Minimum Error Method Research Articles

Easy bootstrap for the 3D Ising model: a hybrid approach of the lightcone bootstrap and error minimization methods

As a simple lattice model that exhibits a phase transition, the Ising model plays a fundamental role in statistical and condensed matter physics. The Ising transition is realized by physical systems, such as the liquid-vapor transition. Its continuum limit also furnishes a basic example of interacting quantum field theories and universality classes. Motivated by a recent hybrid bootstrap study of the quantum quartic oscillator, we revisit the conformal bootstrap approach to the 3D Ising model at criticality, without resorting to positivity constraints. We use at most 10 nonperturbative crossing constraints at low derivatives from the Taylor expansion around a crossing symmetric point. The high-lying contributions are approximated by simple analytic formulae deduced from the lightcone singularity structure. Surprisingly, the low-lying properties are determined to good accuracy by this computationally very cheap approach. For instance, the results for the two relevant scaling dimensions (∆σ, ∆ϵ) ≈ (0.518153, 1.41278) are close to the most precise rigorous bounds obtained at a much higher computational cost.

Using Ant Colony Optimization Method to Detect Dominant Points

This paper uses the ant colony optimization method to detect dominant points. It develops a dominant point detection system for closed target images with simple backgrounds. The process is to perform image preprocessing on the captured object images, then perform object contour tracking and breakpoint detection, and finally use the ant colony optimization method to detect the object's dominant points. In such problems, ant colony calculus is applied to such problems by first defining a fitness value. In addition, three different hybrid strategies, including the minimum error method, the maximum distance method, and the random selection method, were also experimentally compared. Experimental results show that the used hybrid strategy can improve the computational efficiency of all three types of problems.

Continuous Eddy Simulation (CES) of Transonic Shock-Induced Flow Separation

Reynolds-averaged Navier–Stokes (RANS), large eddy simulation (LES), and hybrid RANS-LES, first of all wall-modeled LES (WMLES) and detached eddy simulation (DES) methods, are regularly applied for wall-bounded turbulent flow simulations. Their characteristic advantages and disadvantages are well known: significant challenges arise from simulation performance, computational cost, and functionality issues. This paper describes the application of a new simulation approach: continuous eddy simulation (CES). CES is based on exact mathematics, and it is a minimal error method. Its functionality is different from currently applied simulation concepts. Knowledge of the actual amount of flow resolution enables the model to properly adjust to simulations by increasing or decreasing its contribution. The flow considered is a high Reynolds number complex flow, the Bachalo–Johnson axisymmetric transonic bump flow, which is often applied to evaluate the performance of turbulence models. A thorough analysis of simulation performance, computational cost, and functionality features of the CES model applied is presented in comparison with corresponding features of RANS, DES, WMLES, and wall-resolved LES (WRLES). We conclude that CES performs better than RANS, DES, WMLES, and even WRLES at a little fraction of computational cost applied for the latter methods. CES is independent of usual functionality requirements of other methods, which offers relevant additional advantages.

Evaluation method for insulation degradation of power transformer windings based on incomplete internet of things sensing data

AbstractThis paper proposes a novel evaluation method to address the challenge of evaluating insulation degradation in power transformer windings based on incomplete online Internet of Things (IoT) sensing data. The method leverages the Wasserstein Slim Generative Adversarial Imputation Network with Gradient Penalty algorithm to fill the irregularly missing power transformer IoT perception data, including voltage, current, temperature, and partial discharge. Subsequently, electrical, thermal, and mechanical performance degradation damage indicators for transformer winding insulation are constructed using the filled and complete IoT perception data. By applying the tensor fusion algorithm, the characteristics of these degradation damage indicators are fused, leading to the development of a comprehensive degradation evaluation index for the winding insulation. The evaluation of the winding insulation degradation state is achieved through the minimum quantization error method. The proposed method is validated using the real‐world transformer IoT perception data, and the experimental results demonstrate its ability to accurately assess the degree of winding insulation degradation, regardless of the presence of random or continuous irregularities in IoT sensing data.

