Regression-based projection for learning Mori-Zwanzig operators
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A Nonlinear Regression Method for Composite Protection Modeling of Induction Motor Loads
Protection equipment are used to prevent damages to induction motor loads by isolating those from the power network in the event of severe faults. Modeling the response of induction motor loads and their protection is vital for power system planning and operation, especially in understanding system's response moments after a fault has occurred. This article proposes an optimization based framework to generate composite protection models for commercial building motor loads. Introducing a mathematical abstraction, the task of finding a suitable (simplified) model of the composite protection scheme is formulated as a nonlinear regression problem. Numerical examples are provided to illustrate the application of the framework.
Kundu, Soumya↗
Scalable Hybrid Classification-Regression Solution for High-Frequency Nonintrusive Load Monitoring
Residential buildings with the ability to monitor and control their net-load (sum of load and generation) can provide valuable flexibility to power grid operators. We present a novel multiclass nonintrusive load monitoring (NILM) approach that enables effective net-load monitoring capabilities at high-frequency with minimal additional equipment and cost. The proposed machine learning based solution provides accurate multiclass state predictions while operating at a faster timescale (able to provide a prediction for each 60- Hz ac cycle used in US power grid) without relying on event-detection techniques. We also introduce an innovative hybrid classification-regression method that allows for the prediction of not only load on/off states but also individual load operating power levels. A test bed with eight residential appliances is used for validating the NILM approach. Results show that the overall method has high accuracy, good scaling and generalization properties.
feature extraction↗
Interpreting Write Performance of Supercomputer I/O Systems with Regression Models
This work seeks to advance the state of the art in HPC I/O performance analysis and interpretation. In particular, we demonstrate effective techniques to: (1) model output performance in the presence of I/O interference from production loads; (2) build features from write patterns and key parameters of the system architecture and configurations; (3) employ suitable machine learning algorithms to improve model accuracy. We train models with five popular regression algorithms and conduct experiments on two distinct production HPC platforms. We find that the lasso and random forest models predict output performance with high accuracy on both of the target systems. We also explore use of the models to guide adaptation in I/O middleware systems, and show potential for improvements of at least 15% from model-guided adaptation on 70% of samples, and improvements up to 10× on some samples for both of the target systems.
Xie, Bing↗
Causal mediation analysis in nested case-control studies using conditional logistic regression
Not provided.
Mathematical & Computational Biology↗
Gaussian process regression as a surrogate model for the computation of dispersion relations
Not provided.
Engineering↗
Regression Verification Using Impact Summaries
Regression verification techniques are used to prove equivalence of syntactically similar programs. Checking equivalence of large programs, however, can be computationally expensive. Existing regression verification techniques rely on abstraction and decomposition techniques to reduce the computational effort of checking equivalence of the entire program. These techniques are sound but not complete. In this work, we propose a novel approach to improve scalability of regression verification by classifying the program behaviors generated during symbolic execution as either impacted or unimpacted. Our technique uses a combination of static analysis and symbolic execution to generate summaries of impacted program behaviors. The impact summaries are then checked for equivalence using an o-the-shelf decision procedure. We prove that our approach is both sound and complete for sequential programs, with respect to the depth bound of symbolic execution. Our evaluation on a set of sequential C artifacts shows that reducing the size of the summaries can help reduce the cost of software equivalence checking. Various reduction, abstraction, and compositional techniques have been developed to help scale software verification techniques to industrial-sized systems. Although such techniques have greatly increased the size and complexity of systems that can be checked, analysis of large software systems remains costly. Regression analysis techniques, e.g., regression testing [16], regression model checking [22], and regression verification [19], restrict the scope of the analysis by leveraging the differences between program versions. These techniques are based on the idea that if code is checked early in development, then subsequent versions can be checked against a prior (checked) version, leveraging the results of the previous analysis to reduce analysis cost of the current version. Regression verification addresses the problem of proving equivalence of closely related program versions [19]. These techniques compare two programs with a large degree of syntactic similarity to prove that portions of one program version are equivalent to the other. Regression verification can be