Method for Establishing Prediction Model of Screw Rotor Surface Roughness by Improved BP Algorithm

Abstract

The present invention belongs to the technical field of numerical control machine tool processing, and specifically relates to a method for establishing a surface roughness prediction model of a screw rotor by improving the BP algorithm. First, the surface roughness of the screw rotor under different cutting parameters is measured by a hand-held surface roughness measuring instrument TR200. Secondly, the measured surface roughness values are normalized as the training and prediction data of the roughness prediction model. Then, the BP neural network model is improved by the Sand Cat Swarm Search Algorithm (SCSO) improved by Tent chaotic mapping, and the improved BP neural network is used to establish a surface roughness prediction model. This method reduces the difficulty of measuring the surface roughness of the screw rotor and improves the prediction accuracy and efficiency of the surface roughness of the screw rotor.

Description

Technical Field

[0001] The present invention relates to the field of numerical control machine tool processing, and particularly to a method for establishing a surface roughness prediction model of a screw rotor by improving the BP algorithm. Background Art

[0002] The screw rotor (as Figure 1 shown) is a typical workpiece with a complex curved surface. Its development has been restricted due to problems such as complex profile, difficult profile measurement, imperfect machining theory, and high machining difficulty. The LXK300 series of spiral groove CNC milling machines developed by the Key Laboratory of Complex Surfaces of Shenyang University of Technology ( Figure 2 shown) can machine screw rotors with any profile using the principle of non-instantaneous envelope milling. During the use of the machine tool, the machining efficiency, lead accuracy, surface roughness, etc. of the screw rotor can be controlled by changing the spindle speed, feed rate, and machining ratio of the machine tool. Among them, the problem of the machining surface roughness of the screw rotor has always been a research hotspot. The surface roughness of the screw rotor can directly affect its transmission efficiency, transmission performance, assembly accuracy, and service life. Therefore, if an accurate online prediction model of the machining surface roughness of the screw rotor can be established, it will be of great significance to the service performance of the screw rotor.

[0003] Traditional surface roughness measurement methods are mainly divided into contact measurement and non-contact measurement. First, contact measurement is limited in its application in high-precision detection because the measuring tip is easily worn and scratched on the surface, while non-contact measurement is sensitive to dirt on the part surface and needs to be cleaned before measurement, reducing the efficiency of roughness measurement. Second, due to the complex profile of the screw rotor, its measurement is difficult, and it is difficult to ensure the accuracy of the measurement. Therefore, how to accurately and efficiently establish a part surface roughness prediction model has become one of the key problems in the field of machining.

[0004] Traditional BP neural network prediction of surface roughness has problems such as falling into local optimum, slow convergence speed, overfitting, and large randomness. Directly using the BP neural network cannot meet the requirements of online prediction. Summary of the Invention

[0005] The object of the present invention is to propose a method for establishing a surface roughness prediction model of a screw rotor based on an improved BP algorithm, using the Tent chaos-improved sand cat swarm search algorithm to globally optimize the initial weights and thresholds of the neural network structure, overcoming the disadvantages of difficult measurement of the surface roughness of the screw rotor and local optimum of the neural network algorithm, improving the prediction accuracy and efficiency of the neural network, and improving the prediction accuracy and efficiency of the surface roughness after machining the screw rotor.

[0006] To achieve the above technical objectives, the present invention is implemented by the following solutions:

[0007] Method for establishing a prediction model of the surface roughness of a screw rotor by improving the BP algorithm, characterized in that it includes the following steps:

[0008] 1) Use a TR200 handheld surface roughness measuring instrument to measure the surface roughness of the screw rotor after machining. Select some of the measurement data as training data for establishing a prediction model of surface roughness, and the remaining data as test data for verifying the accuracy of the surface roughness prediction model;

[0009] 2) Determine the number of nodes in the input layer, output layer, and hidden layer according to the number of input variables and output variables of the prediction model, and determine the basic structure of the BP neural network;

[0010] 3) Normalize the training data through a normalization model, and establish a prediction model of the surface roughness of the screw rotor based on the BP neural network using the normalized training data. Define the input data of the BP neural network structure in the training data as P and the output data as T;

[0011] 4) Set the number of training data and test data in the surface roughness measurement data;

