基于LSTM-CAPF框架的岸桥起升减速箱轴承寿命预测方法

图1 LSTM神经元结构图

Fig.1 Structure diagram of LSTM neurons

(1) 首先利用上一时刻的外部状态h_t_-1和当前时刻的输入x_t,计算出3个门以及候选状态 ${\bar{c}}_{t}$ .

(2) 结合遗忘门f_t和输入门i_t来更新记忆单元.

(3) 结合输出门o_t,将内部状态的信息传递给外部状态h_t.

1.3 退化状态方程

维纳过程模型^[20-21]是常用的轴承退化状态模型.通用的维纳过程模型一般表示为

(12)W(t) = W(0) + ηt+σ_BB(t)

式中:W(t)表示系统在t时刻的状态;W(0)表示系统的初始状态值,通常设置为0;η为退化率;σ_B为扩散参数;B(t)是标准布朗运动.基于对时变工况的考虑,建立以下退化方程:

(13)y(t)=

α_{p_{t}, p_{t - 1}}

(y(t-Δt) +

η_{p_{t}}

ΔS+

β_{p_{t}, p_{t - 1}}

) +ω_t_-1

式中:y(t) 为t时刻系统状态; $α_{p_{t}, p_{t - 1}}$ 和 $β_{p_{t}, p_{t - 1}}$ 为由t-1时刻至t时刻工况变化对应的跳变参数; $η_{p_{t}}$ 为t时刻对应工况的退化率,在固定工况下为常数,但会随着工况的变化而变化;ΔS为由t-1时刻至t时刻的载荷变化;ω_t_-1为测量噪声.

1.4 CAPF方法

传统的RUL预测中假设工况保持不变,因此退化参数被认为仅分配给一种工况.当考虑工况随时间变化时,需要为每个不同的工况设置不同的参数,并需要在预测退化状态之前依据预测工况进行参数选择.因此,本文利用Sun等^[16]提出的CAPF方法在状态预测过程中添加了工况系数选择过程,使用条件激活向量来选择操作工况并匹配相应的参数.具体步骤如下.

(1) 粒子初始化.令 $θ_{p_{t}}$ = [ $η_{p_{t}}$ $α_{p_{t - 1}, p_{t}}$ $β_{p_{t - 1}, p_{t}}$ ] 为参数向量,初始时生成N个粒子 { $θ_{0}^{i}$ }_i_=1:_N与对应的权值{ $w_{0}^{i}$ }_i_=1:_N.

(2) 设置工况激活向量.令

(14)

\begin{array}{l} η = {[\begin{array}{l} η_{1} & η_{2} & \dots & η_{i} & \dots & η_{k} \end{array}]}^{T} \\ α = [\begin{array}{l} α_{11} & α_{12} & \dots & \dots & α_{1 k} \\ α_{21} & α_{21} & \dots & \dots & α_{2 k} \\ \dots & \dots & α_{i j} & \dots & \dots \\ α_{k 1} & α_{k 2} & \dots & \dots & α_{k k} \end{array}] \\ β = [\begin{array}{l} β_{11} & β_{12} & \dots & \dots & β_{1 k} \\ β_{21} & β_{22} & \dots & \dots & β_{2 k} \\ \dots & \dots & β_{i j} & \dots & \dots \\ β_{k 1} & β_{k 2} & \dots & \dots & β_{k k} \end{array}] \end{array}\}

式中: 1≤i, j≤k; η是退化率向量, η_i代表i工况下的退化率;α, β为跳变参数矩阵,α_ij, β_ij为 i 工况到j工况的跳变参数.

设置工况激活向量:

(15)V_t=[

\begin{array}{l} v_{1} & v_{2} & \dots & v_{i} & \dots & v_{k} \end{array}

]

(16)v_i=

\{\begin{array}{l} 1, & p_{t} = i \\ 0, & 其 他 \end{array}

工况确定后, 可通过以下方程得到退化率与跳变参数:

(17)

η_{p_{t}}

=V_tη_t_-1

(18)

α_{p_{t - 1}, p_{t}}

=V_t_-1α_t_-1

{V^{T}}_{t}

(19)

β_{p_{t - 1}, p_{t}}

=V_t_-1β_t_-1

{V^{T}}_{t}

(3) 更新系统状态.将更新后的 $θ_{p_{t}}$ 代入系统退化方程并预测系统状态.

