A parameter identification method for mathematical model of machine tool feed system based on gradient optimization

Abstract

The application belongs to the technical field of numerical control machine tools, and discloses a mathematical model parameter identification method for a machine tool feeding system based on gradient optimization. The method comprises the following steps: S1, establishing a mathematical model for the machine tool feeding system; S2, collecting actual operation data of the machine tool; setting initial parameters to be identified; constructing an update model for the parameters to be identified; S3, inputting a preset instruction position signal and the current parameters to be identified into the update model for the parameters to be identified to update the parameters to be identified, simulating and calculating a loss function by using the updated identification parameters, and judging the relationship between the current loss function and an optimal loss function; if the current loss function is smaller than the optimal loss function, the value of the current parameters to be identified is kept, otherwise, the number of times that the loss function increases is increased; S4, updating the number of iterations, and judging whether the current number of iterations reaches a preset maximum number of iterations; if yes, the current parameters to be identified are output; otherwise, the step S3 is returned. By the application, the identification efficiency of parameters with low sensitivity to the global loss function is improved.

Description

Technical Field

[0001] This invention belongs to the technical field of CNC machine tools, and more specifically, relates to a method for identifying mathematical model parameters of machine tool feed systems based on gradient optimization. Background Technology

[0002] CNC machine tools, as a type of high-efficiency, high-precision, and highly automated machining equipment, play a vital role in the manufacturing industry and are widely used in aerospace, automotive, nuclear power, medical equipment, and engineering machinery. CNC machine tools have complex structures, and establishing mathematical models of these tools helps in analyzing their dynamic characteristics, which is crucial for improving machining accuracy and enhancing their dynamic performance.

[0003] The mathematical model of a machine tool feed system mainly involves the servo control system and the mechanical transmission system. The purpose of feed system parameter identification is to enable the constructed feed system simulation model to have higher simulation accuracy, more accurately reflect the dynamic characteristics of the real machine tool feed system, and thus provide better assistance in improving the dynamic performance, tracking accuracy, machining efficiency, and machining quality of the machine tool feed system.

[0004] Machine tool feed systems are complex electromechanical coupling systems. Their mathematical models often contain a large number of parameters, some of which are difficult to obtain directly through measurement and table lookup, such as table mass, table friction parameters, and feed system stiffness and damping. The main focus of feed system parameter identification is these difficult-to-determine parameters that significantly affect the dynamic characteristics of the feed system.

[0005] Existing methods for simultaneous multi-parameter identification of mathematical models are mostly based on genetic algorithms. For example, patent CN102540894B uses a genetic algorithm to identify the parameters of a robotic arm, and patent CN110543727B uses an improved particle swarm optimization algorithm to identify the parameters of a robot. When using genetic algorithms such as particle swarm optimization to identify parameters, the parameter updates during the identification process are often random, resulting in slow algorithm convergence and low parameter identification efficiency. In this patent, the model parameters are updated based on the gradient information between the model parameters and the model simulation error during the parameter identification process, resulting in faster algorithm convergence and higher parameter identification efficiency. Patent CN114169230A identifies robot dynamic parameters based on the backpropagation algorithm. However, during the identification process, the dynamic parameters to be identified are not subjected to sensitivity analysis. All parameters use the same loss function to calculate the gradient. When the sensitivity between the parameter and the loss function is low, the gradient is small, the parameter update step size is small, and the algorithm converges slowly. This patent analyzes the sensitivity between the model parameters and simulation results of different types of models. When calculating the gradient of each parameter, the most sensitive model simulation result is used to construct the loss function, which improves the convergence speed of the algorithm and makes the parameter identification more efficient. SUMMARY

[0006] In view of the above defects or improvement needs of the prior art, the present application provides a mathematical model parameter identification method for a machine tool feeding system based on gradient optimization, which solves the problem of low efficiency of mathematical model parameter identification.

