CN116738123A - Wellhead pressure control method based on improved longhorn beetle whisker algorithm optimization fuzzy PID - Google Patents
Wellhead pressure control method based on improved longhorn beetle whisker algorithm optimization fuzzy PID Download PDFInfo
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Abstract
The invention discloses a wellhead pressure control method based on improved longhorn beetle whisker algorithm optimization fuzzy PID, which belongs to the technical field of shale gas exploitation and comprises the following steps: s101, collecting wellhead pressure data X i And the opening Y of the pressure regulating valve i The method comprises the steps of carrying out a first treatment on the surface of the S102, wellhead pressure data X i And the opening Y of the pressure regulating valve i Performing curve fitting on the relation of the (2); s103, determining a fuzzy rule table through fuzzy reasoning; s104, an improved longhorn beetle whisker algorithm; s105, optimizing the fuzzy PID controller by using an improved longhorn beetle whisker algorithm to obtain an optimal solution of the quantization factor and the scaling factor in a given spatial range. In the way, the invention has nonlinearity and time variation in wellhead pressure dataUnder the condition of sex, the wellhead pressure is regulated by adopting a method of optimizing a fuzzy PID controller by adopting an improved longhorn beetle whisker algorithm, so that the wellhead pressure valve can quickly and accurately regulate the wellhead pressure, thereby ensuring the stability of EUR during shale gas pressure control production and ensuring the safety and stability during shale gas exploitation operation.
Description
Technical Field
The invention relates to the technical field of shale gas exploitation, in particular to a wellhead pressure control method based on improved longhorn beetle whisker algorithm optimization fuzzy PID.
Background
With the continuous increase of shale gas exploitation intensity in China, the problem of shale gas safety and stability operation is increasingly outstanding. At present, a pressure control production mode is adopted when shale gas exploitation is carried out, but due to the fact that pressure differences of different underground layers are different and shale gas reservoir cracks can change with time, problems of continuous sand production, crack closure and the like can be encountered in the exploitation process, and finally EUR (Estimated Ultimate Recovery, ultimate recoverable reserve) is reduced.
Through research on the pressure control production technology of shale gas at home and abroad, the traditional wellhead pressure control mode is to repeatedly adjust the opening of a wellhead pressure valve by field operators, so that safety and stability in pressure control production are ensured, but the solution has certain hysteresis, so that the difficulty of solving the problem is further increased. At present, the production condition during exploitation is indirectly acquired by measuring wellhead parameters in China, wellhead pressure control is carried out through a PID controller so as to maintain stable production, but the control precision and dynamic response speed based on a single PID controller are to be improved, if the problem cannot be solved, EUR and stability in the exploitation process are directly influenced, shale gas exploitation risk is increased, the exploitation life of a shale gas well is shortened, shale gas productivity is influenced, and a plurality of originally developed shale gases cannot be timely developed. In summary, an effective wellhead pressure control method for guaranteeing stable shale gas exploitation operation is not yet available at present.
Based on the method, the wellhead pressure control method based on the improved longhorn beetle whisker algorithm and the fuzzy PID optimization is designed to solve the problems.
Disclosure of Invention
Aiming at the defects existing in the prior art, the invention provides a wellhead pressure control method based on improving the longhorn beetle whisker algorithm to optimize fuzzy PID.
In order to achieve the above purpose, the invention is realized by the following technical scheme:
a wellhead pressure control method based on improved longhorn beetle whisker algorithm optimization fuzzy PID comprises the following steps:
s101, collecting wellhead pressure data X i And the opening Y of the pressure regulating valve i ；
S102, wellhead pressure data X i And the opening Y of the pressure regulating valve i Performing curve fitting on the relation of the (2);
s103, the input quantity is subjected to fuzzification, and a fuzzy rule table is determined through fuzzy reasoning;
s104, an improved longhorn beetle whisker algorithm;
s105, optimizing the fuzzy PID controller by using an improved longhorn beetle whisker algorithm to obtain an optimal solution of the quantization factor and the scaling factor in a given spatial range, and setting a fitness function as an error performance index ITAE.
Further, in step S101, wellhead pressure data X is collected at a sampling frequency of 10ms i And the opening Y of the pressure regulating valve i 。
Further, the specific steps of step S102 are as follows:
s201, setting a curve fitting model; the method comprises the following steps: given the acquired wellhead-related parameters (x i ，y i ) The curve fitting model is:
wherein x is i Representing wellhead pressure data points, y i The valve opening value corresponding to each wellhead pressure data point is a, b, c, d, h which is a parameter to be estimated; e is a natural constant;
s202, determining an objective function; the method comprises the following steps: setting an objective functionSearching for optimal parametersThe number p minimizes ε;
wherein ε: measuring an objective function of the performance quality of the control system; and p: the opening degree of the wellhead pressure valve is regulated to reach the control parameter of the required wellhead pressure value (y); x: the measured wellhead pressure value is used as a feedback regulating control parameter (p) to reach a required wellhead pressure value (y); y: the control system needs to maintain the wellhead pressure value; f (x, p): a model relating the control parameter (p) and the measured wellhead pressure (x) to an actual wellhead pressure value obtained by adjusting the wellhead pressure valve;
s203, iteratively optimizing through a damping least square method, and solving parameters to be estimated; the method comprises the following steps: carrying out iterative solution on parameters to be estimated of the curve fitting model by adopting a damping least square algorithm;
s204, outputting a parameter solving result after convergence judgment;
obtaining a fitting curve: y is Y i ＝F(X i )；
Wherein Y is more than or equal to 0 i N is less than or equal to N, N is the maximum opening value of the valve, and F (-) is a nonlinear fitting model.
