Inferential Modeling and Independent Component Analysis for Redundant Sensor Validation

The calibration of redundant safety critical sensors in nuclear power plants is a manual task that consumes valuable time and resources. Automated, data-driven techniques, to monitor the calibration of redundant sensors have been developed over the last two decades, but have not been fully implemented. Parity space methods such as the Instrumentation and Calibration Monitoring Program (ICMP) method developed by Electric Power Research Institute and other empirical based inferential modeling techniques have been developed but have not become viable options. Existing solutions to the redundant sensor validation problem have several major flaws that restrict their applications. Parity space method, such as ICMP, are not robust for low redundancy conditions and their operation becomes invalid when there are only two redundant sensors. Empirical based inferential modeling is only valid when intrinsic correlations between predictor variables and response variables remain static during the model training and testing phase. They also commonly produce high variance results and are not the optimal solution to the problem. This dissertation develops and implements independent component analysis (ICA) for redundant sensor validation. Performance of the ICA algorithm produces sufficiently low residual variance parameter estimates when compared to simple averaging, ICMP, and principal component regression (PCR) techniques. For stationary signals, it can detect and isolate sensor drifts for as few as two redundant sensors. It is fast and can be embedded into a real-time system. This is demonstrated on a water level control system. Additionally, ICA has been merged with inferential modeling technique such as PCR to reduce the prediction error and spillover effects from data anomalies. ICA is easy to use with, only the window size needing specification. The effectiveness and robustness of the ICA technique is shown through the use of actual nuclear power plant data. A bootstrap technique is used to estimate the prediction uncertainties and validate its usefulness. Bootstrap uncertainty estimates incorporate uncertainties from both data and the model. Thus, the uncertainty estimation is robust and varies from data set to data set. The ICA based system is proven to be accurate and robust; however, classical ICA algorithms commonly fail when distributions are multi-modal. This most likely occurs during highly non-stationary transients. This research also developed a unity check technique which indicates such failures and applies other, more robust techniques during transients. For linear trending signals, a rotation transform is found useful while standard averaging techniques are used during general transients

Calibrating CHIME, A New Radio Interferometer to Probe Dark Energy

The Canadian Hydrogen Intensity Mapping Experiment (CHIME) is a transit interferometer currently being built at the Dominion Radio Astrophysical Observatory (DRAO) in Penticton, BC, Canada. We will use CHIME to map neutral hydrogen in the frequency range 400 -- 800\,MHz over half of the sky, producing a measurement of baryon acoustic oscillations (BAO) at redshifts between 0.8 -- 2.5 to probe dark energy. We have deployed a pathfinder version of CHIME that will yield constraints on the BAO power spectrum and provide a test-bed for our calibration scheme. I will discuss the CHIME calibration requirements and describe instrumentation we are developing to meet these requirements

Redundancy Calibration of Phased Array Stations

Our aim is to assess the benefits and limitations of using the redundant visibility information in regular phased array systems for improving the calibration. Regular arrays offer the possibility to use redundant visibility information to constrain the calibration of the array independent of a sky model and a beam models of the station elements. It requires a regular arrangement in the configuration of array elements and identical beam patterns. We revised a calibration method for phased array stations using the redundant visibility information in the system and applied it successfully to a LOFAR station. The performance and limitations of the method were demonstrated by comparing its use on real and simulated data. The main limitation is the mutual coupling between the station elements, which leads to non-identical beams and stronger baseline dependent noise. Comparing the variance of the estimated complex gains with the Cramer-Rao Bound (CRB) indicates that redundancy is a stable and optimum method for calibrating the complex gains of the system. Our study shows that the use of the redundant visibility does improve the quality of the calibration in phased array systems. In addition it provides a powerful tool for system diagnostics. Our results demonstrate that designing redundancy in both the station layout and the array configuration of future aperture arrays is strongly recommended. In particular in the case of the Square Kilometre Array with its dynamic range requirement which surpasses any existing array by an order of magnitude.Comment: 16 pages, 15 figures, accepted for publication in the A&A in Section 13, acceptance date: 1st May 2012. NOTE: Please contact the first author for high resolution figure

