Academic Journal of Science and Technology 
ISSN: 2771-3032 | Vol. 14, No. 1, 2025 

 

320 

Study	on	Oil	Production	Conditions	Recognition	Based	
on	Standard	Error	Algorithm	
Xinhao Yan1, * 

1 School of Mechanical Engineering, Xi’an Shiyou University, Xi’an 710000, China 
* Corresponding author: Xinhao Yan (Email: 13137882873@163.com) 

 

Abstract: The dynamometer card contains plenty of information features of equipment status, technology, and conditions in 
oil production. It is of great significance to identify such important information accurately, rapidly, and conveniently for safe and 
reliable operation of the pumping unit, improving oil production technology, and real-time monitoring of oil production 
performance. A new method was presented to recognize oil production equipment conditions based on a standard error algorithm 
and also develop a mathematical model of a standard error matching algorithm. An argument about matching algorithms 
correlating to the degree of difference between graphics is first proposed. The reliability of the standard error matching algorithm 
and classic matching algorithm are compared in detail. An intensive study shows that the standard error matching algorithm 
highly correlates to the degree of difference between graphics, and the reliability of the standard error algorithm is better than 
that of the classical matching algorithms. A large number of dynamometer card recognitions have shown that standard error-
matching algorithm has a fairly high reliability. Furthermore, this algorithm has terrific recognition accuracy especially to those 
dynamometer cards with minute differences. 

Keywords: Standard error; oil production conditions; dynamometer cards; recognition technique. 
 

1. Introduction 
At present, indicator diagram diagnosis and identification 

technology has been developed rapidly in China and has 
become the most important practical tool for oil well 
condition diagnosis. China currently has hundreds of 
thousands of pumping wells. In recent years, the oilfield has 
been committed to the research of oil well condition diagnosis 
technology. Because the indicator diagram contains 
multidimensional information characteristics of oil 
production conditions, the establishment of a sample 
indicator diagram database of oil well conditions is the basis 
of oil well conditions diagnosis technology. Through the real-
time acquisition of the pumping unit indicator diagram, and 
the comparison and identification with the sample database, 
the working condition of the oil production system is 
determined, to realize the real-time monitoring and 
production guidance of the oil well working condition. 

The key to oil well condition diagnosis is the accurate 
identification of indicator diagrams. At present, the main 
methods used in indicator diagram recognition are the grid 
method, gray matrix method, vector method, artificial neural 
network method, etc. The core of the above method is feature 
extraction, which is to extract the relevant feature information 
from the two-dimensional array of indicator diagrams of 
different scenes and eliminate the irrelevant information. The 
second is to establish a classifier, which is a kind of matching 
algorithm to identify the working conditions. The key to 
indicator diagram recognition is how to extract its most 
representative features and what kind of classifier to use for 
type recognition. 

Both the grid method and gray matrix extract the 
information of the indicator diagram boundary through the 
characteristic matrix, which is either true (1) or false (0) [1, 
2]. Due to the fluctuation of the contour line of the indicator 
diagram, there is a possibility that different curves will have 
great differences when passing through the same grid point. 

As shown in Fig. 1 (a) and (b), both A and B curves pass 
through the same grid, and the value is 1. However, the local 
difference between a curve and a B curve is very large, so the 
extracted feature matrix cannot accurately reflect the local 
features of the indicator diagram. Even if the classifier 
algorithm is very accurate, it is still inaccurate. The artificial 
neural network method [3-5] is also based on the grid method 
and gray matrix to extract feature information, so it still has 
the defects of the grid method and gray matrix. These three 
methods belong to feature recognition, they are only 
applicable to the classification and recognition of graphics, 
and cannot realize the accurate recognition of graphics. The 
vector method belongs to pattern recognition, its 
characteristic matrix is the quotient of matrix elements and 
matrix modulus, and its matching value is the cosine value of 
the vector angle. Both the grid method and gray matrix extract 
the information of the indicator diagram boundary through the 
characteristic matrix, which is either true (1) or false (0) [1, 
2]. Due to the fluctuation of the contour line of the indicator 
diagram, there is a possibility that different curves will have 
great differences when passing through the same grid point. 
As shown in Fig. 1 (a) and (b), both A and B curves pass 
through the same grid, and the value is 1. However, the local 
difference between the A curve and the B curve is very large, 
so the extracted feature matrix cannot accurately reflect the 
local features of the indicator diagram. Even if the classifier 
algorithm is very accurate, it is still inaccurate. The artificial 
neural network method [3-5] is also based on the grid method 
and gray matrix to extract feature information, so it still has 
the defects of the grid method and gray matrix. These three 
methods belong to feature recognition, they are only 
applicable to the classification and recognition of graphics, 
and cannot realize the accurate recognition of graphics. The 
vector method belongs to pattern recognition, its 
characteristic matrix is the quotient of matrix elements and 
matrix modulus, and its matching value is the cosine value of 
the vector angle. 



