CN112668125A - Method, system, medium and device for improving evaluation precision of incomplete small arc - Google Patents
Method, system, medium and device for improving evaluation precision of incomplete small 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 an incomplete small arc, which comprise the following steps: determining a first optimal smoothing coefficient of a pre-established cubic exponential smoothing prediction model; further determining the rest optimal smooth coefficients; fitting the optimal smooth coefficient to obtain a change trend curve of the smooth coefficient, and acquiring the smooth coefficient of the data point out-of-set prediction period according to a fitting formula; calculating and predicting data points outside the actually measured data point set by using a smoothing coefficient of the prediction period number outside the data point set; judging whether a preset prediction period number is reached, and if so, reversing the sequence of the data point sets; and combining the original measured data point set and the predicted data point set to form a new data point set, and evaluating the 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 method can improve the accuracy of the evaluation of the curvature radius parameters, and effectively improve the stability and the accuracy of the evaluation of the incomplete small arc curvature radius parameters.
Description
Technical Field
The invention relates to the technical field of mechanical part performance detection, in particular to a method, a system, a medium and equipment for improving the evaluation precision of an incomplete small arc.
Background
The incomplete small arc refers to an arc or a cambered surface of which the central angle corresponding to the arc contour is less than 120 degrees and the curvature radius range is 0-25 mm. The incomplete small circular arc profile is widely applied to the national defense science and technology industry and the precision manufacturing industry due to the special performance of the incomplete small circular arc profile: for example, the leading and trailing edge profiles of an aircraft engine blade, have a direct impact on the aerodynamic performance of the engine and the fatigue performance of the blade; the cutter point part of the numerical control machine tool cutter directly determines the processing precision; the edge of some precision parts is chamfered, which is used to remove the processing burr and improve the stress concentration of the parts. The curvature radius parameter is used as a core parameter of the small circular arc profile, and the precision of the curvature radius parameter is extremely important to the production and manufacturing performance of workpieces, so that urgent needs for accurate measurement and evaluation exist. However, due to the characteristics of non-integrity and small radius range of the circular arc, the difficulty of measurement and evaluation is high, and controversy exists in the accuracy of curvature radius parameter estimation.
The main arc parameters influencing the evaluation precision include the theoretical radius of the arc, the central angle of the arc contour point set and the contour degree error of the arc contour point set. In general, the smaller the theoretical radius of the arc, the greater the difficulty and error of evaluation; the smaller the central angle of the arc contour point set is, the poorer the accuracy of the curvature radius evaluation is; the larger the contour degree error of the contour point set is, the lower the evaluation precision is.
Among the three factors of influence, the arc radius is a desired target value, and cannot be adjusted. Therefore, it is common for researchers to improve the accuracy of evaluation by reducing the influence of the contour error or increasing the center angle, starting with the center angle of the arc contour point set and the contour error of the arc contour point set. For example, guervara et al propose a robust geometric method for fitting a set of points based on mean absolute error, which determines an iterative new direction with left and right hand derivatives by minimizing the sum of the geometric distances to the data points, based on a fast iterative algorithm of gradient or second derivative, fitting the data points into a circular arc, and then finding the radius. The algorithm can be used as a substitute method of a conventional algorithm on the aspect of calculation efficiency, the influence of the contour degree error on the evaluation process is reduced in principle, the robustness of the algorithm is enhanced, the algorithm is not sensitive to abnormal values and data noise, and the evaluation precision is further improved. Fei and the like start from the central angle of an 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 time sequence, interpolation is carried out, the central angle of a circular arc contour is increased by increasing the length of the circular arc, and finally the stability and the accuracy of fitting of the method are proved to be far better than those before prediction through training and learning of a large amount of data.
The above methods have good applications in some specific fields and working conditions, but all have certain limitations. For example, a Radial Basis Function Neural Network (RBFNN) based bidirectional prediction method has the disadvantages that the required arc contour data sample size is huge, the arc data sample size for training and learning in actual engineering is basically difficult to meet the requirement, and the application universality is not high.
