摘要
社会的稳定发展离不开制造业的高水平发展,生产是制造业的关键步骤,长期持续稳定的产出依赖于装备系统的稳定运行。系统故障引起的停产势必会造成一定的经济损失。如何尽早地发现装备系统的故障来避免停工停产带来的经济损失,已经成为了当前应用研究中的热点。采用定期人工检查的传统方法不仅提高了生产成本,还使得问题发现较为滞后,达不到实时监控的目的。而且,随着信息技术的高速发展,装备系统的监测也变得更加智能化。利用装备系统的历史数据检测其状态能够更敏捷、更高效地发现装备运行中的“亚健康”问题,能给装备管理者提供有益的决策支持。基于装备剩余使用寿命的数据预测,能够提供高效智能的解决方案,在工业领域有着宽广的应用前景。因此,本文聚焦于装备系统剩余使用寿命预测技术的研究进展,对近年来剩余使用寿命预测的研究进行归纳总结,并讨论各剩余使用寿命预测理论与方法的优缺点。最后,总结并展望装备系统剩余使用寿命预测技术的未来研究方向和发展趋势。
21世纪作为技术创新的时代,国内和国际社会发展日新月异,科技信息量呈现指数式的高速增长。工业设备系统也日趋复杂多样化,航空航天、整车制造、武器装备、智能家电以及工业设计等各个领域的工程体系日趋精密、变得更加复杂和智
早期工业设备的维护方式是故障之后维修,能够很快找到对应的故障,并实现完美的修复,但是会浪费大量的生产时间;随后,提出预防性维护。预防性维护从系统维护发展到基于状态的维护(Condition‑based maintenance,CBM
RUL预测的实现方法在不同的文献中使用了不同的分类标
物理模型是通过工业系统零部件的退化现象的数学或物理模型来构建的,能够用专业的模型对退化进行表征,从而能够将现有的观测数据代入模型求得RUL。例如,滚动轴承的L‑P公
数据驱动模型的建立依靠于先前观察到的数据来预测系统的未来状态,或通过匹配历史上类似的模式来推断RUL。数据驱动模型需要大量的数据进行训练,无需事先对系统的物理行为有专业认识,就能够很好地建模高度非线性、复杂和多维的系统。但是运行到故障的数据很难获得,因为获取系统故障数据可能是一个漫长而昂贵的过程。因此,通常使用公共数据库来验证所提出的模型,如FEMTO‑ST研究所提供的PRONOSTIA‑FEMTO轴承数据
因此有必要对工业系统中的现有RUL预测工作进行回顾,以此来掌握未来工业系统RUL预测的发展。本文介绍并总结了各种RUL预测方法、相应的主要假设和应用领域,并着重于基于数据驱动的RUL预测。接下来,指出并讨论当前和未来的挑战性问题,以期有助于未来的研究工作。
RUL定义为从当前时间到有效寿命结束的长
(1) |
式中:为设备在时刻t的剩余使用寿命,为设备的失效时间,为当前时刻所拥有的所有状态信息。
RUL预测整体方案如

图1 RUL预测整体方案
Fig.1 RUL prediction scheme
数据是RUL预测的基础,其中监控数据能够对设备的健康状态进行度量。监控数据的采集一般由传感器、数据传输设备和数据存储设备组成。采用多种传感器捕捉不同类型的监测数据,能够反映设备的健康状态变化。获取的数据通过数据传输设备传输到电脑或其他设备,并将其存储。随着传感器和通信技术的迅速发展,越来越多的先进数据采集设备被设计并应用到现代工业系统中。
有些数据可以直接作为设备性能或健康状态的表征。有些数据则不具有直接表征的能力,但是可以通过对数据进行更深层次的挖掘来对设备健康状况进行解读,实现间接表征。由此看来利用直接数据来进行RUL预测是最好的选择,但是直接数据的获取具有很大的难度,有些数据通常是不可获取的或者需要付出高昂代价。直接数据难以获取,间接数据的获取更加方便。一般无需停机收集,且使用特定的传感器便可得以实现。间接数据虽然不能直接表征设备性能和健康状态,但是可以通过数据处理将其映射到相应的健康指标上来描述设备的性能。特征提取方法包括但不限于傅里叶变换、均值方差提取、小波变换和主成分分析(Principal component analysis,PCA)法等。
数据处理包含数据去噪、数据标准化/归一化、特征选择和特征提取等。数据去噪是由于原始数据被污染,会存在噪声,但是噪声不能反映设备的真实状态,会影响预测的结果。因此需要将原始数据中的噪声去除,以减少甚至消除噪声的不当干扰。
数据标准化/归一化是由于采集到的原始数据会有多维变量,多维变量可能就会由于量纲的不一致导致数据的大小和方差有很大不同,因此需要消除数据中不同量纲尺度对设备健康状态估计的影响。一般会采用标准化和归一化的处理方法来消除量纲的影响。
特征选择主要针对包含多维变量的原始数据。多维变量中不相关或者冗余的变量可能会导致模型过拟合或者低灵敏度,因此变量选择是十分必要的。特征提取是为了消除数据中不同变量间具有明显或隐藏的相关性,将其变成线性不相关的新向量,新向量将具有更多的有效信息以及代表性。特征选择能够保持数据的原始特征,最终得到的降维数据其实是原数据集的一个子集;而特征提取会通过数据转换或数据映射得到一个新的特征空间,尽管新的特征空间是在原特征基础上得来的,但是新数据集与原始数据集之间的关联无法直接体现。
模型构建是考虑对应已有的数据,是采用物理模型还是数据驱动模型,或者是混合式的模型。针对不同的研究对象,需要分析不同模型的优缺点,再根据目标指导选择最合适的模型。对于单一设备的RUL预测可以选择简单明了的物理模型,能够实现低成本且高效率的预测;而对于复杂的集成系统,构建物理模型是十分困难的,而数据驱动的方法能够取得更佳的效果。
RUL输出以及运维方案是RUL预测最后的步骤,将预测结果以需要的方式展现。运维方案是基于预测结果给予适当的处理方案,将预测结果变得更加立体化,展现出基于RUL预测的智能一体化终端平台。
RUL预测结果一般可以由预测值和实际值进行直接差值对比,但是由于预测对象以及寿命计量单位的不同,会出现较大的差值。因此,对一些常用的评价标准进行简单介绍。常用的评价标准包括预测差值、RMSE、预测误差E、相对精度(Relative accuracy,RA)和惩罚分数(Score)等。
预测差值是真实RUL值与预测RUL值的差值,直观反映了预测的好坏。
(2) |
均方根误差是预测值与真实值偏差的平方和观测次数比值的平方根,能够很好地反映出预测的精密度。
(3) |
预测误差是预测值与真实值的差值除以真实值,反映了预测值与真实值的偏离程度。
(4) |
相对精度是相对于预测误差的另一种表现预测值与真实值的偏离程度的评价指标。
(5) |
惩罚分数为航空发动机数据专用评价指
(6) |
式中:为真实的RUL值,为预测的RUL值,,。
基于物理模型的RUL预测方法能够在拥有少量数据样本的情况下实现工业设备系统RUL的预测,其不需要考虑大规模大数量的采集数据,甚至无需数据分析就可以得到设备的故障或失效情况。在物理模型中,相应的专家知识是必不可少的,这里涉及到的模型构建将会花费大量的时间精力,模型一旦建立完成就具有了专用性,无法很好地适配到其他类似的系统中去,甚至在环境变化过大的情况下也不能很好地工作。故其在专业性上能够表现出可靠的预测效果,但是不具有迁移性,无法为其他类似或相近的工业系统服务。基于数据驱动模型的RUL预测模型则完全不需要考虑系统的专业知识,能够对数据运用不同的数据分析方法进行分析和数据信息的深度挖掘,获取特征信息,再根据特征信息建立模型。基于数据驱动的RUL预测模型的准确性依赖于数据的质量,只有足够且具有完整特征信息的数据才能实现模型的准确预测。数据的大量运用使其能够完成很复杂的物理模型无法完成的系统建模,但这既是其优点也是其缺点。设备运行的完整和准确的数据往往是不易获取的,其中完整的寿命周期数据更是难以获得,同时数据的采集也会受到噪声以及其他的干扰。本文将对近些年关于RUL预测的研究进行归纳,重点将介绍数据驱动模型的RUL预测,其中基于神经网络的RUL预测研究由于其强大的特征提取能力以及计算机算力的大幅提升而出现了爆发式的增长。
物理模型的正确建立是实现准确RUL预测的基础,它涉及系统失效机制的专业知识,以建立系统退化过程的数学模型来估计RUL。模型参数的识别通常需要专门设计的实验和大量的经验数据。Lundberg和Palmgren在1949年对滚动轴承疲劳失效进行研
(7) |
式中: 为工作时间,为额定动载荷,为当量动载荷,为轴承参数。
随着时代的发展,人们意识到L‑P理论存在一定的局限性。1985年,Ioannides和Harris在引进了材料疲劳极限应力和考虑应力体积内各点应力及其深度的情况下,构建了滚动轴承及其他易疲劳机械元件疲劳寿命预测的一种新的数学模
(8) |
式中:为存活率,为材料的疲劳极限应力,为产生疲劳裂纹的诱发应力,为承受应力的体积,为应力所在的深度,为海维赛阶跃函数,为应力循环的次数,为常数。
另一种轴承寿命预测模型是基于断裂力学,假定疲劳寿命取决于裂纹发展至断裂的过程。文献[
电化学阻抗谱(Electrochemical impedance spectroscopy,EIS)被提出用作监测锂电池健康状况的指
以上基于物理模型的RUL预测方法可以在相对稳定的外部条件下较好地提高预测的准确性。物理模型具有专用性,无法推广到其他设备中,而且其准确性很容易受到外界环境影响。随着工业设备系统高度集成化的发展,单个模型的建立已经不能满足整个工业设备系统寿命预测的需求。然而多模型的组合是困难的,无法通过简单叠加得到,需要基于设备的整体组合以及全面的专业知识去实现模型的建立,因此依靠物理模型来预测工业设备系统的RUL十分困难。越来越多学者的研究集中于数据驱动模型的RUL预测。
数据驱动模型的RUL预测方法很多都是着眼于退化模型的构建,其基本原理如

图2 基于退化模型的RUL预测基本框架
Fig.2 RUL prediction framework based on degradation model
支持向量机首先由Cortes和Vapnik提
(9) |
式中:为连接特征空间到输出的模型权值,为核函数,为独立噪声项。
该方法具有出色的小样本处理能力和避开维数灾难的能力,能够将高维空间中的非线性关系映射为线性关系。因此,许多学者尝试将该方法用于其他问题的解决。基于SVM及其扩展的RUL预测被应用到轴承、锂电池、航空发动机和机械部件等方面。文献[

图3 基于支持向量机的RUL预测方法
Fig.3 RUL prediction methods based on SVM
2015年以来,随着新能源汽车产业的蓬勃发展,SVM的分类属性与回归属性结合被用来实现锂离子电池RUL的实时预
