Product reliability assessment based on proportional hazard degradation model

In order to evaluate the reliability of long-lifetime products with degradation data, a new proportional hazard degradation model is proposed. By the similarity between time-degradation data and stress-accelerated lifetime, and the failure rate function of degradation data which is assumed to be proportional to the time covariate, the reliability assessment based on a proportional hazard degradation model is realized. The least squares method is used to estimate the model＇s parameters. Based on the failure rate of the degradation data and the proportion function of the known time, the failure rate and the reliability function under the given time and the predetermined failure threshold can be extrapolated. A long life GaAs laser is selected as a case study and its reliability is evaluated. The results show that the proposed method can accurately describe the degradation process and it is effective for the reliability assessment of long lifetime products.

Reliability estimation and remaining useful lifetime prediction for bearing based on proportional hazard model

As the central component of rotating machine,the performance reliability assessment and remaining useful lifetime prediction of bearing are of crucial importance in condition-based maintenance to reduce the maintenance cost and improve the reliability.A prognostic algorithm to assess the reliability and forecast the remaining useful lifetime(RUL) of bearings was proposed,consisting of three phases.Online vibration and temperature signals of bearings in normal state were measured during the manufacturing process and the most useful time-dependent features of vibration signals were extracted based on correlation analysis(feature selection step).Time series analysis based on neural network,as an identification model,was used to predict the features of bearing vibration signals at any horizons(feature prediction step).Furthermore,according to the features,degradation factor was defined.The proportional hazard model was generated to estimate the survival function and forecast the RUL of the bearing(RUL prediction step).The positive results show that the plausibility and effectiveness of the proposed approach can facilitate bearing reliability estimation and RUL prediction.

Clinical Study on the Impact of Long-term Survival Quality in 204 Postoperative Patients with Breast Cancer by Cox Proportional Hazard Models

The aim of study was to evaluate clinical characteristics, social support and the association with the prognosis of breast cancer patients. A total of 204 participants were followed from 2003 until the end of 2008. Information about patients with breast cancer was submitted by investigators. Data were analyzed by Cox’s proportional hazard model. The clinical staging of breast cancer we used was the TNM classification. A 'T' score is based upon the size and/or extent of invasion. The 'N' score indicates the extent of lymph node involvement. Age at diagnose was associated with protective factors (HR=0.972;95%CI (0.834-1.130)), T staging (HR=2.075;95%CI (1.424-3.022)), N staging (HR=1.513;95%CI (1.066-2.148)), were associated with risk factor. Two survival graphs of nodes with negative effects by histology and nodes with positive effects by histology was analyzed by log-rank test, there was statistically significant relationship between two survival graphs (χ2 =136.8467, p <.0001). Age at diagnoses, Clinical stage tumor and node could contribute to the development of breast cancer and disease free survival in Chinese women.

Comparison of Cox proportional hazards model,Cox proportional hazards with time-varying coefficients model,and lognormal accelerated failure time model:Application in time to event analysis of melioidosis patients

Objective:To compare the prognostic factors of mortality among melioidosis patients between lognormal accelerated failure time(AFT),Cox proportional hazards(PH),and Cox PH with time-varying coefficient(TVC)models.Methods:A retrospective study was conducted from 2014 to 2019 among 453 patients who were admitted to Hospital Sultanah Bahiyah,Kedah and Hospital Tuanku Fauziah,Perlis in Northern Malaysia due to confirmed-cultured melioidosis.The prognostic factors of mortality from melioidosis were obtained from AFT survival analysis,and Cox’s models and the findings were compared by using the goodness of fit methods.The analyses were done by using Stata SE version 14.0.Results:A total of 242 patients(53.4%)survived.In this study,the median survival time of melioidosis patients was 30.0 days(95%CI 0.0-60.9).Six significant prognostic factors were identified in the Cox PH model and Cox PH-TVC model.In AFT survival analysis,a total of seven significant prognostic factors were identified.The results were found to be only a slight difference between the identified prognostic factors among the models.AFT survival showed better results compared to Cox's models,with the lowest Akaike information criteria and best fitted Cox-snell residuals.Conclusions:AFT survival analysis provides more reliable results and can be used as an alternative statistical analysis for determining the prognostic factors of mortality in melioidosis patients in certain situations.