Disclosure of Invention
In view of the above problems, an object of the present invention is to provide a method, a system, a medium, and an apparatus for improving the evaluation accuracy of an incomplete small arc, in which, after a small arc outline data point set is predicted and extended by using the method, the processed data point set is evaluated by using an evaluation method, so that the evaluation accuracy of a curvature radius parameter can be improved, and the stability and the accuracy of the evaluation of the incomplete small arc curvature radius parameter are effectively improved.
In order to achieve the purpose, the invention adopts the following technical scheme: a method for improving the evaluation accuracy of an incomplete small arc comprises the following steps:
step 1), determining a first optimal smoothing coefficient alpha of a pre-established cubic exponential smoothing prediction model1；
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 the n-k optimal smooth coefficients to obtain a variation trend curve of the smooth coefficient alpha, and acquiring the smooth coefficient of the data point out-of-set prediction period number according to a fitting formula;
step 4), calculating and predicting data points outside the actually measured data point set by using the smooth coefficient of the prediction period number outside the data point set;
step 5), judging whether the preset prediction period number is reached, if so, reversing the data point set, and repeating the steps 1) to 4);
and 6), combining the original measured data point set and the predicted data point set to form a new data point set, and evaluating the 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 the step 1), the first optimal smoothing coefficient α1The determination method comprises the following steps: the method comprises the following steps of utilizing an abscissa point set and an ordinate point set of existing actually measured small arc outline data, measuring the number of sample points as n, and regarding ordinal numbers as period numbers of a time sequence; assuming that each prediction fixedly adopts k-phase data; starting from the data in the 1 st stage, carrying out three times of exponential smooth prediction on the data from the 1 st stage to the data in the k stage by the first calculation, and moving the calculation to the right; the smooth coefficient alpha is in the value space [0,1 ]]Internal traversal search is carried out, step length of each calculation is set, a plurality of groups of k + 1-stage predicted values are obtained, the k + 1-stage predicted values are compared with k + 1-stage actual measured data, and the optimal smooth coefficient alpha is determined according to the error square sum minimization principle1。
Further, in the step 2), the determining method includes: removing the data of the 1 st stage, adopting the measured data from the 2 nd stage to the k +1 th stage, repeating the first optimal smooth coefficient determining method to obtain a second optimal smooth coefficient alpha2Finally, the n-k optimal smoothing coefficient alpha is obtainedn-kIn total, n-k optimal smoothing coefficients are obtained.
Further, in the step 4), the calculation method for predicting data points outside the actually measured data point set includes: when the calculation moves to the step of calculating the prediction point of the (n + 1) th period by adopting the actually measured arc data point set from the (n-k) th period to the (n) th period, the smoothing coefficient alpha obtained after fitting is usedn-k+1Substituting the prediction points into a cubic exponential smoothing prediction model, merging the prediction points into a data point set of the previous round of calculation after each prediction, removing the data point of the earliest period, using the obtained new data point set for the next round of calculation, and finally obtaining a new data point setSubstituting data from the n + m-k-1 stage to the n + m-1 stage into alphan-k+mAnd (4) calculating an n + m-th prediction value point.
Further, the cubic exponential smoothing prediction model is as follows:
wherein the content of the first and second substances,
and
is the horizontal and vertical coordinate value of the m-th prediction point, t is the period number of the measured data, m is the predicted step number, at1，bt1，ct1And at2，bt2，ct2And predicting model parameters in the x direction and the y direction of the arc data points respectively.
