A rotor unbalance mass optimization identification method and system based on SVR and differential evolution algorithm

Abstract

The application relates to a rotor unbalanced mass optimization identification method and system based on an SVR and a differential evolution algorithm. The method comprises the following steps: obtaining vibration response data of a rotor system in an initial unbalanced state; initializing a differential evolution algorithm population in a preset counterweight parameter range, and constructing test input features according to corresponding counterweight parameters of the population individuals; inputting the test input features into a support vector regression prediction model to obtain predicted residual vibration response data; calculating a normalized loss function value based on the predicted residual vibration response data and the initial vibration response data; performing fitness evaluation according to the loss function value, and performing mutation, crossover and selection operations of the differential evolution algorithm to generate a new generation population and update the test input features; repeating the above steps until a termination condition is met, and outputting a counterweight parameter corresponding to a minimum loss function value as a global optimal counterweight scheme. The method can realize efficient global optimization of multi-plane counterweight parameters.

Description

Technical Field

[0001] This invention belongs to the field of rotor dynamics and intelligent optimization, and in particular relates to a rotor imbalance quality optimization identification method and system based on SVR and differential evolution algorithm. Background Technology

[0002] As rotating machinery becomes increasingly faster and more complex, dynamic balancing technology for rotor systems is receiving increasing attention. Rotor imbalance is one of the main causes of mechanical vibration, and accurately identifying the imbalance mass and optimizing the counterweight scheme are key to reducing vibration and ensuring the safe operation of equipment.

[0003] Traditional rotor dynamic balancing methods are usually based on the influence coefficient method or the least squares method. These methods assume that the rotor system has linear response characteristics and calculate the corrected mass by measuring the linear relationship between the vibration response and the counterweight.

[0004] However, for complex rotor systems, due to nonlinear coupling effects, multi-point vibration response, and multi-plane counterweight factors, traditional linear methods struggle to accurately describe the system response characteristics, leading to insufficient accuracy in optimization results. In recent years, machine learning methods such as Support Vector Regression (SVR) have been used to build nonlinear surrogate models, but existing methods typically lack effective coupling with global optimization algorithms, making it difficult to achieve high-precision multi-plane counterweight optimization. Therefore, how to achieve efficient and accurate optimization of multi-plane counterweight parameters while considering the system's nonlinear characteristics has become a pressing technical problem in this field. Summary of the Invention

[0005] Therefore, it is necessary to provide a rotor imbalance quality optimization identification method and system based on SVR and differential evolution algorithm to address the above-mentioned technical problems.

[0006] Firstly, this application provides a rotor imbalance quality optimization identification method based on SVR and differential evolution algorithm, including:

[0007] S1. Obtain the vibration response data of the rotor system under the initial unbalanced state to obtain the initial vibration response data;

[0008] S2. Based on the initial vibration response data, initialize the differential evolution algorithm population within the preset counterweight parameter range to obtain the initial population, and construct the corresponding test input features according to the counterweight parameters of each body in the initial population.

[0009] S3. Input the test input features into the support vector regression prediction model to obtain the predicted residual vibration response data;

[0010] S4. The normalized loss function value is calculated based on the predicted residual vibration response data and the initial vibration response data;

[0011] S5. The fitness of the population is evaluated based on the normalized loss function value, and the mutation, crossover and selection operations of the differential evolution algorithm are performed on the population to generate a new generation of population. The test input features are updated according to the weight parameters corresponding to each individual in the new generation of population.

[0012] S6. Repeat S3 to S5 until the preset maximum number of iterations is met or the absolute value of the difference between the normalized loss function value and the previous generation normalized loss function value is less than the preset convergence tolerance. Output the weight parameters corresponding to the minimum value of the normalized loss function value to obtain the globally optimal weight scheme.

[0013] In one embodiment, the support vector regression prediction model is constructed through the following steps:

[0014] S11. Obtain the original experimental data of multiple sets of dynamic balancing experiments conducted on the rotor experimental platform through multiple counterweight planes and multiple measuring points; wherein, the original experimental data includes the counterweight mass, counterweight phase, and vibration response amplitude of each measuring point in the horizontal and vertical directions of each counterweight plane.

[0015] S12. Perform orthogonal component transformation on the counterweight mass and counterweight phase of each counterweight plane to obtain the real part data and imaginary part data of each counterweight plane;

[0016] S13. The real part data, imaginary part data and the corresponding counterweight mass of the counterweight plane in the original experimental data are spliced ​​together to obtain the input feature vector data.

[0017] S14. Perform orthogonal component transformation on the vibration response amplitudes of each measuring point in the horizontal and vertical directions to obtain the output feature vector data;

[0018] S15. Establish a nonlinear mapping relationship between the input feature vector and the output feature vector data to obtain the support vector regression prediction model; wherein, the support vector regression prediction model includes the penalty factor parameter, the kernel function parameter, and the insensitive loss parameter.

[0019] In one embodiment, the support vector regression prediction model is trained through the following steps:

[0020] S21. Combine the input feature vector data and the output feature vector data to obtain the counterweight vibration mapping sample set data. Divide the counterweight vibration mapping sample set data into a validation set and a training set to obtain multiple sets of training and validation partition data.

[0021] S22. Based on the training and validation partition data, train the support vector regression prediction model using the training set, and calculate the prediction error using the validation set to obtain the validation error data for each partition.

[0022] S23. Average the validation error data from multiple partitions to obtain the average cross-validation error data.

[0023] S24. Iterate through multiple different combinations of penalty factor parameters, kernel function parameters, and insensitive loss parameters. Repeat S22 to S23 for each combination of parameter values. Select the combination of parameter values ​​with the smallest average cross-validation error as the final parameters of the support vector regression prediction model, and obtain the trained support vector regression prediction model.

[0024] In one embodiment, the expression for the normalized loss function value is:

[0025]

[0026] in, For the combination of counterweight parameters The normalized loss function value, For the combination of counterweight parameters, The initial vibration response amplitude, Indicates the combination of counterweight parameters Under the conditions The predicted vibration response amplitude of each measuring point channel. This indicates the total number of measuring point channels. It equals the number of measuring points multiplied by 2. This indicates the sequence number of the measuring point channel.

[0027] In one embodiment, S5 includes:

[0028] S51. Based on the normalized loss function value, the fitness of each individual in the population is evaluated to obtain the fitness value data of each individual; among which, the fitness value data and the normalized loss function value have a monotonically decreasing relationship;

[0029] S52. Based on the fitness values ​​of each individual, select the target individual and multiple parent individuals for mutation from the population, perform the mutation operation of the differential evolution algorithm, and obtain the mutation vector data.

[0030] S53. Perform cross operations on the variation vector data and the original weight parameter vector corresponding to the target individual to obtain the experimental vector data;

[0031] S54. Based on fitness value data, perform selection operations on experimental vector data and the original weight parameter vectors corresponding to target individuals to obtain a new generation of population;

[0032] S55. Update the test input features based on the weight parameters of each individual in the new generation population;

[0033] The selection operation follows these rules: if the normalized loss function value corresponding to the experimental vector is less than the normalized loss function value corresponding to the target individual, then the experimental vector is selected as an individual in the new generation population; otherwise, the original weight parameter vector corresponding to the target individual is retained as an individual in the new generation population.

