Santanu Das

Characteristics of planetary candidates observed by Kepler II : Analysis of the first four months of data

On 2011 February 1 the Kepler mission released data for 156,453 stars observed from the beginning of the science observations on 2009 May 2 through September 16. There are 1235 planetary candidates with transit-like signatures detected in this period. These are associated with 997 host stars. Distributions of the characteristics of the planetary candidates are separated into five class sizes: 68 candidates of approximately Earth-size (R_p < 1.25 R_⊕), 288 super-Earth-size (1.25 R_⊕ ≤ R_p < 2 R_⊕), 662 Neptune-size (2 R_⊕ ≤ R_p < 6 R_⊕), 165 Jupiter-size (6 R_⊕ ≤ R_p < 15 R_⊕), and 19 up to twice the size of Jupiter (15 R_⊕ ≤ R_p < 22 R_⊕). In the temperature range appropriate for the habitable zone, 54 candidates are found with sizes ranging from Earth-size to larger than that of Jupiter. Six are less than twice the size of the Earth. Over 74% of the planetary candidates are smaller than Neptune. The observed number versus size distribution of planetary candidates increases to a peak at two to three times the Earth-size and then declines inversely proportional to the area of the candidate. Our current best estimates of the intrinsic frequencies of planetary candidates, after correcting for geometric and sensitivity biases, are 5% for Earth-size candidates, 8% for super-Earth-size candidates, 18% for Neptune-size candidates, 2% for Jupiter-size candidates, and 0.1% for very large candidates; a total of 0.34 candidates per star. Multi-candidate, transiting systems are frequent; 17% of the host stars have multi-candidate systems, and 34% of all the candidates are part of multi-candidate systems.

Multiple kernel learning for heterogeneous anomaly detection: algorithm and aviation safety case study

The world-wide aviation system is one of the most complex dynamical systems ever developed and is generating data at an extremely rapid rate. Most modern commercial aircraft record several hundred flight parameters including information from the guidance, navigation, and control systems, the avionics and propulsion systems, and the pilot inputs into the aircraft. These parameters may be continuous measurements or binary or categorical measurements recorded in one second intervals for the duration of the flight. Currently, most approaches to aviation safety are reactive, meaning that they are designed to react to an aviation safety incident or accident. In this paper, we discuss a novel approach based on the theory of multiple kernel learning to detect potential safety anomalies in very large data bases of discrete and continuous data from world-wide operations of commercial fleets. We pose a general anomaly detection problem which includes both discrete and continuous data streams, where we assume that the discrete streams have a causal influence on the continuous streams. We also assume that atypical sequences of events in the discrete streams can lead to off-nominal system performance. We discuss the application domain, novel algorithms, and also discuss results on real-world data sets. Our algorithm uncovers operationally significant events in high dimensional data streams in the aviation industry which are not detectable using state of the art methods.

Discovering Anomalous Aviation Safety Events Using Scalable Data Mining Algorithms

The worldwide civilian aviation system is one of the most complex dynamical systems created. Most modern commercial aircraft have onboard flight data recorders that record several hundred discrete ...

Detection and Prognostics on Low-Dimensional Systems

This paper describes the application of known and novel prognostic algorithms on systems that can be described by low-dimensional, potentially nonlinear dynamics. The methods rely on estimating the conditional probability distribution of the output of the system at a future time given knowledge of the current state of the system. We show how to estimate these conditional probabilities using a variety of techniques, including bagged neural networks and kernel methods such as Gaussian process regression (GPR). The results are compared with standard method such as the nearest neighbor algorithm. We demonstrate the algorithms on a real-world dataset and a simulated dataset. The real-world dataset consists of the intensity of an NH3 laser. The laser dataset has been shown by other authors to exhibit low-dimensional chaos with sudden drops in intensity. The simulated dataset is generated from the Lorenz attractor and has known statistical characteristics. On these datasets, we show the evolution of the estimated conditional probability distribution, the way it can act as a prognostic signal, and its use as an early warning system. We also review a novel approach to perform GPR with large numbers of data points.

Gaussian Process Time Series Model for Life Prognosis of Metallic Structures

Al 2024-T351 fatigue specimens have been modeled using a kernel-based multi-variate Gaussian Process approach. The Gaussian Process model projects fatigue affecting input variables to output crack growth by probabilistically inferring the underlying nonlinear relationship between input and output. The Gaussian Process approach not only explicitly models the uncertainty due to scatter in material microstructure parameter but it also implicitly models the loading sequence effect due to variable loading. The loading sequence effect is modeled through the Gaussian Process optimal hyperparameters by using the crack length data observed over the entire domain of spectrum loading. The performance in the crack growth prediction is evaluated for two covariance functions, a radial basis-based, anisotropic, covariance function and a neural network-based isotropic covariance function. Furthermore, the performance of different types of scaling, used to scale the input—output data space, is tested. It is found that for the radial basis-based anisotropic covariance function with normalized scaling, the prediction error is consistently lower compared to other combinations. In addition, the Gaussian Process model allows determination of the collapse load condition, which is a desirable feature for the online health monitoring and prognosis.

