CN114995149B - Hydraulic position servo system improved chaos variable weight sparrow search parameter identification method - Google Patents

Hydraulic position servo system improved chaos variable weight sparrow search parameter identification method Download PDF

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CN114995149B
CN114995149B CN202210665775.5A CN202210665775A CN114995149B CN 114995149 B CN114995149 B CN 114995149B CN 202210665775 A CN202210665775 A CN 202210665775A CN 114995149 B CN114995149 B CN 114995149B
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sparrow
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position servo
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李俊红
严俊
蒋一哲
陈楠
程赟
张泓睿
储杰
褚云琨
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Nantong University
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Abstract

The invention provides an improved chaos variable-weight sparrow search parameter identification method for a hydraulic position servo system, and belongs to the technical field of hydraulic position servo system identification. The technical problems of identifying parameters and time delay of a mathematical model established for the hydraulic position servo system when the hydraulic position servo system performs analysis and control are solved. The technical proposal is as follows: the method comprises the following steps: step 1), a single-input single-output model of a hydraulic position servo system is established; and 2) constructing an identification flow of an improved chaos variable weight sparrow search parameter identification method of the hydraulic position servo system, and estimating all parameters and time delay. The beneficial effects of the invention are as follows: the improved chaotic variable-weight sparrow search parameter identification method for the hydraulic position servo system has higher convergence speed and higher convergence precision, and can be better suitable for modeling and parameter identification of a time-lag feedback nonlinear model of the hydraulic position servo system.

Description

Hydraulic position servo system improved chaos variable weight sparrow search parameter identification method
Technical Field
The invention relates to the technical field, in particular to an improved chaos variable weight sparrow search parameter identification method for a hydraulic position servo system.
Background
With the development of military products and civil industry, the requirements for hydraulic position servo systems are increasing. The hydraulic position servo system not only needs to be capable of fast action, but also has higher and higher precision requirements. In order to better analyze and control the hydraulic position servo system, a corresponding mathematical model needs to be built for the hydraulic position servo system, and parameters and time delay of the built model are identified. Through decades of advances in computer technology, many identification methods have been developed, such as genetic algorithms, ant colony algorithms, and whale optimization algorithms. The genetic algorithm has strong global searching capability, but the algorithm has weak local searching capability, and only suboptimal solutions can be obtained. The ant colony algorithm has high convergence speed, but the parameters to be set are more and the search randomness is large, so that a satisfactory identification effect cannot be achieved in actual production; the whale algorithm can perform well on the single-target optimization problem, but the effect of the method on multi-target search is poor and satisfactory, and the method is easy to sink into local optimization, so that the numerical estimation error is larger.
Disclosure of Invention
The invention aims to provide an improved chaotic variable-weight sparrow search parameter identification method for a hydraulic position servo system, which is a group intelligent optimization algorithm, has higher convergence speed and higher convergence precision, and can be well suitable for parameter identification of the hydraulic position servo system.
In order to achieve the aim of the invention, the invention adopts the technical scheme that: the improved chaos variable weight sparrow search parameter identification method for the hydraulic position servo system specifically comprises the following steps:
and 1) constructing a time lag feedback nonlinear identification model of the hydraulic position servo system.
And 2) constructing an identification flow of the hydraulic position servo system improved chaos variable weight sparrow search parameter identification method.
The first step: initializing a sparrow search algorithm, and initializing a sparrow population by adopting improved Circle chaotic mapping;
and a second step of: collecting given voltage signals of a hydraulic position servo system as input data, and load displacement data of the hydraulic position servo system as output data;
and a third step of: calculating individual fitness in the sparrow group, sequencing all the individual fitness of the sparrows, finding out a global optimal fitness value and a global worst fitness value, and then calculating an initial global optimal position;
fourth step: let iteration variable k=1, calculate the initial position of sparrow;
fifth step: calculating a current inertia weight value based on a linear decreasing weight method, and updating the position of the finder;
sixth step: updating the position of the follower;
seventh step: updating the position of the alerter;
eighth step: calculating the fitness of the sparrow population, reordering, and updating the position of the sparrow population;
ninth step: for all sparrows, calculating the optimal sparrow positions of the group;
tenth step: extracting parameter vector and time delay estimated value from the group optimal position;
eleventh step: and adding 1 to the iteration variable k value, and repeating the process.
