CN105257277A

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Info

Publication number: CN105257277A
Application number: CN201510248922.9A
Authority: CN
Inventors: 韩莹; 李琨; 黄海礁; 魏泽飞; 杨一柳; 佘东生
Original assignee: Bohai University
Current assignee: Bohai University
Priority date: 2015-05-15
Filing date: 2015-05-15
Publication date: 2016-01-20
Anticipated expiration: 2035-05-15
Also published as: CN105257277B

Abstract

一种基于多变量灰色模型的有杆泵抽油井井下故障预测方法，由示功图远程数据采集系统采集地面示功图；将地面示功图转化为井下泵功图；根据曲线矩理论提取能够表征井下泵功图图形特征的曲线矩特征向量；由多变量灰色模型对每一个特征向量进行预测；计算预测样本与标准集中每一种故障类型的灰关联度，最大灰关联度所对应的故障类型即为预测样本的故障类型。可合理调整抽油井的工作制度，从而提高抽油井的生产效率，可实现对有杆泵抽油井井下工作状况的故障预测；计算简单，所需要的样本少，并且对于任意分布的数据集都适用；预测的准确度高，特别对于渐变型的故障类型具有较高的预测精度。

A downhole fault prediction method for rod pumped oil wells based on a multivariable gray model. The ground dynamometer diagram is collected by the dynamometer remote data acquisition system; the surface dynamometer diagram is converted into a downhole pump dynamometer diagram; Characterize the curve moment eigenvector of the graphic features of the downhole pump power map; predict each eigenvector by the multivariate gray model; calculate the gray correlation degree between the predicted sample and each fault type in the standard set, and the fault corresponding to the maximum gray correlation degree Type is the failure type of the predicted sample. The working system of the pumping well can be reasonably adjusted to improve the production efficiency of the pumping well, and the fault prediction of the downhole working conditions of the rod pump pumping well can be realized; the calculation is simple, the required samples are few, and it is suitable for any distributed data set ; The prediction accuracy is high, especially for gradual fault types.

Description

Translated fromChinese

基于多变量灰色模型的有杆泵抽油井井下故障预测方法Downhole Fault Prediction Method of Rod Pumped Oil Well Based on Multivariable Gray Model

技术领域technical field

本发明属于有杆泵抽油井故障预测方法领域，具体涉及一种基于多变量灰色模型的有杆泵抽油井井下故障预测方法。The invention belongs to the field of fault prediction methods for rod pumped oil wells, and in particular relates to a downhole fault prediction method for rod pumped oil wells based on a multivariable gray model.

背景技术Background technique

有杆泵抽油井的故障是油田生产所面临的一个主要问题，会影响井下抽油泵的运行状况和油井的产油量。由于抽油泵工作在数千米的井下，工作状况十分复杂，工作环境极其恶劣，故障发生率很高，很大程度会影响油田的正常生产。一旦抽油井发生了故障而不能进行及时诊断，就会造成能源的浪费，并且影响抽油井生产，给企业带来损失。目前已有很多研究关注于有杆泵抽油井井下的故障诊断方法，但是这是建立在故障已经发生的基础上，已经给抽油井的正常生产带来了一定的影响。The failure of rod pump wells is a major problem faced by oil field production, which will affect the operation status of downhole pumps and the oil production of oil wells. Since the oil well pump works thousands of meters underground, the working conditions are very complicated, the working environment is extremely harsh, and the failure rate is very high, which will greatly affect the normal production of the oil field. Once the pumping well breaks down and cannot be diagnosed in time, it will cause waste of energy, affect the production of the pumping well, and bring losses to the enterprise. At present, many studies have focused on the downhole fault diagnosis methods of pumped rod pumping wells, but this is based on the fact that the fault has already occurred, which has already brought a certain impact on the normal production of the pumping well.

发明内容Contents of the invention

本发明要解决的技术问题是提供一种基于多变量灰色模型的有杆泵抽油井井下故障预测方法，实现对有杆泵抽油井井下工作状况的故障预测。The technical problem to be solved by the present invention is to provide a downhole fault prediction method for rod pumped oil wells based on a multivariable gray model, so as to realize fault prediction for the downhole working conditions of rod pumped oil wells.

本发明的技术解决方案是：Technical solution of the present invention is:

一种基于多变量灰色模型的有杆泵抽油井井下故障预测方法，其特殊之处是：A downhole fault prediction method for rod pumped oil wells based on a multivariable gray model, the special features of which are:

1)、采用示功图远程数据采集系统，首先，将无线示功仪安装在有杆泵抽油井的抽油机的驴头上，采集光杆的载荷和位移数据；无线RTU以无线的方式接收无线示功仪采集的数据，由数据采集模块通过无线AP从站模块以无线网络远程传送到无线AP主站模块上；示功图监测及数据处理服务器接收采集到的光杆的载荷和位移数据，绘制采集到的地面示功图图形；1) Using the remote data acquisition system of the dynamometer, firstly, install the wireless dynamometer on the donkey head of the pumping unit of the rod pump well, and collect the load and displacement data of the polished rod; the wireless RTU receives the data in a wireless way The data collected by the wireless dynamometer is remotely transmitted by the data acquisition module to the wireless AP master station module through the wireless AP slave station module; the dynamometer diagram monitoring and data processing server receives the collected load and displacement data of the light rod, Draw the collected ground dynamometer graphics;

2)、将地面示功图转化为井下泵功图，以得到能够真实反映抽油泵工作状况的示功图图形；2) Convert the surface dynamometer diagram into a downhole pump dynamometer diagram to obtain a dynamometer diagram that can truly reflect the working condition of the oil well pump;

3)、提取井下泵功图的曲线矩特征作为特征向量，将井下泵功图划分为上冲程部分和下冲程部分，然后根据曲线矩理论分别提取上冲程部分的7个曲线矩特征向量和下冲程部分的7个曲线矩特征向量，将得到的14个曲线矩特征向量作为下一步预测的变量，具体步骤如下：3) Extract the curve moment feature of the downhole pump power diagram as the eigenvector, divide the downhole pump power diagram into an upstroke part and a downstroke part, and then extract the 7 curve moment eigenvectors and the downstroke part of the upstroke part respectively according to the curve moment theory. The 7 curve moment eigenvectors of the stroke part, and the obtained 14 curve moment eigenvectors are used as the variables for the next prediction. The specific steps are as follows:

a)将井下泵功图划分为上冲程部分和下冲程部分，其中上冲程部分曲线反映了有杆泵抽油井的上冲程过程，是抽油杆柱在动力装置的作用下向上拉动柱塞，抽油泵内吸入油液而井口排出油液的过程；下冲程部分曲线反映了有杆泵抽油井的下冲程过程，是抽油杆柱在动力装置的作用下向下推动柱塞，抽油泵向油管内排出油液的过程；假设井下泵功图由N个采样点组成，那么从第1个点到位移最大的点(假设为第l个点)为上冲程部分；从第l+1个点到第N个点为下冲程部分；a) The downhole pump power diagram is divided into an upstroke part and a downstroke part, wherein the curve of the upstroke part reflects the upstroke process of the rod pump well, and the sucker rod string pulls the plunger upward under the action of the power device, The process of sucking oil in the oil pump and discharging oil from the wellhead; the curve of the downstroke part reflects the downstroke process of the pumped well with the rod pump. The process of discharging oil in the tubing; assuming that the downhole pump power map consists of N sampling points, then the upstroke part is from the first point to the point with the largest displacement (assumed to be the lth point); from the l+1th point The point to the Nth point is the downstroke part;

b)划分后的上冲程部分曲线由l个采样点组成，每个采样点的坐标为(x_i,y_i)，其s+r阶曲线矩m_sr定义为：b) The divided upstroke part curve is composed of l sampling points, and the coordinates of each sampling point are (_xi ,y_i ), and its s+r order curve moment m_sr is defined as:

${m m}_{sr sr} = = {Σ Σ}_{i i = = 11}^{l l} {x x}_{i i}^{s the s} {y the y}_{i i}^{r r} Δ Δ {z z}_{i i} - - - - - - ((11))$

其中i＝1,…,l；s,r＝0,1,2；Δz_i为两个连续的采样点间的距离，Where i=1,...,l; s,r=0,1,2; Δz_i is the distance between two consecutive sampling points,

