Wiener kernels for each of the four response classes of CB chordotonal afferents (position, position-velocity, velocity, and acceleration) were calculated and the gain function for each receptor determined by taking the Fourier transform of the first-order kernel. In all cases, there was a good correspondence between the response of an afferent to deterministic stimulation (trapezoidal movement) and the best-fitting linear transfer function calculated from the first-order kernel. All afferents also had a nonlinear response component and second-order Wiener kernels were calculated for afferents of each response type. Models of afferent responses based on the first- and second-order kernels were able to predict the response of the afferents with an average accuracy of 86%.

Identifying the stiffness and damping of a nonlinear system using its free response perturbed with Gaussian white noise

2019 ◽  
Vol 26 (9-10) ◽  
pp. 830-839
Author(s):  
Bin Tang ◽  
Shibo Wang ◽  
Michael J Brennan ◽  
Liyan Feng ◽  
Weichun Chen
Keyword(s):  
Nonlinear System ◽  
Free Vibration ◽  
Resonant Frequency ◽  
White Noise ◽  
Confidence Intervals ◽  
Signal To Noise Ratio ◽  
Gaussian White Noise ◽  
Parameter Estimates ◽  
Signal To Noise ◽  
Stiffness And Damping

Measurement uncertainty can affect the accuracy of estimating parameters of vibrating systems. This article is concerned with the development of a method for estimating parameters from the free vibration response of a nonlinear system in which the response signal is contaminated with Gaussian white noise. The backbone curve and envelope of the response are first estimated from the free vibration signal. An algorithm based on the Bayesian approach is then used to identify the stiffness and damping parameters of a nonlinear system excited at a single resonant frequency. A numerical example is provided to illustrate the proposed method, which is then applied to the experimental data from a nonlinear vibration absorber system that was excited at its first resonant frequency. The proposed approach provides the distribution and confidence intervals of the parameter estimates, which is an improvement on methods that provide a single number for each estimate. As the signal-to-noise ratio decreases, the variances of the posterior distributions increase as do the confidence intervals, reflecting greater uncertainty in the parameter estimates. The approach is effective provided that the signal-to-noise ratio is greater than about 10.

Optimum Vibration Control of a Nonlinear Damper System under Multi-Axis Excitations

2013 ◽  
Vol 712-715 ◽  
pp. 1678-1681
Author(s):  
Zheng Lu
Keyword(s):  
Nonlinear System ◽  
Vibration Control ◽  
Correlation Functions ◽  
Cross Correlation ◽  
Plug Flow ◽  
Operating Conditions ◽  
Optimum Operating ◽  
Control Performance ◽  
Auto Correlation ◽  
Different Types

This paper presents an investigation of the vibration control performance of a nonlinear damper system under multi-axis excitations, focusing on its optimum strategy. The nonlinear damper system is composed of a particle damper and a primary structure. Cross-correlation functions and auto-correlation functions are shown to be suitable means to interpret the physics involved in the behavior of such a nonlinear system. Using different types of random excitations, the optimum operating regions are all determined, within which particles move in a plug flow pattern and correlation functions decay much faster than that under the inefficient operating conditions.

Equivalent Nonlinear System Method for Stochastically Excited Hamiltonian Systems

1994 ◽  
Vol 61 (3) ◽  
pp. 618-623 ◽  
Author(s):  
W. Q. Zhu ◽  
T. T. Soong ◽  
Y. Lei
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
White Noise ◽  
Probability Density ◽  
Hamiltonian Systems ◽  
Gaussian White Noise ◽  
Energy Balancing ◽  
Dissipation Energy ◽  
System Method ◽  
Approximate Probability

An equivalent nonlinear system method is presented to obtain the approximate probability density for the stationary response of multi-degree-of-freedom nonlinear Hamiltonian systems to Gaussian white noise parametric and/or external excitations. The equivalent nonlinear systems are obtained on the basis of one of the following three criteria: least mean-squared deficiency of damping forces, dissipation energy balancing, and least mean-squared deficiency of dissipation energies. An example is given to illustrate the application and validity of the method and the differences in the three equivalence criteria.

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