As a further optimization scheme of the hydraulic position servo system time lag feedback nonlinear model identification method based on the improved Circle chaotic linear variable weight sparrow search algorithm, the specific modeling steps of the step 1) are as follows:
(1-1) constructing a time lag feedback nonlinear model of the hydraulic position servo system:
Figure BDA0003691605780000021
Figure BDA0003691605780000022
Figure BDA0003691605780000023
Figure BDA0003691605780000024
wherein r (t) is input quantity, y (t) is output quantity,
Figure BDA0003691605780000025
for feedback channel output, v (t) is zero in mean and sigma in variance 2 White noise satisfying gaussian distribution; definition of x (t), u (t) and w (t) areAn undetectable intermediate variable; τ is feedback nonlinear system time lag, z is a backward operator, z -1 y (t) =y (t-1), a (z), B (z) is a polynomial about z, described as follows:
Figure BDA0003691605780000026
Figure BDA0003691605780000027
the nonlinear part of the system can be expressed as a transfer function:
Figure BDA0003691605780000028
wherein the unknown parameter gamma i (i=1, 2,) m is the coefficient of the nonlinear function, m is the number of parameters of the nonlinear block.
The formula is obtained by multiplying both sides of the formula by A (z):
A(z)y(t)＝q -τ B(z)u(t)+v(t) (8)
can be expressed as:
Figure BDA0003691605780000031
wherein the noise model output w (t) and the feedforward tract output x (t) are:
Figure BDA0003691605780000032
Figure BDA0003691605780000033
the feedback nonlinear system model can be expressed as:
Figure BDA0003691605780000034
(1-2) defining the parameter vectors a, b of the linear subsystem and the parameter vector γ of the nonlinear section as:
Figure BDA0003691605780000035
then the parameter vector θ of the entire model is expressed as:
Figure BDA0003691605780000036
corresponding information vector
Figure BDA0003691605780000037
Expressed as:
Figure BDA0003691605780000038
Figure BDA0003691605780000039
wherein ：
Figure BDA00036916057800000310
Figure BDA00036916057800000311
Figure BDA0003691605780000041
wherein ：
f(y(t))＝[f 1 (y(t)),f 2 (y(t)),...,f m (y(t))]∈R 1×m
according to the above definition, the nonlinear part of the system
Figure BDA0003691605780000042
Expressed as:
Figure BDA0003691605780000043
(1-3) we then get a described time-lapse feedback nonlinear model of the hydraulic position servo system:
Figure BDA0003691605780000044
then we get the time-lag feedback nonlinear model of the hydraulic position servo system as:
Figure BDA0003691605780000045
as a further optimization scheme of the hydraulic position servo system improved chaos variable weight sparrow search parameter identification method, the step 2) is constructed, and the specific steps of the hydraulic position servo system improved chaos variable weight sparrow search parameter identification flow are as follows:
(2-1) setting the number of sparrows to N, each sparrow comprising N a +n b +m variables, through (18), the sparrow population is initialized using the modified Circle chaotic map. Set X n X is the current sparrow position n+1 For the updated sparrow position, the maximum iteration number is T, the early warning value is ST, the ratio of the finder PD to the alerter SD and the ratio of the finder PD to the alerter SD are w max 、w min ，w k Is the inertial weight, w max and wmin The maximum and minimum of the linear weights, respectively.
The original Circle chaotic mapping expression is:
Figure BDA0003691605780000051
the modified Circle chaotic mapping expression is as follows:
Figure BDA0003691605780000052
(2-2) collecting given voltage signal input data and load displacement output data { r (t), y (t) } of the hydraulic position servo system. The structure outputs a pile-up vector Y (l) as shown in the following formula (19):
Y(l)＝[y(l),y(l-1),...,y(1)] T ∈R l (19)
construct ψ (l, τ) as information stacking vector as formula (20):
Figure BDA0003691605780000053
where l is the data length.
(2-3) calculating individual fitness in the sparrow group through (21), sequencing all the individual fitness of the sparrows, and finding out a global optimal fitness value f g And a global worst fitness value f w Then calculate the initial global optimum position by (22)
Figure BDA0003691605780000054
Figure BDA0003691605780000055
Figure BDA0003691605780000056
(2-4) setting an iteration variable k=1, starting iteration, the initial position of the individual being
Figure BDA0003691605780000057
Figure BDA0003691605780000058
(2-5) calculating w by (24) based on a linearly decreasing weight method k Updating the finder position to be by the formula (25)
Figure BDA0003691605780000059
Figure BDA00036916057800000510
Figure BDA00036916057800000511
Wherein k is an iteration variable;
Figure BDA0003691605780000061
representing the position of the ith sparrow in the j-th dimension in the k-th generation, and the random number xi [0,1 ]]，
Figure BDA0003691605780000062
For the k generation population global optimum fitness, Q is a random number obeying normal distribution, L is a 1 x d-dimensional matrix with each element being 1; r is R 2 The alarm value is represented, and ST represents the safety threshold.
