CN112765885A - Crank motion law simulation model based on actually measured suspension point displacement - Google Patents
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Abstract
The invention provides a crank motion law simulation model based on actually measured suspension point displacement, which is used for analyzing the motion law of a crank rocker reversing mechanism of an oil pumping unit and establishing a suspension point theoretical displacement calculation model; on the basis of the fluctuation of the crank rotating speed, a Fourier series term is added on the basis of the uniform rotating angular speed of the crank, and an actual rotating angular speed calculation model and a crank rotating angle calculation model of the crank are established; taking the actual rotating angular speed of the crank as a design variable, and taking the minimum error square sum of the theoretical displacement of the suspension point and the actual measured displacement of the suspension point as an optimization objective function to establish an optimal mathematical model of the actual rotating angular speed of the crank; and solving the optimized objective function by using an optimization algorithm so as to obtain the actual rotation angular speed of the crank. According to the method, the fitting degree of the theoretical displacement of the suspension point and the actually measured displacement of the suspension point is effectively improved by establishing the simulation model, and the precision of the crank torque generated in the process of inverting the suspension point load based on the actually measured electrical parameters and the precision of the inversion result suspension point load are improved.
Description
Technical Field
The invention relates to the field of motion law simulation of pumping units, in particular to a crank motion law simulation model based on actually measured suspension point displacement.
Background
At present, oil field oil extraction equipment is mainly a pumping unit, a dynamometer diagram contains a lot of information of oil well working conditions, and an actually measured dynamometer diagram is obtained through a load sensor and a displacement sensor, so that the working conditions of the pumping unit are analyzed. The method is convenient and simple, but the problems of large error, low precision and the like exist in the acquired actually-measured indicator diagram data due to the fact that the sensor is easy to age and short in service life, the acquisition and analysis of working condition information are affected, and accurate identification and diagnosis of faults generated in the operation process of the oil pumping unit cannot be achieved.
The method is low in cost and high in precision, but the rotation angular speeds of the motor and the crank are also fluctuated due to the fact that the suspension point load of the pumping unit, the net torque of a crankshaft and the load torque of the motor are greatly fluctuated. The fluctuation of the crank rotation angular speed not only affects the motion law of the suspension point of the pumping unit, but also affects the inertia torque of the system, so that the accurate acquisition of the crank rotation angular speed is a key factor for improving the fitting degree of the theoretical displacement of the suspension point and the actually measured displacement of the suspension point.
Disclosure of Invention
The invention aims to accurately establish a crank motion law simulation model based on actually measured suspension point displacement and improve the fitting degree of suspension point theoretical displacement and the actually measured suspension point displacement.
Firstly, analyzing the motion law of a crank rocker reversing mechanism of the oil pumping unit, and establishing a suspension point theoretical displacement calculation model; on the basis of the fluctuation of the crank rotating speed, a Fourier series term is added on the basis of the uniform rotating angular speed of the crank, and an actual rotating angular speed calculation model and a crank rotating angle calculation model of the crank are established; taking the actual rotating angular speed of the crank as a design variable, and taking the minimum error square sum of the theoretical displacement of the suspension point and the actual measured displacement of the suspension point as an optimization objective function to establish an optimal mathematical model of the actual rotating angular speed of the crank; and solving the optimized objective function by using an optimization algorithm so as to obtain the actual rotation angular speed of the crank. The target of accurately acquiring the actual rotating angular speed of the crank is achieved, and the fitting degree of the theoretical displacement of the suspension point and the actually measured displacement of the suspension point is improved.