[0007] To achieve the above object, according to the present application, a mathematical model parameter identification method for a machine tool feeding system based on gradient optimization is provided, which comprises the following steps:

[0008] S1 establishing a mathematical model of the machine tool feeding system and determining the upper and lower bounds of the to-be-identified parameters;

[0009] S2 presetting a command position signal, running the machine tool according to the preset command position signal and collecting actual machine tool running data, setting initial to-be-identified parameters, and constructing a to-be-identified parameter update model;

[0010] S3 inputting the preset command position signal and the current to-be-identified parameters into the to-be-identified parameter update model to update the to-be-identified parameters, inputting the updated to-be-identified parameters and the command position signal into the mathematical model to obtain a simulation result, calculating a loss function by using the actual machine tool running data collected in step S2 and the simulation result, and judging the relationship between the current loss function and the optimal loss function;

[0011] when the current loss function is less than the current optimal loss function, taking the value of the current to-be-identified parameters as the optimal to-be-identified parameters, setting the loss function increase number to zero, and taking the current loss function as the current optimal loss function;

[0012] when the current loss function is greater than the current optimal loss function, increasing the loss function increase number, judging whether the current loss function increase number is greater than a preset maximum loss function increase number, if yes, setting the loss function increase number to zero and updating the learning rate and the step size in the to-be-identified parameter update model, and if no, proceeding to the next step;

[0013] S4 updating the iteration number, judging whether the current iteration number reaches a preset maximum iteration number, if yes, outputting the current to-be-identified parameters, and if no, returning to step S3.

[0014] Further preferably, in step S2, the to-be-identified parameter update model is performed as follows:

[0015] S21 for any one of the to-be-identified parameters, updating the parameter by using the step size, inputting the updated parameter into the mathematical model to obtain a simulation result, and calculating a parameter gradient by using the simulation result and the actual machine tool running data in step S2;

[0016] S22 Repeat step S21 until the parameter gradient corresponding to each of the parameters to be identified is obtained. The parameter gradients of all the identified parameters constitute a parameter gradient set. The parameter to be identified is updated using this parameter gradient set, thereby realizing the update of the parameter to be identified.

[0017] More preferably, in step S1, the identification parameter is updated using the step size according to the following relationship:

[0018]

[0019] in, It is parameter p i Increase gradient calculation step size l i The value after that, It is parameter p i Reduce gradient calculation step size l i The value after p i It is the i-th element in the parameters to be identified, where i is the number of the parameter element to be identified.

[0020] More preferably, in step S22, updating the parameter to be identified using the parameter gradient set is performed in the following manner:

[0021] P = PG·lr

[0022] Where P is the parameter to be identified, G is the set of parameter gradients, and lr is the learning rate.

[0023] More preferably, in step S21, the parameter gradient is performed according to the following relationship:

[0024]

[0025] Among them, g i It is parameter p i The gradient, l i It is parameter p i The gradient calculation step size, p i It is the i-th element in the parameters to be identified, where i is the number of the parameter element to be identified.

[0026] More preferably, in step S3, the loss function is related to the parameter to be identified, and different identification parameters correspond to different loss function calculation formulas.

[0027] More preferably, in step S3, the learning rate and step size in the updated model are performed in the following manner:

[0028] lr = lr / 2

[0029] L = L / 2

[0030] Where lr is the learning rate and L is the step size.

[0031] More preferably, the parameters to be identified include position loop gain, velocity loop gain, velocity loop integral constant, axial stiffness of the machine tool feed system, axial damping of the machine tool feed system, equivalent moment of inertia, table mass, Coulomb friction, maximum static friction, Stribeck velocity, and viscous friction coefficient.

[0032] In summary, the technical solutions conceived by this invention have the following beneficial effects compared with the prior art:

[0033] 1. The parameter identification method for the mathematical model of the machine tool feed system of the present invention, compared with the existing parameter identification method for the mathematical model of the CNC machine tool feed system, is based on the dynamic model of the machine tool feed system. The accuracy of parameter identification is judged by the simulation accuracy of the dynamic model. The improvement of parameter identification accuracy can directly improve the simulation accuracy of the dynamic model.