Fundamental Imaging Limits of Radio Telescope Arrays

The fidelity of radio astronomical images is generally assessed by practical experience, i.e. using rules of thumb, although some aspects and cases have been treated rigorously. In this paper we present a mathematical framework capable of describing the fundamental limits of radio astronomical imaging problems. Although the data model assumes a single snapshot observation, i.e. variations in time and frequency are not considered, this framework is sufficiently general to allow extension to synthesis observations. Using tools from statistical signal processing and linear algebra, we discuss the tractability of the imaging and deconvolution problem, the redistribution of noise in the map by the imaging and deconvolution process, the covariance of the image values due to propagation of calibration errors and thermal noise and the upper limit on the number of sources tractable by self calibration. The combination of covariance of the image values and the number of tractable sources determines the effective noise floor achievable in the imaging process. The effective noise provides a better figure of merit than dynamic range since it includes the spatial variations of the noise. Our results provide handles for improving the imaging performance by design of the array.Comment: 12 pages, 8 figure

Non-linear Redundancy Calibration

For radio interferometric arrays with a sufficient number of redundant spacings the multiplicity of measurements of the same sky visibility can be used to determine both the antenna gains as well as the true visibilities. Many of the earlier approaches to this problem focused on linearized versions of the relation between the measured and the true visibilities. Here we propose to use a standard non-linear minimization algorithm to solve for both the antenna gains as well as the true visibilities. We show through simulations done in the context of the ongoing upgrade to the Ooty Radio Telescope that the non-linear minimization algorithm is fast compared to the earlier approaches. Further, unlike the most straightforward linearized approach, which works with the logarithms of the visibilities and the gains, the non-linear minimization algorithm leads to unbiased solutions. Finally we present error estimates for the estimated gains and visibilities. Monte-Carlo simulations establish that the estimator is indeed statistically efficient, achieving the Cramer-Rao bound.Comment: 9 pages, 5 figures. Accepted for publication in MNRAS. The definitive version will be available at http://mnras.oxfordjournals.or

Hydrogen Epoch of Reionization Array (HERA)

The Hydrogen Epoch of Reionization Array (HERA) is a staged experiment to measure 21 cm emission from the primordial intergalactic medium (IGM) throughout cosmic reionization ($z=6-12$), and to explore earlier epochs of our Cosmic Dawn ($z\sim30$). During these epochs, early stars and black holes heated and ionized the IGM, introducing fluctuations in 21 cm emission. HERA is designed to characterize the evolution of the 21 cm power spectrum to constrain the timing and morphology of reionization, the properties of the first galaxies, the evolution of large-scale structure, and the early sources of heating. The full HERA instrument will be a 350-element interferometer in South Africa consisting of 14-m parabolic dishes observing from 50 to 250 MHz. Currently, 19 dishes have been deployed on site and the next 18 are under construction. HERA has been designated as an SKA Precursor instrument. In this paper, we summarize HERA's scientific context and provide forecasts for its key science results. After reviewing the current state of the art in foreground mitigation, we use the delay-spectrum technique to motivate high-level performance requirements for the HERA instrument. Next, we present the HERA instrument design, along with the subsystem specifications that ensure that HERA meets its performance requirements. Finally, we summarize the schedule and status of the project. We conclude by suggesting that, given the realities of foreground contamination, current-generation 21 cm instruments are approaching their sensitivity limits. HERA is designed to bring both the sensitivity and the precision to deliver its primary science on the basis of proven foreground filtering techniques, while developing new subtraction techniques to unlock new capabilities. The result will be a major step toward realizing the widely recognized scientific potential of 21 cm cosmology.Comment: 26 pages, 24 figures, 2 table

Mapping our Universe in 3D with MITEoR

Mapping our universe in 3D by imaging the redshifted 21 cm line from neutral hydrogen has the potential to overtake the cosmic microwave background as our most powerful cosmological probe, because it can map a much larger volume of our Universe, shedding new light on the epoch of reionization, inflation, dark matter, dark energy, and neutrino masses. We report on MITEoR, a pathfinder low-frequency radio interferometer whose goal is to test technologies that greatly reduce the cost of such 3D mapping for a given sensitivity. MITEoR accomplishes this by using massive baseline redundancy both to enable automated precision calibration and to cut the correlator cost scaling from N^2 to NlogN, where N is the number of antennas. The success of MITEoR with its 64 dual-polarization elements bodes well for the more ambitious HERA project, which would incorporate many identical or similar technologies using an order of magnitude more antennas, each with dramatically larger collecting area.Comment: To be published in proceedings of 2013 IEEE International Symposium on Phased Array Systems & Technolog