CN105868557A

CN105868557A - Online prediction method for remaining life of electromechanical equipment under situation of two-stage degradation

Info

Publication number: CN105868557A
Application number: CN201610188456.4A
Authority: CN
Inventors: 徐正国; 柯晓杰; 谢尉扬; 陈积明; 胡伯勇; 张震伟; 刘林; 黄泽毅; 孙优贤
Original assignee: Zhejiang Co Ltd Of Zhe Neng Institute For Research And Technology; Zhejiang University ZJU
Current assignee: Zhejiang Co Ltd Of Zhe Neng Institute For Research And Technology; Zhejiang University ZJU
Priority date: 2016-03-29
Filing date: 2016-03-29
Publication date: 2016-08-17

Abstract

The invention discloses an online prediction method for the remaining life of electromechanical equipment under the situation of two-stage degradation. The online prediction method can be applied to online service life prediction and health management of mechanical equipment and electric and electronic devices. The method comprises the steps that a Wiener process model serves as a basic degradation model of an object, and a degradation drifting coefficient is expanded into a state and described with a closed oblique Wiener process. A new algorithm is proposed to overcome prediction deviation caused by the Markovian feature of a common Wiener process. For state estimation in the online prediction stage, an iteration filter algorithm is proposed to obtain an analytical expression of updated states. On parameter estimation, a two-stage parameter estimation algorithm is proposed. An analytical expression related to remaining life prediction results is obtained by using updated states and parameters. The model proposed in the method better conforms to the general degradation rules, more accurate online remaining life prediction results can be obtained, and great significance is achieved on fault prediction and health management in engineering.

Description

An Online Prediction Method for the Remaining Life of Electromechanical Equipment under Two-Stage Degradation

技术领域technical field

本发明属于可靠性工程技术领域，涉及一种两阶段退化情况下的机电设备剩余寿命在线预测方法。The invention belongs to the technical field of reliability engineering and relates to an online prediction method for the remaining life of electromechanical equipment under the condition of two-stage degradation.

背景技术Background technique

故障预测与健康管理(Prognostics and Health Management，PHM)对于运行中的产品的可靠性和安全性至关重要，并且已经应用在很多不同的产品上。实现故障预测和健康管理的核心在于设备剩余寿命预测。维纳过程模型由于具有良好的数学特性和物理可解释性，因而被广泛应用在不同工业领域的寿命数据分析，比如接触图像扫描仪的LED，自控温加热电缆，铝电解槽，桥梁和轴承。进一步，为了考虑历史退化数据和当前测量量，自适应维纳过程模型成为了广泛采用的预测模型。但是针对广泛存在的具有缓慢退化和加速退化两个阶段的机电设备的剩余寿命预测上，现有基于维纳过程的预测方法的假设存在一定的不合理性，因而不能得到更加精确的预测效果。Prognostics and Health Management (PHM) is critical to the reliability and safety of running products and has been applied to many different products. The core of realizing fault prediction and health management lies in the prediction of equipment remaining life. Due to its good mathematical properties and physical interpretability, the Wiener process model is widely used in life data analysis in different industrial fields, such as LEDs in contact with image scanners, self-temperature heating cables, aluminum electrolytic cells, bridges and bearings . Further, in order to consider historical degradation data and current measurements, the adaptive Wiener process model has become a widely adopted predictive model. However, for the widely existing remaining life prediction of electromechanical equipment with two stages of slow degradation and accelerated degradation, the assumptions of the existing prediction methods based on the Wiener process are somewhat irrational, so more accurate prediction results cannot be obtained.

发明内容Contents of the invention

针对现有的技术状况，本发明的目的是解决现有技术中存在的问题，并针对存在符合两阶段退化特性的机电设备，根据能够得到的性能退化数据，构建能够更加合理描述退化过程特性的模型实现对设备剩余寿命的在线高准确性预测。In view of the existing technical situation, the purpose of the present invention is to solve the problems existing in the prior art, and aiming at the electromechanical equipment that conforms to the two-stage degradation characteristics, according to the available performance degradation data, construct a system that can more reasonably describe the characteristics of the degradation process The model enables online high-accuracy prediction of the remaining life of the equipment.

