CN112668125B - Method, system, medium and equipment for improving evaluation precision of incomplete small circular arc - Google Patents
Method, system, medium and equipment for improving evaluation precision of incomplete small circular arc Download PDFInfo
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Abstract
The invention relates to a method, a system, a medium and equipment for improving the evaluation precision of incomplete small circular arcs, which comprises the following steps: determining a first optimal smoothing coefficient of a pre-established cubic exponential smoothing prediction model; further determining the remaining optimal smoothing coefficients; fitting the optimal smoothing coefficient to obtain a variation trend curve of the smoothing coefficient, and obtaining the smoothing coefficient of the data point out-of-set prediction period according to a fitting formula; calculating data points outside the predicted actual measurement data point set by using the smoothing coefficients of the predicted period number outside the data point set; judging whether a preset prediction period number is reached, and if so, reversing the data point set; and combining the original actual measurement data point set and the predicted data point set to form a new data point set, and evaluating curvature parameters of the new data point set by using an evaluation method, thereby improving the evaluation precision of the incomplete small arc. The invention can improve the accuracy of curvature radius parameter evaluation, and effectively improve the stability and accuracy of incomplete small arc curvature radius parameter evaluation.
Description
Technical Field
The invention relates to the technical field of performance detection of mechanical parts, in particular to a method, a system, a medium and equipment for improving evaluation precision of incomplete small circular arcs.
Background
The incomplete small arc refers to an arc or a cambered surface with the radius of curvature ranging from 0 to 25mm, wherein the arc profile corresponds to an arc or cambered surface with the center angle smaller than 120 degrees. The incomplete small arc profile is widely applied in national defense science and technology industry and precision manufacturing industry due to the special performance of the incomplete small arc profile: for example, the front and rear edge profiles of the aero-engine blades have a direct effect on the aerodynamic performance of the engine and the fatigue performance of the blades; the tool nose part of the numerical control machine tool directly determines the machining precision; the edge chamfer of some precise parts is used for removing processing burrs and improving the stress concentration condition of the parts. The radius of curvature parameter is used as the core parameter of the small circular arc profile, the precision of the radius of curvature parameter is extremely important for the production and manufacturing performances of workpieces, and therefore urgent precise measurement and evaluation needs exist. However, due to the characteristics of non-integrity and small radius of arc, the difficulty of measurement and evaluation is high, and the accuracy of curvature radius parameter estimation is always controversial.
The main arc parameters affecting the evaluation accuracy are the theoretical radius of the arc, the central angle of the arc contour point set and the contour error of the arc contour point set. In general, the smaller the theoretical radius of the arc, the greater the evaluation difficulty and error; the smaller the center angle of the arc profile point set is, the worse the accuracy of curvature radius evaluation is; the greater the contour error of the contour point set is, the lower the evaluation accuracy is correspondingly.
Among the three influencing factors, the radius of the circular arc is a required target value, and cannot be adjusted. Therefore, the scholars generally start from the central angle of the arc contour point set and the contour error of the arc contour point set, and improve the evaluation accuracy by reducing the influence of the contour error or increasing the central angle. For example, guevara et al propose a robust geometric method for fitting a set of points based on an average absolute error by minimizing the sum of geometric distances to the data points, determining new directions of iteration with left and right hand derivatives based on a rapid iterative algorithm of gradient or second derivative, fitting the data points to an arc, and then solving for the radius. The algorithm can be used as a substitute method of a conventional algorithm in calculation efficiency, so that the influence of contour error on the evaluation process is reduced in principle, the robustness of the algorithm is enhanced, the algorithm is insensitive to abnormal values and data noise, and the evaluation accuracy is further improved. Fei and the like start from the center angle of the incomplete small circular arc, a bidirectional prediction method based on a Radial Basis Function Neural Network (RBFNN) is adopted, observation data are regarded as a time sequence, bidirectional extension is carried out on the observation data, interpolation is carried out, the circular arc length is increased, the center angle of the circular arc outline is increased, and the stability and the accuracy of fitting of the method are proved to be far superior to those before prediction through training and learning of a large amount of data.
The above method has good application in some specific fields and working conditions, but has certain limitations. For example, the bidirectional prediction method based on Radial Basis Function Neural Network (RBFNN) requires huge circular arc profile data sample size, the circular arc data sample size available for training and learning in practical engineering is basically difficult to meet the requirement, and the universality of application is not high.
