Adaptive optimization method for precision component numerical control machining parameters

Abstract

The application provides a precision component numerical control machining parameter self-adaptive optimization method, the method comprises the following steps: delimiting a continuous feasible space of multiple machining parameters, and initializing a continuous probability density function for each machining parameter; generating a discrete sampling level dynamically according to the current probability density function, combining with an orthogonal table to construct a candidate parameter combination, forming an actual machining test group after safety constraint verification, and obtaining a multi-dimensional machining quality index; performing non-dominated sorting on the multi-dimensional index, calculating the Pareto expected value of each sampling level according to the reciprocal fitness of the Pareto level, and updating the probability density function accordingly; cyclically executing sampling, testing, sorting and probability updating until the convergence condition is met or the maximum iteration number is reached; constructing a multi-objective proxy model based on the test data, and solving by a multi-objective evolutionary algorithm, and outputting a Pareto optimal machining parameter combination considering multiple machining quality indexes.

Description

Technical Field

[0001] This application belongs to the field of optimization, and in particular relates to an adaptive optimization method for CNC machining parameters of precision components. Background Technology

[0002] In modern industrial manufacturing, the machining quality of precision components is typically influenced by multiple machining parameters, such as spindle speed, feed rate, and depth of cut. These parameters are mostly continuous and are subject to multi-dimensional constraints during actual production, including machine tool power, tool stress, and machining safety boundaries, creating a complex operational space. Furthermore, machining quality evaluation usually requires comprehensive consideration of multiple performance indicators, such as surface roughness, machining efficiency, and resource consumption. These different indicators often have interdependent relationships; improving one indicator may lead to the deterioration of others. Traditional parameter setting methods, relying on engineering experience or basic experimental adjustments, struggle to fully cover the effective feasible area and accurately characterize the trade-offs between different performance indicators when facing machining scenarios with continuous parameter spaces, multiple constraints, and multiple evaluation objectives. This makes it difficult to achieve a comprehensive optimization effect that balances quality, efficiency, and energy consumption when setting machining parameters.

[0003] To address the aforementioned multi-objective parameter optimization needs, existing parameter optimization strategies largely rely on pre-set static discrete sampling points for experimental deployment, making it difficult to dynamically adjust subsequent parameter values ​​in key areas based on feedback from preceding experiments. Within a continuous and constrained parameter space, simply relying on static discretization for large-scale sampling easily increases the number of experiments, thereby raising time, material, and equipment costs, and potentially consuming significant experimental resources in low-value parameter regions. Some conventional algorithm optimization schemes, lacking high-quality representative experimental data in the early stages, struggle to reliably fit the nonlinear mapping relationship between processing parameters and multi-dimensional performance indicators, and the optimization process is easily affected by the distribution of samples in local areas. Therefore, there is an urgent need for a parameter optimization mechanism that can adaptively adjust the parameter probability distribution based on multi-indicator processing evaluation results while controlling actual processing experiment costs, and establish a global evaluation model based on experimental data, to output an optimized parameter combination that can accommodate multiple processing requirements. Summary of the Invention

[0004] To address the problems in existing technologies, such as the influence of multidimensional constraints on continuous machining parameters, the difficulty in adjusting key areas based on experimental feedback during static sampling, and the difficulty in accurately modeling the trade-offs between multiple objective performance indicators, leading to high experimental costs, low optimization efficiency, and difficulty in balancing machining quality and production efficiency in parameter combinations, this invention provides, in a first aspect, an adaptive optimization method for CNC machining parameters of precision components, comprising the following steps:

[0005] The continuous value range of a preset number of processing parameters is determined and the feasible space is defined by a multidimensional constraint function. An initial continuous probability density function is set for each processing parameter. Multiple discrete sampling levels are dynamically discretized according to the current probability density function and candidate parameter combinations are constructed by combining them with an orthogonal table. After the candidate parameter combinations are verified by safety constraints, a test group for actual processing is formed. Actual processing operations are performed on the test group to obtain multidimensional performance indicators representing processing quality. The multidimensional index set composed of multidimensional performance indicators is subjected to non-dominated ranking processing, and corresponding Pareto levels are assigned to each experimental group. The Pareto expected value of each processing parameter at different sampling levels is calculated. The Pareto expected value is specifically determined by the average value of the inverse fitness of the Pareto levels in which the processing parameter participates in the experiment. The Pareto expected value is used as evidence to perform Bayesian update on the current probability density function and generate a posterior probability density function. Based on the generated posterior probability density function, the iterative steps of dynamically discretizing to generate sampling levels and generating the posterior probability density function are repeatedly executed until the algorithm model reaches a convergent state or reaches the preset maximum number of iterations. The experimental dataset after the iteration is completed is obtained. The experimental dataset is used to construct a multi-objective Gaussian process surrogate model group as the fitness function, and the Pareto optimal solution set is output as the parameter combination by global optimization using a multi-objective evolution algorithm.

[0006] Optionally, determining the continuous value range of a preset number of processing parameters and defining the feasible space through a multidimensional constraint function includes: Extract the spindle speed, feed rate and depth of cut of the machine tool as machining parameters, and set the physical limit threshold of each machining parameter to form a continuous range of values; Based on the maximum power limit of the machine tool spindle motor and the allowable cutting force of the tool, a multidimensional constraint function including spindle load constraint and tool force constraint is established. By inputting the continuous range of values ​​into the multidimensional constraint function, parameter regions that violate spindle load constraints or tool force constraints are removed, generating a feasible space that meets safe machining conditions.

[0007] Optionally, setting an initial continuous probability density function for each processing parameter includes: The initial continuous probability density function of each processing parameter is set as a Gaussian mixture model consisting of three independent Gaussian branches; Assign equal initial weights to the three Gaussian branches, and set the expected values ​​of the branches to the 15%, 50%, and 85% quantiles of the continuous range of the corresponding processing parameters, respectively. The standard deviation of each branch is initialized to one-tenth of the range of the corresponding processing parameter values.

