CN110598243B - Virtual sample capacity expansion method based on historical data of mechanical product - Google Patents

Virtual sample capacity expansion method based on historical data of mechanical product Download PDF

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CN110598243B
CN110598243B CN201910681887.8A CN201910681887A CN110598243B CN 110598243 B CN110598243 B CN 110598243B CN 201910681887 A CN201910681887 A CN 201910681887A CN 110598243 B CN110598243 B CN 110598243B
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裘乐淼
李恒
张树有
王自立
谭建荣
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Zhejiang University ZJU
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Abstract

The invention discloses a virtual sample capacity expansion method based on historical data of mechanical products, which comprises the steps of firstly determining the virtual sample capacity of a virtual sample in a small sample problem according to actually measured historical data; then, constructing a sample pool for generating a virtual sample based on historical data of mechanical production and related priori knowledge of the mechanical production; then, sampling samples based on a wheel roulette sampling idea, and designing a virtual sample generation rule based on an agent model idea and a Jacobi's rotation theory; and finally, feasible expansion samples are reserved according to the sample rationality judgment condition, so that the expansion of the virtual sample for training the small sample regression problem for predicting the mechanical assembly precision is realized. The achievement of the invention can be used for expanding the sample capacity of the small-capacity sample machine learning training model, can solve the problem of insufficient sample quantity in the mechanical assembly precision prediction, and has important significance for researching the small sample problem of the tolerance transfer of the customized product by using a machine learning regression method.

Description

Virtual sample capacity expansion method based on historical data of mechanical product
Technical Field
The invention relates to a virtual sample capacity expansion method, in particular to a virtual sample capacity expansion method based on historical data of mechanical products.
Background
Machine learning techniques based on large sample data have been widely used in different fields. With the introduction of intelligent manufacturing concepts, the combination of machine learning techniques and the mechanical field is becoming more and more compact. However, with the continuous improvement of the mechanical design and manufacturing level, the mechanical products have the trend of diversified design requirements, nonstandard production and personalized customized production, so that some mechanical field problems no longer have the condition of generating large-capacity sample data, and the application of the machine learning technology is limited.
At present, machine learning in the mechanical field is limited to application scenes with sufficient sample quantity, such as image identification, signal identification and the like. And in most cases, a classification problem such as object recognition. The machine learning regression problem of small-capacity samples in the related field of traditional mechanical design is not fully taken into consideration. At present, tolerance transfer research mostly adopts a tolerance analysis method, and the method mostly uses a linear transfer model for tolerance transfer research and does not consider nonlinear errors. The introduction of machine learning techniques has helped improve this situation.
Most complex mechanical products are produced in small batches in a personalized and customized mode, and the problem of small samples is necessarily faced in the process of assembly precision prediction and deviation control of the products. At present, the related research in the mechanical field using the virtual sample capacity expansion technology is mostly limited to application scenarios in which sample labels are clear or are easy to obtain, such as single small sample generation. The virtual sample generation methods for regression-like problems are less studied.
For the prediction of the assembly precision of mechanical products, factors influencing the quality of parts in actual machining are various. The factors of production equipment precision, personnel operation factors, production inherent noise and the like cause the sizes of parts produced by different manufacturers to obey a certain probability distribution. At present, the research mostly adopts Gaussian distribution approximation to replace an actual product size distribution model. The data samples generated may not be consistent with the actual production situation. Therefore, historical data of research problems are introduced, and the virtual sample generation method is used for expansion, which is beneficial to introducing priori knowledge in the mechanical field.
Disclosure of Invention
The invention aims to provide a virtual sample capacity expansion method based on historical data of mechanical products aiming at the defects of the prior art.
The purpose of the invention is realized by the following technical scheme: a virtual sample capacity expansion method based on historical data of mechanical products comprises the following steps:
(1) reading historical data of the mechanical product as a sample in an original training set D, wherein the sample comprises input features and output features; obtaining potential parameters including virtual sample capacity n' and initialized candidate sample library capacity n according to the original training set DDc′；
The input features are dimensional tolerance, shape tolerance and position tolerance;
the output characteristic is assembly accuracy;
the original training set D { (x {)1,y1),(x2,y2)...,(xn,yn) }; where n is the number of samples, xiIs a d-dimensional input feature, yiAs an output characteristic, yiIs a one-dimensional vector, i is 1 to n.