In order to achieve the above object, the present invention provides a simulation model for establishing a crank motion law based on measured suspension point displacement, which comprises the following steps:
xt(θ)＝(ψmax-ψ)*A
in the formula, xt(theta) is the theoretical displacement of the suspension point; psi is the included angle of the rear arm of the walking beam relative to the base rod; psimaxThe maximum included angle between the rear arm of the walking beam and the base rod is formed; a is the length of the front arm of the walking beam, and the unit is m;
wherein
Wherein w (t) is the actual rotational angular velocity of the crank, and has the unit of rad/s; omega0The crank rotates at a constant angular speed with the unit of rad/s; k is Fourier series truncation series; t is a time difference with the unit of s; a isiFourier coefficients to be solved; biFourier coefficients to be solved; n is actually measured number of impact of suspension point in unit of min-1；
Determining a functional expression of the instantaneous crank angle according to the actual crank rotation angular speed:
in the formula, F is an optimization objective function of the actual rotation angular speed of the crank, and the obtained value is the actual rotation angular speed omega (t) of the crank; a is1、a2、…、aK、b1、b2、…bKAre all Fourier coefficients; n is the number of time nodes; x is the number oftiIs the theoretical displacement of the suspension point, and the unit is m; x is the number ofmiMeasured displacement of the suspension point is measured in m;
step 4, using F (a)1,a2,…,aK,b1,b2,…,bK) For the objective function, an optimization algorithm is applied to solve the Fourier coefficient a1、a2、…、aKAnd b1、b2、…bKAnd Fourier coefficient a1、a2、…、aKAnd b1、b2、…bKSubstituting the actual rotation angular speed of the crank into the optimization objective function in the step 3 to obtain the actual rotation of the crankAngular velocity ω (t);
the step based on the optimization algorithm comprises the following sub-steps:
step 41, determining learning factor c1And c2The number M of particle groups;
step 42, generating M particles x from the logistic regression analysis mapiAnd velocity v thereofiWhere i is 1, …, N, and finally forming the initial population P of particles0；
Step 43, producing immune memory particles: calculating the adaptive value of the particles in the current particle group P and judging whether the algorithm meets an end condition, if so, ending and outputting a result, otherwise, continuing to operate;
step 44, updating the local and global optimal solutions, and updating the particle position and velocity according to the following formula;
xi,j(t+1)＝xi,j(t)+vi,j(t+1),j＝1…d
vi,j(t+1)＝w·vi,j(t)+c1r1[pi,j-xi,j(t)]+c2r2[pg,j-xi,j(t)]
wherein w is the inertial weight; c. C1、c2Is a learning factor; r is1、r2Is [0,1 ]]The random number of (2); t is the iteration number in the searching process; j is the spatial dimension; p is a radical ofi,jExpressed as the optimal position of the ith particle in the j dimension at the t iteration; p is a radical ofg,jDenoted as the optimal position of the population in the j dimension at the t-th iteration.
Step 45, generating N new particles by the logistic mapping;
step 46, concentration-based particle selection: the percentage of similar antibodies in the population is used to calculate the probability of producing N + M new particles (antibodies), and N particles (antibodies) are selected according to the probability to form a population P of particles (antibodies), which is then transferred to step 43.
Preferably, in said step 1, #maxThe calculation process of (2) is as follows:
when the walking beam is at the two extreme positions of the bottom dead center and the top dead center, the maximum included angle psi between the rear arm of the walking beam and the base rodmaxIs composed of
And analyzing the motion of the crank rocker reversing mechanism of the pumping unit, wherein the psi calculation process is as follows:
θ1＝θ0+θ
θ2＝2π-θ1+α
wherein R is the crank radius in m; p is the length of the connecting rod and is m; c is the length of the rear arm of the walking beam, and the unit is m; k is the length of the base rod and is m; a is the length of the front arm of the walking beam, and the unit is m; i is the horizontal projection of the base rod, and the unit is m; alpha is the included angle between the base rod and the vertical line, and the unit is rad; psi is the reference angle of the back wall of the walking beam relative to the base rod, and the unit is rad; theta is the rotation angle of the crank relative to the position of the crank at the bottom dead center of the suspension point at any time t, rad; theta1The angle of the crank relative to the 12 o' clock direction at the bottom dead center of the suspension point, rad.
Preferably, in step 1, K is 1.
Compared with the prior art, the invention has the following beneficial effects:
according to the method, a Fourier series term is added on the basis of the crank uniform rotation angular velocity, a calculation model of the crank actual rotation angular velocity is established and is used as a design variable, the minimum error square sum of the suspension point theoretical displacement and the suspension point actual measurement displacement is used as an optimization objective function, and the optimization objective function is solved by applying an optimization algorithm, so that the crank actual rotation angular velocity is solved, the target of accurately obtaining the crank actual rotation angular velocity is realized, and the fitting degree of the suspension point theoretical displacement and the suspension point actual measurement displacement is improved.
Drawings
FIG. 1 is a diagram of the analysis of the motion law of the crank rocker reversing mechanism of the pumping unit according to the present invention;
FIG. 2 is a flow chart of an optimization algorithm of the present invention;
fig. 3 shows the optimization results when the fourier coefficient truncation term K is 1 in example 1 of the present invention;
fig. 4 shows the crank motion law when the fourier coefficient truncation term K is 1 in example 1 of the present invention;
fig. 5 is a suspension point motion law when the fourier coefficient truncation term K is 1 in example 1 of the present invention;
fig. 6 shows the optimization results when the fourier coefficient truncation term K is 2 in example 1 of the present invention;
fig. 7 is a crank motion law when the fourier coefficient truncation term K is 2 in example 1 of the present invention;
fig. 8 shows the law of motion of the suspension point when the fourier coefficient truncation term K is 2 in example 1 of the present invention.
