Anti-interference vector analysis and robust optimization method and system for tire unbalance

Abstract

This invention discloses an anti-interference vector analysis and robust optimization method and system for tire imbalance. The method includes: pre-identifying the fixed deviation vector of the molding drum system and a mold deviation vector library; producing normal and test batches of tires, rotating the component to be analyzed by a non-180° angle between 120° and 240° in the test batch, collecting imbalance data and binding it to production parameter tags; preprocessing by grouping by mold number, removing outliers and correcting them using the mold deviation vector library; establishing a vector decomposition model containing known mold deviation terms and comprehensive residual terms, solving for the separated component vectors; establishing an objective function based on Monte Carlo sampling, solving for the optimal positioning angle least sensitive to production fluctuations; and closed-loop adaptively updating the model parameters. This invention solves the symmetry aliasing defect of traditional 180° rotation vector analysis, improving the accuracy and robustness of component vector solving.

Description

Technical Field

[0001] This invention relates to the field of tire manufacturing quality control technology, and in particular to an anti-interference vector analysis and robust optimization method and system for tire imbalance. Background Technology

[0002] Tire imbalance is a key factor affecting vehicle safety, comfort, and tire lifespan. Tire imbalance can cause vibration and noise during vehicle operation, and in severe cases, it can lead to steering wheel vibration, abnormal tire wear, and even affect vehicle handling stability.

[0003] Traditional methods for controlling tire imbalance primarily involve controlling the dimensional and weight tolerances of various components during tire molding and performing counterweight balancing after finished product inspection. However, these methods cannot accurately pinpoint the root cause of the imbalance and are insufficient to systematically reduce tire imbalance during the production process.

[0004] Vector analysis, as a mathematical tool capable of simultaneously characterizing the magnitude and direction of imbalance, is suitable for analyzing tire imbalance problems. Existing technologies disclose a basic vector analysis process based on 180° component rotation. This involves producing normal batches of tires and test batches with components rotated 180°, using vector addition and subtraction to separate the imbalance contributions of different components. However, this method has the following technical drawbacks: First, there is a limitation in the solvability of the model. When a 180° rotation is used, the vector of the component to be analyzed in the test batch is reversed, forming a collinear relationship with the vector of the same component in the normal batch, resulting in a linear correlation in the vector decomposition equation system. At this time, if there is a fixed interference in the same direction as the vector of the component, it will be impossible to separate it from the vector of the component to be analyzed, resulting in an inherent aliasing bias.

[0005] Second, it lacks the ability to resist dynamic interference factors. In actual high-speed automated tire production lines, dynamic time-varying interference factors such as mold size differences caused by uneven heat distribution in vulcanizing molds, mechanical wear deviations after long-term use of molding drums, viscosity fluctuations of rubber materials caused by changes in ambient temperature, and performance differences between different batches of materials are constantly present. Traditional vector analysis methods assume that there is no interference or that the interference is negligible in the production process, and their accuracy drops significantly under the above-mentioned dynamic interference conditions.

[0006] Third, the sample size is fixed and lacks a dynamic adjustment mechanism. Existing methods use a fixed sample size, which either results in insufficient sample size affecting statistical accuracy or excessive sample size increasing experimental costs and time.

[0007] Fourth, outlier detection relies on a single dimension. Existing methods only screen for outliers based on a single dimension, such as the magnitude or angle of the imbalance, which can easily lead to false positives or false negatives.

[0008] Fifth, the uncertainty of the results cannot be quantified. Traditional methods only provide point estimates of component vectors, and cannot provide confidence intervals or quantify the impact of production fluctuations on the final results. Summary of the Invention

[0009] The technical problem to be solved by this invention is the limitation of model solvability and the low accuracy and poor robustness under dynamic disturbances in traditional vector analysis methods. In order to solve the above problems, an anti-interference vector analysis and robust optimization method and system for tire imbalance is provided.

[0010] The object of this invention is achieved in the following manner: An anti-interference vector analysis and robust optimization method for tire imbalance includes: Pre-identification of production interference sources: Obtain the system fixed deviation vector of the forming drum itself through the idling test of the forming drum; establish the mapping relationship between the vulcanizing mold number and the unbalance deviation by statistically analyzing multiple batches of historical data, and obtain the mold deviation vector library; Asymmetric experimental design: Normal batches of NP tires and at least one test batch of TEST tires are produced. The sample size of each batch is dynamically determined using sequential analysis. The components to be analyzed in the test batch are rotated at any angle between 120° and 240° relative to the normal batch, and production process label data of each tire is collected. Data acquisition: Collect the imbalance vector data of each tire and bind the imbalance vector data with the corresponding production process label data; Preprocessing: The data is grouped based on the mold number, and the upper and lower dynamic imbalance angle difference GAP of each group is calculated. Outliers are removed based on the multidimensional features constructed from the imbalance amount, angle, the upper and lower dynamic imbalance angle difference and the production process label data. Preliminary deviation correction is performed using the mold deviation vector library. Vector decomposition: A vector decomposition model containing known mold deviation terms and comprehensive residual terms is established. The model is solved using the least squares method to separate the vector of the component to be analyzed from the vectors of other components. The known mold deviation terms are obtained from the mold deviation vector library, and the comprehensive residual terms include quantifiable production fluctuations and random noise. Robust optimization: Based on the vector of the component to be analyzed, the vectors of other components, and the system fixed deviation vector of the forming drum, an objective function of the total imbalance with respect to the positioning angle is established. Production fluctuation constraints are introduced through Monte Carlo sampling to solve for the optimal positioning angle that minimizes the sensitivity of the total imbalance to production fluctuations; and... Closed-loop update: According to a preset cycle, the regression model parameters of the mold deviation vector library and the comprehensive residual term are updated using online detection data, and the production positioning angle is adjusted according to the optimization results.