[0008] Optionally, the step of dynamically discretizing the current probability density function to generate multiple discrete sampling levels and constructing candidate parameter combinations using orthogonal arrays, and then performing safety constraint verification on the candidate parameter combinations to form an experimental group actually used for processing, includes: Based on the cumulative distribution function of the current probability density function, the feasible space of each processing parameter is divided into multiple discrete sampling intervals using the equal probability interval division method. Extract the peak points of probability density for each sampling interval as representative values ​​for the corresponding sampling level; Substitute the representative values ​​of each processing parameter into a preset multi-level orthogonal array matrix to generate an initial parameter combination; The initial parameter combination is overload-checked by a multidimensional constraint function. Parameter combinations that do not meet the safety conditions are identified as unexecutable candidate combinations and excluded from the actual processing test group. Alternative parameter combinations that satisfy the multidimensional constraint function are regenerated according to the horizontal numbering combination of the corresponding orthogonal table row. The initial parameter combination that meets the safety conditions and the alternative parameter combination are used as the test group for actually performing the processing.

[0009] Optionally, the calculation of the Pareto expected value of each processing parameter at different sampling levels, wherein the Pareto expected value is specifically determined by calculating the average value of the inverse fitness of the Pareto levels in which the processing parameters participate in the experiment, includes: Extract the Pareto levels of all experimental groups participating in the current processing parameters at a specific sampling level; The reciprocal of the Pareto level is used as the fitness score for each experimental group; The average fitness is calculated by taking the arithmetic mean of the fitness scores of all experimental groups participating under the current processing parameters at a specific sampling level. The average fitness is normalized and used as the Pareto expectation of the processing parameter at the sampling level.

[0010] Optionally, the step of performing a Bayesian update on the current probability density function and generating a posterior probability density function based on the Pareto expectation value includes: The Pareto expectation values ​​of each sampling level are mapped to a continuous space using interpolation methods, thus constructing a non-negative update weight function; According to the Bayesian update form, the continuous probability density function of the current iteration is multiplied by the non-negative update weight function to calculate the non-normalized posterior distribution. The Markov chain Monte Carlo method is used to resample the non-normalized posterior distribution to extract high-probability sample points. The weights, expected values, and variances of a Gaussian mixture model are refitted based on high-probability sample points using the expectation-maximization algorithm, and the posterior probability density function is output.

[0011] Optionally, the step of constructing a multi-objective Gaussian process surrogate model set using the experimental dataset as the fitness function, and employing a multi-objective evolutionary algorithm to globally optimize and output the Pareto optimal solution set as the parameter combination, includes: After unifying the multidimensional performance indicators into a minimization objective, the predicted mean of the multi-objective Gaussian process surrogate model group is used as the fitness function of the multi-objective evolution algorithm. Randomly initialize the population within the feasible space, and perform selection, crossover, and mutation operations to generate offspring populations; After merging the parent and offspring populations, the results are input into the fitness function to obtain predicted performance index values, and environmental selection is performed based on non-dominated ranking and crowding distance. After the iteration reaches the maximum number of generations, the evolution stops, and the non-dominated solution set in the population is extracted as the Pareto optimal solution set and output.

[0012] On the other hand, the present invention also provides an adaptive optimization system for CNC machining parameters of precision components, comprising the following modules: The acquisition module is used to determine the continuous value range of a preset number of processing parameters and delineate the feasible space through a multidimensional constraint function. It sets an initial continuous probability density function for each processing parameter, dynamically discretizes and generates multiple discrete sampling levels based on the current probability density function, and constructs candidate parameter combinations by combining them with an orthogonal table. After verifying the candidate parameter combinations with safety constraints, it forms a test group for actual processing. It performs actual processing operations on the test group to obtain multidimensional performance indicators representing processing quality. The calculation module is used to perform non-dominated ranking processing on the multidimensional index set composed of multidimensional performance indicators, assign corresponding Pareto levels to each experimental group, calculate the Pareto expected value of each processing parameter at different sampling levels, and the Pareto expected value is specifically determined by the average value of the inverse fitness of the Pareto levels in which the processing parameter participates in the experiment. The Pareto expected value is used as evidence to perform Bayesian update on the current probability density function and generate a posterior probability density function. The output module is used to repeatedly execute the iterative steps of dynamically discretizing to generate sampling levels and generate the posterior probability density function based on the generated posterior probability density function until the algorithm model reaches the convergence state or reaches the preset maximum number of iterations. After the iteration ends, the experimental dataset is obtained. The experimental dataset is used to construct a multi-objective Gaussian process surrogate model group as the fitness function, and the multi-objective evolution algorithm is used to globally optimize and output the Pareto optimal solution set as the parameter combination.

[0013] Preferably, determining the continuous value range of a preset number of processing parameters and defining the feasible space through a multidimensional constraint function includes: Extract the spindle speed, feed rate and depth of cut of the machine tool as machining parameters, and set the physical limit threshold of each machining parameter to form a continuous range of values; Based on the maximum power limit of the machine tool spindle motor and the allowable cutting force of the tool, a multidimensional constraint function including spindle load constraint and tool force constraint is established. By inputting the continuous range of values ​​into the multidimensional constraint function, parameter regions that violate spindle load constraints or tool force constraints are removed, generating a feasible space that meets safe machining conditions.

[0014] Preferably, setting an initial continuous probability density function for each processing parameter includes: The initial continuous probability density function of each processing parameter is set as a Gaussian mixture model consisting of three independent Gaussian branches; Assign equal initial weights to the three Gaussian branches, and set the expected values ​​of the branches to the 15%, 50%, and 85% quantiles of the continuous range of the corresponding processing parameters, respectively. The standard deviation of each branch is initialized to one-tenth of the range of the corresponding processing parameter values.