现将本发明的构思阐述如下：Design of the present invention is set forth as follows now:

本发明采用维纳过程模型作为对象的基本退化模型，将退化漂移系数扩展为状态，并用封闭斜维纳过程去描述。为了克服一般维纳过程的马尔可夫特性而引起的预测偏差，本发明提出了新的算法。针对在线预测阶段的状态估计，本发明提出了迭代滤波算法来获得更新状态的解析表达式。在参数估计上，本发明提出了两阶段的参数估计算法。利用更新状态和参数，本发明获得了关于剩余寿命预测结果的解析表达式。本发明提出的模型更符合一般退化规律，能够获得更加准确的在线剩余寿命预测结果The invention adopts the Wiener process model as the basic degradation model of the object, expands the degradation drift coefficient into a state, and uses a closed oblique Wiener process to describe it. In order to overcome the prediction deviation caused by the Markov characteristic of the general Wiener process, the present invention proposes a new algorithm. For the state estimation in the online prediction stage, the present invention proposes an iterative filtering algorithm to obtain the analytical expression of the updated state. In terms of parameter estimation, the present invention proposes a two-stage parameter estimation algorithm. Using the updated state and parameters, the present invention obtains an analytical expression for the remaining life prediction result. The model proposed by the invention is more in line with the general degradation law, and can obtain more accurate online remaining life prediction results

根据以上发明构思，本发明提出了一种两阶段退化情况下的机电设备剩余寿命在线预测方法，设备实际退化分为正常退化和加速退化两个阶段，性能退化过程符合自适应斜维纳过程模型，针对模型的参数采用两阶段的参数估计算法，采用迭代滤波算法来实时获得退化状态，在完成退化状态估计和参数估计后，用更新的退化漂移状态、估计的参数和测量量进行设备的剩余寿命预测；具体步骤如下：According to the above inventive concepts, the present invention proposes an online prediction method for the remaining life of electromechanical equipment in the case of two-stage degradation. The actual degradation of the equipment is divided into two stages: normal degradation and accelerated degradation, and the performance degradation process conforms to the adaptive oblique Wiener process model. , a two-stage parameter estimation algorithm is used for the parameters of the model, and an iterative filtering algorithm is used to obtain the degradation state in real time. Life prediction; the specific steps are as follows:

步骤1：建立刻画符合两阶段退化特性设备的性能退化模型，具体步骤如下：Step 1: Establish a performance degradation model that describes equipment that meets the two-stage degradation characteristics. The specific steps are as follows:

步骤1.1：将满足两阶段退化特性的设备退化模型表达如下：Step 1.1: Express the equipment degradation model that satisfies the two-stage degradation characteristics as follows:

η_k＝η_k-1+ν_k η _k ＝η _k-1 + ν _k

δ_k＝η_k-1τ_k+αΒ(τ_k)δ _k ＝η _k-1 τ _k +αΒ(τ _k )

δ_k＝x_k-x_k-1 δ _k ＝x _k -x _k-1

其中，t_k为第k个采样时刻，η_k是t_k的退化漂移系数，用来表征退化速度，且满足封闭斜高斯分布，其概率密度函数f(η)为:Among them, t _k is the kth sampling moment, η _k is the degradation drift coefficient of t _k , which is used to characterize the degradation speed, and satisfies the closed oblique Gaussian distribution, and its probability density function f(η) is:

$f f ((η η)) = = φ φ ((\frac{η η - - μ μ}{σ σ})) Φ Φ [[λ λ ((\frac{η η - - μ μ}{σ σ})) + + ξ ξ]] / / [[σ σ Φ Φ ((\frac{ξ ξ}{\sqrt{11 + + {λ λ}^{22}}}))]]$

上式中，φ(·)为标准高斯分布的概率密度函数，Φ(·)为标准高斯分布的累积分布函数；μ和σ分别为位置参数和尺度参数，ξ为一般参数，λ为形状参数；ν_k是系统白噪声，且ν_k～N(0,ε²)；α是扩散系数，且α>0，τ_k是采样时间间隔，且τ_k＝t_k-t_k-1，Β(τ_k)是标准布朗运动，且x_k表征第k个采样时刻设备的退化程度；δ_k为相邻两个采样时刻的退化程度增量；In the above formula, φ( ) is the probability density function of the standard Gaussian distribution, Φ( ) is the cumulative distribution function of the standard Gaussian distribution; μ and σ are the position parameter and scale parameter respectively, ξ is the general parameter, and λ is the shape parameter ;ν _k is the white noise of the system, and ν _k ～N(0,ε ² ); α is the diffusion coefficient, and α>0, τ _k is the sampling time interval, and τ _k ＝t _k -t _k-1 , Β (τ _k ) is the standard Brownian motion, and x _k represents the degree of degradation of the equipment at the kth sampling moment; δ _k is the increment of the degree of degradation between two adjacent sampling moments;

步骤1.2：一旦产品开始运行，监测系统将在t＝{t₁,...,t_k}对它进行监测，监测到设备状态数据，即设备退化程度为x₀一般假设为0，定义从产品投入使用到第k个采样时刻的历史退化增量为δ_1:k＝{δ₁,...,δ_k}，δ₁＝x₁。Step 1.2: Once the product starts to operate, the monitoring system will monitor it at t={t ₁ ,...,t _k }, and the equipment status data is monitored, that is, the equipment degradation degree is x ₀ is generally assumed to be 0, and the historical degradation increment from the product put into use to the kth sampling moment is defined as δ _1:k ={δ ₁ ,...,δ _k }, δ ₁ =x ₁ .

