Gearbox parallelism prediction method based on NRBO-ELM algorithm
By constructing a gearbox parallelism prediction model based on the NRBO-ELM algorithm, the problem of low prediction accuracy in the existing technology is solved, and higher accuracy gearbox parallelism prediction is achieved, thereby improving the reliability and performance of the mechanical system.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- NO 703 RES INST OF CHINA SHIPBUILDING IND CORP
- Filing Date
- 2026-01-21
- Publication Date
- 2026-05-12
AI Technical Summary
Existing methods for predicting gearbox parallelism suffer from low prediction accuracy, making it difficult to accurately assess the impact of shaft parallelism on dynamic balance during the design and manufacturing stages, thus affecting the reliability and performance of the mechanical system.
A gearbox parallelism prediction method based on the NRBO-ELM algorithm is adopted. By constructing a finite element model of the gearbox, the distribution data of tooth root bending stress of the gear under shaft skew is obtained, a training set is constructed, and the internal parameters are optimized by combining the extreme learning machine model with the NRBO algorithm to improve the prediction accuracy.
This enables more accurate prediction of gearbox parallelism, improves gearbox performance and reliability, and ensures stable operation of the mechanical system.
Smart Images
Figure CN122021144A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of monitoring, and in particular relates to a method for predicting gearbox parallelism based on the NRBO-ELM algorithm. Background Technology
[0002] Dynamic balancing, as a core technology for precision inspection of rotating machinery, primarily aims to improve equipment stability, reliability, and operating efficiency by adjusting the mass distribution of rotating components to reduce vibration and unbalanced forces. In the field of gear transmission, especially in gearboxes, the parallelism of axes has a direct and significant impact on the dynamic balancing effect. Axis parallelism refers to the degree of deviation between the centerlines of multiple shafts. Ideally, axes should remain parallel; however, in actual manufacturing and assembly processes, due to factors such as machining accuracy, assembly accuracy, and installation errors, axis parallelism often fails to fully meet design requirements. Large axis parallelism errors can lead to severe dynamic imbalance.
[0003] High-precision axis parallelism is not only a technical requirement but also a key factor in ensuring the normal operation and long-term stability of mechanical systems. Although axis parallelism is crucial for dynamic balancing, its accurate measurement still faces several challenges. Traditional measurement methods can be affected by a combination of factors, including the accuracy of measuring equipment, operational complexity, time costs, and environmental conditions, often making it difficult to balance convenience and high precision. Therefore, establishing and applying efficient and accurate axis parallelism prediction models is particularly important. These models can predict and optimize axis parallelism during the design and manufacturing stages, accurately assess its impact on dynamic balance, and significantly improve the reliability and performance of mechanical systems. Summary of the Invention
[0004] The purpose of this invention is to address the problem of low prediction accuracy in existing gearbox parallelism prediction methods. A gearbox parallelism prediction method based on the NRBO-ELM algorithm is invented. It includes:
[0005] 1. Construct a gearbox parallelism prediction model and obtain a trained gearbox parallelism prediction model;
[0006] 2. Collect stress distribution data of the gearbox to be predicted, input the stress distribution data of the gearbox to be predicted into the trained gearbox parallelism prediction model, and obtain the parallelism of the gearbox to be predicted.
[0007] The first step involves constructing a gearbox parallelism prediction model to obtain a trained gearbox parallelism prediction model; the specific process is as follows:
[0008] Step 1: Obtain the training set;
[0009] Step 2: Construct a gearbox parallelism prediction model; train the constructed gearbox parallelism prediction model based on the training set to obtain a trained gearbox parallelism prediction model.
[0010] Furthermore, the specific process of obtaining the training set in step one is as follows:
[0011] Step 11: Construct the finite element model of the gearbox; the specific process is as follows:
[0012] Extract the spatial position of the shaft system of each pair of meshing gears in the gearbox. Based on the extracted spatial position of the shaft system of each pair of meshing gears in the gearbox, set the spatial position of the shaft system of each pair of meshing gears in the finite element software; thus obtaining the finite element model of the gearbox.