(2-6) updating follower position according to (26)
Figure BDA0003691605780000063
Figure BDA0003691605780000064
wherein ,
Figure BDA0003691605780000065
the individual position representing the worst k-th generation fitness value,/->
Figure BDA0003691605780000066
The individual position with the best fitness in the k+1 generation is indicated. A represents a 1×d matrix in which each element is preset to-1 or 1, and A + ＝A T (AA T ) -1 。
(2-7) updating the alerter position according to (27)
Figure BDA0003691605780000067
Figure BDA0003691605780000068
wherein ,
Figure BDA0003691605780000069
the global optimal position in the kth generation is represented, beta is taken as a step control parameter, is a random number obeying normal distribution with the mean value of 0 and the variance of 1, lambda represents the direction of sparrow movement and is also taken as the step control parameter, and lambda epsilon [ -1, 1)]. Epsilon is set to a constant to avoid denominator 0.f (f) i Indicating the fitness value of the current individual, f g and fw And the fitness value of the current global optimal and worst individuals is represented.
(2-8) calculating the fitness of the sparrow population, reordering, and updating the position of the sparrow population;
(2-9) passing (28)
Figure BDA00036916057800000610
and
Figure BDA00036916057800000611
From->
Figure BDA00036916057800000612
Separated out. Calculating an information vector by (29)>
Figure BDA00036916057800000613
Then form an information matrix from (30)>
Figure BDA00036916057800000614
Figure BDA00036916057800000615
Figure BDA00036916057800000616
Figure BDA00036916057800000617
(2-10) calculating a parameter vector by (31)
Figure BDA0003691605780000071
And calculating an information vector by (32)>
Figure BDA0003691605780000072
Then form an information matrix from (33)>
Figure BDA0003691605780000073
Figure BDA0003691605780000074
Figure BDA0003691605780000075
Figure BDA0003691605780000076
(2-11) for all the sparrows, the optimal sparrow position is calculated according to (34)
Figure BDA0003691605780000077
Figure BDA0003691605780000078
(2-12) from the optimal position by (35) (36) (37) (38)
Figure BDA0003691605780000079
Extract->
Figure BDA00036916057800000710
and
Figure BDA00036916057800000711
Figure BDA00036916057800000712
Figure BDA00036916057800000713
Figure BDA00036916057800000714
Figure BDA00036916057800000715
Wherein g represents the parameter order,
Figure BDA00036916057800000716
and
Figure BDA00036916057800000717
Estimated values of parameter vectors a, b and gamma, respectively,/->
Figure BDA00036916057800000718
Is an estimate of the time delay τ.
(2-13) increasing the iteration variable kAdd 1 and return to step (2-5). When k reaches the maximum iteration number T, terminating the iteration and obtaining a parameter vector
Figure BDA00036916057800000719
And time delay->
Figure BDA00036916057800000720
The identification method is accurate in calculation, high in identification precision and suitable for parameter estimation of the time-lag feedback nonlinear model of the hydraulic position servo system.
Compared with the prior art, the invention has the beneficial effects that:
(1) The method establishes a model for identifying the time-lag feedback nonlinear parameters of the hydraulic position servo system, takes a given voltage signal of the hydraulic position servo system as input data and takes load displacement data of the hydraulic position servo system as output data; and identifying the model parameters by using an improved Circle chaotic linear variable weight sparrow search algorithm. It can be seen from fig. 5 that the algorithm can well identify the internal parameters of the model.
(2) Compared with a sparrow search algorithm and a particle swarm optimization algorithm, the improved Circle chaotic linear variable weight sparrow search algorithm adopts an improved Circle chaotic map to initialize a population, so that population diversity is increased, and global search capacity and convergence speed of the algorithm are improved; the improvement is made on the position update of the finches of discoverers, so that the risk of easy precocity of a group intelligent algorithm is reduced, and the phenomenon that the algorithm is easy to oscillate near a global optimal solution in the later period is avoided. The improved sparrow search algorithm can better identify a feedback nonlinear system with unknown time lags, and the identification accuracy is higher; meanwhile, the identification method is also proved to have better applicability to the hydraulic servo system.