步骤2：采用迭代滤波算法估计退化的隐藏状态，具体步骤如下：Step 2: Estimate the degraded hidden state using iterative filtering algorithm, the specific steps are as follows:

步骤2.1：机电设备退化速度，也即是斜维纳过程模型的隐藏退化漂移系数，其初始状态满足封闭斜高斯分布，即CSN为封闭斜高斯分布，初始退化漂移状态的未知参数通过拟合同类产品的初始退化数据得到；进一步，设备的初始状态为(δ₁|η₀)～N(η₀τ₁,α²τ₁)，未知参数通过历史退化数据以及估计得到的初始退化漂移状态采用最大似然估计法得到；Step 2.1: The degradation rate of electromechanical equipment, that is, the hidden degradation drift coefficient of the oblique Wiener process model, whose initial state satisfies the closed oblique Gaussian distribution, namely CSN is a closed oblique Gaussian distribution, and the unknown parameters of the initial degradation drift state are obtained by fitting the initial degradation data of similar products; further, the initial state of the equipment is (δ ₁ |η ₀ )～N(η ₀ τ ₁ ,α ² τ ₁ ), the unknown parameters are obtained by the maximum likelihood estimation method through the historical degradation data and the estimated initial degradation drift state;

步骤2.2：在第k个采样时刻，有退化隐藏状态满足分布Step 2.2: At the kth sampling time, there is a degenerated hidden state that satisfies the distribution

$(({η η}_{k k - - 11} | | {δ δ}_{11 : : k k - - 11})) ~ ~ C C S S N N (({μ μ}_{k k - - 11},, {σ σ}_{k k - - 11}^{22},, {λ λ}_{k k - - 11},, {ξ ξ}_{k k - - 11}))$

有退化程度(δ_k|η_k-1,δ_1:k-1)～N(η_k-1τ_k,α²τ_k)。There is a degree of degradation (δ _k |η _k-1 , δ _1:k-1 ) ~ N(η _k-1 τ _k , α ² τ _k ).

步骤2.3：根据获得的新的测量量，设备的退化隐藏状态满足封闭斜高斯分布Step 2.3: According to the new measurements obtained, the degenerate hidden state of the device satisfies the closed skew Gaussian distribution

$(({η η}_{k k - - 11} | | {δ δ}_{11 : : k k})) ~ ~ C C S S N N (({\overset{^^}{μ μ}}_{k k - - 11},, {\overset{^^}{σ σ}}_{k k - - 11}^{22},, {\overset{^^}{λ λ}}_{k k - - 11},, {\overset{^^}{ξ ξ}}_{k k - - 11}))$

其中，in,

式中带^符号的表示该参数的估计值；The ^ symbol in the formula indicates the estimated value of the parameter;

步骤2.4：根据步骤2.3的结果，退化隐藏状态的后验分布服从Step 2.4: According to the result of step 2.3, the posterior distribution of the degenerated hidden state obeys

$(({η η}_{k k} | | {δ δ}_{11 : : k k})) ~ ~ C C S S N N (({μ μ}_{k k},, {σ σ}_{k k}^{22},, {λ λ}_{k k},, {ξ ξ}_{k k}))$

其中in

根据以上四步即构建了退化程度预测和历史退化数据的联系，能够迭代实时更新隐藏状态。According to the above four steps, the relationship between the degradation degree prediction and the historical degradation data is constructed, and the hidden state can be iteratively updated in real time.

步骤3：在线估计性能退化模型参数，具体步骤如下：Step 3: Estimate the performance degradation model parameters online, the specific steps are as follows:

步骤3.1：根据采样得到的退化数据，构造对数似然函数 Step 3.1: Construct the logarithmic likelihood function according to the degradation data obtained by sampling

$ln ln {f f}_{{Δ Δ}_{22 : : k k} | | {Δ Δ}_{11}} (({δ δ}_{22 : : k k} | | {δ δ}_{11})) = = {Σ Σ}_{i i = = 22}^{k k} ln ln {f f}_{{Δ Δ}_{i i} | | {Δ Δ}_{11 : : i i - - 11}} (({δ δ}_{i i} | | {δ δ}_{11 : : i i - - 11}))$

步骤3.2：在得到新测量量，即获得退化程度的条件概率密度函数后，将上式扩展为：Step 3.2: After obtaining the new measurement quantity, that is, obtaining the conditional probability density function of the degree of degradation, expand the above formula to:

$\begin{matrix} ln ln {f f}_{{Δ Δ}_{22 : : k k} | | {Δ Δ}_{11}} (({δ δ}_{22 : : k k} | | {δ δ}_{11})) = = {Σ Σ}_{i i = = 22}^{k k} {{- - \frac{11}{22} ln ln [[22 π π (({τ τ}_{i i}^{22} {σ σ}_{i i - - 22}^{22} + + {τ τ}_{i i}^{22} {ϵ ϵ}^{22} + + {α α}^{22} {τ τ}_{i i}))]] - - \frac{{(({δ δ}_{i i} - - {τ τ}_{i i} {μ μ}_{i i - - 22}))}^{22}}{22 (({τ τ}_{i i} {σ σ}_{i i - - 22}^{22} + + {τ τ}_{i i}^{22} {ϵ ϵ}^{22} + + {α α}^{22} {τ τ}_{i i}))}}} \\ + + {Σ Σ}_{i i = = 22}^{k k} ln ln Φ Φ {{\frac{{λ λ}_{i i - - 22} {σ σ}_{i i - - 22} (({δ δ}_{i i} - - {τ τ}_{i i} {μ μ}_{i i - - 22})) + + {ξ ξ}_{i i - - 22} (({τ τ}_{i i} {σ σ}_{i i - - 22}^{22} + + {τ τ}_{i i}^{22} {ϵ ϵ}^{22} + + {α α}^{22}))}{\sqrt{(({τ τ}_{i i} {σ σ}_{i i - - 22}^{22} + + {τ τ}_{i i}^{22} {ϵ ϵ}^{22} + + {α α}^{22})) [[{τ τ}_{i i} {σ σ}_{i i - - 22}^{22} + + ((11 + + {λ λ}_{i i - - 22}^{22})) (({τ τ}_{i i} {ϵ ϵ}^{22} + + {α α}^{22}))]]}}}} \\ - - {Σ Σ}_{i i = = 22}^{k k} ln ln Φ Φ ((\frac{{ξ ξ}_{i i - - 22}}{\sqrt{11 + + {λ λ}_{i i - - 22}^{22}}})) \end{matrix}$

步骤3.3：采用数值方法搜索获得最大化的参数。Step 3.3: Use numerical methods to search for maximization parameters.

步骤4：获得设备剩余寿命的概率分布表达式，具体步骤如下：Step 4: Obtain the probability distribution expression of the remaining life of the equipment, the specific steps are as follows:

步骤4.1：采用首次通过时间作为连接预测退化程度与剩余寿命预测的纽带，即剩余寿命随机变量定义为L＝inf{l:x(l+t_k)>ω|X_1:k}，其中l是剩余寿命随机变量的实现，ω是预先定义的阈值，X_1:k是历史测量量。Step 4.1: Use the time of first pass as the link between the predicted degradation degree and the remaining life prediction, that is, the remaining life random variable is defined as L=inf{l:x(l+t _k )>ω|X _1:k }, where l is the realization of the remaining life random variable, ω is the pre-defined threshold, and X _1:k is the historical measurement quantity.

步骤4.2：在第k个采样时刻的剩余寿命分布概率密度函数为，Step 4.2: The probability density function of remaining lifetime distribution at the kth sampling moment is,

${f f}_{L L | | {X x}_{11 : : k k}} ((l l | | {X x}_{11 : : k k})) = = \frac{ω ω - - {x x}_{k k}}{\sqrt{22 {πl πl}^{33} (({lσ lσ}_{k k}^{22} + + {α α}^{22}))}} exp exp [[- - \frac{{((ω ω - - {x x}_{k k} - - {μ μ}_{k k} l l))}^{22}}{22 l l (({lσ lσ}_{k k}^{22} + + {α α}^{22}))}]] \frac{Φ Φ ((ζ ζ / / \sqrt{11 + + {γ γ}^{22}}))}{Φ Φ (({ξ ξ}_{k k} / / \sqrt{11 + + {λ λ}_{k k}^{22}}))}$

其中， in,

至此，得到了在线预测设备剩余寿命的概率密度函数精确表达式，用于机电设备剩余寿命在线预测。So far, the exact expression of the probability density function for online prediction of remaining life of equipment is obtained, which is used for online prediction of remaining life of electromechanical equipment.

本发明方法的公式中，未定义的具有下标的参数表示该下标对应的采样时刻的参数值，如μ_k,σ_k分别为第k个采样时刻的位置参数和尺度参数。In the formula of the method of the present invention, an undefined parameter with a subscript represents the parameter value of the sampling time corresponding to the subscript, such as μ _k and σ _k are respectively the position parameter and the scale parameter of the kth sampling time.