Further, the step S203 specifically includes the following steps:
(1) Taking the initial point p 0 Terminating the control parameter epsilon and calculating epsilon 0 K is defined as 0, lambda 0 ＝10 -3 ，v＝10；
(2) Computing jacobian matrix J k Calculate N k ＝J k T J k +λ k diag(J k T J k ) Constructing an incremental normal equation N k ·δ k ＝J k T ε k ；
Wherein diag (·) is to construct a new diagonal matrix with diagonal elements of the matrix; jk: iterating the jacobian matrix at the kth time; nk: iterating the damping law equation matrix in the k; jkT: iterating the transpose of the k-th time jacobian matrix; λk: iterating the damping factor at the kth time; εk: residual vector at iteration k; δk: an increment parameter vector in the iterative k process;
(3) Solving the increment normal equation to obtain delta k 。
Further, step S204 is specifically:
if it isLet p k+1 ＝p k +δ k If delta k ||<Epsilon, stopping iteration and outputting a result, wherein the value of a, b, c, d, h can be calculated according to the iteration result; let lambda get no k+1 ＝λ k V, go to step (2) in step S203; if it isLet lambda get k+1 ＝λ k V, re-solving the normal equation to obtain delta k Turning to step (3) in step S203;
where k of pk and εk represents the kth iteration, V: the constant factor of damping is reduced as the algorithm proceeds.
Further, the fuzzy rule table of the fuzzy PID controller is created as follows:
601. determining the input and output of a controller; the method comprises the following steps: determining the input of the fuzzy PID controller as a deviation e and a deviation variation e c The output is the parameter increment delta k of the fuzzy control P 、Δk I 、ΔK D ；
The calculation formula of the fuzzy control is as follows:
k P ＝k P1 +Δk P
k I ＝k I1 +Δk I
k D ＝k D1 +Δk D ；
wherein k is P 、k I 、K D Parameters of the fuzzy PID controller are finally input; k (k) P1 、k I1 、k D1 Is an initial value; Δk P 、Δk I 、Δk D Is the parameter increment;
602. setting a fuzzy universe and dividing fuzzy subsets; the method comprises the following steps: deviation e and deviation variation e c The actual value range of (2) is the basic argument, and the fuzzy PID controller is converted into fuzzy by quantization factor before inputting the fuzzy PID controllerThe domain, the output needs to be converted from the fuzzy domain to the basic domain by a scale factor, and the fuzzy domain of the input value and the output value is set as follows:
e，e c ＝[-3，3]
Δk P ，Δk D ，Δk D ＝[-1，1]
dividing the fuzzy discourse domain into fuzzy subsets, and determining different numbers of the subsets according to different control requirements:
e，e c ＝{NB，NM，NS，Z，PS，PM，PB}
Δk p ，Δk 1 ，Δk D ＝{NB，NM，NS，Z，PS，PM，PB}
603. creating a fuzzy rule table; the method comprises the following steps: the fuzzy PID controller is based on the deviation e and the deviation change rate e c The size of the input is converted into the blurring amount, and the deviation e and the deviation change rate e which are converted into the domain range are converted c Performing fuzzy processing to convert the original accurate input quantity into fuzzy quantity, and representing by using a corresponding fuzzy set; the argument of the deviation e is [ -3,3]Deviation change rate e c The domain of (1) is [ -1,1]Deviation e and deviation rate of change e. The fuzzy linguistic value of (2) is { NB, NM, NS, Z, PS, PM, PB };
604. setting a fitness function; the fitness function is set as the error performance index ITAE:
wherein t: a time variable representing the evaluation duration; i e (t) |: the absolute value of the error signal e (t) at time t represents the deviation of the system output from the desired reference signal at this time; special (V) 0 And (3) carrying out the following steps: time integration values from the initial time (0) to (++) represent time integration errors.
Furthermore, the improved longhorn beetle whisker algorithm flow is as follows:
step1, initializing parameters and an objective function; generating random direction vectors, and sequentially obtaining whisker positions;
the positions of the longicorn in the n-dimensional space are as follows: x (X1, X2,) xn; the positions of the left antenna and the right antenna of the longicorn are as follows:
wherein l represents the distance between the centroid of the longicorn and the tentacle,representing a random unit vector; xr=x+d: the position of the right antenna is set to be the current position X plus a scaling factor d for each dimension of the search space; xl=x-d: the position of the left antenna is set as the current position X minus the scaling factor d of each dimension of the search space;
normalization operation is required for the unit vector:
wherein, D: an integer representing the step size or distance that the search can move in each iteration; rands (D, 1): d-dimensional random vectors generated by "Rands" functions; ||rands (D, 1) ||: euclidean norms of the random vectors;
step2, updating the position of the longhorn beetle and the optimal objective function value according to the value of the tentacle position;
since the two antennas obtain the objective function information of the two positions, the two positions need to be preferentially advanced:
wherein t represents the iteration number, and the f (·) function is the objective function, δ t Representing the step length of the t-th exploration, wherein sign (·) is a sign function;
the step size needs to be continuously smaller during each iteration, so it can be set to delta t+1 ＝δ t *η；
Wherein η represents the speed at which the step size shortens per iteration;
step3, dynamically improving the Step length factor, and ending when the termination condition is reached; the improvement steps are as follows:
the expression is:
wherein eta and alpha are step factors which change in real time and fixed step factors respectively; n and i are the total iteration times and the current iteration times respectively; f (f) i 、f t The current and historical optimal fitness values, respectively.
Further, the steps of optimizing the fuzzy PID controller by using the improved longhorn beetle whisker algorithm are as follows:
step1, generating/updating the position of the longicorn;
step2, setting the mass center of the longicorn to 5 dimensions and assigning K to the mass center e 、K ec 、K P_u 、K I_u 、K D_u The method comprises the steps of carrying out a first treatment on the surface of the The method comprises the following steps: setting the longicorn centroid as 5 space dimensions, and setting the longicorn centroid position and the longicorn orientationInitializing; decomposing the coordinates of the centroid of the ox in the initialization information into corresponding 5 parameter values K e 、K ec 、K P_u 、K I_u 、K D_u Transmitting the controller system, performing operation calculation to obtain the fitness values of the left and right whiskers, and judging the flight direction of the longicorn in the next step;
step3, calculating to obtain an fitness function value, namely an ITAE index; the method comprises the following steps: updating the position information of the longicorn according to the fitness value, decomposing the position information into 5 parameters again and assigning the 5 parameters to a controller system, and after the system calculates the fitness function value, outputting the fitness function value, namely an ITAE index, and judging whether the fitness function value reaches a preset threshold or reaches a preset iteration number; if the fitness function value reaches a preset threshold value or reaches a preset iteration number, executing the next step; otherwise, executing Step2;
step4, obtaining the optimal quantization factor and the optimal scaling factor of the fuzzy control system, and ending the calculation.
