Auxiliary Variables Research Articles

Estimating neutrosophic finite median employing robust measures of the auxiliary variable

Our study explores neutrosophic statistics, an extension of classical and fuzzy statistics, to address the challenges of data uncertainty. By leveraging accurate measurements of an auxiliary variable, we can derive precise estimates for the unknown population median. The estimators introduced in this research are particularly useful for analysing unclear, vague data or within the neutrosophic realm. Unlike traditional methods that yield single-valued outcomes, our estimators produce ranges, suggesting where the population parameter is likely to be. We present the suggested generalised estimator's bias and mean square error within a first-order approximation framework. The practicality and efficiency of these proposed neutrosophic estimators are demonstrated through real-world data applications and the simulated data set.

A spatiotemporal attention-augmented ConvLSTM model for ocean remote sensing reflectance prediction

Remote sensing reflectance (Rrs) is an essential parameter in ocean color remote sensing and a fundamental input for the estimation of ocean color elements. Predicting Rrs has the potential to enable simultaneous prediction of multiple marine environmental parameters, facilitating multi-perspective analysis of marine environmental changes. This paper proposes a spatiotemporal attention-augmented ConvLSTM-based model for ocean Rrs prediction. The developed model can predict Rrs for up to seven days by simultaneously learning spatiotemporal features from time series Rrs and auxiliary environmental variables. According to the experiments, the proposed model achieves optimal performances on Rrs predictions at 443, 488, and 555 nm, with Root Mean Squared Error (RMSE) and Mean Absolute Percentage Error (MAPE) for the first four prediction days less than 5.6*10-4 sr-1 and 8.6 %, respectively, which are better than the performance of the convolutional neural network (CNN), the LSTM, CNN-LSTM, and the ConvLSTM. The spatial and temporal variations of Rrs are also compared to evaluate the effectiveness of the model, presenting a consistent spatiotemporal pattern between predicted and observed Rrs. We also found that integrating sea surface temperature (SST), photosynthetically available radiation (PAR), and aerosol optical thickness at 869 nm (AOT869) into the model can improve the prediction accuracy in various degrees. This work suggests the proposed deep learning model can predict Rrs for 7 days with a convincing performance, providing critical data and technical support for ocean-related applications, such as algae bloom monitoring.

Spatial modeling of the water table and its historical variations in Northeastern Italy via a geostatistical approach

Groundwater resources are the most important freshwater source for any human use and its preservation in the context of climatic variability is of crucial importance. So far, no systematic spatial estimation of the water table in Northeastern Italy has ever been made available, whereas the Veneto Region (North-Eastern Italy) provides a free database with recorded water table measurements between 1999 and 2022. These starting data have been cleaned, leading to a final database of 53 yearly water table data. The lack of knowledge about the spatial estimation of the water table within the historical period is overcome through the well-known geostatistical technique of cokriging. The latter is the most suitable approach for reproducing water table elevations upon local terrain elevation as an auxiliary variable. Results underline modest decrements between 1999 and 2022, which are more pronounced in the Prealps area and in general in sedimentary soils, and less in the Fontanili belt, a crucial freshwater source area. Moreover, the estimated water table change is highly non-linear in time from year to year and highly varying in space. The results seem particularly interesting in the plain areas and within the Fontanili belt, where the management of groundwater resources is becoming crucial. However, the spatial estimation in the Prealps area needs to be improved for a better assessment and future reliable predictions.

Research on soft sensor modeling method for complex chemical processes based on local semi-supervised selective ensemble learning

To address the adverse effects of nonlinearity and dynamic time-varying in complex chemical processes on the accuracy of the soft sensor model, a local-semi-supervised ensemble learning for soft sensor modeling (local semi-supervised-selective ensemble learning-long short term memory, LS-SEL-LSTM) method is proposed in this article. Firstly, a hierarchical clustering method incorporating spatiotemporal criteria is proposed to reduce the influence of nonlinearity in global model prediction accuracy. The method considers the dynamic time-varying characteristics of temporal data and generates multiple local datasets. Then, to address the issue of multi-rate between auxiliary variables and dominant variables, a semi-supervised weight fusion mechanism based on temporal correlation is proposed, which effectively utilizes auxiliary variables to reconstruct local semi-supervised datasets and establishes local soft sensing models using LSTM. Concurrently, the parameters of the established model were optimized using the flower pollination algorithm. Subsequently, a selective ensemble learning method based on sub-model prediction accuracy and an adaptive combination weight calculation method for sub-models were proposed to improve the prediction accuracy. Finally, the effectiveness of the proposed method was verified through the actual dataset of the sulfur recovery process. The results indicate that LS-SEL-LSTM performs well in handling complex chemical processes with nonlinear and dynamic time-varying characteristics.