[0034] In one embodiment, the counterweight parameter range includes a counterweight mass search range and a counterweight phase search range, wherein the counterweight mass search range is 0 grams to 5 grams and the counterweight phase search range is 0 degrees to 360 degrees.

[0035] In one embodiment, the preset maximum number of iterations is a pre-set iteration number threshold, and the preset convergence tolerance is a pre-set change threshold of the normalized loss function value; the iteration is terminated when the number of iterations reaches the iteration number threshold, or when the absolute value of the difference between the normalized loss function values ​​of two consecutive iterations is less than the change threshold.

[0036] Secondly, this application also provides a rotor imbalance quality optimization identification system based on SVR and differential evolution algorithm, including:

[0037] The data acquisition module is used to acquire the vibration response data of the rotor system under the initial unbalanced state, and obtain the initial vibration response data.

[0038] The initial population and test input feature construction module is used to initialize the differential evolution algorithm population based on the initial vibration response data within the preset counterweight parameter range, obtain the initial population, and construct the corresponding test input features according to the counterweight parameters of each individual in the initial population.

[0039] The residual vibration response prediction module is used to input the test input features into the support vector regression prediction model to obtain the predicted residual vibration response data;

[0040] The loss function calculation module is used to calculate the normalized loss function value based on the predicted residual vibration response data and the initial vibration response data.

[0041] The test input feature update module is used to evaluate the fitness of the population based on the normalized loss function value, perform mutation, crossover and selection operations of differential evolution algorithm on the population to generate a new generation population, and update the test input features according to the weight parameters corresponding to each individual in the new generation population.

[0042] The iterative optimization and counterweight scheme output module is used to re-trigger the residual vibration response prediction module, loss function calculation module, and test input feature update module until the preset maximum number of iterations is met or the absolute value of the difference between the normalized loss function value and the previous generation normalized loss function value is less than the preset convergence tolerance. The counterweight parameters corresponding to the minimum value of the normalized loss function are output to obtain the globally optimal counterweight scheme.

[0043] Thirdly, this application also provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the method described in the first aspect.

[0044] Fourthly, this application also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method described in the first aspect.

[0045] The aforementioned rotor imbalance mass optimization identification method and system based on SVR and differential evolution algorithm first acquires the vibration response data of the rotor system under the initial imbalance state, and constructs a nonlinear surrogate model between the counterweight parameters and the vibration response at multiple measuring points based on support vector regression. This model is used to accurately predict the residual vibration response under different counterweight schemes. Then, a differential evolution algorithm is introduced to initialize the population within the preset counterweight parameter range. With the goal of minimizing the normalized loss function value, it iterative evolution through mutation, crossover, and selection operations globally searches for the optimal combination of counterweight parameters. This method can improve the prediction accuracy of vibration response of complex rotor systems, effectively overcome the insufficient accuracy of traditional linear methods in multi-plane nonlinear coupling cases, reduce the residual vibration amplitude of the rotor system, and achieve synergistic suppression of vibration at multiple measuring points; reduce the number of repeated weight trials required for on-site dynamic balancing, and improve balancing efficiency and operational safety; achieve global optimization of multi-plane counterweight parameters, enhance the stability and convergence of the optimization process, and has good engineering applicability. Attached Figure Description

[0046] To more clearly illustrate the technical solutions in the embodiments or related technologies of this application, the accompanying drawings used in the description of the embodiments or related technologies will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0047] Figure 1 This is a flowchart illustrating a rotor imbalance quality optimization identification method based on SVR and differential evolution algorithm in one embodiment.

[0048] Figure 2This is a flowchart illustrating a rotor dynamic balancing optimization method based on support vector regression and differential evolution algorithm in a specific embodiment.

[0049] Figure 3 This is a schematic diagram of a rotor dynamic balancing optimization system based on support vector regression and differential evolution algorithm in a specific embodiment;

[0050] Figure 4 This is a schematic diagram showing the comparison of vibration amplitudes at various measuring points before and after least squares balancing in a specific embodiment.

[0051] Figure 5 This is a schematic diagram showing the comparison between the prediction results of the support vector regression model for vibration response and the actual vibration response in a specific embodiment.

[0052] Figure 6 This is a schematic diagram showing the comparison of vibration amplitude before and after dynamic balancing using a hybrid model of support vector regression and differential evolution algorithm in a specific embodiment.

[0053] Figure 7 This is a schematic diagram of a rotor imbalance quality optimization identification system based on SVR and differential evolution algorithm in one embodiment. Detailed Implementation

[0054] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0055] refer to Figure 1 The document presents a flowchart illustrating a rotor imbalance quality optimization identification method based on SVR and differential evolution algorithm, which includes the following steps:

[0056] S1. Obtain the vibration response data of the rotor system under the initial unbalanced state to obtain the initial vibration response data.

[0057] For example, when the rotor system is initially unbalanced, the rotor is started to a predetermined operating speed. After the rotor runs smoothly, vibration signals in the horizontal and vertical directions are collected by vibration sensors (such as eddy current displacement sensors or acceleration sensors) installed at various measuring points (usually including multiple bearing seats or journals). The vibration signals are amplified and filtered by a signal conditioning circuit, then converted into digital signals by a data acquisition card, from which the vibration response amplitude of each measurement channel is extracted. Each measurement channel corresponds to one direction (horizontal or vertical) of one measuring point. The initial vibration response amplitudes of all measurement channels are recorded as initial vibration response data, which is used as the basis for subsequent calculation of the normalized objective function. Assume there are a total of... The measurement channel, the first The initial vibration response amplitude of each channel is denoted as: (in This data is not used in model training; it is only used as a reference benchmark in the optimization process.

[0058] S2. Based on the initial vibration response data, initialize the differential evolution algorithm population within the preset counterweight parameter range to obtain the initial population, and construct the corresponding test input features according to the counterweight parameters of each body in the initial population.

[0059] For example, the Differential Evolution (DE) algorithm is a population-based global optimization algorithm. Its core idea is to guide the search direction through the differences between individuals within the population. First, the search range of the decision variables needs to be determined; these decision variables are the weight parameters of each weight plane. Each weight plane contains two variables: weight mass (usually in grams) and weight phase (usually in degrees). Therefore, for a given weight plane... A rotor system with counterweight planes, the decision vector dimension is... Without any prior information, the initial population should be uniformly and randomly generated throughout the search space. Population size (denoted as...) The weighting factor is typically set to 5 to 10 times the dimension of the decision vector to ensure search diversity. Each individual corresponds to a set of weighting parameter vectors. ,in, This represents the individual's index within the population. After generating the initial population, an input feature vector needs to be constructed for each individual to be fed into the support vector regression prediction model. The construction method for the input features is exactly the same as during model training: the weight mass of each weight plane is used as the input feature vector. and counterweight phase Convert to real part in orthogonal coordinate system and the virtual part Then, the real part, imaginary part, and original mass components are concatenated into a feature set. For The weight plane has a total dimension of 3N for the input features. The input feature vector obtained by calculating the weight parameters of each individual is denoted as . The output of this step is the set of weight parameter vectors for all individuals in the initial population. and its corresponding set of input feature vectors The superscript (0) indicates the 0th generation (initial generation).

[0060] S3. Input the test input features into the support vector regression prediction model to obtain the predicted residual vibration response data.

