Rotor coaxiality prediction method based on PSO-BP neural network
By combining particle swarm optimization algorithm with backpropagation neural network method, the problems of long detection cycle and low accuracy of traditional rotor coaxiality are solved, and high-precision coaxiality prediction at different speeds is realized, which is suitable for online control of rotor assembly.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-11-27
- Publication Date
- 2026-03-10
AI Technical Summary
Traditional methods for detecting rotor coaxiality are time-consuming, rely on manual operation, and are difficult to implement online assembly control. Existing neural networks are easily affected by initial values, leading to local optima, and are difficult to accurately predict coaxiality at different speeds.
A method combining particle swarm optimization (PSO) and backpropagation neural network (BP) is adopted. By acquiring multi-speed characteristics, data preprocessing and global optimization of PSO, a BP neural network model adapted to different speeds is constructed. The initial parameters are provided by PSO and combined with BP gradient descent training to achieve accurate prediction of rotor coaxiality.
It achieves high-precision prediction of rotor coaxiality at different speeds, improves prediction accuracy and stability, reduces the error of traditional methods, and is suitable for online control of rotor assembly.
Smart Images
Figure CN121638009A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to a rotor coaxiality prediction method based on PSO-BP neural network, belonging to the field of rotating machinery condition assessment and geometric error control technology. Background Technology
[0002] Coaxiality deviation can induce rotor imbalance forces, oil film oscillations, and premature bearing wear. Traditional detection methods rely on dial indicators, laser coaxial meters, or coordinate measuring machines, which suffer from long cycles, heavy operator dependence, and difficulty in feeding back feedback to online assembly control. The PSO-BP combined prediction algorithm can establish a mapping based on readily available quantities such as rotational speed, temperature, assembly clearance, dynamic imbalance, and vibration characteristics to predict rotor assembly coaxiality at different speeds. While BP networks have good nonlinear fitting capabilities, they are susceptible to local optima due to initial conditions; PSO, on the other hand, possesses global optimization capabilities, providing better initial values and structural hyperparameters for the network. The fusion of these two methods balances accuracy and stability.
[0003] Therefore, it is urgent to propose a rotor coaxiality prediction method based on PSO-BP neural network to solve the above-mentioned technical problems. Summary of the Invention
[0004] To address the aforementioned problems, a rotor coaxiality prediction method based on a PSO-BP neural network is provided. A brief overview of the invention is given below to provide a basic understanding of certain aspects of the invention. It should be understood that this overview is not an exhaustive summary of the invention. It is not intended to identify key or essential parts of the invention, nor is it intended to limit the scope of the invention.
[0005] The technical solution of this invention: A rotor coaxiality prediction method based on PSO-BP neural network includes the following steps: Step 1: Data preparation, including: multi-speed characteristic acquisition and data preprocessing; Step 2, Model Design, including: constructing the BP neural network structure and defining the training objective function; Step 3: Parameter optimization, including global optimization of PSO and refined training of BP gradient descent.
[0006] Preferred method: In step one, to address the direct impact of rotational speed changes on coaxiality error during rotor assembly, collect observable measurements covering the entire rotational speed range and construct a feature vector; All features were normalized using the formula, and the nonlinear correlation between rotational speed and coaxiality error was verified by using a joint screening method of mutual information and Pearson coefficient.
[0007] Preferred: In step one, the feature vector ; in, This refers to the rotor speed; Rotor temperature; This is for assembly clearance; This is the dynamic imbalance quantity; The root mean square of the vibration; For temperature difference; The formula is ; in, Standardized value, σ = the square root of the variance. average value.
[0008] Preferred: In step two, a feedforward neural network adapted to the nonlinear mapping of feature-coaxiality error under different rotation speeds is constructed, with the topology being input layer—hidden layer 1—hidden layer 2—output layer; To avoid overfitting the model on multi-speed samples, a mean squared error with L2 regularization is defined as the mean squared error.
[0009] Preferred: In step two, the topological network is expressed as:
[0010] In the formula, , , These are the weight matrices for input layer - hidden layer 1, hidden layer 1 - hidden layer 2, and hidden layer 2 - output layer, respectively. , , These are the bias vectors for the corresponding layers. , These are the output values of the two hidden layers, respectively; The training objective function is: ; In the formula, , The total number of samples, , The first The predicted and measured coaxiality error for each sample. This is the regularization parameter.