Further, the parameter at1，bt1，ct1Is obtained and the parameter at2，bt2，ct2Similarly, the formula is as follows:
a system for improving the accuracy of an incomplete small arc assessment, comprising: the device comprises a first determining module, a second determining module, a fitting module, an out-of-point data point acquiring module, a judging module and an evaluating module;
the first determining module determines a first optimal smoothing coefficient alpha of a pre-established cubic exponential smoothing prediction model1；
The second determining module is further used for 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 obtain a variation trend curve of the smooth coefficient alpha, and obtains the smooth coefficients of the data point out-of-set prediction period number according to a fitting formula;
the data point outside the data point set is predicted by the smooth coefficient of the data point outside the data point set prediction period;
the judging module is used for judging whether a preset prediction period number is reached or not, and if the preset prediction period number is reached, reversing the data point set, and repeatedly executing the first determining module, the second determining module, the fitting module and the data point acquisition module outside the point set;
the evaluation module combines the original measured data point set and the predicted data point set to form a new data point set, and the new data point set is subjected to curvature parameter evaluation by using an evaluation method, so that the evaluation precision of the incomplete small arc is improved.
Further, in the first determining module, a first optimal smoothing coefficient α1The determination method comprises the following steps: the method comprises the following steps of utilizing an abscissa point set and an ordinate point set of existing actually measured small arc outline data, measuring the number of sample points as n, and regarding ordinal numbers as period numbers of a time sequence; assuming that each prediction fixedly adopts k-phase data; starting from the data in the 1 st stage, carrying out three times of exponential smooth prediction on the data from the 1 st stage to the data in the k stage by the first calculation, and moving the calculation to the right; the smooth coefficient alpha is in the value space [0,1 ]]Internal traversal search is carried out, step length of each calculation is set, a plurality of groups of k + 1-stage predicted values are obtained, the k + 1-stage predicted values are compared with k + 1-stage actual measured data, and the optimal smooth coefficient alpha is determined according to the error square sum minimization principle1。
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 above methods.
A computing device, comprising: one or more processors, memory, and one or more programs stored in the memory and configured to be executed by the one or more processors, the one or more programs including instructions for performing any of the methods described above.
Due to the adoption of the technical scheme, the invention has the following advantages: 1. the invention reduces the research object to the incomplete small circular arc with the center angle below 60 degrees, enhances the stability of the evaluation of the curvature radius parameters of the circular arc and leads the effect of improving the evaluation precision to be more obvious. 2. Aiming at the problems of strong subjectivity and weak sensitivity of selection of a smoothing coefficient alpha in the general cubic exponential smoothing prediction process, the adaptive improvement algorithm is added on the basis of cubic exponential smoothing, and the predicted optimal smoothing coefficient is searched in real time through the trend change of self data. And the original accumulative iteration is changed into fixed sample point moving 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 more accurate predicted points are obtained. 3. The method uses the comparison and analysis of the evaluation results of different data under the same evaluation method, and verifies the best prediction angle of the method for the evaluation precision improvement effect; compared and analyzed by using evaluation results of the same group of data under different evaluation methods, and the universality of the method is verified.
Drawings
FIG. 1 is a schematic overall flow chart of a method in an embodiment of the present invention.
FIG. 2 is a schematic diagram of a fixed sample mobile computing in an embodiment of the present invention;
FIG. 3 is a trend graph of the impact of small arc center angle on the evaluation in an embodiment of the present invention;
FIG. 4 is a graph of a circular arc fit after cubic exponential smoothing alone;
FIG. 5 is a graph of fitting of adaptive cubic exponential smoothing coefficients and a graph of late derived values according to an embodiment of the present invention;
FIG. 6 is a diagram illustrating the fitting effect of bi-directional prediction by adaptive cubic exponential smoothing in the embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the drawings of the embodiments of the present invention. It is to be understood that the embodiments described are only a few embodiments of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the described embodiments of the invention, are within the scope of the invention.
The invention is described in detail below with reference to the figures and examples.