The value range of the virtual sample capacity n' is n multiplied by 22≤n′≤n×2d；
The initialized candidate sample library capacity nDc′＝n′；
(2) Based on the characteristic distribution rule in the original training set D obtained in the step (1), carrying out grouping, copying and expanding on the original training set D to obtain a sample pool DpThe method comprises the following substeps:
(2.1) determining a sample set Gk: according to the output characteristic y obtained in the step (1)iThe distribution of the magnitude of the values divides it into K intervals (g)k-1,gk]The interval end point g is calculated by the following formulak：
Figure BDA0002145053100000021
Wherein K is 1, 2.., K; y isminAs output characteristic yiMinimum value of, ymaxAs output characteristic yiMaximum value of (d); when k is 1, the 1 st interval is (g)0,g1]Wherein g is0＝ymin(ii) a Correspondingly, dividing the original training set D into K groups according to the following formula to obtain a sample set Gk：
When k is 1, G1＝{Di|g0≤yi≤g1,i＝1,2,...,n}
K2, 3, K, Gk＝{Di|gk-1＜yi≤gk,i＝1,2,...,n}
Wherein D isiThe ith sample in the original training set D is taken;
(2.2) determining the extended number n 'of samples'k: for the sample set G obtained in the step (2.1)kRespectively copying the samples in each group, and collecting the samples in each group to obtain a sample set GkNumber n of samples ofkExpanded to original
Figure BDA0002145053100000022
Multiplying to obtain an extended sample set G'k(ii) a Wherein n iskIs a set of samples G of each groupkThe number of samples in (1);
(2.3) expanding sample set G 'obtained in the step (2.2)'kThe groups of samples form a sample pool D togetherp；
(3) Sample cell D obtained from step (2.3)pThe method comprises the following steps of performing medium random sampling, designing a virtual sample generation rule based on an agent model and a Jacobi rotation theory, performing sample capacity expansion operation on a selected sample, and forming a candidate virtual sample library Dc' by all candidate virtual samples obtained after the capacity expansion operation, wherein the method comprises the following substeps:
(3.1) offset of input features: from the sample cell DpIn which a sample (x) is randomly takenp,yp) Generating virtual input x 'by an input feature offset operation'p＝xp± Δ, where positive and negative are randomly determined, and the offset Δ is determined by:
Figure BDA0002145053100000031
(3.2) constructing a response model J (x ') based on Jacobian's moment theory 'p): according to the assembly condition of the mechanical product assembly, a local coordinate system is constructed at the geometric center of each tolerance, and a response model J (x'p) Determined according to the following formula:
Figure BDA0002145053100000032
wherein F is the number of local coordinate systems;
Figure BDA0002145053100000033
in the form of a jacobian matrix,
Figure BDA0002145053100000034
is the tolerance curl.
(3.3) generation of output features: constructing virtual output y 'based on proxy model'pThe construction method comprises the following steps:
y′p＝J(x′p)+εp
wherein epsilonpIs Gaussian random noise;
(3.4) obtaining a set of candidate virtual samples (x'p,y′p)：
Figure BDA0002145053100000035
(3.5) repeating the steps (3.1) - (3.4) until the number of the candidate virtual samples reaches the initial candidate sample library capacity n acquired in the step (1)Dc′And a candidate virtual sample library Dc' is constructed.
(4) And (3) performing sample rationality screening on the candidate virtual sample library Dc' formed in the step (3.5), and reserving the candidate virtual samples meeting the sample rationality judgment condition as virtual expansion samples, wherein the method comprises the following substeps:
(4.1) randomly extracting n from the candidate virtual sample library Dc' constructed in the step (3.5)mMixing the group candidate virtual samples with the original training set D obtained in the step (1) to obtain a mixed sample Dm；
(4.2) formulating rationality judgment indexes and conditions: the rationality determination index Pd (-) includes a sample mean E (-) and a sample variance σ2(. cndot.), sample skewness Skaew (), sample Kurt () expressed as:
Pd(·)＝{E(·),σ2(·),Skew(·),Kurt(·)}
the rationality determination conditions are:
Pd(Dm)≥ξPd(D)
where ξ is the confidence;
(4.3) mixing sample D obtained in the step (4.1)mAnd (3) carrying out rationality judgment according to the rationality judgment condition formulated in the step (4.2) to obtain a virtual capacity expansion sample, wherein the rationality judgment comprises the following two conditions:
(4.3.1) if the sample D is mixedmIf the criterion Pd (-) satisfies the criterion of the rationality judgment in the step (4.2), n extracted in the step (4.1) is retainedmThe group candidate virtual samples are used as virtual expansion samples;
(4.3.2) if the sample D is mixedmDoes not satisfy the rationality judgment condition, and extracts n from the step (4.1)mThe group of candidate virtual samples is put back into the candidate virtual sample library Dc';
(4.4) repeating the steps (4.1) - (4.3) and continuously obtaining the virtual sample capacity n'; when the number of the reserved virtual expansion samples reaches the virtual sample capacity n' obtained in the step (1), or new virtual expansion samples cannot be generated after three continuous screenings, stopping extraction;
(5) judging whether the number of the reserved virtual expansion samples reaches the virtual sample capacity n' obtained in the step (1) or not to obtain a virtual sample set, wherein the method comprises the following two conditions:
(5.1) if the number M of the virtual expansion samples reserved in the step (4) reaches the virtual sample capacity n', completing the expansion of the virtual samples to obtain a virtual sample set;
(5.2) if the number M of the virtual expansion samples reserved in the step (4) does not reach the capacity n' of the virtual samples, updating the capacity of the candidate sample library to be nDc′And (4) n '-M, jumping to the step (3) to form a new candidate virtual sample library Dc', continuously obtaining virtual expansion samples, and supplementing the insufficient part.