[0011] In the asymmetric experimental procedure, the sequential analysis method is as follows: the initial sample size is set according to the standard deviation of historical data, and during the experiment, the sample size is determined to be terminated early or increased further based on the comparison between the area of ​​the confidence ellipse of the current synthetic vector and the preset threshold.

[0012] In the asymmetric testing step, two or three test batches with different preset angles are produced, and an overdetermined system of equations is established: Where rot1 ≠ rot2 and neither is 180°, the overdetermined system of equations is solved by weighted least squares.

[0013] In the preprocessing step, the calculation method for the difference between the upper and lower dynamic imbalance angles is as follows: the upper and lower dynamic imbalance angle sequence is regarded as a periodic signal and a discrete Fourier transform is performed; the amplitude and phase of its first harmonic component are extracted as the representation of the difference between the upper and lower dynamic imbalance angles; the outlier removal is achieved by comparing the Mahalanobis distance with the threshold determined by Monte Carlo simulation.

[0014] In the vector decomposition step, the vector decomposition model is: ,in and These are the combined vectors of the normal batch and the test batch, respectively. The known mold deviation vector is obtained by looking up a table in the mold deviation vector library, and FA is the vector of the part to be analyzed. Let be the vector of the component to be analyzed after rotating by an angle θ. The angular difference is θ, and FB is the vector of the other components. and The comprehensive residual term is obtained by solving the least squares method with regularization, and the regularization parameter is determined by cross-validation based on the sample size.

[0015] In the robust optimization step, the total imbalance is constructed as follows: , The vector of the component to be analyzed after rotation by Δθ, FB is the vector of the other components, and ε m ε is the known mold deviation term, and ε is the comprehensive residual term; The objective function is to minimize the weighted sum of the expectation and variance of the total imbalance, as shown in the following equation: , E is the expected value, Var is the variance, and k is the robustness weighting coefficient, ranging from 0.5 to 2.0. The value of k is determined by normalizing the expected value and variance.

[0016] In the Monte Carlo sampling, the comprehensive residual value under each sampling scenario is calculated based on the pre-established regression model of comprehensive residual and measurable production parameters; the production fluctuation constraints include material Mooney viscosity fluctuation ±5% and ambient temperature fluctuation ±3℃.

[0017] A robust optimization system for tire imbalance to implement the method includes: an interference source identification module, used to obtain the system fixed deviation vector of the forming drum through a forming drum idle test, and to establish a mold deviation vector library by statistical historical data; The experiment design module, whose input is connected to the output of the interference source identification module, is used to generate an asymmetric experiment plan based on the output of the interference source identification module and to collect production process label data. A data acquisition and binding module, wherein the input end of the data acquisition and binding module is connected to the output end of the experimental design module, is used to acquire unbalance measurement data and bind it to the production process label data; A hierarchical preprocessing module, the input of which is connected to the output of the data acquisition and binding module, is used to remove outliers by mold number and to correct deviations using the mold deviation vector library. The vector decomposition calculation module has a first input end connected to the output end of the hierarchical preprocessing module and a second input end connected to the output end of the interference source identification module. It is used to establish and solve a vector decomposition model based on the correction data output by the hierarchical preprocessing module and the mold deviation vector output by the interference source identification module to obtain the separated component vectors. A robust angle optimization module, wherein the first input of the robust angle optimization module is connected to the output of the vector decomposition calculation module, and the second input of the robust angle optimization module is connected to the output of the interference source identification module, is used to solve for the optimal positioning angle based on the component vector and the system fixed deviation vector of the molding drum; and A closed-loop adaptive module is provided, with its input connected to the output of the robust angle optimization module. The output of the closed-loop adaptive module is connected to the feedback inputs of the interference source identification module and the vector decomposition calculation module, respectively. It is used to make production adjustments based on the optimization results and update the mold deviation vector library and residual regression model parameters using online detection data at preset intervals before feeding them back to the corresponding modules.

[0018] The data acquisition and binding module includes a uniformity testing machine and a database. The uniformity testing machine and the database are connected via industrial Ethernet communication to achieve automatic binding of unbalance measurement data and production process label data.

