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At least 19 records

Nonlinear Modeling by Assembling Piecewise Linear Models

To preserve nonlinearity of a full order system over a parameters range of interest, we propose a simple modeling approach by assembling a set of piecewise local solutions, including the first-order Taylor series terms expanded about some sampling states. The work by Rewienski and White inspired our use of piecewise linear local solutions. The assembly of these local approximations is accomplished by assigning nonlinear weights, through radial basis functions in this study. The efficacy of the proposed procedure is validated for a two-dimensional airfoil moving at different Mach numbers and pitching motions, under which the flow exhibits prominent nonlinear behaviors. All results confirm that our nonlinear model is accurate and stable for predicting not only aerodynamic forces but also detailed flowfields. Moreover, the model is robustness-accurate for inputs considerably different from the base trajectory in form and magnitude. This modeling preserves nonlinearity of the problems considered in a rather simple and accurate manner.

Yao, Weigang↗

Hyperplane decision trees as piecewise linear surrogate models for chemical process design

Recent trends in chemical engineering research point towards an increasing reliance on data-driven modeling approaches. Neural networks, for instance, have proven to be accurate when data is plentiful and high-dimensional, but in many cases, they require computationally-intensive training procedures. Here, in this work, we describe hyperplane decision trees (HT) as a highly expressive and low-compute machine learning model architecture. These models are locally linear and have linear decision boundaries, resulting in a piecewise linear model of the data. This property allows them to be converted into mixed-integer linear constraints which can be globally optimized. Our open-source PyTorch implementation of this method is a fast, flexible, and accessible way to build accurate piecewise linear models of data.

Decision trees↗

An analysis of LANDSAT MSS scene-to-scene registration accuracy

Measurements were made for 12 registrations done by ERL for 8 registrations done by SRS. The results indicate that the ERL method is significantly more accurate in five of the eight comparison. The difference between the two methods are not significant in the other three cases. There are two possible reasons for the differences. First, the ERL model is a piecewise linear model and the EDITOR model is a cubic polynomial model. Second, the ERL program resamples using bilinear interpolation while the EDITOR software uses a nearest neighbor resampling. This study did not indicate how much of the difference is attributable to each factor. The average of all merged scene error values for ERL was 31.6 meters and the average for the eight common areas was 32.6 meters. The average of the eight merged scene error values for SRS was 40.1 meters.

Seyfarth, B. R.↗

Hybrid Kalman Filter: A New Approach for Aircraft Engine In-Flight Diagnostics

In this paper, a uniquely structured Kalman filter is developed for its application to in-flight diagnostics of aircraft gas turbine engines. The Kalman filter is a hybrid of a nonlinear on-board engine model (OBEM) and piecewise linear models. The utilization of the nonlinear OBEM allows the reference health baseline of the in-flight diagnostic system to be updated to the degraded health condition of the engines through a relatively simple process. Through this health baseline update, the effectiveness of the in-flight diagnostic algorithm can be maintained as the health of the engine degrades over time. Another significant aspect of the hybrid Kalman filter methodology is its capability to take advantage of conventional linear and nonlinear Kalman filter approaches. Based on the hybrid Kalman filter, an in-flight fault detection system is developed, and its diagnostic capability is evaluated in a simulation environment. Through the evaluation, the suitability of the hybrid Kalman filter technique for aircraft engine in-flight diagnostics is demonstrated.

