Bayesian-based turntable multi-source data reliability prediction method

Abstract

The invention discloses a rotary table multi-source data reliability prediction method based on the Bayesian theory, and belongs to the technical field of numerical control machine tools. The method comprises the following steps: constructing a mechanism reliability model based on geometric errors; according to the constructed mechanism reliability model, obtaining prior distribution and a joint prior probability density function matched with the overall Weibull reliability model under least square method line fitting; a turntable precision degradation test is carried out, and a likelihood function of life data is established according to an overall Weibull reliability model; substituting the likelihood function and the joint prior distribution probability density function into a Bayesian formula to obtain a posteriori distribution probability density function; and estimating parameters by adopting an MCMC sampling method, and carrying out reliability prediction analysis on the worm gear turntable under the condition of fusing different samples. According to the method, the prior information of the mechanism reliability model can be fully utilized under the condition that the service life sample size is small, and the reliability prediction precision in the operation process of the rotary table is effectively improved.

Description

Technical Field

[0001] This invention relates to the field of CNC machine tool technology, and in particular to a Bayesian-based method for predicting the reliability of multi-source data from a rotary table. Background Technology

[0002] The rotary table of a CNC gear milling machine is a key functional component for achieving gear machining accuracy and complex surface machining. Its performance stability and reliability directly affect the overall machining quality and production efficiency of the machine. The rotary table operates under high load, high precision, and continuous operation conditions for extended periods. Its motion accuracy degrades due to factors such as manufacturing errors, assembly errors, and thermal deformation, leading to accumulated machining errors and a decline in transmission performance. With the increasing demands for precision retention and reliability in high-end manufacturing equipment, researching reliability assessment methods for CNC gear milling machine rotary tables is of great significance for ensuring the long-term stable operation of machine tools.

[0003] The rotary table of a CNC gear milling machine is a key functional component for precision gear machining and complex surface milling. Its precise structure and high assembly requirements mean that its performance stability directly affects the overall machining accuracy and reliability of the machine. Because the rotary table operates under high load and high speed conditions for extended periods, its accuracy degradation and lifespan characteristics are influenced by multiple factors, including materials, assembly errors, and wear, making comprehensive reliability data difficult to obtain. Due to limitations such as long testing cycles, high costs, and limited sample sizes, rotary table reliability assessments often face problems of small sample sizes and significant uncertainty. To address this, some researchers have introduced reliability analysis methods based on Bayesian theory, using prior information and posterior update mechanisms to infer reliability results when samples are insufficient. However, existing prior information is mostly derived from empirical data and lacks a mechanistic model to characterize the structural characteristics and performance degradation patterns of the rotary table. Furthermore, existing methods do not fully consider the correlation between different performance indicators during the rotary table's operating stages in data fusion, making it difficult to effectively reduce the uncertainty of assessment results under conditions of small lifespan samples. Summary of the Invention

[0004] Purpose of the invention: The purpose of this invention is to provide a Bayesian-based method for predicting the reliability of turntables based on multi-source data, which can further improve the accuracy of turntable reliability assessment even when the turntable reliability data sample is small.

[0005] Technical solution: A Bayesian-based method for predicting the reliability of multi-source data from a turntable, comprising the following steps: S1, based on the composition of the turntable's motion structure, calculate the cumulative error of the turntable in different directions under the condition of geometric error of the parts at the factory; based on the assumption that the geometric error follows a normal distribution, establish a geometric error cumulative model, and consider the wear error that exists in the actual operation process, take the wear error as the influencing factor that follows a normal distribution, and construct a mechanism reliability model based on the geometric error distribution; S2, the constructed mechanism reliability model is fitted with the lifetime reliability curve under the Weibull distribution using least squares to obtain the parameter point estimates under the initial conditions, and the overall Weibull reliability model and joint prior probability density function are determined accordingly. S3. Conduct turntable accuracy degradation tests, define the accuracy degradation process as conforming to the Wiener process, and obtain a reliability model under accuracy degradation data; establish the likelihood function of lifetime data based on the overall Weibull reliability model; S4. Substitute the likelihood function and the joint prior probability density function into Bayes' formula to obtain the probability density function of the posterior distribution. S5. Based on the probability density function of the posterior distribution obtained by multi-source data fusion, MCMC sampling estimation is performed on the parameters of the mechanism reliability model to obtain the updated parameters after fusion information. The updated parameters are then substituted into the overall Weibull reliability model to obtain the reliability prediction results under different data fusion conditions.