used for guaranteeing backward compatibility, and for showing behavioral equivalence in programs with syntactic differences, e.g., when a program is refactored to improve its performance, maintainability, or readability. Existing regression verification techniques leverage similarities between program versions by using abstraction and decomposition techniques to improve scalability of the analysis [10, 12, 19]. The abstractions and decomposition in the these techniques, e.g., summaries of unchanged code [12] or semantically equivalent methods [19], compute an over-approximation of the program behaviors. The equivalence checking results of these techniques are sound but not complete-they may characterize programs as not functionally equivalent when, in fact, they are equivalent. In this work we describe a novel approach that leverages the impact of the differences between two programs for scaling regression verification. We partition program behaviors of each version into (a) behaviors impacted by the changes and (b) behaviors not impacted (unimpacted) by the changes. Only the impacted program behaviors are used during equivalence checking. We then prove that checking equivalence of the impacted program behaviors is equivalent to checking equivalence of all program behaviors for a given depth bound. In this work we use symbolic execution to generate the program behaviors and leverage control- and data-dependence information to facilitate the partitioning of program behaviors. The impacted program behaviors are termed as impact summaries. The dependence analyses that facilitate the generation of the impact summaries, we believe, could be used in conjunction with other abstraction and decomposition based approaches, [10, 12], as a complementary reduction technique. An evaluation of our regression verification technique shows that our approach is capable of leveraging similarities between program versions to reduce the size of the queries and the time required to check for logical equivalence. The main contributions of this work are: - A regression verification technique to generate impact summaries that can be checked for functional equivalence using an off-the-shelf decision procedure. - A proof that our approach is sound and complete with respect to the depth bound of symbolic execution. - An implementation of our technique using the LLVMcompiler infrastructure, the klee Symbolic Virtual Machine [4], and a variety of Satisfiability Modulo Theory (SMT) solvers, e.g., STP [7] and Z3 [6]. - An empirical evaluation on a set of C artifacts which shows that the use of impact summaries can reduce the cost of regression verification.
Backes, John↗
Demonstration of a Fiber Optic Regression Probe in a High-Temperature Flow
The capability to provide localized, real-time monitoring of material regression rates in various applications has the potential to provide a new stream of data for development testing of various components and systems, as well as serving as a monitoring tool in flight applications. These applications include, but are not limited to, the regression of a combusting solid fuel surface, the ablation of the throat in a chemical rocket or the heat shield of an aeroshell, and the monitoring of erosion in long-life plasma thrusters. The rate of regression in the first application is very fast, while the second and third are increasingly slower. A recent fundamental sensor development effort has led to a novel regression, erosion, and ablation sensor technology (REAST). The REAST sensor allows for measurement of real-time surface erosion rates at a discrete surface location. The sensor is optical, using two different, co-located fiber-optics to perform the regression measurement. The disparate optical transmission properties of the two fiber-optics makes it possible to measure the regression rate by monitoring the relative light attenuation through the fibers. As the fibers regress along with the parent material in which they are embedded, the relative light intensities through the two fibers changes, providing a measure of the regression rate. The optical nature of the system makes it relatively easy to use in a variety of harsh, high temperature environments, and it is also unaffected by the presence of electric and magnetic fields. In addition, the sensor could be used to perform optical spectroscopy on the light emitted by a process and collected by fibers, giving localized measurements of various properties. The capability to perform an in-situ measurement of material regression rates is useful in addressing a variety of physical issues in various applications. An in-situ measurement allows for real-time data regarding the erosion rates, providing a quick method for empirically anchoring any analysis geared towards lifetime qualification. Erosion rate data over an operating envelope could also be useful in the modeling detailed physical processes. The sensor has been embedded in many regressing media to demonstrate the capabilities in a number of regressing environments. In the present work, sensors were installed in the eroding/regressing throat region of a converging-diverging flow, with the working gas heated to high temperatures by means of a high-pressure arc discharge at steady-state discharge power levels up to 500 kW. The amount of regression observed in each material sample was quantified using a later profilometer, which was compared to the in-situ erosion measurements to demonstrate the efficacy of the measurement technique in very harsh, high-temperature environments.