2020年以后,学者们不再只关注已被运用到RUL预测方法的研究,有些未曾被应用的方法也被迁移到RUL预测中,并取得了较好的预测效果。鸟群算法被引入到LS‑SVM参数进行寻优
如
研究对象 | 方法 | 评价标准 | |
---|---|---|---|
RMSE | E/% | ||
轴承 |
HHT‑SVM‑SV | N/A | 0.6/1.1/1.25 |
SV | 34.5 | 2/62 | |
ANN‑SV | 0.058 1 | N/A | |
Deep temporal feature transfer | 30.96 | N/A |
维纳过程是布朗运动的数学模型。以表示运动中一微粒在时刻在轴的位置。,为微粒在时刻的位置,用表示的条件概率密度,则有
(10) |
假定与初始时刻无关,且当趋于零时,有的值无限趋近于初始时刻的值,则有
(11) |
根据中心极限定理,微粒的位移服从正态分布,即
(12) |
如果随机变量满足:(1),且在连续;(2)具有独立增量;(3)对,有;(4)对于任意两个互不相交的区间和,随机变量的增量和相互独立。则称此随机变量服从维纳过程分布。维纳过程有许多种的变形,例如线性带漂移维纳过程、非线性带漂移的维纳过程以及集合布朗运动等。
学者们假设设备随时间的退化是一个维纳过程,提出了一种新的随机退化过程RUL预测方法来更准确地预测退化早期阶段的RU
测量误差(Measurement error,ME)是测量数据的不确定性来源之一,对数据驱动寿命估计的性能影响很大。文献[
基于维纳过程的RUL预测研究对象过于分散,且采用的判定标准不一致,故在此未列表展示近期研究成果的定量对比。基于维纳过程的RUL预测会伴随着大量的公式推导以及计算,虽然具有很好的可解释性,但是其准确率表现并不优异,且随着其他数据驱动方法的快速发展及高准确率的表现,基于维纳过程的RUL预测研究呈现了一种下降的趋势。
GPR是由Williams等在1995年提
(13) |
式中:为均值函数,为协方差函数。为了回归,假设先验均值为零。协方差由所选核指定,核函数有常数、线性、母函数、径向基函数和多核合成等多种选择。常用的指数平方函数用来表示协方差。它是一个平稳核,定义为
(14) |
式中: 为超参数方差,为长度尺度。
在实际应用中,是难以获取的,实际上都是含有噪声的观测数据,是服从独立同分布的高斯白噪声,是噪声的标准偏差。任意有限个观测值可以形成一个高斯过程,即
(15) |
其中当且仅当时,否则。
引入噪声项后,根据高斯过程的定义,观测值和新样本点处的函数值是有限数量的随机变量,服从联合高斯分布
(16) |
式中: 为单位矩阵,为训练数据的协方差矩阵,为测试处的方差,为协方差向量,且。
根据贝叶斯原理以及联合正态分布的条件概率特性有
(17) |
式中
因此,的后验分布可以用来对新样本点进行预测。是高斯过程模型在新的样本输入的预测值,置信区间由描述。
使用GPR构建的通用健康模型被用于预测在各种使用场景下的电池容量退
深度高斯过程算法利用高斯过程对层间映射进行建模,再使用矩阵变量高斯分布对给定层间与节点间相关性进行建
如
研究对象 | 方法 | 评价标准 | |
---|---|---|---|
RMSE | RA | ||
锂电池 |
GPF | 2.69 | N/A |
Dual GP | 2.106/3.49/2.30/8.17 | N/A | |
GP | 0.015 8/0.023 1 | N/A | |
FE‑GP | N/A | 0.739/0.864/0.893 |
Wang等在2008年PHM数据挑战竞赛中提出一种基于轨迹相似度(Trajectory similarity based prediction,TSBP)的RUL预测方
在探究提高相似性方法的路上,文献[


研究对象 | 方法 | 评价标准 | |
---|---|---|---|
RMSE | Score | ||
发动机 |
TSB | N/A | 5 636.06 |
Improved TSB | 17.37 | 1 935.84 | |
Neural network filtering and similarit | N/A | 5 530.12 | |
AE MTS‑H | 14.07 | 291.67 |
ANN是由大量的处理单元(神经元)互相连接而形成的复杂网络结构,是对人脑组织结构和运行机制的某种抽象、简化和模拟,

图5 基于神经网络的RUL预测方法
Fig.5 RUL prediction methods based on neural network
CNN是典型的深度学习模型,基本结构由输入层、卷积层、池化层、全连接层和输出层组成。考虑到CNN强大的特征提取能力,基于双CNN模型结构的智能RUL预测方法被提
DCNN也被用于RUL预测,使用新的特征提取方法在时域和频域上针对不同类型的数据在不同场景、不同预测模型相结合,得到适合于DCNN的特征,将所提取的特征输入到DCNN中进行轴承的RUL预
RNN具有记忆性,在对序列数据的非线性特征的学习方面具有很大的优势,结构如

图6 用于RUL预测的网络结构
Fig.6 Network architectures for RUL prediction
LSTM是为了解决一般的RNN存在的长期依赖问题而专门设计出来的,如
也有其他新型神经网络方法也被提出用来进行RUL的预测,文献[
研究对象 | 方法 | 评价标准 | |
---|---|---|---|
RMSE | Score | ||
发动机 |
CNN‑MT | 12.72/21.24/12.51/21.86 | 279/2 247/386/2 388 |
发动机 |
CNN‑BiLST | 12.51 | 224 |
发动机 |
MLSA‑TC | 13.25/19.57/13.43/21.69 | 235.52/1 655.04/239.02/2 414.69 |
发动机 |
AdaBN‑DCN | 13.17/20.87/14.97/24.57 | 279/2 020/817/3 690 |
发动机 |
新型DCN | 12.18/19.58/15.67/22.12 | N/A |
发动机 |
MS‑DCN | 11.44 | 196.22 |
发动机 |
ESN‑相似 | 15.2 | 387.08 |
发动机 |
LSTM‑CNN‑DA | 11.96/20.34/12.46/22.43 | 229/2 730/535/3 370 |
发动机 |
1‑FCLCNN‑LST | 11.17/9.99 | 204/234 |
轴承 |
Double‑CN | 4.30/72.03 | N/A |
轴承 |
TCN | 0.12±0.02 | N/A |
轴承 |
DCN | 0.119 | N/A |
生成对抗网络(Generative adversarial network,GAN)是2014年由Goodfellow
GAN多用于小样本数据的增强,以改善数据不足的困境。文献[
GAN在无监督学习和迁移学习方面有着优异的性能,它可以利用有限的标记数据和丰富的非标记数据提供更高的分类精度。文献[
迁移学习和GAN都是为了应对发生失效的数据难以收集或数据不足的情况。不同于GAN去生成数据,迁移学习是利用目前已有预测模型迁移到相关研究中去提高RUL预测性能。文献[
对抗性训练也是迁移学习常用的方法,通过建立源域与目标域之间的映射,将域分布差异调整到最小,便可将源域学习到的知识应用于目标域,实际上就是以博弈思想为核心的对抗式训练来实现迁移学习。文献[
对抗学习与迁移学习是近年来兴起的深度学习方法,有助于解决基于数据驱动模型的RUL预测中最关键的数据问题,因此相关研究有着爆发性增长的趋势。对抗网络扩充数据后,相关研究对象的RUL预测效果随着数据量的增强都有一定的提升。迁移学习使得模型的建立变得简单,能够有效利用同类型数据,从而降低建模成本,提高数据有效利用率。对抗性训练为迁移学习提供了优化的参数迁移方式,通过无监督学习便可实现参数有效迁移。
本文对基于物理模型和数据驱动模型的RUL预测方法的优缺点进行比较,如
模型 | 优点 | 缺点 |
---|---|---|
物理模 | 易于解释、计算简单、小样本表现良好 | 适用性很差、构建困难 |
支持向量 | 灵活、小样本表现良好、训练速度快 | 大样本不适用 |
维纳过 | 具有明确物理解释、结构简单、计算方便 | 不能利用历史数据 |
高斯过程回 | 灵活、适合高维度数据、小样本表现良好 | 长期预测结果较差 |
相似性方 | 原理简单、适合大样本 | 需要全周期历史数据 |
神经网络模 | 具有很强的特征提取能力、预测准确 | 训练时间过长、模型复杂、可解释性不强 |
对抗学习和迁移学 | 数据扩充、预测准确、模型建立较为简单 | 伪数据可能不准确、模型匹配存在不足 |
支持向量机具有处理非线性映射问题的能力,在样本数量较少的情况下也有优异的表现,这使得支持向量机在RUL预测中得到了广泛的应用。提高监测数据质量和从监测信息中提取有用特征是重要的研究方向。另外,如今主要研究对象仅包括轴承和电池,对支持向量机的应用进行更多的研究也是具有很大前景的。维纳过程具有良好的数学性质和物理解释能力,它可以很好地描述系统的非单调动态特性。未来需要在预测数据下进行更多的决策研究,增强模型参数的修正。高斯过程回归是一种灵活的非参数贝叶斯模型,允许在函数上直接定义先验概率分布,可以利用高斯过程对函数从输入空间到目标空间的非线性映射进行建模,对高维、小样本、非线性、复杂的分类和回归问题具有良好的适用性。对核函数的研究是一直以来研究的重点,未来的研究应该考虑结合其他方法来扩展其在不同领域的应用。相似性方法主要是基于退化模型的建立来实现基于实例的预测。需要退化模型的有效构建和完整生命周期数据的获取。可以考虑引入数据扩充算法,实现在原始有限数据基础上的扩充。
神经网络方法具有强大的特征提取和非线性映射构建能力,成为当今理论科研和应用研究的热点。但是神经网络存在建模训练成本高昂、模型复杂以及可解释性不强等缺点,导致它的使用受到诸多限制,但是强大的预测能力和提升的算力注定其将是未来RUL预测研究的重点。结合对抗学习和迁移学习能够解决神经网络中存在的数据不足和模型建立困难的问题。神经网络训练需要大量经验数据的问题可以通过数据扩充的方式来解决,对于传感器数据一般可以采用复制、插值、加噪声和使用生成对抗网络生产数据等方法。另外对于小样本场景,可以考虑在神经网络中加入注意力机制以增加有效特征的权重。对于降低建模训练成本方面,可以使用轻型神经网络减少网络的参数量级。神经网络同样存在泛化性不强的问题,对于不同的预测对象往往需要重新训练模型,因此自适应方法也是学者研究的方向。深度神经网络通常过于复杂,一个神经网络往往涉及巨量计算,学者们很难对其内在工作机理进行解释,这也正是神经网络的痛点。未来学者应该考虑原理性解释与神经网络的结合,有着合理性解释的RUL预测才是最合理的。