[0013] Steps 1 and 2: Perform finite element simulation calculations based on the constructed gearbox finite element model to build a training set;
[0014] The training set data consists of the distribution of tooth root bending stress along the tooth width of gearbox gears under shaft misalignment conditions.
[0015] In step two, the gearbox parallelism prediction model is an Extreme Learning Machine (ELM) model.
[0016] The specific process of training the constructed gearbox parallelism prediction model based on the training set to obtain the trained gearbox parallelism prediction model is as follows:
[0017] Step 21: Construct the Extreme Learning Machine (ELM) model and determine the internal parameters to be optimized within the ELM model;
[0018] Step 22: Input the normalized stress distribution data from the training set into the initialized Extreme Learning Machine model, and the Extreme Learning Machine model outputs the prediction results;
[0019] Steps 2 and 3: Based on the input and output of the Extreme Learning Machine model, use the NRBO algorithm, Newton-Raphson iterative method, and trap escape algorithm to optimize the internal parameters of the Extreme Learning Machine model. Stop training when the number of training iterations reaches the maximum, and obtain the trained Extreme Learning Machine model.
[0020] In steps two and three, based on the input and output of the Extreme Learning Machine (ELM) model, the NRBO algorithm, Newton-Raphson iterative method, and trap escape algorithm are used to optimize the internal parameters of the ELM model. Training stops when the maximum number of training iterations is reached, resulting in a trained ELM model. The specific process is as follows:
[0021] Step 231: Set the number of particles N in the NRBO algorithm population. pThe maximum number of iterations (Max_IT) and the coefficient of determination (DF) are determined; and the population position of the NRBO algorithm is initialized, which is represented as follows: ,
[0022] Step 232: Calculate the fitness value of all particles in the population, and select the optimal and worst particle position vectors based on the fitness values of all particles; the particle position vector with the highest fitness is the optimal particle position vector; the particle position vector with the lowest fitness is the worst particle position vector.
[0023] Step 233: Based on the optimal particle position vector and Worst particle position vector Update all particles in the population;
[0024] Steps two, three, and four: Calculate the fitness values of all particles in the updated population, and update the optimal particle position vector based on the fitness values of all particles in the updated population. and worst particle position vector ; Obtain the updated optimal particle position vector and the updated worst particle position vector The specific process is as follows:
[0025] For example, update the best particle position vector of the Kth generation with the particle position vector that has the highest fitness after the Kth generation update; update the worst particle position vector of the Kth generation with the particle position vector that has the lowest fitness after the Kth generation update.
[0026] If the maximum number of iterations has not been reached, return to step two-three-three;
[0027] The iteration stops when the maximum number of iterations is reached, and the updated optimal particle position vector is used. As the trained optimal particle position vector, proceed to steps two, three, and five;
[0028] Steps 2, 3, and 5: Use the trained Extreme Learning Machine model corresponding to the optimal particle position as the trained Extreme Learning Machine model.
[0029] The beneficial effects of this invention are as follows:
[0030] This method utilizes an Extreme Learning Machine (ELM) model for prediction and combines it with the NRBO algorithm to optimize the internal parameters of the ELM model, thereby improving prediction accuracy. Specifically, this method constructs a finite element model of the gearbox and performs finite element simulation calculations to obtain the distribution data of the tooth root bending stress along the tooth width direction under shaft misalignment, thus constructing a training set. Then, this data is used to train the ELM model, and the NRBO algorithm is used to optimize the model parameters to obtain a well-trained gearbox parallelism prediction model. This method can more accurately predict gearbox parallelism, thereby improving gearbox performance and reliability. Attached Figure Description
[0031] Figure 1 This is a schematic diagram of the spatial position of the axis of the present invention;
[0032] Figure 2 This is a schematic diagram of the predictive model structure of the present invention;
[0033] Figure 3 This is a schematic diagram of the optimization process of the NRBO-ELM algorithm for the Extreme Learning Machine model according to the present invention. Detailed Implementation
[0034] Specific implementation method one: Combining Figures 1-3 The present invention includes: 1. Constructing a gearbox parallelism prediction model and obtaining a trained gearbox parallelism prediction model;
[0035] 2. Collect stress distribution data of the gearbox to be predicted, input the stress distribution data of the gearbox to be predicted into the trained gearbox parallelism prediction model, and obtain the parallelism of the gearbox to be predicted.
