CN115289100B - Hydraulic cylinder degradation trend evaluation method - Google Patents

Hydraulic cylinder degradation trend evaluation method Download PDF

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CN115289100B
CN115289100B CN202210901662.0A CN202210901662A CN115289100B CN 115289100 B CN115289100 B CN 115289100B CN 202210901662 A CN202210901662 A CN 202210901662A CN 115289100 B CN115289100 B CN 115289100B
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宋勇
蔺凤琴
荆丰伟
郭金
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Abstract

The invention provides a hydraulic cylinder degradation trend evaluation method, and belongs to the technical field of hot rolled strip steel automatic control. The method comprises the following steps: acquiring piston displacement signals of the hydraulic cylinder in different working time periods in real time; determining an LS algorithm format of a hydraulic cylinder motion model based on the acquired piston displacement signals; estimating the Stribeck parameters based on the LS algorithm format of the determined hydraulic cylinder motion model to obtain the stable Stribeck parameters; comparing the obtained stable Stribeck parameter with the Stribeck parameter in the initial state, establishing a degradation index of the working state of the hydraulic cylinder, drawing a degradation curve of the working state of the hydraulic cylinder, determining the degradation trend of the hydraulic cylinder according to the drawn degradation curve of the working state of the hydraulic cylinder, and determining the current degradation degree of the hydraulic cylinder according to the degradation index at the current moment. By adopting the method and the device, the degradation degree of the hydraulic cylinder can be accurately evaluated.

Description

一种液压缸劣化趋势评价方法A method for evaluating the degradation trend of hydraulic cylinders

技术领域Technical Field

本发明涉及热轧带钢自动化控制技术领域，特别是指一种液压缸劣化趋势评价方法。The invention relates to the technical field of hot-rolled strip steel automation control, in particular to a method for evaluating a hydraulic cylinder degradation trend.

背景技术Background Art

大量工业现场数据表明，液压缸在工作时总会受到一些扰动的影响，导致力平衡状态受到破坏，产生不同幅度的颤振，严重时甚至会造成设备损坏和工厂停产。因此，对液压缸系统进行故障诊断、寿命预测、日常监测和维护等手段都应该重点考虑。现阶段，针对液压缸故障诊断与寿命预测的研究已经十分深入，石家庄铁道大学马怀祥教授团队主要研究盾构机和挖掘机两种典型工程机械液压系统的工作状态，以压力、流量、振动、温度和油液信号为检测量，应用Labview软件开发工程机械液压系统故障诊断与健康评估系统，对液压系统的故障诊断与健康预测的效果提升显著。对于液压系统的日常监测和维护方面，通过引入摩擦模型，分析模型的参数变化来表征液压缸的劣化趋势。常用的摩擦模型包括：库伦模型、库伦+黏性摩擦模型、Stribeck摩擦模型、Karnopp模型以及LuGre模型等；其中，Stribeck摩擦模型的使用率高，应用范围十分广泛。文章(摩擦和反弹的机械系统控制)研究了基于永磁同步电机低速运行时粘滑现象下的控制器设计问题，利用Stribeck摩擦模型对非线性摩擦力矩建模，通过设计补偿控制器解决了系统稳态误差和低速爬行问题。A large amount of industrial field data shows that hydraulic cylinders are always affected by some disturbances when working, which leads to the destruction of the force balance state and the generation of vibrations of different amplitudes. In severe cases, it may even cause equipment damage and factory shutdown. Therefore, the fault diagnosis, life prediction, daily monitoring and maintenance of hydraulic cylinder systems should be given priority consideration. At present, the research on hydraulic cylinder fault diagnosis and life prediction has been very in-depth. The team of Professor Ma Huaixiang of Shijiazhuang Tiedao University mainly studies the working conditions of two typical engineering machinery hydraulic systems, namely shield machines and excavators. With pressure, flow, vibration, temperature and oil signals as detection quantities, the team uses Labview software to develop a fault diagnosis and health assessment system for engineering machinery hydraulic systems, which significantly improves the effect of fault diagnosis and health prediction of hydraulic systems. For the daily monitoring and maintenance of hydraulic systems, the friction model is introduced to analyze the parameter changes of the model to characterize the degradation trend of the hydraulic cylinder. Commonly used friction models include: Coulomb model, Coulomb + viscous friction model, Stribeck friction model, Karnopp model and LuGre model, etc. Among them, the Stribeck friction model has a high usage rate and a wide range of applications. The article (Control of Mechanical Systems with Friction and Rebound) studies the controller design problem based on the stick-slip phenomenon when a permanent magnet synchronous motor runs at low speed. The nonlinear friction torque is modeled using the Stribeck friction model, and the system steady-state error and low-speed creep problems are solved by designing a compensation controller.

目前，大多数研究都是从如何影响系统稳定性能的角度去分析Stribeck摩擦模型，利用Stribeck摩擦模型研究液压缸劣化问题的文献鲜有。At present, most studies analyze the Stribeck friction model from the perspective of how it affects the stability performance of the system, and there are few literatures that use the Stribeck friction model to study the deterioration problem of hydraulic cylinders.

发明内容Summary of the invention

本发明实施例提供了液压缸劣化趋势评价方法，能够对液压缸的劣化程度进行精准评价。所述方法包括：The embodiment of the present invention provides a method for evaluating the deterioration trend of a hydraulic cylinder, which can accurately evaluate the deterioration degree of the hydraulic cylinder. The method comprises:

实时采集液压缸在不同工作时间段的活塞位移信号；Real-time collection of piston displacement signals of hydraulic cylinders in different working time periods;

基于采集的活塞位移信号，确定液压缸运动模型的LS算法格式；其中，LS表示最小二乘；Based on the collected piston displacement signal, the LS algorithm format of the hydraulic cylinder motion model is determined; where LS stands for least squares;

基于确定的液压缸运动模型的LS算法格式，对Stribeck参数进行估计，得到收敛至稳定的Stribeck参数；Based on the LS algorithm format of the determined hydraulic cylinder motion model, the Stribeck parameters are estimated and the Stribeck parameters that converge to stability are obtained;

将得到的稳定的Stribeck参数与初始状态下的Stribeck参数进行比较，建立液压缸工作状态劣化指标，绘制液压缸工作状态劣化曲线，根据绘制的液压缸工作状态劣化曲线，确定液压缸劣化趋势，并根据当前时刻的劣化指标确定液压缸目前的劣化程度。The obtained stable Stribeck parameters are compared with the Stribeck parameters in the initial state, the hydraulic cylinder working state degradation index is established, and the hydraulic cylinder working state degradation curve is drawn. According to the drawn hydraulic cylinder working state degradation curve, the hydraulic cylinder degradation trend is determined, and the current degradation degree of the hydraulic cylinder is determined according to the degradation index at the current moment.