(4) 更新权重与参数矩阵.

通过最新观测更新权重与参数:

(20)

{\tilde{ω}}_{t}^{i}

\frac{ω_{t - 1}^{i}}{\sqrt{2 π {\tilde{σ}}^{2}}}

exp

[- \frac{(y_{t} - x_{t}^{i})^{2}}{2 {\tilde{σ}}^{2}}]

(21)

{\tilde{ω}}_{t}^{i}

\frac{{\tilde{ω}}_{t}^{i}}{\overset{N}{\sum_{i = 1}} {\tilde{ω}}_{t}^{i}}

(22)

θ_{p_{t}}

\overset{N}{\sum_{i = 1}} {\tilde{ω}}_{t}^{i} θ_{p_{t}}^{i}

(5) 重采样.重新进行粒子采样, 将所有权重设置为1/N.

1.5 剩余使用寿命

RUL定义为从当前时间到使用寿命结束的长度:

(23)r_k=t_EoL-t_k

式中:t_EoL 是使用寿命的终点;t_k是预测时间点;r_k是t_k时刻的剩余寿命.

对于状态模型, RUL可以定义为当前时间和系统状态达到失效阈值之间的时间间隔:

(24)r_k=inf (l|y(l+t_k)≥D)

式中:y(l+t_k)是l+t_k时刻的系统状态; inf(·)为下限函数;D为失效阈值.

2 LSTM-CAPF预测框架

本文所提基于 LSTM-CAPF框架的岸桥起升减速箱轴承寿命预测框架如图2所示,具体过程如下.

图2

图2 LSTM-CAPF预测框架路线图

Fig.2 Flow chart of LSTM-CAPF prediction method

(1) 载荷离散化,确定工况边界.

(2) 使用LSTM方法预测运行载荷及对应工况.

(3) 轴承退化至故障期时,根据工况预测结果,采用CAPF方法预测轴承退化状态.

(4) 轴承退化至失效期时,根据预测的轴承退化状态预测轴承RUL.

3 实例分析

3.1 岸桥起升减速箱全寿命数据

本文通过NetCMAS系统采集的某岸桥提升减速箱高速轴轴承自安装至失效的全寿命载荷-状态数据集验证所提出方法的有效性.该岸桥的结构与传感器的布置方式如图3所示.应力测点位于前拉杆和中拉杆之间的大梁上表面,振动测点垂直放置在提升减速箱外壳上.监测系统采样频率设置为 2 500 Hz,单次采样时间为0.8 s,采样间隔为8 s.分别采集并计算上述测点处的应力平均值与振动有效值,并分别以 10 000 点为一组计算平均值,形成载荷-状态序列.

图3

图3 岸桥测点示意图

Fig.3 Schematic diagram of quay crane measuring points

3.2 退化阶段划分与工况分类

图4、图5分别为状态序列与平滑后的状态序列.从图5所示的平滑振动能谱可以看出,轴承退化明显可分为3个阶段:健康阶段、故障阶段和失效阶段^[22].工况分类将在健康阶段完成,载荷及退化状态预测将从故障阶段开始,RUL预测将从失效阶段开始.在健康阶段,系统状态相对稳定,且该阶段下轴承的退化过程能够遍历整个载荷范围.根据港口常用的“轻载-中载-重载” 载荷分类模式,设置离散参数k'=3.失效阈值设置为岸桥维护人员检测到异常噪声时的振动有效值.

图4

图4 起升减速箱全寿命振动有效值

Fig.4 Effective value of hoisting gearbox life cycle vibration

图5

图5 轴承退化阶段划分结果

Fig.5 Division results of degradation stage of bearings

3.3 基于LSTM-CAPF框架的RUL预测

3.3.1 LSTM预测载荷

目前还没有成熟的理论基础来有效地选取LSTM网络超参数^[23].本次模型构建经反复尝试对比来搜索最优超参数.LSTM的最终参数选择如表1所示.