Disclosure of Invention
Aiming at the problems, the invention aims to provide a method, a system, a medium and equipment for improving the evaluation precision of incomplete small circular arcs, which are used for evaluating the processed data point set by using an evaluation method after predicting and extending the small circular arc outline data point set, so that the accuracy of the evaluation of the curvature radius parameters can be improved, and the stability and the accuracy of the evaluation of the incomplete small circular arc curvature radius parameters are effectively improved.
In order to achieve the above purpose, the present invention adopts the following technical scheme: a method for improving the evaluation accuracy of incomplete small circular arcs, comprising:
step 1), determining a first optimal smoothing coefficient alpha of a pre-established cubic exponential smoothing prediction model 1 ；
Step 2), further determining the rest n-k optimal smoothing coefficients; n is the number of actually measured sample points, k is the period number of the time sequence, and k is less than n;
step 3), fitting n-k optimal smoothing coefficients to obtain a variation trend curve of a smoothing coefficient alpha, and obtaining a smoothing coefficient of a data point out-of-set prediction period according to a fitting formula;
step 4), calculating data points outside the predicted actual measurement data point set by using the smoothing coefficients of the predicted period number outside the data point set;
step 5), judging whether a preset prediction period number is reached, and if so, reversing the data point set, and repeating the steps 1) to 4);
and step 6), combining the original actual measurement data point set and the predicted data point set to form a new data point set, and evaluating curvature parameters of the new data point set by using an evaluation method, so that the evaluation precision of the incomplete small arc is improved.
Further, in said step 1), a first optimal smoothing coefficient α 1 The determining method comprises the following steps: using the abscissa point set and the ordinate point set of the existing actually measured small arc profile data, wherein the number of actually measured sample points is n, and taking the ordinal number as the period number of the time sequence; assume that k-period data is adopted for each prediction fix; starting from the data in the 1 st period, performing exponential smoothing prediction on the data in the 1 st period to the data in the k th period for three times in the first calculation, and moving to the right for calculation; the smoothing coefficient alpha is in the value space [0,1 ]]Internal traversal search is carried out, step length calculated each time is set, a plurality of groups of k+1-phase predicted values are obtained, the k+1-phase predicted values are compared with k+1-phase actual measurement data, and the optimal smoothing coefficient alpha is determined according to the error square sum minimization principle 1 。
Further, in the step 2), the determining method is as follows: removing the 1 st period data, repeating the first optimal smoothing coefficient determination method by adopting the 2 nd period to the (k+1) th period measured data to obtain a second optimal smoothing coefficient alpha 2 Finally obtaining the n-k best smoothing coefficient alpha n-k A total of n-k optimal smoothing coefficients are obtained.
Further, in the step 4), the calculation method for predicting the data points outside the actually measured data point set is as follows: when the calculation is moved to the calculation of the (n+1) th stage predicted point by adopting the (n-k) th stage to (n) th stage measured arc data point set, the smoothing coefficient alpha obtained after fitting n-k+1 Substituting into three exponential smoothing prediction models, merging the predicted points into the data point set calculated in the previous round after each prediction, removing the data point in the earliest period, using the obtained new data point set for the next round of calculation, and finally using the n+m-Data from k-1 phase to n+m-1 phase are substituted into alpha n-k+m And calculating an n+m-phase predicted value point.
Further, the three-order exponential smoothing prediction model is:
wherein,,
and->
For the horizontal and vertical coordinate values of the m-th stage predicted point, t is the period number of the measured data, m is the predicted step number, a t1 ，b t1 ，c t1 And a t2 ，b t2 ，c t2 Model parameters are predicted for the x-direction and the y-direction of the arc data points, respectively.