Detailed Description
Hereinafter, embodiments of the present invention will be described with reference to the drawings.
Specifically, the invention provides a crank motion law simulation model based on actually measured suspension point displacement, which comprises the following steps:
as shown in fig. 1 and 2, step 1, analyzing the motion law of the crank rocker reversing mechanism of the oil pumping unit to obtain the corresponding relation x between the theoretical displacement of the suspension point and the crank anglet(theta) function expression
xt(θ)＝(ψmax-ψ)*A
In the formula, psi is a reference angle of the rear arm of the walking beam relative to the base rod;
ψmaxthe maximum included angle between the rear arm of the walking beam and the base rod is formed;
a is the length of the front arm of the walking beam, and the unit is m;
wherein psimaxThe calculation process of (2) is as follows:
when the walking beam is at the two extreme positions of the bottom dead center and the top dead center, the maximum included angle psi between the rear arm of the walking beam and the base rodmaxIs composed of
And analyzing the motion of the crank rocker reversing mechanism of the pumping unit, wherein the psi calculation process is as follows:
θ1＝θ0+θ
θ2＝2π-θ1+α
in the formula, xt(theta) is the theoretical displacement of the suspension point;
psi is the reference angle of the rear arm of the walking beam relative to the base rod;
ψmaxthe maximum included angle between the rear arm of the walking beam and the base rod is formed;
r is the crank radius in m;
p is the length of the connecting rod and is m;
c is the length of the rear arm of the walking beam, and the unit is m;
k is the length of the base rod and is m;
a is the length of the front arm of the walking beam, and the unit is m;
i is the horizontal projection of the base rod, and the unit is m;
alpha is the included angle between the base rod and the vertical line, and the unit is rad;
theta is the rotation angle of the crank relative to the position of the crank at the bottom dead center of the suspension point at any time t, rad;
θ1the angle of the crank relative to the 12 o' clock direction at the bottom dead center of the suspension point, rad.
Wherein
In the formula, ω (t) is the actual rotation angular velocity of the crank, and the unit is rad/s;
ω0the crank rotates at a constant angular speed with the unit of rad/s;
k is Fourier series truncation series;
t is a time difference with the unit of s;
aifourier coefficients to be solved;
bifourier coefficients to be solved;
n is actually measured number of impact of suspension point in unit of min-1；
Determining a functional expression of the instantaneous crank angle from the actual crank rotation angular speed
In the formula, F is an optimization objective function of the actual rotation angular speed of the crank;
a1、a2、…、aK、b1、b2、…bKare all Fourier coefficients;
n is the number of time nodes;
xtiis the theoretical displacement of the suspension point, and the unit is m;
xmimeasured displacement of the suspension point is measured in m;
step 4, using F (a)1,a2,…,aK,b1,b2,…,bK) For the objective function, an optimization algorithm is applied to solve the Fourier coefficient a1、a2、…、aKAnd b1、b2、…bKFurther, the actual rotational angular velocity ω (t) of the crank is obtained)。
As shown in fig. 2, the optimization algorithm steps are as follows:
determining learning factor c1And c2The number of particle (antibody) groups M;
② production of M particles (antibodies) x by logistic regression analysis mappingiAnd velocity v thereofiWhere i is 1, …, N, and finally forming a population P of primary particles (antibodies)0；
Production of immune memory particles (antibodies): calculating the adaptive value of the particles (antibodies) in the current particle (antibody) group P and judging whether the algorithm meets the end condition, if so, ending and outputting the result, otherwise, continuing to operate;
updating the local and global optimal solutions, and updating the particle position and speed according to the following formula;
xi,j(t+1)＝xi,j(t)+vi,j(t+1),j＝1…d
vi,j(t+1)＝w·vi,j(t)+c1r1[pi,j-xi,j(t)]+c2r2[pg,j-xi,j(t)]
wherein w is the inertial weight; c. C1、c2Is a learning factor; r is1、r2Is [0,1 ]]The random number of (2); t is the iteration number in the searching process; j is the spatial dimension; p is a radical ofi,jExpressed as the optimal position of the ith particle in the j dimension at the t iteration; p is a radical ofg,jDenoted as the optimal position of the population in the j dimension at the t-th iteration.
Generating N new particles (antibodies) by logistic mapping;
particle (antibody) selection based on concentration: calculating the probability of producing N + M new particles (antibodies) by using the percentage of similar antibodies in the population, selecting N particles (antibodies) according to the probability to form a particle (antibody) population P, and then transferring to the third step.
