Dependent Errors Research Articles

Maximum Likelihood Identification of Backflow Vortex Instability in Rocket Engine Inducers

Abstract Bayesian estimation is applied to the analysis of backflow vortex instabilities in typical three- and four-bladed liquid propellant rocket engine inducers. The flow in the impeller eye is modeled as a set of equally intense and evenly spaced 2D axial vortices, located at the same radial distance from the axis and rotating at a fraction of the impeller speed. The circle theorem is used to predict the flow pressure in terms of the vortex number, intensity, rotational speed, and radial position. The theoretical spectra so obtained are frequency broadened to mimic the dispersion of the experimental results and parametrically fitted to the measured data by maximum likelihood estimation with equal and independent Gaussian errors. The method is applied to three inducers, tested in water at room temperature and different operating conditions. It successfully characterizes backflow instabilities using the signals of a single pressure transducer flush-mounted in the impeller eye, effectively bypassing the aliasing limitations and the data acquisition/reduction complexities of traditional multiple-sensor cross-correlation methods. The identification returns the estimates of the model parameters and their standard deviations, providing the information necessary for assessing the accuracy and statistical significance of the results. The flowrate is found to be the major factor affecting the backflow vortex instability, which, on the other hand, is rather insensitive to the occurrence of cavitation. The results are consistent with the data reported in the literature, as well as with those generated by the auxiliary models specifically developed for initializing the maximum likelihood searches and supporting the identification procedure.

Evidence of Malaysian Company Performance using Copula and Stochastic Frontier Analysis During the COVID-19 Pandemic

Traditional stochastic frontier analysis (SFA) assumes error independence, potentially leading to estimation and efficiency score errors. The purpose of this paper is to introduce the assumption of dependent errors into SFA to rank the performance of 12 Malaysian companies. In 2019 and 2020, during the global COVID-19 outbreak, the shockwaves it sent through various sectors, including healthcare and transportation, were profound. This study assesses company efficiency performance using the copula stochastic frontier analysis (CSFA) model. Seven Archimedean copulas are considered, and the most suitable copula is selected based on the lowest AIC (Akaike Information Criterion) value. The Cot copula, with an AIC value of -19.707, emerges as the best model. The results also reveal a relationship between random errors and inefficiency errors, as well as evidence that COVID-19 contributes to business inefficiency. According to the Cot copula results, Eita Resources Berhad (0.995), My E.G. Services Berhad (0.994), and KPJ Healthcare Berhad (0.857) are the top-performing companies, while Pansar Berhad (0.316), Suria Capital Holdings Berhad (0.319), and Hap Seng Consolidated Berhad (0.411) are the least efficient ones. Therefore, the primary contribution of this study is the proposition that the Cot copula and SFA are appropriate models for analyzing efficiency results. CSFA is a highly accurate model as it accounts for external factors, or random noise, in efficiency estimation and acknowledges the assumption of dependent errors in SFA, making it more realistic for real-world applications.

Complete [formula omitted]-moment convergence for maximal randomly weighted sums of arrays of rowwise widely orthant dependent random variables and its statistical applications

In this paper, we study the complete f-moment convergence for maximal randomly weighted sums of arrays of rowwise widely orthant dependent random variables under some general conditions. The results obtained in the paper extend and improve some previous known ones. As applications of our main results, we not only present convergence for the state observers of linear-time-invariant systems but also obtain complete consistency for the estimators of errors-in-variables regression models based on widely orthant dependent errors. We further perform a numerical simulation to verify the validity of the theoretical results.

A Study on the Combination Prediction of Anhui Residents’ Consumption Level Based on the IOWA Operator