[0036] The first step involves constructing a gearbox parallelism prediction model to obtain a trained gearbox parallelism prediction model; the specific process is as follows:
[0037] Step 1: Obtain the training set;
[0038] Step 2: Construct a gearbox parallelism prediction model; train the constructed gearbox parallelism prediction model based on the training set to obtain a trained gearbox parallelism prediction model.
[0039] Specific Implementation Method Two: The difference between this implementation method and Specific Implementation Method One is that...
[0040] The specific process for obtaining the training set in step one is as follows:
[0041] Step 11: Construct the finite element model of the gearbox; the specific process is as follows:
[0042] Extract the spatial position of the shaft system of each pair of meshing gears in the gearbox. Based on the extracted spatial position of the shaft system of each pair of meshing gears in the gearbox, set the spatial position of the shaft system of each pair of meshing gears in the finite element software; thus obtaining the finite element model of the gearbox.
[0043] Steps 1 and 2: Perform finite element simulation calculations based on the constructed gearbox finite element model to build a training set;
[0044] The training set data consists of the distribution of tooth root bending stress along the tooth width of gearbox gears under shaft misalignment conditions.
[0045] The other steps and parameters are the same as in Specific Implementation Method 1.
[0046] Specific Implementation Method Three: The difference between this implementation method and Specific Implementation Method One is that...
[0047] The specific process of setting the shaft spatial position of a pair of meshing gears in the finite element software based on the extracted shaft spatial position of a pair of meshing gears in the gearbox is as follows:
[0048] Based on the extracted spatial position of the shaft system of a pair of meshing gears in the gearbox, the finite element software sets one floating bearing position and three fixed bearing positions.
[0049] Because a pair of meshing gears in a gearbox corresponds to two shafts, and each shaft has two bearings to support it, there are four bearing positions. This invention simulates the possible skewing or tilting of the shaft under actual operating conditions by setting one floating bearing position and three fixed bearing positions. This configuration helps analyze the behavior of the shaft under different loads and installation conditions; of the four bearings, one can be floating (i.e., allowing a certain degree of movement to simulate shaft skewing), while the other three are fixed to provide the necessary support and constraints.
[0050] In steps one and two, finite element simulation calculations are performed based on the constructed gearbox finite element model to build a training set; the specific process is as follows:
[0051] Step 121: Set the positions of N floating bearings in the finite element software to obtain N shaft tilt states; N is a positive integer;
[0052] Step 122: Calculate the distribution data Y of the tooth root bending stress along the tooth width of the meshing gears in the gearbox under N shaft system skew conditions using finite element software.
[0053] The distribution data of the tooth root bending stress of the meshing gear in the gearbox under the nth shaft misalignment state along the tooth width direction are expressed as follows: , ; ;
[0054] Steps 1-3: Normalize the distribution data of tooth root bending stress along the tooth width of the meshing gears in the gearbox under N shaft misalignment conditions to obtain N normalized distribution data of tooth root bending stress along the tooth width of the meshing gears in the gearbox. ;
[0055] Among them, the distribution data of tooth root bending stress of meshing gears in the gearbox under the nth shaft misalignment state along the tooth width direction. After normalization, the distribution data of tooth root bending stress of meshing gears in the gearbox under the normalized nth shaft skew state are obtained along the tooth width direction. The specific process is as follows:
[0056]
[0057] In the formula, express The i-th element in; express The maximum value among the elements. express The minimum value among the elements; express The i-th element in the array; i is a positive integer;
[0058] Steps 1-4: Obtain the distribution data of tooth root bending stress along the tooth width of N normalized gearboxes. Shuffle the data to obtain the shuffled data. ; Shuffle the data The training set and the test set are obtained by dividing the data proportionally.