Drawings
The accompanying drawings are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate the invention and together with the embodiments of the invention, serve to explain the invention.
FIG. 1 is a block diagram of a hydraulic position servo system according to the present inventionA composition layout; wherein U is i To input voltage signal, U f For feedback voltage signal, deltaU is error signal, x p Is the load displacement.
FIG. 2 is a schematic diagram of the hydraulic position servo system according to the present invention.
FIG. 3 is a schematic diagram of a hydraulic position servo system time-lag feedback nonlinear model structure in the present invention.
FIG. 4 is a general flow chart of the method for identifying the search parameters of the sparrow with chaos and variable weight based on the hydraulic position servo system.
Fig. 5 is a schematic diagram showing a variation of the parameter estimation error δ with the number of iterations k according to an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. Of course, the specific embodiments described herein are for purposes of illustration only and are not intended to limit the invention.
Examples
The improved chaos variable-weight sparrow search parameter identification method for the hydraulic position servo system is applied to a hydraulic servo system, and the composition distribution diagram of the system is shown in fig. 1. The embodiment of the invention provides a relation between a given voltage signal input and a load displacement output, and nonlinear and linear links of the hydraulic servo system are represented by the following functions:
Figure BDA0003691605780000081
A(z)＝1+a 1 z -1 +a 2 z -2 ＝1+0.80z -1 +0.34z -2
B(z)＝b 1 z -1 +b 2 z -2 ＝0.44z -1 +0.67z -2
the true values of the parameter vectors are as follows:
θ＝[a 1 ,a 2 ,b 1 ,b 2 ,γ 1 ,γ 2 ,τ] Τ ＝[0.80,0.34,0.44,0.67,0.14,0.11,1.00] Τ
definition of the definition
Figure BDA0003691605780000091
For the estimation of θ, parameter estimation error +.>
Figure BDA0003691605780000092
MATLAB software is adopted in the identification process, and a time lag feedback nonlinear model of the hydraulic servo system is established according to input and output data of the system.
The method for identifying the improved chaos variable weight sparrow search parameters of the hydraulic position servo system of the embodiment comprises the following specific steps:
(1) The method comprises the following specific steps of:
the first step: the construction of the time-lapse feedback nonlinear model of the hydraulic position servo system is shown in fig. 3.
And a second step of: according to the model, a time lag feedback nonlinear model expression of the hydraulic position servo system is constructed as follows:
Figure BDA0003691605780000093
Figure BDA0003691605780000094
Figure BDA0003691605780000095
Figure BDA0003691605780000096
wherein r (t) is input quantity, y (t) is output quantity,
Figure BDA0003691605780000097
for feedback channel output, v (t) is zero in mean and sigma in variance 2 White noise satisfying gaussian distribution; defining x (t), u (t) and w (t) as non-measurable intermediate variables; τ is feedback nonlinear system time lag, z is a backward operator, z -1 y (t) =y (t-1), a (z), B (z) is a polynomial about z, described as follows:
Figure BDA0003691605780000098
Figure BDA0003691605780000099
wherein the polynomial factor a i and bj Is the parameter to be estimated, the order n of the denominator a And the order n of the molecule b Are known. The nonlinear part of the system can be expressed as a transfer function:
Figure BDA00036916057800000910
wherein ,γi (i=1, 2,) m is the coefficient of the nonlinear function that needs to be identified, m is the number of parameters of the nonlinear block.
The formula is obtained by multiplying both sides of the formula by A (z):
A(z)y(t)＝q -τ B(z)u(t)+v(t) (8)
can be expressed as:
Figure BDA0003691605780000101
wherein the noise model output w (t) and the feedforward tract output x (t) are:
Figure BDA0003691605780000102
Figure BDA0003691605780000103
the feedback nonlinear system model can be expressed as:
Figure BDA0003691605780000104
the parameter vectors a, b of the linear subsystem and the parameter vector gamma of the nonlinear part are defined as:
Figure BDA0003691605780000105
then the parameter vector θ of the entire model is expressed as:
Figure BDA0003691605780000106
corresponding information vector
Figure BDA0003691605780000107
Expressed as:
Figure BDA0003691605780000108
Figure BDA0003691605780000109
wherein ：
Figure BDA00036916057800001010
Figure BDA00036916057800001011
Figure BDA0003691605780000111
wherein ：
f(y(t))＝[f 1 (y(t)),f 2 (y(t)),...,f m (y(t))]∈R 1×m
according to the above definition, the nonlinear part of the system
Figure BDA0003691605780000112
Expressed as:
Figure BDA0003691605780000113
the time lag feedback nonlinear model of the described hydraulic position servo system is obtained:
Figure BDA0003691605780000114
and a third step of: the time lag feedback nonlinear model of the hydraulic position servo system is obtained as follows:
Figure BDA0003691605780000115
(2) The hydraulic position servo system is constructed to improve the identification flow of the chaotic variable weight sparrow search parameter identification method.