[0034] 2. Compared with existing methods for identifying parameters of mathematical models in CNC machine tool feed systems, the parameter identification method of the present invention simultaneously identifies multiple parameters of the mathematical model, effectively improving the efficiency of parameter identification. It utilizes gradient information between model parameters and model simulation errors to update parameters, calculating the direction and distance of parameter updates from the gradient values. Compared to the random value selection method using genetic algorithms, this method offers higher efficiency in parameter identification. Furthermore, the parameter identification method of the present invention determines the calculation method of the loss function based on the characteristics of each parameter, resulting in different loss functions for each parameter. This improves the identification efficiency of parameters with low sensitivity to the global loss function.

[0035] 3. Compared with existing methods for identifying parameters of mathematical models of CNC machine tool feed systems, the parameter identification method of the present invention determines the loss function used in parameter identification based on the sensitivity analysis results of the model parameters. The identification algorithm can be adjusted according to the structure and composition of the feed system model, thereby achieving higher identification accuracy and efficiency for parameters of different types of feed system models. Attached Figure Description

[0036] Figure 1 This is a schematic flowchart of a machine tool feed system parameter identification method based on gradient optimization constructed according to a preferred embodiment of the present invention;

[0037] Figure 2 This is a mathematical model of a CNC machine tool feed system built using Simulink, according to a preferred embodiment of the present invention.

[0038] Figure 3The parameter identification excitation signal displacement and velocity curves are constructed according to a preferred embodiment of the present invention, wherein (a) is a displacement curve and (b) is a velocity curve;

[0039] Figure 4 The simulation results and simulation errors of a certain type of machine tool mathematical model for table displacement before and after parameter identification, constructed according to the preferred embodiment of the present invention, wherein (a) is a comparison of the simulation results of the mathematical model for table displacement before and after parameter identification with the actual data, and (b) is a comparison of the simulation errors of the mathematical model for table displacement before and after parameter identification. Detailed Implementation

[0040] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0041] A method for parameter identification of a mathematical model of a machine tool feed system based on gradient optimization, the method mainly includes the following steps:

[0042] S1 establishes a mathematical model of the machine tool feed system, and fills the model with parameters that can be obtained through measurement and table lookup. For parameters that need to be identified, the upper and lower bounds of the parameters are determined based on prior knowledge.

[0043] S2 designs G-code based on the excitation signal identified by the parameters, inputs it into the machine tool, and collects machine tool operation data, including motor rotation angle, speed, acceleration, table displacement, velocity, and acceleration.

[0044] Set the hyperparameters of the parameter identification algorithm, including the number of iterations, learning rate, maximum increase in the loss function value, initial rate of change of parameters, and execute the algorithm initialization process;

[0045] Construct an update model for the parameters to be identified;

[0046] S3 inputs the parameter identification signal into the mathematical model of the feed system for simulation. Based on the simulation results of the mathematical model and the machine tool operation data, it calculates the simulation error and loss function to obtain the optimal parameters to be identified.

[0047] S4 repeats S3 until the preset number of iterations is reached, and outputs the identification results of the mathematical model parameters. These identification results are the model parameter values ​​that minimize the loss function value during the algorithm iteration process.

[0048] Furthermore, the S1 mathematical model has no strict requirements, but it should reflect the structure and characteristics of the machine tool feed system and be able to obtain simulation results for the motor's rotation angle, speed, angular acceleration, table displacement, velocity and acceleration, and motor current. The upper and lower bounds of each parameter in the mathematical model, i.e., the range of parameter variation during the mathematical model parameter identification process, need to be determined based on experience or experiments.

[0049] Furthermore, S2 parameter identification of excitation signals requires analyzing the sensitivity of model parameters under different excitation signals and selecting excitation signals that maximize the sensitivity of model parameters for parameter identification.

[0050] Furthermore, the hyperparameters of the S2 parameter identification algorithm include the following four parameters:

[0051] 1. Algorithm iteration count (iter) max The algorithm iterates through iterative steps. max Exit after this.

[0052] 2. Initial learning rate (lr). The learning rate of the algorithm will gradually decrease during the iteration process, and an initial value for the learning rate needs to be provided when identification begins.

[0053] 3. Maximum number of times the loss function value increases (cnt) max During the iteration process, if the number of times the loss function is increased exceeds cnt in the parameter identification algorithm... max Then the learning rate and parameter gradient calculation step size will be reduced to half of the original.