Further, the parameter a t1 ，b t1 ，c t1 Is calculated and parameter a t2 ，b t2 ，c t2 The same applies to the following formula:
a system for improving accuracy of evaluation of incomplete small circular arcs, comprising: the device comprises a first determining module, a second determining module, a fitting module, a point set external data point acquisition module, a judging module and an evaluating module;
the first determination module determines a first optimal smoothing coefficient alpha of a pre-established cubic exponential smoothing prediction model 1 ；
The second determining module is used for further determining the rest n-k optimal smoothing coefficients; n is the number of actually measured sample points, k is the period number of the time sequence, and k is less than n;
the fitting module fits the n-k optimal smooth coefficients to a change trend curve of the smooth coefficient alpha, and obtains the smooth coefficient of the predicted period number outside the data point set according to a fitting formula;
the data point outside the point set obtaining module calculates data points outside the predicted actual measurement data point set by using the smoothing coefficient of the predicted period number outside the data point set;
the judging module judges whether a preset prediction period number is reached, and if so, the data point sets are in reverse order, and the first determining module, the second determining module, the fitting module and the point set external data point acquisition module are repeatedly executed;
and the evaluation module combines the original actual measurement data point set and the predicted data point set to form a new data point set, and evaluates the curvature parameters of the new data point set by using an evaluation method, thereby improving the evaluation precision of the incomplete small circular arc.
Further, in the first determination module, a first optimal smoothing coefficient α 1 The determining method comprises the following steps: using the abscissa point set and the ordinate point set of the existing actually measured small arc profile data, wherein the number of actually measured sample points is n, and taking the ordinal number as the period number of the time sequence; assume that k-period data is adopted for each prediction fix; starting from the data in the 1 st period, performing exponential smoothing prediction on the data in the 1 st period to the data in the k th period for three times in the first calculation, and moving to the right for calculation; the smoothing coefficient alpha is in the value space [0,1 ]]Internal traversal search is carried out, step length calculated each time is set, a plurality of groups of k+1-phase predicted values are obtained, the k+1-phase predicted values are compared with k+1-phase actual measurement data, and the optimal smoothing coefficient alpha is determined according to the error square sum minimization principle 1 。
A computer readable storage medium storing one or more programs, the one or more programs comprising instructions, which when executed by a computing device, cause the computing device to perform any of the methods described above.
A computing apparatus, comprising: one or more processors, memory, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, the one or more programs comprising instructions for performing any of the methods described above.
Due to the adoption of the technical scheme, the invention has the following advantages: 1. according to the invention, the research object is reduced to the incomplete small arc with the central angle of less than 60 degrees, so that the stability of the evaluation of the curvature radius parameters of the arc is enhanced, and the improvement effect of the evaluation precision is more obvious. 2. Aiming at the problems that the subjectivity and the sensitivity of the selection of the smooth coefficient alpha in the general three-time exponential smoothing prediction process are too strong, an adaptive improvement algorithm is added on the basis of three-time exponential smoothing, and the optimal smooth coefficient of the prediction is searched in real time through the trend change of own data. The original accumulated iteration is changed into the fixed sample point movable iteration, so that the influence caused by the change of the number of the predicted sample points in the prediction process is reduced, the change trend of the optimal smooth coefficient is easier to analyze, and the more accurate predicted point is obtained. 3. According to the method, the evaluation results of different data under the same evaluation method are compared and analyzed, and the prediction angle of the method with the best evaluation accuracy improvement effect is verified; and comparing and analyzing the evaluation results of the same group of data under different evaluation methods, and verifying the universality of the application of the method.
Drawings
FIG. 1 is a schematic overall flow chart of a method according to an embodiment of the invention.
FIG. 2 is a schematic diagram of a fixed sample movement calculation in an embodiment of the invention;
FIG. 3 is a trend graph of the impact of small arc center angles on the evaluation in an embodiment of the invention;
FIG. 4 is a graph of a circular arc fit after three exponential smoothing processes alone;
FIG. 5 is a graph of an adaptive cubic exponential smoothing coefficient fit and a post-derivation in an embodiment of the present invention;
FIG. 6 is a graph of the bi-directional predictive fit of an adaptive cubic exponential smoothing method in an embodiment of the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. It will be apparent that the described embodiments are some, but not all, embodiments of the invention. All other embodiments, which are obtained by a person skilled in the art based on the described embodiments of the invention, fall within the scope of protection of the invention.
The invention will now be described in detail with reference to the drawings and examples.