[0011] Preferred method: In step three, the PSO algorithm is introduced to globally optimize the network parameters, ensuring that the initial parameters are suitable for multi-rotation scenarios; each particle corresponds to a set of parameters. Update based on individual optimality and group optimality; The optimization process needs to incorporate training samples across the entire speed range to ensure... and Corresponding parameters It can cover low, medium, and high speed scenarios, avoiding the initial parameters being only adapted to a single speed range; then, the obtained optimal solution is used as the initial point of the BP stage, and a learning rate is adopted. Gradient descent performs refined updates An early stopping criterion and adaptive inertia weight decay are set to ensure stable convergence.
[0012] Preferred: In step three, the individual optimal and group optimal are updated as follows:
[0013] In the formula, , , , The first , The particle velocity and particle position of the step, For inertial weights, , As a learning factor, , A random number within the interval [0,1]. This represents the optimal position for the individual particle. It represents the global optimal position of the particle swarm.
[0014] Preferred options also include: Step 4, Model Validation.
[0015] Preferred method: In step four, the generalization error is estimated using K-fold cross-validation and used to guide... The choice of network size; in online applications, incremental fine-tuning of new batches of data with small steps to ensure that prediction and judgment are completed within the cycle time constraint.
[0016] The present invention has the following beneficial effects: This invention addresses the need for rotor assembly geometric error control, and its prediction method based on PSO-BP neural network shows a significant performance improvement compared to traditional artificial intelligence algorithms. In rotor sample testing, the R² of rotor coaxiality prediction reached over 0.98, and the MAE for rotor geometric error assessment was only 0.15μm. The MSE was reduced by 60%-75% compared to a standalone BP neural network and by 80%-85% compared to a traditional linear model. Attached Figure Description
[0017] Figure 1 This is a flowchart illustrating a rotor coaxiality prediction method based on a PSO-BP neural network according to the present invention.
[0018] Figure 2 This is a scatter plot showing the comparison between the predicted and measured values of the PSO-BP model of the present invention; In the figure, the diagonal line represents ideal consistency, the horizontal axis represents the measured coaxiality error, and the vertical axis represents the predicted coaxiality error.
[0019] Figure 3 It is a trend graph of residual change with rotational speed. Detailed Implementation
[0020] To make the objectives, technical solutions, and advantages of this invention clearer, the invention is described below with reference to specific embodiments shown in the accompanying drawings. However, it should be understood that these descriptions are merely exemplary and not intended to limit the scope of the invention. Furthermore, descriptions of well-known structures and technologies are omitted in the following description to avoid unnecessarily obscuring the concept of the invention.
[0021] Specific implementation method one: Combining Figure 1-3 This embodiment describes a rotor coaxiality prediction method based on a PSO-BP neural network. The invention constructs a PSO-BP neural network model suitable for predicting rotor assembly coaxiality at different speeds, achieving accurate real-time prediction of rotor assembly coaxiality errors under different speed scenarios (including extreme high speeds >7000 rpm). The method includes the following steps: Step 1: Data preparation, including: multi-speed characteristic acquisition and data preprocessing; Step 2, Model Design, including: constructing the BP neural network structure and defining the training objective function; Step 3, parameter optimization, including: global optimization of PSO (including determining the initial parameters of BP) and refined training of BP gradient descent; This invention addresses the need for rotor assembly geometric error control, and its prediction method based on the PSO-BP neural network offers a significant performance improvement over traditional artificial intelligence algorithms.
[0022] Specific Implementation Method Two: Combining Figure 1-3 This embodiment describes a rotor coaxiality prediction method based on a PSO-BP neural network. In step one, multi-speed feature acquisition is performed: to address the direct impact of speed changes on coaxiality error during rotor assembly, observable rotor assembly measurements covering the entire speed range (including low speed, normal speed, and high speed >7000rpm that requires key monitoring) are first acquired to construct a feature vector. Data preprocessing: Subsequently, all features were normalized using the formula, and the nonlinear correlation between rotational speed and coaxiality error was verified by using a joint screening method of mutual information and Pearson coefficient.