[0015] Preferably, the step of dynamically discretizing the current probability density function to generate multiple discrete sampling levels and constructing candidate parameter combinations using an orthogonal array, and then performing safety constraint verification on the candidate parameter combinations to form an experimental group actually used for processing, includes: Based on the cumulative distribution function of the current probability density function, the feasible space of each processing parameter is divided into multiple discrete sampling intervals using the equal probability interval division method. Extract the peak points of probability density for each sampling interval as representative values ​​for the corresponding sampling level; Substitute the representative values ​​of each processing parameter into a preset multi-level orthogonal array matrix to generate an initial parameter combination; The initial parameter combination is overload-checked by a multidimensional constraint function. Parameter combinations that do not meet the safety conditions are identified as unexecutable candidate combinations and excluded from the actual processing test group. Alternative parameter combinations that satisfy the multidimensional constraint function are regenerated according to the horizontal numbering combination of the corresponding orthogonal table row. The initial parameter combination that meets the safety conditions and the alternative parameter combination are used as the test group for actually performing the processing.

[0016] Preferably, the calculation of the Pareto expected value of each processing parameter at different sampling levels, wherein the Pareto expected value is specifically determined by calculating the average value of the inverse fitness of the Pareto levels in which the processing parameters participate in the experiment, includes: Extract the Pareto levels of all experimental groups participating in the current processing parameters at a specific sampling level; The reciprocal of the Pareto level is used as the fitness score for each experimental group; The average fitness is calculated by taking the arithmetic mean of the fitness scores of all experimental groups participating under the current processing parameters at a specific sampling level. The average fitness is normalized and used as the Pareto expectation of the processing parameter at the sampling level.

[0017] Preferably, the step of performing a Bayesian update on the current probability density function and generating a posterior probability density function based on the Pareto expectation value includes: The Pareto expectation values ​​of each sampling level are mapped to a continuous space using interpolation methods, thus constructing a non-negative update weight function; According to the Bayesian update form, the continuous probability density function of the current iteration is multiplied by the non-negative update weight function to calculate the non-normalized posterior distribution. The Markov chain Monte Carlo method is used to resample the non-normalized posterior distribution to extract high-probability sample points. The weights, expected values, and variances of a Gaussian mixture model are refitted based on high-probability sample points using the expectation-maximization algorithm, and the posterior probability density function is output.

[0018] Preferably, the step of constructing a multi-objective Gaussian process surrogate model set using the experimental dataset as the fitness function, and employing a multi-objective evolutionary algorithm to globally optimize and output the Pareto optimal solution set as the parameter combination, includes: After unifying the multidimensional performance indicators into a minimization objective, the predicted mean of the multi-objective Gaussian process surrogate model group is used as the fitness function of the multi-objective evolution algorithm. Randomly initialize the population within the feasible space, and perform selection, crossover, and mutation operations to generate offspring populations; After merging the parent and offspring populations, the results are input into the fitness function to obtain predicted performance index values, and environmental selection is performed based on non-dominated ranking and crowding distance. After the iteration reaches the maximum number of generations, the evolution stops, and the non-dominated solution set in the population is extracted as the Pareto optimal solution set and output.

[0019] This invention reduces experimental costs associated with ineffective parameter combinations and improves sample coverage by defining a continuous feasible space for processing parameters and generating candidate test groups based on probability density functions and orthogonal arrays. Pareto levels are obtained through non-dominated sorting, and parameter probability distributions are updated based on Pareto expectations, guiding subsequent experiments towards regions with superior overall performance and improving multi-objective optimization efficiency. Furthermore, a multi-objective surrogate model is constructed using iterative experimental data, and combined with a multi-objective evolutionary algorithm for optimization. This model characterizes the nonlinear relationship between processing parameters and quality indicators, outputting Pareto parameter combinations that balance surface quality, processing efficiency, and resource consumption, thereby improving the effectiveness of processing parameter configuration. Attached Figure Description

[0020] Figure 1 A flowchart of the first embodiment; Figure 2 This is a schematic diagram of the feasible region for processing parameters. Detailed Implementation

[0021] It should be understood that, when used in this application specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or a collection thereof.

[0022] It should also be understood that the term “and / or” as used in this application specification and the appended claims means any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0023] In the description of this application and the appended claims, the terms "first," "second," "third," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0024] References to "one embodiment" or "some embodiments" as described in this application specification mean that one or more embodiments of this application include a specific feature, structure, or characteristic described in connection with that embodiment. Therefore, the phrases "in one embodiment," "in some embodiments," "in another embodiment," "in yet another embodiment," etc., appearing in different parts of this application specification do not necessarily refer to the same embodiment, but rather mean "one or more, but not all, embodiments," unless otherwise specifically emphasized. The terms "comprising," "including," "having," and variations thereof all mean "including but not limited to," unless otherwise specifically emphasized.

[0025] In the first embodiment, the present invention proposes an adaptive optimization method for CNC machining parameters of precision components, such as... Figure 1As shown, it includes the following steps: S1. Determine the continuous value range of a preset number of processing parameters and define the feasible space through a multidimensional constraint function. Set an initial continuous probability density function for each processing parameter. Dynamically discretize and generate multiple discrete sampling levels based on the current probability density function and construct candidate parameter combinations by combining them with an orthogonal table. After verifying the candidate parameter combinations with safety constraints, form a test group for actual processing. Perform actual processing operations on the test group to obtain multidimensional performance indicators representing processing quality.

[0026] Based on CNC machine tool manuals and expert experience, the maximum and minimum values ​​of spindle speed, feed rate and depth of cut are set as a continuous range. Inequality constraint equations of cutting force and cutting power are established to form a multidimensional constraint function. A grid search algorithm is used to remove regions that violate the multidimensional constraint function within the continuous range to delineate the feasible space.