Fixed-time cooperative output regulation for second-order nonlinear multiagent systems with an unknown exosystem

This paper investigates the fixed-time cooperative output regulation (FTCOR) problem with unknown exosystem of second-order nonlinear multiagent systems. To solve this problem, it is necessary to ensure that each agent can obtain the reference trajectory originating from an unknown exosystem and reconstruct the solution of the regulator equation containing the exogenous signal and unknown parameter vectors within a fixed time, and the unknown exosystem makes it difficult to solve these two problems with existing tools. By using auxiliary filtering variables, we propose a fixed-time adaptive distributed observer (FTADO) and design a fixed-time distributed internal model (FTDIM) based on this FTADO. These two new tools ensure the solvability of the two problems just mentioned. Then, based on these two tools, we transform the problem into a fixed-time stabilization problem of a so-called augmented system. Through the backstepping technique, we propose a distributed controller that solves this fixed-time stabilization problem while relaxing the assumptions of similar references.

Multi-model of ammonia nitrogen in aquaculture water based on EM algorithm1

The factors of water quality in the intensive marine stichopus japonicus aquaculture process are changing with seasons, so water temperature, salinity, pH value and nitrite were selected as auxiliary variables to measure the concentration of ammonia nitrogen. FCM (Fuzzy C-means) algorithm was adopted to classify them. Based on the EM (Expectation Maximization) algorithm, fuzzy sub-models of ammonia nitrogen concentration were constructed around each operating point, and finally the fuzzy sub-models were combined according to the posterior distribution of the characteristics of the sampling data. Based on the data collected at Xinyulong Marine Biological Seed Technology Co., Ltd, in Dalian China, the ammonia nitrogen concentration prediction model was tested and verified.

Distributed Formation–Containment Tracking Control for Multi-Hovercraft Systems with Compound Perturbations

Aiming at the problem of hovercraft formation–containment control with compound perturbations including model uncertainties and ocean disturbances, a distributed control algorithm for underactuated hovercraft formation–containment is proposed by combining adaptive linear extended state observer (ALESO) and radial basis function neural network (RBFNN). Firstly, ALESO and RBFNN are designed to estimate the ocean disturbances and model uncertainties, respectively, for dynamic compensation in the controller. Then, the auxiliary variables are introduced into the formation error function, and the lateral and longitudinal error stabilization is transformed into the design of longitudinal force and rotational torque by using the skew-symmetric matrix transformation, which solves the lateral underactuated problem of the hovercraft. Finally, the uniform ultimate boundedness of formation–containment cooperative errors is proved by the Lyapunov stability theory. Digital simulation verifies the effectiveness of the proposed method.

Solving a class of multi-scale elliptic PDEs by Fourier-based mixed physics informed neural networks

Deep neural networks have garnered widespread attention due to their simplicity and flexibility in the fields of engineering and scientific calculation. In this study, we probe into solving a class of elliptic partial differential equations (PDEs) with multiple scales by utilizing Fourier-based mixed physics informed neural networks (dubbed FMPINN), its solver is configured as a multi-scale deep neural network. In contrast to the classical PINN method, a dual (flux) variable about the rough coefficient of PDEs is introduced to avoid the ill-condition of neural tangent kernel matrix caused by the oscillating coefficient of multi-scale PDEs. Therefore, apart from the physical conservation laws, the discrepancy between the auxiliary variables and the gradients of multi-scale coefficients is incorporated into the cost function, obtaining a satisfactory solution of PDEs by minimizing the defined loss through some optimization methods. Additionally, a trigonometric activation function is introduced for FMPINN, which is suited for representing the derivatives of complex target functions. Handling the input data by Fourier feature mapping will effectively improve the capacity of deep neural networks to solve high-frequency problems. Finally, to validate the efficiency and robustness of the proposed FMPINN algorithm, we present several numerical examples of multi-scale problems in various dimensional Euclidean spaces. These examples cover low-frequency and high-frequency oscillation cases, demonstrating the effectiveness of our approach. All code and data accompanying this manuscript will be publicly available at https://github.com/Blue-Giant/FMPINN.