本文总结了近年来对RUL预测的方法,对基于物理模型和基于数据驱动模型的RUL预测方法进行综述,并分析其优缺点。最后根据当前RUL预测研究的热点,对未来研究方向提出了发展性建议。
参考文献
司小胜,胡昌华.数据驱动的设备剩余寿命预测理论及应用[M].北京:国防工业出版社,2016. [百度学术]
SI Xiaosheng, HU Changhua. Data-driven remaining useful life prediction theory and applications for equipment[M]. Beijing: National Defence Industry Press,2016. [百度学术]
黄金泉, 王启航, 鲁峰. 航空发动机气路故障诊断研究现状与展望[J]. 南京航空航天大学学报, 2020, 52(4): 507-522. [百度学术]
HUANG Jinquan, WANG Qihang, LU Feng. Research status and prospect of gas path fault diagnosis for aeroengine[J]. Journal of Nanjing University of Aeronautics & Astronautics, 2020, 52(4): 507-522. [百度学术]
彭宇,刘大同.数据驱动故障预测和健康管理综述[J].仪器仪表学报,2014, 35(3): 481-495. [百度学术]
PENG Yu, LIU Datong. Data-driven prognostics and health management: A review of recent advances[J]. Chinese Journal of Scientific Instrument,2014, 35(3): 481-495. [百度学术]
Yam R C M, Tse P W, Li L, et al. Intelligent predictive decision support system for condition-based maintenance[J]. The International Journal of Advanced Manufacturing Technology, 2001, 17(5): 383-391. [百度学术]
Mosallam A, Medjaher K, Zerhouni N. Data-driven prognostic method based on Bayesian approaches for direct remaining useful life prediction[J]. Journal of Intelligent Manufacturing, 2016,27(5): 1037-1048. [百度学术]
梅枭央. 基于融合算法的锂离子电池剩余使用寿命预测[D].武汉:华中科技大学, 2019. [百度学术]
MEI Xiaoyang. Remaining useful life prediction of lithium-ion batteries based on fusion algorithm[D]. Wuhan: Huazhong University of Science & Technology, 2019. [百度学术]
Su X, Wang S, Pecht M, et al. Prognostics of lithium-ion batteries based on different dimensional state equations in the particle filtering method[J]. Transactions of the Institute of Measurement & Control, 2017, 39(10): 1537-1546. [百度学术]
Lundberg G, Palmgren A. Dynamic capacity of rolling bearings[J]. Journal of Applied Mechanics, 1949, 16(2): 165-172. [百度学术]
Ioannides E, Harris T A. A new fatigue life model for rolling bearings[J]. Journal of Tribology, 1985, 107(3): 367-377. [百度学术]
Chen W R, Keer L M. Fatigue crack growth in mixed mode loading[J]. Journal of Engineering Materials and Technology, 1991, 113(2): 222-227. [百度学术]
Oppenheimer C H, Loparo K A. Physically based diagnosis and prognosis of cracked rotor shafts[J]. Proceedings of Spie the International Society for Optical Engineering, 2002, 7: 122-132. [百度学术]
Dattoma V, Giancane S, Nobile R, et al. Fatigue life prediction under variable loading based on a new non-linear continuum damage mechanics model[J]. International Journal of Fatigue, 2006, 28(2): 89-95. [百度学术]
Su X, Wang S, Pecht M, et al. Prognostics of lithium-ion batteries based on different dimensional state equations in the particle filtering method[J]. Transactions of the Institute of Measurement & Control, 2017, 39(10): 1537-1546. [百度学术]
Wang R, Zhang B, Hu D, et al. In-phase thermomechanical fatigue lifetime prediction of nickel-based single crystal superalloys from smooth specimens to notched specimens based on coupling damage on critical plane[J]. International Journal of Fatigue, 2019, 126: 327-334. [百度学术]
胡殿印, 杨乾, 刘华伟, 等. GH2036高温合金平板裂纹闭合效应及裂纹扩展模型[J]. 稀有金属材料与工程, 2017, 46(11): 3405-3409. [百度学术]
HU Dianyin, YANG Qian, LIU Huawei, et al. Crack closure effect and crack growth life prediction for GH2036 superalloy plate[J]. Rare Metal Materials and Engineering, 2017, 46(11): 3405-3409. [百度学术]
Bloom I, Cole B W, Sohn J J, et al. An accelerated calendar and cycle life study of Li-ion cells[J]. Journal of Power Sources, 2001, 101(2): 238-247. [百度学术]
Duong P L T, Raghavan N. Heuristic Kalman optimized particle filter for remaining useful life prediction of lithium-ion battery[J]. Microelectronics Reliability, 2018, 81: 232‑243. [百度学术]
Miao Q, Xie L, Cui H, et al. Remaining useful life prediction of lithium-ion battery with unscented particle filter technique[J]. Microelectronics Reliability, 2013, 53(6): 805-810. [百度学术]
Zhang X, Miao Q, Liu Z. Remaining useful life prediction of lithium-ion battery using an improved UPF method based on MCMC[J]. Microelectronics Reliability, 2017, 75: 288-295. [百度学术]
姜媛媛, 曾文文, 沈静静, 等. 基于凸优化-寿命参数退化机理模型的锂离子电池剩余使用寿命预测[J]. 电力系统及其自动化学报, 2019, 31(3): 23-28. [百度学术]
JIANG Yuanyuan, ZENG Wenwen, SHEN Jingjing, et al. Prediction of remaining useful life of lithium-ion battery based on convex optimization-life parameter degradation mechanism model[J]. Proceedings of the CSU-EPSA, 2019, 31(3): 23-28. [百度学术]
