A method, system, computer readable storage medium and computer program product for identifying parameters of a LuGre friction model of a feed system based on an improved Gauss group optimization algorithm

Abstract

The application belongs to the field of system parameter identification, and relates to a feed system LuGre friction model parameter identification method, system, computer readable storage medium and computer program product based on an improved Gauss group optimization algorithm, which comprises the following steps: (1) exciting the feed system by using an identification excitation signal and collecting operation data of the feed system; the operation data are speed, acceleration and corresponding load current of the feed system under the excitation of the identification excitation signal; (2) dividing LuGre model parameters into sliding parameters and pre-sliding parameters; (3) constructing a loss function for identifying the sliding parameters and the pre-sliding parameters; (4) based on the operation data in step (1), first minimizing the loss function of the sliding parameters by using the Gauss group optimization algorithm, and then minimizing the loss function of the pre-sliding parameters by using the Gauss group optimization algorithm, to obtain identification results of the sliding parameters and the pre-sliding parameters. The application has obvious advantages in identification precision and ease of use.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of system parameter identification, and more particularly, to a feed system LuGre friction model parameter identification method, system, computer readable storage medium and computer program product based on an improved Gauss group optimization algorithm. BACKGROUND

[0002] Friction is one of the main factors affecting the tracking performance of machine tool feed systems, and establishing an accurate friction model is the key to model-based friction compensation methods. Parameterized models are the mainstream friction models in current academic research and engineering applications, and are mainly divided into static friction models and dynamic friction models. Among them, dynamic friction models have been widely used in high-precision control scenarios because they can describe dynamic friction characteristics such as pre-sliding, friction hysteresis, and friction hysteresis. LuGre model, as one of the famous dynamic friction models, can describe almost all friction characteristics, so it has received extensive attention.

[0003] Although the LuGre model has strong expression ability, it has a large number of parameters that need to be identified. Due to the difficulty of parameter identification, the LuGre model has been greatly limited in engineering applications. Existing identification methods generally use a strategy of first identifying the static parameters of the model based on steady-state data, and then identifying the dynamic parameters of the model through displacement and friction data in the pre-sliding stage. This identification method has the problems of low identification accuracy and difficulty in engineering application.

[0004] Therefore, the present application proposes a feed system LuGre friction model parameter identification method based on an improved Gauss group optimization algorithm, which has obvious advantages in identification accuracy and ease of use. SUMMARY

[0005] In view of the above defects or improvement needs of the prior art, the present application provides a feed system LuGre friction model parameter identification method, system, computer readable storage medium and computer program product based on an improved Gauss group optimization algorithm, which aims to solve the problems of difficult LuGre model parameter identification and low identification accuracy.

[0006] To achieve the above-mentioned purpose, according to one aspect of the present application, a feed system LuGre friction model parameter identification method based on an improved Gauss group optimization algorithm is provided, comprising the following steps:

[0007] (1) stimulating the feed system with an identification excitation signal and collecting the operating data of the feed system; the operating data are the speed, acceleration and corresponding load current of the feed system under the excitation of the identification excitation signal;

[0008] (2) dividing the LuGre model parameters into sliding parameters P slide ={Fs F c ,v s ,σ2}and pre-sliding parameter P stick ={σ0,σ1}; wherein, F c is the Coulomb friction force, F s is the maximum static friction force, v s is the Stribeck velocity, σ2is the viscous damping coefficient, σ0is the bristle stiffness, and σ1is the bristle damping coefficient;

[0009] (3) constructing loss functions L1and L2for identifying the sliding parameter and the pre-sliding parameter;

[0010] (4) based on the running data of step (1), first using a Gauss group optimization algorithm to minimize the loss function L1to obtain the identification result of the sliding parameter P slide , and then substituting the above identification result into the loss function L2, using the Gauss group optimization algorithm to minimize the loss function L2to obtain the identification result of the pre-sliding parameter P stick .

[0011] Further, the identification excitation signal of step (1) is a velocity signal spliced by truncated and translated Gaussian functions, and its mathematical expression is as follows:

[0012]

[0013] wherein, v(t) is the identification excitation signal about time t, A and ∑ are the amplitude and variance of the Gaussian function respectively, T v is the period of v(t), v1(t) and v2(t) are the two Gaussian functions after truncation and translation, and n = 0, 1, 2, ….