Korman, Valentin↗
Improving Prediction of Peroxide Value of Edible Oils Using Regularized Regression Models
We present four unique prediction techniques, combined with multiple data pre-processing methods, utilizing a wide range of both oil types and oil peroxide values (PV) as well as incorporating natural aging for peroxide creation. Samples were PV assayed using a standard starch titration method, AOCS Method Cd 8-53, and used as a verified reference method for PV determination. Near-infrared (NIR) spectra were collected from each sample in two unique optical pathlengths (OPLs), 2 and 24 mm, then fused into a third distinct set. All three sets were used in partial least squares (PLS) regression, ridge regression, LASSO regression, and elastic net regression model calculation. While no individual regression model was established as the best, global models for each regression type and pre-processing method show good agreement between all regression types when performed in their optimal scenarios. Furthermore, small spectral window size boxcar averaging shows prediction accuracy improvements for edible oil PVs. Best-performing models for each regression type are: PLS regression, 25 point boxcar window fused OPL spectral information RMSEP = 2.50; ridge regression, 5 point boxcar window, 24 mm OPL, RMSEP = 2.20; LASSO raw spectral information, 24 mm OPL, RMSEP = 1.80; and elastic net, 10 point boxcar window, 24 mm OPL, RMSEP = 1.91. The results show promising advancements in the development of a full global model for PV determination of edible oils.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Demonstration of a Fiber Optic Regression Probe
The capability to provide localized, real-time monitoring of material regression rates in various applications has the potential to provide a new stream of data for development testing of various components and systems, as well as serving as a monitoring tool in flight applications. These applications include, but are not limited to, the regression of a combusting solid fuel surface, the ablation of the throat in a chemical rocket or the heat shield of an aeroshell, and the monitoring of erosion in long-life plasma thrusters. The rate of regression in the first application is very fast, while the second and third are increasingly slower. A recent fundamental sensor development effort has led to a novel regression, erosion, and ablation sensor technology (REAST). The REAST sensor allows for measurement of real-time surface erosion rates at a discrete surface location. The sensor is optical, using two different, co-located fiber-optics to perform the regression measurement. The disparate optical transmission properties of the two fiber-optics makes it possible to measure the regression rate by monitoring the relative light attenuation through the fibers. As the fibers regress along with the parent material in which they are embedded, the relative light intensities through the two fibers changes, providing a measure of the regression rate. The optical nature of the system makes it relatively easy to use in a variety of harsh, high temperature environments, and it is also unaffected by the presence of electric and magnetic fields. In addition, the sensor could be used to perform optical spectroscopy on the light emitted by a process and collected by fibers, giving localized measurements of various properties. The capability to perform an in-situ measurement of material regression rates is useful in addressing a variety of physical issues in various applications. An in-situ measurement allows for real-time data regarding the erosion rates, providing a quick method for empirically anchoring any analysis geared towards lifetime qualification. Erosion rate data over an operating envelope could also be useful in the modeling detailed physical processes. The sensor has been embedded in many regressing media for the purposes of proof-of-concept testing. A gross demonstration of its capabilities was performed using a sanding wheel to remove layers of metal. A longer-term demonstration measurement involved the placement of the sensor in a brake pad, monitoring the removal of pad material associated with the normal wear-and-tear of driving. It was used to measure the regression rates of the combustable media in small model rocket motors and road flares. Finally, a test was performed using a sand blaster to remove small amounts of material at a time. This test was aimed at demonstrating the unit's present resolution, and is compared with laser profilometry data obtained simultaneously. At the lowest resolution levels, this unit should be useful in locally quantifying the erosion rates of the channel walls in plasma thrusters. .