进一步地，确定的液压缸运动模型的LS算法格式表示为：Furthermore, the LS algorithm format of the determined hydraulic cylinder motion model is expressed as:

y(t)＝φT(t)θ+d(t)y(t)＝φ T (t)θ+d(t)

Figure BDA0003771089560000027
Figure BDA0003771089560000027

Figure BDA0003771089560000021
Figure BDA0003771089560000021

θ＝[m K fc fv fs]T θ＝[m K f c f v f s ] T

其中，y(t)为LS算法输出，φ(t)为LS算法输入，θ为待估计的参数，d(t)为测量噪声，上标T表示矩阵转置，p1、p2分别为无杆腔压强、有杆腔压强，A1、A2分别为无杆腔有效面积、有杆腔有效面积，p1A1和p2A2分别代表无杆腔和有杆腔的压力，FL表示外部轧制力，c表示粘性阻尼系数，x、

Figure BDA0003771089560000022
分别表示活塞的位移、速度、加速度，sgn(·)为符号函数，m为活塞及负载的折合质量，K表示液压缸系统的等效刚度，fc为库仑摩擦参数，fv为黏性摩擦系数，fs为Stribeck摩擦参数。Where y(t) is the output of the LS algorithm, φ(t) is the input of the LS algorithm, θ is the parameter to be estimated, d(t) is the measurement noise, the superscript T represents the matrix transpose, p 1 and p 2 are the pressure of the rodless cavity and the pressure of the rod cavity, A 1 and A 2 are the effective area of the rodless cavity and the effective area of the rod cavity, p 1 A 1 and p 2 A 2 represent the pressure of the rodless cavity and the rod cavity, F L represents the external rolling force, c represents the viscous damping coefficient, x,
Figure BDA0003771089560000022
represents the displacement, velocity and acceleration of the piston respectively, sgn(·) is the sign function, m is the reduced mass of the piston and the load, K represents the equivalent stiffness of the hydraulic cylinder system, fc is the Coulomb friction parameter, fv is the viscous friction coefficient, and fs is the Stribeck friction parameter.

进一步地，所述基于确定的液压缸运动模型的LS算法格式，对Stribeck参数进行估计，得到收敛至稳定的Stribeck参数包括：Furthermore, the LS algorithm format based on the determined hydraulic cylinder motion model estimates the Stribeck parameters, and the Stribeck parameters that converge to stability include:

A1，在初始采样时间段的LS算法参数估计过程中，给定参数初值θ0、增益矩阵初值P0、位移初值x0和速度初值

Figure BDA0003771089560000026
A1, in the LS algorithm parameter estimation process of the initial sampling time period, given the initial parameter value θ 0 , the initial gain matrix value P 0 , the initial displacement value x 0 and the initial velocity value
Figure BDA0003771089560000026

A2，输入活塞位移信号x1，采用差分算法计算出活塞的速度信号和加速度信号，构建出液压缸运动模型的LS算法格式的输出yk和输入φk，依次更新计算Kk、

Figure BDA0003771089560000023
Pk的值；A2, input piston displacement signal x1 , use differential algorithm to calculate piston velocity signal and acceleration signal, construct output yk and input φk of hydraulic cylinder motion model in LS algorithm format, and update and calculate Kk ,
Figure BDA0003771089560000023
The value of P k ;

A3，更新计算Kk、

Figure BDA0003771089560000024
Pk的值后，k＝k+1，返回步骤A2，输入下一时刻活塞位移信号x2，重新计算Kk、
Figure BDA0003771089560000025
Pk的值，不断循环，直至得到对应的采样时间段收敛至稳定的Stribeck参数，并且每一次采样时间段的参数估计结果作为下一次参数估计的初值加入计算；其中，Stribeck参数包括：fc、fv和fs，下一次指下一采样时间段。A3, update calculation K k ,
Figure BDA0003771089560000024
After the value of P k is obtained, k＝k+1, and the process returns to step A2, inputs the piston displacement signal x 2 at the next moment, and recalculates K k ,
Figure BDA0003771089560000025
The value of P k is continuously cycled until the corresponding sampling time period converges to a stable Stribeck parameter, and the parameter estimation result of each sampling time period is added to the calculation as the initial value of the next parameter estimation; wherein the Stribeck parameters include: f c , f v and f s , and the next time refers to the next sampling time period.

进一步地，所述采用差分算法计算出活塞的速度信号和加速度信号包括：Furthermore, the method of calculating the speed signal and acceleration signal of the piston by using a differential algorithm includes:

通过公式

Figure BDA0003771089560000031
求解活塞的速度信号vk；其中，△为差分间隔，xk为第k时刻活塞的位移信号；By formula
Figure BDA0003771089560000031
Solve for the piston velocity signal v k ; where △ is the differential interval, and x k is the piston displacement signal at the kth moment;

通过公式

Figure BDA0003771089560000032
求解活塞的加速度信号ak；其中，
Figure BDA0003771089560000033
为第k时刻活塞的加速度信号。By formula
Figure BDA0003771089560000032
Solve for the piston acceleration signal ak ; where,
Figure BDA0003771089560000033
is the acceleration signal of the piston at the kth moment.

进一步地，第k时刻Kk、

Figure BDA0003771089560000034
Pk的更新表达式为：Furthermore, at the kth moment K k ,
Figure BDA0003771089560000034
The update expression of P k is:

Figure BDA0003771089560000035
Figure BDA0003771089560000035

Figure BDA0003771089560000036
Figure BDA0003771089560000036

Figure BDA0003771089560000037
Figure BDA0003771089560000037

其中，Kk和Pk都表示第k时刻的增益矩阵；

Figure BDA0003771089560000038
表示第k时刻的参数估计值；Pk-1表示第k-1时刻的增益矩阵；φk表示第k时刻的LS算法输入；
Figure BDA0003771089560000039
表示第k-1时刻的参数估计值；yk表示第k时刻的LS算法输出。Among them, K k and P k both represent the gain matrix at the kth moment;
Figure BDA0003771089560000038
represents the parameter estimation value at the kth moment; P k-1 represents the gain matrix at the k-1th moment; φ k represents the LS algorithm input at the kth moment;
Figure BDA0003771089560000039
represents the parameter estimate at the k-1th moment; y k represents the LS algorithm output at the kth moment.