Aims: In order to study the future trend of Anhui residents’ consumption level and predict the consumption level of Anhui residents in the next three years (2022-2024), this paper constructs a combination prediction model based on the induced ordered weighted averaging (IOWA) operator.
 Study Design: This paper selects the national resident consumption level in Anhui province from 2000 to 2021, which covers a period of 21 years. Based on the data, an IOWA operator combination prediction model is constructed using a multiple regression model, ARIMA (2,2,0) model, and machine learning decision tree model. This is a qualitative analytical study which set the sum of squared errors as dependent variables and error value of different single item prediction method as independent variables.
 Place and Duration of Study: This paper selects the national resident consumption level in Anhui Province from 2000 to 2021.
 Methodology: This paper constructs a combination prediction model based on the IOWA operator based on the multiple regression model, ARIMA (2,2,0) model, and machine learning decision tree model. The combination prediction method that minimizes the sum of squared errors is used to predict the consumption level of Anhui residents in the next three years (2022-2024), and the effectiveness of the IOWA operator-based combination prediction model is evaluated.
 Results: This study finds that the prediction accuracy of the IOWA operator-based combination prediction model is generally greater than that of individual prediction models, and the sum of squared errors is generally significantly lower than that of individual prediction models.
 Conclusion: The prediction results show that the consumption level of Anhui residents in the next three years will not fluctuate greatly, but will have a trend of slight increase. The results of this study can be helpful for the government to improve the consumption level of residents in Anhui Province.

Delta Method Confidence Intervals for Linear Regression Processes With Long-memory Disturbances

This paper provides third and fourth-order coverage probability errors of delta method confidence intervals (CIs) for the covariance parameters of a time series generated by a linear regression model with strongly dependent errors. The CIs are based on the plug-in maximum likelihood (PML) estimators. Bounds have been established on the coverage probability errors of one-and two-sided delta method CIs based on the plug-in log-likelihood (PLL) function under some sets of conditions on the regression coefficients, the spectral density function, and the parameter values. It is shown that the the fourth order delta method CIs in the case of linear regression model with Gaussian, stationary and strongly dependent errors have coverage probability errors of O(n^-1) and that of the third-order has errors of O(n^-1/2) which is the same order of magnitude asymptotically as in the independent and identically distributed (iid) case.

Time Series Regression Modeling with AR(1) Errors

When ordinary regression analysis is performed using time-series variables, it is common for the errors (residuals) to have a time-series structure. This violates the usual assumption of independent errors in ordinary least squares (OLS) regressions. Consequently, the estimates of the coefficients and their standard errors are incorrect if the time-series structure of the errors is ignored. In this study, an investigation of a regression model with time-series variables, particularly a simple case, was conducted using the conventional method. The ‘AirPassengers Dataset’ was downloaded from the R repository used for the analysis. Ordinary least squares and Cochrane-Orcutt procedures were used as methodologies. The results show that the adjusted regression model with autoregressive errors outperformed the ordinary regression model.

Analysis of two conservative fourth-order compact finite difference schemes for the Klein-Gordon-Zakharov system in the subsonic limit regime

We propose two conservative fourth-order compact finite difference (CFD4C) schemes and give the rigorous error analysis for the Klein-Gordon-Zakharov system (KGZS) with ε∈(0,1] being a small parameter. In the case 0<ε≪1, i.e., the subsonic limit regime, the solution of KGZS propagates waves with wavelength O(ε) in time and O(1) in space, respectively, with amplitude at O(εα†) with α†=min⁡{α,β+1,2}, where α and β describe the incompatibility between the initial data of the KGZS and the limiting Klein-Gordon equation (KGE) as ε→0+ and satisfy α≥0,β+1≥0. Different from the standard KGZS, the oscillation in time becomes the main difficulty in constructing numerical schemes and giving the error analysis for KGZS in this regime. We prove that the schemes conserve the discrete energies. By defining a discrete ‘energy’, applying cut-off technique and considering the convergence rate of the KGZS to the limiting KGE, we obtain two independent error estimates with the bounds at O(h4/ε1−α⁎+τ2/ε3−α†) and O(h4+τ2+εα⁎) where α⁎=min⁡{1,α,1+β}, τ is time step and h is mesh size. Hence, we get uniformly accurate error estimates with the bounds at O(h4+τ2/(4−α†)) when α≥1 and β≥0, and O(h4α⁎+τ2α⁎/3) when 0<α<1 or −1<β<0. While for α=0 or β=−1, the meshing requirements of CFD4Cs are h=O(ε1/4) and τ=O(ε3/2) for 0<ε≪1. The compact schemes provide much better spatial resolution compared with the usual second order finite difference schemes. Our numerical results support energy-conserving properties and the results of the convergence analysis.