[0012] 5) Determine the number of initial weights and thresholds in the BP neural network structure according to the number of nodes in the input layer, hidden layer, and output layer, and project the weights and thresholds to the positions of sand cats;

[0013] 6) First determine the number of iterations of the sand cat swarm algorithm, and then use the Tent chaotic mapping method to generate the initial population of the sand cat swarm search algorithm to form the initial position matrix X of the sand cat population; based on the initial sand cat population, train the BP neural network model, and use the error between the pre-test and actual values of the neural network as the fitness function F to calculate the positions of the sand cats, that is, the optimal weights and thresholds;

[0014] 7) Find the optimal fitness value of the sand cat position according to the survival and foraging rules of the sand cat in the desert;

[0015] 8) The foraging process of the sand cat is divided into two stages, the search and attack prey stages. The balance mechanism of these two stages is balanced according to the hearing range R of the sand cat. When R is greater than 1, the sand cat goes out to search for prey. When R is less than 1, the sand cat attacks the prey;

[0016] 9) The sand cat swarm will share the best positions of each sand cat during the foraging process to select the best position of the population. Therefore, the best position of the sand cat is constantly changing with the iteration; when the maximum number of iterations is reached, the sand cat swarm will select the best sand cat position, that is, the best weights and thresholds of the BP neural network;

[0017] 10) Retrain the surface roughness prediction model of the BP neural network with the optimal weights and thresholds found by the sand cat search algorithm, and predict the surface roughness of the screw rotor under different working conditions according to the new BP neural network surface roughness prediction model.

[0018] Compared with the prior art, the advantages and effects of the present invention are as follows:

[0019] 1) The measurement difficulty of the surface roughness of the screw rotor is reduced, the labor and time expenditure in the measurement process are reduced, and the measurement accuracy and efficiency of the surface roughness are significantly improved;

[0020] 2) This method improves the defects such as local minimization, slow convergence speed, and data overfitting existing in the actual use of the BP neural network, and can quickly predict the surface quality of the screw rotor after processing online under given conditions;

[0021] 3) Through data analysis and comparison, it is found that the average BP prediction error is about 30.5%, and the error of the BP neural network optimized by the improved sand cat swarm is about 12.8%. It can be clearly seen from the comparison that the prediction accuracy of the BP neural network optimized by the improved sand cat swarm is significantly improved compared with the traditional BP neural network. Description of the Drawings

[0022] Figure 1 is a schematic structural diagram of a conventional screw rotor in the prior art;

[0023] Figure 2 is a schematic structural diagram of the LXK300 series spiral groove CNC milling machine developed by the Key Laboratory of Complex Surfaces of Shenyang University of Technology;

[0024] Figure 3 is a result comparison diagram of the test values, BP neural network prediction values, and Tent-SCSO-BP prediction values in the embodiment of the present invention;

[0025] Figure 4 is a schematic flow diagram of the Tent-SCSO-BP algorithm in the embodiment of the present invention. Detailed Embodiments

[0026] The technical solutions of the present invention will be clearly and completely described below in conjunction with the embodiments. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention.

[0027] The working principle of the present invention is to use the improved sand cat swarm algorithm to find the global optimal solutions of the weights and thresholds of the BP neural network. Taking the error between the experimental measurement values and the predictions of the BP neural network as the fitness function, the optimal weights and thresholds of the BP neural network are found, solving problems such as low efficiency of local optimum of the BP neural network, and significantly improving the prediction accuracy and efficiency of the BP neural network.

[0028] Foraging pattern of sand cats in the Sand Cat Swarm Optimization (SCSO) algorithm:

[0029] The hunting mechanism of sand cats is very interesting. They use their sensitive hearing ability to obtain low-frequency noises. In this way, sand cats can detect prey moving underground. The auricular flange (outer ear) of the sand cat's ear is no different from that of a domestic cat, but the ear canal length (middle ear) of the sand cat is longer than that of a domestic cat, and the air space in the middle ear is very large, so sand cats can detect the difference in arrival time between different sounds. The acoustic input admittance of a cat's ear is related to the eardrum, and the eardrum of a sand cat is 5 times that of a domestic cat. In addition, the middle ear cavity and ossicular chain affect the acoustic input admittance. Scientific research shows that the ability of sand cats to receive frequencies below 2 kHz is incredible, and at this frequency, sand cats are about 8 dB more sensitive than domestic cats. These unique features may be the reasons why sand cats can detect noises (prey movement), track prey, and successfully attack according to the prey's position. If the prey is underground, sand cats also have a magical ability to dig quickly. According to the behavior of sand cats, foraging is divided into two stages: searching for and attacking prey.