进一步地，参数估计循环终止条件为：Furthermore, the parameter estimation loop termination condition is:

Figure BDA00037710895600000310
Figure BDA00037710895600000310

其中，

Figure BDA00037710895600000311
分别为第n次参数估计得到的第k时刻、k-1时刻的参数估计值，ε为停止条件参数。in,
Figure BDA00037710895600000311
are the parameter estimates at the kth moment and k-1th moment respectively obtained by the nth parameter estimation, and ε is the stopping condition parameter.

进一步地，所述将得到的稳定的Stribeck参数与初始状态下的Stribeck参数进行比较，建立液压缸工作状态劣化指标，绘制液压缸工作状态劣化曲线，根据绘制的液压缸工作状态劣化曲线，确定液压缸目前的劣化程度包括：Further, the obtained stable Stribeck parameters are compared with the Stribeck parameters in the initial state, a hydraulic cylinder working state degradation index is established, a hydraulic cylinder working state degradation curve is drawn, and according to the drawn hydraulic cylinder working state degradation curve, the current degradation degree of the hydraulic cylinder is determined, including:

将每次得到的稳定的Stribeck参数与初始状态下的Stribeck参数进行比较，建立液压缸工作状态劣化指标Jn：The stable Stribeck parameters obtained each time are compared with the Stribeck parameters in the initial state, and the hydraulic cylinder working state degradation index J n is established:

Figure BDA00037710895600000312
Figure BDA00037710895600000312

其中，

Figure BDA00037710895600000313
表示活塞工作时的速度上限；v表示活塞的速度信号；
Figure BDA00037710895600000314
分别表示第n次参数估计得到的库仑摩擦参数、黏性摩擦系数、Stribeck摩擦参数，
Figure BDA00037710895600000315
分别表示液压缸初始状态下的库仑摩擦参数、黏性摩擦系数、Stribeck摩擦参数，函数Fd(·)为线性化后的Stribeck摩擦模型；in,
Figure BDA00037710895600000313
Indicates the upper speed limit of the piston when it is working; v indicates the speed signal of the piston;
Figure BDA00037710895600000314
They represent the Coulomb friction parameter, viscous friction coefficient, and Stribeck friction parameter obtained by the nth parameter estimation, respectively.
Figure BDA00037710895600000315
They represent the Coulomb friction parameter, viscous friction coefficient, and Stribeck friction parameter in the initial state of the hydraulic cylinder, respectively. Function F d (·) is the linearized Stribeck friction model.

以

Figure BDA0003771089560000041
为横坐标，Jn为纵坐标，绘制液压缸工作状态劣化曲线；其中，Ti表示第i次估计参数与第i+1次估计参数之间的时间间隔，τn表示第n次参数估计所用的活塞位移信号对应的采样时间段；by
Figure BDA0003771089560000041
As the horizontal coordinate, J n as the vertical coordinate, the hydraulic cylinder working state degradation curve is drawn; wherein Ti represents the time interval between the i-th estimated parameter and the i+1-th estimated parameter, and τ n represents the sampling time period corresponding to the piston displacement signal used for the n-th parameter estimation;

根据绘制的液压缸工作状态劣化曲线，确定液压缸劣化趋势，并根据当前时刻的劣化指标确定液压缸目前的劣化程度。According to the drawn hydraulic cylinder working state degradation curve, the hydraulic cylinder degradation trend is determined, and the current degradation degree of the hydraulic cylinder is determined according to the degradation index at the current moment.

进一步地，函数Fd(·)表示为：Furthermore, the function F d (·) is expressed as:

Figure BDA0003771089560000042
Figure BDA0003771089560000042

其中，fc为库仑摩擦参数，fv为黏性摩擦系数，fs为Stribeck摩擦参数，sgn(·)为符号函数，

Figure BDA0003771089560000043
表示活塞的速度。Where, f c is the Coulomb friction parameter, f v is the viscous friction coefficient, f s is the Stribeck friction parameter, sgn(·) is the sign function,
Figure BDA0003771089560000043
Indicates the speed of the piston.

本发明实施例提供的技术方案带来的有益效果至少包括：The beneficial effects brought about by the technical solution provided by the embodiment of the present invention include at least:

本发明实施例中，实时采集液压缸在不同工作时间段的活塞位移信号；基于采集的活塞位移信号，确定液压缸运动模型的LS算法格式；基于确定的液压缸运动模型的LS算法格式，对Stribeck参数进行估计，得到收敛至稳定的Stribeck参数；将得到的稳定的Stribeck参数与初始状态下的Stribeck参数进行比较，建立液压缸工作状态劣化指标，绘制液压缸工作状态劣化曲线，根据绘制的液压缸工作状态劣化曲线，确定液压缸劣化趋势，并根据当前时刻的劣化指标确定液压缸目前的劣化程度。这样，通过建立的基于Stribeck曲线的液压缸劣化趋势评价方法，能够对液压缸的劣化程度进行精准评价，辅助液压系统的日常监测和维护，对液压系统的性能监控与评估以及提升生产过程的工作效率有着重要意义，从而解决现有技术无法对液压缸劣化程度进行评价的问题。In the embodiment of the present invention, the piston displacement signal of the hydraulic cylinder in different working time periods is collected in real time; based on the collected piston displacement signal, the LS algorithm format of the hydraulic cylinder motion model is determined; based on the determined LS algorithm format of the hydraulic cylinder motion model, the Stribeck parameter is estimated to obtain the Stribeck parameter that converges to stability; the obtained stable Stribeck parameter is compared with the Stribeck parameter in the initial state, the hydraulic cylinder working state degradation index is established, the hydraulic cylinder working state degradation curve is drawn, the hydraulic cylinder degradation trend is determined according to the drawn hydraulic cylinder working state degradation curve, and the current degradation degree of the hydraulic cylinder is determined according to the degradation index at the current moment. In this way, by establishing a hydraulic cylinder degradation trend evaluation method based on the Stribeck curve, the degradation degree of the hydraulic cylinder can be accurately evaluated, which assists the daily monitoring and maintenance of the hydraulic system, and has important significance for the performance monitoring and evaluation of the hydraulic system and improving the work efficiency of the production process, thereby solving the problem that the existing technology cannot evaluate the degradation degree of the hydraulic cylinder.

