Data rectification and detection of trend shifts in jet engine path measurements using median filters and fuzzy logic

Filtering methods are explored for removing noise from data while preserving sharp edges that many indicate a trend shift in gas turbine measurements. Linear filters are found to be have problems with removing noise while preserving features in the signal. The nonlinear hybrid median filter is found to accurately reproduce the root signal from noisy data. Simulated faulty data and fault-free gas path measurement data are passed through median filters and health residuals for the data set are created. The health residual is a scalar norm of the gas path measurement deltas and is used to partition the faulty engine from the healthy engine using fuzzy sets. The fuzzy detection system is developed and tested with noisy data and with filtered data. It is found from tests with simulated fault-free and faulty data that fuzzy trend shift detection based on filtered data is very accurate with no false alarms and negligible missed alarms.

Noise and outlier removal from jet engine health signals using weighted FIR median hybrid filters

The removal of noise and outliers from measurement signals is a major problem in jet engine health monitoring. Topical measurement signals found in most jet engines include low rotor speed, high rotor speed. fuel flow and exhaust gas temperature. Deviations in these measurements from a baseline 'good' engine are often called measurement deltas and the health signals used for fault detection, isolation, trending and data mining. Linear filters such as the FIR moving average filter and IIR exponential average filter are used in the industry to remove noise and outliers from the jet engine measurement deltas. However, the use of linear filters can lead to loss of critical features in the signal that can contain information about maintenance and repair events that could be used by fault isolation algorithms to determine engine condition or by data mining algorithms to learn valuable patterns in the data, Non-linear filters such as the median and weighted median hybrid filters offer the opportunity to remove noise and gross outliers from signals while preserving features. In this study. a comparison of traditional linear filters popular in the jet engine industry is made with the median filter and the subfilter weighted FIR median hybrid (SWFMH) filter. Results using simulated data with implanted faults shows that the SWFMH filter results in a noise reduction of over 60 per cent compared to only 20 per cent for FIR filters and 30 per cent for IIR filters. Preprocessing jet engine health signals using the SWFMH filter would greatly improve the accuracy of diagnostic systems. (C) 2002 Published by Elsevier Science Ltd.

Performance Evaluation of Distance-Hop Proportionality on Geometric Graph Models of Dense Sensor Networks

Wireless sensor networks can often be viewed in terms of a uniform deployment of a large number of nodes on a region in Euclidean space, e.g., the unit square. After deployment, the nodes self-organise into a mesh topology. In a dense, homogeneous deployment, a frequently used approximation is to take the hop distance between nodes to be proportional to the Euclidean distance between them. In this paper, we analyse the performance of this approximation. We show that nodes with a certain hop distance from a fixed anchor node lie within a certain annulus with probability approach- ing unity as the number of nodes n → ∞. We take a uniform, i.i.d. deployment of n nodes on a unit square, and consider the geometric graph on these nodes with radius r(n) = c q ln n n . We show that, for a given hop distance h of a node from a fixed anchor on the unit square,the Euclidean distance lies within [(1−ǫ)(h−1)r(n), hr(n)],for ǫ > 0, with probability approaching unity as n → ∞.This result shows that it is more likely to expect a node, with hop distance h from the anchor, to lie within this an- nulus centred at the anchor location, and of width roughly r(n), rather than close to a circle whose radius is exactly proportional to h. We show that if the radius r of the ge- ometric graph is fixed, the convergence of the probability is exponentially fast. Similar results hold for a randomised lattice deployment. We provide simulation results that il- lustrate the theory, and serve to show how large n needs to be for the asymptotics to be useful.

Finding a Box Representation for a Graph in $O(n^2\Delta^2\ln n)$ time

An axis-parallel box in $b$-dimensional space is a Cartesian product $R_1 \times R_2 \times \cdots \times R_b$ where $R_i$ (for $1 \leq i \leq b$) is a closed interval of the form $[a_i, b_i]$ on the real line. For a graph $G$, its boxicity is the minimum dimension $b$, such that $G$ is representable as the intersection graph of (axis-parallel) boxes in $b$-dimensional space. The concept of boxicity finds application in various areas of research like ecology, operation research etc. Chandran, Francis and Sivadasan gave an $O(\Delta n^2 \ln^2 n)$ randomized algorithm to construct a box representation for any graph $G$ on $n$ vertices in $\lceil (\Delta + 2)\ln n \rceil$ dimensions, where $\Delta$ is the maximum degree of the graph. They also came up with a deterministic algorithm that runs in $O(n^4 \Delta )$ time. Here, we present an $O(n^2 \Delta^2 \ln n)$ deterministic algorithm that constructs the box representation for any graph in $\lceil (\Delta + 2)\ln n \rceil$ dimensions.