Guha A, Patra A. Online estimation of the electrochemical impedance spectrum and remaining useful life of lithium-ion batteries[J]. IEEE Transactions on Instrumentation and Measurement, 2018,67(8): 1836-1849. [百度学术]
Sadabadi K K, Jin X, Rizzoni G. Prediction of remaining useful life for a composite electrode lithium-ion battery cell using an electrochemical model to estimate the state of health[J]. Journal of Power Sources, 2021, 481: 228861. [百度学术]
He W, Williard N, Osterman M, et al. Prognostics of lithium-ion batteries based on dempster‑shafer theory and the Bayesian Monte Carlo method[J]. Journal of Power Sources, 2011, 196(23): 10314-10321. [百度学术]
Nectoux P, Gouriveau R, Medjaher K, et al. PRONOSTIA: An experimental platform for bearings accelerated degradation tests[C]//Proceedings of IEEE International Conference on Prognostics and Health Management. Denver, Colorado: IEEE, 2012: 1-8. [百度学术]
Saha B, Goebel K. Battery data set[EB/OL].[2022-04-30].http://ti.arc.nasa.gov/project/prognostic-data-repository. [百度学术]
Saxena A, Goebel K. Turbofan engine degradation simulation data set[EB/OL].[2022-04-30].https://ti.arc.nasa.gov/tech/dash/groups/pcoe/prognostic-data-repository/#turbofan. [百度学术]
Sun C, Zhang Z, He Z. Research on bearing life prediction based on support vector machine and its application[J].Journal of Physics: Conference Series, 2011, 305(1): 012028. [百度学术]
Kim H E, Tan A C C, Mathew J, et al. Bearing fault prognosis based on health state probability estimation[J]. Expert Systems with Applications, 2012, 39(5): 5200-5213. [百度学术]
Chen X, Shen Z, He Z, et al. Remaining life prognostics of rolling bearing based on relative features and multivariable support vector machine[J]. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2013, 227(12): 2849-2860. [百度学术]
Soualhi A, Medjaher K, Zerhouni N. Bearing health monitoring based on Hilbert‑Huang transform, support vector machine, and regression[J]. IEEE Transactions on Instrumentation and Measurement, 2014, 64(1): 52-62. [百度学术]
Li X, Miao J, Ye J. Lithium-ion battery remaining useful life prediction based on grey support vector machines[J]. Advances in Mechanical Engineering, 2015, 7(12): 1-8. [百度学术]
Patil M A, Tagade P, Hariharan K S, et al. A novel multistage support vector machine based approach for Li ion battery remaining useful life estimation[J]. Applied Energy, 2015, 159: 285-297. [百度学术]
Liu Z, Zuo M J, Qin Y. Remaining useful life prediction of rolling element bearings based on health state assessment[J]. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2016, 230(2): 314-330. [百度学术]
Sun F, Li X, Liao H, et al. A Bayesian least-squares support vector machine method for predicting the remaining useful life of a microwave component[J]. Advances in Mechanical Engineering, 2017, 9(1): 526-534. [百度学术]
于震梁, 孙志礼, 曹汝男, 等. 基于支持向量机和卡尔曼滤波的机械零件剩余寿命预测模型研究[J]. 兵工学报, 2018, 39(5): 991-997. [百度学术]
YU Zhenliang, SUN Zhili, CAO Runan, et al. Research on remaining useful life predictive model of machine parts based on SVM and Kalman filter[J]. Acta Armamentarii, 2018, 39(5): 991-997. [百度学术]
Kordestani M, Zanj A, Orchard M E, et al. A modular fault diagnosis and prognosis method for hydro-control valve system based on redundancy in multisensor data information[J]. IEEE Transactions on Reliability, 2018, 68(1): 330-341. [百度学术]
Ordóñez C, Lasheras F S, Roca-Pardiñas J, et al. A hybrid ARIMA‑SVM model for the study of the remaining useful life of aircraft engines[J]. Journal of Computational and Applied Mathematics, 2019, 346: 184-191. [百度学术]
王雪莹, 赵全明. 基于改进鸟群算法优化最小二乘支持向量机的锂离子电池寿命预测方法研究[J]. 电气应用, 2020, 39(5): 12-16. [百度学术]
WANG Xueying, ZHAO Quanming. Research on lithium-ion battery life prediction method based on improved fock algorithm least squares support vector machine[J]. Electrotechnical Application, 2020, 39(5): 12-16. [百度学术]
Dameshghi A, Refan M H. Combination of condition monitoring and prognosis systems based on current measurement and PSO‑LS‑SVM method for wind turbine DFIGs with rotor electrical asymmetry[J]. Energy Systems, 2021, 12(1): 203-232. [百度学术]
Zan T, Liu Z, Wang H, et al. Prediction of performance deterioration of rolling bearing based on JADE and PSO‑SVM[J]. Journal of Mechanical Engineering Science, 2021, 235(9): 1684-1697. [百度学术]
邹旺, 江伟, 冯俊杰, 等. 基于 ANN 和 SVM 的轴承剩余使用寿命预测[J]. 组合机床与自动化加工技术, 2021(1): 32-35. [百度学术]