[0054] 4. Initial rate of change of parameter R init The initial step size L for calculating the parameter gradient is determined by the rate of change and the length of the parameter's value range. init Let the upper bound of the parameter be X. h The lower bound is X l ,but:

[0055] L init =R init (X h -X l )

[0056] Furthermore, the initialization process of the parameter identification algorithm includes the following two parts:

[0057] 1. Initialize mathematical model parameters. For model parameters that need to be identified, randomly select values ​​within the upper and lower bounds of the parameters as the initial values ​​of the model parameters.

[0058] 2. Calculate the initial loss function value. Input the command position of the parameter identification signal into the system model, with the model parameters as the initial parameters, and calculate the loss function value, which is taken as the minimum value of the loss function of the identification algorithm.

[0059] Furthermore, depending on the different parameter sensitivities, the calculation method of the loss function for the model parameters also differs. For example, the position loop gain parameter is related to the stage displacement s. wb and motor rotation angle θ m If the sensitivity is higher, then the loss function of the position loop gain parameter is the sum of the root mean square of the two simulation errors, that is:

[0060]

[0061] in and These are the actual collected data and model simulation results of the machine tool table displacement, respectively. and These are the actual collected data and model simulation results of the machine tool motor rotation angle, respectively, and rms is the root mean square calculation function.

[0062] Furthermore, the model for updating the parameters to be identified is performed as follows:

[0063] S21 For any one of the parameters to be identified, update the identified parameter using the step size, input the updated identified parameter into the mathematical model to obtain the simulation result, and use the simulation result and the actual machine tool running data in step S2 to calculate the parameter gradient.

[0064] S22 Repeat step S21 until the parameter gradient corresponding to each of the parameters to be identified is obtained. The parameter gradients of all the identified parameters constitute a parameter gradient set. The parameter to be identified is updated using this parameter gradient set, thereby realizing the update of the parameter to be identified.

[0065] Furthermore, the parameters to be identified include multiple identification parameters, and the command position signal includes multiple values. The above-mentioned parameter to be identified update model needs to update the parameter to be identified corresponding to each value in the command position signal.

[0066] Furthermore, in S22, when updating the model parameter values, the product of the learning rate and the parameter gradient values ​​is used as the parameter update distance.

[0067] Furthermore, in S21, the gradient values ​​of the model parameters are calculated as follows:

[0068] Let parameter p i The step size for calculating the gradient is l. i Then parameter p i gradient value g i For parameter p i Increase l i The loss function value and the reduction l at that time i The difference between the loss function values ​​at time 2l i The ratio, that is:

[0069]

[0070] Where loss(p) i +l i ) is the parameter p i Increase l i The loss function value at time is the parameter p i Increase l i The sum of the root mean square of the simulation errors of the time-mathematical model.

[0071] The present invention will be further described below with reference to specific embodiments.

[0072] like Figure 1 As shown in the embodiment of the present invention, the parameter identification method for the mathematical model of the machine tool feed system based on gradient optimization first requires the establishment of a mathematical model of the CNC machine tool feed system. This embodiment uses Simulink to establish the mathematical model of the feed system, as follows: Figure 2 As shown, the mathematical modeling of a machine tool feed system can be summarized as follows:

[0073] (1) Establish a schematic diagram of a known or preliminary system and determine the basic parameters.

[0074] (2) Simplify the actual structure or divide it into several substructures, and apply dynamic theorems to establish a mathematical model of the system. For cases where dynamic theorems cannot be directly used for modeling, test data can be used to establish an empirical mathematical model of input and output.

[0075] (3) The accuracy of the mathematical model is proven through experiments.

[0076] Based on the actual structure of the machine tool, different dynamic models can be established through simplification in different ways and to varying degrees. The most common are: lumped mass model, distributed mass model, finite element model, and hybrid model. In this embodiment, the mathematical model of the mechanical part of the machine tool feed system is a lumped mass model. The rotational inertia of the motor, coupling, and lead screw is equivalent to a single rotational inertia. The model also includes the equivalent axial stiffness and damping of the feed system. In addition to the above rotational inertia, stiffness, and damping parameters, the mathematical model of the machine tool feed system in this embodiment also contains the following parameters: relevant parameters of the Stribeck friction model of the worktable, and relevant parameters of the servo control model. All of these parameters need to be identified; in this embodiment, a total of 11 parameters need to be identified.