Kobayashi, Takahisa↗

Self‐gated, dynamic contrast‐enhanced magnetic resonance imaging with compressed‐sensing reconstruction for evaluating endothelial permeability in the aortic root of atherosclerotic mice

High‐risk atherosclerotic plaques are characterized by active inflammation and abundant leaky microvessels. We present a self‐gated, dynamic contrast‐enhanced magnetic resonance imaging (DCE‐MRI) acquisition with compressed sensing reconstruction and apply it to assess longitudinal changes in endothelial permeability in the aortic root of Apoe −/− atherosclerotic mice during natural disease progression. Twenty‐four, 8‐week‐old, female Apoe −/− mice were divided into four groups (n = 6 each) and imaged with self‐gated DCE‐MRI at 4, 8, 12, and 16 weeks after high‐fat diet initiation, and then euthanized for CD68 immunohistochemistry for macrophages. Eight additional mice were kept on a high‐fat diet and imaged longitudinally at the same time points. Aortic‐root pseudo‐concentration curves were analyzed using a validated piecewise linear model. Contrast agent wash‐in and washout slopes ( b 1 and b 2 ) were measured as surrogates of aortic root endothelial permeability and compared with macrophage density by immunohistochemistry. b 2 , indicating contrast agent washout, was significantly higher in mice kept on an high‐fat diet for longer periods of time ( p = 0.03). Group comparison revealed significant differences between mice on a high‐fat diet for 4 versus 16 weeks ( p = 0.03). Macrophage density also significantly increased with diet duration ( p = 0.009). Spearman correlation between b 2 from DCE‐MRI and macrophage density indicated a weak relationship between the two parameters (r = 0.28, p = 0.20). Validated piecewise linear modeling of the DCE‐MRI data showed that the aortic root contrast agent washout rate is significantly different during disease progression. Further development of this technique from a single‐slice to a 3D acquisition may enable better investigation of the relationship between in vivo imaging of endothelial permeability and atherosclerotic plaques' genetic, molecular, and cellular makeup in this important model of disease.

Calcagno, Claudia↗

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.

Armstrong, Jeffrey B.↗

Bit-error rates in optical communications

Statistical model, which consists of on/off binary system, assumes Poisson detection process and log-normal atmospheric scintillation. Based upon detection process and atmospheric ionization, piecewise linear model for adaptive threshold system is developed.

Webb, W. E.↗

The influence of ground conductivity on the structure of RF radiation from return strokes

The combination of the finite conductivity of the Earth plus the propagation of the return stroke current up the channel which results in an apparent time delay between the fast field changes and RF radiation for distant observers is shown. The time delay predicted from model return strokes is on the order of 20 micro and the received signal has the characteristics of the data observed in Virginia and Florida. A piecewise linear model for the return stroke channel and a transmission line model for current propagation on each segment was used. Radiation from each segment is calculated over a flat Earth with finite conductivity using asymptotics approximations for the Sommerfeld integrals. The radiation at the observer is processed by a model AM radio receiver. The output voltage was calculated for several frequencies between HF-UHF assuming a system bandwidth (300 kHz) characteristic of the system used to collect data in Florida and Virginia. Comparison with the theoretical fast field changes indicates a time delay of 20 microns.

Levine, D. M.↗

A Model Tree Generator (MTG) Framework for Simulating Hydrologic Systems: Application to Reservoir Routing

Data-driven algorithms have been widely used as effective tools to mimic hydrologic systems. Unlike black-box models, decision tree algorithms offer transparent representations of systems and reveal useful information about the underlying process. A popular class of decision tree models is model tree (MT), which is designed for predicting continuous variables. Most MT algorithms employ an exhaustive search mechanism and a pre-defined splitting criterion to generate a piecewise linear model. However, this approach is computationally intensive, and the selection of the splitting criterion can significantly affect the performance of the generated model. These drawbacks can limit the application of MTs to large datasets. To overcome these shortcomings, a new flexible Model Tree Generator (MTG) framework is introduced here. MTG is equipped with several modules to provide a flexible, efficient, and effective tool for generating MTs. The application of the algorithm is demonstrated through simulation of controlled discharge from several reservoirs across the Contiguous United States (CONUS).