[0059]
[0060]
[0061] In the formula, num_samples is the number of samples, i.e., N; This represents the proportion of the training set, with a value of 0.7. The data is shuffled; train is the training set. Indicates multiplication;
[0062] test is the test set;
[0063] In a total of num_samples training samples, for the i-th discrete training sample ,
[0064] Input training sample data is , m is the feature dimension, and the output data is n is the dimension of the output feature
[0065] The distribution of tooth root bending stress along the tooth width direction under skewed conditions was calculated using the finite element method. The data was then linearly normalized and divided into training and testing datasets to prevent overfitting and increase the randomness of model training.
[0066] The other steps and parameters are the same as in one of the specific implementation methods one or two.
[0067] Specific Implementation Method Four: This implementation method differs from Specific Implementation Methods One through Four in that...
[0068] In step two, the gearbox parallelism prediction model is an Extreme Learning Machine (ELM) model.
[0069] The specific process of training the constructed gearbox parallelism prediction model based on the training set to obtain the trained gearbox parallelism prediction model is as follows:
[0070] Step 21: Construct the Extreme Learning Machine (ELM) model and determine the internal parameters to be optimized within the ELM model;
[0071] Step 22: Input the normalized stress distribution data from the training set into the initialized Extreme Learning Machine model, and the Extreme Learning Machine model outputs the prediction results;
[0072] Steps 2 and 3: Based on the input and output of the Extreme Learning Machine (ELM) model, use the NRBO algorithm, Newton-Raphson iterative method, and trap escape algorithm to optimize the internal parameters of the ELM model. Training stops when the maximum number of iterations is reached, resulting in a well-trained ELM model.
[0073] The other steps and parameters are the same as those in one of the specific implementation methods one to three.
[0074] Specific Implementation Method Five: The difference between this implementation method and Specific Implementation Methods One to Four is that...
[0075] The extreme learning machine in step two includes: an input layer, a hidden layer, and an output layer;
[0076] The specific process of constructing the Extreme Learning Machine model in step two-one is as follows:
[0077] The input layer is set to have M input layer nodes;
[0078] The hidden layer is set to have L hidden layer nodes;
[0079] The output layer is set to have K output layer nodes; M, L, and K are all positive integers.
[0080] The internal parameters to be optimized in the extreme learning machine model include: a first type of optimization parameter set and a second type of optimization parameter set;
[0081] The first type of optimization parameter is the weight from the input layer node to the hidden layer node, where the weight from the i-th input layer node to the j-th hidden layer node is... ,
[0082] The second type of optimization parameter is the weighting value of the hidden layer nodes; where the weighting value of the j-th hidden layer node is... ,
[0083] The theoretical derivation of the above two types of optimization parameters in this invention is as follows:
[0084] Assuming the output weights between the hidden layer and the output layer are β,
[0085] The output of the hidden layer is represented as ;
[0086] Expressed as a formula:
[0087]
[0088] in Indicates the input set data. It is the output of the i-th hidden layer node. It is an activation function, and the output of the activation function is expressed by the formula:
[0089] ;
[0090] In the formula, , , Let be the weight value of the j-th hidden layer. The weights from the i-th node in the input layer to the j-th hidden layer node are: ;
[0091] After output through the hidden layer
[0092] Therefore, the output of the Extreme Learning Machine (ELM) model in step two is:
[0093]
[0094] in, .
[0095] use The training error is evaluated by minimizing the squared difference between the objective function and the sample T. The solution that minimizes this objective function is the optimal solution. The objective function is as follows:
[0096]
[0097]
[0098] Where t is the target matrix of the training data.
[0099] Using knowledge of linear algebra and matrix theory, the optimal solution to the objective function can be derived as follows:
[0100]
[0101] in Let H be the Moore-Penrose generalized inverse matrix. When it is a non-singular matrix, we have:
[0102]
[0103] At this point, the only unknown parameters to be determined in the neural network are... Therefore, these will be used as the first and second optimization parameters of the present invention;
[0104] The other steps and parameters are the same as those in one of the specific implementation methods one to four.