μ_sr为s+r阶中心矩，定义为：μ_sr is the s+r order central moment, defined as:

${μ μ}_{sr sr} = = {Σ Σ}_{i i = = 11}^{l l} {(({x x}_{i i} - - \overset{&OverBar; &OverBar;}{x x}))}^{s the s} {(({y the y}_{i i} - - \overset{&OverBar; &OverBar;}{y the y}))}^{r r} Δ Δ {z z}_{i i} - - - - - - ((22))$

其中 $\overset{&OverBar;}{x} = \frac{m_{10}}{m_{00}}, \overset{&OverBar;}{y} = \frac{m_{01}}{m_{00}};$ 点为曲线的重心坐标；in $\overset{&OverBar;}{x} = \frac{m_{10}}{m_{00}}, \overset{&OverBar;}{the y} = \frac{m_{01}}{m_{00}};$ point is the center of gravity coordinates of the curve;

计算出如下各阶中心矩：μ₀₀＝m₀₀，μ₁₀＝0，μ₀₁＝0， $μ_{11} = m_{11} - \overset{&OverBar;}{y} m_{10}, μ_{20} = m_{20} - \overset{&OverBar;}{x} m_{10}, μ_{02} = m_{02} - \overset{&OverBar;}{x} m_{01},$ $μ_{30} = m_{30} - 3 \overset{&OverBar;}{x} m_{20} + 2 m_{10} {\overset{&OverBar;}{x}}^{2}, μ_{03} = m_{03} - 3 \overset{&OverBar;}{y} m_{02} + 2 m_{01} {\overset{&OverBar;}{y}}^{2}, μ_{12} = m_{12} - 2 \overset{&OverBar;}{y} m_{11} - \overset{&OverBar;}{x} m_{02} + 2 {\overset{&OverBar;}{y}}^{2} m_{10};$ Calculate the central moments of each order as follows: μ₀₀ =m₀₀ , μ₁₀ =0, μ₀₁ =0, $μ_{11} = m_{11} - \overset{&OverBar;}{the y} m_{10}, μ_{20} = m_{20} - \overset{&OverBar;}{x} m_{10}, μ_{02} = m_{02} - \overset{&OverBar;}{x} m_{01},$ $μ_{30} = m_{30} - 3 \overset{&OverBar;}{x} m_{20} + 2 m_{10} {\overset{&OverBar;}{x}}^{2}, μ_{03} = m_{03} - 3 \overset{&OverBar;}{the y} m_{02} + 2 m_{01} {\overset{&OverBar;}{the y}}^{2}, μ_{12} = m_{12} - 2 \overset{&OverBar;}{the y} m_{11} - \overset{&OverBar;}{x} m_{02} + 2 {\overset{&OverBar;}{the y}}^{2} m_{10};$

对提取的各阶中心矩进行规范化处理，由η_sr表示，定义为：Normalize the extracted central moments of each order, denoted by η_sr , defined as:

η_sr＝μ_sr/(μ₀₀)^s+r+1(3)η_sr = μ_sr /(μ₀₀ )^s+r+1 (3)

那么构造的上冲程部分的7个曲线矩特征向量分别定义如下：Then the seven curve moment eigenvectors of the constructed upstroke part are defined as follows:

采用如下修正公式使构造的上冲程部分的7个曲线矩特征向量的取值范围统一，记为ψ₁—ψ₇，定义为：The seven curve moment eigenvectors of the constructed upstroke part are made by using the following correction formula The value range of is unified, recorded as ψ₁ —ψ₇ , defined as:

其中q＝0,1,…,7；where q=0,1,...,7;

c)提取下冲程部分的曲线矩特征向量，划分后的下冲程部分曲线由N-l个采样点组成，每个采样点的坐标为(x_j,y_j)，其s+r阶曲线矩m'_sr定义为：c) Extract the curve moment eigenvector of the downstroke part, the divided downstroke part curve is composed of Nl sampling points, the coordinates of each sampling point are (x_j , y_j ), and its s+r order curve moment m'_sr is defined as:

${m m}_{sr sr}^{' '} = = {Σ Σ}_{j j = = l l + + 11}^{N N} {x x}_{j j}^{s the s} {y the y}_{j j}^{r r} Δ Δ {z z}_{j j} - - - - - - ((1212))$

其中j＝l+1,l+2,…,N；s,r＝0,1,2；Δz_j为两个连续的采样点间的距离，Where j=l+1,l+2,...,N; s,r=0,1,2; Δz_j is the distance between two consecutive sampling points,

μ'_sr为s+r阶中心矩，定义为：μ'_sr is the s+r order central moment, defined as:

${μ μ}_{sr sr}^{' '} = = {Σ Σ}_{j j = = l l + + 11}^{N N} {(({x x}_{j j} - - \overset{&OverBar; &OverBar;}{{x x}^{' '}}))}^{s the s} {(({y the y}_{j j} - - \overset{&OverBar; &OverBar;}{{y the y}^{' '}}))}^{r r} Δ Δ {z z}_{j j} - - - - - - ((1313))$

其中 $\overset{&OverBar;}{x^{'}} = \frac{m_{10}}{m_{00}}, \overset{&OverBar;}{y^{'}} = \frac{m_{01}}{m_{00}};$ 点为曲线的重心坐标；in $\overset{&OverBar;}{x^{'}} = \frac{m_{10}}{m_{00}}, \overset{&OverBar;}{{the y}^{'}} = \frac{m_{01}}{m_{00}};$ point is the center of gravity coordinates of the curve;

计算出如下各阶中心矩：μ′₀₀＝m′₀₀，μ′₁₀＝0，μ′₀₁＝0， $μ_{11}^{'} = m_{11}^{'} - \overset{&OverBar;}{y} m_{10}^{'}, μ_{20}^{'} = m_{20}^{'} - \overset{&OverBar;}{x} m_{10}^{'}, μ_{02}^{'} = m_{02}^{'} - \overset{&OverBar;}{x} m_{01}^{'},$ $μ_{30}^{'} = m_{30}^{'} - 3 \overset{&OverBar;}{x} m_{20}^{'} + 2 m_{10}^{'} {\overset{&OverBar;}{x^{'}}}^{2}, μ_{03}^{'} = m_{03}^{'} - 3 \overset{&OverBar;}{y^{'}} m_{02}^{'} + 2 m_{01}^{'} {\overset{&OverBar;}{y^{'}}}^{2}, μ_{12}^{'} = m_{12}^{'} - 2 \overset{&OverBar;}{y^{'}} m_{11}^{'} - \overset{&OverBar;}{x^{'}} m_{02}^{'} + 2 {\overset{&OverBar;}{y^{'}}}^{2} m_{10}^{'};$ Calculate the central moments of each order as follows: μ′₀₀ ＝m′₀₀ , μ′₁₀ ＝0, μ′₀₁ ＝0, $μ_{11}^{'} = m_{11}^{'} - \overset{&OverBar;}{the y} m_{10}^{'}, μ_{20}^{'} = m_{20}^{'} - \overset{&OverBar;}{x} m_{10}^{'}, μ_{02}^{'} = m_{02}^{'} - \overset{&OverBar;}{x} m_{01}^{'},$ $μ_{30}^{'} = m_{30}^{'} - 3 \overset{&OverBar;}{x} m_{20}^{'} + 2 m_{10}^{'} {\overset{&OverBar;}{x^{'}}}^{2}, μ_{03}^{'} = m_{03}^{'} - 3 \overset{&OverBar;}{{the y}^{'}} m_{02}^{'} + 2 m_{01}^{'} {\overset{&OverBar;}{{the y}^{'}}}^{2}, μ_{12}^{'} = m_{12}^{'} - 2 \overset{&OverBar;}{{the y}^{'}} m_{11}^{'} - \overset{&OverBar;}{x^{'}} m_{02}^{'} + 2 {\overset{&OverBar;}{{the y}^{'}}}^{2} m_{10}^{'};$

对提取的各阶中心矩进行规范化处理，由η'_sr表示，定义为：Normalize the extracted central moments of each order, represented by η'_sr , defined as:

η'_sr＝μ'_sr/(μ'₀₀)^s+r+1(14)η'_sr = μ'_sr /(μ'₀₀ )^s+r+1 (14)

那么构造的下冲程部分的7个曲线矩特征向量分别定义如下：Then the seven curve moment eigenvectors of the constructed downstroke part are defined as follows:

采用如下修正公式使构造的下冲程部分的7个曲线矩特征向量的取值范围统一，记为ψ₈—ψ₁₄，定义为：The seven curve moment eigenvectors of the constructed downstroke part are made by using the following correction formula The value range of is unified, recorded as ψ₈ —ψ₁₄ , defined as:

其中q’＝8,9,…,14；where q'=8,9,...,14;

将提取得到的能够表征井下泵功图图形特征的14个特征向量ψ₁—ψ₁₄，作为下一步预测的变量；The extracted 14 eigenvectors ψ₁ —ψ₁₄ that can characterize the graphical features of the downhole pump power diagram are used as the variables for the next prediction;

4)、根据多变量灰色模型MGM(1,n)的基本理论建立有杆泵抽油井井下故障的多变量灰色预测模型，利用MGM(1,n)模型建立多个变量之间的动态相关性，弥补单变量方法的局限性；将一段连续时间内的泵功图所提取的14个曲线矩特征向量作为多变量灰色模型(MGM(1,14))的输入，建立灰时间序列，每一个曲线矩特征向量作为灰时间序列的一个变量；由所建立的多变量灰色预测模型分别预测14个曲线矩特征向量的下一个时间点的特征向量，所述14个预测的曲线矩特征向量即为能够表征预测样本特征的特征向量；4) According to the basic theory of the multivariable gray model MGM(1,n), a multivariable gray forecasting model for downhole faults of rod pumped oil wells is established, and the dynamic correlation between multiple variables is established by using the MGM(1,n) model , to make up for the limitations of the univariate method; the 14 curve moment eigenvectors extracted from the pump power diagram in a continuous period of time are used as the input of the multivariate gray model (MGM(1,14)), and the gray time series is established, and each The curve moment eigenvector is used as a variable of the gray time series; the eigenvectors of the next time point of the 14 curve moment eigenvectors are respectively predicted by the established multivariate gray prediction model, and the 14 predicted curve moment eigenvectors are A feature vector that can represent the characteristics of the predicted sample;

将所建立的泵功图曲线矩特征向量灰时间序列表示如下：The gray time series of the moment eigenvector of the pump power graph curve is expressed as follows:

${ψ ψ}^{((00))} ((k k)) = = [\begin{matrix} {ψ ψ}_{11}^{((00))} ((11)) & {ψ ψ}_{11}^{((00))} ((22)) & . . . . . . & {ψ ψ}_{11}^{((00))} ((k k)) & . . . . . . & {ψ ψ}_{11}^{((00))} ((m m)) \\ {ψ ψ}_{22}^{((00))} ((11)) & {ψ ψ}_{22}^{((00))} ((22)) & . . . . . . & {ψ ψ}_{22}^{((00))} ((k k)) & . . . . . . & {ψ ψ}_{22}^{((00))} ((m m)) \\ . . & . . & . . & . . & . . & . . \\ . . & . . & . . & . . & . . & . . \\ . . & . . & . . & . . & . . & . . \\ {ψ ψ}_{p p}^{((00))} ((11)) & {ψ ψ}_{p p}^{((00))} ((22)) & . . . . . . & {ψ ψ}_{p p}^{((00))} ((k k)) & . . . . . . & {ψ ψ}_{p p}^{((00))} ((m m)) \\ . . & . . & . . & . . & . . & . . \\ . . & . . & . . & . . & . . & . . \\ . . & . . & . . & . . & . . & . . \\ {ψ ψ}_{1414}^{((00))} ((11)) & {ψ ψ}_{1414}^{((00))} ((22)) & . . . . . . & {ψ ψ}_{1414}^{((00))} ((k k)) & . . . . . . & {ψ ψ}_{1414}^{((00))} ((m m)) \end{matrix}] - - - - - - ((23 twenty three))$

其中p＝1,2,…,14；k＝1,2,…,m，m为所采用的泵功图的数量；表示泵功图曲线矩特征向量灰时间序列中的第p个变量中的第k个影响因素；Where p=1,2,...,14; k=1,2,...,m, m is the number of pump power diagrams used; Represents the kth influencing factor in the pth variable in the gray time series of the curve moment feature vector of the pump power diagram;

令为相应的一次累加生成序列，有：make Generate sequences for a corresponding accumulation, with:

${ψ ψ}_{p p}^{((11))} ((k k)) = = {Σ Σ}_{g g = = 11}^{k k} {ψ ψ}_{p p}^{((00))} ((g g)) - - - - - - ((24 twenty four))$

建立14元一阶常微分方程，有：To establish a 14-element first-order ordinary differential equation, there are:

$\{\begin{matrix} \frac{d d {ψ ψ}_{11}^{((11))}}{dt dt} = = {a a}_{11 - - 11} {ψ ψ}_{11}^{((11))} + + {a a}_{11 - - 22} {ψ ψ}_{22}^{((11))} + + . . . . . . + + {a a}_{11 - - 1414} {ψ ψ}_{1414}^{((11))} + + {b b}_{11} \\ \frac{d d {ψ ψ}_{22}^{((11))}}{dt dt} = = {a a}_{22 - - 11} {ψ ψ}_{11}^{((11))} + + {a a}_{22 - - 22} {ψ ψ}_{22}^{((11))} + + . . . . . . + + {a a}_{22 - - 1414} {ψ ψ}_{1414}^{((11))} + + {b b}_{22} \\ . . \\ . . \\ . . \\ \frac{d d {ψ ψ}_{1414}^{((11))}}{dt dt} = = {a a}_{1414 - - 11} {ψ ψ}_{11}^{((11))} + + {a a}_{1414 - - 22} {ψ ψ}_{22}^{((11))} + + . . . . . . + + {a a}_{1414 - - 1414} {ψ ψ}_{1414}^{((11))} + + {b b}_{1414} \end{matrix} - - - - - - ((2525))$

记remember

$A A = = [\begin{matrix} {a a}_{11 - - 11} & {a a}_{11 - - 22} & . . . . . . & {a a}_{11 - - 1414} \\ {a a}_{22 - - 11} & {a a}_{22 - - 22} & . . . . . . & {a a}_{22 - - 1414} \\ . . & . . & . . & . . \\ . . & . . & . . & . . \\ . . & . . & . . & . . \\ {a a}_{1414 - - 11} & {a a}_{1414 - - 22} & . . . . . . & {a a}_{1414 - - 1414} \end{matrix}] - - - - - - ((2626))$

B＝(b₁,b₁,…,b_n)^T(27)B=(b₁ ,b₁ ,…,b_n )^T (27)

A和B为辨识参数，那么将公式(25)简记为A and B are the identification parameters, then the formula (25) can be abbreviated as

$\frac{d d {Ψ Ψ}^{((11))}}{dt dt} = = A A {Ψ Ψ}^{((11))} + + B B - - - - - - ((2828))$

其中 $Ψ^{(1)} = {(ψ_{1}^{(1)}, ψ_{2}^{(1)}, . . ., ψ_{14}^{(1)})}^{T};$ in $Ψ^{(1)} = {(ψ_{1}^{(1)}, ψ_{2}^{(1)}, . . ., ψ_{14}^{(1)})}^{T};$

在[0,t]区间上积分，得到连续时间响应为Integrating over the [0,t] interval, the continuous time response is obtained as

${Ψ Ψ}^{((11))} ((t t)) = = {e e}^{At At} {Ψ Ψ}^{((11))} ((00)) + + {A A}^{- - 11} (({e e}^{At At} - - I I)) B B - - - - - - ((2929))$

其中 $e^{At} = I + Σ_{u = 1}^{\infty} \frac{A^{u}}{u!} t^{u};$ in $e^{At} = I + Σ_{u = 1}^{\infty} \frac{A^{u}}{u!} t^{u};$

将公式(25)进行离散化，得到：The formula (25) is discretized to get:

${ψ ψ}_{p p}^{((00))} ((k k)) = = {Σ Σ}_{w w = = 11}^{1414} \frac{{a a}_{p p - - w w}}{22} (({ψ ψ}_{w w}^{((11))} ((k k)) + + {ψ ψ}_{w w}^{((11))} ((k k - - 11)))) - - - - - - ((3030))$

其中p＝1,2,…,14；k＝2,3,…,m；where p=1,2,...,14; k=2,3,...,m;

记remember

$E E. = = [\begin{matrix} {a a}_{11 - - 11} & {a a}_{22 - - 11} & . . . . . . & {a a}_{1414 - - 11} \\ {a a}_{11 - - 22} & {a a}_{22 - - 22} & . . . . . . & {a a}_{1414 - - 22} \\ . . & . . & . . & . . \\ . . & . . & . . & . . \\ . . & . . & . . & . . \\ {a a}_{11 - - 1414} & {a a}_{22 - - 1414} & . . . . . . & {a a}_{1414 - - 1414} \\ {b b}_{11} & {b b}_{22} & . . . . . . & {b b}_{1414} \end{matrix}] - - - - - - ((3131))$

由最小二乘法得到E的辨识值E，有：The identification value E of E obtained by the least square method is:

E＝(L^TL)^-1L^TY(32)E＝(L^T L)^-1 L^T Y(32)

其中，in,

$Y Y = = [\begin{matrix} {ψ ψ}_{11}^{((00))} ((22)) & {ψ ψ}_{22}^{((00))} ((22)) & . . . . . . & {ψ ψ}_{1414}^{((00))} ((22)) \\ {ψ ψ}_{11}^{((00))} ((33)) & {ψ ψ}_{22}^{((00))} ((33)) & . . . . . . & {ψ ψ}_{1414}^{((00))} ((33)) \\ . . & . . & . . & . . \\ . . & . . & . . & . . \\ . . & . . & . . & . . \\ {ψ ψ}_{11}^{((00))} ((m m)) & {ψ ψ}_{22}^{((00))} ((m m)) & . . . . . . & {ψ ψ}_{1414}^{((00))} ((m m)) \end{matrix}] - - - - - - ((3434))$

$E E. = = {[\begin{matrix} A A & B B \end{matrix}]}^{T T} = = [\begin{matrix} {a a}_{11 - - 11} & {a a}_{22 - - 11} & . . . . . . & {a a}_{1414 - - 11} \\ {a a}_{11 - - 22} & {a a}_{22 - - 22} & . . . . . . & {a a}_{1414 - - 22} \\ . . & . . & . . & . . \\ . . & . . & . . & . . \\ . . & . . & . . & . . \\ {a a}_{11 - - 1414} & {a a}_{22 - - 1414} & . . . . . . & {a a}_{1414 - - 1414} \\ {\overset{~ ~}{b b}}_{11} & {\overset{~ ~}{b b}}_{22} & . . . . . . & {\overset{~ ~}{b b}}_{1414} \end{matrix}] - - - - - - ((3535))$

由公式(35)得到辨识参数A和B的辨识值A和B，分别为：The identification values A and B of the identification parameters A and B are obtained from formula (35), respectively:

$A A = = [\begin{matrix} {a a}_{11 - - 11} & {a a}_{11 - - 22} & . . . . . . & {a a}_{11 - - 1414} \\ {a a}_{22 - - 11} & {a a}_{22 - - 22} & . . . . . . & {a a}_{22 - - 1414} \\ . . & . . & . . & . . \\ . . & . . & . . & . . \\ . . & . . & . . & . . \\ {a a}_{1414 - - 11} & {a a}_{1414 - - 22} & . . . . . . & {a a}_{1414 - - 1414} \end{matrix}] - - - - - - ((3636))$

$B B = = [\begin{matrix} {\overset{~ ~}{b b}}_{11} \\ {\overset{~ ~}{b b}}_{22} \\ . . \\ . . \\ . . \\ {\overset{~ ~}{b b}}_{1414} \end{matrix}] - - - - - - ((3737))$

根据得到的辨识值A和B，将公式(29)写成如下离散形式，According to the obtained identification values A and B, formula (29) is written in the following discrete form,

Ψ⁽⁰⁾(1)＝Ψ⁽⁰⁾(1)(38)Ψ⁽⁰⁾ (1) = Ψ⁽⁰⁾ (1) (38)

Ψ⁽¹⁾(k)＝e^A(k-1)Ψ⁽¹⁾(1)+A^-1(e^A(k)-I)B(39)Ψ⁽¹⁾ (k)＝e^A(k-1) Ψ⁽¹⁾ (1)+A^-1 (e^A(k) -I)B(39)

其中Ψ⁽¹⁾(k)和Ψ⁽¹⁾(1)可以将公式(36)和公式(38)代入公式(30)求得；Where Ψ⁽¹⁾ (k) and Ψ⁽¹⁾ (1) can be obtained by substituting formula (36) and formula (38) into formula (30);

得到预测模型为：The prediction model obtained is:

Ψ⁽⁰⁾(k)＝Ψ⁽¹⁾(k)-Ψ⁽¹⁾(k-1)(40)Ψ⁽⁰⁾ (k)＝Ψ⁽¹⁾ (k)-Ψ⁽¹⁾ (k-1)(40)

其中k＝2,3,…,m；where k=2,3,...,m;

5、最后，判断预测样本属于哪类故障类型通过已有的示功图信息建立每一种故障类型的标准集，即对已确定故障类型的一定数量的示功图通过将地面示功图转化为井下泵功图和分别提取其14个曲线矩特征向量，得到每一种故障类型中每一个曲线矩特征向量的取值区间；所得到的取值区间由表示，p＝1,2,…,14，其中表示第F_M种故障类型的第p个曲线矩特征向量的下限值，表示第F_M种故障类型的第p个曲线矩特征向量的上限值；5. Finally, determine which type of fault the predicted sample belongs to. Establish a standard set for each fault type through the existing dynamometer information, that is, convert a certain number of dynamometers of the determined fault type by converting the ground dynamometer Extract the 14 curve moment eigenvectors for the downhole pump power map and obtain the value interval of each curve moment eigenvector in each fault type; the obtained value interval is given by means, p=1,2,…,14, where Represents the lower limit value of the pth curve moment eigenvector of the F_Mth fault type, Indicates the upper limit value of the pth curve moment eigenvector of the F_Mth fault type;

计算预测样本的每一个曲线矩特征向量值与每一种故障类型中相应的曲线矩特征向量值的距离，由下式进行计算：Calculate the distance between each curve moment eigenvector value of the predicted sample and the corresponding curve moment eigenvector value in each fault type, which is calculated by the following formula:

$d d (({U u}_{{ψ ψ}_{p p}},, {V V}_{{F f}_{M m} p p})) = = | | {U u}_{{ψ ψ}_{p p}} - - \frac{{V V}_{{F f}_{M m} pa pa} + + {V V}_{{F f}_{M m} pb pb}}{22} | | + + \frac{{V V}_{{F f}_{M m} pb pb} - - {V V}_{{F f}_{M m} pa pa}}{22} - - - - - - ((4141))$

然后由下式计算预测样本与每一种故障类型的灰关联系数，Then calculate the gray correlation coefficient between the predicted sample and each type of failure by the following formula,

${ξ ξ}_{p p {F f}_{M m}} = = \frac{\underset{M m}{min min} \underset{p p}{min min} {{d d (({U u}_{{ψ ψ}_{p p}},, {V V}_{{F f}_{M m} p p}))}} + + ρ ρ \underset{M m}{max max} \underset{p p}{max max} {{d d (({U u}_{{ψ ψ}_{p p}},, {V V}_{{F f}_{M m} p p}))}}}{d d (({U u}_{{ψ ψ}_{p p}},, {V V}_{{F f}_{M m} p p})) + + ρ ρ \underset{M m}{max max} \underset{p p}{max max} {{d d (({U u}_{{ψ ψ}_{p p}},, {V V}_{{F f}_{M m} p p}))}}} - - - - - - ((4242))$

其中p＝1,2,…,14；M＝1,2,3,…。ρ∈[0,1]为分辨系数，在这里取0.5；where p=1,2,...,14; M=1,2,3,.... ρ∈[0,1] is the resolution coefficient, which is 0.5 here;

再由下式计算预测样本与每一种故障类型的灰关联度，Then calculate the gray correlation degree between the predicted sample and each fault type by the following formula,

$Gre Gray {y the y}_{{F f}_{M m}} = = \frac{11}{p p} {Σ Σ}_{p p = = 11}^{1414} {ξ ξ}_{p p {F f}_{M m}} - - - - - - ((4343))$

最大的灰关联度所对应的故障类型即为预测样本的故障类型。The fault type corresponding to the maximum gray correlation degree is the fault type of the predicted sample.