The invention provides a method for improving the evaluation accuracy of an incomplete small arc, which aims at evaluating the curvature radius parameter of the small arc with the central angle of less than 60 degrees relative to a contour. The invention adopts a self-adaptive dynamic cubic exponential smoothing model, namely, a self-adaptive algorithm is added on the basis of the traditional cubic exponential smoothing prediction model for optimization. The self-adaptive cubic exponential smoothing method is not like the traditional cubic exponential smoothing method that all points are substituted into direct prediction, but only a part of points are intercepted to carry out cubic exponential smoothing from first-stage data according to the existing data point set; after the predicted data of the period is calculated, the calculation is carried out by one step backwards, and the data of the first period is removed and added into the actually measured data of the next period in each movement. And traversing the value space of the smoothing coefficient alpha, performing fixed step distance calculation to obtain a series of predicted points, comparing all the predicted points with current actual measured points, obtaining the predicted point with the minimum error according to the error square sum minimization principle, and reversely deducing the smoothing coefficient value of the predicted point, namely the real-time optimal smoothing predicted value. The change trend curve of the smooth coefficient alpha can be fitted through the training of the prior historical data, when the data point set is predicted, due to the lack of comparison of measured values, the later smooth coefficient value needs to be calculated according to the fitting curve equation of the alpha, and the smooth coefficient is directly used for participating in calculation and prediction of data points outside the measured data point set. The invention increases the center angle of the outline data point set based on a method of a self-adaptive cubic exponential smoothing prediction model, thereby improving the evaluation precision of the radius parameter of the incomplete small arc curvature.
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 model1；
The method specifically comprises the following steps: utilizing the existing actually measured number of small arc profilesAccording to an abscissa point set X and an ordinate point set Y, X ═ X1，x2，x3，……]，Y＝[y1，y2，y3，……]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 fixes the use of k periods (k)<n) data, starting from the 1 st stage data, the first calculation makes three times of exponential smooth prediction on the 1 st stage data to the k th stage data, and moves the calculation to the right. The smooth coefficient alpha is in the value space [0,1 ]]Internal traversal search is carried out, step length of each calculation is set, a plurality of groups of k + 1-stage predicted values are obtained, the k + 1-stage predicted values are compared with k + 1-stage actual measured data, and the optimal smooth coefficient alpha is determined according to the error square sum minimization principle1；
Step 2), further determining the rest n-k optimal smoothing coefficients;
the method specifically comprises the following steps: removing the data of the 1 st stage, adopting the measured data from the 2 nd stage to the k +1 th stage, repeating the step 1) to obtain a second optimal smoothing coefficient alpha2And so on, finally obtaining the n-k optimal smooth coefficient alphan-kIn total, n-k optimal smoothing coefficients are obtained.
Step 3), fitting the n-k optimal smooth coefficients to obtain a variation trend curve of the smooth coefficient alpha, and acquiring the smooth coefficient of the data point out-of-set prediction period number according to a fitting formula;
in the prediction outside the point set, due to lack of comparison of measured values, the later stage smoothing coefficient value needs to be calculated according to the variation trend curve of the smoothing coefficient alpha and the fitting formula.
The method specifically comprises the following steps: will be alpha1To alphan-kFitting to obtain a fitting curve and a fitting formula, and calculating to obtain alphan-k+1，αn-k+2，……，αn-k+m(ii) a Wherein m is the number of periods of data point out-of-set prediction.
Step 4), calculating and predicting data points outside the actually measured data point set by using the smooth coefficient of the prediction period number outside the data point set;
the method specifically comprises the following steps: when the calculation moves to the step of calculating the prediction point of the (n + 1) th period by adopting the actually measured arc data point set from the (n-k) th period to the (n) th period, the smoothing coefficient alpha obtained after fitting is usedn-k+1Substituted cubic exponential smoothingAnd the prediction model is used for merging the predicted points into the data point set of the previous round of calculation after each prediction, removing the data point of the earliest period, using the obtained new data point set for the next round of calculation, keeping the number of the points used for prediction each time constant to be k, and repeating the steps by analogy, using the data from the n + m-k-1 stage to the n + m-1 stage, and substituting the data into the data from the n + m-k-1 stage to the n + m-1 stagen-k+mAnd (5) carrying out three times of exponential smoothing to calculate the predicted value of the n + m period.