The first step: initializing a sparrow search algorithm, and initializing a sparrow population by adopting improved Circle chaotic mapping;
and a second step of: collecting given voltage signals of a hydraulic position servo system as input data, and load displacement data of the hydraulic position servo system as output data;
and a third step of: calculating individual fitness in the sparrow group, sequencing all the individual fitness of the sparrows, finding out a global optimal fitness value and a global worst fitness value, and then calculating an initial global optimal position;
fourth step: let iteration variable k=1, calculate the initial position of sparrow;
fifth step: calculating a current inertia weight value based on a linear decreasing weight method, and updating the position of the finder;
sixth step: updating the position of the follower;
seventh step: updating the position of the alerter;
eighth step: calculating the fitness of the sparrow population, reordering, and updating the position of the sparrow population;
ninth step: for all sparrows, calculating the optimal sparrow positions of the group;
tenth step: extracting parameter vector and time delay estimated value from the group optimal position;
eleventh step: and adding 1 to the iteration variable k value, and repeating the process.
(3) Referring to fig. 4, the method for identifying the improved chaos variable weight sparrow search parameters for constructing the hydraulic position servo system is as follows:
Figure BDA0003691605780000121
Figure BDA0003691605780000122
Figure BDA0003691605780000123
Figure BDA0003691605780000124
Figure BDA0003691605780000125
Figure BDA0003691605780000126
Figure BDA0003691605780000127
Figure BDA0003691605780000128
Figure BDA0003691605780000131
Figure BDA0003691605780000132
Figure BDA0003691605780000133
Figure BDA0003691605780000134
Figure BDA0003691605780000135
Figure BDA0003691605780000136
Y(l)＝[y(l),y(l-1),...,y(1)] T (31)
Figure BDA0003691605780000137
Figure BDA0003691605780000138
Figure BDA0003691605780000139
Figure BDA00036916057800001310
referring to fig. 4, the specific steps of the identification flow of the hydraulic position servo system improved chaos variable weight sparrow search parameter identification method are as follows:
(1) Setting the number of sparrows to be N, wherein each sparrow contains N a +n b +m variables, initializing sparrow population by (17) adopting improved Circle chaotic mapping, setting X n X is the current sparrow position n+1 For the updated sparrow position, the maximum iteration number is T, the early warning value is ST, the ratio of the finder PD to the alerter SD and the ratio of the finder PD to the alerter SD are w max 、w min. wherein wk Is the inertial weight, w max and wmin Respectively a maximum value and a minimum value of the linear weight;
(2) The data length l is set, and given voltage signal input data and load displacement output data { r (t), y (t) } of the hydraulic position servo system are collected. Constructing an output pile-up vector form Y (l) and an information pile-up vector ψ (l, τ) by (31);
(3) Calculating individual fitness in the sparrow group by (18), sequencing all the individual fitness of the sparrows, and finding out a global optimal fitness value f g And a global worst fitness value f w Then calculate the initial global optimum position
Figure BDA00036916057800001311
(4) Let k=1, start iteration, the initial position of the individual is
Figure BDA00036916057800001312
(5) Calculating w by (19) based on linear decreasing weight method k Will be found by the formula (20)The location of the person is updated as
Figure BDA00036916057800001313
(6) Updating follower position by (21)
Figure BDA0003691605780000141
(7) Updating the alerter location by means of (22)
Figure BDA0003691605780000142
(8) Calculating the fitness of the sparrow population, reordering, and updating the position of the sparrow population;
(9) Will be by the method (23)
Figure BDA0003691605780000143
and
Figure BDA0003691605780000144
From->
Figure BDA0003691605780000145
By (24) calculating the information vector +.>
Figure BDA0003691605780000146
Then form the information matrix from (25)>
Figure BDA0003691605780000147
(10) Calculating a parameter vector by (26)
Figure BDA0003691605780000148
And calculating an information vector by (27)>
Figure BDA0003691605780000149
Then form the information matrix from (28)>
Figure BDA00036916057800001410