Analysis of Challenges for Blockchain Adoption in Enterprise Distributed Applications

Decentralization, auditability, smart execution, and security are four ways that blockchain technology (BCT) differs from current cutting-edge technologies based on client-server architecture. Without the need of any middlemen, blockchain technology builds trust between untrustworthy parties. By employing its distinctive properties, blockchain technology is presently used to address the problems of enterprise distributed applications (EDAs) to some extent. As a result, businesses involved in a wide range of industries have shown interest in it. Despite being praised as tool for businesses to create secure applications, BCT is still not widely used. The objective of the current study is to use an extension of the technology acceptance model (TAM2), constituted by 15 hypotheses (H1–H15), to address the factors that influence professionals' desire to adopt the BCT in the EDAs. In order to achieve the research objective, the study consists of a quantitative non-experimental correlational method with the goal of creating an empirical model to evaluate the relationship between perceived usefulness, perceived ease of use, scalability, effort, performance, adaptability, maintainability, experience, and blockchain adoption in India with a focus on EDAs. Descriptive analysis, discriminant analysis, multiple linear regression, ANOVA, homoscedasticity, multicollinearity, reliability, linearity, survey question's normality, and independent errors are conducted to analyze survey data from a sample of 396 IT professionals from various firms in India. The findings show that IT professionals' desire to employ the BCT in EDAs are positively impacted by all the hypothesis except H3 and H8 that has no impact on IT professionals' desire to employ BCT.

Statistically Modeling the Fatigue Life of Copper and Aluminum Wires Using Archival Data

It has been known for at least 150 years that fatigue life data exhibits a considerable amount of variability. Furthermore, statistically modeling fatigue life adequately is challenging. Different empirical approaches have been used, each of which has merit; however, none is appropriate universally. Even when a sufficiently robust database exists, the scatter in the fatigue lives may be extremely large and difficult to characterize. The purpose of this work is to review traditional and more modern empirically based methodologies for estimating the statistical behavior of fatigue data. The analyses are performed on two historic sets of data for annealed aluminum wire and annealed electrolytic copper wire tested in reverse torsion fatigue. These data are readily available In publications. Specifically, the review considers a traditional method for stress-cycle (S-N) analysis which includes linear regression through load dependent medians and mean square error (MSE) confidence bounds. Another approach that is used is Weibull distribution estimation for each loading condition, from which estimations for the median behavior and confidence bounds are determined. The preferred technique is the development of a cumulative distribution functions for fatigue life, which contains aspects of traditional reliability, classical S-N, and applied loading modeling. Again, confidence bounds are estimated for this technique. Even though it is an empirical technique, there are mechanistic aspects that underlie the empiricism. This approach is suggested because the method is very robust, and the estimation is more accurate than the other methods.

Bootstrap Probability Errors of the Whittle MLE for Linear Regression Processes with Strongly Dependent Disturbances

This paper determines bounds on the asymptotic orders of the coverage probability errors of parametric bootstrap confidence intervals (CIs) and tests for the covariance parameters of a time series generated by a regression model with Gaussian, stationary, and strongly dependent errors. The CIs and tests are based on the plug-in Whittle maximum&#x0D; likelihood (PWML) estimators. It is shown that, under some sets of conditions on the regression coefficients, the spectral density function, and the parameter values, the bounds on the coverage probability errors of symmetric two-sided and one-sided parametric bootstrap confidence intervals on the plug-in Whittle log-likelihood function are shown to be O(n^{-3/2}\ln{n}) and O(n^{-1}\ln{n}), respectively. Apart from the \ln{n} term, the magnitudes of the coverage probability errors of the one-sided bootstrap confidence intervals for our model is shown to be essentially the same as that of the independent and identically distributed (iid) data. The error for the two-sided confidence intervals is not as small as the error O(n^{-2}) that has been established for many confidence intervals in the literature, see Hall (1992), pp 102-108.

Functional regression with dependent error and missing observation in reproducing kernel Hilbert spaces

Functional regression with dependent error and missing observation in reproducing kernel Hilbert spaces

Asymptotic properties of M estimators in classical linear models with φ-mixing random errors

In this paper, the asymptotic normality and strong consistency for M estimators of the unknown regression coefficients in classical linear models are established under the assumptions that the errors are identically distributed φ-mixing random variables. The results obtained in this paper generalize the corresponding ones of Chen and Zhao [M-methods in linear model. Shanghai: Scientific and Technical Publishers; 1996] and Zhao [Strong consistency of M-estimates in linear model. Sci China Ser A. 2002;45:1420–1427] for independent errors. Finally, the simulation study is provided to verify the finite sample performance of the theoretical results and a real example is analysed for illustration.