本发明提出的两阶段退化情况下的剩余寿命在线预测方法，可应用于机械设备以及电力电子器件的在线寿命预测。通过构建能够合理描述退化过程特性的斜高斯模型，能够获得更加准确的预测效果。这将给后续的设备健康管理提供强有力的数据支撑，对于高可靠性的设备维护管理尤有价值，在实际工程应用方面具有广阔前景。The on-line prediction method of the remaining life under the condition of two-stage degradation proposed by the invention can be applied to the on-line life prediction of mechanical equipment and power electronic devices. By constructing a skewed Gaussian model that can reasonably describe the characteristics of the degradation process, more accurate prediction results can be obtained. This will provide strong data support for subsequent equipment health management, especially valuable for high-reliability equipment maintenance management, and has broad prospects for practical engineering applications.

附图说明Description of drawings

图1为实施例中轴承的振动数据；Fig. 1 is the vibration data of bearing in the embodiment;

图2为实施例中剩余寿命预测的性能对比。Fig. 2 is the performance comparison of remaining life prediction in the embodiment.

具体实施方式detailed description

现结合附图对本发明的具体实施方式作进一步的说明。The specific embodiment of the present invention will be further described in conjunction with the accompanying drawings.

下面本例通过一组来自PRONOSTIA实验平台的实际轴承退化数据来阐述具体操作步骤以及验证方法的效果。In the following example, a set of actual bearing degradation data from the PRONOSTIA experimental platform is used to illustrate the specific operation steps and the effect of the verification method.

在该退化实验的数据采集中，每个采样时刻，实验者收集了2560个振动数据，并且采样时间间隔为10秒。在每个采样时刻，本例计算了2560个振动数据的均方根值作为每个采样时刻的特征值，从而为每个轴承形成了一个新的时间序列数据。均方根特征值的采样时间间隔为10秒。由于本发明的模型是受到自适应高斯-维纳过程模型的启发，故在此例中本例将比较两者的性能差异。In the data collection of the degradation experiment, the experimenter collected 2560 vibration data at each sampling moment, and the sampling time interval was 10 seconds. At each sampling moment, this example calculates the root mean square value of 2560 vibration data as the feature value of each sampling moment, thus forming a new time series data for each bearing. The sampling interval of the RMS eigenvalue is 10 seconds. Since the model of the present invention is inspired by the adaptive Gauss-Wiener process model, the difference in performance between the two will be compared in this example.

步骤1：建立刻画符合两阶段退化特性设备的性能退化模型Step 1: Establish a performance degradation model that describes equipment that conforms to the two-stage degradation characteristics

步骤1.1：将轴承退化模型表达如下：Step 1.1: Express the bearing degradation model as follows:

η_k＝η_k-1+ν_k η _k ＝η _k-1 + ν _k

δ_k＝η_k-1τ_k+αΒ(τ_k)δ _k ＝η _k-1 τ _k +αΒ(τ _k )

δ_k＝x_k-x_k-1 δ _k ＝x _k -x _k-1

上式中，φ(·)为标准高斯分布的概率密度函数，Φ(·)为标准高斯分布的累积分布函数；μ和σ分别为位置参数和尺度参数，ξ为一般参数，λ为形状参数；ν_k是系统白噪声，且ν_k～N(0,ε²)；α是扩散系数，且α>0，τ_k是采样时间间隔，且τ_k＝t_k-t_k-1，Β(τ_k)是标准布朗运动，且x_k表征第k个采样时刻设备的退化程度，也即是振动信号强度。；δ_k为相邻两个采样时刻的退化程度增量。In the above formula, φ( ) is the probability density function of the standard Gaussian distribution, Φ( ) is the cumulative distribution function of the standard Gaussian distribution; μ and σ are the position parameter and scale parameter respectively, ξ is the general parameter, and λ is the shape parameter ;ν _k is the white noise of the system, and ν _k ～N(0,ε ² ); α is the diffusion coefficient, and α>0, τ _k is the sampling time interval, and τ _k ＝t _k -t _k-1 , Β (τ _k ) is the standard Brownian motion, and x _k represents the degradation degree of the equipment at the kth sampling time, that is, the vibration signal strength. ; δ _k is the degradation degree increment of two adjacent sampling moments.

步骤1.2：监测系统在t＝{t₁,...,t_k}对它进行监测，监测到轴承退化状态数据，即设备退化程度为本例定义从产品投入使用到第k个采样时刻的历史退化增量为δ_1:k＝{δ₁,...,δ_k}，δ₁＝x₁。Step 1.2: The monitoring system monitors it at t={t ₁ ,...,t _k }, and monitors the data of bearing degradation status, that is, the degree of equipment degradation is In this example, the historical degradation increment from the product put into use to the kth sampling moment is defined as δ _1:k ={δ ₁ ,...,δ _k }, δ ₁ =x ₁ .