A Cox Proportional Hazard Model Approach to Age at First Sexual Intercourse in Nigeria

Early age at first sexual intercourse comes with many negative sexual outcomes namely: having unprotected sex on first sexual intercourse, condom misuse, high rate of sexually transmitted infections (STIs), teenage pregnancy, increased number of sexual partners, etc. In this paper, we considered some socio-demographic and cultural factors and their relationship with age at first sexual intercourse so as to reduce the numerous negative sexual outcomes of early age at first sexual intercourse using the 2018 Nigerian Demographic and Health Survey data. The analysis was made using the Cox proportional hazard model and the Kaplan-Meier plot. The result shows that some respondents started having their first sexual intercourse at the age of 8 years and about 54.4% of the respondents had their first sexual intercourse before age 17 years. The median age of first sexual intercourse is 16 years which implies that about 50% of the respondents had their first sexual intercourse on or before their 16th birthday. Education, religion, region and residence significantly affects the age of first sexual intercourse while circumcision has no significant effect.

Optimum design of equivalent accelerated life testing plans based on proportional hazards-proportional odds model

The optimum design of equivalent accelerated life testing plan based on proportional hazards-proportional odds model using D-optimality is presented. The defined equivalent test plan is the test plan that has the same value of the determinant of Fisher information matrix. The equivalent test plan of step stress accelerated life testing （SSALT） to a baseline optimum constant stress accelerated life testing （CSALT） plan is obtained by adjusting the censoring time of SSALT and solving the optimization problem for each case to achieve the same value of the determinant of Fisher information matrix as in the baseline optimum CSALT plan. Numer- ical examples are given finally which demonstrate the equivalent SSALT plan to the baseline optimum CSALT plan reduces almost half of the test time while achieving approximately the same estimation errors of model parameters.

A Statistical Model with Non-Linear Effects and Non-Proportional Hazards for Breast Cancer Survival Analysis

The Cox proportional hazard model is being used extensively in oncology in studying the relationship between survival times and prognostic factors. The main question that needs to be addressed with respect to the applicability of the Cox PH model is whether the proportional hazard assumption is met. Failure to justify the subject assumption will lead to misleading results. In addition, identifying the correct functional form of the continuous covariates is an important aspect in the development of a Cox proportional hazard model. The purpose of this study is to develop an extended Cox regression model for breast cancer survival data which takes non-proportional hazards and non-linear effects that exist in prognostic factors into consideration. Non-proportional hazards and non-linear effects are detected using methods based on residuals. An extended Cox model with non-linear effects and time-varying effects is proposed to adjust the Cox proportional hazard model. Age and tumor size were found to have nonlinear effects. Progesterone receptor assay status and age violated the proportional hazard assumption in the Cox model. Quadratic effect of age and progesterone receptor assay status had hazard ratio that changes with time. We have introduced a statistical model to overcome the presence of the proportional hazard assumption violation for the Cox proportional hazard model for breast cancer data. The proposed extended model considers the time varying nature of the hazard ratio and non-linear effects of the covariates. Our improved Cox model gives a better insight on the hazard rates associated with the breast cancer risk factors.

Reliability analysis of web server cluster systems based on proportional hazards model

An approach for web server cluster(WSC)reliability and degradation process analysis is proposed.The reliability process is modeled as a non-homogeneous Markov process(NHMH)composed of several non-homogeneous Poisson processes(NHPPs).The arrival rate of each NHPP corresponds to the system software failure rate which is expressed using Cox s proportional hazards model(PHM)in terms of the cumulative and instantaneous load of the software.The cumulative load refers to software cumulative execution time,and the instantaneous load denotes the rate that the users requests arrive at a server.The result of reliability analysis is a time-varying reliability and degradation process over the WSC lifetime.Finally,the evaluation experiment shows the effectiveness of the proposed approach.

Penalized Empirical Likelihood Via Adaptive LASSO for Cox＇s Proportional Hazards Model

Penalized empirical likelihood inferential procedure is proposed for Cox＇s pro- portional hazards model with adaptive LASSO（ALASSO）. Under reasonable conditions, we show that the proposed method has oracle property and the limiting distribution of a penal- ized empirical likelihood ratio via ALASSO is a chi-square distributions. The advantage of penalized empirical likelihood is illustrated in testing hypothesis and constructing confidence sets by simulation studies and a real example.