Analisis Psikologi Tokoh dan Nilai Moral dalam Novel Surat Dari Bapak Karya Gol A Gong serta Pemanfaatannya sebagai Bahan Ajar di SMA

This study aims to (1) describe the psychological aspects of the main character in Gol A Gong's Novel Surat dari Bapak; (2) describe the moral values ​​in the novel Surat Dari Bapak by Gol A Gong; and (3) describe its use as teaching materials in SMA. The main character psychological theory used in this study is the psychoanalytic theory by Sigmund Freud which consists of three personality structures, namely: the id found 9 data, the ego found 4 data, and the superego found 3 data. Furthermore, the theory of moral values ​​used is the fictional assessment theory put forward by Nurgiyantoro which consists of three relations of problems in life, including the relationship between humans and oneself found 11 data which include firm stance, calm, careful, self-esteem, independent, and aware error; human relations with the social sphere found 14 data including loyalty, social care, courtesy, parental love for children, and critical; and the relationship between humans and God found 3 data including believing in the existence of God. This type of research is descriptive qualitative. The research subject is the novel Surat dari Bapak by Gol A Gong. The object of research is the psychology of the main character and the moral value of the novel Surat dari Bapak. The source of the data is the story description of the novel Surat dari Bapak by Gol A Gong published by Puspa Swara. This data collection technique uses observation techniques. The research instrument was a researcher assisted by a literary support book and notes. The data analysis technique uses content analysis techniques.

Comparative analysis of closed-form expressions and other commonly used seakeeping methods

Closed-form expressions (CFE) are semi-analytical transfer functions for ship wave-induced responses based only on main ship particulars. They are useful in an early stage of ship design and situations when hull lines for seakeeping analysis are not available. As the accuracy of CFE remains an open subject, the aim of the present study is to quantify the frequency independent model error (FIME) of CFE. Measured transfer functions of the heave, pitch, and vertical wave bending moment at midship for 13 ships are acquired from literature, together with calculated transfer functions using the strip theory and the 3D panel method, where several speeds and heading angles are available. FIME is determined by comparing transfer functions calculated by CFE, strip theory, and 3D panel codes with model-scale experiments. Multivariate linear regression analysis is performed for three seakeeping methods to indicate a dependence of FIME on the main parameters of the analysis. Dispersion of the FIME around the regression line is determined, enabling a relative comparison of the uncertainty of seakeeping methods of different complexity. The results of this study may improve the practical applicability of CFE and provide an uncertainty quantification of commonly used seakeeping methods, which is important for probability-based applications.

Beyond independent error assumptions in large GNN atomistic models.

The calculation of relative energy difference has significant practical applications, such as determining adsorption energy, screening for optimal catalysts with volcano plots, and calculating reaction energies. Although Density Functional Theory (DFT) is effective in calculating relative energies through systematic error cancellation, the accuracy of Graph Neural Networks (GNNs) in this regard remains uncertain. To address this, we analyzed ∼483 × 106 pairs of energy differences predicted by DFT and GNNs using the Open Catalyst 2020-Dense dataset. Our analysis revealed that GNNs exhibit a correlated error that can be reduced through subtraction, challenging the assumption of independent errors in GNN predictions and leading to more precise energy difference predictions. To assess the magnitude of error cancellation in chemically similar pairs, we introduced a new metric, the subgroup error cancellation ratio. Our findings suggest that state-of-the-art GNN models can achieve error reduction of up to 77% in these subgroups, which is comparable to the error cancellation observed with DFT. This significant error cancellation allows GNNs to achieve higher accuracy than individual energy predictions and distinguish subtle energy differences. We propose the marginal correct signratio as a metric to evaluate this performance. Additionally, our results show that the similarity in local embeddings is related to the magnitude of error cancellation, indicating the need for a proper training method that can augment the embedding similarity for chemically similar adsorbate-catalyst systems.