表1 LSTM参数

Tab.1 Parameters of LSTM

超参数	取值
LSTM层数	2
初始学习率	0.005
学习率衰减系数	0.2
隐藏层神经元个数	200
输入序列长度	20
输出序列长度	30
迭代次数	500
训练优化算法	Adam

采用平均绝对误差(MAE)对预测结果进行评估:

(25)I_MAE =

\frac{\overset{n}{\sum_{i = 1}}| R_{i} - r_{i} |}{n}

式中:R_i为第i预测点的剩余寿命预测值; r_i为第i预测点的剩余寿命真实值.

为方便展示载荷预测结果,从预测序列中分别提取1、5、10、20、30步预测结果,构成对应步长的预测时序,如图6所示.

图6

图6 不同步长载荷预测结果对比

Fig.6 Comparison of load prediction results with different steps

由图6可知,无论单步或多步预测,LSTM方法都能够跟踪岸桥工作载荷的变化趋势,并准确预测载荷.但随着预测步长的增加,预测载荷与真实值的偏离程度有所增加.表2定量分析了不同步长下的工况预测准确性,随着预测步长的增加,工况预测I_MAE值逐渐上升,预测准确率相应下降,但都保持在可以信赖的水平.试验表明,当预测步长超过30步时,无法获得准确的工况预测信息.

表2 不同步长下工况预测准确性对比

Tab.2 Accuracy comparison of operating condition prediction of different steps

预测步长	I_MAE	工况准确率/%
1	0.085 48	95.8
5	0.265 87	91.3
10	0.315 39	89.8
20	0.367 99	87.3
30	0.598 95	70.6

3.3.2 CAPF预测系统状态

为验证本文所提预测框架的有效性,对比4种预测方法:M1,LSTM-CAPF框架; M2,LSTM-PF框架; M3,单一粒子滤波(PF)方法; M4,LSTM-F2S2^[15]框架.M1、M2、M4均采用LSTM方法预测载荷变化;M2与M3忽略工况水平的影响且M3不考虑时变工况的影响;M4在工况分段稳定且已知的条件下表现良好, 将其作为对照组对比该方法与所提方法在工况连续变化条件下的模型表现.

图7为退化状态单步预测结果对比.在单步预测时,由于不区分工况,M3方法只能通过更大的噪声分布更新参数分布,所以会造成更大的预测误差,产生更多的误报警;M2方法相对M3方法能够取得较好的效果,但由于无法区分工况水平的影响,产生比M1方法更大的误差.表3为不同预测框架下预测MAE结果对比,结合步长为1时的预测I_MAE值,单步预测时M2方法的I_MAE值为0.72,与M4的0.68相近,小于M3方法的0.96,但大于LSTM-CAPF框架的0.37.这是因为LSTM-CAPF框架能够充分利用载荷预测信息,获得更准确的退化状态预测结果.

图7

图7 4种预测方案退化状态预测结果

Fig.7 Prediction results of degradation state of four prediction schemes

表3 预测I_MAE结果对比

Tab.3 Comparison of predicted I_MAE results

预测步长	M1	M2	M3	M4
1	0.37	0.72	0.96	0.68
5	0.42	1.33	1.77	1.29
10	1.08	2.11	2.44	2.01
20	1.50	2.44	3.56	2.21
30	2.01	3.86	7.63	3.47

表4列出了4种方案下单步状态预测分布结果的平均方差.预测结果平均方差越大,表明预测结果分布在更宽的范围内,预测结果的不确定性也越大.由表4可知,所提LSTM-CAPF框架的平均方差明显小于其他3种预测方案,表明所提方法能够降低状态预测的不确定性,从而验证了所提LSTM-CAPF框架在降低不确定性方面的优越性.

表4 单步状态预测结果分布平均方差对比

Tab.4 Comparison of distribution of mean variance of one-step state prediction results