[0030] The foraging process of sand cats has two stages, the searching stage and the attacking prey stage. When the absolute value of the adaptive control parameter R is greater than 1, that is, the prey is outside the attack range of the sand cat, the sand cat will continue to search for the prey according to its own foraging trajectory. When the absolute value of R is less than 1, the prey is within the attack range of the sand cat, and it will actively attack the prey.

[0031] 3) In the mathematical model structure of the BP neural network, the following assumptions are established. The population size of the sand cat swarm is n. Each sand cat follows the foraging pattern of sand cats to search for prey alone and shares its optimal position with the population to facilitate other sand cats to optimize. According to the position sharing mechanism of sand cats, the sand cat swarm algorithm has the advantages of global optimality, high optimization efficiency, and accurate calculation.

[0032] The principle of the BP neural network combined with the improved sand cat swarm algorithm in the present invention is as follows:

[0033] According to the input data and output data, determine the number of input nodes, output nodes, and hidden layer nodes of the neural network, so as to determine the structure of the BP neural network. Normalize the input data and output data through the normalization model, and use the normalized input data and output data as the input P and output T of the BP neural network structure respectively. Determine the number of initial weights and thresholds in the BP neural network according to the parameter number model, and map them to the positions of sand cats. Set the population size and the number of iterations of the sand cat swarm, initialize the population through the Tent mapping to form the sand cat population position matrix X, and then calculate the predicted value of the neural network under the initial weights and thresholds. Take the error function between the network predicted value and the measured value as the fitness function , according to the foraging rules of sand cats in the sand cat swarm search method, calculate the fitness value of the sand cat's position; update the position of the sand cat according to the randomly selected search and attack methods. When the maximum number of iterations is reached, the position corresponding to the minimum fitness value found by the sand cat swarm algorithm is the optimal weight and threshold of the BP neural network. Substitute the optimized weights and thresholds of the BP neural network into the BP neural network for training, and finally predict the surface roughness of the screw rotor after machining under different working conditions according to the training results.

[0034] The method for establishing a prediction model of the surface roughness of a screw rotor by improving the BP algorithm of the present invention is specifically as follows:

[0035] 1) Measurement of the surface roughness of the screw rotor

[0036] Use a TR200 to measure the surface roughness of the screw rotor machined with different cutting parameters.

[0037] 2) Determine the structure of the BP neural network

[0038] Determine the influencing parameters that affect the surface roughness of the screw rotor and the corresponding surface roughness values of the screw rotor for the corresponding parameters, and store the data in the form of a matrix. According to the input dimension m of the matrix, determine that the number of neurons in the input layer of the neural network is m, and determine the number of output neurons n according to the dimension n of the output matrix. Determine the number of hidden layers and their corresponding nodes according to the number of input and output neurons. The number of neurons in the hidden layer is:

[0039]

[0040] In the formula is the number of neurons in the hidden layer, is the number of neurons in the input layer, is the number of neurons in the output layer, is a constant, and its value is [1, 10];

[0041] 3) Normalize the training data through the normalization model

[0042] The normalization model is:

[0043]

[0044] Among them, in the formula, y is the normalized data, and X min is the minimum value of the sample data, and X max is the maximum value of the sample data.

[0045] The input data and output data after sample normalization are used as the input data P and output data T of Tent-SCSO-BP respectively.

[0046] 4) Set the number of training samples and the number of test samples in the measurement data

[0047] Take 85% of the total number of samples as the number of training samples and 15% of the total number of sample data as the number of test samples.

[0048] 5) According to the dimension rule of the sand cat position vector, the sand cat position vector can be established, that is, the sand cat position vector corresponding to the weights and thresholds in the BP neural network.

[0049] The dimension of the sand cat position vector is:

[0050]

[0051] Among them, is the number of optimization parameters, is the number of neurons in the hidden layer, is the number of neurons in the input layer, is the number of neurons in the output layer.