Further, the dimensional tolerance in the step (1) includes a basic size and a dimensional deviation.
Further, the shape tolerance in the step (1) includes straightness, flatness, roundness, cylindricity, line profile, and surface profile.
Further, the position tolerance in the step (1) comprises parallelism, perpendicularity, inclination, coaxiality, symmetry, position degree, circular run-out and full run-out.
Further, the assembling precision in the step (1) comprises assembling size precision, assembling angle deviation, rotation deviation, coaxiality and verticality.
Further, each set of extended sample set G 'in the step (2.2)'kThe number of samples in
Figure BDA0002145053100000041
Further, n in the step (4.1)mGet
Figure BDA0002145053100000042
An internal integer value.
Further, in the step (4.1), when the number of candidate dummy samples in the candidate dummy sample library Dc' is less than nmWhen grouping, all the candidate virtual samples in the current candidate virtual sample library Dc' are taken to be mixed with the original training set D to obtain a mixed sample Dm。
Further, the value range of the confidence coefficient xi in the step (4.2) is 0.9-1.
The invention has the beneficial effects that: firstly, determining the virtual sample capacity of a virtual sample in a small sample problem according to actually measured historical data; then, constructing a sample pool for generating a virtual sample based on historical data of mechanical production and related priori knowledge of the mechanical production; then, sampling samples based on a wheel roulette sampling idea, and designing a virtual sample generation rule based on an agent model idea and a Jacobi's rotation theory; and finally, feasible expansion samples are reserved according to the sample rationality judgment condition, so that the expansion of the virtual sample for training the small sample regression problem for predicting the mechanical assembly precision is realized. The achievement of the invention can be used for expanding the sample capacity of the small-capacity sample machine learning training model, can solve the problem of insufficient sample quantity in the mechanical assembly precision prediction, and has important significance for researching the small sample problem of the tolerance transfer of the customized product by using a machine learning regression method.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is an example assembly view of the present invention;
FIG. 3 is a diagram of example dimensions and local coordinate systems of the present invention;
FIG. 4 is an example tolerance routing diagram of the present invention.
Detailed description of the invention
The method is described below on the basis of examples, but the method is not limited to the example problems. In the following detailed description of the present method, the following specific technical details are set forth in detail. The methods and operations provided are not described in any great detail in order to avoid obscuring the essence of the present method.
The overall flow chart of the virtual sample capacity expansion method based on the historical data of the mechanical product aiming at the problem of small sample regression of mechanical assembly precision prediction is shown in figure 1 and comprises the following steps:
(1) and reading real historical data of the mechanical product as samples in an original training set D, wherein the samples comprise input features and output features. Obtaining potential parameters including virtual sample capacity n' according to original training set D, and initializing candidate sample library capacity nDc′。
The input features are dimensional tolerance, shape tolerance and position tolerance;
the output characteristic is assembly accuracy;
the dimensional tolerance includes a basic size, a dimensional deviation.
The shape tolerance includes straightness, flatness, roundness, cylindricity, line profile, and surface profile.
The position tolerance comprises parallelism, perpendicularity, inclination, coaxiality, symmetry, position degree, circular run-out and full run-out.
The assembly precision refers to the precision actually achieved after assembly, and comprises assembly size precision, assembly angle deviation, rotation deviation, coaxiality and perpendicularity.