Cox Proportional Hazard Model for Survival Time of Neonatal Mortality in Neonatal Intensive Care Unit of Hospitals in River Nile State-Sudan

Cox Proportional Hazard model is a popular statistical technique for exploring the relationship between the survival time of neonates and several explanatory variables. It provides an estimate of the study variables’ effect on survival after adjustment for other explanatory variables, and allows us to estimate the hazard (or risk) of death of newborn in NICU of hospitals in River Nile State-Sudan for the period (2018-2020). Study Data represented (neonate gender, mode of delivery, birth type, neonate weight, resident type, gestational age, and survival time). Kaplan-Meier method is used to estimate survival and hazard function for survival times of newborns that have not completed their first month. Of 700 neonates in the study area, 25% of them died during 2018-2020. Variables of interest that had a significant effect on neonatal death by Cox Proportional Hazard Model analysis were neonate weight, resident type, and gestational age. In Cox Proportional Hazard Model analysis all the variables of interest had an effect on neonatal death, but the variables with a significant effect included, weight of neonate, resident type and gestational age.

A Software Reliability Model for OSS Including Various Fault Data Based on Proportional Hazard-Rate Model

The software reliability model is the stochastic model to measure the software reliability quantitatively. A Hazard-Rate Model is the well-known one as the typical software reliability model. We propose Hazard-Rate Models Considering Fault Severity Levels (CFSL) for Open Source Software (OSS). The purpose of this research is to make the Hazard-Rate Model considering CFSL adapt to baseline hazard function and 2 kinds of faults data in Bug Tracking System (BTS), i.e., we use the covariate vectors in Cox proportional Hazard-Rate Model. Also, we show the numerical examples by evaluating the performance of our proposed model. As the result, we compare the performance of our model with the Hazard-Rate Model CFSL.

Exclusive Hypothesis Testing for Cox's Proportional Hazards Model

Exclusive hypothesis testing is a new and special class of hypothesis testing.This kind of testing can be applied in survival analysis to understand the association between genomics information and clinical information about the survival time.Besides,it is well known that Cox's proportional hazards model is the most commonly used model for regression analysis of failure time.In this paper,the authors consider doing the exclusive hypothesis testing for Cox's proportional hazards model with right-censored data.The authors propose the comprehensive test statistics to make decision,and show that the corresponding decision rule can control the asymptotic TypeⅠerrors and have good powers in theory.The numerical studies indicate that the proposed approach works well for practical situations and it is applied to a set of real data arising from Rotterdam Breast Cancer Data study that motivated this study.

Application of a 2 Parameter Weibull Distribution in Modeling of State Holding Time in HIV/AIDS Transition Dynamics

This study investigates the application of the two-parameter Weibull distribution in modeling state holding times within HIV/AIDS progression dynamics. By comparing the performance of the Weibull-based Accelerated Failure Time (AFT) model, Cox Proportional Hazards model, and Survival model, we assess the effectiveness of these models in capturing survival rates across varying gender, age groups, and treatment categories. Simulated data was used to fit the models, with model identification criteria (AIC, BIC, and R2) applied for evaluation. Results indicate that the AFT model is particularly sensitive to interaction terms, showing significant effects for older age groups (50 - 60 years) and treatment interaction, while the Cox model provides a more stable fit across all age groups. The Survival model displayed variability, with its performance diminishing when interaction terms were introduced, particularly in older age groups. Overall, while the AFT model captures the complexities of interactions in the data, the Cox model’s stability suggests it may be better suited for general analyses without strong interaction effects. The findings highlight the importance of model selection in survival analysis, especially in complex disease progression scenarios like HIV/AIDS.

基于迭代融合优化算法和WPHM的牵引电机轴承可靠性评估

为了评估列车牵引电机轴承的运行可靠性,提出一种基于反向指数鲸鱼群(OEWOA)与粒子群(PSO)迭代融合的优化算法和威布尔比例故障率模型(WPHM)的评估方法。提取振动信号的时域、频域特征指标,利用主成分分析法(PCA)进行特征信息的融合,将融合后的特征指标作为WPHM的响应协变量进行可靠性评估。针对模型中多个参数直接求解困难的问题,利用反向学习策略(OBL)和指数收敛因子提高鲸鱼算法(WOA)的搜索能力,迭代融合PSO算法良好的收敛能力;通过OEWOA的探索指导PSO的迭代,避免PSO陷入局部最优,从而彻底探索搜索空间,同时使用PSO限制OEWOA的搜索,以便更快地将解收敛到全局最优值。应用该优化算法对WPHM中多个参数进行求解,实现牵引电机轴承运行可靠性的评估。结果表明,该方法与PSO、WOA等优化算法比较,具有更快的收敛速度和寻优能力。