Advantageous effects
Under the condition that wellhead pressure data has nonlinearity and time-varying property, the wellhead pressure is regulated by adopting a method for optimizing a fuzzy PID controller by adopting an improved longhorn beetle whisker algorithm, so that the wellhead pressure valve can quickly and accurately regulate the wellhead pressure, thereby ensuring the stability of EUR in shale gas pressure control production and ensuring the safety and stability in shale gas exploitation operation;
according to the invention, the improved longhorn beetle whisker algorithm is combined with the fuzzy PID controller, and under the condition that the wellhead pressure has time variability and nonlinearity, the improved longhorn beetle whisker algorithm can efficiently seek to control optimal parameters, so that the control precision of the wellhead pressure is improved, and then the fuzzy PID controller is used for making control decision on the opening of the wellhead pressure valve according to a fuzzy rule, so that the dynamic response speed of wellhead pressure control is ensured.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below. It is evident that the drawings in the following description are only some embodiments of the present invention and that other drawings may be obtained from these drawings without inventive effort for a person of ordinary skill in the art.
FIG. 1 is a flow chart of a wellhead pressure control method based on an improved longhorn beetle whisker algorithm optimization fuzzy PID in an embodiment of the invention;
FIG. 2 is a flow chart of curve fitting in an embodiment of the present invention;
FIG. 3 is a schematic diagram of a fuzzy controller in accordance with an embodiment of the present invention;
FIG. 4 is a schematic diagram of a fuzzy PID controller in an embodiment of the invention;
FIG. 5 is a flow chart of an improved longhorn beetle whisker algorithm in an embodiment of the invention;
FIG. 6 is a flow chart illustrating rule table creation in an embodiment of the present invention;
FIG. 7 is a flowchart of a Tian Bo whisker algorithm optimized fuzzy PID controller according to an embodiment of the invention;
FIG. 8 is a plot of a fuzzy membership function for bias in an embodiment of the present invention;
FIG. 9 is a plot of a fuzzy membership function for the rate of change of bias in an embodiment of the present invention;
FIG. 10 is a graph illustrating the output membership function of a PID controller according to an embodiment of the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. It will be apparent that the described embodiments are some, but not all, embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The invention is further described below with reference to examples.
Example 1
Referring to fig. 1 of the specification, a wellhead pressure control method based on improved longhorn beetle whisker algorithm to optimize fuzzy PID includes the following steps:
s101, collecting wellhead pressure data X i And the opening Y of the pressure regulating valve i ；
The step S101 specifically includes: during shale gas exploitation operation, wellhead pressure data X are collected at a sampling frequency of 10ms i And the opening Y of the pressure regulating valve i ；
S102, wellhead pressure data X i And the opening Y of the pressure regulating valve i Performing curve fitting on the relation of the (2);
because of the characteristics of nonlinearity and time-varying property of wellhead pressure in the pressure control production process, the wellhead pressure data X is obtained i And the opening Y of the pressure regulating valve i Performing curve fitting on the relation of the (2); as shown in fig. 2, the specific steps are as follows:
S201setting a curve fitting model; the method comprises the following steps: given the acquired wellhead-related parameters (x i ，y i ) The curve fitting model is:
wherein xi represents wellhead pressure data points, yi is a valve opening value corresponding to each wellhead pressure data point, and a, b, c, d, h is a parameter to be estimated; e: the natural constant, symbol e, is a constant in mathematics, is an infinite non-cyclic decimal and is an overrun number, the value of which is about 2.718281828459045, which is the base of a natural logarithmic function; a: representing the amplitude of the first exponential term, which determines the maximum that the function can reach when x goes to infinity; b: representing the rate of change of the first exponential term with respect to x, which determines the rate at which the function rises or falls with x; c: representing the amplitude of the second exponential term, which determines the maximum that the function can reach when x goes to infinity; d: representing the rate of change of the second exponential term with respect to x, which determines the rate at which the function rises or falls with x; h: a fixed offset or baseline value representing the function, which determines the vertical displacement of the function, the purpose of estimating these parameters being to obtain a curve that best fits the observed data points and to use to predict or extrapolate data that is outside the range of observation;
s202, determining an objective function; the method comprises the following steps: setting an objective functionSearching an optimal parameter p to minimize epsilon;
wherein ε: an objective function measuring the quality of the control system performance, in this case defined as the sum of squares of the difference between the desired wellhead pressure value (y) and the actual value (f (x, p)) obtained by manipulating the control parameter (p) from the measured wellhead pressure (x); and p: the opening degree of the wellhead pressure valve is regulated to reach the control parameter of the required wellhead pressure value (y); x: the measured wellhead pressure value is used as a feedback regulating control parameter (p) to reach a required wellhead pressure value (y); y: the control system needs to maintain the wellhead pressure value; f (x, p): a model relating the control parameter (p) and the measured wellhead pressure (x) to an actual wellhead pressure value obtained by adjusting the wellhead pressure valve;
s203, iteratively optimizing through a damping least square method, and solving parameters to be estimated; the method comprises the following steps: carrying out iterative solution on parameters to be estimated of the curve fitting model by adopting a damping least square algorithm; the method comprises the following steps:
(1) Taking the initial point p 0 Terminating the control parameter epsilon and calculating epsilon 0 K is defined as 0, lambda 0 ＝10 -3 ，v＝10；
(2) Computing jacobian matrix J k Calculate N k ＝J k T J k +λ k diag(J k T J k )；