附图说明BRIEF DESCRIPTION OF THE DRAWINGS

为了更清楚地说明本发明实施例中的技术方案，下面将对实施例描述中所需要使用的附图作简单地介绍，显而易见地，下面描述中的附图仅仅是本发明的一些实施例，对于本领域普通技术人员来讲，在不付出创造性劳动的前提下，还可以根据这些附图获得其他的附图。In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

图1为本发明实施例提供的液压缸劣化趋势评价方法的流程示意图；FIG1 is a schematic flow chart of a method for evaluating a hydraulic cylinder degradation trend according to an embodiment of the present invention;

图2(a)-(f)为本发明实施例提供的第1-6次参数估计所用的活塞位移信号以及利用差分算法求解得到的速度、加速度信号曲线示意图；2(a)-(f) are schematic diagrams of piston displacement signals used for the 1st to 6th parameter estimations provided by an embodiment of the present invention and velocity and acceleration signal curves obtained by using a differential algorithm;

图3(a)-(f)为本发明实施例提供的第1-6次参数估计得到的Stribeck参数估计值和真值曲线示意图；3(a)-(f) are schematic diagrams of Stribeck parameter estimation values and true value curves obtained by the 1st to 6th parameter estimations provided by an embodiment of the present invention;

图4为本发明实施例提供的不同采样时间段下Stribeck摩擦模型曲线示意图；FIG4 is a schematic diagram of a Stribeck friction model curve under different sampling time periods provided by an embodiment of the present invention;

图5为本发明实施例提供的液压缸的劣化趋势折线示意图。FIG. 5 is a schematic diagram of a degradation trend line diagram of a hydraulic cylinder provided in an embodiment of the present invention.

具体实施方式DETAILED DESCRIPTION

为使本发明的目的、技术方案和优点更加清楚，下面将结合附图对本发明实施方式作进一步地详细描述。In order to make the objectives, technical solutions and advantages of the present invention more clear, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

如图1所示，本发明实施例提供了一种液压缸劣化趋势评价方法，包括：As shown in FIG1 , an embodiment of the present invention provides a method for evaluating a hydraulic cylinder degradation trend, comprising:

S101，实时采集液压缸在不同工作时间段的活塞位移信号；S101, real-time acquisition of piston displacement signals of the hydraulic cylinder in different working time periods;

S102，基于采集的活塞位移信号，确定液压缸运动模型的LS(Least Squares，最小二乘)算法格式；其中，LS表示最小二乘；S102, based on the collected piston displacement signal, determining the LS (Least Squares) algorithm format of the hydraulic cylinder motion model; wherein LS represents least squares;

本实施例中，确定的液压缸运动模型的LS算法格式表示为：In this embodiment, the LS algorithm format of the determined hydraulic cylinder motion model is expressed as:

y(t)＝φT(t)θ+d(t)y(t)＝φ T (t)θ+d(t)

Figure BDA0003771089560000051
Figure BDA0003771089560000051

Figure BDA0003771089560000052
Figure BDA0003771089560000052

θ＝[m K fc fv fs]T θ＝[m K f c f v f s ] T

其中，y(t)为LS算法输出，φ(t)为LS算法输入，θ为待估计的参数，d(t)为测量噪声，上标T表示矩阵转置，p1、p2分别为无杆腔压强、有杆腔压强，A1、A2分别为无杆腔有效面积、有杆腔有效面积，p1A1和p2A2分别代表无杆腔和有杆腔的压力，FL表示外部轧制力，c表示粘性阻尼系数，x、

Figure BDA0003771089560000053
分别表示活塞的位移、速度、加速度，sgn(·)为符号函数，m为活塞及负载的折合质量，K表示液压缸系统的等效刚度，fc为库仑摩擦参数，fv为黏性摩擦系数，fs为Stribeck摩擦参数。Where y(t) is the output of the LS algorithm, φ(t) is the input of the LS algorithm, θ is the parameter to be estimated, d(t) is the measurement noise, the superscript T represents the matrix transpose, p 1 and p 2 are the pressure of the rodless cavity and the pressure of the rod cavity, A 1 and A 2 are the effective area of the rodless cavity and the effective area of the rod cavity, p 1 A 1 and p 2 A 2 represent the pressure of the rodless cavity and the rod cavity, F L represents the external rolling force, c represents the viscous damping coefficient, x,
Figure BDA0003771089560000053
represents the displacement, velocity and acceleration of the piston respectively, sgn(·) is the sign function, m is the reduced mass of the piston and the load, K represents the equivalent stiffness of the hydraulic cylinder system, fc is the Coulomb friction parameter, fv is the viscous friction coefficient, and fs is the Stribeck friction parameter.

本实施例中，d(t)为测量噪声，假设其服从0均值的高斯分布；根据公式“压力＝压强×表面积”可知，p1A1和p2A2分别代表无杆腔和有杆腔的压力，两腔的压力随着活塞位移变化而变化，可通过压力传感器测量；外部轧制力FL可根据工况的不同自行设计；粘性阻尼系数c在实际系统中被视为已知常数，因此粘性力

Figure BDA0003771089560000054
已知。In this embodiment, d(t) is the measurement noise, which is assumed to obey a Gaussian distribution with a mean of 0. According to the formula “pressure = pressure × surface area”, p 1 A 1 and p 2 A 2 represent the pressure of the rodless chamber and the rod chamber, respectively. The pressures of the two chambers change with the displacement of the piston and can be measured by a pressure sensor. The external rolling force F L can be designed according to different working conditions. The viscous damping coefficient c is regarded as a known constant in the actual system, so the viscous force
Figure BDA0003771089560000054
Known.

本实施例中，由活塞位移求导得到活塞速度、无杆腔和有杆腔的压力、外部轧制力、粘性力组成LS算法输出；由x、

Figure BDA00037710895600000614
组成回归向量，即：LS算法输入。In this embodiment, the piston speed, the pressure of the rodless cavity and the rod cavity, the external rolling force, and the viscous force are obtained by derivation of the piston displacement to form the LS algorithm output; x,
Figure BDA00037710895600000614
Constitute the regression vector, that is, the LS algorithm input.