[0019] The hierarchical preprocessing module includes a GAP value calculation unit, a Mahalanobis distance outlier detection unit, and a mold deviation correction unit, which are connected sequentially and transmit data unidirectionally. The GAP value calculation unit is used to perform discrete Fourier transform on the upper and lower dynamic imbalance angle sequence and extract the first harmonic component. The Mahalanobis distance outlier detection unit is used to calculate the Mahalanobis distance based on the multidimensional feature matrix and compare it with the Monte Carlo simulation threshold. The mold deviation correction unit is used to perform preliminary deviation correction on each group of data according to the mold deviation vector library.

[0020] The beneficial effects of this invention are: it solves the solvability defects of traditional models. By setting the mold deviation as a known quantity and using a non-180° rotation between 120° and 240° to break the symmetry, the vector decomposition equation system changes from linearly dependent to linearly independent, mathematically guaranteeing the uniqueness and unbiasedness of the vector decomposition and eliminating the inherent aliasing bias.

[0021] Strong anti-interference capability. It pre-identifies two types of interference sources: fixed deviation of the forming drum system and mold deviation, and introduces a known mold deviation term ε into the vector decomposition model. m As a compensation amount, the forming drum deviation ε is used in the robust optimization stage. drum Substituting known constants into the total unbalance calculation effectively eliminates the influence of fixed disturbances such as mechanical wear and mold differences. Simultaneously, the residual terms are integrated. ε It explicitly includes quantifiable temperature drift and Mooney viscosity fluctuations, as well as unquantifiable random noise, making the modeling more closely resemble actual production conditions. Attached Figure Description

[0022] Figure 1 This is an overall flowchart of the anti-interference vector analysis and robust optimization method for tire imbalance in this invention; Figure 2 This is a schematic diagram illustrating the principle of vector decomposition with known interference terms in this invention; Figure 3 This is a schematic diagram comparing the symmetry of the present invention with non-180° rotation and 180° rotation; Figure 4 This is a flowchart of the sequential sample size determination method of the present invention; Figure 5 This is a schematic diagram illustrating outlier detection based on Mahalanobis distance according to the present invention. Figure 6 This is a schematic diagram of the robust angle optimization based on Monte Carlo sampling of the present invention; Figure 7 This is a block diagram of the robust optimization system for tire imbalance of the present invention. Detailed Implementation

[0023] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0024] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used herein have the same technical meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0025] A robust vector analysis and optimization method for tire imbalance includes the following steps: S1 Production Interference Source Pre-identification: ① Before the formal test, the system fixed deviation vector of the forming drum itself was identified and quantified by the idling test of the forming drum and the standard weight loading test; ② Collect production data from the past three months, statistically analyze the average unbalance deviation corresponding to different vulcanizing mold numbers, and establish a mold deviation vector library, with each mold number corresponding to a unique known deviation vector. .

[0026] S2 Asymmetric Dynamic Experimental Design: ① Produce normal batches of NP tires and at least one test batch of TEST tires. Use sequential analysis to determine the sample size. The initial sample size should be no less than 8 tires. Specifically, set the initial sample size based on the standard deviation of historical data. During the test, decide whether to terminate early or continue to increase the sample size based on the comparison between the confidence ellipse area of ​​the current synthetic vector and the preset threshold, until the accuracy requirements are met or the maximum sample size of 30 tires is reached. ②The TEST batch rotates the component to be analyzed by any angle between 120° and 240° relative to the NP batch, which is not 180°, to break the symmetry defects caused by the 180° rotation and avoid the mixing of interference items and component vectors. ③Optionally, produce 2-3 TEST batches with different rotation angles and establish an overdetermined system of equations to improve the solution accuracy; The overdetermined system of equations is as follows: , Where rot1≠rot2 and neither is 180°, the overdetermined system of equations is solved by weighted least squares method, which further improves the solution accuracy of FA and FB.

[0027] ④ At the same time, record the production environment temperature, material batch number, molding drum number, and vulcanizing mold number of each tire as data tags.

[0028] S3 Multi-Dimensional Labeled Data Collection: ① Measure the static imbalance S of each tire on a tire uniformity testing machine. v , static unbalance angle S, dynamic unbalance U v Upper dynamic imbalance angle U, lower dynamic imbalance amount Lv The angle of imbalance at the lower position L; ② Bind the production parameter tags recorded in S2 to the measurement data of each tire and store them in the database.

[0029] S4 Layered Data Preprocessing Based on Machine / Mold: ① Group the data according to the mold number label, calculate the upper and lower dynamic imbalance angle difference (GAP) value for each group of data, perform discrete Fourier transform on the upper and lower dynamic imbalance angle sequence, extract the amplitude and phase of the first harmonic component as the GAP value, and filter out higher-order noise; ② Construct a multidimensional feature matrix containing the magnitude of the imbalance, angle, GAP value, ambient temperature, and material batch number; calculate the Mahalanobis distance for each sample; determine the threshold at a 99% confidence level through 10,000 Monte Carlo simulations; and remove samples that exceed the threshold. ③ Using the mold deviation vector library obtained from S1, perform preliminary deviation correction on each set of data to eliminate the influence of mold fixation differences.