A new approach to evaluate Ramberg-Osgood parameters for SS316LN using different types of specimens

A novel methodology is proposed for evaluating the stress-strain curve and determining the Ramberg-Osgood parameters (n, α) of SS316LN material. This involves utilizing load-displacement data from various specimen types, including both smooth and notched tensile specimens with different notch radii, in conjunction with finite element analysis. An error minimization method was used for evaluating the material parameters. The proposed approach for the evaluation of unique Ramberg-Osgood parameters provides a better result than that of the material stress-strain data of smooth specimen test. Ramberg-Osgood parameters were evaluated at two temperatures, i.e., 25°C and 650°C and compared with RCC-MRx code. Stress-strain equation as provided in the RCC-MR, can’t be used in FE analysis if the plastic strain exceeds 1.5% at certain regions of structure containing discontinuity, e.g., regions like shell-nozzle junction, vessel head, T-junction etc. The approach developed in this work shall help to obtain the material stress-strain curve over a wide range of plastic strain values. Ramberg-Osgood parameters were evaluated for the whole temperature range of 25°C and 650°C, which can be used for structural integrity analysis of reactor components made of stainless steel grade SS316LN. The range of applicability of data for RCC-MR code was extended beyond 1.5% of plastic strain in this work. The equations derived in this work shall be useful for structural integrity analysis and life assessment of structural components of nuclear reactors.

Development of a Multiplication Factor for the Kuz-Ram Model to Match the Fragment Size Obtained from Wipfrag Image Analysis

The degree to which the rock is fragmented by blasting operations significantly impacts the productivity of the opencast mining operation. Over image analysis-based tools, the Kuz-Ram empirical model is preferred for determining the mean fragment size of a blasted muck pile. The fragmentation analysis results by the Kuz-Ram model are said to report the overestimation of the size of the fragments. On the other hand, while accurate, measuring the mean fragment size by image-based analysis is also time-consuming and expensive. Therefore, in the present research, the fragmentation difference index (Fdi) is introduced as a new multiplication factor to reduce the discrepancy in the results obtained using the Kuz-Ram model and the image-based analysis. The error minimization method of least squares is used to formulate the objective function of Fdi. The proposed equation is tested using data sets that weren't used in the model's development. Statistical indicators viz. the coefficient of determination (R2 ) and Root Mean Square Error (RMSE) have been used to evaluate the model's performance. These are found to be 0.80 and 0.007, respectively. The values obtained by multiplying Fdi by the Kuz-Ram results match those of the Wipfrag study, with an average error of 2.09%. Therefore, the suggested methodology will assist the field engineers in cost-effectively calculating the mean fragment size before blasting utilizing only the findings from the Fdi and Kuz-Ram models.

Study on the Phase Angle Master Curve of the Polyurethane Mixture with Dense Gradation

The phase angle master curve of the PU mixture is a new research field that is urgently needed to characterize the viscoelastic of the PU mixture under different conditions. In this paper, five master curve models, five shift factor equations, and four error minimization methods were introduced to fitting the phase angle master curve of the PU mixture. The results analysis indicated that the master curves fitted by different error minimization methods had small differences when the loading frequency was higher than 10−3 Hz. The R2 maximization as the main constraint and the others as the additional constraints were recommended as the error minimization method. The combination of the Christensen Anderson and Marasteanu model (CAM) and kaelble shift factor equation was recommended for fitting the phase angle master curve of the PU mixture. The phase angle master curve of the PU mixture did not follow the “Bell” shape of the asphalt mixture. The PU mixture with smaller temperature susceptibility would still be subject to the PU at higher temperatures and was closer to that of the viscoelastic material. The phase angle master curve construction was analyzed for the first time and proper master curve fitting parameters were recommended for pavement performance predicting and analyzing.

Study on the Construction of Dynamic Modulus Master Curve of Polyurethane Mixture with Dense Gradation

The PU mixture considered here is a new kind of pavement material with excellent road performance, which lacks study into its dynamic mechanical and viscoelastic properties. In this study, the dynamic modulus of the polyurethane (PU) mixture was fitted by using five master curve models, five shift factor equations, and four error minimization methods. According to test results, the log–log plot form was able to more effectively display the differences between master curves. The solver method, the sum of square error minimization (≤0.02), proved to be more appropriate and accurate with higher fitting parameter results. The line of equality statistic and Pearson linear correlation analysis results demonstrated that WLF and Kaelble equations were appropriate for five master curve models with trend line R2 values higher than 0.98. The GLS and SCM model with the WLF equation had the most accurate master curve fitting results. The dynamic modulus master curve shape of the PU mixture did not follow the traditional smooth “S” shape and did not show the ultimate dynamic modulus at extreme frequency. The viscoelasticity of the PU mixture is quite different from that of the asphalt mixture. This study recommended the most accurate error minimization method, the master curve model, and shift factor equations for characterizing the dynamic properties of the PU mixture.