Faster Algorithms for Incremental Topological Ordering.Robert Tarjan

We present two online algorithms for maintaining a topological order of a directed acyclic graph as arcs are added, and detecting a cycle when one is created. Our first algorithm takes O(m 1/2) amortized time per arc and our second algorithm takes O(n 2.5/m) amortized time per arc, where n is the number of vertices and m is the total number of arcs. For sparse graphs, our O(m 1/2) bound improves the best previous bound by a factor of logn and is tight to within a constant factor for a natural class of algorithms that includes all the existing ones. Our main insight is that the two-way search method of previous algorithms does not require an ordered search, but can be more general, allowing us to avoid the use of heaps (priority queues). Instead, the deterministic version of our algorithm uses (approximate) median-finding; the randomized version of our algorithm uses uniform random sampling. For dense graphs, our O(n 2.5/m) bound improves the best previously published bound by a factor of n 1/4 and a recent bound obtained independently of our work by a factor of logn. Our main insight is that graph search is wasteful when the graph is dense and can be avoided by searching the topological order space instead. Our algorithms extend to the maintenance of strong components, in the same asymptotic time bounds.

Scan cell reordering to minimize peak power during test cycle: A graph theoretic approach

Scan circuit is widely practiced DFT technology. The scan testing procedure consist of state initialization, test application, response capture and observation process. During the state initialization process the scan vectors are shifted into the scan cells and simultaneously the responses captured in last cycle are shifted out. During this shift operation the transitions that arise in the scan cells are propagated to the combinational circuit, which inturn create many more toggling activities in the combinational block and hence increases the dynamic power consumption. The dynamic power consumed during scan shift operation is much more higher than that of normal mode operation.

Evolving Random Geometric Graph Models for Mobile Wireless Networks

We consider evolving exponential RGGs in one dimension and characterize the time dependent behavior of some of their topological properties. We consider two evolution models and study one of them detail while providing a summary of the results for the other. In the first model, the inter-nodal gaps evolve according to an exponential AR(1) process that makes the stationary distribution of the node locations exponential. For this model we obtain the one-step conditional connectivity probabilities and extend it to the k-step case. Finite and asymptotic analysis are given. We then obtain the k-step connectivity probability conditioned on the network being disconnected. We also derive the pmf of the first passage time for a connected network to become disconnected. We then describe a random birth-death model where at each instant, the node locations evolve according to an AR(1) process. In addition, a random node is allowed to die while giving birth to a node at another location. We derive properties similar to those above.

An (O)over-bar(m(2)n) randomized algorithm to compute a minimum cycle basis of a directed graph

We consider the problem of computing a minimum cycle basis in a directed graph G. The input to this problem is a directed graph whose arcs have positive weights. In this problem a {- 1, 0, 1} incidence vector is associated with each cycle and the vector space over Q generated by these vectors is the cycle space of G. A set of cycles is called a cycle basis of G if it forms a basis for its cycle space. A cycle basis where the sum of weights of the cycles is minimum is called a minimum cycle basis of G. The current fastest algorithm for computing a minimum cycle basis in a directed graph with m arcs and n vertices runs in O(m(w+1)n) time (where w < 2.376 is the exponent of matrix multiplication). If one allows randomization, then an (O) over tilde (m(3)n) algorithm is known for this problem. In this paper we present a simple (O) over tilde (m(2)n) randomized algorithm for this problem. The problem of computing a minimum cycle basis in an undirected graph has been well-studied. In this problem a {0, 1} incidence vector is associated with each cycle and the vector space over F-2 generated by these vectors is the cycle space of the graph. The fastest known algorithm for computing a minimum cycle basis in an undirected graph runs in O(m(2)n + mn(2) logn) time and our randomized algorithm for directed graphs almost matches this running time.

Bond Graph Modeling for Energy-Harvesting Wireless Sensor Networks

Researchers can use bond graph modeling, a tool that takes into account the energy conservation principle, to accurately assess the dynamic behavior of wireless sensor networks on a continuous basis.

Theory and Algorithms for Hop-Count-Based Localization with Random Geometric Graph Models of Dense Sensor Networks

Wireless sensor networks can often be viewed in terms of a uniform deployment of a large number of nodes in a region of Euclidean space. Following deployment, the nodes self-organize into a mesh topology with a key aspect being self-localization. Having obtained a mesh topology in a dense, homogeneous deployment, a frequently used approximation is to take the hop distance between nodes to be proportional to the Euclidean distance between them. In this work, we analyze this approximation through two complementary analyses. We assume that the mesh topology is a random geometric graph on the nodes; and that some nodes are designated as anchors with known locations. First, we obtain high probability bounds on the Euclidean distances of all nodes that are h hops away from a fixed anchor node. In the second analysis, we provide a heuristic argument that leads to a direct approximation for the density function of the Euclidean distance between two nodes that are separated by a hop distance h. This approximation is shown, through simulation, to very closely match the true density function. Localization algorithms that draw upon the preceding analyses are then proposed and shown to perform better than some of the well-known algorithms present in the literature. Belief-propagation-based message-passing is then used to further enhance the performance of the proposed localization algorithms. To our knowledge, this is the first usage of message-passing for hop-count-based self-localization.

Factor graph based joint detection/decoding for LDPC coded large-MIMO systems

In this paper, we employ message passing algorithms over graphical models to jointly detect and decode symbols transmitted over large multiple-input multiple-output (MIMO) channels with low density parity check (LDPC) coded bits. We adopt a factor graph based technique to integrate the detection and decoding operations. A Gaussian approximation of spatial interference is used for detection. This serves as a low complexity joint detection/decoding approach for large dimensional MIMO systems coded with LDPC codes of large block lengths. This joint processing achieves significantly better performance than the individual detection and decoding scheme.