[0030] S5 Vector decomposition calculation with known interference terms: ① Model solvability correction: correcting mold deviations Given a known quantity (obtained from the mold deviation vector library of S1 based on the mold number), define the comprehensive residual term. and Including quantifiable production fluctuations (temperature drift, material Mooney viscosity fluctuations) and unquantifiable random noise, the following vector decomposition model is established: , in For NP batch sum vector, TEST is the batch vector, and FA is the vector of the component to be analyzed. The vector after rotating the component to be analyzed by an angle θ (satisfying) ), where FB is the vector of the non-analyzed component.

[0031] ② The principle of breaking symmetry through non-180° rotation: When rotating 180° in the traditional way, θ = 180° ∘ , Substituting into the above equation, we get: , Subtracting the two equations, we get: If there is a fixed disturbance in the same direction as the FA, it will be impossible to separate from the FA, resulting in an inherent bias in the model.

[0032] If we ignore the random residual term (i.e., assume...) The analytical expression for FA can be obtained as follows: When using a non-180° rotation (such as...) ), At this point, the system of equations is a linearly independent system of equations, and has a unique solution:

[0033] in This is a rotation matrix, representing a counterclockwise rotation of the vector. The solution is unique and free from overlap, fundamentally resolving the symmetry defect of the traditional 180° rotation.

[0034] ③ Solving overdetermined equations: when using two different rotation angles θ 1 and θ For the 2nd TEST batch, establish an overdetermined system of equations: ; By using the weighted least squares method, the weights are proportional to the square root of the sample size in each batch, which can further reduce the influence of residuals and improve the accuracy of the solution.

[0035] ④ Solve the above model using the regularized least squares method to obtain the corrected model. FA and FB The regularization parameter λ is determined through cross-validation. When the sample size is less than 15, λ is 0.1, and when the sample size is greater than or equal to 15, λ is 0.05.

[0036] S6 Robust optimal angle calculation based on Monte Carlo sampling: ①According to the revised FA and FB Based on the fixed deviation vector of the molding drum system obtained from S1, a function of the total unbalance with respect to the positioning angle Δθ is established: , in ξ For random disturbance vectors, ε drum To fix the deviation vector of the forming drum system, ε ( ξ The term represents the composite residual, the value of which is determined by both measurable fluctuations and random noise. ② Monte Carlo sampling update method for integrated residuals: a. Generate N =1000 independent random scenarios (i=1,2,...,N, N=1000 recommended), each scenario corresponds to a set of measurable fluctuation values: Material Mooney viscosity: ; Ambient temperature: ; b. Establish a regression model between the comprehensive residual mean and measurable fluctuations based on historical production data: , where a and b are regression coefficients; c. Superimposed unquantizable random noise: ,in , The standard deviation of the residuals is the random noise, obtained from historical data statistics; d. Calculate the total imbalance for each scenario. Then, the expected value and variance are calculated: ; ③ The normalization selection criterion for robustness weight coefficient k: To make the expected value (average imbalance) and variance (production stability) comparable, both need to be normalized in terms of dimensions: , in This represents the average imbalance obtained using the traditional 180° rotation method. This represents the unbalanced variance in the traditional method.

[0037] The normalized objective function is: =

[0038] At this point, the value of k directly represents the weight ratio of the variance term to the expectation term, and its selection is based on the following criteria: k=1.0: The expected value and variance weights are equal, taking into account both the average imbalance and production stability, and is suitable for most general-purpose tires; k=1.5-2.0: The variance term has a higher weight, which prioritizes production stability and is suitable for OE tires (such as original equipment tires from OEMs) with extremely high requirements for quality consistency. It can minimize the defect rate of mass production. k=0.5-1.0: The expected value has a higher weight, and the average imbalance is reduced first. It is suitable for cost-sensitive replacement tires, and production costs are controlled while ensuring basic stability. ④ Use the gradient descent method to find the minimum value of the objective function and obtain the optimal positioning angle. .

[0039] S7 Closed-Loop Adaptive Verification and Update: ① Verify the optimization effect using small-batch production (no less than 20 lines), and compare the average value, standard deviation, pass rate, and sensitivity to production fluctuations before and after optimization; if the verification effect meets expectations, apply the new positioning angle to normal production. ② Establish a closed-loop update mechanism: According to a preset cycle (update the mold deviation vector library once every 1,000 tires produced, and refit the regression model every 5,000 tires produced), continuously update the mold deviation vector library and the regression model parameters of the comprehensive residual term using online detection data to achieve adaptive optimization of the system.

[0040] The component to be analyzed is any one of the following: tread, belt layer, carcass, bead, or inner liner. When analyzing the belt layer, the rotation angle of the TEST batch is preferably 150° or 210°.