Wherein diag (·) is to construct a new diagonal matrix with diagonal elements of the matrix, and the rest elements of the matrix are 0; jk: iterating the jacobian matrix at the kth time, wherein m is the number of data points, n is the number of parameters in the model, and the (i, j) th element of the Jk represents the partial derivative of the ith data point to the jth parameter of the model and is calculated according to the current estimated value of the parameter vector; nk: the damping law equation matrix at the time of iteration k is an n×n symmetric positive definite matrix, wherein n is the parameter number in the model, and the calculation formula is as follows: nk=jktjk+λkdiag (JkTJk), where diag (JkTJk) is a diagonal matrix with diagonal elements equal to the square of Jk column modes; jkT: iterating the transpose of the k-th time jacobian matrix, which is an n x m matrix, where n is the number of parameters in the model and m is the number of data points; λk: the damping factor at iteration k, which is a non-negative scalar, controls the amount of damping acting on the normal equation matrix Nk, which typically selects a small positive value to ensure Nk is good and reversible; δk: increment parameter vector at iteration k. It is an n-dimensional vector representing the variation of parameter estimation between iterations, the calculation formula is δk= [ (nk+μkl)/(1 ] (JkT εk), where μk is a small positive scalar and I is the identity matrix; εk: the residual vector at the time of iteration k is an m-dimensional vector and represents the difference value between observed data and a model predicted value at the time of iteration k, and the calculation form is epsilon k=y-f (x, pk), wherein y is collected wellhead pressure valve opening data, f (x, pk) is a predicted value of the model at the time of iteration k, and pk is a parameter vector at the time of iteration k;
constructing an incremental normal equation N k ·δ k ＝J k T ε k ；
Wherein Jk: the jacobian matrix at the kth time is iterated. It is an m n matrix, where m is the number of data points and n is the number of parameters in the model; the (i, j) th element of Jk represents the partial derivative of the i data point to the j th parameter of the model, and is calculated by the current estimated value of the parameter vector; nk: the damping law equation matrix at the time of iteration k is an n×n symmetric positive definite matrix, wherein n is the parameter number in the model, and the calculation formula is as follows: nk=jktjk+λkdiag (JkTJk), where diag (JkTJk) is a diagonal matrix with diagonal elements equal to the square of Jk column modes; jkT: iterating the transpose of the k-th time jacobian matrix, which is an n x m matrix, where n is the number of parameters in the model and m is the number of data points; λk: the damping factor at iteration k, which is a non-negative scalar, controls the amount of damping acting on the normal equation matrix Nk, which typically selects a small positive value to ensure Nk is good and reversible; δk: the increment parameter vector at the time of iteration k is an n-dimensional vector and represents the change of parameter estimation among iterations, the calculation formula is δk= [ (Nk+μkI)/(1 ] (JkT εk), wherein μk is a small positive scalar and I is an identity matrix; εk: the residual vector at the time of iteration k is an m-dimensional vector and represents the difference value between observed data and a model predicted value at the time of iteration k, and the calculation form is epsilon k=y-f (x, pk), wherein y is collected wellhead pressure valve opening data, f (x, pk) is a predicted value of the model at the time of iteration k, and pk is a parameter vector at the time of iteration k;
(3) Solving the increment normal equation to obtain delta k ；
S204, outputting a parameter solving result after convergence judgment; the method comprises the following steps:
if it isLet p k+1 ＝p k +δ k If delta k Stopping iteration and outputting a result, wherein the value of a, b, c, d, h can be calculated according to the iteration result; let lambda get no k+1 ＝λ k V, go to step (2) in step S203; if it isLet lambda get k+1 ＝λ k V, re-solving the normal equation to obtain delta k Turning to step (3) in step S203;
where k of pk and εk represents the kth iteration, V: reducing constant factors of damping as the algorithm proceeds;
in the step of outputting the parameter result after convergence judgment, the algorithm checks whether the current estimated parameter pk provides a good fit to the data; the expression Σy-f (x, pk) ] -2 represents the sum of squares of the difference between the input value x and the observed output value y and the predicted value f (x, pk) of the current estimation parameter pk; the value of δk is a threshold that determines how close the predicted value needs to be to the observed value to stop the algorithm from iterating; if the sum of squares of the differences is smaller than a threshold delta, the current estimation parameter pk is considered to be better fitted with the data, and iteration is stopped; the parameter value pk+1 is obtained by adding a small disturbance delta k to the current estimated value pk, and the magnitude of the disturbance is constrained by the value of epsilon k to ensure that the new parameter estimated value is not far different from the previous estimated value; on the other hand, if the sum of squares of the errors is greater than or equal to the threshold value delta k, the current estimation is considered to be inaccurate, and the next iteration is continued; the parameter lambdak represents a damping factor, so that the step length of parameter updating can be reduced; obtaining the value of λk+1 by multiplying λk by a constant factor v, so that the damping of λk decreases as the algorithm proceeds; the parameter δk represents the variation of an estimated parameter obtained by solving an incremental normal equation, which is a linear equation set that links an observed output value with a model predicted value and an unknown parameter value;
obtaining a fitting curve: y is Y i ＝F(X i )；
Wherein Y is more than or equal to 0 i N is less than or equal to N, N is a valveThe maximum opening value of the door, F (·) is a nonlinear fitting model;
preferably, wellhead pressure data X are collected i Performing curve fitting and subsequent processing when the number of data points is at least 100;
s103, the input quantity is subjected to fuzzification, and a fuzzy rule table is determined through fuzzy reasoning;
FIG. 3 is a schematic diagram of the structure of a fuzzy controller, and the composition and function of the fuzzy controller are as follows:
blurring: the input of the fuzzy controller must be used for solving the control output through fuzzification, so that the input is actually an input interface of the fuzzy controller, and the main function of the input is to convert the real definite quantity input into a fuzzy vector;
knowledge base: the knowledge base is composed of a database and a rule base; the database stores membership vector values (namely, a set of corresponding values after being discretized by a domain level) of all fuzzy subsets of all input and output variables, and the membership vector values are membership functions if the domain is a continuous domain; in the solving process of the fuzzy relation equation of rule reasoning, providing data for the fuzzy reasoning process; the rules of the fuzzy controller are based on expert knowledge or experience accumulated by manual operators for a long time, and are a language representation form based on human intuitive reasoning; the fuzzy rule is usually formed by connecting a series of relation words, such as if-then, else, also, end, or, and the relation words must be translated to digitize the fuzzy rule;