ScSTAR reveals hidden heterogeneity with a real-virtual cell pair structure across conditions in single-cell RNA sequencing data.

Cell-state transition can reveal additional information from single-cell ribonucleic acid (RNA)-sequencing data in time-resolved biological phenomena. However, most of the current methods are based on the time derivative of the gene expression state, which restricts them to the short-term evolution of cell states. Here, we present single-cell State Transition Across-samples of RNA-seq data (scSTAR), which overcomes this limitation by constructing a paired-cell projection between biological conditions with an arbitrary time span by maximizing the covariance between two feature spaces using partial least square and minimum squared error methods. In mouse ageing data, the response to stress in CD4+ memory T cell subtypes was found to be associated with ageing. A novel Treg subtype characterized by mTORC activation was identified to be associated with antitumour immune suppression, which was confirmed by immunofluorescence microscopy and survival analysis in 11 cancers from The Cancer Genome Atlas Program. On melanoma data, scSTAR improved immunotherapy-response prediction accuracy from 0.8 to 0.96.

Simplification of earthquake induced vehicle bridge interaction contact simulation for urban viaducts

AbstractThe possibility of motor vehicles parking on or slowly driving on the urban viaducts during earthquakes has been largely increased to a non‐negligible level due to the traffic jams in most of modern cities. As a fact of the earthquake disaster investigation, detachment and collision between motor vehicles and the bridge deck endangered the safety of both drivers and the bridge structure itself. In recent studies, Hertz model was therefore proposed to simulate this nonlinear contact and collision behavior with the complexity and inefficient in solving the kinetic equilibrium equations of earthquake induced vehicle bridge interaction (VBI) system, and hence hindered the comprehensive numerical analysis. In this paper, two linearized contact models, that is, a piecewise linear tangent model derived by Taylor series expansion of the Hertz model and a piecewise secant model derived by least square method of error minimization of the Hertz model, are both proposed to simplify the simulation of the vehicle bridge contact behavior for earthquake induced VBI system. A total of 3*2041VBI parametric systems considering different vehicle masses, frequencies and ground motions, are calculated and statistically analyzed to compare the accuracy of each model with nonlinear Hertz model. Statistical analysis result shows that the vertical contact force calculated by two simplified models are acceptable in earthquake induced VBI analysis with less than 10% error in more than 99% analysis cases. However, the piecewise tangent model is more accurate than the piecewise secant model when the vehicle and bridge stay attached. If detachment occurs, the secant model would have higher accuracy in predicting the initial peak ground acceleration (PGA) of vehicle detachment from the bridge. Based on this result, a formula using the piecewise secant model for predicting the initial detachment PGA of vehicles from the bridge deck is proposed to simplify the increment dynamic analysis (IDA) method in further earthquake induced VBI analysis.

A modified global error minimization method for solving nonlinear Duffing-harmonic oscillators

<abstract> <p>In this paper, a third-order approximate solution of strongly nonlinear Duffing-harmonic oscillators is obtained by extending and improving an analytical technique called the global error minimization method (GEMM). We have made a comparison between our results, those obtained from the other analytical methods and the numerical solution. Consequently, we notice a better agreement with the numerical solution than other known analytical methods. The results are valid for both small and large oscillation amplitude. The obtained results demonstrate that the present method can be easily extended to strongly nonlinear problems, as indicated in the presented applications.</p> </abstract>

Synthetic unit hydrograph for ungauged basin using Synder, Taylor- Schwarz model, SCS method by GIS techniques

In hydrology, estimation of the design hydrograph (DH) is a crucial challenge because of lack of rainfall- runoff data. The lack of rainfall-runoff data makes developing credible DHs particularly difficult in small and ungauged basins. A synthetic unit hydrograph(SUH) is a way to represent the flow of water in a stream or river as a single point. It is used to calculate runoff and other hydraulic functions by using watershed characteristics for similar watershed. On the basis of watershed and watershed features or characteristics, equations for estimate of synthetic unit-hydrograph parameters based on rainfall and runoff data for small watersheds were developed. Estimating runoff is a crucial part of river basin planning, development, and management. This paper discusses the application of synthetic unit hydrographs in the Dhamani drainage basin in Maharashtra, India. Traditional method of SUH are used to calculate the peak discharge and time to peak. The calculated discharge by using Synder method, Taylor- Schwarz model, SCS method were compared with each other. In a drainage basin, the relative mean error (RME) and the root of mean square error (RMSE) were compared for selection of better option or to find minimum error method.