[0105] Specific Implementation Method Six: The difference between this implementation method and Specific Implementation Methods One to Five is that...
[0106] In steps two and three, based on the input and output of the Extreme Learning Machine (ELM) model, the NRBO algorithm, Newton-Raphson iterative method, and trap escape algorithm are used to optimize the internal parameters of the ELM model. Training stops when the maximum number of training iterations is reached, resulting in a trained ELM model. The specific process is as follows:
[0107] Step 231: Set the number of particles N in the NRBO algorithm population. p The maximum number of iterations (Max_IT) and the coefficient of determination (DF) are determined; and the population position of the NRBO algorithm is initialized, which is represented as follows: ,
[0108] Step 232: Calculate the fitness value of all particles in the population, and select the optimal and worst particle position vectors based on the fitness values of all particles; the particle position vector with the highest fitness is the optimal particle position vector; the particle position vector with the lowest fitness is the worst particle position vector.
[0109] Step 233: Based on the optimal particle position vector and Worst particle position vector Update all particles in the population;
[0110] Steps two, three, and four: Calculate the fitness values of all particles in the updated population, and update the optimal particle position vector based on the fitness values of all particles in the updated population. and worst particle position vector ; Obtain the updated optimal particle position vector and the updated worst particle position vector The specific process is as follows:
[0111] For example, update the best particle position vector of the Kth generation with the particle position vector that has the highest fitness after the Kth generation update; update the worst particle position vector of the Kth generation with the particle position vector that has the lowest fitness after the Kth generation update.
[0112] If the maximum number of iterations has not been reached, return to step two-three-three;
[0113] The iteration stops when the maximum number of iterations is reached, and the updated optimal particle position vector is used. As the trained optimal particle position vector, proceed to steps two, three, and five;
[0114] Steps 2, 3, and 5: Use the trained Extreme Learning Machine model corresponding to the optimal particle position as the trained Extreme Learning Machine model. Other steps and parameters are the same as in one of the specific implementation methods 1 to 5.
[0115] Specific Implementation Method Seven: The difference between this implementation method and Specific Implementation Methods One through Six is that...
[0116] In steps two and three, the number of particles N in the NRBO algorithm is set. p The maximum number of iterations (Max_IT) and the coefficient of determination (DF) are determined; and the population position of the NRBO algorithm is initialized, which is represented as follows: This can be expressed as a formula:
[0117]
[0118] In the formula, Indicates the first The position vector of each particle is expressed by the formula:
[0119]
[0120] In the formula, express The Middle There are 10 positional parameters, each representing an internal parameter to be optimized in the Extreme Learning Machine model. Indicates the number of positional parameters;
[0121] The first type of optimization parameter set and the second type of optimization parameter set; the first type of optimization parameter set has A1, A1=ML; the second type of optimization parameter set has A2, A2=L, and there are a total of Nx internal parameters, Nx=ML+L; each positional parameter represents an internal parameter to be optimized in the extreme learning machine model;
[0122] Therefore, a particle represents a set of parameters for an extreme learning machine model;
[0123] In steps two and three, the first [number] in the population is calculated. The fitness value of a particle is expressed as: This can be expressed as a formula:
[0124]
[0125] In the formula, Represents the true value. Indicates the first The predicted value output by the extreme learning machine model for each particle;
[0126] The true value is the data in the dataset obtained from finite element simulation;
[0127] The other steps and parameters are the same as those in any of the specific implementation methods one to six.
[0128] Specific Implementation Method Eight: The difference between this implementation method and Specific Implementation Methods One to Seven is that...
[0129] In steps two and three, the optimal particle position vector is used. and worst particle position vector For the first in the population The process of updating each particle is as follows: According to step 2331: set a random variable rand, the range of which is (1, dim); the size of dim is set manually.
[0130] If the value of the random variable rand is not less than the coefficient of determination DF, then proceed to step two.