54 ENVIRONMENTAL SCIENCES↗

Analysis and modeling of a family of two-transistor parallel inverters

A family of five static dc-to-square-wave inverters, each employing a square-loop magnetic core in conjunction with two switching transistors, is analyzed using piecewise-linear models for the nonlinear characteristics of the transistors, diodes, and saturable-core devices. Four of the inverters are analyzed in detail for the first time. These analyses show that, by proper choice of a frame of reference, each of the five quite differently appearing inverter circuits can be described by a common equivalent circuit. This equivalent circuit consists of a five-segment nonlinear resistor, a nonlinear saturable reactor, and a linear capacitor. Thus, by proper interpretation and identification of the parameters in the different circuits, the results of a detailed solution for one of the inverter circuits provide similar information and insight into the local and global behavior of each inverter in the family.

Lee, F. C. Y.↗

Modeling and analysis of several classes of self-oscillating inverters. I - State-plane representations. II - Model extension, classification, and duality relationships

The present investigation is concerned with an important class of power conditioning networks, taking into account self-oscillating dc-to-square-wave transistor inverters. The considered circuits are widely used both as the principal power converting and processing means in many systems and as low-power analog-to-discrete-time converters for controlling the switching of the output-stage semiconductors in a variety of power conditioning systems. Aspects of piecewise-linear modeling are discussed, taking into consideration component models, and an equivalent-circuit model. Questions of singular point analysis and state plane representation are also investigated, giving attention to limit cycles, starting circuits, the region of attraction, a hard oscillator, and a soft oscillator.

Lee, F. C. Y.↗

Anisotropic constitutive model for nickel base single crystal alloys: Development and finite element implementation

A tool for the mechanical analysis of nickel base single crystal superalloys, specifically Rene N4, used in gas turbine engine components is developed. This is achieved by a rate dependent anisotropic constitutive model implemented in a nonlinear three dimensional finite element code. The constitutive model is developed from metallurigical concepts utilizing a crystallographic approach. A non Schmid's law formulation is used to model the tension/compression asymmetry and orientation dependence in octahedral slip. Schmid's law is a good approximation to the inelastic response of the material in cube slip. The constitutive equations model the tensile behavior, creep response, and strain rate sensitivity of these alloys. Methods for deriving the material constants from standard tests are presented. The finite element implementation utilizes an initial strain method and twenty noded isoparametric solid elements. The ability to model piecewise linear load histories is included in the finite element code. The constitutive equations are accurately and economically integrated using a second order Adams-Moulton predictor-corrector method with a dynamic time incrementing procedure. Computed results from the finite element code are compared with experimental data for tensile, creep and cyclic tests at 760 deg C. The strain rate sensitivity and stress relaxation capabilities of the model are evaluated.

Dame, L. T.↗

Virtual refrigerant charge sensor for variable-speed heat pumps based on feature selection

The refrigerant charge level in heat pump systems significantly impacts their energy efficiency. Virtual refrigerant charge (VRC) sensing technology has been comprehensively investigated and well-established due to its lower cost compared to physical sensors. However, the previous VRC research often relied on expert judgment and physical reasoning for their variable selection, which can potentially select redundant (or highly correlated) or insignificant features, and it is also primarily focused on single-speed systems. To address these challenges, this study proposes a VRC algorithm for variable-speed heat pumps that selects features through a rigorous feature selection method in combination with physical insights. We also propose a piecewise linear model structure segmented by subcooling temperature to accurately predict charge levels, particularly when subcooling temperatures are substantially low. The proposed algorithm was evaluated using experimental data of a residential R410A heat pump, and the performance was compared with two baseline VRC algorithms. The results are: (1) The proposed algorithm outperforms for the case with subcooling temperature less than 1 °C. (2) The proposed algorithm achieves a tested mean absolute percentage error (MAPE) of 4.23%, and improves the overall accuracy for cooling conditions by approximately 60%, compared with the two baseline algorithms. (3) The proposed algorithm uses two fewer features and improves the accuracy for undercharge cooling conditions by 68.0%, compared with baseline algorithm 2. These improvements enhance prediction accuracy and prevent overfitting, providing a more reliable refrigerant charge level prediction and helping improve the heat pump energy efficiency.