S103，基于确定的液压缸运动模型的LS算法格式，对Stribeck参数进行估计，得到收敛至稳定的Stribeck(斯特里贝克)参数；具体可以包括以下步骤：S103, based on the determined LS algorithm format of the hydraulic cylinder motion model, estimating the Stribeck parameters to obtain the Stribeck parameters that converge to stability; specifically, the following steps may be included:

A1，在初始采样时间段的LS算法参数估计过程中，给定参数初值θ0、增益矩阵初值P0、位移初值x0和速度初值

Figure BDA00037710895600000615
A1, in the LS algorithm parameter estimation process of the initial sampling time period, given the initial parameter value θ 0 , the initial gain matrix value P 0 , the initial displacement value x 0 and the initial velocity value
Figure BDA00037710895600000615

A2，输入活塞位移信号x1，采用差分算法计算出活塞的速度信号和加速度信号，构建出液压缸运动模型的LS算法格式的输出yk和输入φk，依次更新计算Kk、

Figure BDA0003771089560000061
Pk的值；A2, input piston displacement signal x1 , use differential algorithm to calculate piston velocity signal and acceleration signal, construct output yk and input φk of hydraulic cylinder motion model in LS algorithm format, and update and calculate Kk ,
Figure BDA0003771089560000061
The value of P k ;

本实施例中，采用差分算法计算出活塞的速度信号和加速度信号，具体可以包括以下步骤：In this embodiment, a differential algorithm is used to calculate the speed signal and acceleration signal of the piston, which may specifically include the following steps:

通过公式

Figure BDA0003771089560000062
求解活塞的速度信号vk；其中，△为差分间隔，xk为第k时刻活塞的位移信号；By formula
Figure BDA0003771089560000062
Solve for the piston velocity signal v k ; where △ is the differential interval, and x k is the piston displacement signal at the kth moment;

通过公式

Figure BDA0003771089560000063
求解活塞的加速度信号ak；其中，
Figure BDA00037710895600000616
为第k时刻活塞的加速度信号。By formula
Figure BDA0003771089560000063
Solve for the piston's acceleration signal ak ; where,
Figure BDA00037710895600000616
is the acceleration signal of the piston at the kth moment.

本实施例中，第1-6次参数估计所用的活塞位移信号以及利用差分算法求解得到的速度、加速度信号曲线示意图，如图2(a)-(f)所示。In this embodiment, the piston displacement signal used for the 1st to 6th parameter estimation and the schematic diagram of the velocity and acceleration signal curves obtained by using the difference algorithm are shown in Figures 2(a)-(f).

本实施例中，已知液压缸运动模型的LS算法格式与液压缸动力学方程如下：In this embodiment, the LS algorithm format of the known hydraulic cylinder motion model and the hydraulic cylinder dynamics equation are as follows:

y(t)＝φT(t)θ+d(t)y(t)＝φ T (t)θ+d(t)

Figure BDA0003771089560000064
Figure BDA0003771089560000064

通过计算，得到第k时刻Kk、

Figure BDA0003771089560000065
Pk的更新表达式为：By calculation, we can get K k at the kth moment,
Figure BDA0003771089560000065
The update expression of P k is:

Figure BDA0003771089560000066
Figure BDA0003771089560000066

Figure BDA0003771089560000067
Figure BDA0003771089560000067

Figure BDA0003771089560000068
Figure BDA0003771089560000068

其中，Kk和Pk都表示第k时刻的增益矩阵；

Figure BDA0003771089560000069
表示第k时刻的参数估计值，初值
Figure BDA00037710895600000610
Pk-1表示第k-1时刻的增益矩阵；φk表示第k时刻的LS算法输入；
Figure BDA00037710895600000611
表示第k-1时刻的参数估计值；yk表示第k时刻的LS算法输出。Among them, K k and P k both represent the gain matrix at the kth moment;
Figure BDA0003771089560000069
Represents the parameter estimate at the kth moment, the initial value
Figure BDA00037710895600000610
P k-1 represents the gain matrix at the k-1th moment; φ k represents the LS algorithm input at the kth moment;
Figure BDA00037710895600000611
represents the parameter estimate at the k-1th moment; y k represents the LS algorithm output at the kth moment.

A3，更新计算Kk、

Figure BDA00037710895600000612
Pk的值后，k＝k+1，返回步骤A2，输入下一时刻活塞位移信号x2，重新计算Kk、
Figure BDA00037710895600000613
Pk的值，不断循环，直至得到对应的采样时间段收敛至稳定的Stribeck参数，并且每一次采样时间段的参数估计结果作为下一次参数估计的初值加入计算；其中，Stribeck参数包括：fc、fv和fs，下一次指下一采样时间段。A3, update calculation K k ,
Figure BDA00037710895600000612
After the value of P k is obtained, k＝k+1, and the process returns to step A2, inputs the piston displacement signal x 2 at the next moment, and recalculates K k ,
Figure BDA00037710895600000613
The value of P k is continuously cycled until the corresponding sampling time period converges to a stable Stribeck parameter, and the parameter estimation result of each sampling time period is added to the calculation as the initial value of the next parameter estimation; wherein the Stribeck parameters include: f c , f v and f s , and the next time refers to the next sampling time period.

本实施例中，参数估计循环终止条件为：In this embodiment, the parameter estimation loop termination condition is:

Figure BDA0003771089560000071
Figure BDA0003771089560000071

其中，

Figure BDA0003771089560000072
分别为第n次参数估计得到的第k时刻、k-1时刻的参数估计值，ε为停止条件参数，ε一般接近于0。in,
Figure BDA0003771089560000072
are the parameter estimates at the kth moment and k-1th moment respectively obtained by the nth parameter estimation. ε is the stopping condition parameter, which is generally close to 0.

本实施例中，第1-6次参数估计得到的Stribeck参数估计值和真值曲线示意图，如图3(a)-(f)所示。In this embodiment, schematic diagrams of Stribeck parameter estimation values and true value curves obtained from the 1st to 6th parameter estimations are shown in FIG. 3(a)-(f).