fuzzy reasoning and defuzzification: the fuzzy reasoning is a functional part in the fuzzy controller for completing the fuzzy reasoning to solve a fuzzy relation equation according to the input fuzzy quantity and obtaining the fuzzy control quantity by a fuzzy control rule; in fuzzy control, an inference method with simpler and more efficient operation is generally adopted in consideration of inference time; the obtaining of the reasoning result indicates that the rule reasoning function of fuzzy control is finished, but the result obtained in the process is still a fuzzy vector, can not be directly used as a control quantity, and also needs to be converted once to obtain clear control quantity output, namely, the fuzzy is solved, and the part of the output end with the function of conversion is generally called defuzzification;
FIG. 4 is a schematic diagram of a fuzzy PID controller according to an embodiment of the invention, in which:
r represents a target optimized value:
c represents the output value of the control quantity, namely the opening value of the wellhead pressure valve which is output after optimal parameter calculation;
e represents deviation, e c Represents the rate of change d of e e /d t E and e c Is the input of the fuzzy controller;
K P ，K I ，K D three parameters of the PID controller;
as shown in fig. 6, the fuzzy rule table creation of the fuzzy PID controller is as follows:
601. determining the input and output of a controller; the method comprises the following steps: determining the input of the fuzzy PID controller as a deviation e and a deviation variation e c The output is the parameter increment delta k of the fuzzy control P 、Δk I 、ΔK D The output parameter increment is used for simplifying the output change range and improving the response speed instead of the direct output parameter;
the calculation formula of the fuzzy control is as follows:
k P ＝k P1 +Δk P
k I ＝k I1 +Δk I
k D ＝k D1 +Δk D ；
wherein k is P 、k I 、K D Parameters of the fuzzy PID controller are finally input; k (k) P1 、k I1 、k D1 Is an initial value; Δk P 、Δk I 、Δk D Is the parameter increment;
602. setting a fuzzy universe and dividing fuzzy subsets; the method comprises the following steps: deviation e and deviation variation e c The actual value range of the (2) is the basic domain, the fuzzy PID controller is converted into the fuzzy domain through a quantization factor before being input, the fuzzy domain is converted into the basic domain through a scale factor after being output, and the fuzzy domains of the input value and the output value are set as follows:
e，e c ＝[-3，3]
Δk P ，Δk D ，Δk D ＝[-1，1]
dividing the fuzzy discourse domain into fuzzy subsets, and determining different numbers of the subsets according to different control requirements:
e，e c ＝{NB，NM，NS，Z，PS，PM，PB}
Δk p ，Δk 1 ，Δk D ＝{NB，NM，NS，Z，PS，PM，PB}
603. creating a fuzzy rule table; the method comprises the following steps: the fuzzy reasoning method uses a triangle membership function, so that the calculation is simpler, the sensitivity of the pressure control precision in a high error range is lower, and the sensitivity is higher when the error is smaller; the fuzzy PID controller is based on the deviation e and the deviation change rate e c The size of the input is converted into the blurring amount, and the deviation e and the deviation change rate e which are converted into the domain range are converted c Performing fuzzy processing to convert the original accurate input quantity into fuzzy quantity, and representing by using a corresponding fuzzy set; the argument of the deviation e is [ -3,3]Deviation change rate e c The domain of (1) is [ -1,1]Deviation e and deviation rate of change e c The fuzzy linguistic value of (2) is { NB, NM, NS, Z, PS, PM, PB };
wherein:
NB is an English abbreviation of Negative Big, which indicates Negative Big;
NM is an English abbreviation of Negative Medium, which indicates Negative Chinese;
NS is an english abbreviation for negotiable small, indicating negative small;
z is an English abbreviation of Zero, representing Zero;
PS is an english abbreviation for Positive Small, indicating Positive Small;
PM is an English abbreviation of Positive Medium, which indicates the center;
PB is an English abbreviation for Positivebig, indicating positive;
the number of the fuzzy rules is related to the number of fuzzy subsets of the input quantity, the fuzzy rules comprise 2 inputs of deviation and deviation variation, 7 fuzzy subsets are respectively arranged, and the established fuzzy rules are as follows:
604. setting a fitness function; the method comprises the following steps: after fuzzy reasoning, the obtained result is a fuzzy set, and then the fuzzy set is deblurred; the barycenter method is adopted for deblurring, namely, the barycenter of the area formed by the curve coordinates and the abscissa of the membership function is taken as an output accurate value; through the above process, the quantization factor and the scale factor of the fuzzy PID controller are not determined, and parameters and control structures of other parts are built; to achieve better control, 5 parameters to be determined, namely a quantization factor k e 、k ec Scale factor k P_u 、k I_u 、k D_u As 5 dimension values of longhorn beetles, searching an optimal solution in a given space range; the fitness function is set as the error performance index ITAE:
wherein t: a time variable representing the evaluation duration; i e (t) |: the absolute value of the error signal e (t) at time t represents the deviation of the system output from the desired reference signal at this time; special (V) 0 And (3) carrying out the following steps: time integration values from the initial time (0) to (++), representing time integration errors;
s104, an improved longhorn beetle whisker algorithm; the method comprises the following steps: the step factor of the longhorn beetle whisker algorithm is dynamically improved, so that the accuracy of the algorithm is higher;
as shown in fig. 5, the modified longhorn beetle whisker algorithm flow is as follows:
step1, initializing parameters and an objective function; generating random direction vectors, and sequentially obtaining whisker positions;
the positions of the longicorn in the n-dimensional space are as follows: x (X1, X2,) xn; the positions of the left antenna and the right antenna of the longicorn are as follows:
wherein l represents the distance between the centroid of the longicorn and the tentacle,representing a random unit vector; xr=x+d: the position of the right antenna is set to the current position X plus a scaling factor d (random unit vector) for each dimension of the search space, which creates a virtual whisker extending from the current position along each dimension to the upper limit of the search space; xl=x-d: the position of the left antenna is set to the current position X minus the scaling factor d (random unit vector) for each dimension of the search space, which creates a virtual whisker extending from the current position to the lower limit of the search space for each dimension;