[0014] Further, the friction force of the feeding system is calculated according to formula (4) using the running data:

[0015]

[0016] wherein, F f is the friction force, K t is the motor torque constant, I is the load current, J is the equivalent total inertia of the feeding system, θ is the motor shaft angle, is the second derivative of θ, and h is the lead of the screw.

[0017] Further, the model of step (2) is the LuGre model, and its mathematical expression is as follows:

[0018]

[0019] where F is the friction force, v is the relative velocity of the contact surface, z is the bristle deformation, g(v) is used to describe the Stribeck characteristic, and sgn() is the sign function;

[0020] The parameters to be identified of the LuGre model include F c , F s , v s , σ0, σ1 and σ2. Further, through parameter sensitivity analysis, when the system enters the macroscopic sliding state, the friction force is strongly related to {F s , F c , v s , σ2} and weakly related to {σ0, σ1}, and the model can be equivalent to the Stribeck model; therefore, the friction parameters are divided into sliding parameters P slide ={F s , F c , v s , σ2} and pre-sliding parameters P stick ={σ0, σ1};

[0021] Let φ be the LuGre model, then

[0022] F f = φ(v|P slide , P stick ) (8)

[0023] When the system enters the sliding state, there is

[0024] F f_slide = φ slide (v slide |P slide ) (9)

[0025] F f_slide is the friction force in the sliding state, φ slide is the LuGre model in the sliding state, and v slide is the relative velocity of the contact surface in the sliding state.

[0026] Further, the loss function described in step (4) is constructed as follows:

[0027] The loss function L1 for identifying the sliding parameters P slide :

[0028]

[0029] where M is the data length of {v slide , F f_slide}, is the estimated friction force, and the superscript (t) represents the t time;

[0030] Then a loss function L2 for identifying the pre-sliding parameter P is constructed stick of the loss function L2

[0031]

[0032] Wherein, K is the data length of {v, F f}, and F is the full-range friction force.

[0033] Further, the update strategy of the four hyperparameters in the Gaussian swarm optimization algorithm is improved; the four hyperparameters are respectively the individual covariance matrix coefficient P c1 , the random update probability P c2 , the learning update probability P c3 , and the mutation probability P c4 ; in each iteration process, adaptive adjustment is respectively made according to formula (27)~formula (30):

[0034]

[0035] Wherein, max_iter is the maximum iteration number, c1 is the covariance factor, c2 is the random factor, c3 is the learning factor, c4 is the mutation factor, c1, c2, c3 and c4 are constants, β1, β2, β3 and β4 are constants, and the superscript q is the current iteration number.

[0036] According to another aspect of the present application, there is provided a feed system LuGre friction model parameter identification system based on an improved Gaussian swarm optimization algorithm, comprising a memory, a processor and a computer program stored on the memory, and the processor executes the computer program to realize the steps of the feed system LuGre friction model parameter identification method based on the improved Gaussian swarm optimization algorithm as claimed in any one of the preceding aspects.

[0037] According to another aspect of the present application, there is provided a computer readable storage medium having a computer program / instruction stored thereon, and the computer program is executed by a processor to realize the steps of the feed system LuGre friction model parameter identification method based on the improved Gaussian swarm optimization algorithm as claimed in any one of the preceding aspects.

[0038] According to another aspect of the present application, there is provided a computer program product comprising a computer program, and the computer program is executed by a processor to realize the steps of the feed system LuGre friction model parameter identification method based on the improved Gaussian swarm optimization algorithm as claimed in any one of the preceding aspects.

[0039] Overall, the above technical solutions conceived by the present application can achieve the following beneficial effects compared with the prior art.

[0040] ​(1) The LuGre model parameter identification method based on the improved Gauss group optimization algorithm of the application divides the parameters into sliding parameters and pre-sliding parameters, reduces the complexity of the parameter identification problem, and identifies the sliding parameters and the pre-sliding parameters in turn through the improved Gauss group optimization algorithm without manual intervention throughout the process, and automatically realizes identification.

[0041] (2) The improved Gauss group optimization algorithm used in the LuGre model parameter identification method has strong optimization performance, and can realize higher-precision identification. Compared with the Gauss group optimization algorithm, the improved super parameter adaptive updating strategy can better balance the exploration and utilization capabilities of the algorithm, avoid falling into a local optimum, and has stronger utilization capability in the later iteration period, thereby improving the convergence precision. BRIEF DESCRIPTION OF DRAWINGS

[0042] Figure 1 The flow chart of the LuGre friction model parameter identification method based on the improved Gauss group optimization algorithm in the preferred embodiment of the application is shown.