进一步的，步骤3)中井下泵功图的上冲程部分为有杆泵抽油井抽油杆的悬点由最低点运动到最高点的部分；下冲程部分为有杆泵抽油井抽油杆的悬点由最高点运动到最低点的部分。Further, the upstroke part of the downhole pump power diagram in step 3) is the part where the suspension point of the rod pump oil well sucker rod moves from the lowest point to the highest point; the downstroke part is the part of the rod pump oil well sucker rod The part of the suspension point that moves from the highest point to the lowest point.

进一步的，步骤4)对于有杆泵抽油井井下故障的多变量灰色预测模型中所采用的一段连续时间内的样本，连续时间的单位可以为小时或天，所述样本的数量为50－200个，以提高预测模型的计算效率和准确度。Further, in step 4) for the samples in a period of continuous time used in the multivariate gray prediction model for the downhole failure of rod pumped oil wells, the unit of continuous time can be hours or days, and the number of samples is 50-200 to improve the computational efficiency and accuracy of the forecasting model.

进一步的，步骤5)由已有的信息建立每一种故障类型的标准集，已有的信息由已知道故障类型的示功图得到，用来建立每一种故障类型的标准集的示功图的数量大于2个。Further, step 5) establishes a standard set of each fault type from the existing information, and the existing information is obtained from the dynamometer diagram of the known fault type, and is used to establish the dynamometer of the standard set of each fault type The number of graphs is greater than 2.

进一步的，所述有杆泵抽油井井下故障类型有以下9种：“正常”、“气体影响”、“供液不足”、“抽油杆断落”、“游动阀漏失”、“固定阀漏失”、“泵上碰”、“泵下碰”、“油井出砂”。Further, the downhole failure types of rod pumped wells include the following nine types: "normal", "gas influence", "insufficient liquid supply", "sucker rod broken", "swimming valve leakage", "fixed Valve leakage", "pump up bump", "pump down bump", "oil well sand".

本发明的有益效果是：The beneficial effects of the present invention are:

1、有杆泵抽油井是一个复杂的机械系统，具有很强的非线性，其故障具有随机性、不确定性和相对性。本发明发掘并利用有杆泵抽油井生产中的有用信息，对有杆泵抽油井的故障进行预测，进而合理调整抽油井的工作制度，从而提高抽油井的生产效率，这对保证油田正常生产是具有十分重要的意义的。1. Rod pumped oil well is a complex mechanical system with strong nonlinearity, and its faults are random, uncertain and relativity. The invention excavates and utilizes the useful information in the production of rod pump wells, predicts the faults of rod pump wells, and then rationally adjusts the working system of the pump wells, thereby improving the production efficiency of the pump wells, which is of great help to ensure the normal production of the oil field. is of great significance.

2、示功图是油田生产中分析有杆泵抽油井井下工作状况的主要方法，是采集光杆位移变化一个完整周期内载荷和位移数据并绘制的光杆载荷和光杆位移关系的曲线，示功图图形的不同形状反映了有杆泵抽油井井下不同的工作状况。由于有杆泵抽油井的生产过程是一个连续的过程，其井下的工作状况也是一个渐变的过程，因此，可以通过采集一段时间内的有杆泵抽油井的示功图，根据其图形形状的渐变过程实现对有杆泵抽油井井下工作状况的故障预测。2. The dynamometer diagram is the main method for analyzing the downhole working conditions of rod pumped wells in oilfield production. It is the curve of the relationship between the polished rod load and the polished rod displacement after collecting the load and displacement data within a complete cycle of the displacement change of the polished rod, and the dynamometer diagram The different shapes of the graphics reflect the different working conditions of the pumped rod wells downhole. Since the production process of the rod pumped oil well is a continuous process, the downhole working condition is also a gradual process. Therefore, by collecting the dynamometer diagram of the rod pumped oil well for a period of time, according to its graphic shape The gradual change process realizes the fault prediction of the downhole working conditions of rod pumped wells.

3、本发明所建立的有杆泵抽油井井下故障的多变量灰色预测模型，计算简单，所需要的样本少，并且对于任意分布的数据集都适用。根据所建立的各故障类型的标准集进行预测样本的判断，准确度高，特别对于渐变型的故障类型具有较高的预测精度。3. The multi-variable gray prediction model for downhole faults of rod pumped oil wells established by the present invention is simple to calculate, requires few samples, and is applicable to data sets with any distribution. According to the established standard set of each fault type, the prediction sample is judged with high accuracy, especially for gradual fault types with high prediction accuracy.

附图说明Description of drawings

图1是本发明的示功图远程数据采集系统示意图；Fig. 1 is a schematic diagram of a remote data acquisition system for a dynamometer diagram of the present invention;

图2是本发明的工作原理图；Fig. 2 is a working principle diagram of the present invention;

图3是采集的地面示功图和转化后的井下泵功图示意图；Fig. 3 is a schematic diagram of the surface dynamometer diagram collected and the transformed downhole pump dynamism diagram;

图4是井下泵功图的划分示意图；Fig. 4 is a schematic diagram of the division of the downhole pump power map;

图5是曲线矩特征向量Ψ1的灰色模型预测结果示意图；Fig. 5 is a schematic diagram of gray model prediction results of curve moment eigenvector Ψ1;

图6是曲线矩特征向量Ψ2的灰色模型预测结果示意图；Fig. 6 is the gray model prediction result schematic diagram of curve moment feature vector Ψ2;

图7是曲线矩特征向量Ψ3的灰色模型预测结果示意图；Fig. 7 is a schematic diagram of gray model prediction results of curve moment feature vector Ψ3;

图8是曲线矩特征向量Ψ4的灰色模型预测结果示意图；Fig. 8 is a schematic diagram of gray model prediction results of curve moment eigenvector Ψ4;

图9是曲线矩特征向量Ψ5的灰色模型预测结果示意图；Fig. 9 is a schematic diagram of gray model prediction results of curve moment eigenvector Ψ5;

图10是曲线矩特征向量Ψ6的灰色模型预测结果示意图；Fig. 10 is a schematic diagram of gray model prediction results of curve moment eigenvector Ψ6;

图11是曲线矩特征向量Ψ7的灰色模型预测结果示意图；Fig. 11 is a schematic diagram of gray model prediction results of curve moment eigenvector Ψ7;

图12是曲线矩特征向量Ψ8的灰色模型预测结果示意图；Fig. 12 is a schematic diagram of gray model prediction results of curve moment eigenvector Ψ8;

图13是曲线矩特征向量Ψ9的灰色模型预测结果示意图；Fig. 13 is a schematic diagram of the prediction result of the gray model of the curve moment eigenvector Ψ9;

图14是曲线矩特征向量Ψ10的灰色模型预测结果示意图；Fig. 14 is a schematic diagram of gray model prediction results of curve moment eigenvector Ψ10;

图15是曲线矩特征向量Ψ11的灰色模型预测结果示意图；Fig. 15 is a schematic diagram of gray model prediction results of curve moment eigenvector Ψ11;

图16是曲线矩特征向量Ψ12的灰色模型预测结果示意图；Fig. 16 is a schematic diagram of gray model prediction results of curve moment eigenvector Ψ12;

图17是曲线矩特征向量Ψ13的灰色模型预测结果示意图；Fig. 17 is a schematic diagram of gray model prediction results of curve moment eigenvector Ψ13;

图18是曲线矩特征向量Ψ14的灰色模型预测结果示意图。Fig. 18 is a schematic diagram of gray model prediction results of curve moment eigenvector Ψ14.