A deep neural network for predicting soil texture using airborne radiometric data

The ternary nature of soil texture, defined by its proportions of clay, silt, and sand, makes it challenging to predict through linear regression models from other soil attributes and auxiliary variables. The most promising results in this field have been recently achieved by Machine Learning methods which are able to derive non-linear, non-site-specific models to predict soil texture. In this paper we present a method of constructing a pair of Deep Neural Network (DNN) algorithms that can predict clay and sand soil contents from Airborne Gamma Ray Spectrometry data of K and Th ground abundances.We tested the algorithm's hyperparameters through various configurations to optimize the DNNs' performance, effectively avoiding underfitting and overfitting of the models. This led to the creation of a high-resolution 20 m × 20 m soil texture map from dense AGRS data, significantly refining the previous map's granularity. The application of the obtained DNN models to unseen sites can be supported by future training on additional textural classes.

Observer‐based distributed dynamic event‐triggered control of multi‐agent systems with adjustable interevent time

AbstractIn this paper, a novel dynamic event‐triggered control protocol for leader‐following problems of generic linear multi‐agent systems is proposed. Compared with the existing static event‐triggered strategy, the developed event‐triggered approach significantly reduces the utilization of communication resources while guaranteeing asymptotic consensus, and the interevent time is adjustable. Under this event scheduling mechanism, a synthesis approach combining controller and observer design is presented. The observer‐based control and event‐triggered rules are distributed, which only require local information of each agent to implement. The proposed methods incorporate model‐based estimation and auxiliary dynamic variables with a clock‐like behavior to prolong the interevent time as long as possible. The sufficient conditions for leader‐following consensus are established using linear matrix inequalities (LMIs) formulation to facilitate numerical computation. Comparative simulations in different scenarios demonstrate the validity of the proposed theoretical results.

The Causal Relationship between Angina Pectoris and Gout Based on Two Sample Mendelian Randomization.

Two-sample Mendelian randomization (MR) was conducted to assess the causal relationship between angina pectoris and gout. Material and Methods. Based on genome-wide association studies, single nucleotide polymorphisms (SNPs) that were closely associated with gout were selected from the UK Biobank-Neale Lab (ukb-a-107) as genetic instrumental variables. Considering that gout is characterized by elevated blood uric acid levels, SNPs related to blood uric acid levels were screened from BioBank Japan (bbj-a-57) as auxiliary gene instrumental variables. SNPs closely associated with angina pectoris onset were screened from the FINN dataset (finn-b-I9_ANGINA) as outcome variables. Two-sample MR was conducted, with inverse variance weighting (IVW) of the random effects model as the primary result, along with the weighted median method (WME) and the MR-Egger regression method. To further confirm the causal relationship between angina and gout incidence, a meta-analysis was conducted on the IVW results of the ukb-a-107 and bbj-a-57. The odds ratios and 95% confidence intervals of the IVW, WME, and MR-Egger results of ukb-a-107 were (OR = 33.72; 95% CI: 2.07∼550.38), (OR = 57.94; 95% CI: 2.75∼1219.82), and (OR = 96.38; 95% CI: 0.6∼15556.93), respectively. The P values of IVW and WME were 0.014 and 0.014 (both <0.05), respectively, indicating that the development of angina pectoris was significantly associated with the incidence of gout. The odds ratios and 95% confidence intervals of the IVW, WME, and MR-Egger about bbj-a-57 were (OR = 1.20; 95% CI: 1.07∼1.34), (OR = 1.19; 95% CI: 1.02∼1.38), and (OR = 1.30; 95% CI; 1.06∼1.60), respectively. The P values of IVW, WME and MR-Egger were 0.001, 0.027 and 0.017 (all <0.05), respectively, indicating a significant correlation between angina and blood uric acid levels. Scatter plots of ukb-a-107 and bbj-a-57 showed that the causal association estimates of the IVW, MR-Egger, and weighted median methods were similar and that the MR results were accurate. Funnel plots and the MR-Egger intercept of ukb-a-107 and bbj-a-57 showed the absence of horizontal pleiotropy. The leave-out sensitivity analysis results of ukb-a-107 and bbj-a-57 are stable. The meta-analysis of IVW results for ukb-a-107 and bbj-a-57 showed (OR = 1.20; 95% CI: 1.07-1.34, P=0.02), confirming that gout characterized by high blood uric acid levels significantly increases the risk of angina attacks. This MR study found a clear causal relationship between angina pectoris and gout, which increases the risk of angina pectoris.