 

321 

 
Figure 1. Difference diagram of dynamometer card 

contour through the grid 
 
With the continuous accumulation of the historical data of 

the indicator diagram of the oilfield, the types of oil 
production conditions that have been identified are more and 
more accurate and refined. The fine classification of indicator 
diagrams of the same working condition type can reach 
several or even dozens. The accuracy of the final condition-
type diagnosis results depends heavily on the quality of the 
contour extraction of the indicator diagram, Or the low 
correlation between the matching algorithm and the degree of 
graphic difference is low. Therefore, they cannot meet the 
requirements of fine identification of modern indicator 
diagrams. 

This paper proposes a matching algorithm based on the 
standard error (SE) algorithm to realize the matching between 
the indicator diagram to be identified and the sample indicator 
diagram. The recognition algorithm based on Se theory can 
also be applied to the accurate recognition of two-dimensional 
graphics. At present, there are many algorithms to measure 
the similarity of graphics. The main algorithms are cross-
correlation algorithm [6] (COR), mean absolute difference 
algorithm (MAD) [6,7], mean square deviation algorithm 
(MSD) [6,8,9], camper distance algorithm [10], Hausdorff 
algorithm [8,11], normalized product correlation algorithm 
(NPROD) [12], which are the most widely used and classic 
graphics recognition algorithms. The reliability of these 
algorithms is studied in detail. 

2. Working Condition Identification of 
Indicator Diagram Based on 
Standard Error Algorithm 

2.1. Isometric displacement and dimensionless 
calibration of the indicator diagram 

The indicator diagram data is a discrete two-dimensional 
array [Si, Wi] (i=1, 2,...), Si is the displacement, and Wi is the 
load. Since the displacement value points of the indicator 
diagram are different, it is necessary to carry out Si coordinate 
equivalent calibration for the indicator diagram to be 
identified and the sample indicator diagram. Our value can be 
obtained by the Lagrange algorithm.  

The geometric contour shape of a figure is the relevant 
element to be extracted, while the size of the actual [Si, Wi] 
value is irrelevant to the figure recognition. Therefore, the 
graph must be dimensionless calibrated. 

 

𝑌

𝑋
              (1) 

 

In equation (1), Wmax is the maximum load on the 
dynamometer diagram, N. Wmin is the minimum load on the 
dynamometer diagram, N. Smax is the maximum displacement, 

m. Smin is the minimum displacement, m。 

2.2. Classifier Algorithm——Standard Error 
In a dimensionless coordinate system, the similarity 

between two geometric shapes is characterized by the degree 
of convergence of the same displacement point. The indicator 
diagram consists of a dataset, with the calibration sample 
indicator diagram dataset being the true value and the 
identification indicator diagram dataset being the measured 
value. In this way, the similarity between the indicator 
diagram to be identified and the sample indicator diagram can 
be defined as the degree to which the measured value 
approaches the true value, that is, the deviation between the 
measured value and the true value, which is called the 
standard error (SE). SE is very sensitive to large or small 
errors in a set of measurement values, so, SE can effectively 
reflect the degree to which the identified indicator diagram 
dataset approaches the sample indicator diagram dataset. 

The SE of the indicator diagram dataset A (yA, xA) is to be 
identified and the sample indicator diagram dataset B (yB, xB) 
is 

 
 

𝑑 𝐴, 𝐵
1
𝑁

  𝑦 𝑥 𝑦 𝑥  
 

(2) 

 
SE matching value range: 0 ≤ d ≤ 1. Two geometric shapes 

that are completely similar have d=0; The closer the 
geometric shape, the smaller the SE value of the shape. 0 
similarity is an equivalent scale used to measure the degree of 
similarity between two geometric shapes. The similarity of 
completely similar shapes is 1, and the more similar the 
shapes are, the higher their similarity. Define the similarity 
between two graphics as 

 
𝑅 1 𝑑                   (3) 

 
By performing similarity recognition between the 

comparison image and the reference image, the degree of 
similarity of the graphics can be accurately determined based 
on the similarity level. 

