Systems analysis for planning of air fleets and maintenance facilities

The high cost and extraordinary demands made on sophisticated air defence systems, pose hard challenges to the managers and engineers who plan the operation and maintenance of such systems. This paper presents a study aimed at developing simulation and systems analysis techniques for the effective planning and efficient operation of small fleets of aircraft, typical of the air force of a developing country. We consider an important aspect of fleet management: the problem of resource allocation for achieving prescribed operational effectiveness of the fleet. At this stage, we consider a single flying-base, where the operationally ready aircraft are stationed, and a repair-depot, where the planes are overhauled. An important measure of operational effectiveness is ‘ availability ’, which may be defined as the expected fraction of the fleet fit for use at a given instant. The tour of aircraft in a flying-base, repair-depot system through a cycle of ‘ operationally ready ’ and ‘ scheduled overhaul ’ phases is represented first by a deterministic flow process and then by a cyclic queuing process. Initially the steady-state availability at the flying-base is computed under the assumptions of Poisson arrivals, exponential service times and an equivalent singleserver repair-depot. This analysis also brings out the effect of fleet size on availability. It defines a ‘ small ’ fleet essentially in terms of the important ‘ traffic ’ parameter of service rate/maximum arrival rate.A simulation model of the system has been developed using GPSS to study sensitivity to distributional assumptions, to validate the principal assumptions of the analytical model such as the single-server assumption and to obtain confidence intervals for the statistical parameters of interest.

Optimal local polynomial regression of noisy time varying signals

We address the problem of local-polynomial modeling of smooth time-varying signals with unknown functional form, in the presence of additive noise. The problem formulation is in the time domain and the polynomial coefficients are estimated in the pointwise minimum mean square error (PMMSE) sense. The choice of the window length for local modeling introduces a bias-variance tradeoff, which we solve optimally by using the intersection-of-confidence-intervals (ICI) technique. The combination of the local polynomial model and the ICI technique gives rise to an adaptive signal model equipped with a time-varying PMMSE-optimal window length whose performance is superior to that obtained by using a fixed window length. We also evaluate the sensitivity of the ICI technique with respect to the confidence interval width. Simulation results on electrocardiogram (ECG) signals show that at 0dB signal-to-noise ratio (SNR), one can achieve about 12dB improvement in SNR. Monte-Carlo performance analysis shows that the performance is comparable to the basic wavelet techniques. For 0 dB SNR, the adaptive window technique yields about 2-3dB higher SNR than wavelet regression techniques and for SNRs greater than 12dB, the wavelet techniques yield about 2dB higher SNR.

Adaptive window zero-crossing-based instantaneous frequency estimation

We address the problem of estimating instantaneous frequency (IF) of a real-valued constant amplitude time-varying sinusoid. Estimation of polynomial IF is formulated using the zero-crossings of the signal. We propose an algorithm to estimate nonpolynomial IF by local approximation using a low-order polynomial, over a short segment of the signal. This involves the choice of window length to minimize the mean square error (MSE). The optimal window length found by directly minimizing the MSE is a function of the higher-order derivatives of the IF which are not available a priori. However, an optimum solution is formulated using an adaptive window technique based on the concept of intersection of confidence intervals. The adaptive algorithm enables minimum MSE-IF (MMSE-IF) estimation without requiring a priori information about the IF. Simulation results show that the adaptive window zero-crossing-based IF estimation method is superior to fixed window methods and is also better than adaptive spectrogram and adaptive Wigner-Ville distribution (WVD)-based IF estimators for different signal-to-noise ratio (SNR).