Improvement in variance estimation using transformed auxiliary variable under simple random sampling

This paper offers a novel approach to formulate efficient ratio estimator of the population variance using a transformed auxiliary variable. The impact of transformation on auxiliary information has also been discussed. It is observed that incorporating a transformed auxiliary variable result in a high gain in efficiency. Theoretical properties of the newly developed estimators have been derived. The empirical and simulation studies show that the suggested estimators outperformed the existing estimators.

A data-driven approach to understanding non-response and restoring sample representativeness in the UK Next Steps cohort

Non-response is common in longitudinal surveys, reducing efficiency and introducing the potential for bias. Principled methods, such as multiple imputation, are generally required to obtain unbiased estimates in surveys subject to missingness which is not completely at random. The inclusion of predictors of non-response in such methods, for example as auxiliary variables in multiple imputation, can help improve the plausibility of the missing at random assumption underlying these methods and hence reduce bias. We present a systematic data-driven approach used to identify predictors of non-response at Wave 8 (age 25–26) of Next Steps, a UK national cohort study that follows a sample of 15,770 young people from age 13–14 years. The identified predictors of non-response were across a number of broad categories, including personal characteristics, schooling and behaviour in school, activities and behaviour outside of school, mental health and well-being, socio-economic status, and practicalities around contact and survey completion. We found that including these predictors of non-response as auxiliary variables in multiple imputation analyses allowed us to restore sample representativeness in several different settings, though we acknowledge that this is unlikely to universally be the case. We propose that these variables are considered for inclusion in future analyses using principled methods to explore and attempt to reduce bias due to non-response in Next Steps. Our data-driven approach to this issue could also be used as a model for investigations in other longitudinal studies.

Optimizing population mean estimation using regression and factor type estimators in the presence of non-response

This paper addresses the problem of estimating the population mean of the study variable, Y, in the presence of non-response. To address this, we incorporated two additional variables, X and Z, as auxiliary variables. We introduced two classes of estimators that combine regression and factor type estimators, each applied under distinct circumstances, and described their properties. The biases and mean square errors (MSEs) of these proposed estimators were computed using a large sample approximation. To assess the effectiveness of our estimators compared to existing ones, we conducted an empirical study. The results from both empirical and theoretical investigations indicate promising outcomes for the proposed estimators.

Event-Triggered Adaptive Saturated Fault-Tolerant Control for Unknown Nonlinear Systems With Full State Constraints

This paper investigates the issue of event-triggered adaptive saturated fault-tolerant control (ESFC) for uncertain nonlinear systems with time-varying full state constraints (TFSCs), actuator saturation and faults as well as unknown control direction. A bounded function with an auxiliary variable is constructed by utilizing a novel dynamics of the auxiliary system, which contributes to reducing the adverse impact of actuator saturation. Different from the previous backstepping-based event-triggered control methods such specifications by either using fuzzy approximation or by employing neural approximation techniques, this paper skillfully addresses the unknown nonlinearities, actuator saturation and faults without involving any approximation structures, and thus, we proposes the ESFC on the basis of low-complexity design framework as contributing to communication and computational resource reduction. A rigorous theoretical analysis shows that the proposed control method is an effective way to handle with the problems of actuator saturation and faults, full state constraints, and unknown system uncertainties, while simultaneously simplifying the backstepping design and avoiding the issue of explosion of complexity. The asymptotic stability of the closed-loop system is guaranteed and the Zeno behavior can be effectively removed. We present an application example of a linear motor scenario to illustrate the effectiveness of the method. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Since state constraints, actuator saturation and faults, unknown mechanism model, and limited bandwidths exist extensively in practical engineering systems, which constantly degrade the operation performance of the plant. To handle these disadvantages, this paper is focus on providing simple but effective ESFC methods to ensure the asymptotic stability and enhance reliability. Compared to existing results, the presented method only uses the state signals of system without using system dynamic functions under mild conditions, which provides a theoretical basis, and has the advantages of low-complexity design, and easy implementation in practical engineering. Preliminary physical experimental comparisons demonstrate that this method is applicable to practical liner-motor platform, and achieves satisfactory control performance.