[0077] After establishing the mathematical model of the machine tool feed system, it is necessary to conduct sensitivity analysis experiments to determine the calculation method of the loss function value based on the simulation result type of the model that is most sensitive to each parameter. In this embodiment, the simulation result type of the model that is most sensitive to each parameter and the calculation formula of the loss function are shown in Table 1.

[0078] Table 1. Simulation result types with the most sensitive model parameters and loss function calculation formulas.

[0079]

[0080] The symbol correspondence of the simulation result types is shown in Table 2.

[0081] Table 2 Simulation Results

[0082]

[0083] The table displacement error and speed error are the differences between the table displacement and speed and the lead screw and nut displacement and speed. The lead screw and nut displacement and speed can be obtained by converting the motor angle and speed through the ball screw transmission pair, that is:

[0084]

[0085]

[0086] Where h is the ball screw lead, which in this embodiment is h = 16 mm. The loss function and gradient calculation method for each parameter can be determined from the simulation result type that is most sensitive to the model parameters.

[0087] In this embodiment, the excitation signal for parameter identification is a sinusoidal offset velocity signal with a velocity amplitude of 3000 mm / min and a frequency of 0.05 Hz. The velocity and displacement curves are shown below. Figure 3 As shown. The parameter identification excitation signal is input into the machine tool, and the machine tool response data is collected. The experimental steps for collecting experimental data in this embodiment are as follows:

[0088] (1) Warm up the machine tool for 1 hour.

[0089] (2) Design a G-code input machine tool based on the excitation signal identification parameters, run the machine tool and collect data from the motor encoder and grating ruler.

[0090] (3) Process the data to obtain the machine tool operation results such as table displacement, speed, and acceleration shown in Table 2.

[0091] Next, we need to set the hyperparameters of the parameter identification algorithm. The hyperparameter settings in this embodiment are as follows:

[0092] Table 3 shows the hyperparameters of the parameter identification algorithm in the embodiments.

[0093]

[0094] The upper and lower bounds of each parameter of the mathematical model in this embodiment are set as shown in Table 4.

[0095] Table 4 shows the upper and lower bounds of the mathematical model parameters in the embodiments.

[0096]

[0097] Model iterative execution parameter identification method, optimize model parameters, based on Figure 1 The identification method flow shown in this embodiment includes the following identification steps:

[0098] 1) Initialization. Randomly select parameter values ​​within the parameter range as initial parameters, and set the gradient calculation step size L to L0. init .

[0099] 2) Calculate the initial loss function value. Input the command position of the parameter identification signal into the system model, with the model parameters as initial parameters, and calculate the loss function value.

[0100] 3) Segment the command position signal. Divide the command position signal s... cmd The data is segmented according to time sequence, into multiple sets. n is the number of data groups after splitting. Then, for each data group after splitting... Perform the parameter optimization process. That is, the process from step 4) to step 5).

[0101] 4) Calculation of parameter gradients. For each parameter p in the model parameter set P... i Calculate parameter p i gradient g i The gradients of all parameters constitute the gradient set G = {g 1 ,g 2 ,...,g N}, where N is the number of parameters, 11.

[0102] 5) Update model parameters. Based on the gradient of the parameters and the learning rate lr, determine the direction and length of parameter shift, and modify each parameter in the parameter set P.

[0103] 6) Calculate the loss function value of the mathematical model. Set the updated parameter set P as the model parameters, calculate the loss function value, and if the loss function value is less than the current minimum loss function value, update the minimum loss function value, record the current model parameter value, and reset the count of the increase in the loss function value to 0; otherwise, increment the count of the increase in the loss function value by 1. If the count of the increase in the loss function value exceeds the set threshold cnt... max Then the learning rate lr and the step size L for calculating the parameter gradient will be reduced to half of their original values.

[0104] 7) Increment the iteration count by 1. If the iteration count has reached the maximum iteration count, output the identification results of the model parameters. Otherwise, repeat the parameter identification process from step 3) to step 6).

