Remaining useful life prediction based on nonlinear random coefficient regression model with fusing failure time data

Remaining useful life(RUL) prediction is one of the most crucial elements in prognostics and health management(PHM). Aiming at the imperfect prior information, this paper proposes an RUL prediction method based on a nonlinear random coefficient regression(RCR) model with fusing failure time data.Firstly, some interesting natures of parameters estimation based on the nonlinear RCR model are given. Based on these natures,the failure time data can be fused as the prior information reasonably. Specifically, the fixed parameters are calculated by the field degradation data of the evaluated equipment and the prior information of random coefficient is estimated with fusing the failure time data of congeneric equipment. Then, the prior information of the random coefficient is updated online under the Bayesian framework, the probability density function(PDF) of the RUL with considering the limitation of the failure threshold is performed. Finally, two case studies are used for experimental verification. Compared with the traditional Bayesian method, the proposed method can effectively reduce the influence of imperfect prior information and improve the accuracy of RUL prediction.

Adaptive Random Effects/Coefficients Modeling

Adaptive fractional polynomial modeling of general correlated outcomes is formulated to address nonlinearity in means, variances/dispersions, and correlations. Means and variances/dispersions are modeled using generalized linear models in fixed effects/coefficients. Correlations are modeled using random effects/coefficients. Nonlinearity is addressed using power transforms of primary (untransformed) predictors. Parameter estimation is based on extended linear mixed modeling generalizing both generalized estimating equations and linear mixed modeling. Models are evaluated using likelihood cross-validation (LCV) scores and are generated adaptively using a heuristic search controlled by LCV scores. Cases covered include linear, Poisson, logistic, exponential, and discrete regression of correlated continuous, count/rate, dichotomous, positive continuous, and discrete numeric outcomes treated as normally, Poisson, Bernoulli, exponentially, and discrete numerically distributed, respectively. Example analyses are also generated for these five cases to compare adaptive random effects/coefficients modeling of correlated outcomes to previously developed adaptive modeling based on directly specified covariance structures. Adaptive random effects/coefficients modeling substantially outperforms direct covariance modeling in the linear, exponential, and discrete regression example analyses. It generates equivalent results in the logistic regression example analyses and it is substantially outperformed in the Poisson regression case. Random effects/coefficients modeling of correlated outcomes can provide substantial improvements in model selection compared to directly specified covariance modeling. However, directly specified covariance modeling can generate competitive or substantially better results in some cases while usually requiring less computation time.

EFFICIENT ESTIMATION OF FUNCTIONAL-COEFFICIENT REGRESSION MODELS WITH DIFFERENT SMOOTHING VARIABLES

In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the local linear technique and the averaged method,the initial estimates of the coefficient functions are given.Second step,based on the initial estimates,the efficient estimates of the coefficient functions are proposed by a one-step back-fitting procedure.The efficient estimators share the same asymptotic normalities as the local linear estimators for the functional-coefficient models with a single smoothing variable in different functions.Two simulated examples show that the procedure is effective.

FUNCTIONAL-COEFFICIENT REGRESSION MODEL AND ITS ESTIMATION

In this paper,a class of functional-coefficient regression models is proposed and an estimation procedure based on the locally weighted least equares is suggested.This class of models,with the proposed estimation method,is a powerful means for exploratory data analysis.

LIMITING BEHAVIOR OF RECURSIVE M-ESTIMATORS IN MULTIVARIATE LINEAR REGRESSION MODELS AND THEIR ASYMPTOTIC EFFICIENCIES

Recursive algorithms are very useful for computing M-estimators of regression coefficients and scatter parameters. In this article, it is shown that for a nondecreasing ul （t）, under some mild conditions the recursive M-estimators of regression coefficients and scatter parameters are strongly consistent and the recursive M-estimator of the regression coefficients is also asymptotically normal distributed. Furthermore, optimal recursive M-estimators, asymptotic efficiencies of recursive M-estimators and asymptotic relative efficiencies between recursive M-estimators of regression coefficients are studied.