the purpose of these parameters is to simulate the behavior of the antenna of a longhorn beetle, which exploits the antenna exploration environment and locates food sources, in BWA the virtual beards are used to explore the search space and guide the search forward towards the global optimum, by setting Xr and Xl in such a way that the algorithm encourages the virtual beards to explore the search space around the current location of the population while keeping them close to the current location, which allows the algorithm to effectively search the space around the current optimum solution while also exploring other areas of the search space;
normalization operation is required for the unit vector:
wherein, D: an integer representing the step size or distance that the search can move in each iteration; rands (D, 1): d-dimensional random vectors generated by "Rands" functions; ||rands (D, 1) ||: the euclidean norm of the random vector, using double vertical bar symbols "| … |" calculation, the result is a scalar value; the expression "d=ranges (D, 1)/|ranges (D, 1) |" normalizes a random vector of length D, expressed as "||ranges (D, 1) |" by dividing it by its euclidean norm, and the result is a unit vector that specifies the moving direction of the search;
step2, updating the position of the longhorn beetle and the optimal objective function value according to the value of the tentacle position;
since the two antennas obtain the objective function information of the two positions, the two positions need to be preferentially advanced:
wherein t represents the iteration number, and the f (·) function is the objective function, δ t Representing the step length of the t-th exploration, wherein sign (·) is a sign function;
the step size needs to be continuously smaller during each iteration, so it can be set to delta t+1 ＝δ t *η；
Where η represents the speed of step shortening per iteration, typically set to 0.95;
step3, dynamically improving the Step length factor, and ending when the termination condition is reached; the method comprises the following steps: in the running process of the longhorn beetle whisker algorithm, the step length factor eta is fixed and not suitable for multidimensional space searching, and in order to bring the longhorn beetle whisker algorithm into play, the step length factor eta is dynamically improved, and the improvement steps are as follows:
in the optimization process of the early algorithm, the step factor eta is increased, so that the search range is enlarged, and the optimization speed is increased;
in the later optimizing process, the searching tends to be stable because the earlier stage is calculated, and the step factor eta is reduced and the precision requirement is increased;
the expression is:
wherein eta and alpha are respectively a step factor which changes in real time and a fixed step factor (0.95); n and i are the total iteration times and the current iteration times respectively; f (f) i 、f t Respectively the current and the history optimal fitness values;
in the early-stage optimizing process, when the current fitness value is smaller than the history optimal value, eta adopts a default step factor; in the later optimizing process, when the current fitness value is larger than the history optimal value, the optimizing performance is poor, the step factor is reduced, the convergence speed is increased, and the accuracy requirement is improved;
s105, optimizing the fuzzy PID controller by using an improved longhorn beetle whisker algorithm to obtain an optimal solution of a quantization factor and a scale factor in a given space range, and setting a fitness function as an error performance index ITAE;
as shown in fig. 7, the steps for optimizing the fuzzy PID controller using the modified longhorn beetle whisker algorithm are as follows:
step1, generating/updating the position of the longicorn;
step2, setting the mass center of the longicorn to 5 dimensions and assigning K to the mass center e 、K ec 、K P_u 、K I_u 、K D_u The method comprises the steps of carrying out a first treatment on the surface of the The method comprises the following steps: the longicorn centroid is set to 5 space dimensions, and the longicorn centroid position (composed of initial values of 5 parameters) and longicorn orientation are calculatedInitializing; decomposing the coordinates of the centroid of the ox in the initialization information into corresponding 5 parameter values K e 、K ec 、K P_u 、K I_u 、K D_u Transmitting the controller system, performing operation calculation to obtain the fitness values of the left and right whiskers, and judging the flight direction of the longicorn in the next step;
step3, calculating to obtain an fitness function value, namely an ITAE index; the method comprises the following steps: updating the position information of the longicorn according to the fitness value, decomposing the position information into 5 parameters again and assigning the 5 parameters to a controller system, and after the system calculates the fitness function value, outputting the fitness function value, namely an ITAE index, and judging whether the fitness function value reaches a preset threshold or reaches a preset iteration number; if the fitness function value reaches a preset threshold value or reaches a preset iteration number, executing the next step; otherwise, executing Step2;
step4, obtaining an optimal quantization factor and a scale factor of the fuzzy control system, and ending calculation;
the control amount can be output by a fuzzy PID controller: the control quantity can be subjected to anti-fuzzy according to the obtained optimal quantization factor, the scale factor and the fuzzy rule, and the opening of the valve of the control quantity is adjusted according to the anti-fuzzy result through a related control component of the wellhead pressure valve, so that the wellhead pressure is rapidly and accurately controlled;
FIG. 8 is a plot of a fuzzy membership function for bias in an embodiment of the present invention; FIG. 9 is a plot of a fuzzy membership function for the rate of change of bias in an embodiment of the present invention; FIG. 10 is a graph illustrating the output membership function of a PID controller according to an embodiment of the invention. The fuzzy membership function curve of the deviation represents one way to map the deviation between the desired set point and the actual wellhead pressure to membership in linguistic variables; a fuzzy membership function curve is a mathematical function that assigns a degree of membership to each possible input value based on the degree of matching of the input value to a particular linguistic variable. In the case of wellhead pressure control, linguistic variables may be similar to "low", "medium" or "high" pressures, and the fuzzy membership function curves will be used to determine the extent of the current deviation setpoints corresponding to these linguistic variables; the fuzzy membership curve of the bias is an important component of the fuzzy PID control system, which allows the system to infer the current state of the wellhead pressure control system in a more human-like manner and make more informed decisions on how to adjust the control parameters.