[0006] Furthermore, the specific implementation steps for constructing a mechanism-based reliability model based on geometric error distribution are as follows: S11, divide the turntable into structural sections and define the fit of parts in different directions in each structure; Part mating methods include planar mating constraints and cylindrical mating constraints. Different degrees of freedom can be achieved through planar-cylindrical mating. The assembly process in the X direction has accumulated [resources / capabilities]. The nth plane error, let the nth... The distribution of the errors is as follows The tolerance range is ,but Orientation assembly error for: , , in, These are the directional error component coefficients, with each directional interval ranging from [0,1]. Similarly, the assembly errors in the Y and Z directions can be obtained using the above formulas. , ; Step 12: Calculate the wear model in the machining error using the Archard wear model to obtain the theoretical wear amount. : , in, The coefficient of friction, For contact stress, The relative sliding speed, The single contact time of the tooth surface. The rotational speed is, The total running time is used to obtain the wear error. ; Step 13, calculate the wear impact rate; set up express The first structure Geometric error of individual parts , , , For tooth thickness tolerance, This is the lower limit of the tooth thickness tolerance. This is the upper limit of the tooth thickness tolerance; To indicate The first structure The tooth thickness and wear error of each part are... Wear impact rate The error affected by wear error is calculated as follows: , , in, The total structural error is due to wear error. The overall accuracy of the turntable system is expressed as: ; If the accuracy of the turntable system still conforms to a Gaussian distribution, then: , in, The mean of the total Gaussian distribution is... The variance of the total Gaussian distribution is... This is the lower limit of the total accuracy tolerance. This represents the upper limit of the total precision tolerance. The reliability change over time is predicted as follows: , in, For the precision threshold, This is the initial precision value.

[0007] Furthermore, in step S2, the overall distribution type of the turntable lifetime is defined as a Weibull distribution, then the overall Weibull distribution reliability model is: , in, Let be the scale parameter of the Weibull distribution. Let be the shape parameter of the Weibull distribution; Total running time; The mechanistic reliability model is fitted to the overall Weibull reliability model, and the initial Weibull distribution parameters under the fitted model are obtained by the least squares method. The prior distribution type is assumed to be normal. , To obtain the joint prior probability density function for: , in, , scale parameters and shape parameters The prior mean, , scale parameters The variance of shape parameters.

[0008] Furthermore, in step S3, the overall distribution likelihood function is expressed as: , in, For the total sample size, For lifespan data The Middle Sample data.

[0009] Furthermore, the expression for the probability density function of the posterior distribution is as follows: , in, For lifespan data The Middle One sample data, To obtain lifetime data samples under accurate and reliable fitting, To integrate and collect samples of after-sales lifespan data.

[0010] Furthermore, MCMC estimation is performed on the posterior distribution parameters, and initial values ​​for the parameters are set. , And the number of iterations N, and determine the step size variance. , Subsequently, based on the normal distribution , Generate candidate samples and calculate the acceptance probability r; determine whether to update the parameters based on the comparison between the random number and the acceptance probability r: if the random number is less than the acceptance probability, accept the candidate sample and complete the parameter update; otherwise, retain the current sample.

[0011] Compared with the prior art, the significant advantages of this invention are as follows: 1. This invention constructs a mechanism reliability model through geometric error modeling and finite element simulation to obtain prior information on the reliability of the turntable. This significantly reduces the uncertainty in reliability assessment and improves the reliability and interpretability of the assessment when the amount of life sample data is small. 2. This invention achieves unified fusion of multi-source heterogeneous data from a turntable within a Bayesian inference framework. Combined with the Markov chain Monte Carlo evaluation method, it predicts and analyzes the lifetime reliability of the fused data. This method fully considers the uncertainties in the multi-source data fusion process, enabling the evaluation results to possess both higher stability and prediction accuracy under small sample conditions. Attached Figure Description

[0012] Figure 1 This is a flowchart of the present invention; Figure 2 A comparison chart showing the mechanism, lifetime data, and reliability prediction under fused lifetime data. Detailed Implementation

[0013] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0014] like Figure 1 The flowchart of the Bayesian-based turntable multi-source data reliability prediction method of this invention is shown below. The specific steps are as follows: Step 1: Divide the turntable according to its structural components and calculate the cumulative error in different directions of the turntable under the condition of geometric errors at the factory. Based on the assumption that the geometric error follows a normal distribution, establish a geometric error cumulative model. Consider the thermal and wear errors that may exist during actual operation in the geometric error cumulative model, introducing them as influencing factors that follow a normal distribution, thereby obtaining a mechanism-based reliability model. This includes the following steps: Step 11: Divide the turntable into structural sections and define the fit of parts in different directions within each structure; Part mating methods include planar mating constraints and cylindrical mating constraints. Different degrees of freedom can be achieved through planar-cylindrical mating, defined in the X-direction assembly process, accumulating constraints. The nth plane error, let the nth... The distribution of the errors is as follows The tolerance range is ,in Let the mean and variance of the error distribution be denoted as . , Let these be the lower and upper tolerance limits, respectively. Orientation assembly error for: (1) (2) in, It is the directional error component coefficient, with a range of [0,1] for each direction, which can be determined based on the measurement data.

