High-Order Multivariable Transfer Function Curve Fitting: Algorithms, Space Matrix Methods and Experimental Results
This paper develops a computational approach to multivariable frequency domain curve fitting, based on 2-norm minimization.
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This paper develops a computational approach to multivariable frequency domain curve fitting, based on 2-norm minimization.
A parametric cost model for ground-based telescopes is developed using multivariable statistical analysis of both engineering and performance parameters. While diameter continues to be the dominant cost driver, diffraction-limited wavelength is found to be a secondary driver. Other parameters such as radius of curvature are examined. The model includes an explicit factor for primary mirror segmentation and/or duplication (i.e., multi-telescope phased-array systems). Additionally, single variable models Based on aperture diameter are derived.
Global optimization of a multivariable function - constrained by bounds specified on each variable and also unconstrained - is an important problem with several real world applications. Deterministic methods such as the gradient algorithms as well as the randomized methods such as the genetic algorithms may be employed to solve these problems. In fact, there are optimization problems where a genetic algorithm/an evolutionary approach is preferable at least from the quality (accuracy) of the results point of view. From cost (complexity) point of view, both gradient and genetic approaches are usually polynomial-time; there are no serious differences in this regard, i.e., the computational complexity point of view. However, for certain types of problems, such as those with unacceptably erroneous numerical partial derivatives and those with physically amplified analytical partial derivatives whose numerical evaluation involves undesirable errors and/or is messy, a genetic (stochastic) approach should be a better choice. We have presented here the pros and cons of both the approaches so that the concerned reader/user can decide which approach is most suited for the problem at hand. Also for the function which is known in a tabular form, instead of an analytical form, as is often the case in an experimental environment, we attempt to provide an insight into the approaches focusing our attention toward accuracy. Such an insight will help one to decide which method, out of several available methods, should be employed to obtain the best (least error) output. *
A new regression model search algorithm was developed that may be applied to both general multivariate experimental data sets and wind tunnel strain-gage balance calibration data. The algorithm is a simplified version of a more complex algorithm that was originally developed for the NASA Ames Balance Calibration Laboratory. The new algorithm performs regression model term reduction to prevent overfitting of data. It has the advantage that it needs only about one tenth of the original algorithm's CPU time for the completion of a regression model search. In addition, extensive testing showed that the prediction accuracy of math models obtained from the simplified algorithm is similar to the prediction accuracy of math models obtained from the original algorithm. The simplified algorithm, however, cannot guarantee that search constraints related to a set of statistical quality requirements are always satisfied in the optimized regression model. Therefore, the simplified algorithm is not intended to replace the original algorithm. Instead, it may be used to generate an alternate optimized regression model of experimental data whenever the application of the original search algorithm fails or requires too much CPU time. Data from a machine calibration of NASA's MK40 force balance is used to illustrate the application of the new search algorithm.
HED (Howardite, Eucrite and Diogenite) are meteorites with mafic and ultramafic igneous composition. Previous studies suggested HED came from asteroid (4) Vesta and they were generated by magmatic melting followed by differentiation crystallization, metamorphic, and impact. Uniform oxygen isotopic composition of HED samples favors global magma ocean for (4) Vesta. However, the petrological diversity of HED may indicate more complex magma processes in the meteorites. In general, most of the geochemical studies are using traditional methods (e.g. element to element or ratio to ratio plots) to classify the different rock type and groups. With the traditional methods, only limited elements can be shown in a figure. As such, some meteorites may have been identified as HED by a traditional method but found different either in isotopic composition or other elemental characteristic. These anomalous HED meteorites may or may not come from asteroid (4) Vesta. In fact, magma is a unit system where any elemental change should affect to all other elements as a whole, it would be reasonable to consider all elements together to look for the systematical changes. Using multivariable discriminant analysis (MDA) method is one of such testing for their geochemical variation. The method may be able to help us to better understand the petrologic processes and the relationship among elements. This study is to test the MDA method by focus mainly on pyroxene composition of eucrite and diogenite.
Howardite, eucrite and diogenite clan (HED) is the largest magmatic achondrite group and has been suggested to be derived from asteroid (4) Vesta (e.g., [1]). Previous geochemical studies have suggested HEDs were generated by asteroid melting followed by crystallization, metamorphism, and impact [1-6]. However, numerous eucrites and diogenites have anomalous compositional, isotopic or petrological characteristics compared to the norm. This diversity might indicate more complex magma processes on the parent asteroid, or they could be linked to different parental asteroids (e.g., [5]). The former case would imply that the parent asteroid is more heterogenous than currently thought, and that our petrologic models are too simple. The latter case would increase the number of asteroids known to have formed mafic crusts, and would allow for petrological comparisons across numerous bodies. We apply multivariable discrimination analysis (MDA) to a large database of HED pyroxene analyses. This technique allows all elemental information to be considered simultaneously to facilitate identification of groupings, trends, and outliers within the dataset.