[0043] Figure 2 The identification excitation signal in the preferred embodiment of the application is shown.

[0044] Figure 3 The friction force of the machine tool feeding system under the excitation of the identification excitation signal in the preferred embodiment of the application is shown.

[0045] Figure 4 The prediction effect of the actual friction force by the identified LuGre model in the preferred embodiment of the application is shown. DETAILED DESCRIPTION

[0046] In order to make the purpose, technical scheme and advantages of the application clearer, the application is further described in detail below with reference to the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the application and do not limit the application. In addition, the technical features involved in each embodiment of the application described below can be combined with each other as long as they do not conflict with each other.

[0047] As shown in Figure 1 The LuGre friction model parameter identification method based on the improved Gauss group optimization algorithm of the feeding system of the application mainly includes the following steps:

[0048] (1) The identification excitation signal is used to excite the feeding system and collect the running data of the feeding system;

[0049] (2) The model parameters are divided into sliding parameters and pre-sliding parameters;

[0050] (3) A loss function is constructed;

[0051] (4) using improved Gauss group optimization algorithm to identify the sliding parameters and pre-sliding parameters;

[0052] Further, as shown in Figure 2 , the identification excitation signal of step (1) is a speed signal spliced by truncated and translated Gaussian functions, and its mathematical expression is as follows:

[0053]

[0054] Wherein, v(t) is the identification excitation signal about time t, A and ∑ are the amplitude and variance of Gaussian function respectively, T v is the period of v(t), v1(t) and v2(t) are two truncated and translated Gaussian functions, n=0,1,2,…

[0055] Further, in order to avoid overfitting, Gaussian signals with different amplitudes and frequencies can be mixed as the final excitation signal for identification.

[0056] Further, the running data of step (1) is the speed, acceleration and corresponding load current of the feeding system under the excitation of the identification excitation signal. Using the running data, the friction of the feeding system can be calculated according to formula (4), and the friction is shown in figure (3).

[0057]

[0058] Wherein, F f is the friction, K t is the motor torque constant, I is the load current, J is the equivalent total inertia of the feeding system, θ is the motor shaft angle, and h is the lead of the screw.

[0059] Further, the model of step (2) is LuGre model, and its mathematical expression is as follows:

[0060]

[0061] Wherein, F is the friction, v is the relative motion speed of the contact surface, z is the bristle deformation, g(v) is used to describe the Stribeck characteristic, and sgn() is the sign function.

[0062] The identification parameters of LuGre model include F c , F s , v s , σ0, σ1 and σ2. Further, through parameter sensitivity analysis, it can be known that when the system enters the macro sliding state, the friction and {F s , F c , v s,σ2}correlation is strong, and the correlation of {σ0,σ1} is not strong, the model can be equivalent to Stribeck model; therefore, the friction parameters are divided into sliding parameters P slide s c s ,σ2}pre-sliding parameters P stick

[0063] Let φ be the LuGre model, then

[0064] f slide stick (8)

[0065] When the system enters the sliding state, there is

[0066] f_slide slide (v slide |P slide ) (9)

[0067] F f_slide is the friction force in the sliding state, φ slide is the LuGre model in the sliding state, and v slide is the relative motion speed of the contact surface in the sliding state. Further, the loss function described in step (3) is constructed as follows:

[0068] First, use a truncated Gaussian signal to excite the system, and obtain the speed v and friction force F f . Then select the data between the maximum value point and the zero crossing point of the speed curve (sliding state data), denoted as {v slide ,F f_slide}. The v slide and are brought into the sliding stage friction force model φ slide , and the estimated friction force is obtained as shown in equation (10).

[0069]

[0070] Then construct the loss function L1 slide for identifying the sliding parameters P

[0071]

[0072] Next, all the speed and friction force data {v,F f} and the sliding parameter identification result are brought into equation (8) to estimate the full-range friction force ​​​​​​​​​

[0073]

[0074] Then a loss function L2 stick for identifying the pre-sliding parameter P

[0075]

[0076] where X is the data length of {v, F f}, M is the data length of {v slide , F f_slide}, and F is the initial friction force in the sliding state.

[0077] Further, the process of identifying the sliding parameter and the pre-sliding parameter in step (4) is: using the improved Gaussian swarm optimization algorithm to minimize the loss function L1 to obtain the identification result of the sliding parameter P slide , and then using the improved Gaussian swarm optimization algorithm to minimize the loss function L2 to obtain the identification result of the pre-sliding parameter P stick .