(11) For all sparrows, calculating the optimal sparrow position according to (29)
Figure BDA00036916057800001411
By the formula (30) will->
Figure BDA00036916057800001412
and
Figure BDA00036916057800001413
From the slave
Figure BDA00036916057800001414
Separating;
(12) From the optimal position by (32) (33) (34) (35)
Figure BDA00036916057800001415
Extract->
Figure BDA00036916057800001416
and
Figure BDA00036916057800001417
(13) Increasing the iteration variable k by 1 and returning to the step (2-5), and stopping iteration and obtaining the parameter vector when k reaches the maximum iteration number T
Figure BDA00036916057800001418
and
Figure BDA00036916057800001419
Wherein the variables are defined as follows:
defining an input quantity as r (t) and an output quantity as y (t); definition v (t) is a mean of zero and variance of sigma 2 White noise satisfying gaussian distribution; define x (t) and w (t) as non-measurable intermediate variables; defining theta as a parameter vector;
Figure BDA00036916057800001420
as an information vector; l is a numberAccording to the length, psi (l) is an information accumulation vector, and Y (l) is an output accumulation vector;
setting the number of sparrows to be N, wherein each sparrow contains N a +n b +m variables, maximum iteration number T, early warning value ST, finder proportion PD, alerter proportion SD, w is inertial weight, w max and wmin The maximum and minimum of the linear weights, respectively.
k is an iteration variable;
Figure BDA00036916057800001421
representing the position of the ith sparrow in the j-th dimension in the k-th generation, and the random number xi [0,1 ]]，
Figure BDA00036916057800001422
For the k generation population global optimum fitness, Q is a random number obeying normal distribution, L is a 1 x d-dimensional matrix with each element being 1; r is R 2 The alarm value is represented, and ST represents the safety threshold.
Figure BDA00036916057800001423
Represents the individual position of the k-th generation with worst fitness,/->
Figure BDA00036916057800001424
The individual position with the best fitness in the k+1 generation is indicated. A represents a 1×d matrix in which each element is preset to-1 or 1, and A + ＝A T (AA T ) -1 。
Figure BDA0003691605780000151
The global optimal position in the kth generation is represented, beta is taken as a step control parameter, is a random number obeying normal distribution with the mean value of 0 and the variance of 1, lambda represents the direction of sparrow movement and is also taken as the step control parameter, and lambda epsilon [ -1, 1)]. Epsilon is set to a constant to avoid denominator 0.f (f) i Indicating the fitness value of the current individual, f g and fw Indicating the fitness of the current globally optimal and worst individualsValues.
Definition of the definition
Figure BDA0003691605780000152
Estimated value for parameter vector θ at the kth iteration,
Figure BDA0003691605780000153
For the estimated value of the time delay τ at the kth iteration, define +.>
Figure BDA0003691605780000154
Is information vector->
Figure BDA0003691605780000155
At the estimated value of the kth iteration, define +.>
Figure BDA0003691605780000156
An estimated value of the information accumulation vector psi (l) at the kth iteration;
definition of the definition
Figure BDA0003691605780000157
For parameter vector->
Figure BDA0003691605780000158
Is the individual best solution of->
Figure BDA0003691605780000159
For time delay->
Figure BDA00036916057800001510
Is the individual optimum value of (1); definition of the definition
Figure BDA00036916057800001511
Is information vector->
Figure BDA00036916057800001512
Is optimal for the individual; definitions->
Figure BDA00036916057800001513
For letterInformation accumulation vector->
Figure BDA00036916057800001514
Is optimal for the individual; g represents the parameter order, < >>
Figure BDA00036916057800001515
and
Figure BDA00036916057800001516
Estimated values of parameter vectors a, b and gamma, respectively,/->
Figure BDA00036916057800001517
An estimated value of the time delay τ;
the foregoing description of the preferred embodiments of the invention is not intended to limit the invention to the precise form disclosed, and any such modifications, equivalents, and alternatives falling within the spirit and scope of the invention are intended to be included within the scope of the invention.