[0061] For example, the support vector regression model is a nonlinear regression method based on the principle of minimizing structural risk. After the preliminary steps (S11 to S24), the model has been trained and has learned a high-dimensional nonlinear mapping from the input feature vector (orthogonal representation and amplitude concatenation of the counterweight parameters) to the output feature vector (orthogonal components of the vibration response at multiple measurement points). The test input feature vector obtained in S2... The input features are fed into the support vector regression prediction model, which performs forward computation: first, the input features are mapped to a high-dimensional feature space using a kernel function; then, linear regression is performed in this space using support vectors; finally, the regression result in the high-dimensional space is converted into a vector in the output space through inverse mapping. The model's output directly corresponds to the orthogonal component form of the vibration response of each measurement channel, but this invention requires the vibration response amplitude. Therefore, for each measurement channel k, the composite amplitude needs to be calculated from the orthogonal components (horizontal and vertical components) of the model output. The calculation formula is as follows:

[0062]

[0063] in, Indicates the first The predicted vibration corresponding to each individual is measured in the channel. Orthogonal components in the horizontal direction, This represents the orthogonal component in the vertical direction. The predicted amplitudes from all M channels are combined to form a predicted residual vibration response data vector. This vector reflects the level of residual vibration that the rotor system is expected to produce under a given counterweight scheme.

[0064] S4. The normalized loss function value is calculated based on the predicted residual vibration response data and the initial vibration response data.

[0065] For example, the loss function can be used to evaluate the merits of a candidate weighting scheme. This invention employs a normalized form of the relative residual sum of squares to eliminate the influence of differences in vibration amplitude magnitudes between different measuring points. Specifically, for the th... Individuals (corresponding to the counterweight parameter vector) First, the predicted residual vibration amplitude of each measurement channel is obtained from S3. (k = 1, ..., M), obtain the initial vibration amplitude from S1 Then calculate the normalized loss function value using the following formula:

[0066]

[0067] In the formula, The total number of measurement channels is equal to the number of measurement points multiplied by 2 (each measurement point has both horizontal and vertical directions). Ratio It can be used to reflect the first The degree to which residual vibrations on a channel are reduced or amplified relative to the initial vibrations. The squaring operation amplifies the effect of larger ratios, thus guiding the optimization algorithm to prioritize suppressing the channels with the most prominent vibrations. Summing the square ratios of all channels yields a scalar. The smaller this value, the better the counterweight scheme. The better the vibration reduction effect. When When this occurs, it means that, on average, the vibration of each channel has decreased; when In theory, all channel vibrations are completely eliminated (which is difficult to achieve in practice). This loss function value is directly used as the basis for fitness evaluation in the subsequent differential evolution algorithm.

[0068] S5. The fitness of the population is evaluated based on the normalized loss function value, and the mutation, crossover and selection operations of the differential evolution algorithm are performed on the population to generate a new generation of population. The test input features are updated according to the weight parameters corresponding to each individual in the new generation of population.

[0069] For example, the fitness of the population is evaluated based on the normalized loss function value, and the mutation, crossover and selection operations of the differential evolution algorithm are performed on the population to generate a new generation of population. The test input features are updated according to the weight parameters corresponding to each individual in the new generation of population.

[0070] S6. Repeat S3 to S5 until the preset maximum number of iterations is met or the absolute value of the difference between the normalized loss function value and the previous generation normalized loss function value is less than the preset convergence tolerance. Output the weight parameters corresponding to the minimum value of the normalized loss function value to obtain the globally optimal weight scheme.

[0071] For example, S3 through S5 are repeated, with each iteration producing a new generation of the population. The iterative process stops when any of the following termination conditions are met:

[0072] Condition 1 (Maximum number of iterations): Current iteration number (Starting from 0) Reaching a pre-set threshold This threshold can be set according to the complexity of the problem and computational resources, and is typically between 50 and 500 generations.

[0073] Condition 2 (Convergence Tolerance): The absolute value of the change in the normalized loss function value of the best individual between two consecutive generations is less than the preset convergence tolerance. Let the first... The optimal loss value is The stopping condition is:

[0074]

[0075] in, It is a small positive number, which can be taken as... to This indicates that the optimization process has entered a plateau, and further iterations are unlikely to bring significant improvements.

[0076] After the iteration stops, select the individual with the smallest loss function value from the last generation of the population, denoted as . The counterweight parameters corresponding to this individual component represent the globally optimal counterweight scheme. This counterweight scheme is then applied to the rotor system under actual load, and the vibration response is measured again to verify the optimization effect. The final output is the globally optimal counterweight scheme. It can be represented as:

[0077]

[0078] in, and They represent the first The weight mass and phase to be added to each counterweight plane.

[0079] In the aforementioned rotor imbalance mass optimization identification method based on SVR and differential evolution algorithm, the initial unbalanced vibration response data of the rotor is first obtained, and a differential evolution population is initialized within the preset counterweight parameter range. Then, the counterweight parameters corresponding to each individual in the population are converted into test input features consisting of orthogonal components and amplitude concatenation, which are input into a pre-trained support vector regression prediction model to quickly obtain predicted values ​​of residual vibration response at multiple measurement points. A normalized loss function is constructed based on the predicted values ​​and initial values, and then the mutation, crossover, and selection mechanisms of the differential evolution algorithm are used to iteratively optimize the population, minimizing the loss function and ultimately outputting the globally optimal counterweight scheme. This method significantly improves the modeling accuracy of the mapping relationship between multi-plane counterweight parameters and multi-point nonlinear vibration response, effectively reduces the residual vibration level of the rotor system, achieves globally efficient optimization of dynamic balancing counterweight schemes for complex rotor systems, reduces optimization bias caused by linear assumptions in traditional methods, and enhances the stability and engineering applicability of the optimization results.

[0080] To further illustrate the solutions of the embodiments of this application, the following description uses a specific example applied to the above-mentioned rotor imbalance quality optimization identification method based on SVR and differential evolution algorithm, as follows: Figure 2 As shown, this embodiment provides a rotor dynamic balancing optimization method based on support vector regression and differential evolution algorithm, which is applied to applications such as... Figure 3 The rotor dynamic balancing optimization system based on Support Vector Regression and Differential Evolution (DE) algorithm is shown. This system comprises four modules: Module 1: Data preprocessing; Module 2: SVR forward surrogate model training; Module 3: DE algorithm closed-loop optimization; and Module 4: Optimal solution output. The method includes the following steps:

[0081] Step S100: Acquisition of Nonlinear Experimental Data: Multi-condition dynamic balancing experiments are conducted on a rotor experimental platform to obtain nonlinear vibration response data for training the support vector regression model. Specifically, a rotor test system containing multiple counterweight planes is constructed, multiple vibration measuring points are arranged on the rotor shaft system, and vibration sensors are installed in the horizontal and vertical directions of each measuring point to collect vibration response signals during rotor operation.

[0082] During the experiment, multiple sets of unbalanced excitation conditions were created by changing the mass and phase of the counterweights on each counterweight plane. Under each condition, the rotor system was driven to a stable operating state, and steady-state vibration response data in the horizontal and vertical directions were collected at each measuring point, along with the corresponding counterweight parameter information. This experimental process was repeated to obtain multiple sets of experimental samples covering different counterweight combinations, thus constructing an experimental dataset containing the nonlinear relationship between counterweight parameters and the vibration response at multiple measuring points.