According to the invention, nonlinear function fitting and damping least square algorithm are utilized to iterate optimization data, so that the relation between wellhead pressure data and the opening degree of the pressure regulating valve is fitted, the robustness is high, and the relation is conveniently converted into the identifiable input quantity of the fuzzy PID controller;
under the condition that wellhead pressure data has nonlinearity and time-varying property, the wellhead pressure is regulated by adopting a method for optimizing a fuzzy PID controller by adopting an improved longhorn beetle whisker algorithm, so that the wellhead pressure valve can quickly and accurately regulate the wellhead pressure, thereby ensuring the stability of EUR in shale gas pressure control production and ensuring the safety and stability in shale gas exploitation operation;
according to the invention, an improved longhorn beetle whisker algorithm is combined with a fuzzy PID controller, and under the condition that the wellhead pressure has time variability and nonlinearity, the improved longhorn beetle whisker algorithm can efficiently seek to control optimal parameters, so that the control precision of the wellhead pressure is improved, and then the fuzzy PID controller carries out control decision on the opening of the wellhead pressure valve according to a fuzzy rule, so that the dynamic response speed of wellhead pressure control is ensured;
the dynamic response time of the fuzzy PID controller is faster than that of the PID controller, and the fuzzy PID controller can adapt to the time-varying characteristic of wellhead pressure, so that quick response adjustment is realized; compared with the traditional optimization algorithm, the longhorn beetle whisker algorithm has the advantages of few parameters, high-efficiency optimization and the like. If the step factor of the longhorn beetle whisker algorithm is dynamically improved, the accuracy of the algorithm is higher. Therefore, the wellhead pressure control method utilizing the fuzzy PID controller and the improved longhorn beetle whisker optimizing algorithm can show stronger advantages than the traditional mode in shale gas pressure control production.
The above embodiments are only for illustrating the technical solution of the present invention, and are not limiting; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims (8)
1. The wellhead pressure control method based on the improved longhorn beetle whisker algorithm for optimizing the fuzzy PID is characterized by comprising the following steps of:
s101, collecting wellhead pressure data X i And the opening Y of the pressure regulating valve i ；
S102, wellhead pressure data X i And the opening Y of the pressure regulating valve i Performing curve fitting on the relation of the (2);
s103, the input quantity is subjected to fuzzification, and a fuzzy rule table is determined through fuzzy reasoning;
s104, an improved longhorn beetle whisker algorithm;
s105, optimizing the fuzzy PID controller by using an improved longhorn beetle whisker algorithm to obtain an optimal solution of the quantization factor and the scaling factor in a given spatial range, and setting a fitness function as an error performance index ITAE.
2. The wellhead pressure control method based on improved longhorn beetle whisker algorithm optimization fuzzy PID of claim 1, wherein in step S101, wellhead pressure data X is collected at a sampling frequency of 10ms i And the opening Y of the pressure regulating valve i 。
3. The wellhead pressure control method based on improved longhorn beetle whisker algorithm optimization fuzzy PID of claim 1, wherein the specific steps of step S102 are:
s201, setting a curve fitting model; the method comprises the following steps: given the acquired wellhead-related parameters (x i ，y i ) The curve fitting model is:
wherein x is i Representing wellhead pressure data points, y i The valve opening value corresponding to each wellhead pressure data point is a, b, c, d, h which is a parameter to be estimated; e is a natural constant;
s202, determining an objective function; the method comprises the following steps: setting an objective functionSearching an optimal parameter p to minimize epsilon;
wherein ε: measuring an objective function of the performance quality of the control system; and p: the opening degree of the wellhead pressure valve is regulated to reach the control parameter of the required wellhead pressure value (y); x: the measured wellhead pressure value is used as a feedback regulating control parameter (p) to reach a required wellhead pressure value (y); y: the control system needs to maintain the wellhead pressure value; f (x, p): a model relating the control parameter (p) and the measured wellhead pressure (x) to an actual wellhead pressure value obtained by adjusting the wellhead pressure valve;
s203, iteratively optimizing through a damping least square method, and solving parameters to be estimated; the method comprises the following steps: carrying out iterative solution on parameters to be estimated of the curve fitting model by adopting a damping least square algorithm;
s204, outputting a parameter solving result after convergence judgment;
obtaining a fitting curve: y is Y i ＝F(X i )；
Wherein Y is more than or equal to 0 i N is less than or equal to N, N is the maximum opening value of the valve, and F (-) is a nonlinear fitting model.
4. The wellhead pressure control method based on improved longhorn beetle whisker algorithm optimizing fuzzy PID of claim 3, wherein step S203 specifically comprises the steps of:
(1) Taking the initial point p 0 Terminating the control parameter epsilon and calculating epsilon 0 K is defined as 0, lambda 0 ＝10 -3 ，v＝10；
(2) Computing jacobian matrix J k Calculate N k ＝J k T J k +λ k diag(J k T J k ) Constructing an incremental normal equation N k ·δ k ＝J k T ε k ；
Wherein diag (·) is to construct a new diagonal matrix with diagonal elements of the matrix; jk: iterating the jacobian matrix at the kth time; nk: iterating the damping law equation matrix in the k; jkT: iterating the transpose of the k-th time jacobian matrix; λk: iterating the damping factor at the kth time; εk: residual vector at iteration k; δk: an increment parameter vector in the iterative k process;
(3) Solving the increment normal equation to obtain delta k 。
5. The wellhead pressure control method based on improved longhorn beetle whisker algorithm optimizing fuzzy PID of claim 4, wherein step S204 is specifically:
if it isLet p k+1 ＝p k +δ k If delta k Stopping iteration and outputting a result, wherein the value of a, b, c, d, h can be calculated according to the iteration result; let lambda get no k+1 ＝λ k V, go to step (2) in step S203; if it isLet lambda get k+1 ＝λ k V, re-solving the normal equation to obtain delta k Turning to step (3) in step S203;
where k of pk and εk represents the kth iteration, V: the constant factor of damping is reduced as the algorithm proceeds.