S104，将得到的稳定的Stribeck参数与初始状态下的Stribeck参数进行比较，建立液压缸工作状态劣化指标，绘制液压缸工作状态劣化曲线，根据绘制的液压缸工作状态劣化曲线，确定液压缸劣化趋势，并根据当前时刻的劣化指标确定液压缸目前的劣化程度，具体可以包括以下步骤：S104, comparing the obtained stable Stribeck parameters with the Stribeck parameters in the initial state, establishing a hydraulic cylinder working state degradation index, drawing a hydraulic cylinder working state degradation curve, determining the hydraulic cylinder degradation trend according to the drawn hydraulic cylinder working state degradation curve, and determining the current degradation degree of the hydraulic cylinder according to the degradation index at the current moment, which may specifically include the following steps:

B1，将每次得到的稳定的Stribeck参数与初始状态下的Stribeck参数进行比较，建立液压缸工作状态劣化指标Jn：B1, compare the stable Stribeck parameters obtained each time with the Stribeck parameters in the initial state, and establish the hydraulic cylinder working state degradation index Jn :

Figure BDA0003771089560000073
Figure BDA0003771089560000073

其中，

Figure BDA0003771089560000074
表示活塞工作时的速度上限；v表示活塞的速度信号；
Figure BDA0003771089560000075
分别表示第n次参数估计得到的库仑摩擦参数、黏性摩擦系数、Stribeck摩擦参数，
Figure BDA0003771089560000076
分别表示液压缸初始状态下的库仑摩擦参数、黏性摩擦系数、Stribeck摩擦参数，函数Fd(·)为线性化后的Stribeck摩擦模型；in,
Figure BDA0003771089560000074
Indicates the upper speed limit of the piston when it is working; v indicates the speed signal of the piston;
Figure BDA0003771089560000075
They represent the Coulomb friction parameter, viscous friction coefficient, and Stribeck friction parameter obtained by the nth parameter estimation, respectively.
Figure BDA0003771089560000076
They represent the Coulomb friction parameter, viscous friction coefficient, and Stribeck friction parameter in the initial state of the hydraulic cylinder, respectively. Function F d (·) is the linearized Stribeck friction model.

本实施例中，函数Fd(·)表示为：In this embodiment, the function F d (·) is expressed as:

Figure BDA0003771089560000077
Figure BDA0003771089560000077

其中，fc为库仑摩擦参数，fv为黏性摩擦系数，fs为Stribeck摩擦参数，sgn(·)为符号函数，

Figure BDA0003771089560000078
表示活塞的速度。Where, f c is the Coulomb friction parameter, f v is the viscous friction coefficient, f s is the Stribeck friction parameter, sgn(·) is the sign function,
Figure BDA0003771089560000078
Indicates the speed of the piston.

本实施例中，不同采样时间段下Stribeck摩擦模型曲线，如图4所示。In this embodiment, the Stribeck friction model curves at different sampling time periods are shown in FIG4 .

B2，以

Figure BDA0003771089560000079
为横坐标，Jn为纵坐标，绘制液压缸工作状态劣化曲线；其中，Ti表示第i次估计参数与第i+1次估计参数之间的时间间隔，τn表示第n次参数估计所用的活塞位移信号对应的采样时间段；B2, with
Figure BDA0003771089560000079
As the horizontal coordinate, J n as the vertical coordinate, the hydraulic cylinder working state degradation curve is drawn; wherein Ti represents the time interval between the i-th estimated parameter and the i+1-th estimated parameter, and τ n represents the sampling time period corresponding to the piston displacement signal used for the n-th parameter estimation;

B3，根据绘制的液压缸工作状态劣化曲线，确定液压缸劣化趋势，并根据当前时刻的劣化指标确定液压缸目前的劣化程度。B3, determine the hydraulic cylinder degradation trend according to the drawn hydraulic cylinder working state degradation curve, and determine the current degradation degree of the hydraulic cylinder according to the degradation index at the current moment.

本实施例中，可以根据经验设定4个阈值范围，从而将劣化程度分为：轻微损耗、中度损耗、设备故障和完全报废四个等级。本实施例中，通过判断液压缸当前时刻劣化指标所属的阈值范围，得到液压缸目前的劣化程度。In this embodiment, four threshold ranges can be set based on experience, so that the degree of degradation is divided into four levels: slight loss, moderate loss, equipment failure and complete scrapping. In this embodiment, the current degree of degradation of the hydraulic cylinder is obtained by determining the threshold range to which the degradation index of the hydraulic cylinder belongs at the current moment.

本实施例中，液压缸的劣化趋势折线示意图如图5所示。In this embodiment, a schematic diagram of the degradation trend of the hydraulic cylinder is shown in FIG5 .

本实施例中，通过对液压缸工作状态劣化曲线进行分析，可以确定液压缸目前的劣化程度，为是否更换系统部件提供依据。In this embodiment, by analyzing the degradation curve of the hydraulic cylinder working state, the current degradation degree of the hydraulic cylinder can be determined, providing a basis for whether to replace system components.

本发明实施例所述的液压缸劣化趋势评价方法，实时采集液压缸在不同工作时间段的活塞位移信号；基于采集的活塞位移信号，确定液压缸运动模型的LS算法格式；基于确定的液压缸运动模型的LS算法格式，对Stribeck参数进行估计，得到收敛至稳定的Stribeck参数；将得到的稳定的Stribeck参数与初始状态下的Stribeck参数进行比较，建立液压缸工作状态劣化指标，绘制液压缸工作状态劣化曲线，根据绘制的液压缸工作状态劣化曲线，确定液压缸劣化趋势，并根据当前时刻的劣化指标确定液压缸目前的劣化程度。这样，通过建立的基于Stribeck曲线的液压缸劣化趋势评价方法，能够对液压缸的劣化程度进行精准评价，辅助液压系统的日常监测和维护，对液压系统的性能监控与评估以及提升生产过程的工作效率有着重要意义，从而解决现有技术无法对液压缸劣化程度进行评价的问题。The method for evaluating the deterioration trend of a hydraulic cylinder described in the embodiment of the present invention collects the piston displacement signal of the hydraulic cylinder in different working time periods in real time; determines the LS algorithm format of the hydraulic cylinder motion model based on the collected piston displacement signal; estimates the Stribeck parameters based on the determined LS algorithm format of the hydraulic cylinder motion model to obtain the Stribeck parameters that converge to stability; compares the obtained stable Stribeck parameters with the Stribeck parameters in the initial state, establishes the deterioration index of the hydraulic cylinder working state, draws the deterioration curve of the hydraulic cylinder working state, determines the deterioration trend of the hydraulic cylinder based on the drawn deterioration curve of the hydraulic cylinder working state, and determines the current deterioration degree of the hydraulic cylinder based on the deterioration index at the current moment. In this way, by establishing the deterioration trend evaluation method of the hydraulic cylinder based on the Stribeck curve, the deterioration degree of the hydraulic cylinder can be accurately evaluated, which assists the daily monitoring and maintenance of the hydraulic system, and has important significance for the performance monitoring and evaluation of the hydraulic system and the improvement of the work efficiency of the production process, thereby solving the problem that the prior art cannot evaluate the deterioration degree of the hydraulic cylinder.