ZOU Wang, JIANG Wei, FENG Junjie, et al. Bearing remaining useful life prediction based on artificial neural network and support vector machine[J]. Modular Machine Tool & Automatic Manufacturing Technique, 2021(1): 32-35. [百度学术]
陈佳鲜, 毛文涛, 刘京, 等. 基于深度时序特征迁移的轴承剩余寿命预测方法[J]. 控制与决策, 2021, 36(7): 1699-1706. [百度学术]
CHEN Jiaxian, MAO Wentao, LIU Jing, et al. Remaining useful life prediction of bearing based on deep temporal feature transfer[J]. Control and Decision, 2021, 36(7): 1699-1706. [百度学术]
Zhang Y, Yang Y, Xiu X, et al. A remaining useful life prediction method in the early stage of stochastic degradation process[J]. IEEE Transactions on Circuits and Systems Ⅱ: Express Briefs, 2020, 68(6): 2027-2031. [百度学术]
Zhai Q, Ye Z S. RUL prediction of deteriorating products using an adaptive Wiener process model[J]. IEEE Transactions on Industrial Informatics, 2017, 13(6): 2911-2921. [百度学术]
Wang X, Guo B, Cheng Z, et al. Residual life estimation based on bivariate Wiener degradation process with measurement errors[J]. Journal of Central South University, 2013, 20(7): 1844-1851. [百度学术]
Yu W, Shao Y, Xu J, et al. An adaptive and generalized Wiener process model with a recursive filtering algorithm for remaining useful life estimation[J]. Reliability Engineering & System Safety, 2022, 217: 108099. [百度学术]
Tang S, Yu C, Wang X, et al. Remaining useful life prediction of lithium-ion batteries based on the wiener process with measurement error[J]. Energies, 2014, 7(2): 520-547. [百度学术]
Tang S, Guo X, Yu C, et al. Real time remaining useful life prediction based on nonlinear Wiener based degradation processes with measurement errors[J]. Journal of Central South University, 2014, 21(12): 4509-4517. [百度学术]
Li T, Pei H, Pang Z, et al. A sequential Bayesian updated Wiener process model for remaining useful life prediction[J]. IEEE Access, 2019, 8: 5471-5480. [百度学术]
Juan L I, Bo J, Hongde D A I, et al. Remaining useful life prediction based on variation coefficient consistency test of a Wiener process[J]. Chinese Journal of Aeronautics, 2018, 31(1): 107-116. [百度学术]
Lin J, Liao G, Chen M, et al. Two-phase degradation modeling and remaining useful life prediction using nonlinear wiener process[J]. Computers & Industrial Engineering, 2021, 160: 107533. [百度学术]
Feng J, Kvam P, Tang Y. Remaining useful lifetime prediction based on the damage-marker bivariate degradation model: A case study on lithium-ion batteries used in electric vehicles[J]. Engineering Failure Analysis, 2016, 70: 323-342. [百度学术]
Jin G, Matthews D E, Zhou Z. A Bayesian framework for on-line degradation assessment and residual life prediction of secondary batteries inspacecraft[J]. Reliability Engineering & System Safety, 2013, 113: 7-20. [百度学术]
Richardson R R, Osborne M A, Howey D A. Battery health prediction under generalized conditions using a Gaussian process transition model[J]. Journal of Energy Storage, 2019, 23: 320-328. [百度学术]
Lyu Z, Gao R, Chen L. Li-ion battery state of health estimation and remaining useful life prediction through a model-data-fusion method[J]. IEEE Transactions on Power Electronics, 2020, 36(6): 6228-6240. [百度学术]
Liu D, Pang J, Zhou J, et al. Prognostics for state of health estimation of lithium-ion batteries based on combination Gaussian process functional regression[J]. Microelectronics Reliability, 2013, 53(6): 832-839. [百度学术]
Celaya J R, Saxena A, Saha S, et al. Prognostics of power MOSFETs under thermal stress accelerated aging using data-driven and model-based methodologies[C]//Proceedings of Annual Conference of the PHM Society.Montreal, Canada: International Journal of Prognostics and Health Management, 2011: 443-452. [百度学术]
Li X, Wang Z, Yan J. Prognostic health condition for lithium battery using the partial incremental capacity and Gaussian process regression[J]. Journal of power sources, 2019, 421: 56-67. [百度学术]
Tagade P, Hariharan K S, Ramachandran S, et al. Deep Gaussian process regression for lithium-ion battery health prognosis and degradation mode diagnosis[J]. Journal of Power Sources, 2020, 445: 227281. [百度学术]
Li L, Wang P, Chao K H, et al. Remaining useful life prediction for lithium-ion batteries based on Gaussian processes mixture[J]. PLoS One, 2016, 11(9): e0163004. [百度学术]
Kang W, Xiao J, Xiao M, et al. Research on remaining useful life prognostics based on fuzzy evaluation-Gaussian process regression method[J]. IEEE Access, 2020, 8: 71965-71973. [百度学术]
Mohanty S, Teale R, Chattopadhyay A, et al. Mixed Gaussian process and state-space approach for fatigue crack growth prediction[J].International Workshop on Structural Heath Monitoring, 2007, 2: 1108-1115. [百度学术]
