A Stochastic Model for the Random Impact Series Method in Modal Testing

2003 ◽  
Author(s):  
C. N. Wong ◽  
W. D. Zhu ◽  
N. A. Zheng
Keyword(s):  
Stochastic Model ◽  
Energy Input ◽  
Shape Function ◽  
Signal To Noise Ratio ◽  
Modal Testing ◽  
Time Interval ◽  
Series Method ◽  
Finite Time Interval ◽  
Random Series ◽  
Arrival Times

A novel stochastic model is developed to describe a random series of impacts in modal testing. The number of the force pulses in a finite time interval is modeled as a Poisson process. The force pulses in the series are assumed to have an arbitrary, deterministic shape function and random amplitudes and arrival times. A detailed stochastic analysis is undertaken and is validated by numerical simulation. The main advantages of the random impact series method are increased energy input to the test structure and improved signal-to-noise ratio. The method can also average out the slight nonlinearities that can exist in the structure and extract the linearized modal parameters. The model developed in this work can be used to describe a random series of pulses in other applications.

A Stochastic Model for the Random Impact Series Method in Modal Testing

2006 ◽  
Vol 129 (3) ◽  
pp. 265-275 ◽  
Author(s):  
W. D. Zhu ◽  
N. A. Zheng ◽  
C. N. Wong
Keyword(s):  
Stochastic Model ◽  
Numerical Solutions ◽  
Average Power ◽  
Modal Testing ◽  
Time Interval ◽  
Wide Sense ◽  
Random Series ◽  
Arrival Times ◽  
Stationary Part ◽  
Force Signal

A novel stochastic model is developed to describe a random series of impacts in modal testing that can be performed manually or by using a specially designed random impact device. The number of the force pulses, representing the impacts, is modeled as a Poisson process with stationary increments. The force pulses are assumed to have an arbitrary, deterministic shape function, and random amplitudes and arrival times. The force signal in a finite time interval is shown to consist of a wide-sense stationary part and two nonstationary parts. The expectation of the force spectrum is obtained from two approaches. The expectations of the average power densities associated with the entire force signal and the stationary part of it are determined and compared. The analytical expressions are validated by numerical solutions for two different types of shape functions. A numerical example is given to illustrate the advantages of the random impact series over a single impact and an impact series with deterministic arrival times of the pulses in estimating the frequency response function. The model developed can be used to describe a random series of pulses in other applications.

Technical Note. Optimization of Parameters for a Damped Oscillator Excited by a Sequence of Random Pulses

2015 ◽  
Vol 39 (4) ◽  
pp. 645-652 ◽  
Author(s):  
Agnieszka Ozga
Keyword(s):  
Technical Note ◽  
Time Interval ◽  
Finite Time Interval ◽  
Random Series ◽  
Stochastic Problem ◽  
Actual Distribution ◽  
Optimization Of Parameters ◽  
Applied Model ◽  
The Difference ◽  
Damped Oscillator

Abstract The paper is another step in discussion concerning the method of determining the distributions of pulses forcing vibrations of a system. Solving a stochastic problem for systems subjected to random series of pulses requires determining the distribution for a linear oscillator with damping. The goal of the study is to minimize the error issuing from the finite time interval. The applied model of investigations is supposed to answer the question how to select the parameters of a vibrating system so that the difference between the actual distribution of random pulses and that determined from the waveform is as small as possible.

scholarly journals Transient and Stationary Losses in a Finite-Buffer Queue with Batch Arrivals

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Andrzej Chydzinski ◽  
Blazej Adamczyk
Keyword(s):  
Batch Size ◽  
Buffer Size ◽  
Arrival Process ◽  
Time Interval ◽  
Finite Buffer ◽  
Finite Time Interval ◽  
Batch Arrivals ◽  
Batch Markovian Arrival Process ◽  
Buffer Overflows ◽  
Finite Buffer Queue

We present an analysis of the number of losses, caused by the buffer overflows, in a finite-buffer queue with batch arrivals and autocorrelated interarrival times. Using the batch Markovian arrival process, the formulas for the average number of losses in a finite time interval and the stationary loss ratio are shown. In addition, several numerical examples are presented, including illustrations of the dependence of the number of losses on the average batch size, buffer size, system load, autocorrelation structure, and time.