Korman, Valentin↗
Automated and efficient local adaptive regression for principal component-based reduced-order modeling of turbulent reacting flows
Principal Component Analysis can be used to reduce the cost of Computational Fluid Dynamics simulations of turbulent reacting flows by reducing the dimensionality of the transported variables through projection of the thermochemical state onto a lower-dimensional manifold. However, because of the nonlinearity of the principal component source terms, nonlinear regression techniques must be utilized for the source terms in terms of the principal components. Unfortunately, widely available and utilized nonlinear regression techniques can have prohibitive computational requirements and/or accuracy that is highly dependent on user experience in ad hoc tuning of model architecture and hyperparameters. Here, in this work, a new nonlinear regression approach is proposed that is both computationally efficient and automated so does not require any user input. The approach is evaluated through a priori prediction of principal component source terms using data from a Direct Numerical Simulation of a turbulent nonpremixed n-heptane/air jet flame. In particular, the proposed framework consists of local regressions whose complexity is adapted according to the local nonlinearity of the data: local linear regression when accurate enough and local Artificial Neural Networks when nonlinear regression is required. The number of local clusters for local regression is determined automatically using the Davies-Bouldin index. In addition, Bayesian optimization is utilized for model training (i.e., to select the best architectures and hyperparameters of the nonlinear regressions in an unsupervised fashion), eliminating ad hoc hand-tuning and/or expensive grid searches. Overall, compared to a single, global neural network, the new local adaptive regression approach is shown to have comparable accuracy but 69% less training time due to the utilization of local linear regression and faster training of local neural networks.
42 ENGINEERING↗
Embedded Sensors for Measuring Surface Regression
The development and evaluation of new hybrid and solid rocket motors requires accurate characterization of the propellant surface regression as a function of key operational parameters. These characteristics establish the propellant flow rate and are prime design drivers affecting the propulsion system geometry, size, and overall performance. There is a similar need for the development of advanced ablative materials, and the use of conventional ablatives exposed to new operational environments. The Miniature Surface Regression Sensor (MSRS) was developed to serve these applications. It is designed to be cast or embedded in the material of interest and regresses along with it. During this process, the resistance of the sensor is related to its instantaneous length, allowing the real-time thickness of the host material to be established. The time derivative of this data reveals the instantaneous surface regression rate. The MSRS could also be adapted to perform similar measurements for a variety of other host materials when it is desired to monitor thicknesses and/or regression rate for purposes of safety, operational control, or research. For example, the sensor could be used to monitor the thicknesses of brake linings or racecar tires and indicate when they need to be replaced. At the time of this reporting, over 200 of these sensors have been installed into a variety of host materials. An MSRS can be made in either of two configurations, denoted ladder and continuous (see Figure 1). A ladder MSRS includes two highly electrically conductive legs, across which narrow strips of electrically resistive material are placed at small increments of length. These strips resemble the rungs of a ladder and are electrically equivalent to many tiny resistors connected in parallel. A substrate material provides structural support for the legs and rungs. The instantaneous sensor resistance is read by an external signal conditioner via wires attached to the conductive legs on the non-eroding end of the sensor. The sensor signal can be transmitted from inside a high-pressure chamber to the ambient environment, using commercially available feedthrough connectors. Miniaturized internal recorders or wireless data transmission could also potentially be employed to eliminate the need for producing penetrations in the chamber case. The rungs are designed so that as each successive rung is eroded away, the resistance changes by an amount that yields a readily measurable signal larger than the background noise. (In addition, signal-conditioning techniques are used in processing the resistance readings to mitigate the effect of noise.) Hence, each discrete change of resistance serves to indicate the arrival of the regressing host material front at the known depth of the affected resistor rung. The average rate of regression between two adjacent resistors can be calculated simply as the distance between the resistors divided by the time interval between their resistance jumps. Advanced data reduction techniques have also been developed to establish the instantaneous surface position and regression rate when the regressing front is between rungs.
Gramer, Daniel J.↗
Regression Bias in using Solar Wind Measurements
Simultaneous solar wind measurements from the solar wind monitors, WIND and ACE, differ due to the spatial and temporal structure of the solar wind. Correlation studies that use these measurements as input may infer an incorrect correlation due to uncertainties arising from this spatial and temporal structure, especially at extreme and rare solar wind values. In particular, regression analysis will lead to a regression function whose slope is biased towards the mean value of the measurement parameter. This article demonstrates this regression bias by comparing simultaneous ACE and WIND solar wind measurements. A non-linear regression analysis between them leads to a perception of underestimation of extreme values of one measurement on average over the other. Using numerical experiments, we show that popular regression analysis techniques such as linear least-squares, orthogonal least-squares, and non-linear regression are not immune to this bias. Hence while using solar wind parameters as an independent variable in a correlation or regression analysis, random uncertainty in the independent variable can create unintended biases in the response of the dependent variable. More generally, the regression to the mean effect can impact both event-based, statistical studies of magnetospheric response to solar wind forcing.