Huang W, Zhao D, Sun F, et al. Scalable Gaussian process regression using deep neural networks[C]//Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence. Buenos Aires, Argentina: IJCAI-INT Joint Conf Artif Intell,2015: 3576‑3582. [百度学术]
Wang T, Yu J, Siegel D, et al. A similarity-based prognostics approach for remaining useful life estimation of engineered systems[C]//Proceedings of 2008 International Conference on Prognostics and Health Management.[S.l.]: IEEE, 2008: 1-6. [百度学术]
Wang T. Trajectory similarity based prediction for remaining useful life estimation[D]. Cincinnati: University of Cincinnati, 2010. [百度学术]
You M Y, Meng G. A generalized similarity measure for similarity-based residual life prediction[J]. Journal of Process Mechanical Engineering, 2011, 225(3): 151-160. [百度学术]
Lam J, Sankararaman S, Stewart B. Enhanced trajectory based similarity prediction with uncertainty quantification[C]//Proceedings of Annual Conference of the PHM Society. Fort Worth, United states: [s.n.], 2014: 623-634. [百度学术]
Khelif R, Malinowski S, Chebel-Morello B, et al. RUL prediction based on a new similarity-instance based approach[C]//Proceedings of 2014 IEEE 23rd International Symposium on Industrial Electronics (ISIE).[S.l.]: IEEE, 2014: 2463-2468. [百度学术]
梁泽明, 姜洪权, 周秉直, 等. 多参数相似性信息融合的剩余寿命预测[J]. 计算机集成制造系统, 2018, 24(4): 813-819. [百度学术]
LIANG Zeming, JIANG Hongquan, ZHOU Bingzhi, et al. Multi-variable similarity-based information fusion method for remaining useful life prediction[J]. Computer Integrated Manufacturing Systems, 2018, 24(4): 813-819. [百度学术]
Liu Y, Hu X, Zhang W. Remaining useful life prediction based on health index similarity[J]. Reliability Engineering & System Safety, 2019, 185: 502-510. [百度学术]
Huang C G, Huang H Z, Peng W, et al. Improved trajectory similarity-based approach for turbofan engine prognostics[J]. Journal of Mechanical Science and Technology, 2019, 33(10): 4877-4890. [百度学术]
Bektas O, Jones J A, Sankararaman S, et al. A neural network filtering approach for similarity-based remaining useful life estimation[J]. The International Journal of Advanced Manufacturing Technology, 2019, 101(1): 87-103. [百度学术]
许昱晖, 舒俊清, 宋亚,等. 基于多时间尺度相似性的涡扇发动机寿命预测[J]. 浙江大学学报(工学版), 2021, 55(10): 1937-1947. [百度学术]
XU Yuhui, SHU Junqing, SONG Ya, et al. Remaining useful life prediction of turbofan engine based on similarity in multiple time scales[J]. Journal of Zhejiang University(Engineering Science), 2021, 55(10): 1937-1947. [百度学术]
Teng W, Zhang X, Liu Y, et al. Prognosis of the remaining useful life of bearings in a wind turbine gearbox[J]. Energies, 2016, 10(1): 1-16. [百度学术]
TAVAKOLI R,NAJAFI M,SHARIFARA A. Arti ficial neural networks and adaptive neuro-fuzzy models for prediction of remaining useful life[EB/OL].(2019-02-01). Https://arxiv.org/abs/1909. 02115. [百度学术]
Xia M, Li T, Liu L, et al. Remaining useful life prediction of rotating machinery using hierarchical deep neural network[C]//Proceedings of 2017 IEEE International Conference on Systems, Man, and Cybernetics (SMC). [S.l.]: IEEE, 2017: 2778-2783. [百度学术]
Zhao Z, Liang B, Wang X, et al. Remaining useful life prediction of aircraft engine based on degradation pattern learning[J]. Reliability Engineering & System Safety, 2017, 164: 74-83. [百度学术]
Mei X, Fang H. A novel fusion prognostic approach for the prediction of the remaining useful life of a lithiumion battery[C]//Proceedings of 2018 37th Chinese Control Conference (CCC). [S.l.]: IEEE, 2018: 5801-5805. [百度学术]
Huang R, Xi L, Li X, et al. Residual life predictions for ball bearings based on self-organizing map and back propagation neural network methods[J]. Mechanical Systems and Signal Processing, 2007, 21(1): 193-207. [百度学术]
Rai A, Upadhyay S H. Intelligent bearing performance degradation assessment and remaining useful life prediction based on self-organising map and support vector regression[J]. Journal of Mechanical Engineering Science, 2018, 232(6): 1118-1132. [百度学术]
Pan Y, Hong R, Chen J, et al. A hybrid DBN-SOM-PF-based prognostic approach of remaining useful life for wind turbine gearbox[J]. Renewable Energy, 2020, 152: 138-154. [百度学术]
Yang B, Liu R, Zio E. Remaining useful life prediction based on a double-convolutional neural network architecture[J]. IEEE Transactions on Industrial Electronics, 2019, 66(12): 9521-9530. [百度学术]
Kim T S, Sohn S Y. Multitask learning for health condition identification and remaining useful life prediction: deep convolutional neural network approach[J]. Journal of Intelligent Manufacturing, 2020, 32(8): 2169-2179. [百度学术]