[0027] A Gaussian mixture model consisting of multiple Gaussian branches is established as the initial continuous probability density function for each processing parameter. The quantile nodes corresponding to the equal-area intervals under the current probability density function are calculated using the equal-probability area partitioning method and the percentile function. The probability density peak points within each equal-probability interval are extracted as discrete sampling levels generated through dynamic discretization. A preset orthogonal array is invoked, and an orthogonal matrix is ​​determined based on the processing parameter dimension and the number of sampling levels. The elements of the orthogonal matrix are mapped to specific sampling levels, generating multiple sets of candidate parameter combinations within the feasible space. These candidate parameter combinations are verified using multi-dimensional constraint functions. The candidate parameter combinations that meet the safe processing conditions are determined as the actual test group. The test group is sent to the machine tool for actual processing via the CNC system communication interface. Processing data is collected using a built-in power sensor and an external surface roughness measuring instrument. After signal filtering and analog-to-digital conversion, material removal rate, processing energy consumption, and surface roughness are calculated as multi-dimensional performance indicators reflecting processing quality.

[0028] In an optional embodiment, determining the continuous value range of a preset number of processing parameters and defining the feasible space through a multidimensional constraint function includes: Extract the spindle speed, feed rate and depth of cut of the machine tool as machining parameters, and set the physical limit threshold of each machining parameter to form a continuous range of values; Based on the maximum power limit of the machine tool spindle motor and the allowable cutting force of the tool, a multidimensional constraint function including spindle load constraint and tool force constraint is established. By inputting the continuous range of values ​​into the multidimensional constraint function, parameter regions that violate spindle load constraints or tool force constraints are removed, generating a feasible space that meets safe machining conditions.

[0029] Taking a typical CNC milling operation as an example, the continuous range of spindle speed is set to [1000, 8000] r / min, the continuous range of feed rate is set to [100, 2000] mm / min, and the continuous range of depth of cut is set to [0.1, 4.0] mm. To ensure the safety of the machine tool and cutting tool, the maximum effective power of the machine tool spindle motor is obtained, for example... =15kW, and the maximum allowable cutting force of the carbide cutting tool used, for example =2500N. A multidimensional constraint function is constructed based on empirical formulas or mechanistic models, and the main cutting force is expressed as... Cutting power is expressed as ,in, Let n be the depth of cut, n be the spindle speed, D be the tool diameter, and f be the feed rate. The calculated feed per revolution and f= / n; , , These are empirical coefficients obtained based on material and tool calibration. This is a correction factor.

[0030] During the feasible space delineation stage, parameter mesh points are generated within the aforementioned continuous value range according to a set step size. For example, the spindle speed step size is 100 r / min, the feed rate step size is 50 mm / min, and the depth of cut step size is 0.1 mm. All mesh points are then input into a multidimensional constraint function for individual verification. All power overload regions exceeding 15 kW and stress over-limit regions exceeding 2500 N are removed. The remaining parameter boundaries and mesh sets constitute a safe machining feasible space with nonlinear boundaries. A schematic diagram of the machining parameter feasible domain is shown below. Figure 2 As shown.

[0031] In an optional embodiment, setting an initial continuous probability density function for each processing parameter includes: The initial continuous probability density function of each processing parameter is set as a Gaussian mixture model consisting of three independent Gaussian branches; Assign equal initial weights to the three Gaussian branches, and set the expected values ​​of the branches to the 15%, 50%, and 85% quantiles of the continuous range of the corresponding processing parameters, respectively. The standard deviation of each branch is initialized to one-tenth of the range of the corresponding processing parameter values.

[0032] For each defined processing parameter, a Gaussian mixture model (GMM) with three independent components is initialized as the continuous probability density function of the parameter. The three branches respectively cover the low, medium, and high value regions of the parameter space, and the same initial weight coefficient is uniformly assigned to each branch. = = =1 / 3. Taking the cutting depth parameter as an example, assuming the value range is [0.1, 4.0] mm, that is, the value span L = 3.9 mm, calculate the corresponding quantile.

[0033] According to the above rules, the expected value of the first Gaussian branch of the cutting depth is set to the low quantile. =0.685mm; the expected value of the second branch is set at the median point. =2.05mm; the expected value of the third branch is set at the high quantile. =3.415mm. The standard deviation of each branch is uniformly set to 10% of the span, i.e. = = =0.39mm. By setting this Gaussian distribution, the algorithm can cover the boundary and central regions of the parameter space during the first round of sampling, reducing the risk of the optimization process prematurely focusing on local areas.

[0034] In an optional embodiment, the step of dynamically discretizing multiple discrete sampling levels based on the current probability density function and constructing candidate parameter combinations using an orthogonal array, and then performing safety constraint verification on the candidate parameter combinations to form an experimental group actually used for processing, includes: Based on the cumulative distribution function of the current probability density function, the feasible space of each processing parameter is divided into multiple discrete sampling intervals using the equal probability interval division method. Extract the peak points of probability density for each sampling interval as representative values ​​for the corresponding sampling level; Substitute the representative values ​​of each processing parameter into a preset multi-level orthogonal array matrix to generate an initial parameter combination; The initial parameter combination is overload-checked by a multidimensional constraint function. Parameter combinations that do not meet the safety conditions are identified as unexecutable candidate combinations and excluded from the actual processing test group. Alternative parameter combinations that satisfy the multidimensional constraint function are regenerated according to the horizontal numbering combination of the corresponding orthogonal table row. The initial parameter combination that meets the safety conditions and the alternative parameter combination are used as the test group for actually performing the processing.

[0035] If five sampling levels are required, the cumulative distribution function (CDF) of the Gaussian mixture model is used to divide the probability space [0,1] into five equal intervals: [0,0.2), [0.2,0.4), [0.4,0.6), [0.6,0.8), and [0.8,1.0]. The actual machining parameter values ​​corresponding to each probability boundary are calculated using numerical inversion. This divides the continuous parameter space into five equally probable sampling intervals. The extreme values ​​of the probability density function within each interval are then calculated, and the parameter coordinates with the highest probability are extracted as the representative value for that level. For example, five representative levels for spindle speeds are generated as 2100, 3400, 4500, 5600, and 7100 r / min. When multiple local peak points exist within a single equally probable interval, the peak point with the highest probability density value is selected as the representative value for that interval.