[0015] Similarly, the assembly errors in the Y and Z directions can be obtained. , .

[0016] Step 12: Calculate the wear model in the machining error using the Archard wear model to obtain the theoretical wear amount. : (3) in, The coefficient of friction, For contact stress, The relative sliding speed, The single contact time of the tooth surface. The rotational speed is, This represents the total runtime.

[0017] The wear error can be obtained in the end. .

[0018] Step 13, calculate the wear impact rate; set up express The first structure Geometric error of individual parts , , , For tooth thickness tolerance, This is the lower limit of the tooth thickness tolerance. This represents the upper limit of the tooth thickness tolerance. To indicate The first structure The tooth thickness of each part and the wear effect rate The error affected by wear error can be calculated as follows: , (4) in, Structural errors affected by wear error; The overall accuracy of the turntable system is expressed as: ; If the accuracy of the turntable system still conforms to a Gaussian distribution, then the total accuracy can be expressed as: (5) in, The mean of the total Gaussian distribution is... The variance of the total Gaussian distribution is... This is the lower limit of the total accuracy tolerance. This represents the upper limit of the total precision tolerance. The reliability change over time is predicted as follows: (6) in, For the precision threshold, This is the initial precision value.

[0019] Step 2: For the constructed mechanism reliability model, perform least squares fitting on the lifetime reliability curve under the Weibull distribution to obtain the parameter point estimates under the initial conditions, and determine the prior distribution of the overall Weibull reliability model accordingly. If we define the overall distribution type of the turntable lifetime as a Weibull distribution, then the overall Weibull reliability model is: (7) in, Let be the scale parameter of the Weibull distribution. Let be the shape parameter of the Weibull distribution.

[0020] The mechanistic reliability model obtained in step 1 is fitted to the overall Weibull reliability model. The initial Weibull distribution parameters under the fitted model are obtained by the least squares method. Assume that its prior distribution type is normal, i.e. , , , scale parameters and shape parameters The prior mean, , These are the corresponding variances. The joint prior probability density function can be obtained as follows: (8) in, This represents the joint prior probability density function.

[0021] Step 3: Conduct turntable accuracy degradation tests, define the accuracy degradation process as conforming to the Wiener process, and obtain a reliability model under the accuracy degradation data: (9) in, This is the initial value for degraded precision. It is the degradation rate drift coefficient. It is the non-diffusion coefficient. The accuracy threshold is used as the basis for calculating the lifetime under different accuracy thresholds, and lifetime data samples under accuracy-reliability fitting are obtained. And integrate the collected after-sales life data samples The two types of data are merged to form a total lifetime sample set. Based on the overall Weibull reliability model, establish the likelihood function for lifetime data: (10) in, For the total sample size, For lifespan data The Middle Sample data.

[0022] Step 4: Within the Bayesian inference framework, substitute the likelihood function and the joint prior probability density function into Bayes' formula to obtain the probability density function of the posterior distribution: (11) As can be seen from the posterior probability density function, the unknowns in the posterior distribution include the Weibull distribution parameters of the overall Weibull reliability model. , .

[0023] Step 5: Based on the probability density function of the posterior distribution obtained from multi-source data fusion, perform MCMC (Markov Chain Monte Carlo Method) sampling estimation on the parameters of the mechanism reliability model to obtain the updated parameters after fusion. Further, substitute the updated parameters into formula (7) of the Weibull reliability model to obtain the reliability prediction results under different data fusion conditions.

[0024] MCMC estimation is performed on the posterior distribution parameters, and the parameters to be estimated have been identified in step 4. , And variable lifetime time t, set initial values ​​for design parameters. , And the number of iterations N, and determine the step size variance. , Subsequently, based on the normal distribution , Generate candidate samples and calculate the acceptance probability r. Based on the comparison between the random number and the acceptance probability r, determine whether to update the parameters: if the random number is less than the acceptance probability, accept the candidate sample and update the parameters; otherwise, retain the current sample. Repeat the iteration until convergence, discarding the early samples as the burning period, retaining the posterior samples, and calculating the parameter estimates.