The invention provides a method for improving evaluation precision of incomplete small circular arcs, which aims at evaluating small circular arc curvature radius parameters with a central angle of less than 60 degrees relative to a contour. The invention adopts a self-adaptive dynamic cubic exponential smoothing model, namely, an adaptive algorithm is added to optimize on the basis of a traditional cubic exponential smoothing prediction model. The self-adaptive three-time exponential smoothing method is not used for substituting all points into direct prediction like the traditional three-time exponential smoothing method, but only intercepting part of points from the first period data according to the existing data point set for three-time exponential smoothing; after the predicted data of the period is calculated, the data of the first period is removed and added into the measured data of the later period after one step of calculation is moved backwards. And traversing the value space of the smoothing coefficient alpha, performing step distance calculation to obtain a series of predicted points, comparing all the predicted points with the actual points in the current period, and obtaining the predicted point with the minimum error according to the error square sum minimization principle, and reversely deducing the smoothing coefficient value for predicting the point to obtain the real-time optimal smoothing predicted value. Through training of early historical data, a change trend curve of a smooth coefficient alpha can be fitted, and when the point set is predicted outside, the comparison of measured values is lacking, at the moment, the later smooth coefficient value is required to be calculated according to a fitting curve equation of alpha, and the smooth coefficient is directly used for participating in calculation and prediction of data points outside the measured data point set. The central angle of the contour data point set is increased based on the method of the self-adaptive three-time exponential smoothing prediction model, so that the evaluation accuracy of the incomplete small circular arc curvature radius parameter is improved.
As shown in fig. 1 and 2, the method of the present invention specifically includes the following steps:
step 1), determining a first optimal smoothing coefficient alpha of a pre-established cubic exponential smoothing prediction model 1 ；
The method comprises the following steps: utilize the existing actually measured small arc outline data to crossCoordinate point set X and ordinate point set Y, x= [ X ] 1 ，x 2 ，x 3 ，……]，Y＝[y 1 ，y 2 ，y 3 ，……]The number of the actually measured sample points is n, and the ordinal number is regarded as the period number of the time sequence; assume that each prediction fix takes a k period (k<n) data, starting from the 1 st data, performing exponential smoothing prediction on the 1 st to the k th data three times in the first calculation, and moving to the right for calculation. The smoothing coefficient alpha is in the value space [0,1 ]]Internal traversal search is carried out, step length calculated each time is set, a plurality of groups of k+1-phase predicted values are obtained, the k+1-phase predicted values are compared with k+1-phase actual measurement data, and the optimal smoothing coefficient alpha is determined according to the error square sum minimization principle 1 ；
Step 2), further determining the rest n-k optimal smoothing coefficients;
the method comprises the following steps: removing the 1 st period data, adopting the actual measurement data from the 2 nd period to the k+1 st period, and repeating the step 1) to obtain a second optimal smoothing coefficient alpha 2 And the like, finally obtaining the n-k best smoothing coefficient alpha n-k A total of n-k optimal smoothing coefficients are obtained.
Step 3), fitting n-k optimal smoothing coefficients to obtain a variation trend curve of a smoothing coefficient alpha, and obtaining a smoothing coefficient of a data point out-of-set prediction period according to a fitting formula;
when the point set is predicted, due to the lack of comparison of measured values, the later-stage smoothing coefficient value needs to be calculated according to the change trend curve and the fitting formula of the smoothing coefficient alpha.
The method comprises the following steps: will be alpha 1 To alpha n-k Fitting to obtain a fitting curve and a fitting formula, and calculating to obtain alpha n-k+1 ，α n-k+2 ，……，α n-k+m The method comprises the steps of carrying out a first treatment on the surface of the Where m is the number of epochs of the data point out-of-set prediction.
Step 4), calculating data points outside the predicted actual measurement data point set by using the smoothing coefficients of the predicted period number outside the data point set;
the method comprises the following steps: when the calculation is moved to the calculation of the (n+1) th stage predicted point by adopting the (n-k) th stage to (n) th stage measured arc data point set, the smoothing coefficient alpha obtained after fitting n-k+1 Substitution cubic exponential smoothing predictionThe model, after each prediction, the predicted point is integrated into the data point set of the previous round of calculation, the data point of the earliest first period is removed, the obtained new data point set is used for the next round of calculation, the number of the points used for each prediction is kept to be k, and the like, the data from the n+m-k-1 stage to the n+m-1 stage are used for substituting alpha n-k+m And (5) carrying out exponential smoothing for three times to calculate an n+m-th phase predicted value.
And 5) judging whether the preset prediction period number is reached, if so, changing the data point set into the reverse order, namely changing the data of the 1 st period into the n period, changing the n period into the 1 st period, and repeating the steps 1) to 4). And if the predicted period number is not reached, returning to the step 1) to repeatedly execute.