[0023] Specific implementation method three: Combining Figure 1-3 This embodiment describes a rotor coaxiality prediction method based on a PSO-BP neural network. In step one, the feature vector... ; in, This refers to the rotor speed; Rotor temperature; This is for assembly clearance; This is the dynamic imbalance quantity; The root mean square of the vibration; For temperature difference; The formula is ; in, Standardized value, σ = the square root of the variance. average value.
[0024] Specific implementation method four: Combination Figure 1-3 This embodiment describes a rotor coaxiality prediction method based on a PSO-BP neural network. In step two, a BP neural network structure is constructed: a feedforward neural network is constructed to adapt to the nonlinear mapping of "feature-coaxiality error" under different speeds, with a topology of "input layer-hidden layer 1-hidden layer 2-output layer". Define the training objective function: To avoid overfitting the model on multi-rotational samples, define the mean squared error with L2 regularization as the objective function.
[0025] Specific Implementation Method Five: Combining Figure 1-3 This embodiment describes a rotor coaxiality prediction method based on a PSO-BP neural network. In step two, the topological network representation is as follows:
[0026] In the formula, , , These are the weight matrices for input layer - hidden layer 1, hidden layer 1 - hidden layer 2, and hidden layer 2 - output layer, respectively. , , These are the bias vectors for the corresponding layers. , These are the output values of the two hidden layers, respectively; The training objective function is: ; In the formula, , The total number of samples, , The first The predicted and measured coaxiality error for each sample. This is the regularization parameter.
[0027] Specific Implementation Method Six: Combination Figure 1-3This embodiment describes a rotor coaxiality prediction method based on a PSO-BP neural network. In step three, PSO global optimization is performed: the PSO algorithm is introduced to globally optimize the network parameters, ensuring that the initial parameters are adapted to multi-speed scenarios; each particle corresponds to a set of parameters. Update based on individual optimality and group optimality; BP gradient descent refined training: The optimization process needs to incorporate training samples across the entire speed range to ensure... and Corresponding parameters It can cover low, medium, and high speed scenarios, avoiding the initial parameters being only adapted to a single speed range; then the obtained optimal solution is used as the initial point of the BP stage, followed by the use of a learning rate. Gradient descent performs refined updates An early stopping criterion and adaptive inertia weight decay are set to ensure stable convergence.
[0028] Specific implementation method seven: Combination Figure 1-3 This embodiment describes a rotor coaxiality prediction method based on a PSO-BP neural network. In step three, the PSO global optimization involves each particle corresponding to a set of parameters. Based on individual optimality and group optimality, the update is as follows:
[0029] In the formula, , , , The first , The particle velocity and particle position of the step, For inertial weights, , As a learning factor, , A random number within the interval [0,1]. This represents the optimal position for the individual particle. It represents the global optimal position of the particle swarm.
[0030] Specific implementation method eight: Combination Figure 1-3 This embodiment describes a rotor coaxiality prediction method based on a PSO-BP neural network, which further includes: Step 4, model verification (online application).
[0031] Specific Implementation Method Nine: Combining Figure 1-3 This embodiment describes a rotor coaxiality prediction method based on a PSO-BP neural network. In step four, the generalization error is estimated using K-fold cross-validation, and this estimation guides... The choice of network size improves stability and reliability; in online applications, incremental fine-tuning is performed on new batches of data with small steps to ensure that prediction and judgment are completed within the cycle time constraint (<100 ms / item).
[0032] Example 1: like Figure 1-3 The method for predicting rotor coaxiality based on PSO-BP neural network disclosed here is an online prediction method for coaxiality error at different rotor speeds, combining particle swarm optimization algorithm (PSO) and backpropagation neural network (BP). It is geared towards predicting geometric errors in the assembly process of the spindle and rotor, including: Sixty rotor samples were selected and collected. Features such as [specific features] are used to partition the training / validation sets in an 8:2 ratio. The PSO population size is 30, with a maximum iteration length of 200 steps and inertial weights. The learning rate decreases linearly from 0.9 to 0.4. 0.01, the network structure is [6-32-16-1]; the residual on the validation set after training (measured). (Prediction) Changes with rotational speed, such as Figure 3 As shown.