具体实施方式detailed description

一种基于多变量灰色模型的有杆泵抽油井井下故障预测方法，其步骤如下：A downhole fault prediction method for rod pumped oil wells based on a multivariable gray model, the steps of which are as follows:

1、如图1和图2所示，采用示功图远程数据采集系统，首先将无线示功仪安装在有杆泵抽油井的抽油机的驴头上，采集光杆的载荷和位移数据；无线RTU以无线的方式接收无线示功仪采集的数据，由数据采集模块经交换机2通过无线AP从站模块以无线网络远程传送到无线AP主站模块上，再经交换机1传至示功图监测及数据处理服务器；示功图监测及数据处理服务器接收采集到的光杆的载荷和位移数据，绘制采集到的地面示功图图形。1. As shown in Figure 1 and Figure 2, the remote data acquisition system for the dynamometer diagram is used. First, the wireless dynamometer is installed on the donkey head of the pumping unit of the rod pump well, and the load and displacement data of the polished rod are collected; The wireless RTU receives the data collected by the wireless dynamometer in a wireless manner, and the data acquisition module transmits the data to the wireless AP master station module remotely through the switch 2 through the wireless AP slave station module through the wireless network, and then transmits it to the dynamometer diagram through the switch 1 Monitoring and data processing server; the dynamometer diagram monitoring and data processing server receives the collected load and displacement data of the polished rod, and draws the collected ground dynamometer diagram graphics.

2、如图3所示，将地面示功图转化为井下泵功图，以得到能够真实反映抽油泵工作状况的示功图图形；由于受到抽油柱变形及振动等因素的影响，地面示功图并不能真实反映有杆泵抽油井井下的实际工作状况。因此，通过将地面示功图转化为井下泵功图，以消除这些影响。2. As shown in Figure 3, the surface dynamometer diagram is transformed into a downhole pump dynamometer diagram to obtain a dynamometer diagram that can truly reflect the working condition of the oil well pump; The work diagram cannot truly reflect the actual working conditions of the rod pump wells downhole. Therefore, these effects are eliminated by converting the surface dynamometer diagram into a downhole pump dynamometer diagram.

3、由于井下泵功图的图形形状反映了有杆泵抽油井井下的工作状况，因此，若要实现对井下故障的预测，可以先提取能够表征井下泵功图图形特征的若干特征向量，通过一段时间内各特征向量的变化趋势来预测未来的特征向量，从而得到该特征向量所对应的故障类型。本发明提取井下泵功图的曲线矩特征作为特征向量，具体步骤如下：3. Since the graphic shape of the downhole pumping diagram reflects the downhole working conditions of rod pumped wells, in order to realize the prediction of downhole faults, some eigenvectors that can characterize the graphic features of the downhole pumping diagram can be extracted first, through The change trend of each feature vector in a period of time is used to predict the future feature vector, so as to obtain the fault type corresponding to the feature vector. The present invention extracts the curve moment feature of the downhole pump power diagram as a feature vector, and the specific steps are as follows:

a)将图3中的井下泵功图划分为上冲程部分和下冲程部分，井下泵功图的上冲程部分为有杆泵抽油井抽油杆的悬点由最低点运动到最高点的部分；下冲程部分为有杆泵抽油井抽油杆的悬点由最高点运动到最低点的部分。如图4所示，其中上冲程部分曲线反映了有杆泵抽油井的上冲程过程，是抽油杆柱在动力装置的作用下向上拉动柱塞，抽油泵内吸入油液而井口排出油液的过程；下冲程部分曲线反映了有杆泵抽油井的下冲程过程，是抽油杆柱在动力装置的作用下向下推动柱塞，抽油泵向油管内排出油液的过程。假设井下泵功图由N个采样点组成，那么从第1个点到位移最大的点(假设为第l个点)为上冲程部分；从第l+1个点到第N个点为下冲程部分。a) Divide the downhole pumping diagram in Figure 3 into an upstroke part and a downstroke part, and the upstroke part of the downhole pumping diagram is the part where the suspension point of the sucker rod of the rod pumped oil well moves from the lowest point to the highest point ; The part of the down stroke is the part where the suspension point of the sucker rod of the rod pump oil well moves from the highest point to the lowest point. As shown in Figure 4, the upstroke part of the curve reflects the upstroke process of the rod pump well. The sucker rod string pulls the plunger upward under the action of the power device, and the oil pump sucks oil and the wellhead discharges oil. The process of the downstroke part of the curve reflects the downstroke process of the rod pump well, which is the process in which the sucker rod string pushes the plunger downward under the action of the power device, and the oil well pump discharges oil into the tubing. Assuming that the downhole pump power map is composed of N sampling points, the upstroke part is from the first point to the point with the largest displacement (assumed to be the lth point); the downstroke part is from the l+1th point to the Nth point. stroke part.

计算出如下各阶中心矩：μ₀₀＝m₀₀，μ₁₀＝0，μ₀₁＝0， $μ_{11} = m_{11} - \overset{&OverBar;}{y} m_{10}, μ_{20} = m_{20} - \overset{&OverBar;}{x} m_{10}, μ_{02} = m_{02} - \overset{&OverBar;}{x} m_{01},$ $μ_{30} = m_{30} - 3 \overset{&OverBar;}{x} m_{20} + 2 m_{10} {\overset{&OverBar;}{x}}^{2}, μ_{03} = m_{03} - 3 \overset{&OverBar;}{y} m_{02} + 2 m_{01} {\overset{&OverBar;}{y}}^{2}, μ_{12} = m_{12} - 2 \overset{&OverBar;}{y} m_{11} - \overset{&OverBar;}{x} m_{02} + 2 {\overset{&OverBar;}{y}}^{2} m_{10} .$ Calculate the central moments of each order as follows: μ₀₀ =m₀₀ , μ₁₀ =0, μ₀₁ =0, $μ_{11} = m_{11} - \overset{&OverBar;}{the y} m_{10}, μ_{20} = m_{20} - \overset{&OverBar;}{x} m_{10}, μ_{02} = m_{02} - \overset{&OverBar;}{x} m_{01},$ $μ_{30} = m_{30} - 3 \overset{&OverBar;}{x} m_{20} + 2 m_{10} {\overset{&OverBar;}{x}}^{2}, μ_{03} = m_{03} - 3 \overset{&OverBar;}{the y} m_{02} + 2 m_{01} {\overset{&OverBar;}{the y}}^{2}, μ_{12} = m_{12} - 2 \overset{&OverBar;}{the y} m_{11} - \overset{&OverBar;}{x} m_{02} + 2 {\overset{&OverBar;}{the y}}^{2} m_{10} .$

η_sr＝μ_sr/(μ₀₀)^s+r+1(3)η_sr = μ_sr /(μ₀₀ )^s+r+1 (3)

其中q＝0,1,…,7。where q=0,1,...,7.

计算出如下各阶中心矩：μ′₀₀＝m′₀₀，μ′₁₀＝0，μ′₀₁＝0， $μ_{11}^{'} = m_{11}^{'} - \overset{&OverBar;}{y} m_{10}^{'}, μ_{20}^{'} = m_{20}^{'} - \overset{&OverBar;}{x} m_{10}^{'}, μ_{02}^{'} = m_{02}^{'} - \overset{&OverBar;}{x} m_{01}^{'},$ $μ_{30}^{'} = m_{30}^{'} - 3 \overset{&OverBar;}{x} m_{20}^{'} + 2 m_{10}^{'} {\overset{&OverBar;}{x^{'}}}^{2}, μ_{03}^{'} = m_{03}^{'} - 3 \overset{&OverBar;}{y^{'}} m_{02}^{'} + 2 m_{01}^{'} {\overset{&OverBar;}{y^{'}}}^{2}, μ_{12}^{'} = m_{12}^{'} - 2 \overset{&OverBar;}{y^{'}} m_{11}^{'} - \overset{&OverBar;}{x^{'}} m_{02}^{'} + 2 {\overset{&OverBar;}{y^{'}}}^{2} m_{10}^{'} .$ Calculate the central moments of each order as follows: μ′₀₀ ＝m′₀₀ , μ′₁₀ ＝0, μ′₀₁ ＝0, $μ_{11}^{'} = m_{11}^{'} - \overset{&OverBar;}{the y} m_{10}^{'}, μ_{20}^{'} = m_{20}^{'} - \overset{&OverBar;}{x} m_{10}^{'}, μ_{02}^{'} = m_{02}^{'} - \overset{&OverBar;}{x} m_{01}^{'},$ $μ_{30}^{'} = m_{30}^{'} - 3 \overset{&OverBar;}{x} m_{20}^{'} + 2 m_{10}^{'} {\overset{&OverBar;}{x^{'}}}^{2}, μ_{03}^{'} = m_{03}^{'} - 3 \overset{&OverBar;}{{the y}^{'}} m_{02}^{'} + 2 m_{01}^{'} {\overset{&OverBar;}{{the y}^{'}}}^{2}, μ_{12}^{'} = m_{12}^{'} - 2 \overset{&OverBar;}{{the y}^{'}} m_{11}^{'} - \overset{&OverBar;}{x^{'}} m_{02}^{'} + 2 {\overset{&OverBar;}{{the y}^{'}}}^{2} m_{10}^{'} .$

η'_sr＝μ'_sr/(μ'₀₀)^s+r+1(14)η'_sr = μ'_sr /(μ'₀₀ )^s+r+1 (14)

其中q’＝8,9,…,14。where q'=8,9,...,14.