3. Research on the Correlation 
Between Similarity Matching 
Algorithm and Graphic Difference 
Degree 

At present, the main similarity-matching algorithm models 
based on graphics include Vector, COR, MAD, MSD, 
Comberra, Hausdorff, and NProd algorithms. These 
algorithms are classic algorithms for determining whether 
two shapes are similar. However, there is currently no report 
in domestic and foreign literature on whether these algorithms 
can accurately determine the similarity of graphics, or which 
algorithm can more accurately determine the degree of 
similarity of graphics. The argument that there is a correlation 
between the similarity-matching calculation model and the 
degree of geometric difference has been proposed for the first 
time. The size of the matching value should be able to reflect 
the degree of difference between two geometric shapes, that 
is, the greater the difference between two geometric shapes, 
the greater the difference in their matching values should also 
be, and they should have monotonicity. Therefore, the 
correlation between the similarity matching algorithm and the 



 

322 

degree of graphical difference between the identified 
indicator diagram A and the sample indicator diagram dataset 
B based on dimensionless calibration can be expressed as 
follows: the change in matching value Δ d has the same trend 
as the degree of graphical difference Δ R. 

 
Δ𝑑 𝐴, 𝐵 ∝ Δ𝑅 𝐴, 𝐵                (4) 

 
Figure 2 shows a sample dynamometer diagram B. 

Applying fluctuations locally to this sample diagram can 
obtain the dynamometer diagram A to be recognized, as 
shown in Figure 3. By gradually increasing the fluctuation 
points of Dataset A, the difference between Dataset A and 
Dataset B is increased. Apply Vector, COR, MAD, MSD, 
Comberra, Hausdorff, NProd, and SE algorithms to study the 
changing trends of matching values. 

 

 
Figure 2. Sample dynamometer card B 

 

 
Figure 3. Waiting for recognizing dynamometer card A 

3.1. Vector Algorithm 
The indicator diagram to be identified and the sample 

indicator diagram are represented by 2n dimensional vectors, 
and their matching algorithm is the dot product of the two, 
which is the cosine value of the vector angle. 

 

𝑅 𝐴, 𝐵 𝐴 ⋅ 𝐵               (5) 

 

3.2. COR Algorithm 
Cross-correlation algorithm. 

𝑅 𝐴, 𝐵
∑  

∑   ∑  

      (6) 

 

3.3. MAD Algorithm 
Mean absolute difference algorithm. 
 

 
𝑅 𝐴, 𝐵 1

1
𝑁

  |𝑦 𝑥 𝑦 𝑥 | (7) 

 

3.4. MSD Algorithm 
Mean square deviation algorithm. 
 

 
𝑅 𝐴, 𝐵 1

1
𝑁

  𝑦 𝑥 𝑦 𝑥  (8) 

 

3.5. Camberra Algorithm 
The Camberra distance between the identified indicator 

vector and the sample indicator vector can be used as a 
distance measure between the two feature vectors. 

 
 𝑅 𝐴, 𝐵 1

∑   |𝑦 𝑥 𝑦 𝑥 |
∑   |𝑦 𝑥 𝑦 𝑥 |

 (9) 

 

3.6. SE Algorithm 
Standard error algorithm. 

 
 

𝑅 𝐴, 𝐵 1
1
𝑁

  𝑦 𝑥 𝑦 𝑥  (10) 

 

3.7. Hausdorff Algorithm 
The Hausdorff distance is defined by a general 

mathematical formula, which describes a measure of the 
similarity between two sets of points. It is a definition of the 
distance between two sets of points. 