[0131] If the value of the random number rand is less than the determination coefficient DF, proceed to step two:
[0132] Step 2332: Based on the optimal particle position vector and worst particle position vector Use the first update rule to update the population. Update each particle;
[0133] Step 2333: Based on the optimal particle position vector and worst particle position vector Use the second update rule to update the population. Update each particle;
[0134] The other steps and parameters are the same as those in any of the specific implementation methods one to seven.
[0135] Specific Implementation Method Nine: The difference between this implementation method and Specific Implementation Methods One through Eight is that...
[0136] In step two, three, three, two, based on the optimal particle position vector and worst particle position vector Use the first update rule to update the population. Each particle is updated once; expressed by the formula:
[0137]
[0138] In the formula, IT represents the iteration number variable; IT is a positive integer; In the (IT+1)th iteration, the... The position vector of each particle, i.e., the updated position vector;
[0139] Represents a random variable (a random integer ranging from 1 to Nx); IT represents the iteration count variable; Indicates the first intermediate position variable, Indicates the second intermediate position variable, This represents the third intermediate position variable; expressed by the formula:
[0140]
[0141]
[0142]
[0143] In the formula, In the IT-th iteration, the i-th iteration is... The position vectors of the particles, where a and b represent random variables, and r² represents a random variable.
[0144] Random variables a and b take values between 0 and 1.
[0145] The random variable r2 takes values from 1 to Nx random integers;
[0146] Indicates the first intermediate variable, Indicates the second intermediate variable, The third intermediate variable is represented by the formula:
[0147]
[0148]
[0149]
[0150] In the formula, Mean() represents calculating the average value. Indicates the fourth intermediate variable. The fifth intermediate variable is represented by the formula:
[0151]
[0152] .
[0153] The other steps and parameters are the same as those in one of the specific implementation methods one to eight.
[0154] Specific Implementation Method Ten: The difference between this implementation method and Specific Implementation Methods One through Nine is that...
[0155] In step two, three, three, three, based on the optimal particle position vector and worst particle position vector Use the second update rule to update the population. Each particle is updated, and the specific process is as follows:
[0156] Construct random numbers The random number The range is between (0, 1).
[0157] When random number When it is less than 0.5, the first in the population The update of each particle can be expressed by the following formula:
[0158]
[0159] In the formula, , , All are random numbers between (0, 1);
[0160] When random number When less than or equal to 0.5, for the th in the population The update of each particle can be expressed by the following formula:
[0161]
[0162] The other steps and parameters are the same as those in any of the specific implementation methods one to nine.
[0163] The above description is merely of preferred embodiments of the present invention. It should be understood that the present invention is not limited to the specific embodiments described above. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent substitutions, and improvements made to the above embodiments without departing from the scope of the present invention, based on the technical essence of the present invention, and within the spirit and principles of the present invention, shall still fall within the protection scope of the present invention.
Claims
1. A method for predicting gearbox parallelism based on the NRBO-ELM algorithm, characterized in that, Includes the following steps:
1. Construct a gearbox parallelism prediction model and obtain a trained gearbox parallelism prediction model; 2. Collect stress distribution data of the gearbox to be predicted, input the stress distribution data of the gearbox to be predicted into the trained gearbox parallelism prediction model, and obtain the parallelism of the gearbox to be predicted. The first step involves constructing a gearbox parallelism prediction model to obtain a trained gearbox parallelism prediction model; the specific process is as follows: Step 1: Obtain the training set; Step 2: Construct a gearbox parallelism prediction model; train the constructed gearbox parallelism prediction model based on the training set to obtain a trained gearbox parallelism prediction model.
2. The gearbox parallelism prediction method based on the NRBO-ELM algorithm according to claim 1, characterized in that, The specific process for obtaining the training set in step one is as follows: Step 11: Construct the finite element model of the gearbox; the specific process is as follows: Extract the spatial position of the shaft system of each pair of meshing gears in the gearbox, and set the spatial position of the shaft system of each pair of meshing gears in the finite element software based on the extracted spatial position of the shaft system of each pair of meshing gears. The finite element model of the gearbox was obtained; Steps 1 and 2: Perform finite element simulation calculations based on the constructed gearbox finite element model to build a training set.