Step 6), combining the original actual measurement data point set and all the predicted data points to form a new data point set, and evaluating curvature parameters of the new data point set by using an evaluation method, so that the evaluation precision of the incomplete small arc is improved; the evaluation method can be a mature evaluation method in the prior art, and is not described herein.
In the above steps, knowing the abscissa point set X and the ordinate point set Y of the existing actually measured small arc profile data, the three-time exponential smoothing prediction model is:
wherein,,
and->
For the horizontal and vertical coordinate values of the m-th stage predicted point, t is the period number of the original measured data, m is the predicted step number, a t1 ，b t1 ，c t1 And a t2 ，b t2 ，c t2 Model parameters are predicted for the x-direction and the y-direction, respectively.
The method for predicting by adopting the three-time exponential smoothing prediction model comprises the following steps:
setting a smoothing coefficient alpha value and a smoothing initial value
Smoothing X three times (Y is the same):
x-direction model parameter a t1 ，b t1 ，c t1 The formula for the calculation of (2) is as follows:
model parameters a are predicted in the y-direction t2 ，b t2 ，c t2 And the same is done;
will a t1 ，b t1 ，c t1 And a t2 ，b t2 ，c t2 Substituting the index into the formula (1) to obtain the prediction point of the 1 st period, merging the obtained prediction points into a point set, carrying out exponential smoothing prediction for three times again, and setting the predicted step number m to obtain the m-period prediction value. The effect diagram of evaluating the new data point set is shown in fig. 3 by combining the predicted point of the three-time exponential smoothing prediction with the actual point.
Analysis of the results of the three exponential smoothing predictions in fig. 3, it was observed that although the accuracy of the previous data predictions was high, a significant shift occurred after less than 3 days of prediction, as shown in fig. 4. The reason for the deviation in analysis is that the selected smoothing coefficient alpha is too strong in subjectivity and too weak in sensitivity, so that the method is only suitable for one-time prediction, and the error is gradually accumulated due to poor adaptability to sample environment fluctuation. Aiming at the problem, the invention adds the self-adaptive algorithm to the traditional three-time exponential smoothing method for optimization, such as step 1) to step 6), thereby solving the optimization problem of the smoothing coefficient.
The invention also provides a system for improving the evaluation precision of the incomplete small circular arc, which comprises: the device comprises a first determining module, a second determining module, a fitting module, a point set external data point acquisition module, a judging module and an evaluating module;
a first determination module for determining a first optimal smoothing coefficient alpha of a pre-established cubic exponential smoothing prediction model 1 ；
The second determining module is used for further determining the rest n-k optimal smoothing coefficients; n is the number of actually measured sample points, k is the period number of the time sequence, and k is less than n;
the fitting module is used for fitting the n-k optimal smoothing coefficients to obtain a variation trend curve of a smoothing coefficient alpha, and obtaining a smoothing coefficient of the data point out-of-set prediction period number according to a fitting formula;
the data point outside the point set acquisition module calculates data points outside the predicted actual measurement data point set by using the smoothing coefficient of the predicted period number outside the data point set;
the judging module judges whether a preset prediction period number is reached, and if so, the data point set is in reverse order, and the first determining module, the second determining module, the fitting module and the point set outside data point acquisition module are repeatedly executed;
and the evaluation module combines the actual measurement data point set and the predicted data point set to form a new data point set, and evaluates the curvature parameters of the new data point set by using an evaluation method, thereby improving the evaluation precision of the incomplete small arc.
In the above embodiment, in the first determination module, the first optimal smoothing coefficient α 1 The determining method comprises the following steps: using the abscissa point set and the ordinate point set of the existing actually measured small arc profile data, wherein the number of actually measured sample points is n, and taking the ordinal number as the period number of the time sequence; assume that k-period data is adopted for each prediction fix; starting from the data in the 1 st period, performing exponential smoothing prediction on the data in the 1 st period to the data in the k th period for three times in the first calculation, and moving to the right for calculation; the smoothing coefficient alpha is in the value space [0,1 ]]Internal traversal search is carried out, step length calculated each time is set, a plurality of groups of k+1-phase predicted values are obtained, the k+1-phase predicted values are compared with k+1-phase actual measurement data, and the optimal smoothing coefficient alpha is determined according to the error square sum minimization principle 1 。
The present invention also provides a computer readable storage medium storing one or more programs, the one or more programs comprising instructions, which when executed by a computing device, cause the computing device to perform any of the methods described above.