[0078] Further, the improved Gaussian swarm optimization algorithm in step (4) is an improved version of the Gaussian swarm optimization algorithm. The algorithm mainly includes initialization, fitness calculation, individual update, individual mutation, and hyperparameter update.

[0079] Further, the Gaussian swarm optimization algorithm uses a Gaussian function as an individual, as shown in equation (14).

[0080]

[0081] where G(X|μ,∑) is a Gaussian function individual, K=(x1,x2,...,x D ) is a D-dimensional random variable, D represents the number of parameters to be identified, x1-x D represent the corresponding parameters to be identified, μ∈R D is the mean vector, representing a set of possible parameter identification results, is the covariance matrix, T is the matrix transpose operation; R D is a D-dimensional real number space, is a D-dimensional positive definite matrix.

[0082] Further, a plurality of individuals in the algorithm population are linearly iterated and then normalized to obtain a superimposed Gaussian probability function P(X)(SGPF), as shown in equation (15).

[0083]

[0084] z=∑ p ∫wp G p (X) (16)

[0085] where Z is a normalization factor, w p is the weight of the pth individual, G p (X) is the pth individual;

[0086] Further, the specific steps of the Gaussian swarm optimization algorithm initialization are as follows:

[0087] For the identification problem of D parameters, suppose the identification space is Ω. A certain number of Gaussian probability functions are randomly generated as individuals, and all individuals constitute a population. The mean μ p and the covariance matrix Σ p of the Gaussian function are initialized according to formula (17) and formula (18) respectively.

[0088]

[0089] where n is the population size, lb and ub are D-dimensional vectors composed of the lower bound and the upper bound of Ω respectively, r is a D-dimensional random vector with a value of [0, 1], is the Hadamard product, P c1 ∈ [0, 1] is the covariance matrix coefficient, a j , b j (j = 1, 2,..., D) are the lower bound and the upper bound of the jth dimension of Ω.

[0090] Further, the specific steps of individual fitness calculation are as follows:

[0091] First, let the mean of the pth individual in the qth iteration be Calculate the individual fitness according to formula (19) and formula (20).

[0092]

[0093] where, is the objective function value of the pth individual at the qth iteration, F obj () is the optimization objective function, Fit() is the fitness function, is the fitness of the pth individual at the qth iteration.

[0094] Further, the specific steps of individual update are as follows:

[0095] First, select an individual from the population with a probability of , denoted as Then get The specific process is shown in formula (21) to formula (23).

[0096]

[0097]

[0098] where, is the mean vector of is the covariance matrix of sample({G p}) with probability represents sampling of G p based on discrete probability distribution Gaussian_sample() is Gaussian sampling.

[0099] The above update strategy is called Gaussian-update. In order to improve the exploration and exploitation ability of the algorithm, the algorithm also uses random-update and learning-update as auxiliary strategies. Random-update is to randomly select a D-dimensional vector from Ω as the new individual mean with a probability of P c2 ∈ [0, 1].

[0100]

[0101] where, Uniform_sample() is uniform sampling, and rand() represents generating a random number in [0, 1].

[0102] Learning-update is to randomly move the mean generated by Gaussian-update to the current optimal individual with a probability of P c3 ∈ [0, 1].

[0103]

[0104] where, is the current optimal mean, and r is a random number in [0, 1].

[0105] Further, the specific steps of individual mutation operation are as follows:

[0106] An individual is selected from the population with a mutation probability P c4 ∈ [0, 1], then a dimension k ∈ {1, 2,..., D} is randomly selected, and the covariance matrix of the individual is mutated according to formula (26).

[0107]

[0108] where, is the element of the kth row and the kth column of the covariance matrix, and a k ​and b k are the lower and upper bounds of the k-th dimension of Ω, and r is a random number in [0, 1].

[0109] Further, the algorithm hyper-parameter updating is mainly to balance the exploration and exploitation ability of the algorithm. The individual covariance matrix coefficient P c1 , the random update probability P c2 , the learning update probability P c3 , and the mutation probability P c4 are adaptively adjusted according to equations (27)-(30), respectively.

[0110]

[0111] where max itre is the maximum number of iterations, c1 is the covariance factor, c2 is the random factor, c3 is the learning factor, c4 is the mutation factor, c1, c2, c3, and c4 are constants, β1, β2, β3, and β4 are constants, and the superscript q is the current iteration number.