将提取得到的能够表征井下泵功图图形特征的14个特征向量ψ₁—ψ₁₄，作为下一步预测的变量。对图4所示的划分后的井下泵功图进行曲线矩特征向量的提取，得到的14个特征向量如表1所示。The extracted 14 eigenvectors ψ₁ —ψ₁₄ that can characterize the graphic features of the downhole pump power diagram are used as the variables for the next prediction. The curve moment eigenvectors are extracted from the divided downhole pump power diagram shown in Fig. 4, and the obtained 14 eigenvectors are shown in Table 1.

表1提取的泵功图曲线矩特征向量Table 1 Extracted pump power diagram curve moment eigenvectors

上冲程部分upstroke partψ₁ψ₁ψ₂ψ₂ψ₃ψ₃ψ₄ψ₄ψ₅ψ₅ψ₆ψ₆ψ₇ψ₇曲线矩特征向量值curve moment eigenvector value1.70601.70600.25770.25771.68421.68420.74750.74751.88871.88870.18780.18781.69551.6955下冲程部分downstroke partψ₈ψ₈ψ₉ψ₉ψ₁₀ψ₁₀ψ₁₁ψ₁₁ψ₁₂ψ₁₂ψ₁₃ψ₁₃ψ₁₄ψ₁₄曲线矩特征向量值curve moment eigenvector value1.36391.36390.40360.40362.27772.27771.32361.32363.12413.12411.18771.18771.32601.3260

4、根据多变量灰色模型MGM(1,n)的基本理论建立有杆泵抽油井井下故障的多变量灰色预测模型。4. According to the basic theory of multivariable gray model MGM(1,n), a multivariable gray prediction model for downhole faults of rod pumped wells is established.

所建立的泵功图曲线矩特征向量灰时间序列如下：The gray time series of the moment eigenvector of the pump power diagram is as follows:

记remember

B＝(b₁,b₁,…,b_n)^T(27)B=(b₁ ,b₁ ,…,b_n )^T (27)

A和B为辨识参数，那么公式(25)可以简记为A and B are identification parameters, then formula (25) can be written as

将公式(25)进行离散化，得到：The formula (25) is discretized to get:

其中p＝1,2,…,14；k＝2,3,…,m；where p=1,2,...,14; k=2,3,...,m;

记remember

E＝(L^TL)^-1L^TY(32)E＝(L^T L)^-1 L^T Y(32)

其中，in,

根据得到的辨识值A和B，可以将公式(29)写成如下离散形式，According to the obtained identification values A and B, formula (29) can be written in the following discrete form,

Ψ⁽⁰⁾(1)＝Ψ⁽⁰⁾(1)(38)Ψ⁽⁰⁾ (1) = Ψ⁽⁰⁾ (1) (38)

其中Ψ⁽¹⁾(k)和Ψ⁽¹⁾(1)，将公式(36)和公式(38)代入公式(30)求得；Where Ψ⁽¹⁾ (k) and Ψ⁽¹⁾ (1) are obtained by substituting formula (36) and formula (38) into formula (30);

则得到预测模型为：Then the prediction model is obtained as:

其中k＝2,3,…,m。where k=2,3,...,m.

对于有杆泵抽油井井下故障的多变量灰色预测模型中所采用的一段连续时间内的样本，连续时间的单位可以为小时或天，所述样本的数量为50－200个，以提高预测模型的计算效率和准确度。本实施例采集实际生产中某口有杆泵抽油井在50天内的50幅示功图作为样本，首先将地面示功图转化为井下泵功图；然后分别提取50幅井下泵功图的14个曲线矩特征作为特征向量；再根据公式(23)—公式(40)进行预测模型的计算，得到的结果如图5－图18所示。由图5－图18，采用多变量灰色模型分别对提取的井下泵功图的14个曲线矩特征向量进行预测，预测值都能达到满意的效果。For the samples of a period of continuous time used in the multivariate gray prediction model of the downhole failure of the pumped oil well with rods, the unit of the continuous time can be hour or day, and the number of the samples is 50-200, so as to improve the prediction model computational efficiency and accuracy. In this embodiment, 50 dynamometer diagrams of a rod pumped oil well in actual production were collected as samples within 50 days. First, the surface dynamometer diagrams were converted into downhole pump dynamism diagrams; Curve moment features are used as feature vectors; then the prediction model is calculated according to formula (23) - formula (40), and the results are shown in Fig. 5-Fig. 18. From Fig. 5 to Fig. 18, the 14 curve-moment feature vectors of the extracted downhole pump power map are respectively predicted by using the multivariate gray model, and the predicted values can all achieve satisfactory results.

采用上述50个样本通过多变量灰色模型预测第51个样本，得到其14个曲线矩特征向量值如表2所示。The above 50 samples are used to predict the 51st sample through the multivariate gray model, and the 14 curve moment eigenvector values are obtained as shown in Table 2.

表2预测样本的曲线矩特征向量Table 2 Curve moment eigenvectors of predicted samples

上冲程部分upstroke partψ₁ψ₁ψ₂ψ₂ψ₃ψ₃ψ₄ψ₄ψ₅ψ₅ψ₆ψ₆ψ₇ψ₇曲线矩特征向量值curve moment eigenvector value1.18701.18700.52460.52461.48331.48330.91480.91481.09451.09450.35790.35791.00451.0045下冲程部分downstroke partψ₈ψ₈ψ₉ψ₉ψ₁₀ψ₁₀ψ₁₁ψ₁₁ψ₁₂ψ₁₂ψ₁₃ψ₁₃ψ₁₄ψ₁₄曲线矩特征向量值curve moment eigenvector value0.96990.96990.61870.61873.01283.01281.72861.72861.98721.98721.50461.50460.89670.8967

5、最后，判断所预测的样本属于哪类故障类型。假设有杆泵抽油井井下故障的类型由F_M表示，其中M＝1,2,3,…。可以通过已有的示功图信息建立每一种故障类型的标准集，已有的信息由已知道故障类型的示功图得到，用来建立每一种故障类型的标准集的示功图的数量大于2个。即对已确定故障类型的一定数量的示功图通过将地面示功图转化为井下泵功图和分别提取其14个曲线矩特征向量，得到每一种故障类型中每一个曲线矩特征向量的取值区间。所得到的取值区间由表示，p＝1,2,…,14，其中表示第F_M种故障类型的第p个曲线矩特征向量的下限值，表示第F_M种故障类型的第p个曲线矩特征向量的上限值。由已有的信息建立每一种故障类型的标准集。5. Finally, determine which type of fault the predicted sample belongs to. Assume that the downhole failure type of the rod pumped well is represented by F_M , where M=1, 2, 3, . . . . The standard set of each fault type can be established through the existing dynamometer information, and the existing information is obtained from the dynamometer diagram of the known fault type, which is used to establish the standard set of each fault type. The quantity is greater than 2. That is, for a certain number of dynamometer diagrams with identified fault types, by converting the surface dynamometer diagrams into downhole pump dynamometer diagrams and extracting their 14 curve moment eigenvectors, the eigenvectors of each curve moment eigenvector in each fault type are obtained. range of values. The resulting range of values is given by means, p=1,2,…,14, where Represents the lower limit value of the pth curve moment eigenvector of the F_Mth fault type, Indicates the upper limit value of the pth curve moment eigenvector of the F_Mth fault type. A set of criteria for each fault type is established from the available information.