[0083] The experimental dataset includes: counterweight mass data for multiple counterweight planes; counterweight phase data for multiple counterweight planes; vibration response data for multiple measuring points in the horizontal and vertical directions; and steady-state vibration amplitude information corresponding to each working condition. Vibration data were collected after the rotor system reached steady-state operation under each working condition to reduce the impact of transient processes on model training results and improve data quality and model stability.

[0084] S200: Data Preprocessing: First, obtain simulation datasets of the rotor system under different counterweight conditions. These datasets include counterweight parameter data and vibration response data. Clean the original simulation data, removing outliers or missing values ​​to improve the reliability of subsequent model training. Then, perform feature space fusion processing on the cleaned data, unifying the counterweight mass, phase, and corresponding vibration response information. To eliminate the influence between different feature dimensions, the fused input data can be standardized using the StandardScaler method, ensuring that each feature follows a distribution with a mean of 0 and a standard deviation of 1, thereby improving the stability and convergence speed of the support vector regression model training process.

[0085] S300: Input / Output Feature Construction: At each prediction step, feature transformation processing is performed on the counterweight mass and phase parameters of the four counterweight planes. Specifically, the counterweight mass and phase of each counterweight plane are converted into real and imaginary parts in orthogonal directions, and concatenated with the amplitude of the corresponding counterweight to form the input features. Each counterweight plane generates three feature components: real part, imaginary part, and amplitude; the four counterweight planes together form a 12-dimensional input feature vector X. Simultaneously, orthogonal component transformation processing is performed on the vibration responses of the four measuring points in the horizontal and vertical directions. Specifically, this includes horizontal and vertical vibration responses, with each measuring point generating vibration data in two directions, which are further converted into orthogonal component representations. The four measuring points together form a 16-dimensional output feature vector Y, thus establishing a multivariate mapping relationship between the input and output features.

[0086] S400: Support Vector Regression Model Training: Based on the input feature vector X and output feature vector Y constructed above, a support vector regression prediction model is established. In this embodiment, the support vector regression model uses a radial basis function (RBF) to enhance the model's ability to express complex nonlinear relationships. The main parameters of the support vector regression model include: penalty factor. Kernel function parameters and insensitive loss parameters Among them: penalty factor Kernel function parameters are used to control the trade-off between model complexity and training error. This is used to control the distribution range of the radial basis functions. To obtain the optimal combination of model parameters, a 10-fold cross-validation method is used to optimize the model parameters. Specifically, the training data is divided into 10 subsets, with 9 subsets used for training and 1 subset used for validation. This process is repeated 10 times, and the average validation error is calculated as the evaluation index to determine the optimal parameter combination. After parameter optimization, a trained multi-output support vector regression prediction model is obtained. This model is used to achieve a high-precision nonlinear mapping between counterweight parameters and vibration responses at multiple measurement points.

[0087] S500: Differential Evolutionary Algorithm Initialization: After training the Support Vector Regression model, a differential evolutionary algorithm is introduced to globally optimize the counterweight parameters. First, vibration response data of the rotor system under initial unbalanced conditions is extracted and used as a reference benchmark for the optimization process. The differential evolutionary algorithm population is initialized within the preset counterweight parameter range. Specifically, this includes randomly generating several sets of counterweight parameters within the allowable mass and phase range of each counterweight plane to form the initial population. Each individual in the population represents a set of candidate counterweight parameter schemes. Subsequently, based on the counterweight parameters corresponding to the individuals in the population, the corresponding test input features are constructed.

[0088] S600: Predicting Residual Vibrations and Calculating the Objective Function: The test input features corresponding to each individual in the population are input into the trained support vector regression prediction model to obtain the corresponding predicted vibration response. A normalized objective function is constructed based on the prediction results to measure the residual vibration level. The objective function is defined as follows: ,in, This is the normalized objective function value; To the first under the condition of counterweight parameters Predicted vibration amplitude for each measurement channel; For the initial state, the first Vibration amplitude of each measurement channel; This indicates the measurement channel number. By calculating the objective function value, the advantages and disadvantages of different weighting schemes can be evaluated.

[0089] S700: Differential Evolutionary Algorithm Iterative Optimization: The fitness of the population is evaluated based on the objective function value, and mutation, crossover, and selection operations of the differential evolutionary algorithm are performed. Specifically, this includes: First, a mutation operation is performed on each individual in the population to generate a mutation vector; then, a crossover operation is performed between the mutation vector and the original individual to generate experimental individuals; finally, a selection operation is performed based on the objective function value, retaining individuals with better fitness to enter the next generation of the population. The above process is repeated until a termination condition is met. The termination condition includes: reaching a preset maximum number of iterations or the change in the objective function being less than a preset convergence threshold.

[0090] S800: Output the optimal weighting scheme: After the differential evolution algorithm iterations are completed, the individual with the smallest objective function value is selected from the final population as the optimal solution. The weighting parameters corresponding to this optimal solution are: the global optimal weighting scheme. Subsequently, this optimal weighting scheme is input into the support vector regression prediction model for verification to confirm whether the residual vibration meets the preset requirements. If the requirements are met, the final optimization result is output.

[0091] To verify the effectiveness of the method of this invention, the constructed support vector regression model and differential evolution algorithm were used to perform dynamic balance optimization on the rotor system, and a comparative analysis was conducted with the traditional least squares method. First, the traditional least squares method was used to perform dynamic balance calculations on the system, and the corresponding counterweight parameter scheme was obtained. The calculation results are shown in Table 1 below:

[0092] Table 1: Example Table of System Output Counterweight Schemes

[0093]

[0094] Meanwhile, the vibration amplitude changes of each measurement channel under the least squares method were calculated, and the vibration reduction effect is shown in Table 2 below:

[0095] Table 2: Examples of Expected Vibration Reduction Effects for Each Channel

[0096]

[0097] The comparison of vibration amplitudes at each measuring point before and after balancing using the least squares method is as follows: Figure 4 As shown.

[0098] Subsequently, the vibration response was predicted based on the support vector regression model constructed according to this invention. The comparison between the prediction results and the actual vibration response is as follows: Figure 5 As shown. From Figure 5 It can be seen that the support vector regression model can fit the actual vibration response data well, and the prediction results have a high consistency with the actual data, indicating that the model has good nonlinear mapping ability.

[0099] Furthermore, based on the support vector regression model, a differential evolution algorithm is introduced for global optimization to obtain the recommended weighting scheme. The calculation results are shown in Table 3 below:

[0100] Table 3: Example of Recommended Counterweight Schemes Output by the System

[0101]

[0102] The vibration reduction effects of each measurement channel are shown in Table 4 below:

[0103] Table 4: Example of Recommended Counterweight Schemes Output by the System

[0104]

[0105] Finally, the results of comparing the vibration amplitude before and after dynamic balancing using a hybrid model of support vector regression and differential evolution algorithm are as follows: Figure 6 As shown. From Figure 6 It can be seen that after adopting this method, the vibration amplitude at each measuring point is significantly reduced, and it has a better vibration reduction effect than the traditional least squares method, which verifies the effectiveness and superiority of this method.