Liang, Chenjiyu↗

Determining the bubble nucleation efficiency of low-energy nuclear recoils in superheated C 3 F 8 dark matter detectors

The bubble nucleation efficiency of low-energy nuclear recoils in superheated liquids plays a crucial role in interpreting results from direct searches for weakly interacting massive particle (WIMP) dark matter. Here, the PICO collaboration presents the results of the efficiencies for bubble nucleation from carbon and fluorine recoils in superheated C 3 F 8 from calibration data taken with five distinct neutron spectra at various thermodynamic thresholds ranging from 2.1 to 3.9 keV. Instead of assuming any particular functional forms for the nuclear recoil efficiency, a generalized piecewise linear model is proposed with systematic errors included as nuisance parameters to minimize model-introduced uncertainties. A Markov chain Monte Carlo routine is applied to sample the nuclear recoil efficiency for fluorine and carbon at 2.45 and 3.29 keV thermodynamic thresholds simultaneously. The nucleation efficiency for fluorine was found to be ≥ 50% for nuclear recoils of 3.3 keV (3.7 keV) at a thermodynamic Seitz threshold of 2.45 keV (3.29 keV), and for carbon the efficiency was found to be ≥ 50% for recoils of 10.6 keV (11.1 keV) at a threshold of 2.45 keV (3.29 keV). Simulated datasets are used to calculate a p value for the fit, confirming that the model used is compatible with the data. The fit paradigm is also assessed for potential systematic biases, which although small, are corrected for. Additional steps are performed to calculate the expected interaction rates of WIMPs in the PICO-60 detector, a requirement for calculating WIMP exclusion limits.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Hypothalamic stimulation and baroceptor reflex interaction on renal nerve activity.

The basal level of mean renal nerve activity (MRNA-0) measured in anesthetized cats was found to be modified by the additive interaction of hypothalamic and baroceptor reflex influences. Data were collected with the four major baroceptor nerves either intact or cut, and with mean aortic pressure (MAP) either clamped with a reservoir or raised with l-epinephrine. With intact baroceptor nerves, MRNA stayed essentially constant at level MRNA-0 for MAP below an initial pressure P1, and fell approximately linearly to zero as MAP was raised to P2. Cutting the baroceptor nerves kept MRNA at MRNA-0 (assumed to represent basal central neural output) independent of MAP. The addition of hypothalamic stimulation produced nearly constant increments in MRNA for all pressure levels up to P2, with complete inhibition at some level above P2. The increments in MRNA depended on frequency and location of the stimulus. A piecewise linear model describes MRNA as a linear combination of hypothalamic, basal central neural, and baroceptor reflex activity.

Wilson, M. F.↗

Threshold detection in an on-off binary communications channel with atmospheric scintillation

The optimum detection threshold in an on-off binary optical communications system operating in the presence of atmospheric turbulence was investigated assuming a poisson detection process and log normal scintillation. The dependence of the probability of bit error on log amplitude variance and received signal strength was analyzed and semi-emperical relationships to predict the optimum detection threshold derived. On the basis of this analysis a piecewise linear model for an adaptive threshold detection system is presented. Bit error probabilities for non-optimum threshold detection system were also investigated.

Webb, W. E.↗

Threshold detection in an on-off binary communications channel with atmospheric scintillation

The optimum detection threshold in an on-off binary optical communications system operating in the presence of atmospheric turbulence was investigated assuming a poisson detection process and log normal scintillation. The dependence of the probability of bit error on log amplitude variance and received signal strength was analyzed and semi-empirical relationships to predict the optimum detection threshold derived. On the basis of this analysis a piecewise linear model for an adaptive threshold detection system is presented. The bit error probabilities for nonoptimum threshold detection systems were also investigated.

Webb, W. E.↗