以上所述仅为本发明的较佳实施例，并不用以限制本发明，凡在本发明的精神和原则之内，所作的任何修改、等同替换、改进等，均应包含在本发明的保护范围之内。The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (7)

1.一种液压缸劣化趋势评价方法，其特征在于，包括：1. A method for evaluating the degradation trend of a hydraulic cylinder, comprising: 实时采集液压缸在不同工作时间段的活塞位移信号；Real-time collection of piston displacement signals of hydraulic cylinders in different working time periods; 基于采集的活塞位移信号，确定液压缸运动模型的LS算法格式；其中，LS表示最小二乘；Based on the collected piston displacement signal, the LS algorithm format of the hydraulic cylinder motion model is determined; where LS stands for least squares; 基于确定的液压缸运动模型的LS算法格式，对Stribeck参数进行估计，得到收敛至稳定的Stribeck参数；Based on the LS algorithm format of the determined hydraulic cylinder motion model, the Stribeck parameters are estimated and the Stribeck parameters that converge to stability are obtained; 将得到的稳定的Stribeck参数与初始状态下的Stribeck参数进行比较，建立液压缸工作状态劣化指标，绘制液压缸工作状态劣化曲线，根据绘制的液压缸工作状态劣化曲线，确定液压缸劣化趋势，并根据当前时刻的劣化指标确定液压缸目前的劣化程度；The obtained stable Stribeck parameters are compared with the Stribeck parameters in the initial state, the hydraulic cylinder working state degradation index is established, the hydraulic cylinder working state degradation curve is drawn, the hydraulic cylinder degradation trend is determined according to the drawn hydraulic cylinder working state degradation curve, and the current degradation degree of the hydraulic cylinder is determined according to the degradation index at the current moment; 其中，所述将得到的稳定的Stribeck参数与初始状态下的Stribeck参数进行比较，建立液压缸工作状态劣化指标，绘制液压缸工作状态劣化曲线，根据绘制的液压缸工作状态劣化曲线，确定液压缸目前的劣化程度包括：The step of comparing the obtained stable Stribeck parameters with the Stribeck parameters in the initial state, establishing a hydraulic cylinder working state degradation index, drawing a hydraulic cylinder working state degradation curve, and determining the current degradation degree of the hydraulic cylinder according to the drawn hydraulic cylinder working state degradation curve includes: 将每次得到的稳定的Stribeck参数与初始状态下的Stribeck参数进行比较，建立液压缸工作状态劣化指标Jn：The stable Stribeck parameters obtained each time are compared with the Stribeck parameters in the initial state, and the hydraulic cylinder working state degradation index J n is established:
Figure FDA0004112877360000011
Figure FDA0004112877360000011
 其中，
Figure FDA0004112877360000012
表示活塞工作时的速度上限；v表示活塞的速度信号；
Figure FDA0004112877360000013
分别表示第n次参数估计得到的库仑摩擦参数、黏性摩擦系数、Stribeck摩擦参数，
Figure FDA0004112877360000014
分别表示液压缸初始状态下的库仑摩擦参数、黏性摩擦系数、Stribeck摩擦参数，函数Fd(·)为线性化后的Stribeck摩擦模型；in,
Figure FDA0004112877360000012
Indicates the upper speed limit of the piston when it is working; v indicates the speed signal of the piston;
Figure FDA0004112877360000013
They represent the Coulomb friction parameter, viscous friction coefficient, and Stribeck friction parameter obtained by the nth parameter estimation, respectively.
Figure FDA0004112877360000014
They represent the Coulomb friction parameter, viscous friction coefficient, and Stribeck friction parameter in the initial state of the hydraulic cylinder, respectively. Function F d (·) is the linearized Stribeck friction model. 以
Figure FDA0004112877360000015
为横坐标，Jn为纵坐标，绘制液压缸工作状态劣化曲线；其中，Ti表示第i次估计参数与第i+1次估计参数之间的时间间隔，τn表示第n次参数估计所用的活塞位移信号对应的采样时间段；by
Figure FDA0004112877360000015
As the horizontal coordinate, J n as the vertical coordinate, the hydraulic cylinder working state degradation curve is drawn; wherein Ti represents the time interval between the i-th estimated parameter and the i+1-th estimated parameter, and τ n represents the sampling time period corresponding to the piston displacement signal used for the n-th parameter estimation; 根据绘制的液压缸工作状态劣化曲线，确定液压缸劣化趋势，并根据当前时刻的劣化指标确定液压缸目前的劣化程度。According to the drawn hydraulic cylinder working state degradation curve, the hydraulic cylinder degradation trend is determined, and the current degradation degree of the hydraulic cylinder is determined according to the degradation index at the current moment. 2.根据权利要求1所述的液压缸劣化趋势评价方法，其特征在于，确定的液压缸运动模型的LS算法格式表示为：2. The method for evaluating the deterioration trend of a hydraulic cylinder according to claim 1, wherein the LS algorithm format of the determined hydraulic cylinder motion model is expressed as: y(t)＝φT(t)θ+d(t)y(t)＝φ T (t)θ+d(t)
Figure FDA0004112877360000021
Figure FDA0004112877360000021
Figure FDA0004112877360000022
Figure FDA0004112877360000022
 θ＝[m K fc fv fs]T θ＝[m K f c f v f s ] T 其中，y(t)为LS算法输出，φ(t)为LS算法输入，θ为待估计的参数，d(t)为测量噪声，上标T表示矩阵转置，p1、p2分别为无杆腔压强、有杆腔压强，A1、A2分别为无杆腔有效面积、有杆腔有效面积，p1A1和p2A2分别代表无杆腔和有杆腔的压力，FL表示外部轧制力，c表示粘性阻尼系数，x、
Figure FDA0004112877360000023
分别表示活塞的位移、速度、加速度，sgn(·)为符号函数，m为活塞及负载的折合质量，K表示液压缸系统的等效刚度，fc为库仑摩擦参数，fv为黏性摩擦系数，fs为Stribeck摩擦参数。Where y(t) is the output of the LS algorithm, φ(t) is the input of the LS algorithm, θ is the parameter to be estimated, d(t) is the measurement noise, the superscript T represents the matrix transpose, p 1 and p 2 are the pressure of the rodless cavity and the pressure of the rod cavity, A 1 and A 2 are the effective area of the rodless cavity and the effective area of the rod cavity, p 1 A 1 and p 2 A 2 represent the pressure of the rodless cavity and the rod cavity, F L represents the external rolling force, c represents the viscous damping coefficient, x,
Figure FDA0004112877360000023