Step 5), judging whether the preset prediction period number is reached, if so, reversing the data point set, namely changing the 1 st period data into the nth period data and changing the nth period into the 1 st period data, and repeating the steps 1) to 4). And if the predicted period number is not reached, returning to the step 1) to be repeatedly executed.
Step 6), combining the original measured data point set with all predicted data points to form a new data point set, and evaluating the 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 adopt a mature evaluation method in the prior art, and is not described herein again.
In the above steps, if the abscissa point set X and the ordinate point set Y of the existing actually measured small arc contour data are known, the cubic exponential smoothing prediction model is:
wherein the content of the first and second substances,
and
is the horizontal and vertical coordinate value of the predicted point of the mth stage, t is the stage number of the original measured data, m is the predicted step number, at1，bt1，ct1And at2，bt2，ct2The model parameters are predicted for the x-direction and y-direction, respectively.
The method for predicting by adopting the cubic exponential smoothing prediction model comprises the following steps:
setting a smoothing coefficient alpha value and a smoothing initial value
Three smoothing passes were performed on X (Y is the same):
the x-direction model parameter at1，bt1，ct1The formula of (2) is as follows:
y-direction prediction model parameter at2，bt2，ct2The same process is carried out;
a is tot1，bt1，ct1And at2，bt2，ct2And substituting the predicted point into the formula (1) to obtain the predicted point of the 1 st period, merging the obtained predicted point into the point set, performing three times of exponential smoothing prediction again, and setting the predicted step number m to obtain the predicted value of the m period. The effect graph of combining the predicted points predicted by the three-time exponential smoothing prediction with the actual measured points and evaluating the new data point set is shown in fig. 3.
Analysis of the results of the three-time exponential smoothing prediction in fig. 3 shows that although the accuracy of the data prediction in the first few periods is high, a significant deviation occurs after the prediction is less than 3 periods, as shown in fig. 4. The reason for analyzing the deviation is that the selected smoothing coefficient alpha is too strong in subjectivity and too weak in sensitivity and is only suitable for one-time prediction, and errors are gradually accumulated due to the fact that the adaptability to sample environment fluctuation is poor. Aiming at the problem, the invention adds an adaptive algorithm to the traditional cubic 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 arc, which comprises the following steps: the device comprises a first determining module, a second determining module, a fitting module, an out-of-point data point acquiring module, a judging module and an evaluating module;
a first determining module for determining a first optimal smoothing coefficient alpha of a pre-established cubic exponential smoothing prediction model1；
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 smooth coefficients to obtain a change trend curve of the smooth coefficient alpha and acquiring the smooth coefficient of the data point out-of-set prediction period number according to a fitting formula;
the data point outside the data point set is predicted by the smooth coefficient of the data point outside the data point set prediction period;
the judging module is used for judging whether the preset prediction period number is reached or not, and if the preset prediction period number is reached, the data point set is in a reverse order, and the first determining module, the second determining module, the fitting module and the point out-of-set data point obtaining module are repeatedly executed;
and the evaluation module is used for combining the actually measured data point set and the predicted data point set to form a new data point set, and evaluating the 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.
In the above embodiment, in the first determining module, the first optimal smoothing coefficient α1The determination method comprises the following steps: the method comprises the following steps of utilizing an abscissa point set and an ordinate point set of existing actually measured small arc outline data, measuring the number of sample points as n, and regarding ordinal numbers as period numbers of a time sequence; assuming that each prediction fixedly adopts k-phase data; starting from the data in the 1 st stage, carrying out three times of exponential smooth prediction on the data from the 1 st stage to the data in the k stage by the first calculation, and moving the calculation to the right; the smooth coefficient alpha is in the value space [0,1 ]]Internal traversal search is carried out, step length of each calculation is set, a plurality of groups of k + 1-stage predicted values are obtained, the k + 1-stage predicted values are compared with k + 1-stage actual measured data, and the optimal smooth coefficient alpha is determined according to the error square sum minimization principle1。
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 including instructions for performing any of the above-described methods.