Kitai M, Kobayashi T, Fujiwara H, et al. A framework for predicting remaining useful life curve of rolling bearings under defect progression based on neural network and Bayesian method[J]. IEEE Access, 2021, 9: 62642-62652. [百度学术]
Zhao C, Huang X, Li Y, et al. A double-channel hybrid deep neural network based on CNN and BiLSTM for remaining useful life prediction[J]. Sensors, 2020, 20(24): 1-15. [百度学术]
Cheng H, Kong X, Chen G, et al. Transferable convolutional neural network based remaining useful life prediction of bearing under multiple failure behaviors[J]. Measurement, 2021, 168: 108286. [百度学术]
Shang Z, Zhang B, Li W, et al. Machine remaining life prediction based on multi-layer self-attention and temporal convolution network[J]. Complex & Intelligent Systems, 2022, 8(2): 1409-1424. [百度学术]
Ren L, Sun Y, Wang H, et al. Prediction of bearing remaining useful life with deep convolution neural network[J]. IEEE Access, 2018, 6: 13041-13049. [百度学术]
Li J, Li X, He D. Domain adaptation remaining useful life prediction method based on AdaBN-DCNN[C]//Proceedings of 2019 Prognostics and System Health Management Conference (PHM-Qingdao). [S.l.]:IEEE, 2019: 1-6. [百度学术]
Yang H, Zhao F, Jiang G, et al. A novel deep learning approach for machinery prognostics based on time windows[J]. Applied Sciences, 2019, 9(22): 1-15. [百度学术]
Li J, He D. A Bayesian optimization AdaBN-DCNN method with self-optimized structure and hyperparameters for domain adaptation remaining useful life prediction[J]. IEEE Access, 2020, 8: 41482-41501. [百度学术]
Li H, Zhao W, Zhang Y, et al. Remaining useful life prediction using multi-scale deep convolutional neural network[J]. Applied Soft Computing, 2020, 89: 106113. [百度学术]
Zhang Y, Li Y, Wei X, et al. Adaptive spatio-temporal graph convolutional neural network for remaining useful life estimation[C]//Proceedings of 2020 International Joint Conference on Neural Networks (IJCNN).[S.l.]: IEEE, 2020: 1-7. [百度学术]
Zhang Y, Li Y, Wang Y, et al. Adaptive spatio-temporal graph information fusion for remaining useful life prediction[J]. IEEE Sensors Journal, 2021,22(4):3334-3347. [百度学术]
Guo L, Li N, Jia F, et al. A recurrent neural network based health indicator for remaining useful life prediction of bearings[J]. Neurocomputing, 2017, 240: 98-109. [百度学术]
Wang B, Lei Y, Yan T, et al. Recurrent convolutional neural network: A new framework for remaining useful life prediction of machinery[J]. Neurocomputing, 2020, 379: 117-129. [百度学术]
Dong D, Li X Y, Sun F Q. Life prediction of jet engines based on LSTM-recurrent neural networks[C]//Proceedings of 2017 Prognostics and System Health Management Conference (PHM-Harbin). [S.l.]: IEEE, 2017: 1-6. [百度学术]
Li Z, Zheng Z, Outbib R. A prognostic methodology for power MOSFETs under thermal stress using echo state network and particle filter[J]. Microelectronics Reliability, 2018, 88: 350-354. [百度学术]
Wang H, Chen Y, Zhao H, et al. Similarity-based echo state network for remaining useful life prediction[J]. Journal of Physics, 2022, 2171(1): 012016. [百度学术]
Yuan M, Wu Y, Lin L. Fault diagnosis and remaining useful life estimation of aero engine using LSTM neural network[C]//Proceedings of 2016 IEEE International Conference on Aircraft Utility Systems (AUS).[S.l.]: IEEE, 2016: 135-140. [百度学术]
Wang S, Zhang X, Gao D, et al. A remaining useful life prediction model based on hybrid long-short sequences for engines[C]//Proceedings of 2018 21st International Conference on Intelligent Transportation Systems (ITSC).[S.l.]: IEEE, 2018: 1757-1762. [百度学术]
Hinchi A Z, Tkiouat M. Rolling element bearing remaining useful life estimation based on a convolutional long-short-term memory network[J]. Procedia Computer Science, 2018, 127: 123-132. [百度学术]
Li J, Li X, He D. A directed acyclic graph network combined with CNN and LSTM for remaining useful life prediction[J]. IEEE Access, 2019, 7: 75464-75475. [百度学术]
Peng C, Chen Y, Chen Q, et al. A remaining useful life prognosis of turbofan engine using temporal and spatial feature fusion[J]. Sensors, 2021, 21(2): 1-20. [百度学术]
Chen J, Jing H, Chang Y, et al. Gated recurrent unit based recurrent neural network for remaining useful life prediction of nonlinear deterioration process[J]. Reliability Engineering & System Safety, 2019, 185: 372-382. [百度学术]