[0106] In an optional embodiment, the support vector regression prediction model is constructed through the following steps:

[0107] S11. Obtain the original experimental data of multiple sets of dynamic balancing experiments conducted on the rotor experimental platform through multiple counterweight planes and multiple measuring points; wherein, the original experimental data includes the counterweight mass, counterweight phase and vibration response amplitude of each measuring point in the horizontal and vertical directions of each counterweight plane.

[0108] Optionally, to construct a training dataset that reflects the nonlinear characteristics of the rotor system, a systematic dynamic balancing experiment needs to be conducted on a rotor experimental platform. The rotor experimental platform typically includes a rotor shaft, multiple counterweight plates (i.e., counterweight planes), bearing housings, a drive motor, and vibration sensors. Specifically, the rotor system is first installed on the experimental platform, ensuring it can operate stably to the predetermined operating speed. Adjustable counterweights are pre-installed on each counterweight plane; the mass and installation angle (phase) of the counterweights can be precisely controlled. For each experimental condition, a set of counterweight parameters is first set: that is, a mass of [missing value] is added to the first counterweight plane. Phase is The trial weight was performed by adding a mass of [mass value] to the second counterweight plane. Phase is The trial is repeated, and so on until the [number]th trial. A counterweight plane is used. The rotor is then started to the target speed and allowed to run smoothly (usually for several seconds to tens of seconds to eliminate transient effects). Vibration signals are then synchronously acquired using vibration sensors placed at various measuring points. Two sensors are installed at each measuring point to measure the horizontal and vertical vibration displacement or velocity, respectively. The acquired analog signals are filtered and amplified using anti-aliasing filtering, then converted into digital signals by a high-precision data acquisition card. The amplitude of the fundamental frequency component (i.e., the vibration component with the same frequency as the rotor speed) is extracted. The vibration response amplitude at each measuring point and in each direction under this condition is recorded. The experiment is repeated by changing the counterweight mass and phase combination of the counterweight plane to obtain multiple sets of different counterweight parameters and corresponding vibration response data. The raw experimental data for all conditions constitute a multivariate dataset, where the input is the mass and phase of each counterweight plane, and the output is the vibration response amplitude at each measuring point in the horizontal and vertical directions.

[0109] S12. Perform orthogonal component transformation on the counterweight mass and counterweight phase of each counterweight plane to obtain the real part data and imaginary part data of each counterweight plane.

[0110] In the original counterweight parameter space, the counterweight mass and counterweight phase These are two parameters with different physical meanings and dimensions. Phase The vibration exhibits periodicity (from 0° to 360°), and directly using angle values ​​as input features makes it difficult for the model to handle its cyclic boundary characteristics (e.g., 0° and 360° differ by 360 degrees numerically, but are physically equivalent). Simultaneously, there is a natural vector superposition relationship between the vibration response and the counterweight vector: a vector superposition of magnitude... , direction is The counterweight vector can be decomposed into a horizontal component (real part) and a vertical component (imaginary part) in an orthogonal coordinate system. Therefore, converting the counterweight mass and phase into orthogonal components not only eliminates the phase cyclicity problem but also matches the input characteristics with the vector characteristics of the vibration response. The specific conversion formula is as follows: For the Each counterweight plane In fact, data and imaginary part data They are respectively:

[0111]

[0112]

[0113] in, This indicates the mass of the counterweight added to the counterweight plane (usually in grams). This indicates the counterweight installation angle (the unit is either radians or degrees, but it should be converted to radians when calculating trigonometric functions). and Units and To maintain consistency, phase information is encoded into the relative magnitudes of the two components. After the transformation, each counterweight plane is uniquely characterized by two numerical features (real and imaginary parts) that are numerically continuous without periodic jumps. The transformation is reversible: given the real and imaginary parts, the counterweight mass can be determined by... Recovery, the counterweight phase can be achieved through Recovery. The real and imaginary data obtained after transformation will be used as components of the subsequent input feature vector.

[0114] S13. The real part data, imaginary part data and the corresponding counterweight mass of the counterweight plane in the original experimental data are spliced ​​together to obtain the input feature vector data.

[0115] Optionally, the transformed real and imaginary part data can be fused with the original weight mass data at the feature layer to generate a complete input feature vector. The reason for retaining the original weight mass is that although the real and imaginary parts implicitly contain mass information (magnitude), the model may find it difficult to directly extract the magnitude relationship of the mass from the real and imaginary parts independently. Treating mass as a separate feature dimension can provide the model with more direct information.

[0116] The specific assembly method is as follows: For each experimental sample, arrange the three components (real part, imaginary part, and mass) of each plane sequentially according to the order of the counterweight planes. Let there be a total of... If there are multiple counterweight planes, then the input feature vector... It is A dimensional row or column vector can have the following structure: ,in, This indicates transpose. The order of the components must remain fixed throughout the modeling process and cannot be arbitrarily changed. This feature vector contains both the direction information of the counterweight vector (through its real and imaginary parts) and its magnitude information (through its mass), enabling the support vector regression model to fully learn the nonlinear vector mapping relationship between the counterweight parameters and the vibration response. During model training and usage, each input sample must undergo the same feature construction process. The dimension of this feature vector is proportional to the number of counterweight planes; for common dual-plane or multi-plane rotor systems, the input dimension is typically between 6 and 12 dimensions.

[0117] S14. Perform orthogonal component transformation on the vibration response amplitudes of each measuring point in the horizontal and vertical directions to obtain the output feature vector data.

[0118] Each measuring point in the rotor system typically acquires data in the horizontal direction (denoted as ). Direction) and perpendicular direction (denoted as The vibration response signals are located in two orthogonal directions. The amplitudes of the vibration response in these two directions are themselves orthogonal components of the rotor vibration vector, therefore no additional trigonometric function transformation is required as with the counterweight parameters. However, to maintain consistency with the model output format, the responses in both directions at each measurement point need to be processed as independent output components. Let there be a total of... One measuring point ( Each measuring point provides the horizontal vibration amplitude. and vertical vibration amplitude The total number of measurement channels Output feature vector It is A dimensional vector can be constructed as follows: ,in, This represents the measurement point number. Each component is the vibration amplitude, with the same physical units and dimensions. This orthogonal component representation preserves the vector characteristics of the vibration response, allowing the support vector regression model to predict the response components in each direction separately, which can then be used for subsequent calculation of the synthesized amplitude. It is important to note that the vibration amplitude usually refers to the amplitude of the fundamental frequency component of the rotor under steady-state operation, not the total vibration value. To obtain the fundamental frequency amplitude, the original vibration signal needs to undergo Fast Fourier Transform or tracking filtering. The output feature vector data of this step corresponds one-to-one with the input feature vector data obtained in S13, together forming training sample pairs. ,in, This is the sample number.

[0119] S15. Establish a nonlinear mapping relationship between the input feature vector and the output feature vector data to obtain the support vector regression prediction model; wherein, the support vector regression prediction model includes the penalty factor parameter, the kernel function parameter, and the insensitive loss parameter.