[0041] To achieve the above method, the present invention also provides a robust optimization system for tire imbalance, comprising: The interference source identification module is used to obtain the system fixed deviation vector of the forming drum through the idling test of the forming drum, and to establish a mold deviation vector library by statistically analyzing historical data. The experiment design module, whose input is connected to the output of the interference source identification module, is used to generate an asymmetric experiment plan based on the output of the interference source identification module and to collect production process label data. The data acquisition and binding module, whose input end is connected to the output end of the experimental design module, includes a uniformity testing machine and a database. The uniformity testing machine and the database are connected via industrial Ethernet communication and are used to acquire unbalance measurement data and automatically bind it with the production process label data. The layered preprocessing module, whose input end is connected to the output end of the data acquisition and binding module, includes a GAP value calculation unit, a Mahalanobis distance outlier detection unit, and a mold deviation correction unit that are connected in sequence and transmit data unidirectionally. It is used to remove outliers by mold number and correct deviations using a mold deviation vector library. The vector decomposition calculation module has a first input terminal connected to the output terminal of the hierarchical preprocessing module and a second input terminal connected to the output terminal of the interference source identification module. It is used to establish a vector decomposition model and solve for the separated component vectors. A robust angle optimization module, wherein the first input of the robust angle optimization module is connected to the output of the vector decomposition calculation module, and the second input of the robust angle optimization module is connected to the output of the interference source identification module, is used to solve for the optimal positioning angle based on the component vector and the system fixed deviation vector of the molding drum; A closed-loop adaptive module is provided, with its input connected to the output of the robust angle optimization module. The output of the closed-loop adaptive module is connected to the feedback inputs of the interference source identification module and the vector decomposition calculation module, respectively. It is used to make production adjustments based on the optimization results and update the mold deviation vector library and residual regression model parameters using online detection data at preset intervals before feeding them back to the corresponding modules.

[0042] Implementation Case 1: This case study presents a method for optimizing tire belt layer imbalance based on disturbance correction, combined with... Figures 1-7 Explanation: 1. Pre-identification of production interference sources (corresponding to) Figure 1 Step S1) The idling test and standard weight loading test were carried out on the No. 10 molding drum, and the fixed deviation vector of the system was measured to be: modulus 5.2g, angle 125°. Production data for each mold number of the D02 vulcanizing machine over the past three months was collected, and the mold deviation vectors for each mold number were statistically analyzed. A mold deviation vector library was established, including the known deviation vectors for D02-1. The modulus is 3.8g and the angle is 210°.

[0043] 2. Asymmetric dynamic experimental design (corresponding to) Figure 1 Step S2 Figure 3 ) Analysis object: 225 / 45R17 tire, the component to be analyzed is the belt layer; The initial sample size n0 = 8 samples, which is dynamically adjusted using sequential analysis. The TEST batch rotates the belt-driven drum 150° (not 180°) relative to the NP batch to avoid symmetrical aliasing; Record the production environment temperature (23±2℃), material batch number (B20260501), molding drum number (10#), and vulcanization mold number (D02-1) for each tire.

[0044] 3. Multi-dimensional labeled data collection (corresponding to) Figure 1 Step S3) Measure and record the static imbalance and angle of each tire. Some data are as follows: 1 233.189 338 D02-1 22.5 27 204.648 57 D02-1 23.1 2 364.471 185 D02-1 23 28 135.38 90 D02-1 22.8 3 118.397 45 D02-1 22.7 29 112.272 50 D02-1 23.3 6 260.316 72 D02-1 23.2 46 299.583 46 D02-1 22.9 7 203.088 15 D02-1 22.6 47 46.806 205 D02-1 23.4 8 238.564 208 D02-1 23.1 52 239.221 200 D02-1 22.7 - - - - - 90 366.246 50 D02-1 23 - - - - - 91 258.555 42 D02-1 22.6 4. Layered data preprocessing based on machine tool / mold (corresponding to) Figure 1 Step S4 Figure 5 ) All data are from the D02-1 module and do not require grouping. Perform a discrete Fourier transform on the upper and lower dynamic unbalance angle sequence, extract the first harmonic component, and calculate the GAP value; A multidimensional feature matrix was constructed, and the Mahalanobis distance of each sample was calculated. After 10,000 Monte Carlo simulations, the threshold was found to be 12.5. The Mahalanobis distance of all samples was less than the threshold, and there were no outliers. ε is obtained by looking up a table in the mold deviation vector library. m =(3.8g, 210°), preliminary corrections to the original data: F′ NP =F NP −ε m F′ TEST =F TEST −ε m .

[0045] 5. Vector decomposition calculation with known interference terms (corresponding to) Figure 1 Step S5 Figure 2 , Figure 3 ) Establish a vector decomposition model with a rotation angle θ = 150°; The solution is obtained using the least squares method with regularization, where the regularization parameter λ = 0.05 (sample size n = 16 ≥ 15). The corrected belt layer vector FA was calculated to have a modulus of 58.4 g, an angle of 234.1°, and a 95% confidence interval of ±2.3 g. Non-belt layer vector FB: modulus 80.7g, angle 64.5°, 95% confidence interval ±3.1g; Comprehensive residual statistical characteristics: regression coefficients for the measurable fluctuation component: a = 0.15 g / %, b = 0.2 g / ℃, and standard deviation of random noise. σ ε =1.2g.