He A, Jin X. NARNET-based prognostics modeling for deteriorating systems under dynamic operating conditions[C]//Proceedings of 2018 IEEE 14th International Conference on Automation Science and Engineering (CASE).[S.l.]: IEEE, 2018: 1322-1327. [百度学术]
Goodfellow I, Pouget-Abadie J, Mirza M, et al. Generative adversarial nets[J]. Advances in Neural Information Processing Systems, 2014(27):2672-2680. [百度学术]
Wang Z, Wang J, Wang Y. An intelligent diagnosis scheme based on generative adversarial learning deep neural networks and its application to planetary gearbox fault pattern recognition[J]. Neurocomputing, 2018, 310: 213-222. [百度学术]
于广滨, 卓识, 于军, 等. 基于InfoLSGAN和AC算法的滚动轴承剩余寿命预测[J]. 航空动力学报, 2020,35(6): 1212-1221. [百度学术]
YU Guangbin, ZHUO Shi, YU Jun, et al. Remaining useful life prediction of rolling bearings using InfoLSGAN and AC algorithm[J]. Journal of Aerospace Power, 2020,35(6): 1212-1221. [百度学术]
于军, 刘可, 郭帅, 等. 基于条件深度循环生成对抗网络和动作探索的行星轮轴承剩余寿命预测[J]. 兵工学报, 2020, 41(11): 2170-2178. [百度学术]
YU Jun, LIU Ke, GUO Shuai, et al. Remaining useful life prediction of planet bearings based on conditional deep recurrent generative adversarial network and action discovery[J]. Acta Armamentarii, 2020, 41(11): 2170-2178. [百度学术]
He R, Tian Z, Zuo M J. A semi-supervised GAN method for RUL prediction using failure and suspension histories[J]. Mechanical Systems and Signal Processing, 2022, 168: 108657. [百度学术]
王峰. 面向复杂劣化信号的预测健康指数构造方法研究及应用[D]. 北京: 北京交通大学, 2021. [百度学术]
WANG Feng. Research and application on methods for constructing prognostic health index with complicated degradation signals[D]. Beijing: Beijing Jiaotong University, 2021. [百度学术]
Liu W, Luo Z, Li S. Improving deep ensemble vehicle classification by using selected adversarial samples[J]. Knowledge-Based Systems, 2018, 160: 167-175. [百度学术]
Zhang X Y, Shi H, Zhu X, et al. Active semi-supervised learning based on self-expressive correlation with generative adversarial networks[J]. Neurocomputing, 2019, 345: 103-113. [百度学术]
Zhang A, Wang H, Li S, et al. Transfer learning with deep recurrent neural networks for remaining useful life estimation[J]. Applied Sciences, 2018, 8(12): 1-22. [百度学术]
Fan Y, Nowaczyk S, Rögnvaldsson T. Transfer learning for remaining useful life prediction based on consensus self-organizing models[J]. Reliability Engineering & System Safety, 2020, 203: 107098. [百度学术]
Sun C, Ma M, Zhao Z, et al. Deep transfer learning based on sparse autoencoder for remaining useful life prediction of tool in manufacturing[J]. IEEE Transactions on Industrial Informatics, 2018, 15(4): 2416-2425. [百度学术]
Mao W, He J, Zuo M J. Predicting remaining useful life of rolling bearings based on deep feature representation and transfer learning[J]. IEEE Transactions on Instrumentation and Measurement, 2019, 69(4): 1594-1608. [百度学术]
Zhu J, Chen N, Shen C. A new data-driven transferable remaining useful life prediction approach for bearing under different working conditions[J]. Mechanical Systems and Signal Processing, 2020, 139: 106602. [百度学术]
Guo L, Lei Y, Xing S, et al. Deep convolutional transfer learning network: A new method for intelligent fault diagnosis of machines with unlabeled data[J]. IEEE Transactions on Industrial Electronics, 2018, 66(9): 7316-7325. [百度学术]
da Costa P R O, Akçay A, Zhang Y, et al. Remaining useful lifetime prediction via deep domain adaptation[J]. Reliability Engineering & System Safety, 2020, 195: 106682. [百度学术]
闫美玲. 基于域自适应对抗学习的货车车轮剩余使用寿命预测研究与应用[D]. 北京: 北京交通大学, 2021. [百度学术]
YAN Meiling. Research and application of remaining useful life prediction of railway wagon wheels based on domain adaption adversarial learning[D]. Beijing: Beijing Jiaotong University, 2021. [百度学术]
Si X S, Wang W, Hu C H, et al. Remaining useful life estimation-A review on the statistical data driven approaches[J]. European Journal of Operational Research, 2011, 213(1): 1-14. [百度学术]
尤明懿. 基于状态监测数据的产品寿命预测与预测维护规划方法研究[D]. 上海: 上海交通大学, 2012. [百度学术]
YOU Mingyi. Research on methods for condition-based product residual life prediction and predictive maintenance scheduling[D]. Shanghai: Shanghai Jiao Tong University, 2012. [百度学术]
Cortes C, Vapnik V. Support-vector networks[J]. Machine Learning, 1995, 20(3): 273-297. [百度学术]
Murphy K P. Machine learning: A probabilistic perspective[M]. Cambridge, MA:MIT Press, 2012. [百度学术]
Tipping M E. The relevance vector machine[J]. Advances in Neural Information Processing Systems, 2000, 12: 652-658. [百度学术]
Williams C, Rasmussen C. Gaussian processes for regression[J]. Advances in Neural Information Processing Systems, 1995(8): 514-520. [百度学术]