Constructing an Efficient Self-Tuning Aircraft Engine Model for Control and Health Management Applications

Self-tuning aircraft engine models can be applied for control and health management applications. The self-tuning feature of these models minimizes the mismatch between any given engine and the underlying engineering model describing an engine family. This paper provides details of the construction of a self-tuning engine model centered on a piecewise linear Kalman filter design. Starting from a nonlinear transient aerothermal model, a piecewise linear representation is first extracted. The linearization procedure creates a database of trim vectors and state-space matrices that are subsequently scheduled for interpolation based on engine operating point. A series of steady-state Kalman gains can next be constructed from a reduced-order form of the piecewise linear model. Reduction of the piecewise linear model to an observable dimension with respect to available sensed engine measurements can be achieved using either a subset or an optimal linear combination of "health" parameters, which describe engine performance. The resulting piecewise linear Kalman filter is then implemented for faster-than-real-time processing of sensed engine measurements, generating outputs appropriate for trending engine performance, estimating both measured and unmeasured parameters for control purposes, and performing on-board gas-path fault diagnostics. Computational efficiency is achieved by designing multidimensional interpolation algorithms that exploit the shared scheduling of multiple trim vectors and system matrices. An example application illustrates the accuracy of a self-tuning piecewise linear Kalman filter model when applied to a nonlinear turbofan engine simulation. Additional discussions focus on the issue of transient response accuracy and the advantages of a piecewise linear Kalman filter in the context of validation and verification. The techniques described provide a framework for constructing efficient self-tuning aircraft engine models from complex nonlinear simulations.Self-tuning aircraft engine models can be applied for control and health management applications. The self-tuning feature of these models minimizes the mismatch between any given engine and the underlying engineering model describing an engine family. This paper provides details of the construction of a self-tuning engine model centered on a piecewise linear Kalman filter design. Starting from a nonlinear transient aerothermal model, a piecewise linear representation is first extracted. The linearization procedure creates a database of trim vectors and state-space matrices that are subsequently scheduled for interpolation based on engine operating point. A series of steady-state Kalman gains can next be constructed from a reduced-order form of the piecewise linear model. Reduction of the piecewise linear model to an observable dimension with respect to available sensed engine measurements can be achieved using either a subset or an optimal linear combination of "health" parameters, which describe engine performance. The resulting piecewise linear Kalman filter is then implemented for faster-than-real-time processing of sensed engine measurements, generating outputs appropriate for trending engine performance, estimating both measured and unmeasured parameters for control purposes, and performing on-board gas-path fault diagnostics. Computational efficiency is achieved by designing multidimensional interpolation algorithms that exploit the shared scheduling of multiple trim vectors and system matrices. An example application illustrates the accuracy of a self-tuning piecewise linear Kalman filter model when applied to a nonlinear turbofan engine simulation. Additional discussions focus on the issue of transient response accuracy and the advantages of a piecewise linear Kalman filter in the context of validation and verification. The techniques described provide a framework for constructing efficient self-tuning aircraft engine models from complex nonlinear simulatns

On the estimation algorithm used in adaptive performance optimization of turbofan engines

The performance seeking control algorithm is designed to continuously optimize the performance of propulsion systems. The performance seeking control algorithm uses a nominal model of the propulsion system and estimates, in flight, the engine deviation parameters characterizing the engine deviations with respect to nominal conditions. In practice, because of measurement biases and/or model uncertainties, the estimated engine deviation parameters may not reflect the engine's actual off-nominal condition. This factor has a necessary impact on the overall performance seeking control scheme exacerbated by the open-loop character of the algorithm. The effects produced by unknown measurement biases over the estimation algorithm are evaluated. This evaluation allows for identification of the most critical measurements for application of the performance seeking control algorithm to an F100 engine. An equivalence relation between the biases and engine deviation parameters stems from an observability study; therefore, it is undecided whether the estimated engine deviation parameters represent the actual engine deviation or whether they simply reflect the measurement biases. A new algorithm, based on the engine's (steady-state) optimization model, is proposed and tested with flight data. When compared with previous Kalman filter schemes, based on local engine dynamic models, the new algorithm is easier to design and tune and it reduces the computational burden of the onboard computer

Optimal linear quadratic Gaussian control based frequency regulation with communication delays in power system

In this paper, load frequency regulator based on linear quadratic Gaussian (LQG) is designed for the MAPS with communication delays. The communication delay is considered to denote the small time delay in a local control area of a wide-area power system. The system is modeled in the state space with inclusion of the delay state matrix parameters. Since some state variables are difficult to measure in a real modern multi-area power system, Kalman filter is used to estimate the unmeasured variables. In addition, the controller with the optimal feedback gain reduces the frequency spikes to zero and keeps the system stable. Lyapunov function based on the LMI technique is used to re-assure the asymptotically stability and the convergence of the estimator error. The designed LQG is simulated in a two area connected power network with considerable time delay. The result from the simulations indicates that the controller performed with expectation in terms of damping the frequency fluctuations and area control errors. It also solved the limitation of other controllers which need to measure all the system state variables