Land surface models are crucial tools for many earth science applications including numerical weather prediction, water resource and crop monitoring, and climatological analysis. Given a set of atmospheric forcings, seasonal data, and static parameters, models like Noah-LSM solve for land surface quantities including skin temperature, sensible heat flux, and soil moisture. While these calculations are theoretically robust, they are often computationally expensive. Since artificial neural networks (ANNs) are universal function approximators, they can learn to emulate the output of a deterministic numerical model given a time series of input forcings, with the learned ANN having substantially shorter execution time. The ANN could efficiently parameterize other models, generate ensembles, and provide first-guess inputs for retrievals. As such, with the goal of developing a model that efficiently mimics the output of Noah-LSM given NLDAS2 forcings on a region covering much of the central US, we examine and compare several neural network architectures for the multi-horizon multivariate time series forecasting problem. Recent literature includes a diverse set of approaches including autoregressive architectures like LSTM and GRU, parametric and non-parametric statistical predictors (ForecastNet and MQRNN), self-attention (LSTM-attention-LSTM), and temporal convovlution (DeepTCN). We implement several of these models for the Noah-LSM prediction task, highlighting the features and challenges for each and providing practical insight on the training process.
Meniere's disease (MD) and migraine associated dizziness (MAD) are two disorders that can have similar symptomatologies, but differ vastly in treatment. Vestibular testing is sometimes used to help differentiate between these disorders, but the inefficiency of a human interpreter analyzing a multitude of variables independently decreases its utility. Our hypothesis was that we could objectively discriminate between patients with MD and those with MAD using select variables from the vestibular test battery. Sinusoidal harmonic acceleration test variables were reduced to three vestibulo-ocular reflex physiologic parameters: gain, time constant, and asymmetry. A combination of these parameters plus a measurement of reduced vestibular response from caloric testing allowed us to achieve a joint classification rate of 91%, independent quadratic classification algorithm. Data from posturography were not useful for this type of differentiation. Overall, our classification function can be used as an unbiased assistant to discriminate between MD and MAD and gave us insight into the pathophysiologic differences between the two disorders.
We have elicited a reliable Raman spectral signature for glucose in rabbit aqueous humor across mammalian physiological ranges in a rabbit model stressed by recent myocardial infarction.
Tropical forest tree mortality is increasing due to more severe droughts, yet our understanding of how tree traits and life strategies are linked to drought stress has been limited by measurement scarcity. The BIONTE (BIOmass and NuTrient Experiment) near Manaus, Brazil hosts one of the world’s largest sap flow installations, with sensors in 90 canopy trees across a wood density gradient monitored since June 2022. The 2023 El Niño drought provided a unique opportunity to evaluate how water availability impacts tree transpiration. An interpretable machine learning framework was used to study the complex interactions between transpiration and multiple environmental variables such as soil water availability and vapor pressure deficit (VPD), and how these interactions vary with wood density and individual trees. We found varying responses of transpiration from different trees during the El Niño drought. Transpiration generally increased with temperature, with stronger effects in wetter areas and in trees with low to medium wood density. However, this response was modulated by stomatal sensitivity to VPD, which constrained transpiration under high atmospheric demand, particularly in intermediate-moisture area. The inflection in transpiration rate at high temperatures (>32°C) underscores the role of stomatal and hydraulic regulation in limiting water loss and protecting trees from excessive evaporative demand. Analysis of soil water contribution to transpiration revealed unimodal patterns in wetter area, with peak contributions near 0.45 cm 3 cm -3 of surface soil water and declining or flat responses beyond that threshold, suggesting a shift from water- to energy-limited transpiration. In contrast, drier areas exhibited limited transpiration sensitivity to soil water conditions and minimal trait-based variation in VPD responses, indicating supply-limited conditions. Despite higher wood density trees being generally more resilient, this study shows diverse tree drought resilience, prompting further investigation into the specific traits and dynamics between environmental variables in regulating transpiration and other physiological processes in trees.