The original training set D { (x {)1,y1),(x2,y2)...,(xn,yn) }; where n is the number of samples, xiIs a d-dimensional input feature, yiAs an output characteristic, yiIs a one-dimensional vector, i is 1 to n.
The virtual sample capacity n' ranges from n × 22≤n′≤n×2dN' is arbitrarily taken within the range;
the initialized candidate sample library capacity nDc′＝n′；
(2) Based on the characteristic distribution rule in the original training set D obtained in the step (1), carrying out grouping, copying and expanding on the original training set D to obtain a sample pool Dp(ii) a The characteristic distribution refers to the distribution of the magnitude of the output characteristic value; the method comprises the following substeps:
(2.1) determining a sample set Gk: according to the output characteristic y obtained in the step (1)iThe distribution of the magnitude of the values divides it equally into K intervals (g)k-1,gk]The interval end point g is calculated by the following formulak：
Figure BDA0002145053100000061
Wherein K is 1, 2.., K; y isminAs output characteristic yiMinimum value of, ymaxAs output characteristic yiMaximum value of (d); in particular, when k is 1, the 1 st interval is (g)0,g1]Wherein g is0＝ymin；
Correspondingly, dividing the original training set D into K groups according to the following formula to obtain a sample set Gk：
Gk＝{Di|gk-1＜yi≤gk,i＝1,2,...,n}
Wherein D isiThe ith sample in the original training set D is taken; in particular, when k is 1, G1＝{Di|g0≤yi≤g1,i＝1,2,...,n}；
(2.2) determining the extended number n 'of samples'k: for the sample set G obtained in the step (2.1)kRespectively copying the samples in each group, and collecting the samples in each group to obtain a sample set GkNumber n of samples ofkExpanded to original
Figure BDA0002145053100000062
Multiplying to obtain an extended sample set G'k(ii) a Respective sets of extended sample sets G'kThe number of samples in
Figure BDA0002145053100000063
Wherein n iskIs a set of samples G of each groupkAnd the number of samples in (2) and the output characteristic y in step (2.1)iThe distribution of the numerical values is related; e (n)k) Represents nkThe average value of (a) of (b),
Figure BDA0002145053100000064
indicating a ceiling operation.
(2.3) expanding sample set G 'obtained in the step (2.2)'kThe groups of samples form a sample pool D togetherp：
Figure BDA0002145053100000065
(3) Sample cell D obtained from step (2.3)pIn-process random sampling, designing a virtual sample generation rule based on a proxy model and a Jacobi momentum theory, and performing sample expansion on a selected sampleCapacity operation, wherein all candidate virtual samples obtained after the capacity expansion operation form a candidate virtual sample library Dc', and the method comprises the following substeps:
(3.1) offset of input features: from the sample cell DpIn which a sample (x) is randomly takenp,yp) Generating virtual input x 'by an input feature offset operation'p＝xp± Δ, where positive and negative are determined randomly, and the offset Δ is a parametric estimate of the original training set D, determined by:
Figure BDA0002145053100000066
wherein the content of the first and second substances,
Figure BDA0002145053100000071
is to xiAveraging;
(3.2) constructing a response model J (x ') based on Jacobian's moment theory 'p): according to the assembly condition of the mechanical product assembly, a local coordinate system is constructed at the geometric center of each tolerance, and a response model J (x'p) Determined according to the following formula:
Figure BDA0002145053100000072
wherein F is the number of local coordinate systems;
Figure BDA0002145053100000073
in the form of a jacobian matrix,
Figure BDA0002145053100000074
is the tolerance curl.
Jacobian matrix
Figure BDA0002145053100000075
Calculated by the following formula:
dxf F＝dxF-dxf
dyf F＝dyF-dyf
dzf F＝dzF-dzf
Figure BDA0002145053100000076
Figure BDA0002145053100000077
Figure BDA0002145053100000078
wherein dx isF,dyF,dzFIs the global coordinate of the F-th coordinate system, dxf,dyf,dzfIs the global coordinate of the f-th coordinate system. When the x-axis direction of the f-th coordinate system is the same as the x-axis direction of the 0 th coordinate system, cx is 1; otherwise, cx is 0; cy and cz are the same.
Tolerance rotation
Figure BDA0002145053100000079
Calculated by the following formula:
Figure BDA00021450531000000710
wherein u, v, w represent the linear deviations in the x, y, z directions; α, β, γ represent angular deviations about the x, y, z axes.