[0046] 6. Robust optimal angle calculation based on Monte Carlo sampling (corresponding to) Figure 1 Step S6 Figure 6 ) The baseline values ​​for the traditional method are: E0 = 123.4g, Var0 = 3906g. 2 ; This embodiment uses OE-matched tires, which have high stability requirements, so k=1.5 is selected; Generate 1000 Monte Carlo scenes, with the Mooney viscosity and temperature of each scene being randomized within ±5% and ±3℃, respectively. The comprehensive residual ε for each scenario is calculated based on the regression model. i =0.15×(ML i −ML0)+0.2×(T i −T0)+η i ; Calculate the total imbalance in each scenario to obtain the normalized expectation E. * and variance Var * The curve relating to the rotation angle Δθ; The optimal rotation angle Δθ is obtained by solving the problem. * =-168.2°, approximately equal to -168°; That is, the belt layer drum should be rotated counterclockwise by 168°. At this angle, the expected total imbalance is 112.7g, the variance is 2421g², and the sensitivity to production fluctuations is the lowest.

[0047] 7. Closed-loop adaptive verification and update (corresponding to) Figure 1 Step S7) Small-batch production of 20 tires, using a new belt layer positioning angle; The test results showed that the average static imbalance decreased from 185.6g to 112.7g, a reduction of 39.3%. The static imbalance standard deviation decreased from 78.5g to 49.2g, a reduction of 37.3%; The pass rate increased from 75% to 95%; Under the condition that the Mooney viscosity of the material fluctuates by ±5%, the fluctuation range of the unbalance is only 42% of that of the traditional method; The new positioning angle was applied to normal production, and the mold deviation vector library and residual regression model were updated.

[0048] Comparative experiment: To verify the superiority of this invention, the same batch of tires was analyzed using the traditional 180° rotation vector analysis method, and the results are compared below: Experimental results show that the method of the present invention not only significantly reduces the average value and fluctuation amplitude of the imbalance, but also fundamentally solves the problem of large component vector solution error in traditional methods, and greatly improves the robustness to production fluctuations.

[0049] Implementation Case 2: This case study presents a method for optimizing tire tread dynamic imbalance based on overdetermined equations, combined with... Figures 1-7 Explanation: 1. Pre-identification of production interference sources The No. 8 molding drum was tested, and its system fixed deviation vector was measured to be: modulus 4.7g, angle 95°; Establish a mold deviation vector library for each mold number of the C05 vulcanizing machine.

[0050] 2. Asymmetric dynamic experimental design Object of analysis: 205 / 75R17.5 tire, the part to be analyzed is the tread; The initial sample size was n0 = 10 samples, and sequential analysis was used. Two test batches were produced, with the tread rotated by 150° and 210° respectively, and an overdetermined system of equations was established. Record production parameter labels.

[0051] 3. Multi-dimensional labeled data collection Measure and record the static and dynamic imbalance data for each tire, and attach production parameter labels.

[0052] 4. Layered data preprocessing based on machine tool / mold - Divide the data into 3 groups according to the mold number, and calculate the GAP value for each group; - Remove two outliers based on Mahalanobis distance; - Initial corrections are made using the mold deviation vector library.

[0053] 5. Vector decomposition calculation with known interference terms Establish an overdetermined system of equations containing two test batches; The weighted least squares method is used to solve the problem, and the weights are proportional to the square root of the sample size of each batch. The corrected tread vector FA is obtained: modulus 121.9g, angle 313.7°, 95% confidence interval ±1.8g; Non-tread vector FB: modulus 68.4g, angle 223.8°, 95% confidence interval ±2.5g.

[0054] 6. Robust Optimal Angle Calculation Based on Monte Carlo Sampling In this embodiment, since the tires are being replaced in the market, k=0.8 is selected; Generate 1000 Monte Carlo scenes and calculate their expectation and variance; The optimal rotation angle Δθ is obtained by solving the problem. * = -88.7°, approximately equal to -89°; That is, the tire tread should be rotated 89° counterclockwise.

[0055] 7. Closed-loop adaptive verification and update A small batch of 30 tires was produced, and the verification results showed that the average dynamic imbalance decreased from 98.7g to 58.2g, a reduction of 41.0%. The standard deviation of dynamic imbalance decreased from 56.3g to 32.7g, a reduction of 41.9%; The pass rate increased from 80% to 96.7%; Apply the new positioning angle to production and update the parameters.

[0056] This invention addresses the solvability limitations of traditional models. By setting the mold deviation as a known quantity and employing a non-180° rotation between 120° and 240° to break the symmetry, the vector decomposition equations are transformed from linearly dependent to linearly independent, mathematically guaranteeing the uniqueness and unbiasedness of the vector decomposition and eliminating inherent aliasing bias. Comparative experiments show that the component vector solution error is reduced from 12.6g in the traditional method to 2.3g, an improvement of 81.7%.