magnetosphere↗
Measurement of hybrid rocket solid fuel regression rate for a slab burner using deep learning
This study presents an imaging-based deep learning tool to measure the fuel regression rate in a 2D slab burner experiment for hybrid rocket fuels. The slab burner experiment is designed to verify mechanistic models of reacting boundary layer combustion in hybrid rockets by the measurement of fuel regression rates. A DSLR camera with a high intensity flash is used to capture images throughout the burn and the images are then used to find the fuel boundary to calculate the regression rate. A U-net convolutional neural network architecture is explored to segment the fuel from the experimental images. Here, a Monte-Carlo Dropout process is used to quantify the regression rate uncertainty produced from the network. The U-net computed regression rates are compared with values from other techniques from literature and show error less than 10%. An oxidizer flux dependency study is performed and shows the U-net predictions of regression rates are accurate and independent of the oxidizer flux, when the images in the training set are not over-saturated. Training with monochrome images is explored and is not successful at predicting the fuel regression rate from images with high noise. The network is superior at filtering out noise introduced by soot, pitting, and wax deposition on the chamber glass as well as the flame when compared to traditional image processing techniques, such as threshold binary conversion and spatial filtering. U-net consistently provides low error image segmentations to allow accurate computation of the regression rate of the fuel.
42 ENGINEERING↗
Predicting Li-Ion Battery Capacity Fade Using Early-Life Data and a Hybrid Data-Driven Gaussian Process-Bayesian Regression Approach
Accurately predicting Li-ion battery capacity trajectories using early-life data can dramatically improve battery-life understandings and be used to rapidly evaluate design/cost/performance trade-offs when developing new battery materials. Accurate early-life predictions enable researchers to quickly iterate over cell designs and material precursor properties without consistently cycling cells to failure. To this end, we present a toolbox that uses a combined Gaussian Process and Bayesian regression approach that capitalizes on signals other than just capacity (e.g., dQ/dV, voltage drops) to rapidly predict capacity-fade trajectories. The prediction tool uses Bayesian regression to fit functional forms, e.g., power law, sigmoids, etc., to predict capacity-fade dynamics. By fitting functional forms, the capacity fade can be interrogated at any point in the future, allowing for early cell-failure prediction. Additionally, Bayesian regression allows for accurate uncertainty estimates that account for cell-to-cell variability (aleatoric uncertainty) and the lack of observation data (epistemic uncertainty). By only using early cycle data to predict the capacity fade trajectory, uncertainty bounds at end-of-life can be extremely large. The large uncertainty bounds are further exacerbated because there is no systematic way to define the prior distribution of the functional forms' parameters. We improve our the predicted trajectory confidence interval of our predicted trajectory using two methods. First, we shows that a small amount of held-out cycling data is sufficientuse some train cells, that have been cycled to failure to derive information regarding the appropriate prior distributions for the functional forms' parameters of the functional form, effectively leading to data-driven priors.. We propose constructing the data-driven priors by first running a Bayesian regression starting with uninformed priors to generate intermediate cell-specific posterior parameter distributions. These posterior distributions are combined using a Ggaussian mixture model for each parameter to create the data-driven priors. These mixture models serve as the data-driven prior distributions for the parameters for. Second, we derive multiple features, e.g., C_dchg 0.5 DoD 0.5, log (|mean(dQ/dV_(w_3-w_0 ) (V)|), etc., from the train cellsheld-out cycling data, identify which the features are that best predicting capacity at early/mid-life cycles, and then create Ggaussian process regression models that are used for predicting capacity at early/mid-life cycles for the test cells (see blue dots with error bars in Fig 1b). Finally, these predicted data-points are used in addition to the actual early cycle data capacity fade to construct the Bayesian regression trajectory for the test cell s. Notably. We note that these two methods are complementary and can be combined with each other. We evaluate the performance of our proposed method on an testing open-source dataset from Iowa State University and Iowa Lakes Community College (ISU-ILCC). This dataset comprises of 251 nickel-manganese-cobalt/graphite Lithium-ion cells that are cycled under 63 different conditions. We compute the mean average percentage error (MAPE) and negative log predictive density (NLPD) to quantify the efficacy of our method. Our initial findings suggest that, when only few observations are available, for test cells, when using only Bayesian regression with uninformed priors, a power law functional provides the most accurate predictions. with very few data points. However, asHowever, a the number of data points increases, a twin sigmoidal function becomes more accurate as the number of observations further increases. We also find that using as little as 10% of the data set towards generating data-driven priors can lead to significant improvement in prediction accuracy when using early cycle data. Lastly, we found that augmenting early-cycle data with Gaussian process-predicted capacity data for Bayesian regression greatly improves the prediction accuracy. We will present a comprehensive comparison of our methods to other methods available in the literature and apply this method to additional battery datasets.