本发明中有杆泵抽油井井下故障类型有以下9种：“正常”、“气体影响”、“供液不足”、“抽油杆断落”、“游动阀漏失”、“固定阀漏失”、“泵上碰”、“泵下碰”、“油井出砂”。所建立的各故障类型的标准集如表3所示。In the present invention, there are the following 9 types of downhole faults in rod pumped wells: "normal", "gas influence", "insufficient fluid supply", "sucker rod broken", "swimming valve leakage", "fixed valve leakage" ", "Pump up bump", "Pump down bump", "Oil well sand production". The established standard set of each fault type is shown in Table 3.

表3各故障类型的标准集Table 3 Standard set of each fault type

ψ₁ψ₁ψ₂ψ₂ψ₃ψ₃ψ₄ψ₄ψ₅ψ₅ψ₆ψ₆ψ₇ψ₇正常normal[0.05,0.45][0.05,0.45][0.87,2.45][0.87,2.45][0.76,2.49][0.76,2.49][3.14,5.78][3.14,5.78][0.03,0.17][0.03,0.17][0.66,2.06][0.66,2.06][0.66,2.24][0.66,2.24]气体影响gas effect[0.06,0.58][0.06,0.58][1.13,1.44][1.13,1.44][1.23,1.94][1.23,1.94][2.42,2.71][2.42,2.71][0.12,1.08][0.12,1.08][1.04,2.19][1.04,2.19][1.12,3.16][1.12,3.16]供液不足Insufficient fluid supply[0.22,0.36][0.22,0.36][0.79,2.88][0.79,2.88][0.8,3.16][0.8,3.16][3.57,5.91][3.57,5.91][1.31,1.73][1.31,1.73][2.8,5.58][2.8,5.58][1.47,2.86][1.47,2.86]抽油杆断落sucker rod broken[0.27,0.39][0.27,0.39][0.7,0.91][0.7,0.91][0.78,0.94][0.78,0.94][3.1,3.35][3.1,3.35][0.04,0.11][0.04,0.11][1.97,2.65][1.97,2.65][3.75,5.19][3.75,5.19]游动阀漏失floating valve leakage[0.05,0.68][0.05,0.68][1.14,3.02][1.14,3.02][1.17,3.26][1.17,3.26][3.55,5.65][3.55,5.65][0.09,0.2][0.09,0.2][0.64,1.1][0.64,1.1][0.67,1.26][0.67,1.26]固定阀漏失fixed valve leakage[0.06,0.64][0.06,0.64][1.16,3.08][1.16,3.08][1.16,3.45][1.16,3.45][0.04,0.17][0.04,0.17][0.64,1.77][0.64,1.77][1.27,3.33][1.27,3.33][3.96,5.68][3.96,5.68]泵上碰bump on the pump[0.94,3.11][0.94,3.11][0.94,3.98][0.94,3.98][0.94,4.19][0.94,4.19][0.03,0.47][0.03,0.47][0.74,2.3][0.74,2.3][0.76,2.41][0.76,2.41][2.97,5.34][2.97,5.34]泵下碰pump under bump[0.02,0.06][0.02,0.06][0.74,1.28][0.74,1.28][1.47,2.56][1.47,2.56][0.77,1.28][0.77,1.28][3.65,5.51][3.65,5.51][0.73,1.99][0.73,1.99][1.46,4.07][1.46,4.07]油井出砂oil well sand[0.08,0.45][0.08,0.45][0.29,1.14][0.29,1.14][0.3,1.16][0.3,1.16][0.02,0.14][0.02,0.14][0.34,2.3][0.34,2.3][0.36,2.34][0.36,2.34][0.53,1.92][0.53,1.92]ψ₈ψ₈ψ₉ψ₉ψ₁₀ψ₁₀ψ₁₁ψ₁₁ψ₁₂ψ₁₂ψ₁₃ψ₁₃ψ₁₄ψ₁₄正常normal[3.91,5.66][3.91,5.66][0.01,1.09][0.01,1.09][0.52,2.62][0.52,2.62][0.53,2.69][0.53,2.69][0.65,1.03][0.65,1.03][1.31,2.11][1.31,2.11][4.5,5.06][4.5,5.06]气体影响gas effect[2.1,3.98][2.1,3.98][0.56,0.9][0.56,0.9][2.56,3.99][2.56,3.99][2.41,2.83][2.41,2.83][0.47,0.67][0.47,0.67][1.5,2.42][1.5,2.42][1.99,2.49][1.99,2.49]供液不足Insufficient fluid supply[0.01,0.19][0.01,0.19][0.67,2.56][0.67,2.56][0.7,2.74][0.7,2.74][0.66,3.01][0.66,3.01][1.35,5.93][1.35,5.93][0.71,2.97][0.71,2.97][0.02,0.18][0.02,0.18]抽油杆断落sucker rod broken[4.16,5.93][4.16,5.93][0.22,0.38][0.22,0.38][0.55,0.89][0.55,0.89][0.58,0.91][0.58,0.91][0.08,0.09][0.08,0.09][1.69,1.99][1.69,1.99][0.66,1.07][0.66,1.07]游动阀漏失floating valve leakage[1.5,2.67][1.5,2.67][3.02,8.12][3.02,8.12][1.52,3.98][1.52,3.98][0,0.23][0,0.23][0.64,2.46][0.64,2.46][0.64,2.6][0.64,2.6][2.93,4.94][2.93,4.94]固定阀漏失fixed valve leakage[0.09,0.84][0.09,0.84][0.48,1.55][0.48,1.55][0.49,1.56][0.49,1.56][0.07,0.17][0.07,0.17][1.29,2.64][1.29,2.64][1.3,2.68][1.3,2.68][3.82,6.37][3.82,6.37]

泵上碰bump on the pump[1.38,2.77][1.38,2.77][2.77,5.66][2.77,5.66][5.87,7.29][5.87,7.29][0.64,1.16][0.64,1.16][1.3,2.33][1.3,2.33][0.65,1.17][0.65,1.17][4.28,5.65][4.28,5.65]泵下碰pump under bump[4.58,5.81][4.58,5.81][3.17,4.33][3.17,4.33][1.27,3.89][1.27,3.89][1.27,4.09][1.27,4.09][2.54,8.08][2.54,8.08][1.27,4.21][1.27,4.21][6.8,9.38][6.8,9.38]油井出砂oil well sand[1.06,3.97][1.06,3.97][0.53,2.08][0.53,2.08][0.4,1.76][0.4,1.76][0.41,1.8][0.41,1.8][0.81,3.57][0.81,3.57][0.41,1.81][0.41,1.81][0.53,2][0.53,2]

多变量灰色模型所预测的第51个样本的曲线矩特征向量值由表示，那么预测样本的每一个曲线矩特征向量值与每一种故障类型中相应的曲线矩特征向量值的距离可以由下式进行计算，The curve moment eigenvector value of the 51st sample predicted by the multivariate gray model is given by , then the distance between each curve moment eigenvector value of the predicted sample and the corresponding curve moment eigenvector value in each fault type can be calculated by the following formula,

根据公式(41)—公式(43)，计算预测样本与每一种故障类型的灰关联度，得到的结果如表4所示。According to the formula (41) - formula (43), calculate the gray correlation degree between the predicted sample and each fault type, and the results are shown in Table 4.

表4预测样本与各故障类型的灰关联度Table 4 Gray correlation degree between prediction sample and each fault type

由表4，预测样本与“气体影响”故障类型的灰关联度最大，认为属于“气体影响”故障类型。From Table 4, the gray correlation degree between the prediction sample and the "gas impact" fault type is the largest, and it is considered to belong to the "gas impact" fault type.

以上仅为本发明的具体实施例而已，并不用于限制本发明，对于本领域的技术人员来说，本发明可以有各种更改和变化。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 are only specific embodiments of the present invention, and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and changes. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.