STRONG CONVERGENCE RATES OF SEVERAL ESTIMATORS IN SEMIPARAMETRIC VARYING-COEFFICIENT PARTIALLY LINEAR MODELS

This article is concerned with the estimating problem of semiparametric varyingcoefficient partially linear regression models. By combining the local polynomial and least squares procedures Fan and Huang （2005） proposed a profile least squares estimator for the parametric component and established its asymptotic normality. We further show that the profile least squares estimator can achieve the law of iterated logarithm. Moreover, we study the estimators of the functions characterizing the non-linear part as well as the error variance. The strong convergence rate and the law of iterated logarithm are derived for them, respectively.

Fuzzy Varying Coefficient Bilinear Regression of Yield Series

We construct a fuzzy varying coefficient bilinear regression model to deal with the interval financial data and then adopt the least-squares method based on symmetric fuzzy number space. Firstly, we propose a varying coefficient model on the basis of the fuzzy bilinear regression model. Secondly, we develop the least-squares method according to the complete distance between fuzzy numbers to estimate the coefficients and test the adaptability of the proposed model by means of generalized likelihood ratio test with SSE composite index. Finally, mean square errors and mean absolutely errors are employed to evaluate and compare the fitting of fuzzy auto regression, fuzzy bilinear regression and fuzzy varying coefficient bilinear regression models, and also the forecasting of three models. Empirical analysis turns out that the proposed model has good fitting and forecasting accuracy with regard to other regression models for the capital market.

Empirical Likelihood Test for Regression Coefficients in High Dimensional Partially Linear Models

This paper considers tests for regression coefficients in high dimensional partially linear Models.The authors first use the B-spline method to estimate the unknown smooth function so that it could be linearly expressed.Then,the authors propose an empirical likelihood method to test regression coefficients.The authors derive the asymptotic chi-squared distribution with two degrees of freedom of the proposed test statistics under the null hypothesis.In addition,the method is extended to test with nuisance parameters.Simulations show that the proposed method have a good performance in control of type-I error rate and power.The proposed method is also employed to analyze a data of Skin Cutaneous Melanoma(SKCM).

Development of Empirical Models for the Estimation of CBR Value of Soil from Their Index Properties: A Case Study of the Ogbia-Nembe Road in Niger Delta Region of Nigeria

This study developed empirical-mathematical models to predict the California Bearing Ratio (CBR) using soil index properties in Ogbia-Nembe road in the Niger Delta region of Nigeria. The determination of CBR of soil is a laborious operation that requires a longer time and materials leading to increased cost and schedule;this can be reduced by adopting an empirical-mathematical model that can predict the CBR using other simpler soil index properties such as Plastic Limit (PL), the Liquid Limit (LL), the Plasticity Index (PI) and the Moisture Content (MC), which are less laborious and take lesser time to obtain. Thirteen models were developed to understand the relationship between these soil index properties: the independent variable and the California Bearing Ratio (CBR): the dependent variable;Six linear, Six quadratic and One multiple linear regression models were developed for this relationship. Analysis of variance (ANOVA) on the thirteen models showed that the Optimum Moisture Content (OMC) and the Maximum Dry Density (MDD) are better independent variables for the prediction of the CBR value of Ogbia-Nembe soil generating a quadratic model and a multiple linear regression model having a better coefficient of determination R2 = 0.96 and 0.94 respectively, mean square error (MSE) of 0.74 and 1.152 respectively with Root mean square errors of 0.861 and 1.073 accordingly. These models were used to predict the CBR of the soil. The CBR values predicted by the model were further compared with those of the actual experimental test and found to be relatively consistent with minimal variance. This establishes that CBR of any soil can be predicted from the Index Property of the soil and this is more economical and takes lesser time and can be universally adopted for soil investigation.

耦合均值-相关性的起重伤害事故致因ZIP模型研究

近些年来,起重伤害事故高发频发,导致了较大的直接经济损失和人员伤亡,受到行业的高度关注。为探究起重伤害事故致因的影响程度,采集2011—2021年376份起重伤害事故调查报告,依据事故致因24Model和系统安全分析法识别事故致因,构建起重伤害事故致因的零膨胀泊松回归模型(Zero-Inflated Poisson,ZIP),并通过Vuong方法和拟合优度检验准则进行检验;综合考虑事故致因发生频次的均值、致因和事故发生的相关性,运用弹性分析方法对事故致因的影响程度进行定量排序。结果表明:ZIP回归模型拟合效果优于泊松回归模型,各事故致因对起重伤害事故的影响程度排序为安全监管不到位C_(6)(T_(k)=1.0221)、安全意识淡薄H_(1)(T_(k)=0.5117)、作业人员违规作业H_(3)(T_(k)=0.4758)、作业人员无证上岗H_(2)(T_(k)=0.2116)、专项施工方案不合格C_(7)(T_(k)=0.1234)和结构构件破坏或连接不可靠M_(3)(T_(k)=0.1045)。研究从事故致因发生频次的均值、致因和事故发生的相关性两个维度刻画事故致因对起重伤害事故的影响程度,为起重伤害事故风险分级管控提供了新的研究思路和方法。