基于WPHM的动车组牵引传动系统可靠性分析

提出了一种考虑天气因素的威布尔比例故障率模型(WPHM),采用威布尔分布的基准故障率函数,构建能够反映动车组外部运行环境的天气因素协变量,建立牵引传动系统的部件WPHM,利用遗传算法进行模型参数估计,依据所估计参数得出正常天气状态和恶劣天气状态下各部件的故障率和可靠度。实例研究表明,当牵引传动系统各部件均处于耗损失效期,部件均不同程度受天气因素影响,其中影响程度较大的部件有M2S车牵引电机及冷却风机,TP车主断路器,TPB车主断路器,MH车牵引电机及冷却风机等;不同天气状态下系统各部件的故障率和可靠度随服役时间推移均有明显变化,尤其恶劣天气状态下部件故障率更高,可靠度更低。因此,模型能有效地度量天气因素对部件可靠性的影响,为运用维修决策提供理论依据。

糖尿病肾脏疾病预后影响因素的COX比例风险回归模型分析

目的基于COX比例风险回归模型分析糖尿病肾脏疾病(diabetic kidney disease,DKD)预后的影响因素,为临床早期评估和防治DKD提供科学的依据。方法收集多中心(河南中医药大学第一附属医院、河南中医药大学第三附属医院、河南省中医院及郑州市人民医院)2010—2021年就诊治疗的DKD患者资料,包括一般资料、实验室指标、中医辨证分型及中医药治疗,以肾小球滤过率(eGFR)下降≥50%、血肌酐(Scr)翻倍、DKD 5期、死亡为结局指标,随访其发生时间及情况,利用COX比例风险回归模型分析筛选DKD预后影响因素。结果本研究最终纳入1947例患者,随访时间为4.65(4.557~4.746)年,发生复合终点事件305例(15.67%)。单因素COX回归分析结果表明,不同年龄、DKD病程≥4年、饮酒史、吸烟史、高血压、冠心病、脑血管病、糖尿病足、糖尿病眼病、糖化血红蛋白(HbA1c)、血尿酸(SUA)、Scr、24 h尿蛋白定量(24 h-UTP)、eGFR、湿热血瘀证、脾肾气虚兼湿聚血瘀证、脾肾阳虚兼血瘀证、中药熏洗、服用中药患者DKD预后情况比较,差异有统计学意义(P<0.05)。多因素COX回归分析结果表明,年龄[HR(95%CI)=2.52(1.92,3.30)]、DKD病程[HR(95%CI)=1.62(1.09,2.42)]、吸烟史[HR(95%CI)=1.61(1.13,2.29)]、饮酒史[HR(95%CI)=1.41(1.01,1.95)]、脑血管病[HR(95%CI)=1.33(1.01,1.75)]、糖尿病眼病[HR(95%CI)=1.43(1.13,1.82)]、SUA[HR(95%CI)=1.72(1.26,2.33)]、24 h-UTP[HR(95%CI)=1.48(1.14,1.91)]、脾肾气虚兼湿聚血瘀证[HR(95%CI)=2.22(1.44,3.43)]与DKD发生终点事件的风险关系密切(P<0.05),服用中药[HR(95%CI)=2.57(2.00,3.31)]能够减少终点事件的发生(P<0.05)。结论年龄、DKD病程、吸烟史、饮酒史、脑血管病、糖尿病眼病、SUA、24 h-UTP、脾肾气虚兼湿聚血瘀证是影响DKD患者预后的危险因素,而服用中药治疗为其保护因素。