3. The gearbox parallelism prediction method based on the NRBO-ELM algorithm according to claim 2, characterized in that, The specific process of setting the shaft spatial position of a pair of meshing gears in the finite element software based on the extracted shaft spatial position of a pair of meshing gears in the gearbox is as follows: Based on the extracted spatial position of the shaft system of a pair of meshing gears in the gearbox, the finite element software sets one floating bearing position and three fixed bearing positions. In steps one and two, finite element simulation calculations are performed based on the constructed gearbox finite element model to build a training set; the specific process is as follows: Step 121: Set the positions of N floating bearings in the finite element software to obtain N shaft tilt states; N is a positive integer; Step 122: Calculate the distribution data Y of the tooth root bending stress along the tooth width of the meshing gears in the gearbox under N shaft system skew conditions using finite element software. The distribution data of the tooth root bending stress of the meshing gear in the gearbox under the nth shaft misalignment state along the tooth width direction are expressed as follows: , ; ; Steps 1-3: Normalize the distribution data of tooth root bending stress along the tooth width of the meshing gears in the gearbox under N shaft misalignment conditions to obtain N normalized distribution data of tooth root bending stress along the tooth width of the meshing gears in the gearbox. ; Among them, the distribution data of tooth root bending stress of meshing gears in the gearbox under the nth shaft misalignment state along the tooth width direction. After normalization, the distribution data of tooth root bending stress of meshing gears in the gearbox under the normalized nth shaft skew state are obtained along the tooth width direction. The specific process is as follows: In the formula, express The i-th element in; express The maximum value among the elements. express The minimum value among the elements; express The i-th element in the array; i is a positive integer; Steps 1-4: Obtain the distribution data of tooth root bending stress along the tooth width of N normalized gearboxes. Shuffle the data to obtain the shuffled data. ; Shuffle the data The training set is obtained by dividing the data proportionally.
4. The gearbox parallelism prediction method based on the NRBO-ELM algorithm according to claim 3, characterized in that, The gearbox parallelism prediction model in step two is an extreme learning machine model. The specific process of training the constructed gearbox parallelism prediction model based on the training set to obtain the trained gearbox parallelism prediction model is as follows: Step 21: Construct the Extreme Learning Machine (ELM) model and determine the internal parameters to be optimized within the ELM model; Step 22: Input the normalized stress distribution data from the training set into the initialized Extreme Learning Machine model, and the Extreme Learning Machine model outputs the prediction results; Steps 2 and 3: Based on the input and output of the Extreme Learning Machine (ELM) model, use the NRBO algorithm to optimize the internal parameters of the ELM model. Stop training when the maximum number of training iterations is reached, and obtain the trained ELM model.
5. The gearbox parallelism prediction method based on the NRBO-ELM algorithm according to claim 4, characterized in that, The extreme learning machine in step two includes: an input layer, a hidden layer, and an output layer; The specific process of constructing the Extreme Learning Machine model in step two-one is as follows: The input layer is set to have M input layer nodes; The hidden layer is set to have L hidden layer nodes; The output layer is set to have K output layer nodes; M, L, and K are all positive integers. The internal parameters to be optimized in the extreme learning machine model include: a first type of optimization parameter set and a second type of optimization parameter set; The first type of optimization parameter is the weight from the input layer node to the hidden layer node, where the weight from the i-th input layer node to the j-th hidden layer node is... , The second type of optimization parameter is the weighting value of the hidden layer nodes; where the weighting value of the j-th hidden layer node is... .