42 ENGINEERING↗
Subsonic Aircraft With Regression and Neural-Network Approximators Designed
At the NASA Glenn Research Center, NASA Langley Research Center's Flight Optimization System (FLOPS) and the design optimization testbed COMETBOARDS with regression and neural-network-analysis approximators have been coupled to obtain a preliminary aircraft design methodology. For a subsonic aircraft, the optimal design, that is the airframe-engine combination, is obtained by the simulation. The aircraft is powered by two high-bypass-ratio engines with a nominal thrust of about 35,000 lbf. It is to carry 150 passengers at a cruise speed of Mach 0.8 over a range of 3000 n mi and to operate on a 6000-ft runway. The aircraft design utilized a neural network and a regression-approximations-based analysis tool, along with a multioptimizer cascade algorithm that uses sequential linear programming, sequential quadratic programming, the method of feasible directions, and then sequential quadratic programming again. Optimal aircraft weight versus the number of design iterations is shown. The central processing unit (CPU) time to solution is given. It is shown that the regression-method-based analyzer exhibited a smoother convergence pattern than the FLOPS code. The optimum weight obtained by the approximation technique and the FLOPS code differed by 1.3 percent. Prediction by the approximation technique exhibited no error for the aircraft wing area and turbine entry temperature, whereas it was within 2 percent for most other parameters. Cascade strategy was required by FLOPS as well as the approximators. The regression method had a tendency to hug the data points, whereas the neural network exhibited a propensity to follow a mean path. The performance of the neural network and regression methods was considered adequate. It was at about the same level for small, standard, and large models with redundancy ratios (defined as the number of input-output pairs to the number of unknown coefficients) of 14, 28, and 57, respectively. In an SGI octane workstation (Silicon Graphics, Inc., Mountainview, CA), the regression training required a fraction of a CPU second, whereas neural network training was between 1 and 9 min, as given. For a single analysis cycle, the 3-sec CPU time required by the FLOPS code was reduced to milliseconds by the approximators. For design calculations, the time with the FLOPS code was 34 min. It was reduced to 2 sec with the regression method and to 4 min by the neural network technique. The performance of the regression and neural network methods was found to be satisfactory for the analysis and design optimization of the subsonic aircraft.
Patnaik, Surya N.↗
Hidden Connections between Regression Models of Strain-Gage Balance Calibration Data
Hidden connections between regression models of wind tunnel strain-gage balance calibration data are investigated. These connections become visible whenever balance calibration data is supplied in its design format and both the Iterative and Non-Iterative Method are used to process the data. First, it is shown how the regression coefficients of the fitted balance loads of a force balance can be approximated by using the corresponding regression coefficients of the fitted strain-gage outputs. Then, data from the manual calibration of the Ames MK40 six-component force balance is chosen to illustrate how estimates of the regression coefficients of the fitted balance loads can be obtained from the regression coefficients of the fitted strain-gage outputs. The study illustrates that load predictions obtained by applying the Iterative or the Non-Iterative Method originate from two related regression solutions of the balance calibration data as long as balance loads are given in the design format of the balance, gage outputs behave highly linear, strict statistical quality metrics are used to assess regression models of the data, and regression model term combinations of the fitted loads and gage outputs can be obtained by a simple variable exchange.
Ulbrich, Norbert↗