激素治疗慢性肾脏病进展高风险IgA肾病患者的预后分析——一项回顾性研究

背景IgA肾病(IgAN)是世界范围内常见的原发性肾小球肾炎之一,目前糖皮质激素是否能改善慢性肾脏病(CKD)进展高风险IgAN患者肾脏预后尚无明确结论。目的本研究旨在探讨激素治疗对CKD进展高风险IgAN患者的治疗反应及肾脏预后的影响。方法回顾性纳入2017年1月—2021年10月于郑州大学第一附属医院就诊的CKD进展高风险IgAN患者。根据是否进行激素治疗将患者分为激素治疗组和支持治疗组,采用倾向匹配法按照性别、年龄、24 h尿蛋白定量、估算肾小球滤过率(eGFR)对患者进行1∶1匹配筛选病例,收集患者的临床及病理资料,记录患者治疗1年内疾病缓解情况及不良反应发生情况。以开始支持治疗的日期作为随访起点,随访至2022-10-31,主要终点事件定义为:进展为终末期肾脏病(ESRD)或接受透析治疗。复合终点事件定义为:eGFR较基线持续下降超过30%或进入ESRD或接受透析或患者死亡;运用Kaplan-Meier法绘制生存曲线,并采用Log-rank检验比较两组患者主要/复合终点事件累积发生率的差异。运用Cox比例风险回归分析探究影响CKD进展高风险IgAN患者预后的可能因素。结果共有236例原发性IgAN患者符合纳入标准,经过1∶1匹配,激素治疗组97例与支持治疗组97患者匹配成功,两组基线数据匹配均衡。激素治疗组患者完全缓解率、部分缓解率均高于支持治疗组(χ^(2)=6.171,P=0.013;χ^(2)=3.973,P=0.046)。中位随访时间为18.00(9.75,28.00)个月。Kaplan-Meier生存分析结果显示,激素治疗组的主要终点事件累积发生率低于支持治疗组(χ^(2)=4.495,P=0.034);激素治疗组的复合终点事件累积发生率低于支持治疗组(χ^(2)=4.419,P=0.036)。符合纳入标准的236例患者中有177例中等量蛋白尿患者,采用倾向匹配法按照性别、年龄、24 h尿蛋白定量、eGFR对激素治疗和支持治疗的177例患者进行1∶1匹配后,激素治疗中等量蛋白尿者和支持治疗中等量蛋白尿者各有76例患者匹配成功。Kaplan-Meier生存曲线结果显示,激素治疗中等量蛋白尿者的主要终点事件累积发生率低于支持治疗中等量蛋白尿者(χ^(2)=4.127,P=0.042);激素治疗中等量蛋白尿者的复合终点事件累积发生率低于支持治疗中等量蛋白尿者(χ^(2)=4.934,P=0.026)。多因素Cox比例风险回归分析结果显示血红蛋白(HR=0.982)、血肌酐(HR=1.019)、eGFR(HR=1.020)、24 h尿蛋白定量(HR=1.205)是影响CKD进展高风险IgAN患者发生主要终点事件的影响因素(P<0.05)。激素治疗组感染发生率高于支持治疗组(P<0.05)。结论在CKD进展高风险IgAN肾病患者中,与单纯支持治疗相比,激素治疗可以显著提升肾脏缓解率,降低肾功能下降、肾衰竭风;但仍需警惕其不良反应的发生。

残余胆固醇水平与缺血性脑卒中复发风险的关联性及其预测价值研究

背景血清残余胆固醇(RC)与缺血性脑卒中发病相关,然而RC水平与缺血性脑卒中复发的相关性研究较少,且尚少有研究探讨RC在缺血性脑卒中患者脑卒中复发中的预测价值。目的通过检测缺血性脑卒中患者血清RC水平,探讨RC水平与脑卒中复发的相关性及其预测价值。方法纳入2019年3月—2021年3月在南昌大学第一附属医院、南昌大学第二附属医院、南昌市第二医院和南昌市第三医院住院且确诊为缺血性脑卒中的住院患者为研究对象,收集入院后48 h内的相关临床信息,并对其随访12个月,明确脑卒中复发情况。采用Cox比例风险回归模型及限制性立方样条(RCS)分析RC水平与缺血性脑卒中复发的相关性。通过受试者工作特征(ROC)曲线分析RC水平对缺血性脑卒中复发的预测价值。结果研究共纳入1023例患者,其中107例(10.46%)缺血性脑卒中患者1年内复发。多因素Cox比例风险回归模型分析结果显示,高RC水平是缺血性脑卒中复发的独立危险因素(HR=2.709,95%CI=1.150~6.382,P<0.05)。RC水平与缺血性脑卒中患者复发风险存在非线性的正性剂量-反应关系(P-Nonlinear=0.0193)。RC预测缺血性脑卒中患者1年内复发的ROC曲线下面积为0.687(95%CI=0.631~0.743),最佳截断值为0.58 mmol/L。RC联合Essen卒中风险评分量表(ESRS)与单独ESRS预测缺血性脑卒中患者1年内复发的ROC曲线下面积比较,差异有统计学意义(Z=2.3562,P<0.05)。结论高RC水平是缺血性脑卒中患者复发的独立危险因素,并对于缺血性脑卒中复发具有一定的预测价值。