6. The gearbox parallelism prediction method based on the NRBO-ELM algorithm according to claim 5, characterized in that, In steps two and three, based on the input and output of the Extreme Learning Machine (ELM) model, the NRBO algorithm is used to optimize and train the internal parameters of the ELM model. Training stops when the maximum number of training iterations is reached, resulting in a trained ELM model. The specific process is as follows: Step 231: Set the number of particles N in the NRBO algorithm population. p The maximum number of iterations (Max_IT) and the coefficient of determination (DF) are determined; and the population position of the NRBO algorithm is initialized, which is represented as follows: , Step 232: Calculate the fitness value of all particles in the population, and select the best particle position vector and the worst particle position vector based on the fitness values of all particles; Step 233: Based on the optimal particle position vector and Worst particle position vector Update all particles in the population; Steps two, three, and four: Calculate the fitness values of all particles in the updated population, and update the optimal particle position vector based on the fitness values of all particles in the updated population. and worst particle position vector ; Obtain the updated optimal particle position vector and the updated worst particle position vector ; If the maximum number of iterations has not been reached, return to step two-three-three; The iteration stops when the maximum number of iterations is reached, and the updated optimal particle position vector is used. As the trained optimal particle position vector, proceed to steps two, three, and five; Steps 2, 3, and 5: Use the trained Extreme Learning Machine model corresponding to the optimal particle position as the trained Extreme Learning Machine model.
7. The gearbox parallelism prediction method based on the NRBO-ELM algorithm according to claim 6, characterized in that, In steps two and three, the number of particles N in the NRBO algorithm is set. p The maximum number of iterations (Max_IT) and the coefficient of determination (DF) are determined; and the population position of the NRBO algorithm is initialized, which is represented as follows: This can be expressed as a formula: In the formula, Indicates the first The position vector of each particle is expressed by the formula: In the formula, express The Middle There are 10 positional parameters, each of which represents an internal parameter to be optimized in the Extreme Learning Machine model. Indicates the number of positional parameters; In steps two and three, the first [number] in the population is calculated. The fitness value of a particle is expressed as: This can be expressed as a formula: In the formula, Represents the actual value. Indicates the first The predicted value output by the extreme learning machine model for each particle.
8. The gearbox parallelism prediction method based on the NRBO-ELM algorithm according to claim 7, characterized in that, In steps two and three, the optimal particle position vector is used. and worst particle position vector For the first in the population Each particle is updated, and the specific process is as follows: Step 2331: Define a random variable rand, whose range is between (1, dim); If the value of the random variable rand is not less than the coefficient of determination DF, then proceed to step two. If the value of the random number rand is less than the determination coefficient DF, proceed to step two: Step 2332: Based on the optimal particle position vector and worst particle position vector Use the first update rule to update the population. Update each particle; Step 2333: Based on the optimal particle position vector and worst particle position vector Use the second update rule to update the population. Each particle is updated.
9. The gearbox parallelism prediction method based on the NRBO-ELM algorithm according to claim 8, characterized in that, In step two, three, three, two, based on the optimal particle position vector and worst particle position vector Use the first update rule to update the population. Each particle is updated once; expressed by the formula: In the formula, IT represents the iteration number variable; IT is a positive integer; In the (IT+1)th iteration, the... The position vector of each particle, i.e., the updated position vector; Represents a random variable; IT represents the number of iterations. Indicates the first intermediate position variable, Indicates the second intermediate position variable, This represents the third intermediate position variable; expressed by the formula: In the formula, In the IT-th iteration, the i-th iteration is... The position vectors of the particles, where a and b represent random variables, and r² represents a random variable. Indicates the first intermediate variable, Indicates the second intermediate variable, The third intermediate variable is represented by the formula: In the formula, Mean() represents calculating the average value. Indicates the fourth intermediate variable. The fifth intermediate variable is represented by the formula: 。 10. A gearbox parallelism prediction method based on the NRBO-ELM algorithm according to claim 9, characterized in that, In step two, three, three, three, based on the optimal particle position vector and worst particle position vector Use the second update rule to update the population. Each particle is updated, and the specific process is as follows: Construct random numbers The random number The range is between (0, 1). When random number When it is less than 0.5, the first in the population The update of each particle can be expressed by the following formula: In the formula, , , All are random numbers between (0, 1); When random number When less than or equal to 0.5, for the th in the population The update of each particle can be expressed by the following formula: 。