Classification of Damage Signatures in Composite Plates using One-Class SVMs

Damage characterization through wave propagation and scattering is of considerable interest to many non-destructive evaluation techniques. For fiber-reinforced composites, complex waves can be generated during the tests due to the non-homogeneous and anisotropic nature of the material when compared to isotropic materials. Additional complexities are introduced due to the presence of the damage and thus results in difficulty to characterize these defects. The inability to detect damage in composite structures limits their use in practice. A major task of structural health monitoring is to identify and characterize the existing defects or defect evolution through the interactions between structural features and multidisciplinary physical phenomena. In a wave-based approach to addressing this problem, the presence of damage is characterized by the changes in the signature of the resultant wave that propagates through the structure. In order to measure and characterize the wave propagation, we use the response of the surface-mounted piezoelectric transducers as input to an advanced machine-learning based classifier known as a support vector machine.

Analysis of Flight Data Using Clustering Techniques for Detecting Abnormal Operations

The airline industry is moving toward proactive risk management, which aims to identify and mitigate risks before accidents occur. However, existing methods for such efforts are limited. They rely on predefined criteria to identify risks, leaving emergent issues undetected. This paper presents a new method, cluster-based anomaly detection to detect abnormal flights, which can support domain experts in detecting anomalies and associated risks from routine airline operations. The new method, enabled by data from the flight data recorder, applies clustering techniques to detect abnormal flights of unique data patterns. Compared with existing methods, the new method no longer requires predefined criteria or domain knowledge. Tests were conducted using two sets of operational data consisting of 365 B777 flights and 25,519 A320 flights. The performance of cluster-based anomaly detection to detect abnormal flights was compared with those of multiple kernel anomaly detection, which is another data-driven anomaly ...

Simulation of Damage-features in a Lug Joint using Guided Waves

A lug joint is one of the several `hotspots in an aerospace structure which experiences fatigue damage. Several fatigue tests on lug joint samples prepared from 0.25 in plate of Aluminum (Al) 2024 T351 indicated a distinct failure pattern. All samples failed at the shoulders. Therefore, in the current study, different notch sizes are introduced at the shoulders and both experimental and modeled active health monitoring with piezoelectric transducers is performed. Simulations of the real time experiments are carried out using FE analysis. The crack geometry and piezoelectric transducer orientation in lug joint samples are kept same both in experiments and in simulation. Results presented illustrate the feasibility of guided waves in interrogating damage in lug joints. A comparison of sensor signals between experimental and simulated signals, in the time-frequency domain, show fairly good correlation. The frequency transform on the sensor signal data yield useful information for characterizing damage. Sensor sensitivity studies using a distance-based outlier technique are conducted to classify sensor data for different damage states. This information can be used in a number of applications including damage localization by reducing redundant sensors, and optimal sensor placement for SHM.

Detection of Fatigue Cracks and Torque Loss in Bolted Joints

Fatigue crack growth during the service life of aging aircraft is a critical issue and monitoring of such cracks in structural hotspots is the goal of this research. This paper presents a procedure for classification and detection of cracks generated in bolted joints which are used at numerous locations in aircraft structures. Single lap bolted joints were equipped with surface mounted piezoelectric (pzt) sensors and actuators and were subjected to cyclic loading. Crack length measurements and sensor data were collected at different number of cycles and with different torque levels. A classification algorithm based on Support Vector Machines (SVMs) was used to compare signals from a healthy and damaged joint to classify fatigue damage at the bolts. The algorithm was also used to classify the amount of torque in the bolt of interest and determine if the level of torque affected the quantification and localization of the crack emanating from the bolt hole. The results show that it is easier to detect the completely loose bolt but certain changes in torque, combined with damage, can produce some non-unique classifier solutions.

Monte Carlo Matching Pursuit Decomposition Method for Damage Quantification in Composite Structures

In wave-based approach, the presence of damage is visualized in terms of the changes in the signature of the resultant wave that propagates through the structure. In structural health monitoring, the fundamental goal is to detect, localize, and quantify these damage signatures. The current approach uses matching pursuit decomposition (MPD) to compare signals from healthy and damaged structures. However, the major drawback of the MPD is that, in the decomposition process, it performs an exhaustive search over a large dictionary of elementary functions. Therefore, this method of decomposition is associated with a large computational expense. In this research, the Monte Carlo matching pursuit decomposition (MCMPD) is proposed, that adapts a smaller dictionary to the signal structure, thus avoiding the exhaustive search over the time-frequency plane. The proposed algorithm, sequentially estimates a dictionary that contains only those components that match the waveform structure, uses the matching pursuits for the decomposition of the signal and if necessary, adapts the dictionary to the structure of the residues for further decomposition. Finally, we demonstrate using real life data that the MCMPD retains the ability of the matching pursuit to decompose waveforms and quantify them accurately while reducing computational expense.