[0120] Optionally, this step aims to construct a system capable of processing the input feature vector. Nonlinear mapping to output feature vector The predictive model can be achieved using Support Vector Regression (SVR). Its basic principle is to construct a linear regression function in a high-dimensional feature space, while implicitly mapping the original input to a high-dimensional space through a kernel function to handle nonlinear relationships. The core objective of the SVR model is to minimize the following optimization problem:

[0121]

[0122] in, For weight vectors in high-dimensional space, For bias terms, The total number of training samples, This is the sample number. and Let be slack variables, representing the th , respectively The extent to which the prediction error of a sample exceeds the upper and lower bounds of the insensitive interval. The penalty factor parameter can be used to control model complexity (i.e., Trade-offs between training error and training error: The larger the value, the heavier the penalty for training error in the model, which may lead to overfitting; The smaller the value, the simpler the model, but the more likely it is to underfit. Kernel function parameters To define the shape of the kernel function, a radial basis function (RBF) can be used, and its expression is as follows:

[0123]

[0124] in, and Given two input feature vectors, The distance is Euclidean. Controlling the width of the kernel function: The larger the value, the stronger the locality of the kernel function and the more complex the model decision boundary; The smaller the value, the wider the influence of the kernel function, and the smoother the model. Insensitive loss parameter. The width of the insensitive pipe is defined as: when the absolute error between the predicted and actual values ​​is less than... When this is not considered in the loss function, the sparsity and robustness of the model are enhanced. The above three parameters... The value of has a decisive impact on model performance and needs to be optimized through subsequent training steps. The support vector regression model established in this step is a multi-output model, meaning it can simultaneously predict... Each output component shares the same high-dimensional feature space but has an independent weight vector and bias term.

[0125] In an optional embodiment, the support vector regression prediction model is trained through the following steps:

[0126] S21. Combine the input feature vector data and the output feature vector data to obtain the counterweight vibration mapping sample set data. Divide the counterweight vibration mapping sample set data into a validation set and a training set to obtain multiple sets of training and validation partition data.

[0127] Optionally, to objectively evaluate the generalization ability of support vector regression models under different parameter combinations, the K-fold cross-validation method can be used. First, all the results obtained in S13 and S14 are... Each input-output sample pair is combined to form a complete sample set. Then, the sample set is randomly divided into... A subset of sizes that are as equal as possible ( Usually taken as 10), denoted as Each subset contains approximately There are 10 samples. When partitioning, the diversity of sample distribution in each subset should be ensured; random sampling or stratified sampling strategies can be used. Next, for each fold... , will the Subset As a validation set, the rest The union of these subsets is used as the training set to form a training and validation partition, resulting in a total of [number] partitions. The dataset is divided into multiple partitions, each containing a training set and a disjoint validation set. The validation set is used to evaluate the model's predictive performance on unseen data, while the training set is used to fit the model parameters. Multiple partitions make the model performance evaluation more robust, avoiding the random bias introduced by a single partition. In subsequent steps, each set of candidate parameter combinations needs to be evaluated across all partitions. Training and validation are performed separately for each group, and the average validation error is calculated.

[0128] S22. Based on the training and validation partition data, train the support vector regression prediction model using the training set, and calculate the prediction error using the validation set to obtain the validation error data for each partition.

[0129] Optionally, for a given set of parameter combinations and a certain set of training and validation partitions (let the first set be the first set of partitions). Group division, training set is The validation set is Specifically, firstly, using the training set Input feature vector and the corresponding output target vector Training a support vector regression model. The training process is essentially solving the dual form of the optimization problem described in S15. This can be achieved using algorithms such as Sequential Minimal Optimization (SMO) to obtain the set of support vectors and their corresponding Lagrange multipliers. After training, the model establishes a mapping function from input to output. Then, the validation set Each input feature vector The input is fed into the trained model to obtain the predicted output vector. For each sample in the validation set, calculate its prediction error. Since the output is a multi-channel vector, the commonly used error metric is the mean squared error (MSE), which can be calculated using the following formula:

[0130]

[0131] in, To determine the number of samples in the validation set, To determine the dimension of the output feature vector, For the first The verification sample is at the ... Predicted values ​​for each output component This corresponds to the true value. This error value... It can be used to reflect the prediction accuracy of the model under the current parameter combination and the current partition. The above training and validation processes were performed on the groups respectively, resulting in... One verification error data .

[0132] S23. Average the validation error data from multiple partitions to obtain the average cross-validation error data.

[0133] Optionally, upon obtaining After validating the error data under the group division, The validation error data under each group partition are averaged to obtain the average cross-validation error for that parameter combination. This averaging operation comprehensively evaluates the model's performance on different data subsets and reduces the impact of a specific partitioning method on the evaluation results. The average cross-validation error is... The expression can be:

[0134]

[0135] in, For folds, For the first Verification error under group partitioning. It is a scalar value that can be used to reflect the current combination of parameters. The overall generalization performance of the support vector regression model. The smaller the value, the smaller the prediction error of the model on validation data that was not used in the training process, meaning the stronger the model's generalization ability. Conversely, a larger value indicates a lower prediction error. This indicates that the model may be overfitting or underfitting on the training set. By comparing the average cross-validation error of different parameter combinations, the optimal parameter combination can be selected. It should be noted that when calculating the average error, the standard deviation can also be calculated to assess the dispersion of each cross-validation error, but this invention only uses the average value as the basis for parameter selection.

[0136] S24. Iterate through multiple different combinations of penalty factor parameters, kernel function parameters, and insensitive loss parameters. Repeat S22 to S23 for each combination of parameter values. Select the combination of parameter values ​​with the smallest average cross-validation error as the final parameters of the support vector regression prediction model, and obtain the trained support vector regression prediction model.

[0137] Optionally, S23 obtains a specific set of parameter combinations. Corresponding average cross-validation error Afterwards, the punishment factor Kernel function parameters and insensitive loss parameters The optimal value is usually unknown and needs to be optimized by traversing a predefined parameter search space. Specifically, the search ranges for the three parameters are first defined: Usually in Values ​​are taken on a logarithmic scale within the range; Usually in Values ​​are taken on a logarithmic scale within the range; Usually in The parameter is selected from a range of values. Then, multiple different combinations of parameter values ​​are generated using either a grid search or a random search method, denoted as... ,in, This is the combination number. For each parameter combination, repeat steps S22 and S23 to obtain the corresponding average cross-validation error. After iterating through all preset parameter combinations, a parameter-error mapping table is generated. The parameter combination that minimizes the average cross-validation error is selected as the optimal parameter, i.e.:

[0138]

[0139] Finally, the entire sample set (not just the training set) and the optimal parameter combination are used. The support vector regression model is retrained to obtain the final trained support vector regression prediction model, which can then be used to predict residual vibration response data in S3. The entire training process ensures that the model has optimal generalization performance and avoids overfitting to the training data.

[0140] In an optional embodiment, the expression for the normalized loss function value is:

[0141]

[0142] in, For the combination of counterweight parameters The normalized loss function value, For the combination of counterweight parameters, The initial vibration response amplitude, Indicates the combination of counterweight parameters Under the conditions The predicted vibration response amplitude of each measuring point channel. This indicates the total number of measuring point channels. It equals the number of measuring points multiplied by 2. This indicates the sequence number of the measuring point channel.

[0143] In an optional embodiment, S5 includes:

[0144] S51. Based on the normalized loss function value, the fitness of each individual in the population is evaluated to obtain the fitness value data of each individual.