方法	平均方差×10³
M1	1.972
M2	1.039
M3	3.159
M4	1.028

进一步分析表3可以得出,在多步预测中,在考虑时变工况的情况下,所提LSTM-CAPF框架能够明显提高轴承退化状态预测的准确性.同时对比M4方法可知,F2S2模型在工况已知且分段恒定的条件下表现良好,但在应对连续变化的载荷条件时,相较所提的LSTM+CAPF模型,其预测能力尚有不足.M3方法的I_MAE显著增加,并在不同预测步长中达到最高.这是因为PF方法缺乏载荷变化和工况条件的预测信息.随着预测步长的增加,将导致状态预测误差逐渐累积.PF方法的预测结果表明,在动态负载条件下,如果没有负载预测,则无法完成准确的系统状态预测.M2方法由于忽略了工况条件对跳跃系数和退化率的影响,所以在每个预测步长的系统状态预测中生成比LSTM-CAPF框架更大的I_MAE.同时,结合表3与表4可以看出,PF模型的偏差、方差均明显高于其他模型,LSTM-CAPF框架的偏差、方差均明显低于其他模型,这表明单一的模型难以同时处理变化工况与状态预测的任务,而所提方法能够控制预测偏差与预测不确定性,实现更精准的预测.

图8为RUL预测结果.可以看出,PF方法没有预测RUL的能力.在多步预测时,PF方法缺乏准确的载荷和工况预测,退化状态更新仅依赖于预测时间点的已知载荷,无法在变化的载荷水平条件下获得准确的退化状态,从而无法准确预测RUL.一旦当前时刻的工况条件为“重载”模式,RUL预测结果将显著降低.这也解释了表3中PF方法在不同步长条件下均产生最大MAE的原因.LSTM-PF方法具备了载荷变化信息,能够获得一定的轴承退化状态预测能力,但由于PF方法无法区分工况水平变化产生的退化率及跳变参数差异,预测退化状态时会产生更大的预测误差,产生更多误报警,使预测RUL值偏低;与LSTM-PF方法相比,LSTM-F2S2方案考虑了工况水平的影响,因此能够获得更准确的RUL预测结果,但由于该方法考虑的是分段恒定载荷,对实时变化的载荷条件对退化状态与RUL的影响不敏感,所以该方法的RUL预测准确度低于LSTM-CAPF框架.本文LSTM-CAPF框架能够克服以上方案的缺陷,提前预测载荷变化,并通过CAPF方法将该信息从载荷变化量和载荷水平两个方面进行处理,通过更新每个工况下的退化率与工况转换时的跳变参数,获得更精确的退化状态预测结果,从而获得更准确的RUL预测结果.

图8

图8 4种预测方法RUL预测结果对比

Fig.8 Comparison of RUL prediction results of four prediction methods

4 结论

提出了一种基于LSTM-CAPF的岸桥起升减速箱轴承寿命预测框架,首先通过LSTM方法对岸桥工作载荷与对应工况进行预测,进而利用CAPF方法预测起升减速箱轴承的退化状态与RUL,得出以下结论:

(1) LSTM能够学习时序数据随时间变化规律的能力,利用岸桥工作载荷在时间上的依赖关系,准确预测应力载荷及其对应工况.

(2) CAPF算法可以解决工况动态切换时的参数匹配与更新问题.该方法根据载荷变化与工况切换情况,自适应地选择相应的条件参数并实时更新,能够更准确地预测系统退化状态.

(3) 在变工况条件下,LSTM-CAPF预测框架在预测过程中增加了载荷及工况预测环节,通过动态匹配工况参数,能够处理岸桥起升减速箱轴承在变工况条件下的寿命预测问题.

(4) 将岸桥前大梁上的应力测量点作为工况条件的特征.对于复杂系统,多个测量点的融合特征能够更准确地反映外部工况的变化.在未来的工作中,将考虑多传感器融合技术在动态工况分类与预测中的应用.

参考文献

原文顺序

文献年度倒序

文中引用次数倒序

被引期刊影响因子

[1]

侯美慧, 胡雄, 王冰, 等.

基于Weibull分布的岸桥铰点退化特征提取方法研究

[J]. 振动与冲击, 2019, 38(22): 198-203.

HOU

Meihui

, HU

Xiong

, WANG

Bing

, et al.

Degradation feature extraction for the ship-to-shore crane turning point based on Weibull distribution

[J]. Journal of Vibration and Shock, 2019, 38(22):198-203.

DOI:10.1109/TII.2016.2643693 URL [本文引用: 1]

[2]

SINGLETON

R K

, STRANGAS

E G

, AVIYENTE

The use of bearing currents and vibrations in lifetime estimation of bearings

[J]. IEEE Transactions on Industrial Informatics, 2016, 13(3): 1301-1309.