Deep Learning Approach for Dynamic Sampling for High-Throughput Nano-DESI MSI

Mass Spectrometry Imaging (MSI) extracts molecular mass data to form visualizations of molecular spatial distributions. The involved scanning procedure is conducted by moving a probe across and around a rectilinear grid, as in the case of nanoscale Desorption Electro-Spray Ionization (nano-DESI) MSI, where singular measurements can take up to ~5 seconds to acquire high-resolution (better than 10 μm) results. This temporal expense creates a high inefficiency in sample processing and throughput. For example, in a high-resolution nano-DESI study, a single mouse uterine tissue section (2.5 mm by 1.7 mm) had an acquisition time of ~4 hours to acquire 104,400 pixels. Anywhere from ~25-30% of those pixels were outside the actual tissue, and a further portion of those locations lacked relevant information. An existing method, a Supervised Learning Approach for Dynamic Sampling (SLADS), utilizes information obtained during an active scan to infer, using a least-squares regression, regions of interest that most likely contain meaningful information, and a computationally inexpensive weighted mean interpolation to perform sparse sample reconstruction. This approach could potentially be used to significantly improve throughput in this and other biological tissue scanning applications. However, existing SLADS implementations were neither designed nor optimized for leveraging or handling the 3rd dimension in MSI of molecular spectra. Further, integrating more recent advances in machine learning since the last SLADS publication issuance, such as Convolutional Neural Network (CNN) architectures, offers additional performance gains. The objective of this research is the updating, re-design, and optimization of the SLADS methodology, to form a Deep Learning Approach for Dynamic Sampling (DLADS) for high-resolution biological tissues and integration with nano-DESI MSI instrumentation

Fault Diagnosis of Lubrication Decay in Reaction Wheels Using Temperature Estimation and Forecasting via Enhanced Adaptive Particle Filter

Reaction wheel (RW), the most common Attitude Control Systems (ACS) in satellites, are highly prone to failure. A satellite needs to be oriented in a particular direction to maneuver and accomplish its mission goals; losing the RW can lead to a complete or partial mission failure. Therefore, estimating the remaining useful life (RUL) in long and short spans can be extremely valuable. The short-period prediction allows the satellite\u27s operator to manage and prioritize mission tasks based on the RUL and increases the chances of a total mission failure becoming a partial one. Studies show that lack of proper bearing lubrication and uneven frictional torque distribution, which lead to variation in motor torque, are the leading causes of failure in RWs. Hence, this study aims to develop a three-step prognostic method for longterm RUL estimation of RWs based on the remaining lubricant for the bearing unit and potential fault in the supplementary lubrication system. In the first step of this method, the temperature of the lubricants is estimated as the non-measurable state of the system, using a proposed Adaptive particle filter (APF) with an-gular velocity and motor current of RW as the available measurements. In the second step, the estimated lubricant\u27s temperature and amount of injected lubrication in the bearing alongside the lubrication degradation model are fed to a two-step Particle Filter (PF) for online model parameter estimation. In the last step, the performance of the proposed prognostics method is evaluated by predicting the RW\u27s RUL under two fault scenarios, including excessive loss of lubrication and insufficient injection of lubrication. The results show promising performance for the proposed scheme with accuracy in estimation of degradation model\u27s parameters around 2–3% of root mean squared percentage error (RMSPE) and prediction of RUL around 0.1- 4% percentage error