[0052] Take the upper limit 1 and the lower limit 0 of the parameters to be optimized, and limit them between [0,1].

[0053] 6) Set the sand cat population size and the maximum number of iterations. Generate the initial sand cat population through Tent chaos to form the sand cat population position matrix X. Input the training data into the initial BP neural network model to optimize the initial weights and thresholds. Take the minimum error value between the predicted value and the actual value as the fitness function F to evaluate the best position of the sand cat.

[0054] The initial position transformation model of the sand cat population using Tent chaos is:

[0055]

[0056] Among them, , represents a randomly generated initial individual of a j-dimensional vector within [0,1] dimensional vector.

[0057] The process of initializing the population is as follows;

[0058] First, randomly generate a j-dimensional vector within [0,1] as the initial individual, then substitute the initial individual into the above formula to iterate each dimension and generate i - 1 new sand cat individuals. Finally, map all sand cat individuals to the variable value range to generate the sand cat population position matrix. The initial population generated by Tent chaos mapping has better diversity compared with the randomly generated population and can be evenly distributed in the solution space, thus improving the defect that the algorithm is prone to premature convergence and making the optimization efficiency of the algorithm improved.

[0059] The sand cat population location is represented by the following matrix:

[0060]

[0061] Wherein, represents the number of sand cats.

[0062] The fitness function of the sand cat location can be expressed as:

[0063]

[0064] Wherein, represents the fitness (error value) of each sand cat location.

[0065] 7) Calculate the fitness value of the sand cat location according to the foraging rule and fitness function of the sand cat in the sand cat search method;

[0066] 8) Judge the movement trajectory of the sand cat according to the sand cat search and attack phase control parameters. In the search phase, the sand cat continuously approaches the prey according to its auditory characteristics, and continuously updates its optimal position according to the sensitivity range and its own position. In the attack phase, the sand cat will directly attack the prey;

[0067]

[0068]

[0069]

[0070] Wherein, is the auditory perception range of the sand cat; is the auditory characteristic of the sand cat, and its default value is 2; represents the maximum number of iterations of the population; is the current iteration number of the sand cat algorithm population; represents the conversion parameter for the sand cat to search and attack the prey; is the sensitivity range of each sand cat.

[0071] (1) Case 1, in the search phase, the sand cat will update its new position according to its current position and sensitivity range, so as to be able to search for the best prey position:

[0072]

[0073] In the formula is the global optimal position of the sand cat group, is the current position of the sand cat;

[0074] (2) Case 2, when the sand cat detects the prey according to the hearing of its ears, the sand cat will attack the prey, and its mathematical model is:

[0075]

[0076]

[0077] In the formula is the optimal position of the sand cat group, is the current position of the sand cat, is a random angle between 0 and 360 degrees;

[0078] 9) During each iteration of the sand cat group algorithm, the optimal position of the sand cat, i.e., the optimal weights and thresholds of the BP neural network, are changing. When the maximum number of iterations is reached, the sand cat algorithm directly outputs the global optimal position of the sand cat that minimizes the fitness value;

[0079] 10) Retrain the BP neural network surface roughness prediction model with the optimal weights and thresholds found by the sand cat algorithm, and calculate the surface roughness of the screw rotor after machining under different working conditions according to the new BP neural network surface roughness prediction model.

[0080] Model verification example

[0081] A cutting test was carried out on the screw rotor. The spindle speed n (r / min), machining ratio (%), and feed rate f (mm / min) of the machine tool were used as the input variables of the neural network, and the surface roughness of the screw rotor corresponding to the machining parameters was used as the output variable, which was organized into Table 1 as shown.