[0057] It exhibits strong anti-interference capabilities. By pre-identifying two types of interference sources—fixed deviations and mold deviations—and introducing a known mold deviation term εm as a compensation quantity into the vector decomposition model, the forming drum deviation εdrum is substituted as a known constant into the calculation of the total unbalance during the robust optimization stage, effectively eliminating the influence of fixed interferences such as mechanical wear and mold differences. Simultaneously, the comprehensive residual term εε explicitly includes quantifiable temperature drift and Mooney viscosity fluctuations, as well as unquantifiable random noise, making the modeling more closely resemble actual production conditions.

[0058] It exhibits good robustness and quantifiable controllability. The Monte Carlo sampling method is employed to quantify the impact of production fluctuations, and a normalized k-value (range 0.5-2.0) is used to flexibly balance average performance and stability. Comparative experiments show that the method of this invention reduces the static imbalance standard deviation from 62.5g in the traditional method to 49.2g, a reduction of 21.3%; the sensitivity to temperature fluctuations from 3.2g / ℃ to 1.3g / ℃, a reduction of 59.4%; and the sensitivity to Mooney viscosity fluctuations from 2.8g / % to 1.1g / %, a reduction of 60.7%.

[0059] The experiment is highly efficient. A sequential analysis method is used to dynamically adjust the sample size. During the experiment, the area of ​​the confidence ellipse is compared with a threshold to determine whether to terminate the experiment early. This reduces the average sample size by 30% while maintaining accuracy, thus lowering experimental costs and time.

[0060] Outlier detection is accurate. The multidimensional outlier detection method based on Mahalanobis distance comprehensively considers multiple dimensions such as the magnitude of the imbalance, angle, GAP value, ambient temperature, and material batch number. The false positive rate and false negative rate are both less than 5%, which is far superior to traditional single-dimensional screening methods.

[0061] It possesses adaptive capabilities. Through a closed-loop update mechanism, it automatically adjusts model parameters using online detection data at preset intervals (updating the mold deviation library every 1000 records and refitting the regression model every 5000 records), enabling it to continuously learn from slow changes in the production process and ensure long-term stable operation of the system.

[0062] The above description is only a preferred embodiment of the present invention. It should be noted that those skilled in the art can make several changes and improvements without departing from the overall concept of the present invention, and these should also be considered within the scope of protection of the present invention.

Claims

1. A robust vector analysis and optimization method for tire imbalance, characterized in that, include: Pre-identification of production interference sources: Obtain the system fixed deviation vector of the forming drum itself through the idling test of the forming drum; establish the mapping relationship between the vulcanizing mold number and the unbalance deviation by statistically analyzing multiple batches of historical data, and obtain the mold deviation vector library; Asymmetric experimental design: Normal batches of NP tires and at least one test batch of TEST tires are produced. The sample size of each batch is dynamically determined using sequential analysis. The components to be analyzed in the test batch are rotated at any angle between 120° and 240° relative to the normal batch, and production process label data of each tire is collected. Data acquisition: Collect the imbalance vector data of each tire and bind the imbalance vector data with the corresponding production process label data; Preprocessing: The data is grouped based on the mold number, and the upper and lower dynamic imbalance angle difference GAP of each group is calculated. Outliers are removed based on the multidimensional features constructed from the imbalance amount, angle, the upper and lower dynamic imbalance angle difference and the production process label data. Preliminary deviation correction is performed using the mold deviation vector library. Vector decomposition: A vector decomposition model containing known mold deviation terms and comprehensive residual terms is established. The model is solved using the least squares method to separate the vector of the component to be analyzed from the vectors of other components. The known mold deviation terms are obtained from the mold deviation vector library, and the comprehensive residual terms include quantifiable production fluctuations and random noise. Robust optimization: Based on the vector of the component to be analyzed, the vectors of other components, and the system fixed deviation vector of the forming drum, an objective function of the total imbalance with respect to the positioning angle is established. By introducing production fluctuation constraints through Monte Carlo sampling, the optimal positioning angle that makes the total imbalance least sensitive to production fluctuations is solved. as well as, Closed-loop update: According to a preset cycle, the regression model parameters of the mold deviation vector library and the comprehensive residual term are updated using online detection data, and the production positioning angle is adjusted according to the optimization results.

2. The anti-interference vector analysis and robust optimization method for tire imbalance according to claim 1, characterized in that, In the asymmetric experimental procedure, the sequential analysis method is as follows: the initial sample size is set according to the standard deviation of historical data, and during the experiment, the sample size is determined to be terminated early or increased further based on the comparison between the area of ​​the confidence ellipse of the current synthetic vector and the preset threshold.