[0025] A computer-readable storage medium stores a computer program thereon, which, when executed by a processor, implements the turntable multi-source data reliability prediction method of the present invention. The processor contains a kernel that retrieves the corresponding program unit from memory.

[0026] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is executed, it implements the steps of the turntable multi-source data reliability prediction method of the present invention.

[0027] The memory may include non-permanent memory in computer-readable media, such as random access memory (RAM) and / or non-volatile memory, such as read-only memory (ROM) or flash RAM, and the memory includes at least one memory chip.

[0028] A computer program product includes a computer program / instructions that, when executed by a processor, implement the steps of the turntable multi-source data reliability prediction method of the present invention.

[0029] The modules or steps of the present invention described above can be implemented using general-purpose computing devices. They can be centralized on a single computing device or distributed across a network of multiple computing devices. They can be implemented using computer-executable program code, and thus can be stored in a storage device for execution by a computing device. In some cases, the steps shown or described can be performed in a different order than those described herein, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. Thus, the present invention is not limited to any particular hardware and software combination.

[0030] Embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, this application may take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention may be implemented as a computer program product on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0031] In this embodiment, taking the acquisition of data on the three main motion structures of the turntable—gear transmission, worm gear transmission, and table rotation—as an example, the specific implementation steps are as follows: Step F1: Based on the design drawings and product specifications, the turntable is structurally divided, and the tolerance range and distribution parameters of each structural component are confirmed. Through calculation, the overall assembly accuracy index of the turntable is obtained as follows: , corresponding distribution interval Based on the material parameters, speed, and torque of the worm gear pair, the wear error of the turntable system is calculated to be... .

[0032] Step F2: For the constructed accuracy reliability model, under the lifetime reliability model of the Weibull distribution, complete the curve fitting, obtain the point estimate under the initial conditions, and determine the prior distribution value under the overall Weibull lifetime reliability model. Using the Weibull distribution as the reliability model for the turntable lifetime, the reliability curve of the mechanism model is fitted using the least squares method to obtain the prior distribution of the Weibull distribution: , Its prior probability density function can be expressed as: .

[0033] Step F3: Conduct a turntable accuracy degradation test to obtain lifetime data samples under different thresholds and parameter assumptions, and combine them with the collected lifetime data of the same model products, based on the likelihood function under the overall Weibull distribution of the turntable lifetime. Based on the results of the turntable accuracy reliability test, the change in indexing accuracy of the turntable over time was measured under 750 hours of operation. Based on the measurement results, the Wiener process was used to model the accuracy degradation process, and the parameters under the Wiener process were obtained. By setting different thresholds, approximate lifetime data under specific precision threshold conditions can be derived. Collect sample lifetime data By combining the lifetime data obtained from the experiment with the lifetime data collected from after-sales samples, a complete lifetime sample set is formed, and a likelihood function for the lifetime samples is established under the Weibull distribution assumption: .

[0034] Step F4: Within the Bayesian inference framework, substitute the probability density function and likelihood function of the prior distribution into the Bayes formula. After normalization, the probability density function of the posterior distribution can be obtained. Further analysis can determine the type of posterior distribution and its corresponding parameters. Based on the established prior distribution and the likelihood function of the lifetime samples, Bayesian inference is performed on the model parameters to obtain the posterior distribution function: .

[0035] Step F5: Based on the posterior distribution of reliability parameters under fused multi-source data, perform MCMC parameter estimation on the overall distribution to obtain reliability prediction results under different data.

[0036] In the MATLAB software environment, Markov chain Monte Carlo estimation is performed on the posterior distribution parameters. The parameters to be estimated are: Known lifetime time sample Set the initial value of the parameter and number of iterations And determine the step size variance The posterior distribution of the parameters after obtaining the MCMC estimate is as follows: Substituting the obtained parameters into the reliability function of the Weibull distribution yields the corresponding reliability prediction curve. For example... Figure 2 As shown, this paper presents a comparison of reliability change trends after mechanistic model prediction, accuracy model prediction (i.e., lifetime data prediction based on accuracy degradation), and fusion of multi-source data.