[0082] Table 1 Measurement data of the surface roughness of the screw rotor

[0083] Number Spindle speed (r / min) Feed rate (mm) Processing magnification (%) Surface roughness (Ra) 1 162 2 10 1.449 2 180 2 20 1.174 3 180 2.5 10 1.156 4 198 2.5 10 1.794 5 162 2.5 20 1.753 6 198 2 30 1.62 7 180 2.5 30 0.641 8 162 5 30 0.445 9 180 5 10 1.739 10 198 5 20 0.456 11 180 2 10 0.546 12 198 2 10 0.978 13 162 2 20 0.919 14 180 2.5 20 0.808 15 162 2.5 30 0.744 16 198 2 20 1.171 17 180 2 30 1.287 18 162 5 20 1.086 19 162 5 10 1.772 20 162 2.5 10 1.142 21 198 2.5 30 0.914 22 198 2.5 20 1.267 23 189 5 20 0.767 24 189 5 10 1.682 25 189 5 30 0.71 26 189 2.5 30 0.365 27 189 2.5 20 0.252 28 189 2.5 10 0.713 29 189 2 30 0.254 30 189 2 20 1.417 31 189 2 10 2.123 32 189 3.5 30 1.232 33 189 2.5 20 0.604 34 189 2.5 10 1.746 35 198 3.5 30 1.059 36 198 3.5 20 0.862 37 198 3.5 10 1.727 38 180 3.5 30 0.655 39 180 3.5 20 1.448 40 180 3.5 10 1.822 41 162 3.5 30 1.089 42 162 3.5 20 1.43 43 162 3.5 10 2.042 44 198 5 30 0.461 45 198 5 10 1.679 46 180 5 30 0.519 47 180 5 20 0.663 48 198 3 20 1.145 49 189 3 30 0.658 50 162 3 20 1.37 51 180 3 30 1.043 52 171 2 30 0.889 53 171 3 30 1.075 54 171 3 20 1.200 55 171 2 10 1.118 56 171 5 10 1.674 57 171 5 10 1.448 58 171 3 10 1.268 59 171 5 30 0.652 60 189 3 10 1.637

[0084] The input P dimension is 3, so the number of input layer units is determined to be 3; the output T dimension is 1, so the number of output layer units is determined to be 1. The number of hidden layer neurons is calculated to be 5, the population size is set to 20, the number of iterations maxgen = 30, and the proportion of the training set is set to 85%.

[0085] According to the data in (1) and (2), the improved sand cat group algorithm is used to optimize the BP neural network, and the training results are compared with the output data of the original BP neural network, and the results are shown in the table.

[0086] Table 2 Error comparison of prediction results between BP and Tent-SCSO-BP

[0087] Number Test value / Ra BP predicted value / Ra BP error / % Tent-HBA-BP value / Ra Tent-SCSO-BP error / % 1 1.043 0.818 22 0.875 16 2 0.889 0.560 37 0.918 3 3 1.075 1.273 18 1.111 4 4 1.228 2.205 79 1.482 21 5 1.118 1.508 34 1.011 10 6 1.674 1.804 7 1.681 0.5 7 1.448 1.804 24 1.681 16 8 1.268 0.915 27 1.025 20 9 0.652 0.538 17 0.849 30 10 1.637 0.950 40 1.746 7

[0088] Through the analysis of test data, BP prediction data, and Tent-SCSO-BP prediction data, it is found that the evaluation error of BP prediction data is about 30.5%, and the prediction error of the BP neural network optimized by the sand cat swarm is about 12.8%. It can be clearly seen that the prediction accuracy of the BP neural network optimized by the sand cat swarm has been significantly improved compared with the traditional BP neural network.

[0089] In summary, compared with the traditional BP neural network, it can be found that Tent-SCSO-BP can more accurately predict the accuracy after the processing of the screw rotor.

[0090] Obviously, the above embodiments are only examples for clear illustration and not limitations on the implementation manners. For those of ordinary skill in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the implementation manners here. And the obvious changes or modifications derived therefrom are still within the protection scope of the present invention.