步骤2：采用迭代滤波算法估计退化的隐藏状态Step 2: Estimate the degraded hidden state using an iterative filtering algorithm

步骤2.1：机电设备退化速度，也即是模型的隐藏退化漂移系数，其初始状态满足封闭斜高斯分布，即进一步，设备的初始状态为(δ₁|η₀)～N(η₀τ₁,α²τ₁)Step 2.1: The degradation rate of electromechanical equipment, that is, the hidden degradation drift coefficient of the model, its initial state satisfies the closed oblique Gaussian distribution, namely Further, the initial state of the device is (δ ₁ |η ₀ )～N(η ₀ τ ₁ ,α ² τ ₁ )

本例首先随机选取了轴承#1-4，#2-6和#3-1作为训练数据。利用该训练数据，估计得到斜维纳过程模型和高斯-维纳过程模型的未知参数初始值，分别为μ0＝0.088，σ0＝0.155，λ0＝1.393，ξ0＝1.105，ε＝0.003，α＝0.009μ′0＝0.0015，σ′0＝0.1265，ε′＝0.0005，α′＝0.012。This example first randomly selects bearings #1-4, #2-6 and #3-1 as training data. Using the training data, the initial values of the unknown parameters of the oblique Wiener process model and the Gauss-Wiener process model are estimated to be μ0=0.088, σ0=0.155, λ0=1.393, ξ0=1.105, ε=0.003, α=0.009 μ'0=0.0015, σ'0=0.1265, ε'=0.0005, α'=0.012.

其中，in,

其中in

步骤3：在线估计模型参数Step 3: Estimate model parameters online

步骤3.1：根据采样得到的退化数据，构造对数似然函数：Step 3.1: According to the degradation data obtained by sampling, construct the logarithmic likelihood function:

步骤3.2：在得到新测量量，即获得退化程度，的条件概率密度函数后，将上式扩展为：Step 3.2: After obtaining the conditional probability density function of the new measured quantity, that is, the degree of degradation, expand the above formula to:

步骤3.3：采用数值方法搜索获得最大化上式的参数，针对轴承#1-3，得到两个模型的参数估计结果如下表。Step 3.3: Use the numerical method to search to obtain the parameters that maximize the above formula. For bearing #1-3, the parameter estimation results of the two models are obtained in the following table.

表1斜维纳过程模型和高斯-维纳过程模型中未知参数的估计Table 1 Estimation of unknown parameters in the oblique Wiener process model and the Gauss-Wiener process model

斜维纳过程模型Slope Wiener process model 高斯-维纳过程模型Gauss-Wiener process model αalpha 3.91×10^-2 3.91×10 ^-2 7.275×10^-2 7.275×10 ^-2 εε 8.30×10^-4 8.30×10 ^-4 3.207×10^-4 3.207×10 ^-4

步骤4：获得设备剩余寿命的分布表达式Step 4: Obtain the distribution expression for the remaining lifetime of the equipment

步骤4.1：采用首次通过时间作为连接预测退化程度与剩余寿命预测的纽带，即剩余寿命随机变量定义为L＝inf{l:x(l+t_k)>ω|X_1:k}，其中斜体的l是剩余寿命随机变量的实现，ω是预先定义的阈值，X_1:k是历史测量量。在实验中，原始振动信号的失效阈值为20g，其中，g表示重力加速度。本例定义均方根特征值的阈值为包含首次超过20g原始振动信号的采样时刻的均方根特征值。以轴承#1-3为例，在第2342个采样时刻，原始振动数据首次超过20g，因此，其均方根特征值的阈值即为第2342个均方根特征值，即4，7145。Step 4.1: Use the time of first pass as the link between the predicted degradation degree and the remaining life prediction, that is, the remaining life random variable is defined as L=inf{l:x(l+t _k )>ω|X _1:k }, where italics where l is the realization of the remaining life random variable, ω is the pre-defined threshold, and X _1:k is the historical measurement quantity. In the experiment, the failure threshold of the original vibration signal is 20g, where g represents the acceleration of gravity. In this example, the threshold of the root mean square eigenvalue is defined as the root mean square eigenvalue at the sampling moment of the original vibration signal exceeding 20 g for the first time. Taking bearing #1-3 as an example, at the 2342nd sampling time, the original vibration data exceeds 20g for the first time, therefore, the threshold of its RMS eigenvalue is the 2342th RMS eigenvalue, which is 4,7145.