Claims

1. A Bayesian-based method for predicting the reliability of multi-source data from a turntable, characterized in that, Includes the following steps: S1, based on the composition of the turntable's motion structure, calculates the cumulative error of the turntable in different directions under the condition of the geometric error of the parts at the factory. Based on the assumption that geometric errors follow a normal distribution, a geometric error accumulation model is established. Considering the wear error that exists in actual operation, the wear error is used as an influencing factor that follows a normal distribution to construct a mechanism reliability model based on the geometric error distribution. S2, the constructed mechanism reliability model is fitted with the lifetime reliability curve under the Weibull distribution using least squares to obtain the parameter point estimates under the initial conditions, and to determine the overall Weibull reliability model and the joint prior probability density function; S3. Conduct turntable accuracy degradation tests, define the accuracy degradation process as conforming to the Wiener process, and obtain a reliability model under accuracy degradation data; establish the likelihood function of lifetime data based on the overall Weibull reliability model; S4. Substitute the likelihood function and the joint prior probability density function into Bayes' formula to obtain the probability density function of the posterior distribution. S5. Based on the probability density function of the posterior distribution obtained by multi-source data fusion, MCMC sampling estimation is performed on the parameters of the mechanism reliability model to obtain the updated parameters after fusion information. The updated parameters are then substituted into the overall Weibull reliability model to obtain the reliability prediction results under different data fusion conditions.

2. The Bayesian-based multi-source data reliability prediction method for turntables according to claim 1, characterized in that, The specific implementation steps for constructing a mechanism-based reliability model based on geometric error distribution are as follows: S11, divide the turntable into structural sections and define the fit of parts in different directions in each structure; Part mating methods include planar mating constraints and cylindrical mating constraints. Different degrees of freedom can be achieved through planar-cylindrical mating. The assembly process in the X direction has accumulated [resources / capabilities]. The nth plane error, let the nth... The distribution of the errors is as follows The tolerance range is ,but Orientation assembly error for: in, These are the directional error component coefficients, with each directional interval ranging from [0,1]. Similarly, the assembly errors in the Y and Z directions can be obtained using the above formulas. , ; Step 12: Calculate the wear model in the machining error using the Archard wear model to obtain the theoretical wear amount. : in, The coefficient of friction, For contact stress, The relative sliding speed, The single contact time of the tooth surface. The rotational speed is, The total running time is used to obtain the wear error. ; Step 13, calculate the wear impact rate; set up express The first structure Geometric error of individual parts , , , For tooth thickness tolerance, This is the lower limit of the tooth thickness tolerance. This is the upper limit of the tooth thickness tolerance; To indicate The first structure The tooth thickness and wear error of each part are... Wear impact rate The error affected by wear error is calculated as follows: ， ， in, Structural errors affected by wear error; The overall accuracy of the turntable system is expressed as: ; If the accuracy of the turntable system still conforms to a Gaussian distribution, then: in, The mean of the total Gaussian distribution is... The variance of the total Gaussian distribution is... This is the lower limit of the total accuracy tolerance. This represents the upper limit of the total precision tolerance. The reliability change over time is predicted as follows: in, For the precision threshold, This is the initial precision value.

3. The Bayesian-based turntable multi-source data reliability prediction method according to claim 1, characterized in that, In step S2, the overall distribution type of the turntable lifetime is defined as the Weibull distribution. Therefore, the overall Weibull distribution reliability model is: in, Let be the scale parameter of the Weibull distribution. Let be the shape parameter of the Weibull distribution; Total running time; The mechanistic reliability model is fitted to the overall Weibull reliability model, and the initial Weibull distribution parameters under the fitted model are obtained by the least squares method. The prior distribution type is assumed to be normal. , To obtain the joint prior probability density function for: in, , scale parameters and shape parameters The prior mean, , scale parameters and shape parameters The variance.

4. The Bayesian-based multi-source data reliability prediction method for turntables according to claim 3, characterized in that, In step S3, the overall distribution likelihood function is expressed as: in, For the total sample size, For lifespan data The Middle One sample data, To obtain lifetime data samples under accurate and reliable fitting, To integrate and collect samples of after-sales lifespan data.

5. The Bayesian-based multi-source data reliability prediction method for turntables according to claim 3, characterized in that, The probability density function of the posterior distribution is expressed as follows: in, For lifespan data The Middle Sample data.

6. The Bayesian-based turntable multi-source data reliability prediction method according to claim 3, characterized in that, Perform MCMC estimation on the posterior distribution parameters and set initial parameter values. , And the number of iterations N, and determine the step size variance. , Subsequently, based on the normal distribution , Generate candidate samples and calculate the acceptance probability r; determine whether to update the parameters based on the comparison between the random number and the acceptance probability r: if the random number is less than the acceptance probability, accept the candidate sample and complete the parameter update; otherwise, retain the current sample.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the method as described in any one of claims 1 to 6.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the computer program is executed, it implements the steps of the method as described in any one of claims 1 to 5.

9. A computer program product, comprising a computer program / instructions, characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the method according to any one of claims 1 to 6.

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