The present invention also provides a computing device comprising: one or more processors, memory, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, the one or more programs comprising instructions for performing any of the methods described above.
Examples:
in this embodiment, the evaluation results before and after prediction of the different arc data are compared.
Nine groups of data point sets with theoretical radiuses of 0.05mm,1mm and 25mm respectively and contour corresponding to central angle gradients of 15 degrees, 30 degrees and 45 degrees are adopted, contour degree errors of the point sets are about 2.6% of theoretical radius values, and the number of the point sets is 50. And (3) performing bidirectional prediction of data by using a self-adaptive three-time exponential smoothing method, evaluating the curvature radius by using a least square method, comparing with a direct least square method, and analyzing the change condition of curvature radius evaluation accuracy under two conditions.
The principle of the method is that the change trend of the smoothing coefficient is analyzed by utilizing the earlier-stage data, the later-stage smoothing coefficient is adjusted by utilizing the trend, and the obtained smoothing coefficient is utilized to predict the data points outside the actually measured contour data point set. In the process of searching the optimal smooth coefficient through each iteration traversal in the earlier stage, the step length is set to be 0.001, the value space of alpha is set to be 0-1, and in order to improve the iteration speed, unnecessary calculation is reduced, and the value range of alpha can be reduced according to actual conditions; the k value of the number of sample points used for prediction is fixed to be 20 each time, so that 30 alpha values can be obtained from 50 actually measured point set data in the whole moving iteration process, the change trend of the alpha values is observed, a change curve and a change formula are obtained through fitting the alpha values, the change formula is utilized to obtain a smoothing coefficient used for predicting point set external data in the later period, and the obtained alpha values are utilized to continuously carry out fixed sample number moving calculation to obtain accurate outline point set external prediction points. The trend and fit of the smoothing coefficient α are shown in fig. 5.
In the process of fitting the smooth coefficient, a polyat function of matlab is used for fitting the smooth coefficient, and the alpha variation trend at the later stages of different fitting times has certain difference. And (3) through comprehensive analysis of multiple groups of data, selecting tertiary fitting from secondary fitting, tertiary fitting and quaternary fitting to have higher fitting goodness.
As shown in fig. 6, the same group of data prediction is used, compared with the prediction result of three times of exponential smoothing in fig. 4, the prediction error after the self-adaptive optimization is added is obviously reduced, the error accumulation speed is greatly delayed, the offset of the later prediction point relative to an ideal circle is greatly reduced, the prediction angle is increased, and the evaluation accuracy of the curvature radius is improved to a certain extent.
Through evaluation analysis of the data, the feasibility of the self-adaptive three-time exponential smoothing prediction method applied to incomplete small circular arc curvature radius parameter evaluation is verified, the method has an improvement effect on the evaluation precision, and a prediction angle with the best influence on the improvement effect is determined; and comparing and analyzing the evaluation results of the same group of data under different evaluation methods, and verifying the universality of the application of the method.
In summary, aiming at the problem of low evaluation accuracy of curvature radius parameters caused by poor integrity of small circular arcs in metering, the influence trend of the central angle of the small circular arc profile on the evaluation process is analyzed by utilizing simulation, and according to the result of the simulation analysis, the central angle of the profile data point set is increased by a method based on a self-adaptive three-time exponential smoothing prediction model, so that the evaluation accuracy of the curvature radius parameters is improved. According to the invention, the self-adaptive optimization algorithm is added on the basis of the three-time exponential smoothing method, so that the problem that the optimal smoothing coefficient is difficult to determine in the prediction process is solved, the traditional prediction model and the selection standard of each parameter are optimized, and the accuracy of the prediction point is improved. Experimental results show that aiming at a non-complete small arc profile data point set with the angle below 60 degrees, the method is utilized to expand the central angle of the profile by about 5 degrees so as to be optimal for the later evaluation process; and the method can be used as a previous data processing method and combined with different evaluation methods, and the evaluation accuracy of curvature radius parameters is improved to different degrees.
It will be appreciated by those skilled in the art that embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
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