其中， in,

图1给出了轴承的振动数据。图2给出了两种模型从第1800个采样时刻到第2300个采样时刻，每隔100个采样时刻的剩余寿命预测的性能对比。显然，真的剩余寿命值都被两个模型的剩余寿命分布所覆盖。并且，随着测量数据的增多，可以观察到两个模型一些共同的现象：1.两个模型的剩余寿命分布都往更少的剩余寿命方向移动；2.两个模型的剩余寿命分布的峰值逐渐变高；3.剩余寿命预测的不确定性逐渐变小。这些结果都验证了模型的有效性，此外，斜维纳过程模型得到的剩余寿命分布比高斯-维纳过程模型紧凑，这表明本发明的斜维纳过程模型能为后续的管理决策的制定提供更加可靠的信息。Figure 1 presents the vibration data of the bearing. Figure 2 shows the performance comparison of the remaining life prediction of the two models at every 100th sampling time from the 1800th sampling time to the 2300th sampling time. Clearly, the true remaining life values are covered by the remaining life distributions of both models. Moreover, with the increase of measured data, some common phenomena of the two models can be observed: 1. The remaining life distributions of the two models move towards less remaining life; 2. The peak value of the remaining life distribution of the two models 3. The uncertainty of remaining life prediction gradually decreases. These results have verified the effectiveness of the model. In addition, the residual life distribution obtained by the oblique Wiener process model is more compact than the Gauss-Wiener process model, which shows that the oblique Wiener process model of the present invention can provide information for subsequent management decisions. more reliable information.

Claims

1. An online prediction method for the residual life of electromechanical equipment under the condition of two-stage degradation is characterized in that: the actual degradation of the equipment is divided into two stages of normal degradation and accelerated degradation, the performance degradation process conforms to a self-adaptive oblique wiener process model, a two-stage parameter estimation algorithm is adopted for the parameters of the model, an iterative filtering algorithm is adopted to obtain the degradation state in real time, and after the degradation state estimation and the parameter estimation are finished, the residual life of the equipment is predicted by using the updated degradation drift state, the estimated parameters and the measured quantity; the method comprises the following specific steps:

step 1: establishing a performance degradation model describing equipment conforming to the two-stage degradation characteristics;

step 2: estimating a degraded hidden state by adopting an iterative filtering algorithm;

and step 3: estimating performance degradation model parameters on line;

and 4, step 4: and obtaining a probability distribution expression of the residual service life of the equipment.

2. The method for predicting the residual life of the electromechanical device under the condition of two-stage degradation according to claim 1, wherein: the specific steps of establishing a performance degradation model characterizing the equipment conforming to the two-stage degradation characteristics in the step 1 are as follows:

step 1.1: a device degradation model satisfying the two-stage degradation characteristic is expressed as follows:

η_k＝η_k-1+ν_k

_k＝η_k-1τ_k+αΒ(τ_k)

_k＝x_k-x_k-1

wherein, t_kAt the kth sampling instant, η_kIs t_kIs used for characterizing the degradation speed and satisfies a closed oblique gaussian distribution, and the probability density function f (η) is:

f (η) = φ (\frac{η - μ}{σ}) Φ [λ (\frac{η - μ}{σ}) + ξ] / [σ Φ (\frac{ξ}{\sqrt{1 + λ^{2}}})]

in the above formula, phi (DEG) is a probability density function of the standard Gaussian distribution, phi (DEG) is a cumulative distribution function of the standard Gaussian distribution, mu and sigma are a position parameter and a scale parameter respectively, ξ is a general parameter, lambda is a shape parameter, and v_kIs system white noise, and v_k～N(0,²) α is the diffusion coefficient, and α>0，τ_kIs the sampling time interval, and_k＝t_k-t_k-1，Β(τ_k) Is a standard brownian motion, andx_kcharacterizing the degradation degree of the device at the kth sampling moment;_kthe degradation degree increment of two adjacent sampling moments is obtained;

step 1.2: once the product starts to run, the monitoring system will start to run at t ═ { t ═ t₁,...,t_kIt is monitored for equipment state data, i.e. equipment degradation degree is Defining the historical degradation increment from the product to the kth sampling time as_1:k＝{₁,...,_k}，₁＝x₁。

3. The online prediction method of the remaining life of the electromechanical device under the condition of two-stage degradation according to claim 1, characterized in that: the specific steps of "estimating the degraded hidden state by using the iterative filtering algorithm" described in step 2 are as follows:

step 2.1: the degradation speed of the electromechanical equipment, namely the hidden degradation drift coefficient of the oblique wiener process model, and the initial state of the model satisfies the closed oblique Gaussian distribution, namelyCSN is closed oblique Gaussian distribution, and unknown parameters of an initial degradation drift state are obtained by fitting initial degradation data of similar products; further, the initial state of the apparatus is (₁|η₀)～N(η₀τ₁,α²τ₁) The unknown parameters are obtained by a maximum likelihood estimation method through historical degradation data and an initial degradation drift state obtained through estimation;

step 2.2: at the kth sampling instant, there is a degenerate hidden state satisfying the distribution