A finite-time ruin probability formula for continuous claim severities

2004 ◽  
Vol 41 (2) ◽  
pp. 570-578 ◽  
Author(s):  
Zvetan G. Ignatov ◽  
Vladimir K. Kaishev
Keyword(s):  
Real Function ◽  
Finite Time ◽  
Ruin Probability ◽  
Joint Distribution ◽  
Time Interval ◽  
Insurance Company ◽  
Finite Time Interval ◽  
Appell Polynomials ◽  
Premium Income ◽  
Inverted Dirichlet

An explicit formula for the probability of nonruin of an insurance company in a finite time interval is derived, assuming Poisson claim arrivals, any continuous joint distribution of the claim amounts and any nonnegative, increasing real function representing its premium income. The formula is compact and expresses the nonruin probability in terms of Appell polynomials. An example, illustrating its numerical convenience, is also given in the case of inverted Dirichlet-distributed claims and a linearly increasing premium-income function.

scholarly journals Finite-Time Boundedness for a Class of Delayed Markovian Jumping Neural Networks with Partly Unknown Transition Probabilities

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Li Liang
Keyword(s):  
Neural Networks ◽  
Finite Time ◽  
Transition Probabilities ◽  
The State ◽  
Time Interval ◽  
Finite Time Interval ◽  
Markovian Jumping ◽  
Stochastic Boundedness ◽  
Partly Unknown Transition Probabilities ◽  
Finite Time Boundedness

This paper is concerned with the problem of finite-time boundedness for a class of delayed Markovian jumping neural networks with partly unknown transition probabilities. By introducing the appropriate stochastic Lyapunov-Krasovskii functional and the concept of stochastically finite-time stochastic boundedness for Markovian jumping neural networks, a new method is proposed to guarantee that the state trajectory remains in a bounded region of the state space over a prespecified finite-time interval. Finally, numerical examples are given to illustrate the effectiveness and reduced conservativeness of the proposed results.

On robust controllability of uncertain non-linear jump systems with respect to the finite-time interval

2011 ◽  
Vol 34 (7) ◽  
pp. 841-849 ◽  
Author(s):  
Shuping He ◽  
Fei Liu
Keyword(s):  
Finite Time ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Interval ◽  
Finite Time Interval ◽  
Markov Jump ◽  
Non Linear ◽  
Robust Controllability ◽  
Jump Systems ◽  
Takagi Sugeno

In this paper we study the robust control problems with respect to the finite-time interval of uncertain non-linear Markov jump systems. By means of Takagi–Sugeno fuzzy models, the overall closed-loop fuzzy dynamics are constructed through selected membership functions. By using the stochastic Lyapunov–Krasovskii functional approach, a sufficient condition is firstly established on the stochastic robust finite-time stabilization. Then, in terms of linear matrix inequalities techniques, the sufficient conditions on the existence of the stochastic finite-time controller are presented and proved. Finally, the design problem is formulated as an optimization one. The simulation results illustrate the effectiveness of the proposed approaches.

Novel Method for Detecting Weak AE Signals Based on the Similarity of Time-Frequency Spectra

Geophysics ◽  
2021 ◽  
pp. 1-62
Author(s):  
Wencheng Yang ◽  
Xiao Li ◽  
Yibo Wang ◽  
Yue Zheng ◽  
Peng Guo
Keyword(s):  
Mathematical Morphology ◽  
Signal To Noise Ratio ◽  
Critical Role ◽  
Real Data ◽  
Monitoring Method ◽  
Frequency Spectra ◽  
Arrival Times ◽  
Time Frequency ◽  
Fracturing Process ◽  
Ae Signals

As a key monitoring method, the acoustic emission (AE) technique has played a critical role in characterizing the fracturing process of laboratory rock mechanics experiments. However, this method is limited by low signal-to-noise ratio (SNR) because of a large amount of noise in the measurement and environment and inaccurate AE location. Furthermore, it is difficult to distinguish two or more hits because their arrival times are very close when AE signals are mixed with the strong background noise. Thus, we propose a new method for detecting weak AE signals using the mathematical morphology character correlation of the time-frequency spectrum. The character in all hits of an AE event can be extracted from time-frequency spectra based on the theory of mathematical morphology. Through synthetic and real data experiments, we determined that this method accurately identifies weak AE signals. Compared with conventional methods, the proposed approach can detect AE signals with a lower SNR.

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