[0036] The representative values ​​extracted from all processing parameters are filled into a standard orthogonal array, for example. In the corresponding columns of the orthogonal matrix, when only three machining parameters—spindle speed, feed rate, and depth of cut—are involved in this embodiment, the first three columns of the orthogonal matrix corresponding to the three machining parameters are selected to generate 25 initial candidate parameter combinations, and the remaining columns are not involved in the generation of this parameter combination.

[0037] To ensure safety during actual machining, constraint boundary checks were performed on 25 candidate parameter combinations. If a parameter combination exceeded the spindle power threshold or tool force threshold, it was marked as an unexecutable candidate combination and not sent to the machine tool for machining, nor included in the multidimensional performance index set, non-dominated sorting, Pareto expectation value calculation, or surrogate model training dataset. For the excluded candidate parameter combinations, parameter values ​​were reselected within the corresponding sampling level interval and checked again to generate alternative parameter combinations that satisfy the multidimensional constraint function. The checked parameter combinations and alternative parameter combinations were transmitted to the machine tool CNC system and used as the test group to perform cutting to obtain multidimensional performance index data.

[0038] S2, perform non-dominated sorting on the multidimensional index set composed of multidimensional performance indicators, assign corresponding Pareto levels to each experimental group, calculate the Pareto expected value of each processing parameter at different sampling levels, the Pareto expected value is specifically determined by the average value of the inverse fitness of the Pareto levels in which the processing parameter participates in the experiment, and use the Pareto expected value as evidence to perform Bayesian update on the current probability density function and generate a posterior probability density function.

[0039] A fast non-dominated sorting algorithm is applied to the multidimensional index set. Before performing the non-dominated sorting, the multidimensional performance indices are unified to the same optimization direction. The material removal rate that needs to be maximized is converted into a minimization objective by taking the opposite value, while the processing energy consumption and surface roughness are retained as minimization objectives. The dominance relationship is then determined by comparing the values ​​of the converted material removal rate, processing energy consumption, and surface roughness of any two experimental groups.

[0040] Based on the dominance relationship, the experimental groups are divided into multiple disjoint sets, and each experimental group is assigned a Pareto level increasing sequentially from 1. The Pareto level values ​​of all experimental groups corresponding to each processing parameter at a specific sampling level are extracted. The reciprocal of the Pareto level number is used as the fitness score, and the fitness score is arithmetically averaged and normalized to obtain the Pareto expectation value of the processing parameter at that sampling level. A Bayesian distribution update model based on the Markov chain Monte Carlo method is constructed. The Pareto expectation value is interpolated to generate a non-negative update weight function. A non-normalized posterior distribution is formed by multiplying the current probability density function with the non-negative update weight function. The Metropolis-Hastings sampling algorithm is used to resample the non-normalized posterior distribution, making the subsequent sampling region tend towards the parameter space with a better Pareto level, thereby generating an updated posterior probability density function.

[0041] In an optional embodiment, the calculation of the Pareto expected value of each processing parameter at different sampling levels, specifically determined by the average of the inverse fitness of the Pareto levels in which the processing parameters participate in the experiment, includes: Extract the Pareto levels of all experimental groups participating in the current processing parameters at a specific sampling level; The reciprocal of the Pareto level is used as the fitness score for each experimental group; The average fitness is calculated by taking the arithmetic mean of the fitness scores of all experimental groups participating under the current processing parameters at a specific sampling level. The average fitness is normalized and used as the Pareto expectation of the processing parameter at the sampling level.

[0042] In multidimensional performance evaluation, non-dominated ranking assigns all samples obtained from orthogonal experiments to different Pareto levels (Rank). A smaller Rank value indicates better overall machining performance, where Rank=1 represents the current non-dominated frontier. Taking the spindle speed in the orthogonal table at the second sampling level as an example, assuming this level appears in 5 different experimental groups, the Pareto levels assigned to these 5 groups by non-dominated ranking are Rank=1, 3, 2, 4, 1, respectively. The fitness scores of these 5 experimental groups are calculated by taking the reciprocal, and mapped to... =1.0, =0.33, =0.5, =0.25, =1.0.

[0043] The sum of the five fitness scores is 3.08, which, divided by the number of test groups (5), yields an average fitness of 0.616 for the spindle speed at the second sampling level. After calculating the average fitness for each of the five sampling levels of this spindle speed, assuming the values ​​are 0.42, 0.616, 0.85, 0.55, and 0.30 respectively, a summation normalization strategy is applied to the five average fitness results, dividing each average fitness by the sum of these five values ​​(2.736). The output Pareto expectation value for the second level of the spindle speed is 0.225, falling between [0,1], representing the potential of this machining parameter to guide the machining process closer to a Pareto optimum at this specific value.

[0044] In an optional embodiment, the step of performing a Bayesian update on the current probability density function based on Pareto expectation and generating a posterior probability density function includes: The Pareto expectation values ​​of each sampling level are mapped to a continuous space using interpolation methods, thus constructing a non-negative update weight function; According to the Bayesian update form, the continuous probability density function of the current iteration is multiplied by the non-negative update weight function to calculate the non-normalized posterior distribution. The Markov chain Monte Carlo method is used to resample the non-normalized posterior distribution to extract high-probability sample points. The weights, expected values, and variances of a Gaussian mixture model are refitted based on high-probability sample points using the expectation-maximization algorithm, and the posterior probability density function is output.