(η_{k - 1} | δ_{1 : k - 1}) ~ C S N (μ_{k - 1}, σ_{k - 1}^{2}, λ_{k - 1}, ξ_{k - 1})

With a degree of deterioration (_k|η_k-1,_1:k-1)～N(η_k-1τ_k,α²τ_k)。

Step 2.3: according to the obtained new measurement quantity, the degradation hidden state of the equipment satisfies a closed oblique Gaussian distribution

(η_{k - 1} | δ_{1 : k}) ~ C S N ({\hat{μ}}_{k - 1}, {\hat{σ}}_{k - 1}^{2}, {\hat{λ}}_{k - 1}, {\hat{ξ}}_{k - 1})

Wherein,

step 2.4: the posterior distribution of degenerate hidden states is obeyed according to the result of step 2.3

(η_{k} | δ_{1 : k}) ~ C S N (μ_{k}, σ_{k}^{2}, λ_{k}, ξ_{k})

Wherein

According to the four steps, the relation between the degradation degree prediction and the historical degradation data is established, and the hidden state can be updated in an iterative and real-time manner.

4. The method for predicting the residual life of the electromechanical device under the condition of two-stage degradation according to claim 1, wherein: the specific steps of the online estimation of the performance degradation model parameters in the step 3 are as follows:

step 3.1: according to the degradation data obtained by sampling, a log-likelihood function is constructed

\ln f_{Δ_{2 : k} | Δ_{1}} (δ_{2 : k} | δ_{1}) = Σ_{i = 2}^{k} {lnf}_{Δ_{i} | Δ_{1 : i - 1}} (δ_{i} | δ_{1 : i - 1})

Step 3.2: after obtaining a new measurement, i.e. obtaining a conditional probability density function of the degree of degradation, the above equation is expanded to:

\begin{matrix} \ln f_{Δ_{2 : k} | Δ_{1}} (δ_{2 : k} | δ_{1}) = Σ_{i = 2}^{k} {- \frac{1}{2} \ln [2 π (τ_{i}^{2} σ_{i - 2}^{2} + τ_{i}^{2} ϵ^{2} + α^{2} τ_{i})] - \frac{{(δ_{i} - τ_{i} μ_{i - 2})}^{2}}{2 (τ_{i} σ_{i - 2}^{2} + τ_{i}^{2} ϵ^{2} + α^{2} τ_{i})}} \\ + Σ_{i = 2}^{k} \ln Φ {\frac{λ_{i - 2} σ_{i - 2} (δ_{i} - τ_{i} μ_{i - 2}) + ξ_{i - 2} (τ_{i} σ_{i - 2}^{2} + τ_{i}^{2} ϵ^{2} + α^{2})}{\sqrt{(τ_{i} σ_{i - 2}^{2} + τ_{i}^{2} ϵ^{2} + α^{2}) [τ_{i} σ_{i - 2}^{2} + (1 + λ_{i - 2}^{2}) (τ_{i} ϵ^{2} + α^{2})]}}} \\ - Σ_{i = 2}^{k} \ln Φ (\frac{ξ_{i - 2}}{\sqrt{1 + λ_{i - 2}^{2}}}) \end{matrix}

step 3.3: maximization by searching using numerical methodsThe parameter (c) of (c).

5. The online prediction method of the remaining life of the electromechanical device under the condition of two-stage degradation according to claim 1, characterized in that: the specific steps of obtaining the distribution expression of the remaining life of the equipment in the step 4 are as follows:

step 4.1: the first-pass time is used as a link for connecting the prediction of the degradation degree and the prediction of the residual life, namely, the random variable of the residual life is defined as L ═ inf { L: x (L + t)_k)>ω|X_1:kWhere l is the implementation of a random variable for remaining life, ω is a predefined threshold, X_1:kIs a historical measurement.

Step 4.2: the remaining lifetime distribution probability density function at the kth sampling instant is,

f_{L | X_{1 : k}} (l | X_{1 : k}) = \frac{ω - x_{k}}{\sqrt{2 {πl}^{3} ({lσ}_{k}^{2} + α^{2})}} \exp [- \frac{{(ω - x_{k} - μ_{k} l)}^{2}}{2 l ({lσ}_{k}^{2} + α^{2})}] \frac{Φ (ζ / \sqrt{1 + γ^{2}})}{Φ (ξ_{k} / \sqrt{1 + λ_{k}^{2}})}

wherein,

therefore, a probability density function accurate expression of the online prediction of the residual life of the equipment is obtained and is used for online prediction of the residual life of the electromechanical equipment.