This paper presents a new stochastic relay-based extremum-seeking controller (ESC) for multi-input-single-output (MISO) systems. The algorithm was developed with the goal of simplifying configuration to enable easier deployment to real-world problems. A solution is developed first for a static map and then adapted for a general class of dynamic systems. The number of configurable parameters is one per input channel for the static case and only one additional parameter is needed for the dynamic version. The problem of gradient identifiability is solved via the use of stochastic relay gains and a simple stability proof for the static case is presented. Simulation tests demonstrate the performance of the strategy for optimizing both static and dynamic systems.
The climate crisis demands clean energy technologies to cut CO 2 emissions from fossil fuels. Hydrogen fuel cells and solar-driven CO 2 reduction are promising, but both rely on efficient water oxidation. Polypyridyl ruthenium complexes are active catalysts for water oxidation; however, they exhibit poor stability and recyclability. Our group improved performance by embedding these complexes into metal−organic frameworks (MOFs). As water oxidation is pH-dependent, proton management further enhances reactivity. To address the issue, we introduced proton transfer pathways into the MOF structure. Specifically, we incorporated −SO 3 H groups onto the biphenyl linkers of UiO-67 loaded with [Ru(tpy)(dcbpy)OH 2 ]PF 6 catalyst (where tpy = 2,2′:6′,2″-terpyridine; dcbpy = 5,5-dicarboxy-2,2′- bipyridine). The sulfonated MOF exhibited a 2.5-fold increase in oxygen evolution compared to the nonsulfonated analogue. After 1 h of electrolysis, the sulfonated MOF exhibited a turnover number of 25 for oxygen evolution reaction compared to 10 for the native MOF, demonstrating the benefits of built-in proton management.
With the increased use of data-driven approaches and machine learning-based methods in material science, the importance of reliable uncertainty quantification (UQ) of the predicted variables for informed decision-making cannot be overstated. UQ in material property prediction poses unique challenges, including multi-scale and multi-physics nature of materials, intricate interactions between numerous factors, limited availability of large curated datasets, etc. In this work, we introduce a physics-informed Bayesian Neural Networks (BNNs) approach for UQ, which integrates knowledge from governing laws in materials to guide the models toward physically consistent predictions. To evaluate the approach, we present case studies for predicting the creep rupture life of steel alloys. Experimental validation with three datasets of creep tests demonstrates that this method produces point predictions and uncertainty estimations that are competitive or exceed the performance of conventional UQ methods such as Gaussian Process Regression. Additionally, we evaluate the suitability of employing UQ in an active learning scenario and report competitive performance. The most promising framework for creep life prediction is BNNs based on Markov Chain Monte Carlo approximation of the posterior distribution of network parameters, as it provided more reliable results in comparison to BNNs based on variational inference approximation or related NNs with probabilistic outputs.
In this contribution we demonstrate that metal–organic frameworks (MOFs) with suitable underlying topological structure are amenable for the preparation of MOF-based substitutional solid-solutions (SSS) that follow Vegard's law.
This study addresses the challenges inherent in building use type classification, particularly focusing on the issue of class imbalance in the training datasets for machine learning classifiers. We comprehensively analyze the efficacy of various class-balancing sampling techniques. Employing Monte Carlo simulations and Bayesian optimization, we evaluated the performance of multiple sampling methods, including Random Oversampling, Random Undersampling, SMOTE, Borderline-SMOTE, and ADASYN, across a dataset encompassing nine southeastern coastal states of the United States. Our findings reveal that simple random over- and undersampling techniques outperform more sophisticated methods. Additionally, we show inherent value in creating an imbalance in training data to effectively train a machine learning classifier for distinguishing between residential and nonresidential buildings. This study provides valuable guidance for future research on building use type classification research and lays essential groundwork for developing attribute-rich building stock datasets.
Fault detection in Controller Area Network (CAN) systems is crucial for ensuring the reliability and safety of automotive and industrial applications. This study investigates and compares the effectiveness of time series classification models for supervised fault detection in CAN data. This repository contains the code and data for our benchmarking experiment aimed at detecting intermittent faults in automotive Controller Area Network (CAN) data. The goal of this project is to compare various machine learning (ML) and deep learning (DL) models using different Time Series Cross-Validation (TSCV) techniques to evaluate their effectiveness in a streaming environment for fault detection.
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A method of applying Principal Component Analysis, Soft Independent Modeling of Class Analysis, and statistical analysis is described that can be applied to many types of testers to ascertain how well matched the performance of the testers in the analysis are to one another or how well matched a tester is to itself at a later time. This method is most useful for situations for which the same units have not been run across the testers being analyzed for matched performance.