Example (b):
in this embodiment, the evaluation results before and after prediction are compared for different arc data.
Nine groups of data point sets with theoretical radiuses of 0.05mm, 1mm and 25mm respectively and with central angle gradients of 15 degrees, 30 degrees and 45 degrees respectively are adopted, the profile error of the point sets is about 2.6 percent of the theoretical radius value, and the number of the point sets is 50. And performing bidirectional prediction on data by using a self-adaptive cubic exponential smoothing method, evaluating the curvature radius by using a least square method, and analyzing the change condition of the evaluation precision of the curvature radius under two conditions compared with the condition of directly using the least square method.
The principle of the method is that the change trend of the smoothing coefficient is analyzed by using the early-stage data, the later-stage smoothing coefficient is adjusted by the trend, and the obtained smoothing coefficient is used for predicting data points outside the actually measured contour data point set. In the process of searching the optimal smooth coefficient in each iteration traversal in the previous period, the step length is set to be 0.001, the value space of alpha is 0-1, and in order to improve the iteration speed and reduce unnecessary calculation, the value range of alpha can be reduced according to the actual condition; the number k of the sample points used for prediction each time is fixed to be 20, so that 30 alpha values can be obtained from 50 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 smooth coefficient used for predicting the data outside the point set in the later period can be obtained by using the change formula, and the accurate outline point outside the set can be obtained by using the obtained alpha values and continuing to perform fixed sample number moving calculation. The trend of the change of the smoothing coefficient α and the fitting are shown in fig. 5.
In the process of fitting the smooth coefficient, fitting the matlab by using a polyfit function of the matlab, wherein alpha variation trends in later stages of different fitting times have certain difference. Through comprehensive analysis of multiple groups of data, the third fitting is selected to have higher goodness of fit among the second fitting, the third fitting and the fourth fitting.
As shown in fig. 6, by using the same set of data prediction and comparing the prediction result obtained by using cubic exponential smoothing alone in fig. 4, the prediction error is obviously reduced after adding the adaptive optimization, the error accumulation speed is greatly delayed, the offset of the later prediction point relative to the 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 the evaluation and analysis of the data, the feasibility of the adaptive cubic exponential smoothing prediction method applied to the evaluation of the radius parameter of the incomplete small arc is verified, the method has a promotion effect on the evaluation precision, and a prediction angle with the best influence on the promotion effect is determined; compared and analyzed by using evaluation results of the same group of data under different evaluation methods, and the universality of the method is verified.
In conclusion, aiming at the problem of low evaluation precision of the curvature radius parameter caused by poor integrity of small arcs in metrology, the invention utilizes simulation to analyze the influence trend of the central angle of the small arc profile on the evaluation process, and according to the result of the simulation analysis, the invention increases the central angle of the profile data point set based on a method of a self-adaptive cubic exponential smoothing prediction model, thereby improving the evaluation precision of the curvature radius parameter. According to the method, the self-adaptive optimization algorithm is added on the basis of the cubic exponential smoothing method, 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 precision of the predicted point is improved. The experimental result shows that aiming at the incomplete small arc outline data point set below 60 degrees, the central angle of the outline is enlarged by about 5 degrees by using the method, so that the later evaluation process is optimal; and the method can be used as an early-stage data processing method and combined with different evaluation methods, and the evaluation precision of the curvature radius parameter is improved to different degrees.
As will be appreciated by one skilled in the art, 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 flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams 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.
Claims (10)
1. A method for improving the evaluation accuracy of an incomplete small arc is characterized by comprising the following steps:
step 1), determining a first optimal smoothing coefficient alpha of a pre-established cubic exponential smoothing prediction model1；
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 the n-k optimal smooth coefficients to obtain a variation trend curve of the smooth coefficient alpha, and acquiring the smooth coefficient of the data point out-of-set prediction period number according to a fitting formula;
step 4), calculating and predicting data points outside the actually measured data point set by using the smooth coefficient of the prediction period number outside the data point set;
step 5), judging whether the preset prediction period number is reached, if so, reversing the data point set, and repeating the steps 1) to 4);
and 6), combining the original measured data point set and the predicted data point set to form a new data point set, and evaluating the 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.