Claims (1)

1. The method for identifying the search parameters of the chaos variable-weight sparrow by using the hydraulic position servo system is characterized by comprising the following steps of:
step 1), constructing a time-lag feedback nonlinear identification model of a hydraulic position servo system;
step 2), constructing an identification flow of an improved chaos variable weight sparrow search parameter identification method of a hydraulic position servo system; the method comprises the following steps:
2-1) initializing a sparrow search algorithm, and initializing a sparrow population by adopting improved Circle chaotic mapping;
2-2) collecting a given voltage signal of the hydraulic position servo system as input data and load displacement data of the hydraulic position servo system as output data;
2-3) calculating individual fitness in the sparrow group, sorting all the individual fitness of the sparrows, finding out a global optimal fitness value and a global worst fitness value, and then calculating an initial global optimal position;
2-4) making the iteration variable k=1, and calculating the initial position of the sparrow;
2-5) calculating a current inertia weight value based on a linear decreasing weight method, and updating the position of the finder;
2-6) updating the location of the follower;
2-7) updating the position of the alerter;
2-8) calculating the fitness of the sparrow population, reordering, and updating the position of the sparrow population;
2-9) for all sparrows, calculating the group best sparrow position;
2-10) separating and extracting parameter vectors and estimated values of time delay from the optimal positions of the groups;
2-11) adding 1 to the iteration variable k value, and repeating the process;
the modeling step of the step 1) is as follows:
(1-1) constructing a time lag feedback nonlinear model of the hydraulic position servo system:
Figure FDA0004209444910000011
Figure FDA0004209444910000012
Figure FDA0004209444910000013
Figure FDA0004209444910000014
wherein r (t) is input quantity, y (t) is output quantity,
Figure FDA0004209444910000015
for feedback channel output, v (t) is zero in mean and sigma in variance 2 White noise satisfying gaussian distribution; defining x (t), u (t) and w (t) as non-measurable intermediate variables;τ is feedback nonlinear system time lag, z is a backward operator, z -1 y (t) =y (t-1), a (z), B (z) is a polynomial about z, described as follows:
Figure FDA0004209444910000021
Figure FDA0004209444910000022
the nonlinear part of the system can be expressed as a transfer function:
Figure FDA0004209444910000023
wherein the unknown parameter gamma i (i=1, 2,., m) is the coefficient of the nonlinear function, m is the number of parameters of the nonlinear block;
the formula is obtained by multiplying both sides of the formula by A (z):
A(z)y(t)＝q -τ B(z)u(t)+v(t) (8)
can be expressed as:
Figure FDA0004209444910000024
wherein the noise model output w (t) and the feedforward tract output x (t) are:
Figure FDA0004209444910000025
Figure FDA0004209444910000026
the feedback nonlinear system model is expressed as:
Figure FDA0004209444910000027
(1-2) defining the parameter vectors a, b of the linear subsystem and the parameter vector γ of the nonlinear section as:
Figure FDA0004209444910000028
the parameter vector θ of the entire model is expressed as:
Figure FDA0004209444910000029
corresponding information vector
Figure FDA00042094449100000210
Expressed as:
Figure FDA0004209444910000031
Figure FDA0004209444910000032
wherein ：
Figure FDA0004209444910000033
Figure FDA0004209444910000034
Figure FDA0004209444910000035
wherein ：
f(y(t))＝[f 1 (y(t)),f 2 (y(t)),...,f m (y(t))]∈R 1×m
according to the above definition, the nonlinear part of the system
Figure FDA0004209444910000036
Expressed as:
Figure FDA0004209444910000037
(1-3) then deriving a described time-lapse feedback nonlinear model of the hydraulic position servo system:
Figure FDA0004209444910000041
then, a time lag feedback nonlinear model of the hydraulic position servo system is obtained as follows:
Figure FDA0004209444910000042
the step 2) of constructing a hydraulic position servo system improved chaos variable weight sparrow search parameter identification process comprises the following steps:
(2-1) setting the number of sparrows to N, each sparrow comprising N a +n b +m variables, by equation (18), using modified Circle chaotic map to initialize sparrow population, setting X n X is the current sparrow position n+1 For the updated sparrow position, the maximum iteration number is T, the early warning value is ST, the ratio of the finder PD to the alerter SD and the ratio of the finder PD to the alerter SD are w max 、w min ，w k Is the inertial weight, w max and wmin Respectively a maximum value and a minimum value of the linear weight;