(3.3) generation of output features: constructing virtual output y 'based on proxy model'pThe assembled functional requirement, i.e. the output signature in the sample, is considered to be a combination of a fixed response model and a local bias to the input signature, hence the virtual output y'pThe construction method comprises the following steps:
y′p＝J(x′p)+εp
wherein epsilonpIs Gaussian random noise;
(3.4) obtaining a set of candidate virtual samples (x'p,y′p)：
Figure BDA0002145053100000081
(3.5) repeating the steps (3.1) - (3.4) until the number of the candidate virtual samples reaches the initial candidate sample library capacity n acquired in the step (1)Dc′And a candidate virtual sample library Dc' is constructed.
(4) And (3) performing sample rationality screening on the candidate virtual sample library Dc' formed in the step (3.5), and reserving the candidate virtual samples meeting the sample rationality judgment condition as virtual expansion samples, wherein the method comprises the following substeps:
(4.1) randomly extracting n from the candidate virtual sample library Dc' constructed in the step (3.5)mMixing the group candidate virtual samples with the original training set D obtained in the step (1) to obtain a mixed sample Dm(ii) a Wherein n ismCan take any value, but should not be too large, it is recommended to take
Figure BDA0002145053100000082
An internal integer value; when the number of candidate virtual samples in the candidate virtual sample library Dc' is less than nmAnd when the virtual samples are grouped, the remaining candidate virtual samples are taken to be mixed with the original training set D.
(4.2) formulating rationality judgment indexes and conditions: the rationality determination index Pd (-) includes a sample mean E (-) and a sample variance σ2(. cndot.), sample skewness Skaew (), sample Kurt () expressed as:
Pd(·)＝{E(·),σ2(·),Skew(·),Kurt(·)}
the rationality determination conditions are:
Pd(Dm)≥ξPd(D)
and xi is a confidence coefficient and ranges from 0.9 to 1.
(4.3) mixing sample D obtained in the step (4.1)mPerforming rationality judgment according to the rationality judgment conditions formulated in the step (4.2), and judging the mixed sample DmCharacteristic pointWhether cloth changes obviously relative to original training set D, obtains virtual dilatation sample, includes following two kinds of situations:
(4.3.1) if the sample D is mixedmIf the rationality judgment index Pd (-) satisfies the rationality judgment condition in the step (4.2), the selected n is retainedmThe group candidate virtual sample is used as the final virtual expansion sample;
(4.3.2) if the sample D is mixedmDoes not satisfy the rationality determination condition, nmThe group samples are placed back in the candidate virtual sample library Dc'.
(4.4) repeating the steps (4.1) - (4.3) and continuing random extraction of nmPerforming rationality judgment on the candidate virtual samples, and stopping extraction when the number of reserved virtual expansion samples reaches the virtual sample capacity n' obtained in the step (1) or new reasonable virtual expansion samples cannot be generated by continuous and repeated screening;
(5) judging whether the number of the reserved virtual expansion samples reaches the virtual sample capacity n' obtained in the step (1) or not to obtain a virtual sample set, wherein the method comprises the following two conditions:
(5.1) if the number of the virtual expansion samples reserved in the step (4) reaches the virtual sample capacity n', completing the expansion of the virtual samples to obtain a virtual sample set;
(5.2) if the number M of the reserved virtual expansion samples does not reach the virtual sample capacity n', updating the capacity of the candidate sample library to be nDc′And (4) jumping back to the step (3) to form a new candidate virtual sample library Dc', continuously obtaining virtual expansion samples, and supplementing the insufficient part.
Therefore, virtual sample capacity expansion operation based on actual measurement historical data is completed, and the virtual and real mixed sample set subjected to capacity expansion can be used for regression problem training in small sample machine learning.
Examples
Fig. 1 is a flowchart of a virtual sample capacity expansion method implemented by an example of the method. As shown in fig. 1, the virtual sample capacity expansion method based on historical data for the machine field according to the present invention includes the following steps:
(1) reading the existing real historical data of the research problem, extracting effective actual measurement samples, and obtaining potential parameters according to the actual samples.
In this example, a handle base assembly is illustrated, and FIG. 2 is a schematic view of an example assembly of the method. The assembly body consists of two parts: a handle and a base. Although relatively simple in construction, the assembly contains 3 dimensional tolerance variables, and 4 typical form and position tolerances; figure 3 identifies the 7 tolerance elements and associated dimensions of the mechanical product assembly described above.
And analyzing the assembly body, and extracting effective characteristic variables to construct a sample (x, y). Where x is a 4-dimensional input feature, in this example, 3 dimensional tolerance variables with 1 independent shape tolerance;yfor a 1-dimensional output characteristic, the output characteristic in this example refers to the deviation of the handle end face in the direction of the axis of rotation after assembly is complete. Table 1 shows the input characteristics and the corresponding variables.