2. The method as set forth in claim 1, wherein in step 1), the first optimal smoothing coefficient α is1The determination method comprises the following steps: the method comprises the following steps of utilizing an abscissa point set and an ordinate point set of existing actually measured small arc outline data, measuring the number of sample points as n, and regarding ordinal numbers as period numbers of a time sequence; assuming that each prediction fixedly adopts k-phase data; starting from the data in the 1 st stage, carrying out three times of exponential smooth prediction on the data from the 1 st stage to the data in the k stage by the first calculation, and moving the calculation to the right; the smooth coefficient alpha is in the value space [0,1 ]]Internal traversal search is carried out, step length of each calculation is set, a plurality of groups of k + 1-stage predicted values are obtained, the k + 1-stage predicted values are compared with k + 1-stage actual measured data, and the optimal smooth coefficient alpha is determined according to the error square sum minimization principle1。
3. The method as claimed in claim 2, wherein in the step 2), the determination method is: removing data of phase 1Repeating the first optimal smoothing coefficient determining method by adopting the measured data from the 2 nd period to the k +1 th period to obtain a second optimal smoothing coefficient alpha2Finally, the n-k optimal smoothing coefficient alpha is obtainedn-kIn total, n-k optimal smoothing coefficients are obtained.
4. The method of claim 1, wherein the step 4) of predicting data points outside the set of measured data points is performed by: when the calculation moves to the step of calculating the prediction point of the (n + 1) th period by adopting the actually measured arc data point set from the (n-k) th period to the (n) th period, the smoothing coefficient alpha obtained after fitting is usedn-k+1Substituting into a cubic exponential smoothing prediction model, merging the predicted points into a data point set of the previous round of calculation after each prediction, removing the data point of the earliest period, using the obtained new data point set for the next round of calculation, and finally substituting alpha into the data from the (n + m-k-1) th period to the (n + m-1) th periodn-k+mAnd (4) calculating an n + m-th prediction value point.
5. The method of claim 1, wherein the cubic exponential smoothing prediction model is:
wherein the content of the first and second substances,
and
is the horizontal and vertical coordinate value of the m-th prediction point, t is the period number of the measured data, m is the predicted step number, at1，bt1，ct1And at2，bt2，ct2And predicting model parameters in the x direction and the y direction of the arc data points respectively.
6. The method of claim 5, wherein the parameter at1，bt1，ct1Is obtained and the parameter at2，bt2，ct2Similarly, the formula is as follows:
7. a system for improving the evaluation accuracy of incomplete small arcs is characterized by comprising: the device comprises a first determining module, a second determining module, a fitting module, an out-of-point data point acquiring module, a judging module and an evaluating module;
the first determining module determines a first optimal smoothing coefficient alpha of a pre-established cubic exponential smoothing prediction model1；
The second determining module is further used for 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 obtain a variation trend curve of the smooth coefficient alpha, and obtains the smooth coefficients of the data point out-of-set prediction period number according to a fitting formula;
the data point outside the data point set is predicted by the smooth coefficient of the data point outside the data point set prediction period;
the judging module is used for judging whether a preset prediction period number is reached or not, and if the preset prediction period number is reached, reversing the data point set, and repeatedly executing the first determining module, the second determining module, the fitting module and the data point acquisition module outside the point set;
the evaluation module combines the original measured data point set and the predicted data point set to form a new data point set, and the new data point set is subjected to curvature parameter evaluation by using an evaluation method, so that the evaluation precision of the incomplete small arc is improved.