[0145] Optionally, the fitness values ​​and the normalized loss function values ​​exhibit a monotonically decreasing relationship; that is, the smaller the loss function value, the larger the fitness value. A simple and feasible mapping method is to take the reciprocal or a negative number. Since selection operations typically favor individuals with higher fitness, the fitness value can be defined as the negative of the loss function value, or a ranking method can be used to assign fitness. For example, all individuals in the current population are sorted in ascending order of their loss function values, and then assigned linearly decreasing fitness scores. The output of this step is the fitness value for each individual. , ,in, Population size.

[0146] S52. Based on the fitness values ​​of each individual, select the target individual and multiple parent individuals for mutation from the population, perform the mutation operation of the differential evolution algorithm, and obtain the mutation vector data.

[0147] Optionally, mutation is the primary method by which differential evolution algorithms generate new candidate solutions. For the current... Each target individual in the population ( (For individual indexing), randomly select three distinct individuals. , , ,in , , Dissimilar and neither equal to Then generate the mutation vector. , The calculation formula can be:

[0148]

[0149] In the formula, This is the scaling factor for variation (typically taking values ​​within the interval [0.4, 1]), used to control the difference vector. The magnification factor. Each component (weight mass or phase) in the mutation vector may exceed the preset search range, in which case it is necessary to pull it back into the effective range through boundary absorption or reflection.

[0150] S53. Perform cross-operation on the mutation vector data and the original weight parameter vector corresponding to the target individual to obtain the experimental vector data.

[0151] Optionally, the crossover operation mixes the target individual with the mutation vector to increase population diversity. For the first... The first individual Decision variables Generate a random number that is uniformly distributed in the interval [0,1]. ,if ( The crossover probability is typically taken as 0.8 to 0.9, or... Equal to a randomly selected dimension Then the test vector The Each component is taken from the mutation vector. The One component; otherwise, it is taken from the target individual. The Each component. This operation ensures that at least one dimension of the experimental vector comes from the mutation vector, thus ensuring that the new individual is different from the original individual.

[0152] S54. Based on fitness value data, perform selection operations on the experimental vector data and the original weight parameter vector corresponding to the target individual to obtain a new generation population.

[0153] Optionally, the selection rule is as follows: if the normalized loss function value corresponding to the experimental vector is less than the normalized loss function value corresponding to the target individual, then the experimental vector is included in the next generation of the population; otherwise, the original weight parameter vector corresponding to the target individual is retained as an individual in the next generation of the population. For example, the selection operation is used to determine whether the experimental vector can enter the next generation of the population. The experimental vector is calculated. Corresponding loss function value (Obtained by re-executing S3 and S4), and with the target individual loss function value The comparison is performed. If the loss function value of the trial vector is smaller, the trial vector replaces the target individual as a member of the next generation population; otherwise, the target individual is retained. This selection rule can be expressed as:

[0154]

[0155] After examining all After performing the above mutation, crossover, and selection operations on each individual, the first individual is generated. Generation population .

[0156] S55. Update the test input features based on the weight parameters of each individual in the new generation population;

[0157] Optionally, based on the weight parameter vectors of each individual in the new generation population, the corresponding test input feature vectors are constructed in the same manner as in S2. This provides input data for S3 in the next iteration.

[0158] In an optional embodiment, the counterweight parameter range includes a counterweight mass search range and a counterweight phase search range, wherein the counterweight mass search range is 0 grams to 5 grams and the counterweight phase search range is 0 degrees to 360 degrees.

[0159] In an optional embodiment, the preset maximum number of iterations is a pre-set iteration number threshold, and the preset convergence tolerance is a pre-set threshold for the change in the normalized loss function value; the iteration is terminated when the number of iterations reaches the iteration number threshold, or when the absolute value of the difference between the normalized loss function values ​​of two consecutive iterations is less than the change threshold.

[0160] In the aforementioned rotor imbalance mass optimization identification method based on SVR and differential evolution algorithm, a nonlinear surrogate model based on support vector regression is constructed to convert the counterweight mass and phase of multiple counterweight planes of the rotor system into orthogonal real and imaginary parts and concatenate them with the amplitude to form input features. At the same time, the vibration response of each measuring point in the horizontal and vertical directions is converted into orthogonal components as output features, thereby accurately learning the nonlinear mapping relationship between counterweight parameters and vibration response of multiple measuring points. On this basis, vibration response data of the rotor in the initial imbalance state are extracted, a differential evolution population is initialized within the preset counterweight parameter range, and test input features are constructed according to individual counterweight parameters. The trained support vector regression model is used to quickly predict the residual vibration response, and then the normalized objective function value is calculated to comprehensively evaluate the vibration reduction effect of each counterweight scheme. Subsequently, the population is iteratively optimized through fitness evaluation, mutation, crossover and selection operations of differential evolution, the test input features are updated generation by generation and re-predicted and evaluated, until the termination condition is met and the globally optimal counterweight scheme is output. This method can accurately capture the nonlinear coupling characteristics of complex rotor systems, significantly improve the optimization accuracy and efficiency of multi-plane counterweight parameters, effectively reduce the residual vibration amplitude at each measuring point, and achieve synergistic suppression of multi-channel vibration. It can overcome the shortcomings of insufficient prediction accuracy and unstable optimization results of traditional linear methods, and provide a reliable technical means for high-precision dynamic balancing of complex rotor systems.

[0161] It should be understood that although the steps in the flowcharts of the embodiments described above are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowcharts of the embodiments described above may include multiple steps or multiple stages. These steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the steps or stages of other steps.

[0162] Based on the same inventive concept, this application also provides a rotor imbalance quality optimization identification system based on SVR and differential evolution algorithm for implementing the rotor imbalance quality optimization identification method based on SVR and differential evolution algorithm described above. The solution provided by this system is similar to the implementation scheme described in the above method. Therefore, the specific limitations of one or more embodiments of the rotor imbalance quality optimization identification system based on SVR and differential evolution algorithm provided below can be found in the limitations of the rotor imbalance quality optimization identification method based on SVR and differential evolution algorithm described above, and will not be repeated here.

[0163] In one exemplary embodiment, such as Figure 7 As shown, a schematic diagram of a rotor imbalance quality optimization identification system 10 based on SVR and differential evolution algorithm is provided, including:

[0164] Data acquisition module 11 is used to acquire vibration response data of the rotor system under initial unbalanced state, and obtain initial vibration response data;

[0165] The initial population and test input feature construction module 12 is used to initialize the differential evolution algorithm population within the preset counterweight parameter range based on the initial vibration response data, obtain the initial population, and construct the corresponding test input features according to the counterweight parameters of each body in the initial population.

[0166] The residual vibration response prediction module 13 is used to input the test input features into the support vector regression prediction model to obtain the predicted residual vibration response data;

[0167] The loss function calculation module 14 is used to calculate the normalized loss function value based on the predicted residual vibration response data and the initial vibration response data.

[0168] The test input feature update module 15 is used to evaluate the fitness of the population based on the normalized loss function value, perform mutation, crossover and selection operations of differential evolution algorithm on the population to generate a new generation population, and update the test input features according to the weight parameters corresponding to each individual in the new generation population.

[0169] The iterative optimization and counterweight scheme output module 16 is used to re-trigger the residual vibration response prediction module, loss function calculation module and test input feature update module until the preset maximum number of iterations is met or the absolute value of the difference between the normalized loss function value and the previous generation normalized loss function value is less than the preset convergence tolerance. The counterweight parameters corresponding to the minimum value of the normalized loss function are output to obtain the globally optimal counterweight scheme.