represents the displacement, velocity and acceleration of the piston respectively, sgn(·) is the sign function, m is the reduced mass of the piston and the load, K represents the equivalent stiffness of the hydraulic cylinder system, fc is the Coulomb friction parameter, fv is the viscous friction coefficient, and fs is the Stribeck friction parameter. 3.根据权利要求2所述的液压缸劣化趋势评价方法，其特征在于，所述基于确定的液压缸运动模型的LS算法格式，对Stribeck参数进行估计，得到收敛至稳定的Stribeck参数包括：3. The method for evaluating the deterioration trend of a hydraulic cylinder according to claim 2, wherein the LS algorithm format based on the determined hydraulic cylinder motion model estimates the Stribeck parameters to obtain the Stribeck parameters that converge to stability, including: A1，在初始采样时间段的LS算法参数估计过程中，给定参数初值θ0、增益矩阵初值P0、位移初值x0和速度初值
Figure FDA0004112877360000024
A1, in the LS algorithm parameter estimation process of the initial sampling time period, given the initial parameter value θ 0 , the initial gain matrix value P 0 , the initial displacement value x 0 and the initial velocity value
Figure FDA0004112877360000024
 A2，输入活塞位移信号x1，采用差分算法计算出活塞的速度信号和加速度信号，构建出液压缸运动模型的LS算法格式的输出yk和输入φk，依次更新计算Kk、
Figure FDA0004112877360000025
Pk的值；A2, input piston displacement signal x1 , use differential algorithm to calculate piston velocity signal and acceleration signal, construct output yk and input φk of hydraulic cylinder motion model in LS algorithm format, and update and calculate Kk ,
Figure FDA0004112877360000025
The value of P k ; A3，更新计算Kk、
Figure FDA0004112877360000026
Pk的值后，k＝k+1，返回步骤A2，输入下一时刻活塞位移信号x2，重新计算Kk、
Figure FDA0004112877360000027
Pk的值，不断循环，直至得到对应的采样时间段收敛至稳定的Stribeck参数，并且每一次采样时间段的参数估计结果作为下一次参数估计的初值加入计算；其中，Stribeck参数包括：fc、fv和fs，下一次指下一采样时间段。A3, update calculation K k ,
Figure FDA0004112877360000026
After the value of P k is obtained, k＝k+1, and the process returns to step A2, inputs the piston displacement signal x 2 at the next moment, and recalculates K k ,
Figure FDA0004112877360000027
The value of P k is continuously cycled until the corresponding sampling time period converges to a stable Stribeck parameter, and the parameter estimation result of each sampling time period is added to the calculation as the initial value of the next parameter estimation; wherein the Stribeck parameters include: f c , f v and f s , and the next time refers to the next sampling time period. 4.根据权利要求3所述的液压缸劣化趋势评价方法，其特征在于，所述采用差分算法计算出活塞的速度信号和加速度信号包括：4. The method for evaluating the deterioration trend of a hydraulic cylinder according to claim 3, wherein the step of calculating the speed signal and the acceleration signal of the piston using a differential algorithm comprises: 通过公式
Figure FDA0004112877360000028
求解活塞的速度信号vk；其中，△为差分间隔，xk为第k时刻活塞的位移信号；By formula
Figure FDA0004112877360000028
Solve for the piston velocity signal v k ; where △ is the differential interval, and x k is the piston displacement signal at the kth moment; 通过公式
Figure FDA0004112877360000031
求解活塞的加速度信号ak；其中，
Figure FDA00041128773600000312
为第k时刻活塞的加速度信号。By formula
Figure FDA0004112877360000031
Solve for the piston acceleration signal ak ; where,
Figure FDA00041128773600000312
is the acceleration signal of the piston at the kth moment. 5.根据权利要求1所述的液压缸劣化趋势评价方法，其特征在于，第k时刻Kk、
Figure FDA0004112877360000032
Pk的更新表达式为：5. The method for evaluating the deterioration trend of a hydraulic cylinder according to claim 1, wherein at the kth moment K k ,
Figure FDA0004112877360000032
The update expression of P k is:
Figure FDA0004112877360000033
Figure FDA0004112877360000033
Figure FDA0004112877360000034
Figure FDA0004112877360000034
Figure FDA0004112877360000035
Figure FDA0004112877360000035
 其中，Kk和Pk都表示第k时刻的增益矩阵；
Figure FDA0004112877360000036
表示第k时刻的参数估计值；Pk-1表示第k-1时刻的增益矩阵；φk表示第k时刻的LS算法输入；
Figure FDA0004112877360000037
表示第k-1时刻的参数估计值；yk表示第k时刻的LS算法输出。Among them, K k and P k both represent the gain matrix at the kth moment;
Figure FDA0004112877360000036
represents the parameter estimation value at the kth moment; P k-1 represents the gain matrix at the k-1th moment; φ k represents the LS algorithm input at the kth moment;
Figure FDA0004112877360000037
represents the parameter estimate at the k-1th moment; y k represents the LS algorithm output at the kth moment. 6.根据权利要求1所述的液压缸劣化趋势评价方法，其特征在于，参数估计循环终止条件为：6. The method for evaluating the deterioration trend of a hydraulic cylinder according to claim 1, wherein the parameter estimation cycle termination condition is:
Figure FDA0004112877360000038
Figure FDA0004112877360000038
 其中，
Figure FDA0004112877360000039
分别为第n次参数估计得到的第k时刻、k-1时刻的参数估计值，ε为停止条件参数。in,
Figure FDA0004112877360000039
are the parameter estimates at the kth moment and k-1th moment respectively obtained by the nth parameter estimation, and ε is the stopping condition parameter. 7.根据权利要求1所述的液压缸劣化趋势评价方法，其特征在于，函数Fd(·)表示为：7. The method for evaluating the deterioration trend of a hydraulic cylinder according to claim 1, wherein the function F d (·) is expressed as:
Figure FDA00041128773600000310
Figure FDA00041128773600000310
 其中，fc为库仑摩擦参数，fv为黏性摩擦系数，fs为Stribeck摩擦参数，sgn(·)为符号函数，
Figure FDA00041128773600000311
表示活塞的速度。Where, f c is the Coulomb friction parameter, f v is the viscous friction coefficient, f s is the Stribeck friction parameter, sgn(·) is the sign function,
Figure FDA00041128773600000311
Indicates the speed of the piston.
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