TABLE 1
Input feature xd Type of tolerance Range of variables
x1 Dimensional deviation of 15 + -0.05 14.95～15.05
x2 Shaft dimensional tolerance phi 15g6 14.983～14.994
x3 Hole size tolerance phi 15H7 15～15.018
x4 Face profile degree of 0.1 -0.05～0.05
Reading historical data to obtain 20 original training sets
Figure BDA0002145053100000091
As shown in table 2:
TABLE 2
Figure BDA0002145053100000101
From the actual sample volumes, the final produced virtual sample volume is determined according to the following equation:
n×22≤n′≤n×2d
in the formula, n' is 100 since n is 20 and d is 4. Simultaneous initialization of candidate sample pool capacity nDc′＝100。
(2) Based on the prior knowledge of the original training set D and the mechanical assembly, the characteristic distribution rule in the original training set D is mined, the original training set D is subjected to grouping, copying and expanding, and the copied actual measurement sample set is used as a sample pool D for expanding operationp。
Further, the step 2 specifically includes:
according to the steps 2.1-2.2, dividing the original training set D into 5 groups, and equally dividing the output characteristics of the samples into 5 groups. Table 3 shows the statistics of the parameters, and the expansion factor of each group. The extended groups of samples jointly form a sample pool D for generating virtual samplesp。
TABLE 3
Figure BDA0002145053100000102
(3) From the sample cell DpAnd (3) performing random sampling, performing virtual sample expansion on the selected samples based on virtual generation rules generated by a proxy model and a Jacobi's momentum theory, and forming a candidate virtual sample library by all generated virtual samples.
Step 3.1 is performed from the expanded sample pool DpIn which a sample (x) is randomly takenp,yp) And determining a sample characteristic offset as [ 0.010.0010.0010.01 ]]Wherein positive and negative are randomly generated.
Tolerance transfer model is constructed based on Jacobian's rotation theory, and response model J (x ') is constructed by simple assembly structure shown in FIG. 2 'p) The description is given; from the assembly of the mechanical product assembly shown in fig. 2, a local coordinate system as shown in fig. 3 is constructed at the geometric center of each tolerance.
First, a local coordinate system is determined, as shown in FIG. 3, with coordinate system 0 at the geometric center of reference A, coordinate system 1/2 at the geometric center of the base end face, coordinate 3/4 at the geometric center of the handle mating face, and coordinate 5 at the handle tip. According to the Jacobi's rotation theory, and the relevant parameters in Table 1, the Jacobi matrix of the local coordinate system is as follows:
Figure BDA0002145053100000111
the overall jacobian matrix is:
Figure BDA0002145053100000112
fig. 4 is a delivery route for the base handle assembly, which includes two sets of internal delivery (FE1, FE3) and one set of external delivery (FE 2). The tolerance expression for the input features to which the present invention relates can be obtained from tables 4 and 5, where simple constraints are determined by the formula in table 4, such as dimensional tolerances in the input features. The composite constraint tolerance representation is determined by the formula in table 5. The examples herein are given by way of illustration.
TABLE 4
Figure BDA0002145053100000113
Figure BDA0002145053100000121
TABLE 5
Figure BDA0002145053100000122
Figure BDA0002145053100000131
Figure BDA0002145053100000141
The fit of the shaft hole in this example is a composite constraint of class 1 in Table 5, corresponding to external transfer FE2 in FIG. 4. While bringing in the corresponding quantity and constant, T1、T2、T3Is determined by the following formula:
Figure BDA0002145053100000142
J(xi')＝[J]·[T1T2T3]
yi'＝J(xi')+εi
and (5) repeatedly executing the steps 3.1-3.4 to generate 100 candidate virtual sample libraries Dc' to be screened.
(4) And (4) performing reasonableness screening on the candidate virtual sample library Dc' generated in the step (3).
The confidence ξ is determined to be 0.95.
Randomly extracting n from the candidate virtual sample library DcmMixing 5 groups of data with original training set D, and judging mixed sample DmSample mean E (-) and sample variance σ of2(. cndot.), sample skewness Skaew (. cndot.), and sample kurtosis K urt (. cndot.).
If Pd (D)m) 0.95Pd (D) and not more than Pd (D), the selected 5 groups of data are retained as the final virtual sample. If the above condition is not satisfied, the 5 groups of samples are put back into the candidate virtual sample library Dc'; the random drawing of 5 groups of data is continued and step 4.3 is executed.