Local Least Product Relative Error Estimation for Varying Coefficient Multiplicative Regression Model

In this article, we consider the varying coefficient multiplicative regression model, which is very useful to model the positive response. The criterion of least product relative error(LPRE) is extended to the varying coefficient multiplicative regression model by kernel smoothing techniques. Consistency and asymptotic normality of the proposed estimator are established. Some numerical simulations are carried out to assess the performance of the proposed estimator. As an illustration, the ethanol data is analyzed.

基于随机森林回归算法的抽油机井系统效率分析与预测

抽油机井系统效率过低,则无功损耗大,必然造成能耗的浪费,因此有必要对系统效率进行分析研究。首先根据系统效率计算公式进行分析,构建了12类属性指标数据集,用于有功功率的分析和回归;采用随机森林回归算法,对指标数据集进行训练集回归,并对测试集测试;最后,采用随机森林回归算法对现场的抽油机井系统效率进行了预测。对训练集2560口抽油机井进行回归,得出系统效率主要受日产液量影响,其次为有功功率,二者重要性占72.2%;全样本特征属性预测和缺样本特征属性预测的测试集的确定系数分别为0.852和0.701,说明在有功功率缺失时,拟合质量降低,但系统效率的变异中可由各属性指标参数解释部分的占比仍较大;根据缺样本特征属性预测回归模型,在现场对系统效率低于15%的188口井进行措施调整,累计节电15.28×10^(4)kWh,折合经济效益9.73万元。

中国农业水土资源时空匹配特征及影响因素研究

分析农业水土资源的时空匹配特征与影响因素,可为农业水土资源优化配置提供科学依据。以中国除港澳台的31个省(自治区、直辖市)为研究对象,运用基尼系数法和农业水土资源匹配系数法对2009~2019年的农业水土资源时空匹配特征进行评价分析,并利用Sen+Mann-Kendall法分析农业水土资源匹配系数的变化趋势,最后运用面板回归模型探究变化的主要影响因素。研究结果表明:①2019年与2009年相比,中国水资源总量增加4860.90亿m^(3),耕地面积总量减少75295 km^(2),农业水土资源匹配系数由0.6018升高到0.6652,整体仍高度不匹配且呈不显著变差的趋势。②中国各省(自治区、直辖市)农业水土资源匹配整体呈现“西南优于东北,边缘优于腹地,林区优于农区,山丘优于平原”的空间格局。③北京农业水土资源匹配系数显著下降,上海、广西、重庆、贵州、云南以及宁夏显著上升。④农业用水量和人均水资源量是影响农业水土资源匹配的主要因子。中国农业水土资源匹配协调度仍处于高度不平衡状态,依据匹配系数划分不同等级的调控区并制定差异化的调控措施是缓解农业水土资源匹配不协调的有效途径。

结合机器学习的SA湍流模型闭合系数修正

将修正Morris分类筛选法与极端梯度提升(extreme gradient boosting,XGBoost)相结合,在计算流体动力学(computational fluid dynamics,CFD)数据驱动下,用于SA(Spalart-Allmaras)湍流模型闭合系数的修正.利用分类筛选法有效缩小闭合系数研究范围,同时依据XGBoost方法在小规模数据集下取得精度较高的拟合模型,有效提升系数修正效率.在三维DLR-F6-WB构型下进行了数值实验,实验结果显示利用本方法能够在三维复杂模型上基于小样本数据进行系数修正,修正后的升阻力系数计算精度得到了显著提升.