[0170] In one embodiment, a computer device is provided, including a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the steps of the rotor imbalance quality optimization identification method based on SVR and differential evolution algorithm as described above.

[0171] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the steps in the above method embodiments.

[0172] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to in the description of the method embodiments. The device embodiments described above are merely illustrative. The components described as separate parts may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this disclosure according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0173] The above-described embodiments are merely illustrative of several implementation methods of the embodiments of this application, and their descriptions are relatively specific and detailed. However, they should not be construed as limiting the scope of the patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the embodiments of this application, and these modifications and improvements all fall within the protection scope of the embodiments of this application.

Claims

1. A method for identifying rotor imbalance quality optimization based on SVR and differential evolution algorithm, characterized in that, The method includes: S1. Obtain the vibration response data of the rotor system under the initial unbalanced state to obtain the initial vibration response data; S2. Based on the initial vibration response data, initialize the differential evolution algorithm population within the preset counterweight parameter range to obtain the initial population, and construct the corresponding test input features according to the counterweight parameters corresponding to each body in the initial population. S3. Input the test input features into the support vector regression prediction model to obtain the predicted residual vibration response data; S4. Calculate the normalized loss function value based on the predicted residual vibration response data and the initial vibration response data; S5. The fitness of the population is evaluated based on the normalized loss function value, and the mutation, crossover and selection operations of the differential evolution algorithm are performed on the population to generate a new generation population. The test input features are updated according to the weight parameters corresponding to each individual in the new generation population. S6. Repeat S3 to S5 until the preset maximum number of iterations is met or the absolute value of the difference between the normalized loss function value and the previous generation normalized loss function value is less than the preset convergence tolerance. Take the weight parameter corresponding to the minimum value of the normalized loss function value and output it to obtain the globally optimal weight scheme.

2. The method according to claim 1, characterized in that, The support vector regression prediction model is constructed through the following steps: S11. Obtain the original experimental data of multiple sets of dynamic balancing experiments conducted on a rotor experimental platform using multiple counterweight planes and multiple measuring points; wherein, the original experimental data includes the counterweight mass and phase of each counterweight plane and the vibration response amplitude of each measuring point in the horizontal and vertical directions. S12. Perform orthogonal component transformation on the counterweight mass and counterweight phase of each counterweight plane to obtain the real part data and imaginary part data of each counterweight plane; S13. The real part data, the imaginary part data, and the counterweight mass corresponding to the counterweight plane in the original experimental data are concatenated to obtain the input feature vector data; S14. Perform orthogonal component transformation on the vibration response amplitudes of each measuring point in the horizontal and vertical directions to obtain output feature vector data; S15. Establish a nonlinear mapping relationship between the input feature vector and the output feature vector data to obtain the support vector regression prediction model; wherein, the support vector regression prediction model includes a penalty factor parameter, a kernel function parameter, and an insensitive loss parameter.

3. The method according to claim 2, characterized in that, The support vector regression prediction model is trained through the following steps: S21. Combine the input feature vector data and the output feature vector data to obtain the counterweight vibration mapping sample set data, and divide the counterweight vibration mapping sample set data into a validation set and a training set to obtain multiple sets of training and validation partition data. S22. Based on the training and validation partition data, train the support vector regression prediction model using the training set, and calculate the prediction error using the validation set to obtain the validation error data for each partition. S23. Average the verification error data from the multiple groups of divisions to obtain the average cross-validation error data. S24. Iterate through multiple different combinations of the parameter values ​​of the penalty factor parameter, the kernel function parameter, and the insensitive loss parameter. Repeat S22 to S23 for each combination of parameter values. Select the combination of parameter values ​​with the smallest average cross-validation error as the final parameter of the support vector regression prediction model to obtain the trained support vector regression prediction model.

4. The method according to claim 1, characterized in that, The expression for the normalized loss function value is: in, For the combination of counterweight parameters The normalized loss function value, For the combination of counterweight parameters, The initial vibration response amplitude, Indicates the combination of counterweight parameters Under the conditions The predicted vibration response amplitude of each measuring point channel. This indicates the total number of measuring point channels. It equals the number of measuring points multiplied by 2. This indicates the sequence number of the measuring point channel.

5. The method according to claim 1, characterized in that, S5 includes: S51. Based on the normalized loss function value, the fitness of each individual in the population is evaluated to obtain fitness value data for each individual; wherein the fitness value data and the normalized loss function value have a monotonically decreasing relationship. S52. Based on the fitness value data of each individual, select the target individual and multiple parent individuals for mutation from the population, perform the mutation operation of the differential evolution algorithm, and obtain mutation vector data. S53. Perform a cross operation on the mutation vector data and the original weight parameter vector corresponding to the target individual to obtain experimental vector data; S54. Based on the fitness value data, a selection operation is performed on the experimental vector data and the original weight parameter vector corresponding to the target individual to obtain the new generation population. S55. Update the test input features according to the weight parameters corresponding to each individual in the new generation population; The selection operation follows these rules: if the normalized loss function value corresponding to the test vector is less than the normalized loss function value corresponding to the target individual, then the test vector is selected as an individual in the new generation population; otherwise, the original weight parameter vector corresponding to the target individual is retained as an individual in the new generation population.

6. The method according to claim 1, characterized in that, The counterweight parameter range includes a counterweight mass search range and a counterweight phase search range. The counterweight mass search range is 0 grams to 5 grams, and the counterweight phase search range is 0 degrees to 360 degrees.

7. The method according to claim 1, characterized in that, The preset maximum number of iterations is a pre-set iteration number threshold, and the preset convergence tolerance is a pre-set threshold for the change in the normalized loss function value. The iteration is terminated when the number of iterations reaches the iteration number threshold, or when the absolute value of the difference between the normalized loss function values ​​of two consecutive iterations is less than the change threshold.

8. A rotor imbalance quality optimization identification system based on SVR and differential evolution algorithm, characterized in that, The system includes: The data acquisition module is used to acquire the vibration response data of the rotor system under the initial unbalanced state, and obtain the initial vibration response data. The initial population and test input feature construction module is used to initialize the differential evolution algorithm population within the preset counterweight parameter range based on the initial vibration response data, obtain the initial population, and construct the corresponding test input features according to the counterweight parameters corresponding to each individual in the initial population. The residual vibration response prediction module is used to input the test input features into the support vector regression prediction model to obtain the predicted residual vibration response data; The loss function calculation module is used to calculate the normalized loss function value based on the predicted residual vibration response data and the initial vibration response data. The test input feature update module is used to evaluate the fitness of the population based on the normalized loss function value, perform mutation, crossover and selection operations of differential evolution algorithm on the population to generate a new generation population, and update the test input features according to the weight parameters corresponding to each individual in the new generation population. The iterative optimization and counterweight scheme output module is used to re-trigger the residual vibration response prediction module, loss function calculation module, and test input feature update module until the preset maximum number of iterations is met or the absolute value of the difference between the normalized loss function value and the previous generation normalized loss function value is less than the preset convergence tolerance. The counterweight parameter corresponding to the minimum value of the normalized loss function value is output to obtain the globally optimal counterweight scheme.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the method of any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the method of any one of claims 1 to 7.

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