[0045] A cubic spline interpolation algorithm is employed, using discrete sampling level values ​​as the x-axis and the Pareto expectation calculated for each sampling level as the y-axis for curve fitting. This extends the discrete Pareto expectation to a continuous parameter space. The interpolation results are then subjected to non-negative truncation and normalization to form a non-negative normalized update weight function W(x). W(x) represents the update weights for different parameter values ​​relative to the Pareto-optimal region. In the first iteration, the Gaussian mixture model initialized in S1 is used as the prior probability density function P(x); in subsequent iterations, the updated Gaussian mixture model from the previous iteration is used as the prior probability density function P(x). Applying a Bayesian update form, the prior probability density function P(x) is multiplied point-by-point with the update weight function W(x) to obtain a non-normalized posterior probability function representing the parameter performance distribution. =P(x)·W(x).

[0046] For nonnormalized posterior probability functions To address the difficulty of directly parsing the sampling, the Metropolis-Hastings mechanism from the Markov Chain Monte Carlo resampling algorithm is invoked to set step size control parameters within the normalized parameter space. The random walk proposal distribution with a value of 0.2 is used, and based on... The corresponding acceptance probability generates, for example, 10,000 candidate samples. After removing the first 2,000 samples that have not reached a steady state in the initial stage (i.e., discarding them during the Burn-in period), 8,000 high-probability posterior samples are retained. These 8,000 samples are input into the expectation-maximization algorithm module. In each expectation step, the posterior probability of the sample points to each Gaussian branch, i.e., the responsibility, is calculated based on the current Gaussian mixture model parameters. In the maximization step, the weights, expected values, and variances of each Gaussian branch are updated based on the responsibility. The expectation and maximization steps are repeated until the convergence condition is met, and the updated weights of the three Gaussian branches are output. Expected value and variance The updated weights Expected value and variance The Gaussian mixture model for the next iteration cycle is reconstructed. This reconstructed Gaussian mixture model is used as the posterior probability density function generated in the current iteration cycle and as the prior probability density function P(x) for the next iteration cycle. This is then used to perform equal probability interval partitioning and sampling level generation again, thus completing the update of the distribution law of the single processing parameters.

[0047] S3, based on the generated posterior probability density function, repeatedly execute the iterative steps of dynamically discretizing to generate sampling levels until the algorithm model reaches convergence or reaches the preset maximum number of iterations, obtain the test dataset after the iteration ends, use the test dataset to construct a multi-objective Gaussian process surrogate model group as the fitness function, and use the multi-objective evolution algorithm to globally optimize and output the Pareto optimal solution set as the parameter combination.

[0048] After discretizing and normalizing the probability density functions generated in two consecutive iterations on a unified parameter grid, the KL divergence between the two functions is calculated. When the KL divergence is less than the preset 1×10⁻⁶, the KL divergence is considered to be within the range specified in the original text. -4 Alternatively, the iteration can be stopped when the loop control variable reaches the preset maximum number of 100 iterations, and all test groups that meet the safety conditions and have completed the actual processing collected in each iteration, along with their corresponding multidimensional performance indicators, can be extracted and merged into a test dataset.

[0049] A Gaussian process regression algorithm was employed, using a combination of the Matérn kernel function and a white noise kernel function as the covariance function. Gaussian process regression sub-models were trained with material removal rate conversion, processing energy consumption, and surface roughness as output objectives, respectively. Multiple Gaussian process regression sub-models together constituted a multi-objective Gaussian process surrogate model group. Maximum likelihood estimation was used to optimize hyperparameters using the experimental dataset. A multi-objective surrogate model was constructed with processing parameters as independent variables and material removal rate conversion, processing energy consumption, and surface roughness as dependent variables, serving as the fitness function. Population size and number of generations were set. The NSGA-II fast non-dominated sorting genetic algorithm with an elite retention strategy was used as the multi-objective evolutionary algorithm. The mean of the three objective predictions output by the multi-objective surrogate model was used as the fitness evaluation result for candidate individuals. Simulated binary crossover and polynomial mutation operators were executed for global optimization, deriving a Pareto optimal solution set composed of all non-dominated solutions on the Pareto front, which served as the parameter combination for CNC machining.

[0050] In an optional embodiment, the step of constructing a multi-objective Gaussian process surrogate model set using the experimental dataset as the fitness function, and employing a multi-objective evolutionary algorithm to globally optimize and output the Pareto optimal solution set as the parameter combination, includes: After unifying the multidimensional performance indicators into a minimization objective, the predicted mean of the multi-objective Gaussian process surrogate model group is used as the fitness function of the multi-objective evolution algorithm. Randomly initialize the population within the feasible space, and perform selection, crossover, and mutation operations to generate offspring populations; After merging the parent and offspring populations, the results are input into the fitness function to obtain predicted performance index values, and environmental selection is performed based on non-dominated ranking and crowding distance. After the iteration reaches the maximum number of generations, the evolution stops, and the non-dominated solution set in the population is extracted as the Pareto optimal solution set and output.

[0051] After the algorithm converges, all experimental groups that meet the safety conditions and complete the actual processing test in each iteration cycle are summarized to form a training dataset. The training dataset includes the processing parameter combinations corresponding to each experimental group, as well as the corresponding measured surface roughness Ra, processing energy consumption, and material removal rate MRR. If the actual processing objective is to minimize surface roughness Ra, minimize processing energy consumption, and maximize material removal rate MRR, then the inverse of the material removal rate MRR is taken to obtain the converted material removal rate value -MRR, thus unifying surface roughness Ra, processing energy consumption, and the converted material removal rate value -MRR into a unified minimization objective.

[0052] A multi-objective Gaussian process surrogate model group is established based on the training dataset. Specifically, the combination of processing parameters is used as the model input, and surface roughness Ra, processing energy consumption, and material removal rate conversion value -MRR are used as the output objectives to train the corresponding Gaussian process regression sub-models. The Gaussian process regression sub-models corresponding to the three output objectives together constitute the multi-objective Gaussian process surrogate model group. For any candidate combination of processing parameters generated by the NSGA-II evolutionary algorithm, the candidate combination of processing parameters is input into the multi-objective Gaussian process surrogate model group, and the corresponding predicted mean of surface roughness, predicted mean of processing energy consumption, and predicted mean of material removal rate conversion value are output. The above three predicted mean values ​​are used as the multi-objective fitness evaluation results of the candidate processing parameter combination to replace repeated cutting tests in NSGA-II evolutionary optimization.