Example (b): take an oilfield well Y1-1 as an example.
Table 1 gives the raw data for a certain oilfield well Y1-1.
TABLE 1Y 1-1 well raw data
Analyzing the motion rule of a crank rocker reversing mechanism of the oil pumping unit according to the original data in the table 1 to obtain the theoretical displacement of a suspension point; adding Fourier series terms on the basis of the crank constant-speed rotation angular speed, and establishing an actual crank rotation angular speed calculation model; and taking the actual rotating angular speed of the crank as a design variable, taking the minimum error square sum of the theoretical displacement of the suspension point and the actual measurement displacement of the suspension point as an optimization objective function, and solving the optimization objective function by applying an optimization algorithm so as to obtain the actual rotating angular speed of the crank.
As shown in fig. 3, an optimization algorithm is applied, which converges to a global optimal solution when taking the fourier coefficient cutoff K as 1, at which the actual crank rotation angular velocity:
ω(t)＝ω0-0.08*sin(ω0t)+0.05*cos(ω0t)
in the formula, ω (t) is the actual rotation angular velocity of the crank, and the unit is rad/s;
ω0the crank rotates at a constant angular speed with the unit of rad/s;
as shown in fig. 4 and 5, the crank motion law and the suspension point motion law when the fourier coefficient truncation term K is 1 are shown.
As shown in fig. 6, an optimization algorithm is applied, which converges to a global optimum solution when taking the fourier coefficient cutoff term K2, at which the actual crank rotational angular velocity
ω(t)＝ω0+(-0.01*sin(ω0t)+0.05*cos(ω0t))+(-0.12*sin(2ω0t)-0.06*cos(2ω0t))
In the formula, ω (t) is the actual rotation angular velocity of the crank, and the unit is rad/s;
ω0the crank rotates at a constant angular speed with the unit of rad/s;
as shown in fig. 7 and 8, the crank motion law and the suspension point motion law when the fourier coefficient truncation term K is 1 are shown.
As shown in fig. 5 and 8, when K is 1 and K is 2, respectively, the fourier coefficient truncation term has a high matching degree between the simulated displacement and the measured displacement, and both satisfy engineering applications. When the optimization precision is high enough, a small fourier coefficient truncation term should be taken to prevent overfitting, so in practical application, the fourier coefficient truncation term K is taken to be 1.
The method comprises the steps of forming a crank motion rule simulation model based on actual measurement suspension point displacement based on all the steps, taking actual rotation angular speed of a crank as a design variable, taking the minimum sum of squares of errors of theoretical displacement of the suspension point and the actual measurement displacement of the suspension point as an optimization objective function, and solving the optimization objective function by applying an optimization algorithm to obtain the actual rotation angular speed of the crank, so that the obtained theoretical displacement of the suspension point is highly fitted with the actual displacement of the suspension point. It is expected that the embodiment of the invention is only a specific display of the simulation model of the crank motion law based on the measured suspension point displacement, and not all contents. Any form of embodiment obtained by simulation in the technical field shall be within the scope of the present invention.
The above-mentioned embodiments are merely illustrative of the preferred embodiments of the present invention, and do not limit the scope of the present invention, and various modifications and improvements made to the technical solution of the present invention by those skilled in the art without departing from the spirit of the present invention shall fall within the protection scope defined by the claims of the present invention.