 
𝑅 𝑦 , 𝑦 1 𝑚𝑎𝑥 𝑑 𝑦 , 𝑦 , 𝑑 𝑦 , 𝑦
𝑑 maxmin ∈ ∈ ‖𝑦 𝑦 ‖
𝑑 maximin ∈ ∈ ‖𝑦 𝑦 ‖

(11) 

 

3.8. NProd Algorithm 
Normalized product correlation algorithm. 

𝑅 𝐴, 𝐵  
 

∑  

∑   ∑  
        (12) 

 

In equations (5) to (12), 𝑦 , 𝑦   The mean values of 
datasets A and B respectively; N 1, 2, 3..., where N is the 
number of fluctuating points; ‖ ⋅ ‖is the distance norm of 
datasets A and B e.g., L2 or Euclidean distance . 



 

323 

According to the above algorithm, a similarity curve can be 
drawn. The relationship curve between similarity and 

fluctuation points of the above algorithm is shown in Figure 4. 
Table 1 shows the similarity values of the above algorithm. 

 

 

Figure 4. Relation curves of similarity and fluctuation points indifferent algorithms 

 

Table 1. Similarity value of different algorithms 

 
 

As shown in Figure 4 and Table 1, without applying point 
fluctuations, datasets A and B are completely similar, The 
similarity of Vector, MAD, MSD, Camberra, SE, Hausdorff, 
and NProd algorithms is all 1, while the similarity of COR 
algorithm is an uncertain value. As the number of fluctuation 
points in dataset A gradually increases, it indicates that the 
degree of difference between the identified indicator diagram 
A and the sample indicator diagram B will gradually increase, 
that is, the degree of dissimilarity between A and B will 
increase. Research has shown that.  

(1) As the degree of difference between datasets A and B 
gradually increases, The similarity changes of Vector, COR, 
MSD, and NProd are very small, and the difference in 
similarity cannot reflect the degree of difference between the 
identified indicator diagram A and the sample indicator 
diagram B. This indicates that these four algorithms have low 
sensitivity to local fluctuations in the graph and low reliability. 
When the fluctuation of the indicator diagram A to be 
identified is significant, it clearly indicates that the indicator 
diagram A to be identified is not similar to the sample 
indicator diagram B. However, the matching values of Vector, 
COR, MSD, and NProd are still equal to 0.977, 0.987, 0.957, 
and 0.933, respectively. In actual discrimination, this may 
lead to incorrect identification.  

(2) As the number of fluctuation points increases, The 
Hausdorff similarity value no longer changes, as shown in 
Figure 4 and Table 1. This is because the degree of difference 

between the two datasets A and B is determined by the 
Hausdorff distance of the least similar point. Once the 
Hausdorff distance of the newly added wave point is not 
greater than the distance of that point, its similarity will no 
longer change. Therefore, The Hausdorff algorithm is not 
suitable for discriminating overall similarity between two 
datasets A and B.  

(3) As the degree of difference between datasets A and B 
gradually increases, The similarity changes between MAD 
and Camberra basically reflect the degree of difference 
between datasets A and B.  

(4) The similarity change of SE can well reflect the degree 
of difference between datasets A and B. This algorithm is 
highly sensitive to local fluctuations in graphics. Figure 4 and 
Table 1 indicate that The reliability of the SE algorithm is the 
highest among all matching algorithms. Figure 5 shows the 
displacement load dynamometer diagram of the oil well, the 
sample dynamometer diagram NWC is the dynamometer 
diagram under standard operating conditions of the oil well, 
and the to-be-identified dynamometer diagram AWC1-7 is the 
dynamometer diagram under non-standard operating 
conditions of the oil well. The difference between AWC1-7 
and NWC gradually increases. Apply Vector, MSD, COR, 
MAD, Camberra, Hausdorff, NProd, and SE algorithms to 
perform similarity recognition on NWC and AWC1-7. The 
similarity relationship curve between NWC and AWC1-7 of 
the above algorithm is shown in Figure 6. Table 2 shows the 



 

324 

similarity between NWC and AWC1-7.  
As shown in Figure 6 and Table 2, when the difference 

between the sample dynamometer and the dynamometer to be 
identified gradually increases, we can draw the following 
conclusions: (1) The similarity changes of Vector, MSD, and 
Hausdorff are small, which is consistent with the conclusion 
of point fluctuation, indicating that the reliability of the 
algorithm is not high. (2) The similarity between COR and 
NProd varies greatly, which is inconsistent with the results of 
fluctuating application points, indicating that the reliability of 

these two algorithms is unstable, and the similarity between 
COR shows non-monotonic changes. (3) The conclusion 
regarding the similarity changes and application point 
fluctuations between MAD and Camberra is consistent. (4) 
The similarity of SE changes the most and is highly consistent 
with the fluctuation of the application point. Therefore, The 
SE algorithm has high reliability. Figure 6 and Table 2 
indicate that The reliability of the SE algorithm is the highest 
among all algorithms. 