Joint Design of Transmit Antenna Selection and Beamforming for MIMO NOMA Networks

This letter investigates the joint design of transmit antenna selection (AS) and beamforming for downlink multiple-input-multiple-output (MIMO) networks, in which non-orthogonal multiple access (NOMA) transmission scheme is applied. We aim to maximize the achievable sum rate under the AS constraint and successful successive interference cancellation (SIC) constraints. The penalty dual decomposition (PDD) method coupled with the weighted mean squared error minimization (WMMSE) method is proposed to tackle this problem and a local optimal solution is obtained. Simulation results are provided to show the effectiveness of the proposed scheme.

An Improved Overmodulation Strategy for a Three-Level NPC Inverter Considering Neutral-Point Voltage Balance and Common-Mode Voltage Suppression

The three-level neutral-point clamped voltage source inverter (3L-NPC-VSI) is widely used in the maglev traction systems due to its high output voltage, large output capacity and low output current harmonics. In order to improve the utilization of the DC-bus voltage, an overmodulation strategy is necessary. This paper proposes an improved overmodulation strategy based on the minimum amplitude error method for a 3L-NPC-VSI. Compared with the conventional overmodulation strategy based on the minimum amplitude error method, the utilization of the DC-bus voltage is higher. Meanwhile, a virtual space vector modulation strategy is adopted for inverter neutral-point (NP) voltage balance and common-mode voltage (CMV) suppression. Furthermore, the suppression of leakage current also has been verified. Furthermore, the implementation details of the proposed overmodulation strategy based on minimum amplitude error method is elaborated. The effectiveness of the proposed method is verified by simulation and experimental results.

Unsupervised and Supervised Feature Selection for Incomplete Data via L2,1-Norm and Reconstruction Error Minimization

Feature selection has been widely used in machine learning and data mining since it can alleviate the burden of the so-called curse of dimensionality of high-dimensional data. However, in previous works, researchers have designed feature selection methods with the assumption that all the information from a data set can be observed. In this paper, we propose unsupervised and supervised feature selection methods for use with incomplete data, further introducing an L2,1 norm and a reconstruction error minimization method. Specifically, the proposed feature selection objective functions take advantage of an indicator matrix reflecting unobserved information in incomplete data sets, and we present pairwise constraints, minimizing the L2,1-norm-robust loss functionand performing error reconstruction simultaneously. Furthermore, we derive two alternative iterative algorithms to effectively optimize the proposed objective functions and the convergence of the proposed algorithms is proven theoretically. Extensive experimental studies were performed on both real and synthetic incomplete data sets to demonstrate the performance of the proposed methods.

Equivalent damping ratio for mixed structures including the soil-structure interaction

The behavior of a mixed structure and its interaction with the underlying soil are challenging problems for engineers. Current codes and available commercial software packages do not present solutions for such structures. Due to irregular damping ratios, engineers assumed a uniform damping ratio of 2% or 5% for the entire structure, but the dynamic response of the mixed structure differs from the actual one, significantly. In addition, when the structure is subjected to seismic loads, the effects of the soil-structure interaction cannot be neglected. To manage these issues, 12 mixed structures in two categories are investigated with different numbers of concrete and steel storeys. However, the findings are not generally applicable to all structures. The proposed method provides a much better approximation than the model in which a uniform damping ratio of 2% or 5% is used for the whole structure. This study has suggested an equivalent damping ratio for mixed structures using a semi-empirical error minimization method in which soil-structure interaction is considered. The results of numerical simulations indicate that the equivalent damping ratios make results closer to the actual ones in different soil types and storeys number of the concrete and steel.