Strong Consistency of Least-Squares Estimators in the Simple Linear Errors-in-Variables Regression Model with Widely Orthant Dependent Random Variables

ABSTRACT In this paper, we establish some results on strong consistency for the least square estimator in a simple linear errors-in-variables regression models based on widely orthant dependent errors. The results obtained in the paper generalize or improve the corresponding ones for dependent random variables. We also carry out some simulation studies to verify the validity of our theoretical results.

NeuroSketch: Fast and Approximate Evaluation of Range Aggregate Queries with Neural Networks.

Range aggregate queries (RAQs) are an integral part of many real-world applications, where, often, fast and approximate answers for the queries are desired. Recent work has studied answering RAQs using machine learning (ML) models, where a model of the data is learned to answer the queries. However, there is no theoretical understanding of why and when the ML based approaches perform well. Furthermore, since the ML approaches model the data, they fail to capitalize on any query specific information to improve performance in practice. In this paper, we focus on modeling "queries" rather than data and train neural networks to learn the query answers. This change of focus allows us to theoretically study our ML approach to provide a distribution and query dependent error bound for neural networks when answering RAQs. We confirm our theoretical results by developing NeuroSketch, a neural network framework to answer RAQs in practice. Extensive experimental study on real-world, TPC-benchmark and synthetic datasets show that NeuroSketch answers RAQs multiple orders of magnitude faster than state-of-the-art and with better accuracy.

A calibration system for hadron synchrotrons with a large frequency swing

The synchronization of radio frequency (RF) systems in hadron synchrotrons relies on the availability of reference RF signals with a precise phase. For accelerators with a large frequency swing, frequency dependent phase errors can exceed the required phase margin and therefore have to be compensated. In this paper a new method for the phase calibration of RF signals with variable frequency is described. All the signals are measured with a digital oscilloscope and no complex signal processing is necessary. The described approach utilizes a three-parameter sine wave fit algorithm to estimate the phase of the relevant sine wave signals. A phase difference between RF signals with different frequencies is then calculated with respect to a reference pulse train. A detailed analysis of the measurement parameters is given. The method is applied for the calibration of the RF reference signals of the heavy ion synchrotron SIS18 at GSI.

Demonstrating multi-round subsystem quantum error correction using matching and maximum likelihood decoders

Quantum error correction offers a promising path for performing high fidelity quantum computations. Although fully fault-tolerant executions of algorithms remain unrealized, recent improvements in control electronics and quantum hardware enable increasingly advanced demonstrations of the necessary operations for error correction. Here, we perform quantum error correction on superconducting qubits connected in a heavy-hexagon lattice. We encode a logical qubit with distance three and perform several rounds of fault-tolerant syndrome measurements that allow for the correction of any single fault in the circuitry. Using real-time feedback, we reset syndrome and flag qubits conditionally after each syndrome extraction cycle. We report decoder dependent logical error, with average logical error per syndrome measurement in Z(X)-basis of ~0.040 (~0.088) and ~0.037 (~0.087) for matching and maximum likelihood decoders, respectively, on leakage post-selected data.

A unified multi-step wind speed forecasting framework based on numerical weather prediction grids and wind farm monitoring data

Wind speed forecasting is the basis of wind farm operation, which provides a reference for the future operation status evaluation of wind farms. For the wind speed forecast of wind turbines in the whole wind farm, a strategy combining unified forecast and single site error correction is proposed in this paper. The unified forecast framework is composed of a unified forecast model and multiple single site error correction models, which combines the forecasted grids of numerical weather prediction (NWP) with the monitoring data of wind farms. The proposed unified forecast model is called spatiotemporal conversion deep predictive network (STC-DPN), which is composed of temporal convolution network (TCN) and 2D convolution long short-term memory network (ConvLSTM). Firstly, the NWP forecasted grids are interpolated to the fan location, and the sequence matrix is composed of the NWP data and the monitored data of each wind turbine according to the time series, which is entered into the TCN network for time sequence feature extraction. Then, the output of the TCN network is converted into a regular spatio-temporal data matrix, which is entered into the ConvLSTM network for joint learning of spatio-temporal features to obtain the wind speed sequence forecasted in the whole wind farm. Finally, an independent TCN-LSTM error correction model is added for each site. Variational modal decomposition (VMD) is used to process data series, and different processing methods are adopted in unified forecast and single site error correction. In the 96 steps forecast test of a wind farm from Jining City, China, the proposed method is superior to several baseline methods and has important practical application value.