6. The wellhead pressure control method based on improved longhorn beetle whisker algorithm optimization fuzzy PID of claim 1, wherein the fuzzy rule table of the fuzzy PID controller is created as follows:
601. determining the input and output of a controller; the method comprises the following steps: determining the input of the fuzzy PID controller as a deviation e and a deviation variation e c The output is the parameter increment delta k of the fuzzy control P 、Δk I 、ΔK D ；
The calculation formula of the fuzzy control is as follows:
k P ＝k P1 +Δk P
k I ＝k I1 +Δk I
k D ＝k D1 +Δk D ；
wherein k is P 、k I 、K D Parameters of the fuzzy PID controller are finally input; k (k) P1 、k I1 、k D1 Is an initial value; Δk P 、Δk I 、Δk D Is the parameter increment;
602. setting a fuzzy universe and dividing fuzzy subsets; the method comprises the following steps: deviation e and deviation variation e c The actual value range of (2) is the basic domain, the fuzzy PID controller is converted into the fuzzy domain by the quantization factor before being input, and the output is required to pass through the scale factorThe son converts the fuzzy theory domain into the basic theory domain, and sets the fuzzy theory domain of the input value and the output value as follows:
e，e c ＝[-3，3]
Δk P ，Δk D ，Δk D ＝[-1，1]
dividing the fuzzy discourse domain into fuzzy subsets, and determining different numbers of the subsets according to different control requirements:
e，e c ＝{NB，NM，NS，Z，PS，PM，PB}
Δk p ，Δk 1 ，Δk D ＝{NB，NM，NS，Z，PS，PM，PB}
603. creating a fuzzy rule table; the method comprises the following steps: the fuzzy PID controller is based on the deviation e and the deviation change rate e c The size of the input is converted into the blurring amount, and the deviation e and the deviation change rate e which are converted into the domain range are converted c Performing fuzzy processing to convert the original accurate input quantity into fuzzy quantity, and representing by using a corresponding fuzzy set; the argument of the deviation e is [ -3,3]Deviation change rate e c The domain of (1) is [ -1,1]Deviation e and deviation rate of change e c The fuzzy linguistic value of (2) is { NB, NM, NS, Z, PS, PM, PB };
604. setting a fitness function; the fitness function is set as the error performance index ITAE:
ITAE＝∫ 0 ∞ t|e(t)|dt；
wherein t: a time variable representing the evaluation duration; i e (t) |: the absolute value of the error signal e (t) at time t represents the deviation of the system output from the desired reference signal at this time; special (V) 0 And (3) carrying out the following steps: time integration values from the initial time (0) to (++) represent time integration errors.
7. The wellhead pressure control method based on improved longhorn beetle whisker algorithm optimization fuzzy PID of claim 1, wherein the improved longhorn beetle whisker algorithm flow is as follows:
step1, initializing parameters and an objective function; generating random direction vectors, and sequentially obtaining whisker positions;
the positions of the longicorn in the n-dimensional space are as follows: x (X1, X2,) xn; the positions of the left antenna and the right antenna of the longicorn are as follows:
wherein l represents the distance between the centroid of the longicorn and the tentacle,representing a random unit vector; xr=x+d: the position of the right antenna is set to be the current position X plus a scaling factor d for each dimension of the search space; xl=x-d: the position of the left antenna is set as the current position X minus the scaling factor d of each dimension of the search space;
normalization operation is required for the unit vector:
wherein, D: an integer representing the step size or distance that the search can move in each iteration; rands (D, 1): d-dimensional random vectors generated by "Rands" functions; ||rands (D, 1) ||: euclidean norms of the random vectors;
step2, updating the position of the longhorn beetle and the optimal objective function value according to the value of the tentacle position;
since the two antennas obtain the objective function information of the two positions, the two positions need to be preferentially advanced:
wherein t represents the iteration number, and the f (·) function is the objective function, δ t Representing the step length of the t-th exploration, wherein sign (·) is a sign function;
the step size needs to be continuously smaller during each iteration, so it can be set to delta t+1 ＝δ t *η；
Wherein η represents the speed at which the step size shortens per iteration;
step3, dynamically improving the Step length factor, and ending when the termination condition is reached; the improvement steps are as follows:
the expression is:
wherein eta and alpha are step factors which change in real time and fixed step factors respectively; n and i are the total iteration times and the current iteration times respectively; f (f) i 、f t The current and historical optimal fitness values, respectively.
8. The wellhead pressure control method based on improved longhorn beetle whisker algorithm optimizing fuzzy PID of claim 1, wherein the step of optimizing fuzzy PID controller using improved longhorn beetle whisker algorithm is as follows:
step1, generating/updating the position of the longicorn;
step2, setting the mass center of the longicorn to 5 dimensions and assigning K to the mass center e 、K ec 、K P_u 、K I_u 、K D_u The method comprises the steps of carrying out a first treatment on the surface of the The method comprises the following steps: setting the longicorn centroid as 5 space dimensions, and setting the longicorn centroid position and the longicorn orientationInitializing; decomposing the coordinates of the centroid of the ox in the initialization information into corresponding 5 parameter values K e 、K ec 、K P_u 、K I_u 、K D_u Transmitting the controller system, performing operation calculation to obtain the fitness values of the left and right whiskers, and judging the flight direction of the longicorn in the next step;
step3, calculating to obtain an fitness function value, namely an ITAE index; the method comprises the following steps: updating the position information of the longicorn according to the fitness value, decomposing the position information into 5 parameters again and assigning the 5 parameters to a controller system, and after the system calculates the fitness function value, outputting the fitness function value, namely an ITAE index, and judging whether the fitness function value reaches a preset threshold or reaches a preset iteration number; if the fitness function value reaches a preset threshold value or reaches a preset iteration number, executing the next step; otherwise, executing Step2;
step4, obtaining the optimal quantization factor and the optimal scaling factor of the fuzzy control system, and ending the calculation.
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