[0112] Further, after the algorithm initialization is completed, the fitness calculation, individual update, individual mutation, and hyper-parameter update will be looped until the termination condition is met. The termination condition can be set as the number of iteration steps. The algorithm records the optimal identification result of each iteration in the loop, i.e., the mean μ best of the individual with the highest fitness.

[0113] In a preferred embodiment, the process of minimizing the loss function L1 by the Gaussian swarm algorithm is as follows:

[0114] T1: Set the parameters of the Gaussian swarm algorithm, including: population size n, maximum number of iteration steps max iter, covariance factor c1, random factor c2, learning factor c3, mutation factor c4, and update factors β1, β2, β3, and β4.

[0115] T2: Set the current iteration step number to 1;

[0116] T3: Calculate the individual covariance matrix coefficient P c1 , the random update probability P c2 , the learning update probability P c3 , and the mutation probability P c4 according to equations (27)-(30);

[0117] T4: Initialize the population according to equations (17) and (18);

[0118] T5: Calculate the individual fitness according to equation (20);

[0119] T6: Record the mean of the optimal individual, i.e., the optimal parameter identification result;

[0120] T7: generate a random number between 0 and 1, if the random number is less than P c2 , update the individual mean according to equation (24), otherwise update the individual mean according to equation (22);

[0121] T8: generate a random number between 0 and 1, if the random number is less than P c3 , update the individual mean according to equation (25), otherwise execute T9;

[0122] T9: generate a random number between 0 and 1, if the random number is less than P c4 , update the individual covariance matrix according to equation (26), otherwise execute T10;

[0123] T10: update the individual covariance matrix coefficients P c1 , the random update probability P c2 , the learning update probability P c3 , and the mutation probability P c4 according to equations (27)-(30);

[0124] T11: increase the current iteration step number by 1;

[0125] T12: if the current iteration step number is less than max_iter, execute T5-T11, otherwise output the optimal individual mean and end the optimization.

[0126] Then, the L2 is minimized again using the Gaussian swarm algorithm according to steps T1-T12 to identify P stick .

[0127] To further demonstrate the correctness and superiority of the improved Gaussian swarm optimization algorithm-based feed system LuGre friction model parameter identification method of the application, LuGre model parameter identification experiments were conducted in a simulation environment and an actual machine tool feed shaft. The LuGre model was built in MATLAB, and Table 1 shows the model parameter settings and identification ranges.

[0128] Table 1 Parameter settings and identification ranges of LuGre model

[0129]

[0130] Table 2 shows the identification results of the improved Gaussian swarm optimization algorithm (MGSO) and the Gaussian swarm optimization algorithm (GSO). As can be seen from the table, the improved Gaussian swarm optimization algorithm-based feed system LuGre friction model parameter identification method can achieve accurate identification of friction parameters, and has higher identification accuracy than the Gaussian swarm algorithm.

[0131] Table 2 LuGre model simulation identification results and relative error (%)

[0132]

[0133]

[0134] Figure 4 The identification effect of the improved Gauss group optimization algorithm-based feed system LuGre friction model parameter identification method on the actual machine tool feed shaft is shown. As can be seen from the figure, the identified LuGre model can accurately describe the friction characteristics of the system.

[0135] Those skilled in the art can easily understand that the above description is only preferred embodiments of the present application, and is not used to limit the present application, and any modifications, equivalent replacements and improvements made within the spirit and principles of the present application shall be included in the protection scope of the present application.

Claims

1. A feed system LuGre friction model parameter identification method based on an improved Gauss group optimization algorithm, characterized in that, The method comprises the following steps: (1) exciting the feeding system with an identification excitation signal and collecting operation data of the feeding system; the operation data are speed, acceleration and corresponding load current of the feeding system under excitation of the identification excitation signal; (2) dividing LuGre model parameters into sliding parameters P slide ={F s ,F c ,v s ,σ2} and pre-sliding parameters P stick ={σ0,σ1}; wherein F c is the Coulomb friction force, F s is the maximum static friction force, v s is the Stribeck velocity, σ2 is the viscous damping coefficient, σ0 is the bristle stiffness, and σ1 is the bristle damping coefficient; (3) constructing loss functions L1 and L2 for identifying the sliding parameter and the pre-sliding parameter; (4) Based on the running data of step (1), first use the improved Gauss group optimization algorithm to minimize the loss function L1 to obtain the sliding parameter P slide The identification result is then substituted into the loss function L2, and the improved Gauss group optimization algorithm is used to minimize the loss function L2 to obtain the pre-sliding parameter P stick The identification result.