[3]

唐刚, 李建霞, 胡雄.

准确近似聚类算法及其在岸桥拉杆状态监测中的应用

[J]. 东华大学学报(自然科学版), 2018, 44(4): 590-594.

TANG

Gang

, LI

Jianxia

, HU

Xiong

Accurate approximate clustering algorithm and its application in the state monitoring of crane

[J]. Journal of Donghua University (Natural Science), 2018, 44(4): 590-594.

DOI:10.1016/j.ress.2022.108717 URL [本文引用: 1]

[4]

CHEN

, QIN

, WANG

, et al.

Health indicator construction by quadratic function-based deep convolutional auto-encoder and its application into bearing RUL prediction

[J]. ISA Transactions, 2021, 114: 44-56.

DOI:10.1016/j.isatra.2020.12.052 PMID:33402262 [本文引用: 1]

As one of the most important components of machinery, once the bearing has a failure, serious catastrophe may happen. Hence, for avoiding the catastrophe, it is valuable to predict the remaining useful life (RUL) of bearing. Health indicators (HIs) construction plays a greatly important role in the data-driven RUL prediction. Unfortunately, most of the existing HIs construction methods need prior knowledge and few of them construct HIs from raw vibration signals. For dealing with the above issues, a novel quadratic function-based deep convolutional auto-encoder is developed in this work. The raw bearing vibration signals are first preprocessed by low-pass filtering. Then the cleaned vibration signals are input into the quadratic function-based DCAE neural networks for constructing HIs of bearings. Compared with AE, DNN, KPCA, ISOMAP, PCA and VAE, it is revealed that the proposed methodology can construct a better HI from the raw bearing vibration signal in terms of comprehensive performance. Several comparative experiments have been implemented, and the results indicate that the HI constructed by quadratic function-based DCAE neural network has stronger predictive power than the traditional data-driven HIs.Copyright © 2020 ISA. Published by Elsevier Ltd. All rights reserved.

[5]

BAE

, XI

Learning of physical health timestep using the LSTM network for remaining useful life estimation

[J]. Reliability Engineering & System Safety, 2022, 226: 108717.

[6]

LEI

, LI

, GONTARZ

, et al.

A model-based method for remaining useful life prediction of machinery

[J]. IEEE Transactions on Reliability, 2016, 65(3): 1314-1326.

DOI:10.1109/TR.2016.2570568 URL [本文引用: 1]

[7]

QIAN

, YAN

, GAO

R X

A multi-time scale approach to remaining useful life prediction in rolling bearing

[J]. Mechanical Systems and Signal Processing, 2017, 83: 549-567.

DOI:10.1016/j.ymssp.2016.06.031 URL [本文引用: 1]

[8]

AYE

S A

, HEYNS

P S

An integrated Gaussian process regression for prediction of remaining useful life of slow speed bearings based on acoustic emission

[J]. Mechanical Systems and Signal Processing, 2017, 84: 485-498.

DOI:10.1016/j.ymssp.2016.07.039 URL [本文引用: 1]

[9]

WANG

, XU

, KONG

, et al.

A linear mapping method for predicting accurately the RUL of rolling bearing

[J]. Measurement, 2021, 176: 109127.

DOI:10.1016/j.measurement.2021.109127 URL [本文引用: 1]

[10]

ALI

J B

, CHEBEL-MORELLO

, SAIDI

, et al.

Accurate bearing remaining useful life prediction based on Weibull distribution and artificial neural network

[J]. Mechanical Systems and Signal Processing, 2015, 56: 150-172.

DOI:10.1080/0740817X.2014.955153 URL [本文引用: 1]

[11]

BIAN

, GEBRAEEL

, KHAROUFEH

J P

Degradation modeling for real-time estimation of residual lifetimes in dynamic environments

[J]. Iie Transactions, 2015, 47(5): 471-486.

[12]

LIAO

, TIAN

A framework for predicting the remaining useful life of a single unit under time-varying operating conditions

[J]. Iie Transactions, 2013, 45(9): 964-980.

DOI:10.1080/0740817X.2012.705451 URL [本文引用: 1]

[13]

PENG

, LI

Y F

, YANG

Y J

, et al.