Sloppiness, Modeling, and Evolution in Biochemical Networks

The wonderful complexity of livings cells cannot be understood solely by studying one gene or protein at a time. Instead, we must consider their interactions and study the complex biochemical networks they function in. Quantitative computational models are important tools for understanding the dynamics of such biochemical networks, and we begin in Chapter 2 by showing that the sensitivities of such models to parameter changes are generically `sloppy', with eigenvalues roughly evenly spaced over many decades. This sloppiness has practical consequences for the modeling process. In particular, we argue that if one's goal is to make experimentally testable predictions, sloppiness suggests that collectively fitting model parameters to system-level data will often be much more efficient that directly measuring them. In Chapter 3 we apply some of the lessons of sloppiness to a specific modeling project involving in vitro experiments on the activation of the heterotrimeric G protein transducin. We explore how well time-series activation experiments can constrain model parameters, and we show quantitatively that the T177A mutant of transducin exhibits a much slower rate of rhodopsin-mediated activation than the wild-type. All the preceding biochemical modeling work is performed using the SloppyCell modeling environment, and Chapter 4 briefly introduces SloppyCell and some of the analyses it implements. Additionally, the two appendices of this thesis contain preliminary user and developer documentation for SloppyCell. Modelers tweak network parameters with their computers, and nature tweaks such parameters through evolution. We study evolution in Chapter 5 using a version of Fisher's geometrical model with minimal pleiotropy, appropriate for the evolution of biochemical parameters. The model predicts a striking pattern of cusps in the distribution of fitness effects of fixed mutations, and using extreme value theory we show that the consequences of these cusps should be observable in feasible experiments. Finally, this thesis closes in Chapter 6 by briefly considering several topics: sloppiness in two non-biochemical models, two technical issues with building models, and the effect of sloppiness on evolution beyond the first fixed mutation

Operational Estimation and Prediction of Nitrification Dynamics in the Activated Sludge Process

This report examines the feasibility and discusses the potential of applications of on-line real-time state estimation and prediction in operational control of the activated sludge process. In particular, the dynamics of nitrification are considered with reference to the activated sludge unit at the Norwich Sewage Works in eastern England. A recursive estimation algorithm, the extended Kalman filter, is applied both for reconstructing operating information on the variations in nitrifying bacterial population concentrations and for making predictions of process performance under assumed scenarios for the short-term future operating conditions of the plant. Time-series field data from the Norwich Works are used for the former analysis. Considerations of uncertainty and the possibility of rapid major perturbations in performance, for example, due to spillage of toxic substances or the loss of solids over the clarifier weir, are of special importance to the discussion. The report is introduced and concluded with some more general comments on the roles of operator experience and decision-making and man-machine interaction in wastewater treatment plant control

Multicountry Modeling of Financial Markets

After a survey of alternative theoretical approaches to modeling financial markets, the domestic and international financial linkages of major multicountry models are examined and assessed. The properties of these models are compared by calculating the slopes of their UI and BP curves for the United States, Germany, and Japan. The BP curves (horizontal by assumption in several models) are almost always found to be flatter than the estimated UN curves. International differences in UI slopes are not generally greater than inter-model differences in the estimated slopes of LN curves for any given country. Models with rational or model-consistent expectations in their financial markers tend to show mere appreciation of the U.S. dollar, in response to fiscal expansion, than do models with adaptive expectations, although in both types of model the induced nominal exchange rate changes play a modest role in the transmission linking domestic spending to the current account. Suggestions are made for modeling the increasing globalization of financial markets, and for more explicit treatment of learning behaviour in the modeling of expectations.

Robust techniques for developing empirical models of fluidized bed combustors

This report is designed to provide a review of those data analysis techniques that are most useful for fitting m-dimensional empirical surfaces to very large sets of data. One issue explored is the improvement of data (1) using estimates of the relative size of measurement errors and (2) using known or assumed theoretical relationships. An apparently new concept is developed, named robust weighting, which facilitates the incorporation of a Driori knowledge, based upon the values of input and response variables, about the relative quality of different experiments. This is a particularly useful technique for obtaining statistical inferences from the most relevant portions of the data base, such as concentrating on important ranges of variables or extrapolating off the leading edge of the frontier of knowledge for an emerging technology. The robust weightings are also useful for forcing a priori known asymptotic behaviors, as well as for fighting biases due to shear size of conflicting data clusters and for formulating separate models for conflicting clusters. Another new development has evolved from the two very different objectives of the empirical modeling in this project. The first objective is the usual requirement for the best possible predictive mechanism, and standard techniques are useful with their emphasis on model building, specifically the successive separation of trend techniques. In addition, a second objective involves the pursuit of high-dimensional, yet simple, models that could provide insight into analytic gaps and scientific theories that might govern the situation. For this second objective a new stepwise process was developed for rapidly sweeping the data base and producing crude quantitative measures of the next (or the first) most important m-tuple relationship to incorporate into the empirical model. These quantitative guidelines have been named the fit improvement factors. Some of the standard statistical techniques reviewed include: graphical displays, resistant models, smoothing processes, nonlinear and nonparametric regressions, stopping rules, and spline functions for model hypothesis; and robust estimators and data splitting are reviewed as polishing and validating procedures. The concepts of setting, depth and scope of the validation process are described along with an array of about sixty techniques for validating models. Actual data from the recent literature about the performance of fluidized bed combustors is used as an example of some of the methods presented. Also included is a bibliography of more than 150 references on empirical model development and validation.Sponsored by Contract. no. E49-18-2295 from the U.S. Dept. of Energy