2. The feed system LuGre friction model parameter identification method based on the improved Gauss group optimization algorithm according to claim 1, wherein, The identification excitation signal in step (1) is a speed signal spliced by a truncated and translated Gaussian function, and a mathematical expression thereof is as follows: where v(t) is the recognition excitation signal as a function of time t, A and ∑ are the amplitude and variance of the Gaussian function, respectively, T v is the period of v(t), v1(t), v2(t) are two truncated and shifted Gaussian functions, n = 0, 1, 2,....

3. The feed system LuGre friction model parameter identification method based on the improved Gauss group optimization algorithm according to claim 1, characterized in that, The friction of the feeding system is calculated according to formula (4) by using the operation data: where F f is the friction force, K t is the motor torque constant, I is the load current, J is the equivalent total inertia of the feed system, θ is the motor shaft angle, is the second derivative of θ, and h is the lead of the screw.

4. The feed system LuGre friction model parameter identification method based on the improved Gauss group optimization algorithm according to claim 3, characterized in that, The model in step (2) is a LuGre model, and a mathematical expression thereof is as follows: Wherein, F is the friction, v is the relative motion speed of the contact surface, z is the bristle deformation, g(v) is used to describe the Stribeck characteristic, and sgn() is a sign function; The parameters to be identified of the LuGre model include F c , F s , v s , σ0, σ1 and σ2.

5. The feed system LuGre friction model parameter identification method based on the improved Gauss group optimization algorithm according to claim 4, characterized in that, By parameter sensitivity analysis, when the system enters the macroscopic sliding state, the friction force is strongly related to {F s ,F c ,v s ,σ2} and not strongly related to {σ0,σ1}, and the model can be equivalent to the Stribeck model; therefore, the friction parameters are divided into sliding parameters P slide ={F s ,F c ,v s ,σ2} and pre-sliding parameters P stick ={σ0,σ1}. Let φ be the LuGre model, then F f = φ(v | P slide , P stick ) (8) When the system enters a sliding state, there is F f_slide is the friction force in the sliding state, φ slide is the LuGre model in the sliding state, v slide is the relative velocity of the contact surface in the sliding state.

6. The feed system LuGre friction model parameter identification method based on the improved Gauss group optimization algorithm according to claim 5, characterized in that, The loss function in step (4) is constructed as follows: Identifying sliding parameters P slide Loss function L1: wherein M is {v slide ,Ff _slide} the data length, for estimating the friction force, the superscript (t) denotes the time t; A loss function L2 is then constructed for identifying the pre-sliding parameter P stick of the model M2: where K is the data length of {v, F f}, is the total friction force.

7. The feed system LuGre friction model parameter identification method based on the improved Gauss group optimization algorithm according to claim 6, characterized in that, The updating strategy of four hyper-parameters in the Gaussian group optimization algorithm is improved, and the four hyper-parameters are respectively individual covariance matrix coefficient P c1 , random updating probability P c2 , learning updating probability P c3 and mutation probability P c4 ; in each iteration process, adaptive adjustment is carried out according to formula (27) to formula (30) respectively: Wherein, max_iter is the maximum iteration number, c1 is a covariance factor, c2 is a random factor, c3 is a learning factor, c4 is a variation factor, c1, c2, c3 and c4 are constants, β1, β2, β3 and β4 are constants, and the superscript q is the current iteration number.

8. A feed system LuGre friction model parameter identification system based on an improved Gauss group optimization algorithm, comprising a memory, a processor and a computer program stored on the memory, characterized in that, The processor executes the computer program to realize the steps of the feeding system LuGre friction model parameter identification method based on the improved Gaussian swarm optimization algorithm in any one of claims 1-7.

9. A computer readable storage medium having stored thereon computer programs / instructions, characterized in that, The computer program is executed by the processor to realize the steps of the feeding system LuGre friction model parameter identification method based on the improved Gaussian swarm optimization algorithm in any one of claims 1-7.

10. A computer program product comprising a computer program, characterized in that, The computer program is executed by the processor to realize the steps of the feeding system LuGre friction model parameter identification method based on the improved Gaussian swarm optimization algorithm in any one of claims 1-7.

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