Claims

1. A method for establishing a prediction model of the surface roughness of a screw rotor by improving the BP algorithm, characterized in that: It includes the following steps: 1) Use a TR200 handheld surface roughness measuring instrument to measure the surface roughness of the machined screw rotor. Select part of the measurement data as training data for establishing a prediction model of surface roughness, and the remaining data as test data for verifying the accuracy of the surface roughness prediction model; 2) Determine the number of nodes in the input layer, output layer, and hidden layer according to the number of input variables and output variables of the prediction model, and determine the basic structure of the BP neural network; 3) Normalize the training data through a normalization model. Use the normalized training data to establish a surface roughness prediction model of the screw rotor based on the BP neural network. Define the input data of the BP neural network structure in the training data as P and the output data as T; 4) Set the number of training data and test data in the surface roughness measurement data; 5) Determine the number of initial weights and thresholds in the BP neural network structure according to the number of nodes in the input layer, hidden layer, and output layer, and project the weights and thresholds to the positions of sand cats; 6) First, determine the number of iterations of the sand cat swarm algorithm, and then use the Tent chaotic mapping method to generate the initial population of the sand cat swarm search algorithm to form the initial position matrix X of the sand cat population; based on the initial sand cat population, train the BP neural network model, and use the error between the pre-test and actual values of the neural network as the fitness function F to calculate the positions of the sand cats, that is, the optimal weights and thresholds; 7) Find the best fitness value of the sand cat positions according to the survival and foraging rules of sand cats in the desert; 8) The foraging process of sand cats is divided into two stages: the search and attack prey stages. The balance mechanism of these two stages is balanced according to the hearing range R of sand cats. When R is greater than 1, sand cats enter the search prey stage. When R is less than 1, sand cats attack the prey; 9) The sand cat swarm will share the best positions of each sand cat during the foraging process to select the best position of the population. Therefore, the best position of the sand cat is constantly changing with the iteration; when the maximum number of iterations is reached, the sand cat swarm will select the best sand cat position, that is, the best weights and thresholds of the BP neural network; 10) Retrain the surface roughness prediction model of the BP neural network with the best weights and thresholds found by the sand cat search algorithm, and predict the surface roughness of the screw rotor under different working conditions according to the new surface roughness prediction model of the BP neural network; In step 5), the dimension of the sand cat position vector is: Among them, is the number of optimization parameters, is the number of neurons in the hidden layer, is the number of neurons in the input layer, is the number of neurons in the output layer; In step 5), the initial sand cat population is generated through Tent mapping, and the matrix X of the initial sand cat population positions is: Among them, represents the number of sand cats; In step 6), the initial position transformation model of the sand cat population using Tent chaotic mapping is: Among them, , represents the initial individual of a random generated [[0, 1]]-dimensional vector. ​ 2. The method for establishing a prediction model of the surface roughness of a screw rotor by improving the BP algorithm according to claim 1, characterized in that: In step 1), use a TR200 handheld surface roughness measuring instrument to measure the surface roughness of the machined screw rotor under different cutting parameters. Select a part of the measurement data as training data for establishing a prediction model of surface roughness, and the remaining data as test data for verifying the accuracy of the surface roughness prediction model.

3. The method for establishing a screw rotor surface roughness prediction model by improving the BP algorithm according to claim 1, characterized in that: In step 2), the framework of the BP neural network is three-layer, namely the input layer, hidden layer, and output layer. The number of neurons in the input layer is 3, the number of neurons in the hidden layer is 5, and the number of neurons in the output layer is 1.

4. The method for establishing a prediction model of the surface roughness of a screw rotor by improving the BP algorithm according to claim 1, characterized in that: The normalization formula in step 3) is as follows: Among them, in the formula is the normalized data, is the minimum value of the sample data, is the maximum value of the sample data.

5. The method for establishing a screw rotor surface roughness prediction model by improving the BP algorithm according to claim 1, characterized in that: The fitness function in step 6) is as follows: Among them, represents the fitness of the position of each sand cat.

6. The method for establishing a screw rotor surface roughness prediction model by improving the BP algorithm according to claim 1, characterized in that: In step 8), the foraging pattern of the sand cat. According to the parameter R, it controls whether the sand cat searches or attacks the prey. When the absolute value of R is greater than 1, the sand cat is in the food search stage. When the absolute value of R is less than 1, the sand cat directly attacks the prey. Among them, is the auditory perception range of the sand cat; is the auditory characteristic of the sand cat, and its default value is 2; represents the maximum number of iterations of the population; represents the conversion parameter for the sand cat to search and attack prey; is the sensitivity range of each sand cat.

7. The method for establishing a screw rotor surface roughness prediction model by improving the BP algorithm according to claim 6, characterized in that: (1) During the search stage, the sand cat will update its new position based on its current position and the sensitivity range, so as to be able to search for the best prey position. where is the global optimal position of the sand cat swarm, is the current position of the sand cat; (2) When the sand cat detects the prey based on the hearing of its ears, the sand cat will attack the prey, and its mathematical model is: where is the optimal position of the sand cat group, is the current position of the sand cat, is a random angle between 0 and 360 degrees.

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