[0033] Depend on Figure 2 As can be seen, the residuals have a near-zero mean and stable variance, indicating that the model fits well and has good generalization ability. In rotor sample testing, the R² of rotor coaxiality prediction reached over 0.98, and the MAE for rotor geometric error assessment was only 0.15μm. The MSE was reduced by 60%-75% compared to a standalone BP neural network and by 80%-85% compared to a traditional linear model.
[0034] It should be noted that in the above embodiments, as long as the technical solutions are not contradictory, they can be permuted and combined. Those skilled in the art can exhaust all possibilities based on the mathematical knowledge of permutation and combination. Therefore, the present invention will not describe the technical solutions after permutation and combination one by one, but it should be understood that the technical solutions after permutation and combination have been disclosed by the present invention.
[0035] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.
Claims
1. A rotor coaxiality prediction method based on PSO-BP neural network, characterized in that: Comprising the following steps: Step one, data preparation, including: multi-speed feature acquisition and data preprocessing; Step two, model design, including: building BP neural network structure and defining training objective function; Step three, parameter optimization, including: PSO global optimization and BP gradient descent refinement training.
2. The rotor coaxiality prediction method based on PSO-BP neural network according to claim 1, characterized in that: In step one, in view of the direct influence of speed change on the coaxiality error in the rotor assembly process, the rotor assembly observable is collected covering the full speed range, and the feature vector is constructed; All features are normalized using the formula, and the mutual information and Pearson coefficient joint screening method is used to verify the nonlinear correlation between speed and coaxiality error.
3. The rotor coaxiality prediction method based on PSO-BP neural network according to claim 2, characterized in that: In step one, the feature vector ; wherein, is the rotor speed; is the rotor temperature; is the assembly clearance; is the dynamic unbalance; is the vibration root mean square; is the temperature difference; The formula is ; wherein standardized value, square root of the variance, average value.
4. The rotor coaxiality prediction method based on PSO-BP neural network according to claim 3, characterized in that: In step two, a feedforward neural network suitable for nonlinear mapping of features-coaxiality error at different speeds is constructed, and the topological structure is input layer-hidden layer 1-hidden layer 2-output layer; In order to avoid overfitting of the model on multiple speed samples, the mean square error with L2 regularization is defined as.
5. The rotor coaxiality prediction method based on PSO-BP neural network according to claim 4, characterized in that: In step two, the topological structure network is expressed as: wherein , , are weight matrices for input layer - hidden layer 1, hidden layer 1 - hidden layer 2, hidden layer 2 - output layer, respectively; , , are bias vectors for the respective layers, , are output values of the two hidden layers, respectively; The training objective function is: In the formula, , The total number of samples, , The first The predicted and measured coaxiality error of a single sample. This is the regularization parameter.
6. The rotor coaxiality prediction method based on PSO-BP neural network according to claim 5, characterized in that: In step three, the PSO algorithm is introduced to globally optimize the network parameters, ensuring that the initial parameters adapt to multiple speed scenarios; each particle corresponds to a set of parameters , and is updated according to the individual optimum and the group optimum; The optimization process needs to integrate training samples in the whole speed range to ensure With The corresponding parameters Can cover low, medium and high speed scenarios, avoiding initial parameters that only fit a single speed range; then the optimal solution obtained is used as the initial point of the BP phase, and gradient descent with learning rate is used to perform refined update , and early stopping criteria and adaptive inertia weight decay are set to stabilize convergence.
7. The rotor coaxiality prediction method based on PSO-BP neural network according to claim 6, characterized in that: In step three, the individual optimal and group optimal are updated as: In the formula, , , , The first , The particle velocity and particle position of the step, For inertial weights, , As a learning factor, , A random number within the interval [0,1]. This represents the optimal position for the individual particle. It represents the global optimal position of the particle swarm.
8. The rotor coaxiality prediction method based on PSO-BP neural network according to claim 7, characterized in that: Also includes: Step four, model verification.
9. The rotor coaxiality prediction method based on PSO-BP neural network according to claim 8, characterized in that: In step four, the generalization error is estimated by K-fold cross-validation and guides With the choice of network size; in online applications, incremental fine-tuning of the newly added batch data in small steps ensures that the prediction and decision-making are completed within the beat constraints.