Claims (3)
1. A crank motion law simulation model based on actually measured suspension point displacement is characterized by comprising the following steps:
step 1, analyzing the motion law of the crank rocker reversing mechanism of the oil pumping unit to obtain the theoretical displacement of the suspension point and the crank rotation angleCorresponding relation x betweent(θ) is expressed as a function of:
xt(θ)＝(ψmax-ψ)*A
in the formula, xt(theta) is the theoretical displacement of the suspension point; psi is the included angle of the rear arm of the walking beam relative to the base rod; psimaxThe maximum included angle between the rear arm of the walking beam and the base rod is formed; a is the length of the front arm of the walking beam, and the unit is m;
step 2, rotating the angular velocity omega at the crank at a constant speed0On the basis of the method, a K-order Fourier series is added to determine a functional expression of the actual rotation angular speed omega (t) of the crank:
wherein
In the formula, ω (t) is the actual rotation angular velocity of the crank, and the unit is rad/s; omega0The crank rotates at a constant angular speed with the unit of rad/s; k is Fourier series truncation series; t is a time difference with the unit of s; a isiFourier coefficients to be solved; biFourier coefficients to be solved; n is actually measured number of impact of suspension point in unit of min-1；
Then, according to the actual rotational angular speed of the crank, a functional expression of the instantaneous crank angle is determined:
step 3, substituting the crank angle theta (t) in the step 2 into x in the step 1t(theta) functional expression, xt(t) is a function of the complex Fourier coefficients, assuming time of displacement of the suspension point t1，t2，…，tNTheoretical displacement of suspension point is xt(ti) Simplified as xti(ii) a Measured displacement of suspension point is xm(ti) Simplified as xmi(ii) a Based on the principle of least square method, the theoretical displacement x of the suspension pointtiMeasured displacement x from suspension pointmiThe minimum sum of squared errors is used as an optimization objective function, and an optimization objective function expression of the actual rotation angular speed of the crank is determined:
in the formula, F is an optimization objective function of the actual rotation angular speed of the crank, and the obtained value is the actual rotation angular speed omega (t) of the crank; a is1、a2、…、aK、b1、b2、…bKAre all Fourier coefficients; n is the number of time nodes; x is the number oftiIs the theoretical displacement of the suspension point, and the unit is m; x is the number ofmiMeasured displacement of the suspension point is measured in m;
step 4, using F (a)1,a2,…,aK,b1,b2,…,bK) For the objective function, an optimization algorithm is applied to solve the Fourier coefficient a1、a2、…、aKAnd b1、b2、…bKAnd Fourier coefficient a1、a2、…、aKAnd b1、b2、…bKSubstituting the actual rotating angular speed of the crank in the step 3 into an optimization objective function to obtain the actual rotating angular speed omega (t) of the crank;
the step based on the optimization algorithm comprises the following sub-steps:
step 41, determining learning factor c1And c2The number M of particle groups;
step 42, generating M particles x from the logistic regression analysis mapiAnd velocity v thereofiWhere i is 1, …, N, and finally forming the initial population P of particles0；
Step 43, producing immune memory particles: calculating the adaptive value of the particles in the current particle group P and judging whether the algorithm meets an end condition, if so, ending and outputting a result, otherwise, continuing to operate;
step 44, updating the local and global optimal solutions, and updating the particle position and velocity according to the following formula;
xi,j(t+1)＝xi,j(t)+vi,j(t+1),j＝1…d
vi,j(t+1)＝w·vi,j(t)+c1r1[pi,j-xi,j(t)]+c2r2[pg,j-xi,j(t)]
wherein w is the inertial weight; c. C1、c2Is a learning factor; r is1、r2Is [0,1 ]]The random number of (2); t is the iteration number in the searching process; j is the spatial dimension; p is a radical ofi,jExpressed as the optimal position of the ith particle in the j dimension at the t iteration; p is a radical ofg,jExpressed as the optimal position of the population in the j dimension at the t iteration;
step 45, generating N new particles by the logistic mapping;
step 46, concentration-based particle selection: the percentage of similar antibodies in the population is used to calculate the probability of producing N + M new particles (antibodies), and N particles (antibodies) are selected according to the probability to form a population P of particles (antibodies), which is then transferred to step 43.
2. The model of claim 1, wherein the model comprises a model body, a model body and a model body, wherein the model body comprises a plurality of crank motion rules, the crank motion rules are based on measured suspension point: in said step 1, #maxThe calculation process of (2) is as follows:
when the walking beam is positioned at two extreme positions of a bottom dead center and a top dead center, the maximum included angle psi between the rear arm of the walking beam and the base rodmaxIs composed of
Analyzing the motion of the crank rocker reversing mechanism of the oil pumping unit, wherein the calculation process of psi is as follows:
θ1＝θ0+θ
θ2＝2π-θ1+α
wherein R is the crank radius in m; p is the length of the connecting rod and is m; c is the length of the rear arm of the walking beam, and the unit is m; k is the length of the base rod and is m; a is the length of the front arm of the walking beam, and the unit is m; i is the horizontal projection of the base rod, and the unit is m; alpha is the included angle between the base rod and the vertical line, and the unit is rad; psi is the reference angle of the back wall of the walking beam relative to the base rod, and the unit is rad; theta is the rotation angle of the crank relative to the position of the crank at the bottom dead center of the suspension point at any time t, and the unit is rad; theta1The angle of the crank relative to the 12 o' clock direction at the bottom dead center of the suspension point is in rad.
3. The model of claim 2, wherein the model comprises a model body, a model body and a model body, wherein the model body comprises a crank motion rule simulation model body and a crank motion rule simulation model body, the model body comprises: in step 1, K is 1.
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