Bayesian degradation analysis with inverse Gaussian process models under time-varying degradation rates

[J]. IEEE Transactions on Reliability, 2017, 66(1): 84-96.

DOI:10.1109/TR.2016.2635149 URL [本文引用: 1]

[14]

KUNDU

, DARPE

A K

, KULKARNI

M S

Weibull accelerated failure time regression model for remaining useful life prediction of bearing working under multiple operating conditions

[J]. Mechanical Systems and Signal Processing, 2019, 134: 106302.

DOI:10.1016/j.ymssp.2019.106302 URL [本文引用: 1]

[15]

, GEBRAEEL

, LEI

, et al.

Remaining useful life prediction of machinery under time-varying operating conditions based on a two-factor state-space model

[J]. Reliability Engineering & System Safety, 2019, 186: 88-100.

DOI:10.1016/j.ress.2019.02.017 URL [本文引用: 2]

[16]

SUN

, HU

, DONG

Remaining useful life prediction of quay crane hoist gearbox bearing under dynamic operating conditions based on ARIMA-CAPF framework

[J]. Shock and Vibration, 2021, 2021: 9403401.

[本文引用: 3]

[17]

WANG

, WANG

, HE

, et al.

A practical chiller fault diagnosis method based on discrete Bayesian network

[J]. International Journal of Refrigeration, 2019, 102: 159-167.

DOI:10.1016/j.ijrefrig.2019.03.008 URL [本文引用: 1]

[18]

HUANG

, LI

, ZHU

An improved convolutional neural network with load range discretization for probabilistic load forecasting

[J]. Energy, 2020, 203: 117902.

DOI:10.1016/j.energy.2020.117902 URL [本文引用: 1]

[19]

王玉静, 李少鹏, 康守强, 等.

结合CNN和LSTM的滚动轴承剩余使用寿命预测方法

[J]. 振动、测试与诊断, 2021, 41(3): 439-446.

WANG

Yujing

, LI

Shaopeng

, KANG

Shouqiang

, et al.

Method of predicting remaining useful life of rolling bearing combining CNN and LSTM

[J]. Journal of Vibration, Measurement & Diagnosis, 2021, 41(3): 439-446.

DOI:10.1016/j.measurement.2021.109706 URL [本文引用: 1]

[20]

, HUANG

, DING

, et al.

Wiener-based remaining useful life prediction of rolling bearings using improved Kalman filtering and adaptive modification

[J]. Measurement, 2021, 182: 109706.

[21]

侯美慧, 胡雄, 王冰, 等.

基于Weibull和GG模糊聚类的岸桥减速箱健康状态识别方法

[J]. 机械强度, 2019, 41(5): 1023-1028.

DOI:10.16579/j.issn.1001.9669.2019.05.002 [本文引用: 1]

针对岸桥减速箱健康状态的识别问题，研究并提出一种威布尔分布与GG（Gath-Geva）模糊聚类相结合的健康状态识别方法。首先应用包络法对因岸桥工况的复杂性引起的噪声进行数据去噪，然后通过对低速轴振动信号进行威布尔分布拟合得到形状参数和尺度参数，定量反映了采集样本的变化特征。为了进一步对减速箱振动信号进行状态识别，采用GG模糊聚类方法对减速箱健康状态的不同阶段进行划分，实现对不同健康状态的识别。采用来自NetCMAS系统采集的试验数据进行实例分析，并与GK、FCM算法进行对比，结果表明该方法的有效性，聚类效果更好。

HOU

Meihui

, HU

Xiong

, WANG

Bing

, et al.

Health condition recognition for quayside container crane reducer based on Weibull and GG fuzzy clustering

[J]. Journal of Mechanical Strength, 2019, 41(5): 1023-1028.

DOI:10.1109/TIE.2015.2455055 URL [本文引用: 1]

[22]

, LEI

, LIN

, et al.

An improved exponential model for predicting remaining useful life of rolling element bearings

[J]. IEEE Transactions on Industrial Electronics, 2015, 62(12): 7762-7773.

[23]

WANG

, YANG

, XU

, et al.

Evaluation and prediction method of rolling bearing performance degradation based on attention-LSTM

[J]. Shock and Vibration, 2021, 2021: 6615920.