胰岛素抵抗代谢评分与慢性心力衰竭患者不良预后的相关性研究

背景胰岛素抵抗(IR)与心血管疾病的发生、发展关系密切,目前多项研究已经证实了IR在心力衰竭(HF)患者中非常普遍,并与不良心血管结局有关,而反映IR的指标——胰岛素抵抗代谢评分(Mets-IR)与慢性心力衰竭(CHF)患者不良预后之间的关联目前尚不明确。目的分析Mets-IR与CHF患者不良预后之间的相关性。方法本研究为回顾性研究,选取2020年1月—2021年1月在郑州大学第二附属医院心血管内科确诊为CHF的患者313例为研究对象。根据是否发生全因死亡将患者分为两组:全因死亡组(61例)和对照组(252例)。将Mets-IR作为分类变量进行分析,以中位数将Mets-IR分为两类:低水平Mets-IR(Mets-IR<37.28)和高水平Mets-IR(Mets-IR≥37.28)。收集患者基线资料,其中包括Mets-IR及其年龄、血清生物标志物和超声心动图指标,随访截至2022-12-31。通过本院电子病历系统或电话随访收集患者预后情况,主要终点事件为全因死亡,次要终点事件为因HF再入院。不同水平Mets-IR患者全因死亡及因HF再入院的生存曲线采用Kaplan-Meier图和Log-rank检验进行分析。应用Cox比例风险回归模型分析Mets-IR与全因死亡及因HF再入院风险的相关性。构建受试者工作特征(ROC)曲线,分析Mets-IR对CHF患者全因死亡及因HF再入院风险的预测价值。结果中位随访时间25.0(9.0,28.5)个月,313例CHF患者中出现全因死亡61例(19.5%)、因HF再入院121例(38.7%)。全因死亡组患者年龄、BMI、空腹血糖、Mets-IR、N末端B型钠尿肽前体、血尿酸、中性粒细胞计数、红细胞分布宽度、心房颤动、高血压、利尿剂、醛固酮受体拮抗剂、美国纽约心脏病学会分级高于对照组,三酰甘油、高密度脂蛋白胆固醇、低密度脂蛋白胆固醇、白蛋白、血红蛋白、血钠、左心室射血分数、血管紧张素转化酶抑制剂/血管紧张素受体拮抗剂/血管紧张素受体-脑啡肽酶抑制剂低于对照组(P<0.05)。Log-rank检验结果显示,高水平Mets-IR患者的全因死亡率及因HF再入院率均高于低水平Mets-IR患者(P<0.001)。调整多个混杂因素后的Cox比例风险回归分析结果显示,与低水平Mets-IR患者相比,高水平Mets-IR患者全因死亡风险(HR=2.90,95%CI=1.51~5.54,P=0.001)、因HF再入院风险(HR=1.55,95%CI=1.04~2.30,P=0.030)均升高。Mets-IR预测全因死亡风险、因HF再入院风险的ROC曲线下面积分别为0.68(95%CI=0.62~0.75)、0.62(95%CI=0.55~0.68)。结论Mets-IR水平升高可能会增加CHF患者的全因死亡及因HF再入院风险,可用于CHF患者的危险分层。

基于KPCA和WPHM的滚动轴承可靠性评估与寿命预测

为了评估滚动轴承的可靠性和预测剩余使用寿命,选取能够反映性能退化过程的特征参数作为寿命预测模型的输入参数,提出一种基于核主元分析(kernel principal component analysis,简称KPCA)和威布尔比例故障率模型(Weibull proportional hazards model,简称WPHM)的方法。首先,提取滚动轴承全寿命周期的时域、频域及时频域等多特征参数,从中筛选出有效的特征参数,构建高维相对特征集;其次,进行核主元分析,选取能够反映轴承全寿命周期性能退化过程的核主元,进而作为WPHM的协变量来进行可靠性评估和剩余寿命预测。通过滚动轴承全寿命试验,验证了该方法能够对轴承进行准确的可靠性评估和剩余寿命预测,以提供及时的维修决策。同时,由于提取的是相对特征,降低了同种轴承间在制造、安装及工况的差异,增强了该方法的适用性和稳定性。