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

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.

The Effect of Pulse Amplitudes on Quality of Determining Distribution of Pulses Forcing Vibration of an Damped Oscillator

“…Using high-performance computers and the PLgrid platform it was possible to calculate the distributions for six values of η i . The conclusions drawn on the basis of a former study [6] allowed to design the experiment so that a qualitative analysis of the presented results become possible.…”

“…In all qualitative investigations described below, the difficulties encountered in determining a series of pulses forcing an oscillator are analyzed by computing the difference between the distributions |p i −p i |. Earlier simulations [2,6] show that the differences between distributions generated in MATLAB environmentp i and the distributionsp i which were determined on the basis of the function representing deflection of the system are influenced by: the parameters b and c of the oscillator, pulse rate λ, length of the analyzed time interval, and the instant of time at which the difference is being determined. In the applied algorithm, the difference is determined with the step of 10 6 , at every second.…”

“…To confirm that minor differences in pulse amplitudes influence the errors in the determined distributions, it was sufficient to present just one such case subjected to qualitative studies, and this was done in the previous section. However, if the analysis concerns differences |p i −p i | that occur as a result of significant differences between pulse amplitudes, the experience acquired in the previous studies [6] shows that this case should be considered in the context of oscillators characterized with different parameters or, in other words, for different oscillators. Simulations were conducted for three damped oscillators ( Fig.…”

“…The study started with construction of a mathematical model [2] and further, some research methods were developed [3] which allowed to find the distribution of amplitudes of vibration forcing pulses in spite of numerical errors [4] or for the time interval subjected to analysis being too short. The problem was also considered specifically in context of the pulse rate [5] and parameters of the vibrating system [6]. Both qualitative and quantitative methods were used while approaching the issue [7].…”

An Application of Fractional Brownian Motion to Vessel Identification Based on its Sound Spectrum

“…Problem of ship identification by its radiated sound is regarded as difficult. This is by the reason of its complexity [1][2]. On the other hand, vessel recognition is very important, particularly from the military point of view.…”