[0105] In this embodiment, the mathematical modeling object of the feed system is the Y-axis of a three-axis vertical machining center, and the parameter identification results are shown in Table 5.

[0106] Table 5. Results of Mathematical Model Parameter Identification in Examples

[0107]

[0108] The simulation results and simulation errors of the mathematical model for the table displacement before and after parameter identification are as follows: Figure 4 As shown.

[0109] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for parameter identification of a mathematical model of a machine tool feed system based on gradient optimization, characterized in that, The identification method includes the following steps: S1. Establish a mathematical model of the machine tool feed system and determine the upper and lower bounds of the parameters to be identified; S2 presets the command position signal, runs the machine tool according to the preset command position signal and collects the actual operation data of the machine tool; sets the initial parameters to be identified; and constructs an update model for the parameters to be identified. S3 inputs the preset command position signal and the current parameters to be identified into the parameter update model to update the parameters to be identified. The updated identification parameters and command position signal are then input into the mathematical model for simulation to obtain simulation results. The actual machine tool operating data collected in step S2 and the simulation results are used to calculate the loss function and determine the relationship between the current loss function and the optimal loss function. When the current loss function is less than the current optimal loss function, the value of the current parameter to be identified is taken as the optimal parameter to be identified, and the number of increments of the loss function is set to zero. The current loss function is then taken as the current optimal loss function. When the current loss function is greater than the current optimal loss function, the number of times the loss function is increased increases. It is then determined whether the number of times the current loss function is increased is greater than the preset maximum number of times the loss function is increased. If so, the number of times the loss function is increased is set to zero, and the learning rate and step size in the model are updated by updating the parameters to be identified; otherwise, proceed to the next step. S4 updates the iteration count and determines whether the current iteration count has reached the preset maximum iteration count. If yes, it outputs the current parameter to be identified. No, then return to step S3; In step S2, the model for updating the parameters to be identified is performed as follows: S21 For any one of the parameters to be identified, update the identified parameter using the step size, input the updated identified parameter into the mathematical model to obtain simulation results, and use the simulation results and the actual machine tool operating data in step S2 to calculate the parameter gradient. S22 Repeat step S21 until the parameter gradient corresponding to each of the parameters to be identified is obtained. The parameter gradients of all the identified parameters constitute a parameter gradient set. The parameter to be identified is updated using this parameter gradient set, thereby realizing the update of the parameter to be identified. In step S21, the parameter gradient is performed according to the following relationship: in, It is a parameter gradient, It is a parameter The gradient calculation step size, It is the first of the parameters to be identified i One element, i It is the number of the parameter element to be identified; In step S3, the learning rate and step size in the updated model are performed in the following manner: lr=lr / 2 L=L / 2 Where lr is the learning rate and L is the step size.

2. The method for parameter identification of a mathematical model of a machine tool feed system based on gradient optimization as described in claim 1, characterized in that, In step S1, the identification parameter is updated using the step size according to the following relationship: in, It is a parameter Increase gradient calculation step size The value after that, It is a parameter Reduce gradient calculation step size The value after that, It is the first of the parameters to be identified i One element, i It is the number of the parameter element to be identified.

3. The method for parameter identification of a mathematical model of a machine tool feed system based on gradient optimization as described in claim 2, characterized in that, In step S22, updating the parameters to be identified using the parameter gradient set is performed in the following manner: P=PG·lr Where P is the parameter to be identified, G is the set of parameter gradients, and lr is the learning rate.

4. The method for parameter identification of a mathematical model of a machine tool feed system based on gradient optimization as described in claim 1 or 2, characterized in that, In step S3, the loss function is related to the parameters to be identified, and different identification parameters correspond to different loss function calculation formulas.

5. The method for parameter identification of a mathematical model of a machine tool feed system based on gradient optimization as described in claim 1, characterized in that, The parameters to be identified include position loop gain, velocity loop gain, velocity loop integral constant, axial stiffness of the machine tool feed system, axial damping of the machine tool feed system, equivalent moment of inertia, table mass, Coulomb friction, maximum static friction, Stribeck velocity, and viscous friction coefficient.

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