A one-dimensional branching rule based branch-and-bound algorithm for minimax linear fractional programming

This paper investigates a type of minimax linear fractional program (MLFP) that often occurs in practical problems such as design of electronic circuits, finance and investment. We first transform the MLFP problem into an equivalent problem (EP) by using the Charnes-Cooper transformation and introducing an auxiliary variable. A linear relaxation strategy should simplify the nonconvex parts of the constraints in (EP). For globally solving MLFP, a branch-and-bound algorithm is then developed. It integrates the presented relaxation with the one-dimensional branching. The convergence of the algorithm is demonstrated and the number of worst-case iterations is estimated. Finally, preliminary numerical experiments verify that the proposed algorithm in this article is robust and efficient for solving the tested instances.

Efficient energy stable numerical schemes for Cahn–Hilliard equations with dynamical boundary conditions

In this paper, we propose a unified framework for studying the Cahn–Hilliard equation with two distinct types of dynamic boundary conditions, namely, the Allen–Cahn and Cahn–Hilliard types. Using this unified framework, we develop a linear, second-order, and energy-stable scheme based on the multiple scalar auxiliary variables (MSAV) approach. We design efficient and decoupling algorithms for solving the corresponding linear system in which the unknown variables are intricately coupled both in the bulk and at the boundary. Several numerical experiments are shown to validate the proposed scheme, and to investigate the effect of different dynamical boundary conditions on the dynamics of phase evolution under different scenarios.

Uniqueness of conservative solutions to the modified Camassa-Holm equation via characteristics

In this paper, for a given conservative solution, we introduce a set of auxiliary variables tailored to this particular solution, and prove that these variables satisfy a particular semilinear system having unique solutions. In turn, we get the uniqueness of the conservative solution in the original variables.

Fixed-Time Adaptive Parameter Estimation for Hammerstein Systems Subject to Dead-Zone

The Hammerstein model has proven its ability for modeling many industrial servo systems, but the corresponding parameter estimation remains as a challenging problem, especially for the purpose of achieving fast convergence. This paper presents a fixed-time (FxT) adaptive parameter estimation scheme for Hammerstein systems with an asymmetric dead-zone to ensure the convergence of estimated parameters in fixed-time. A continuous piecewise linear (CPL) function is adopted to model the nonlinear dead-zone dynamics to remedy the use of intermediate variable. To avoid using the system state information, a K-filter is used to construct a relationship between the unknown system parameters and the input/output signals. Then a new adaptive law based on the parameter error and the FxT scheme is developed to online estimate the lumped unknown parameters and ensure the fixed-time convergence, where an online updated auxiliary variable of regressor is suggested to eliminate the impact of the regressor on the convergence performance. Both numerical simulations and experimental results are given to demonstrate the effectiveness of proposed methods.

AN EFFICIENT FAMILY OF RATIO TYPE ESTIMATORS FOR SIMPLE RANDOM SAMPLING

The study provides an enhanced estimation of the population mean using known information on an auxiliary variable. An enhanced class of estimators is suggested for the same. The proposed estimator's bias and mean squared error (MSE) are calculated up to the first order of approximation. The optimum values of the characterizing constants are obtained by minimizing the MSE of the proposed estimator. The minimum MSE and the bias values are achieved by optimising the characterizing scalar. The MSE of the proposed estimator has also been compared both conceptually and empirically with the MSEs of competing estimators. Real and simulated data sets are adopted to verify the theoretical prerequisites for the proposed estimator's greater efficiency over competing estimators. The most efficient estimator is recommended for practical utility in different areas of applications and the suggested estimator filfills the requirement.