巷道通风摩擦阻力系数遗传投影寻踪回归预测

为满足智能通风准确获得巷道摩擦风阻的需求,基于遗传算法的投影寻踪回归预测方法预测矿井通风摩擦阻力系数。研究空气密度变化和巷道有无支护两种类型时模型预测的准确性。利用通风摩擦阻力系数影响因素进行训练,对不同支护类型巷道采集学习样本建立模型,使用部分样本进行验证。将模型预测结果与主成分分析预测和BP神经网络预测结果进行比较。对不同支护类型巷道进行了预测,最大误差为1.76%,平均误差为1.07%;仅对圆木支护进行了分析,最大误差为1.73%,平均误差为0.79%;对不同密度无支护巷道预测表明,平均误差为-0.99%,最大误差为-1.01%,风流密度对模型预测结果的准确性基本没有影响。无论是风流密度还是支护形式,该方法预测精度均优于主成分分析和BP神经网络。

时空团状系数回归模型及其在海洋时空断面数据中的应用

为揭示变量间的回归关系在时空域上的变化结构,本文提出了一种新的变系数回归模型——时空团状系数(Spatio-temporally clustered coefficient, STCC)回归模型。STCC模型通过对时空上相邻点的回归系数之差施加惩罚,从而估计出存在时空变化的回归关系。该模型可在没有先验信息的情况下探索回归关系的时空结构。数值模拟实验表明:STCC模型不仅能有效捕捉回归关系在时空域上的团状结构,对随时空连续变化的回归系数也表现出了较好的估计性能。本文运用STCC模型探索了大西洋25°W断面上的海水温度和盐度之间的回归关系,并据此初步分析了南极中层水的季节性演变特征。

小样本纱线质量预测的机器学习算法适用性分析

为了解决当前基于神经网络的纱线质量预测模型针对小样本预测精度偏低和预测精度不稳定的问题,建立了随机森林(RF)算法预测模型、多层感知机神经网络(MLP)算法预测模型和线性回归(LR)算法预测模型,就各算法模型在小样本情况下对不同数据特点的数据集的敏感性、不同数据维度的敏感性和不同训练样本数的敏感性进行了预测性能对比试验。用决定系数和均方根误差进行模型预测性能评估。试验结果表明:在小样本情况下,相比于MLP算法和LR算法,大多数情况下RF算法预测准确性更高、预测精度稳定性更好、对小训练样本量的适应性更好,具有较高的综合预测性能。

Efficient Estimation of a Varying-coefficient Partially Linear Binary Regression Model

This article considers a semiparametric varying-coefficient partially linear binary regression model. The semiparametric varying-coefficient partially linear regression binary model which is a generalization of binary regression model and varying-coefficient regression model that allows one to explore the possibly nonlinear effect of a certain covariate on the response variable. A Sieve maximum likelihood estimation method is proposed and the asymptotic properties of the proposed estimators are discussed. One of our main objects is to estimate nonparametric component and the unknowen parameters simultaneously. It is easier to compute, and the required computation burden is much less than that of the existing two-stage estimation method. Under some mild conditions, the estimators are shown to be strongly consistent. The convergence rate of the estimator for the unknown smooth function is obtained, and the estimator for the unknown parameter is shown to be asymptotically efficient and normally distributed. Simulation studies are carried out to investigate the performance of the proposed method.

Inference on Varying-Coefficient Partially Linear Regression Model

The varying-coefficient partially linear regression model is proposed by combining nonparametric and varying-coefficient regression procedures. Wong, et al. （2008） proposed the model and gave its estimation by the local linear method. In this paper its inference is addressed. Based on these estimates, the generalized like- lihood ratio test is established. Under the null hypotheses the normalized test statistic follows a x2-distribution asymptotically, with the scale constant and the degrees of freedom being independent of the nuisance param- eters. This is the Wilks phenomenon. Furthermore its asymptotic power is also derived, which achieves the optimal rate of convergence for nonparametric hypotheses testing. A simulation and a real example are used to evaluate the performances of the testing procedures empirically.

STATISTICAL INFERENCES FOR VARYING-COEFFICINT MODELS BASED ON LOCALLY WEIGHTED REGRESSION TECHNIQUE

Some fundamental issues on statistical inferences relating to varying-coefficient regression models are addressed and studied. An exact testing procedure is proposed for checking the goodness of fit of a varying-coefficient model fited by the locally weighted regression technique versus an ordinary linear regression model. Also, an appropriate statistic for testing variation of model parameters over the locations where the observations are collected is constructed and a formal testing approach which is essential to exploring spatial non-stationarity in geography science is suggested.