Channel Estimation Based on Complex-Valued Neural Networks in IM/DD FBMC/OQAM Transmission System

Filter bank multicarrier with offset quadrature amplitude modulation (FBMC/OQAM) is a promising candidate for 5G mobile fronthaul system. Due to the inherent imaginary interference of FBMC/OQAM signals, an accurate channel estimation is particularly indispensable. In this paper, an efficient method is proposed based on complex-valued neural networks (CVNN) for an accurate channel estimation of FBMC/OQAM signals with low computational complexity and pilot overhead. Here, the channel frequency response (CFR) is first calculated for training the CVNN. Next, the CFR estimated from the extracted pilots is exploited as the input of the trained CVNN to yield the CFR of data symbols. We experimentally demonstrate a 12.5-GBd intensity modulation direct detection (IM/DD) FBMC/OQAM transmission system over 30-km and 50-km standard single mode fibers (SSMF). The experimental results show that the proposed method achieves 3-dB and 1-dB receiver sensitivity improvement at the bit error ratio (BER) of 3.8×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−3</sup> with only 5% pilot overhead respectively, compared to the conventional least square (LS) and linear minimum mean error (LMMSE) methods. When the pilot overhead decreases from 10% to 1%, its BER performance is always better than LS and LMMSE. For the computational complexity, its complexity is the same order of magnitude as LS and lower than LMMSE. On the other hand, the CVNN requires less hidden neurons to keep the similar BER performance as real-valued neural networks (RVNN). Meanwhile, it has excellent resilience to fiber chromatic dispersion over 30-km and 50-km SSMF.

Monitoring multistage multivariate therapeutic processes using risk‐adjusted model‐based group multivariate EWMA control chart

AbstractThere exist multitude of therapeutic processes and the results are commonly observed during various dependent steps. For studying such processes that are referred to as multistage therapeutic processes, two concepts are of particular importance; risk adjustment and cascade property. To monitor such processes, a variety of control charts including model‐based control charts are used. In order to design model‐based control charts, analysts must first recognize a suitable model to identify the multistage processes by considering process risks and cascade property. Based on the identified model, the control charts can be proposed. In this study, a risk‐adjusted time‐variant linear state space model is introduced. Afterward, the model order and its parameters are estimated based on Hankel singular value decomposition (HSVD) and prediction error minimization (PEM) methods. Then, the group multivariate exponentially weighted moving average (GMEWMA) control chart is used to monitor a multistage multivariate therapeutic process. To evaluate the performance of the model‐based control chart, a simulation study as well as a two‐stage thyroid cancer surgery was used. Results show that the proposed control chart performs well for predicting and monitoring of multistage multivariate therapeutic processes in real world.

Synergistic Evaluation of Passive Microwave and Optical/IR Data for Modelling Vegetation Transmissivity towards Improved Soil Moisture Retrieval.

Vegetation cover and soil surface roughness are vital parameters in the soil moisture retrieval algorithms. Due to the high sensitivity of passive microwave and optical observations to Vegetation Water Content (VWC), this study assesses the integration of these two types of data to approximate the effect of vegetation on passive microwave Brightness Temperature (BT) to obtain the vegetation transmissivity parameter. For this purpose, a newly introduced index named Passive microwave and Optical Vegetation Index (POVI) was developed to improve the representativeness of VWC and converted into vegetation transmissivity through linear and nonlinear modelling approaches. The modified vegetation transmissivity is then applied in the Simultaneous Land Parameters Retrieval Model (SLPRM), which is an error minimization method for better retrieval of BT. Afterwards, the Volumetric Soil Moisture (VSM), Land Surface Temperature (LST) as well as canopy temperature (TC) were retrieved through this method in a central region of Iran (300 × 130 km2) from November 2015 to August 2016. The algorithm validation returned promising results, with a 20% improvement in soil moisture retrieval.

A Modified Minimal Error Method for Solving Nonlinear Integral Equations via Multiscale Galerkin Methods

A modified minimal error method for nonlinear integral equations is established. Such method, combined with the discrepancy principle as stopping rule, is a regularization method, which yields convergence to an exact solution when the nonlinear operator F satisfies certain conditions. Furthermore, the convergence of the modified minimal error method via multiscale Galerkin methods is also proved. Finally, numerical results show the accuracy and efficiency of the proposed method.