(5) And if the number of the reserved virtual expansion samples reaches the virtual sample capacity of 100, completing the expansion operation and obtaining a virtual sample library.
If the number of the reserved virtual expansion samples reaches the virtual sample capacity, the number of the reserved virtual expansion samples is m, and the capacity of the updated candidate sample library is nDc′N' -m; executing the step 3-4, judging whether the number of the currently reserved virtual expansion samples reaches the virtual sample capacity 100, and completing the expansion of the virtual samples if the number of the currently reserved virtual expansion samples reaches the virtual sample capacity 100 to obtain a virtual sample set; and if not, executing the steps 3-4 again until the number of the currently reserved virtual expansion samples reaches the virtual sample capacity 100 and obtaining a virtual sample set.
Therefore, the virtual sample capacity expansion operation based on the measured historical data is completed.

Claims (9)

1. A virtual sample capacity expansion method based on historical data of mechanical products is characterized by comprising the following steps:
(1) reading historical data of the mechanical product as a sample in an original training set D, wherein the sample comprises input features and output features; obtaining potential parameters including virtual sample capacity n' and initialized candidate sample library capacity n according to the original training set DDc′；
The input features are dimensional tolerance, shape tolerance and position tolerance;
the output characteristic is assembly accuracy;
the original training set D { (x {)1,y1),(x2,y2)...,(xn,yn) }; where n is the number of samples, xiIs a d-dimensional input feature, yiAs an output characteristic, yiIs a one-dimensional vector, i is 1 to n;
the value range of the virtual sample capacity n' is n multiplied by 22≤n′≤n×2d；
The initialized candidate sample library capacity nDc′＝n′；
(2) Based on the characteristic distribution rule in the original training set D obtained in the step (1), carrying out grouping, copying and expanding on the original training set D to obtain a sample pool DpThe method comprises the following substeps:
(2.1) determining a sample set Gk: according to the output characteristic y obtained in the step (1)iThe distribution of the magnitude of the values divides it into K intervals (g)k-1,gk]The interval end point g is calculated by the following formulak：
Figure FDA0002928121020000011
Wherein K is 1, 2.., K; y isminAs output characteristic yiMinimum value of, ymaxAs output characteristic yiMaximum value of (d); when k is 1, the 1 st interval is (g)0,g1]Wherein g is0＝ymin(ii) a Correspondingly, dividing the original training set D into K groups according to the following formula to obtain a sample set Gk：
When k is 1, G1＝{Di|g0≤yi≤g1,i＝1,2,...,n}
K2, 3, K, Gk＝{Di|gk-1＜yi≤gk,i＝1,2,...,n}
Wherein D isiThe ith sample in the original training set D is taken;
(2.2) determining the extended number n 'of samples'k: for the sample set G obtained in the step (2.1)kRespectively copying the samples in each group, and collecting the samples in each group to obtain a sample set GkNumber n of samples ofkExpanded to original
Figure FDA0002928121020000012
Multiplying to obtain an extended sample set G'k(ii) a Wherein n iskIs a set of samples G of each groupkThe number of samples in (1);
(2.3) expanding sample set G 'obtained in the step (2.2)'kThe groups of samples form a sample pool D togetherp；
(3) Sample cell D obtained from step (2.3)pThe method comprises the following steps of performing medium random sampling, designing a virtual sample generation rule based on an agent model and a Jacobi rotation theory, performing sample capacity expansion operation on a selected sample, and forming a candidate virtual sample library Dc' by all candidate virtual samples obtained after the capacity expansion operation, wherein the method comprises the following substeps:
(3.1) offset of input features: from the sample cell DpIn which a sample (x) is randomly takenp,yp) Generating virtual input x 'by an input feature offset operation'p＝xp± Δ, where positive and negative are randomly determined, and the offset Δ is determined by:
Figure FDA0002928121020000021
(3.2) constructing a response model J (x ') based on Jacobian's moment theory 'p): according to the assembly condition of the mechanical product assembly, a local coordinate system is constructed at the geometric center of each tolerance, and a response model J (x'p) Determined according to the following formula:
Figure FDA0002928121020000022
wherein F is the number of local coordinate systems;
Figure FDA0002928121020000023
in the form of a jacobian matrix,
Figure FDA0002928121020000024
is the tolerance rotation;
(3.3) generation of output features: constructing virtual output y 'based on proxy model'pThe construction method comprises the following steps:
y′p＝J(x′p)+εp
wherein epsilonpIs Gaussian random noise;
(3.4) obtaining a set of candidate virtual samples (x'p,y′p)：
Figure FDA0002928121020000025