the original Circle chaotic mapping expression is:
Figure FDA0004209444910000043
the modified Circle chaotic mapping expression is as follows:
Figure FDA0004209444910000044
(2-2) collecting given voltage signal input data and load displacement output data { r (t), Y (t) } of the hydraulic position servo system, and constructing an output pile-up vector Y (l) as follows (19):
Y(l)＝[y(l),y(l-1),...,y(1)] T ∈R l (19)
the information pile-up vector ψ (l, τ) is constructed as in equation (20):
Figure FDA0004209444910000045
wherein l is the data length;
(2-3) calculating individual fitness in the sparrow group through (21), sequencing all the individual fitness of the sparrows, and finding out a global optimal fitness value f g And a global worst fitness value f w Then calculate the initial global optimum position by (22)
Figure FDA0004209444910000051
Figure FDA0004209444910000052
Figure FDA0004209444910000053
(2-4) setting an iteration variable k=1, starting iteration, the initial position of the individual being
Figure FDA0004209444910000054
Figure FDA0004209444910000055
(2-5) calculating w by (24) based on a linearly decreasing weight method k Updating the finder position to be by the formula (25)
Figure FDA0004209444910000056
Figure FDA0004209444910000057
Figure FDA0004209444910000058
Wherein k is an iteration variable;
Figure FDA0004209444910000059
representing the position of the ith sparrow in the j-th dimension in the k-th generation, and the random number xi [0,1 ]]，
Figure FDA00042094449100000510
For the k generation population global optimum fitness, Q is a random number obeying normal distribution, L is a 1 x d-dimensional matrix with each element being 1; r is R 2 Representing an alarm value, and ST representing a safety threshold;
(2-6) updating follower position according to (26)
Figure FDA00042094449100000511
Figure FDA00042094449100000512
wherein ,
Figure FDA00042094449100000513
the individual position representing the worst k-th generation fitness value,/->
Figure FDA00042094449100000514
Represents the individual position of the best fitness in the k+1th generation, A represents a 1×d matrix in which each element is preset to-1 or 1, and A + ＝A T (AA T ) -1 ；
(2-7) updating the alerter position according to (27)
Figure FDA00042094449100000515
Figure FDA00042094449100000516
wherein ,
Figure FDA00042094449100000517
the global optimal position in the kth generation is represented, beta is taken as a step control parameter, is a random number obeying normal distribution with the mean value of 0 and the variance of 1, lambda represents the direction of sparrow movement and is also taken as the step control parameter, and lambda epsilon [ -1, 1)]Epsilon is set to be constant to avoid denominator of 0, f i Indicating the fitness value of the current individual, f g and fw The fitness value of the current global optimum and worst individuals is represented; />
(2-8) calculating the fitness of the sparrow population, reordering, and updating the position of the sparrow population;
(2-9) passing (28)
Figure FDA0004209444910000061
and
Figure FDA0004209444910000062
From->
Figure FDA0004209444910000063
By (29) calculating the information vector +.>
Figure FDA0004209444910000064
Then form an information matrix from (30)>
Figure FDA0004209444910000065
Figure FDA0004209444910000066
Figure FDA0004209444910000067
Figure FDA0004209444910000068
(2-10) calculating a parameter vector by (31)
Figure FDA0004209444910000069
And calculating an information vector by (32)>
Figure FDA00042094449100000610
Then form an information matrix from (33)>
Figure FDA00042094449100000611
Figure FDA00042094449100000612
Figure FDA00042094449100000613
Figure FDA00042094449100000614
(2-11) for all the sparrows, the optimal sparrow position is calculated according to (34)
Figure FDA00042094449100000615
Figure FDA00042094449100000616
(2-12) from the optimal position by (35) (36) (37) (38)
Figure FDA00042094449100000617
Extract->
Figure FDA00042094449100000618
and
Figure FDA00042094449100000619
Figure FDA00042094449100000620
Figure FDA00042094449100000621
Figure FDA00042094449100000622
Figure FDA00042094449100000623
Wherein g represents the parameter order,
Figure FDA00042094449100000624
and
Figure FDA00042094449100000625
Estimated values of parameter vectors a, b and gamma, respectively,/->
Figure FDA00042094449100000626
An estimated value of the time delay τ;
(2-13) increasing the iteration variable k by 1 and returning to step (2-5), terminating the iteration and obtaining the parameter vector when k reaches the maximum number of iterations T
Figure FDA0004209444910000071
And time delay->
Figure FDA0004209444910000072
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