[0053] During the evolutionary phase, the scale is randomly generated within the feasible space of processing parameters, for example... An initial population of 100 is formed, with each individual representing a set of candidate processing parameter combinations. Parent individuals are selected from the current population using a tournament selection mechanism. The probability of performing an action on the parent individual is... Simulated binary crossover operation with a value of 0.9 and a probability of . A polynomial mutation operation of 0.33 is performed to generate a progeny population of 100 new individuals. The parent population is then merged with the progeny population to obtain a candidate population of 200 individuals. The processing parameters corresponding to each individual are then input into a multi-objective Gaussian process surrogate model group, and the corresponding predicted mean values ​​of surface roughness, processing energy consumption, and material removal rate conversion are output as the multi-objective fitness evaluation results for each individual.

[0054] Individuals are ranked according to their Pareto non-dominated levels in the multi-objective space. For individuals at the same non-dominated level, their crowding distance in the multi-dimensional objective space is calculated to maintain population diversity. Following a ranking rule prioritizing non-dominated levels and aided by crowding distance, the top 100 individuals from the merged candidate population are selected as the next generation. The selection, crossover, mutation, surrogate model evaluation, non-dominated ranking, and population selection steps are repeated until a preset number of iterations is reached, for example, 200 iterations. From the last generation, the non-dominated frontier solution with Rank=1 is extracted, for example, outputting 20 sets of mutually non-dominated optimal processing parameter combinations as the Pareto optimal solution set for operators to select according to on-site processing needs.

[0055] In a second embodiment, the present invention also provides an adaptive optimization system for CNC machining parameters of precision components, comprising the following modules: The acquisition module is used to determine the continuous value range of a preset number of processing parameters and delineate the feasible space through a multidimensional constraint function. It sets an initial continuous probability density function for each processing parameter, dynamically discretizes and generates multiple discrete sampling levels based on the current probability density function, and constructs candidate parameter combinations by combining them with an orthogonal table. After verifying the candidate parameter combinations with safety constraints, it forms a test group for actual processing. It performs actual processing operations on the test group to obtain multidimensional performance indicators representing processing quality. The calculation module is used to perform non-dominated ranking processing on the multidimensional index set composed of multidimensional performance indicators, assign corresponding Pareto levels to each experimental group, calculate the Pareto expected value of each processing parameter at different sampling levels, and the Pareto expected value is specifically determined by the average value of the inverse fitness of the Pareto levels in which the processing parameter participates in the experiment. The Pareto expected value is used as evidence to perform Bayesian update on the current probability density function and generate a posterior probability density function. The output module is used to repeatedly execute the iterative steps of dynamically discretizing to generate sampling levels and generate the posterior probability density function based on the generated posterior probability density function until the algorithm model reaches the convergence state or reaches the preset maximum number of iterations. After the iteration ends, the experimental dataset is obtained. The experimental dataset is used to construct a multi-objective Gaussian process surrogate model group as the fitness function, and the multi-objective evolution algorithm is used to globally optimize and output the Pareto optimal solution set as the parameter combination.

[0056] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A method for adaptive optimization of CNC machining parameters for precision components, characterized in that, Includes the following steps: The continuous value range of a preset number of processing parameters is determined and the feasible space is defined by a multidimensional constraint function. An initial continuous probability density function is set for each processing parameter. Multiple discrete sampling levels are dynamically discretized according to the current probability density function and candidate parameter combinations are constructed by combining them with an orthogonal table. After the candidate parameter combinations are verified by safety constraints, a test group for actual processing is formed. Actual processing operations are performed on the test group to obtain multidimensional performance indicators representing processing quality. The multidimensional index set composed of multidimensional performance indicators is subjected to non-dominated ranking processing, and corresponding Pareto levels are assigned to each experimental group. The Pareto expected value of each processing parameter at different sampling levels is calculated. The Pareto expected value is specifically determined by the average value of the inverse fitness of the Pareto levels in which the processing parameter participates in the experiment. The Pareto expected value is used as evidence to perform Bayesian update on the current probability density function and generate a posterior probability density function. Based on the generated posterior probability density function, the iterative steps of dynamically discretizing to generate sampling levels and generating the posterior probability density function are repeatedly executed until the algorithm model reaches a convergent state or reaches the preset maximum number of iterations. The experimental dataset after the iteration is completed is obtained. The experimental dataset is used to construct a multi-objective Gaussian process surrogate model group as the fitness function, and the Pareto optimal solution set is output as the parameter combination by global optimization using a multi-objective evolution algorithm.

2. The method according to claim 1, characterized in that, The process of determining the continuous value range of a preset number of processing parameters and defining the feasible space through a multidimensional constraint function includes: Extract the spindle speed, feed rate and depth of cut of the machine tool as machining parameters, and set the physical limit threshold of each machining parameter to form a continuous range of values; Based on the maximum power limit of the machine tool spindle motor and the allowable cutting force of the tool, a multidimensional constraint function including spindle load constraint and tool force constraint is established. By inputting the continuous range of values ​​into the multidimensional constraint function, parameter regions that violate spindle load constraints or tool force constraints are removed, generating a feasible space that meets safe machining conditions.

3. The method according to claim 1, characterized in that, Setting an initial continuous probability density function for each processing parameter includes: The initial continuous probability density function of each processing parameter is set as a Gaussian mixture model consisting of three independent Gaussian branches; Assign equal initial weights to the three Gaussian branches, and set the expected values ​​of the branches to the 15%, 50%, and 85% quantiles of the continuous range of the corresponding processing parameters, respectively. The standard deviation of each branch is initialized to one-tenth of the range of the corresponding processing parameter values.