 

 
Figure 5. Displacement-load dynamometer card of oil well 

 

 
Figure 6. The similarity curves of NWC and AWC1-7 

 

4. Application Examples 
Nearly 10000 dynamometer diagrams were collected from 

more than 1000 wells in the Chuankou Oil Production Plant 
of Yanchang Oilfield, and nearly 300 suspected faulty pump 
dynamometer diagrams were selected. Table 3 shows some of 
the main fault types selected. The SE algorithm was used to 
perform similarity recognition between the indicator diagram 

to be recognized and the established sample indicator diagram 
database. The recognition results are shown in Table 3, and 
the recognition success rate reached 100%. This algorithm is 
particularly suitable for identifying indicator diagrams with 
slight differences. Table 3 shows the results of identifying the 
standard error of oil production conditions. 

 



 

325 

Table 2. The similarity values of NWC and AWC1-7 

 

 

Table 3. Results of production condition recognition by SE algorithm (%) 
 

Failure Mode 
Similarity 

1 2 3 4 5 6 7 8 9 10 11 12 
1. Fixed Valve 

Leakage 
99.9 76.3 79.1 77.6 80.5 79.3 80.4 82.8 77.1 76.8 82.1 53.1 

2. Moving Valve 
Leakage 

82.9 99.7 73.1 91.0 75.1 86.6 69.9 80.1 82.1 73.3 83.0 57.2 

3. Tubing 
Breakage 

78.6 72.6 97.8 72.4 82.5 72.7 59.3 79.6 71.8 76.9 74.4 59.2 

4. Sucker Rod 
Upper Breakage 

77.7 91.0 72.9 98.6 71.8 86.3 71.9 76.3 84.0 72.3 79.8 59.0 

5. Tubing Bending 80.2 74.9 82.6 71.7 99.2 75.1 59.0 84.6 71.6 78.7 76.9 56.5 
6. Sand Lock 79.1 80.8 74.3 85.2 75.5 96.5 74.2 81.5 85.8 78.1 86.2 61.7 

7. Gas 
Interference 

61.9 70.1 59.9 72.2 59.3 74.4 98.4 63.3 77.9 67.6 69.1 66.1 

8. Gearbox Wear 83 78 81 77 85 82 64 98 79 86 83 57.9 
9. Belt Slippage 76.7 81.8 72.1 83.9 71.7 85.8 78.2 77.0 98.8 76.3 80.0 65.6 

10. Gas Lock 73.8 71.2 74.7 70.9 75.4 75.6 68.6 79.7 75.4 95.4 79.7 61.5 
11. Subsurface 
Pump Collision 

82.1 82.9 74.9 79.8 77.1 85.8 68.8 83.4 80.0 81.7 99.1 62.6 

12. Stuck Pump 52.9 57.1 59.1 58.9 56.2 60.8 65.5 56.5 65.2 61.9 62.2 99.2 
 

5. Conclusions 
For the first time, the SE algorithm was proposed to 

achieve accurate recognition of oil well conditions, and the 
algorithm was compared and analyzed with existing 
similarity recognition matching algorithms. The argument 
that similarity matching algorithms have a great correlation 
with the degree of graphic differences was also put forward 
for the first time, and the degree of correlation determines the 
superiority or inferiority of the algorithm. Algorithms with 
high correlation have high sensitivity to recognizing graphics 
with slight differences, indicating high accuracy in 
recognition. On the contrary, algorithms with low correlation 
have low sensitivity to recognizing graphics with small 
differences, that is, the accuracy of recognition is low. Figures 
4, 6, Table 1, and Table 2 fully demonstrate this argument. 
The research results indicate that there is a high degree of 
correlation between the SE algorithm and the graphics, and 
the reliability of this algorithm is the highest among all 
algorithms. The application of this algorithm reduces the 
probability of misjudging similar working conditions and 
improves the accuracy and precision of recognition. 

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