(3.5) repeating the steps (3.1) - (3.4) until the number of the candidate virtual samples reaches the initial candidate sample library capacity n acquired in the step (1)Dc′Forming a candidate virtual sample library Dc';
(4) and (3) performing sample rationality screening on the candidate virtual sample library Dc' formed in the step (3.5), and reserving the candidate virtual samples meeting the sample rationality judgment condition as virtual expansion samples, wherein the method comprises the following substeps:
(4.1) randomly extracting n from the candidate virtual sample library Dc' constructed in the step (3.5)mMixing the group candidate virtual samples with the original training set D obtained in the step (1) to obtain a mixed sample Dm；
(4.2) formulating rationality judgment indexes and conditions: the rationality determination index Pd (-) includes a sample mean E (-) and a sample variance σ2(. cndot.), sample skewness Skaew (), sample Kurt () expressed as:
Pd(·)＝{E(·),σ2(·),Skew(·),Kurt(·)}
the rationality determination conditions are:
Pd(Dm)≥ξPd(D)
where ξ is the confidence;
(4.3) mixing sample D obtained in the step (4.1)mAnd (3) carrying out rationality judgment according to the rationality judgment condition formulated in the step (4.2) to obtain a virtual capacity expansion sample, wherein the rationality judgment comprises the following two conditions:
(4.31) if the sample D is mixedmIf the criterion Pd (-) satisfies the criterion of the rationality judgment in the step (4.2), n extracted in the step (4.1) is retainedmThe group candidate virtual samples are used as virtual expansion samples;
(4.3.2) if the sample D is mixedmDoes not satisfy the rationality judgment condition, and extracts n from the step (4.1)mThe group of candidate virtual samples is put back into the candidate virtual sample library Dc';
(4.4) repeating the steps (4.1) - (4.3) and continuously obtaining the virtual sample capacity n'; when the number of the reserved virtual expansion samples reaches the virtual sample capacity n' obtained in the step (1), or new virtual expansion samples cannot be generated after three continuous screenings, stopping extraction;
(5) judging whether the number of the reserved virtual expansion samples reaches the virtual sample capacity n' obtained in the step (1) or not to obtain a virtual sample set, wherein the method comprises the following two conditions:
(5.1) if the number M of the virtual expansion samples reserved in the step (4) reaches the virtual sample capacity n', completing the expansion of the virtual samples to obtain a virtual sample set;
(5.2) if the number M of the virtual expansion samples reserved in the step (4) does not reach the capacity n' of the virtual samples, updating the capacity of the candidate sample library to be nDc′And (4) n '-M, jumping to the step (3) to form a new candidate virtual sample library Dc', continuously obtaining virtual expansion samples, and supplementing the insufficient part.
2. The method for virtual sample expansion based on historical data of mechanical products according to claim 1, wherein the dimensional tolerance in step (1) comprises basic dimensions and dimensional deviation.
3. The method for virtual sample expansion based on historical data of mechanical products according to claim 1, wherein the shape tolerance in step (1) comprises straightness, flatness, roundness, cylindricity, line profile and surface profile.
4. The method for virtual sample capacity expansion based on historical data of mechanical products according to claim 1, wherein the position tolerance in the step (1) comprises parallelism, perpendicularity, inclination, coaxiality, symmetry, position degree, circular run-out and full run-out.
5. The virtual sample capacity expansion method based on historical data of mechanical products as claimed in claim 1, wherein the assembly precision in the step (1) comprises assembly dimension precision, assembly angle deviation, rotation deviation, coaxiality and verticality.
6. The method for virtual sample expansion based on mechanical product historical data according to claim 1, wherein each set of extended sample set G 'in the step (2.2)'kThe number of samples in
Figure FDA0002928121020000031
7. The method for virtual sample expansion based on historical data of mechanical products according to claim 1, wherein n in the step (4.1)mGet
Figure FDA0002928121020000041
An internal integer value.
8. The method for expanding virtual samples based on historical data of mechanical products according to claim 1, wherein in the step (4.1), when the number of candidate virtual samples in the candidate virtual sample library Dc' is less than nmWhen grouping, all the candidate virtual samples in the current candidate virtual sample library Dc' are taken to be mixed with the original training set D to obtain a mixed sample Dm。
9. The virtual sample capacity expansion method based on historical data of mechanical products as claimed in claim 1, wherein the confidence coefficient xi in the step (4.2) is in a range of 0.9-1.
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