4. The method according to claim 1, characterized in that, The process of dynamically discretizing the current probability density function to generate multiple discrete sampling levels and constructing candidate parameter combinations using orthogonal arrays, followed by performing safety constraint verification on the candidate parameter combinations to form an experimental group actually used for processing, includes: Based on the cumulative distribution function of the current probability density function, the feasible space of each processing parameter is divided into multiple discrete sampling intervals using the equal probability interval division method. Extract the peak points of probability density for each sampling interval as representative values ​​for the corresponding sampling level; Substitute the representative values ​​of each processing parameter into a preset multi-level orthogonal array matrix to generate an initial parameter combination; The initial parameter combination is overload-checked by a multidimensional constraint function. Parameter combinations that do not meet the safety conditions are identified as unexecutable candidate combinations and excluded from the actual processing test group. Alternative parameter combinations that satisfy the multidimensional constraint function are regenerated according to the horizontal numbering combination of the corresponding orthogonal table row. The initial parameter combination that meets the safety conditions and the alternative parameter combination are used as the test group for actually performing the processing.

5. The method according to claim 1, characterized in that, The calculation of the Pareto expected value of each processing parameter at different sampling levels, specifically determined by the average of the inverse fitness of the Pareto levels in which the processing parameters participated in the experiment, includes: Extract the Pareto levels of all experimental groups participating in the current processing parameters at a specific sampling level; The reciprocal of the Pareto level is used as the fitness score for each experimental group; The average fitness is calculated by taking the arithmetic mean of the fitness scores of all experimental groups participating under the current processing parameters at a specific sampling level. The average fitness is normalized and used as the Pareto expectation of the processing parameter at the sampling level.

6. The method according to claim 5, characterized in that, The step of performing a Bayesian update on the current probability density function and generating a posterior probability density function based on the Pareto expectation value includes: The Pareto expectation values ​​of each sampling level are mapped to a continuous space using interpolation methods, thus constructing a non-negative update weight function; According to the Bayesian update form, the continuous probability density function of the current iteration is multiplied by the non-negative update weight function to calculate the non-normalized posterior distribution. The Markov chain Monte Carlo method is used to resample the non-normalized posterior distribution to extract high-probability sample points. The weights, expected values, and variances of a Gaussian mixture model are refitted based on high-probability sample points using the expectation-maximization algorithm, and the posterior probability density function is output.

7. The method according to claim 1, characterized in that, The method of constructing a multi-objective Gaussian process surrogate model set using the experimental dataset as the fitness function, and employing a multi-objective evolutionary algorithm to globally optimize and output the Pareto optimal solution set as the parameter combination, includes: After unifying the multidimensional performance indicators into a minimization objective, the predicted mean of the multi-objective Gaussian process surrogate model group is used as the fitness function of the multi-objective evolution algorithm. Randomly initialize the population within the feasible space, and perform selection, crossover, and mutation operations to generate offspring populations; After merging the parent and offspring populations, the results are input into the fitness function to obtain predicted performance index values, and environmental selection is performed based on non-dominated ranking and crowding distance. After the iteration reaches the maximum number of generations, the evolution stops, and the non-dominated solution set in the population is extracted as the Pareto optimal solution set and output.

8. A precision component CNC machining parameter adaptive optimization system, characterized in that, Includes the following modules: The acquisition module is used to determine the continuous value range of a preset number of processing parameters and delineate the feasible space through a multidimensional constraint function. It sets an initial continuous probability density function for each processing parameter, dynamically discretizes and generates multiple discrete sampling levels based on the current probability density function, and constructs candidate parameter combinations by combining them with an orthogonal table. After verifying the candidate parameter combinations with safety constraints, it forms a test group for actual processing. It performs actual processing operations on the test group to obtain multidimensional performance indicators representing processing quality. The calculation module is used to perform non-dominated ranking processing on the multidimensional index set composed of multidimensional performance indicators, assign corresponding Pareto levels to each experimental group, calculate the Pareto expected value of each processing parameter at different sampling levels, and the Pareto expected value is specifically determined by the average value of the inverse fitness of the Pareto levels in which the processing parameter participates in the experiment. The Pareto expected value is used as evidence to perform Bayesian update on the current probability density function and generate a posterior probability density function. The output module is used to repeatedly execute the iterative steps of dynamically discretizing to generate sampling levels and generate the posterior probability density function based on the generated posterior probability density function until the algorithm model reaches the convergence state or reaches the preset maximum number of iterations. After the iteration ends, the experimental dataset is obtained. The experimental dataset is used to construct a multi-objective Gaussian process surrogate model group as the fitness function, and the multi-objective evolution algorithm is used to globally optimize and output the Pareto optimal solution set as the parameter combination.

9. The system according to claim 8, characterized in that, The process of determining the continuous value range of a preset number of processing parameters and defining the feasible space through a multidimensional constraint function includes: Extract the spindle speed, feed rate and depth of cut of the machine tool as machining parameters, and set the physical limit threshold of each machining parameter to form a continuous range of values; Based on the maximum power limit of the machine tool spindle motor and the allowable cutting force of the tool, a multidimensional constraint function including spindle load constraint and tool force constraint is established. By inputting the continuous range of values ​​into the multidimensional constraint function, parameter regions that violate spindle load constraints or tool force constraints are removed, generating a feasible space that meets safe machining conditions.

10. The system according to claim 8, characterized in that, Setting an initial continuous probability density function for each processing parameter includes: The initial continuous probability density function of each processing parameter is set as a Gaussian mixture model consisting of three independent Gaussian branches; Assign equal initial weights to the three Gaussian branches, and set the expected values ​​of the branches to the 15%, 50%, and 85% quantiles of the continuous range of the corresponding processing parameters, respectively. The standard deviation of each branch is initialized to one-tenth of the range of the corresponding processing parameter values.

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