3. The anti-interference vector analysis and robust optimization method for tire imbalance according to claim 1, characterized in that, In the asymmetric testing step, two or three test batches with different preset angles are produced, and an overdetermined system of equations is established: Where rot1 ≠ rot2 and neither is 180°, the overdetermined system of equations is solved by weighted least squares.

4. The anti-interference vector analysis and robust optimization method for tire imbalance according to claim 1, characterized in that, In the preprocessing step, the calculation method for the difference between the upper and lower dynamic imbalance angles is as follows: the upper and lower dynamic imbalance angle sequence is regarded as a periodic signal and a discrete Fourier transform is performed; the amplitude and phase of its first harmonic component are extracted as the representation of the difference between the upper and lower dynamic imbalance angles; the outlier removal is achieved by comparing the Mahalanobis distance with the threshold determined by Monte Carlo simulation.

5. The anti-interference vector analysis and robust optimization method for tire imbalance according to claim 1, characterized in that, In the vector decomposition step, the vector decomposition model is: ,in and These are the combined vectors of the normal batch and the test batch, respectively. The known mold deviation vector is obtained by looking up a table in the mold deviation vector library, and FA is the vector of the part to be analyzed. Let θ be the vector of the component to be analyzed after rotation by an angle θ. The angular difference is θ, and FB is the vector of the other components. and The comprehensive residual term is obtained by solving the least squares method with regularization, and the regularization parameter is determined by cross-validation based on the sample size.

6. The anti-interference vector analysis and robust optimization method for tire imbalance according to claim 1, characterized in that, In the robust optimization step, the total imbalance is constructed as follows: , The vector of the component to be analyzed after rotation by Δθ, FB is the vector of the other components, and ε m ε is the known mold deviation term, and ε is the comprehensive residual term; The objective function is to minimize the weighted sum of the expectation and variance of the total imbalance, as shown in the following equation: ， E is the expected value, Var is the variance, and k is the robustness weighting coefficient, ranging from 0.5 to 2.

0. The value of k is determined by normalizing the expected value and variance.

7. The anti-interference vector analysis and robust optimization method for tire imbalance according to claim 6, characterized in that, In the Monte Carlo sampling, the comprehensive residual value under each sampling scenario is calculated based on the pre-established regression model of comprehensive residual and measurable production parameters; the production fluctuation constraints include material Mooney viscosity fluctuation ±5% and ambient temperature fluctuation ±3℃.

8. A robust optimization system for tire imbalance implementing the method as described in any one of claims 1 to 7, characterized in that, include: The interference source identification module is used to obtain the system fixed deviation vector of the forming drum through the idling test of the forming drum, and to establish a mold deviation vector library by statistically analyzing historical data. The experiment design module, whose input is connected to the output of the interference source identification module, is used to generate an asymmetric experiment plan based on the output of the interference source identification module and to collect production process label data. A data acquisition and binding module, wherein the input end of the data acquisition and binding module is connected to the output end of the experimental design module, is used to acquire unbalance measurement data and bind it to the production process label data; A hierarchical preprocessing module, the input of which is connected to the output of the data acquisition and binding module, is used to remove outliers by mold number and to correct deviations using the mold deviation vector library. The vector decomposition calculation module has a first input end connected to the output end of the hierarchical preprocessing module and a second input end connected to the output end of the interference source identification module. It is used to establish and solve a vector decomposition model based on the correction data output by the hierarchical preprocessing module and the mold deviation vector output by the interference source identification module to obtain the separated component vectors. A robust angle optimization module, wherein the first input of the robust angle optimization module is connected to the output of the vector decomposition calculation module, and the second input of the robust angle optimization module is connected to the output of the interference source identification module, is used to solve for the optimal positioning angle based on the component vector and the system fixed deviation vector of the molding drum; and A closed-loop adaptive module is provided, with its input connected to the output of the robust angle optimization module. The output of the closed-loop adaptive module is connected to the feedback inputs of the interference source identification module and the vector decomposition calculation module, respectively. It is used to make production adjustments based on the optimization results and update the mold deviation vector library and residual regression model parameters using online detection data at preset intervals before feeding them back to the corresponding modules.

9. The robust optimization system for tire imbalance according to claim 8, characterized in that, The data acquisition and binding module includes a uniformity testing machine and a database. The uniformity testing machine and the database are connected via industrial Ethernet communication to achieve automatic binding of unbalance measurement data and production process label data.

10. The robust optimization system for tire imbalance according to claim 8, characterized in that, The hierarchical preprocessing module includes a GAP value calculation unit, a Mahalanobis distance outlier detection unit, and a mold deviation correction unit, which are connected sequentially and transmit data unidirectionally. The GAP value calculation unit is used to perform discrete Fourier transform on the upper and lower dynamic imbalance angle sequence and extract the first harmonic component. The Mahalanobis distance outlier detection unit is used to calculate the Mahalanobis distance based on the multidimensional feature matrix and compare it with the Monte Carlo simulation threshold. The mold deviation correction unit is used to perform preliminary deviation correction on each group of data according to the mold deviation vector library.

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