Delay-Doppler resolution performance of large time-bandwidth product linear FM signals in a multipath ocean environment

Abstract

will produce low levels of inherent vibration. As the gear teeth wear, however, backlash between meshing teeth increases and this is reflected in an increase in the vibration energy. As the vibration energy is dissipated through the gear box, it excites resonances and exerts extra dynamic loads on gear teeth. It is of great interest to the maintenance engineers to predict the occurrence of backlash between gear teeth. The fact that vibration signals carry much information relating to running conditions of gear boxes can be used to solve this problem. In this study, a mathematical model was formulated to simulate the effect of backlash between gear teeth on the vibration spectrum of gear boxes. A single stage helical gear box was used to demonstrate this model. In this simulation, the transmission shafts were treated as lumped parameter systems. The elasticity of shafts, bearings, and gear teeth were also included. The grounded-chair representation was used to obtain the equations of motion that were solved using the Runge-Kutta method. The vibration spectra of the gear box system were obtained using fast Fourier transform (FFT). These spectra can be used to construct a vibration chart which, in turn, can be used to determine the proper times for maintenance of gear boxes to avoid failure of such units.

Time delay and Doppler estimation for wideband acoustic signals in multipath environments

“…In the numerical simulations, the transmitted signal s(t) is adopted as a widely used linear frequency modulated (LFM) signal 11 with carrier frequency f c and pulse duration T. The LFM signal is also referred to as chirp signal, which can be expressed as As pointed out in Sec. III, the delay-Doppler resolution of the transmitted signal is related to its time duration and bandwidth.…”

“…5,11 Here v m is the maximum radial velocity of the source relative to the receiver. In other words, the narrowband assumption requires that the bandwidth is much smaller than the carrier frequency and the time-bandwidth product is much smaller than c=2v m Usually the narrowband approximation is sufficiently accurate for most wireless and radar applications but less accurate for sonar and other acoustic systems due to the low carrier frequency as well as the low sound velocity.…”

Source motion detection, estimation, and compensation for underwater acoustics inversion by wideband ambiguity lag-Doppler filtering

“…Hence the set of reference signals is composed of time delayed and Dopplerscaled versions of the emitted signal for the range of time delays and speeds expected. 4,18 The WAF depends on s and v because of its dependency from g and is computed by…”

“…Time delay and Doppler scaling factors are estimated by cross-correlating the received signal with a set of reference signals. 4,18 Our new IR estimation method proposes the use of time-warping filtering tools in order to iteratively estimate the propagation parameters of each ray. We estimate the parameters of the time-warping filtering from the WAF of the received signal.…”

“…Both narrowband ambiguity function and WAF are fully described and formulated for active sonar systems in Ref. 18. The motion effects, which represent a compression in time for approaching sources and an expansion for receding sources, are approximated as simple carrier-frequency shifts of the transmitted signal.…”