8. The system of claim 7, wherein the first determining module determines the first optimal smoothing factor α1The determination method comprises the following steps: utilizing existing actual measurement of small arc contourData abscissa point set and ordinate point set, the number of actually measured sample points is n, and regard ordinal number as the period number of the time series; assuming that each prediction fixedly adopts k-phase data; starting from the data in the 1 st stage, carrying out three times of exponential smooth prediction on the data from the 1 st stage to the data in the k stage by the first calculation, and moving the calculation to the right; the smooth coefficient alpha is in the value space [0,1 ]]Internal traversal search is carried out, step length of each calculation is set, a plurality of groups of k + 1-stage predicted values are obtained, the k + 1-stage predicted values are compared with k + 1-stage actual measured data, and the optimal smooth coefficient alpha is determined according to the error square sum minimization principle1。
9. 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 of claims 1-6.
10. A computing device, comprising: one or more processors, memory, and one or more programs stored in the memory and configured to be executed by the one or more processors, the one or more programs including instructions for performing any of the methods of claims 1-6.
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN115223365A (en) * | 2022-07-15 | 2022-10-21 | 北京市智慧交通发展中心(北京市机动车调控管理事务中心) | Road network speed prediction and anomaly identification method based on damping Holt model |
Citations (13)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2004334328A (en) * | 2003-04-30 | 2004-11-25 | Nri & Ncc Co Ltd | Merchandise demand predicting system and same system at beginning/end of year |
| CN101425158A (en) * | 2008-12-04 | 2009-05-06 | 清华大学 | Short term load prediction method based on information |
| US20120303411A1 (en) * | 2011-05-25 | 2012-11-29 | International Business Machines Corporation | Demand modeling and prediction in a retail category |
| CN103559563A (en) * | 2013-11-20 | 2014-02-05 | 国家电网公司 | Method for predicting wind speed of wind power plant at short term |
| CN103617548A (en) * | 2013-12-06 | 2014-03-05 | 李敬泉 | Medium and long term demand forecasting method for tendency and periodicity commodities |
| CN103809521A (en) * | 2012-11-14 | 2014-05-21 | 中国科学院沈阳计算技术研究所有限公司 | Spline curve interpolation method based on secant method |
| CN105761489A (en) * | 2016-04-13 | 2016-07-13 | 南京邮电大学 | Cubic exponential smoothing optimal method of traffic flow prediction |
| US20160336154A1 (en) * | 2015-05-12 | 2016-11-17 | Hitachi High-Technologies Corporation | Plasma processing apparatus, data processing apparatus and data processing method |
| CN107239849A (en) * | 2017-04-17 | 2017-10-10 | 西安电子科技大学 | One kind is based on improved exponential smoothing gray model Methods of electric load forecasting |
| CN107527118A (en) * | 2017-08-31 | 2017-12-29 | 佛山科学技术学院 | A kind of self-adapted tolerance exponential smoothing forecasting procedure |
| CN107942139A (en) * | 2017-12-28 | 2018-04-20 | 哈尔滨工业大学 | A kind of novel electric power harmonic parameters synchronous sampling by software method |
| CN108038040A (en) * | 2017-12-08 | 2018-05-15 | 上海市信息网络有限公司 | Computer cluster performance indicator detection method, electronic equipment and storage medium |
| CN109116716A (en) * | 2018-08-27 | 2019-01-01 | 中国人民解放军空军工程大学 | Based on the clock deviation forecasting procedure for improving exponential smoothing |
-
2021
- 2021-01-06 CN CN202110010711.7A patent/CN112668125B/en active Active
Patent Citations (13)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2004334328A (en) * | 2003-04-30 | 2004-11-25 | Nri & Ncc Co Ltd | Merchandise demand predicting system and same system at beginning/end of year |
| CN101425158A (en) * | 2008-12-04 | 2009-05-06 | 清华大学 | Short term load prediction method based on information |
| US20120303411A1 (en) * | 2011-05-25 | 2012-11-29 | International Business Machines Corporation | Demand modeling and prediction in a retail category |
| CN103809521A (en) * | 2012-11-14 | 2014-05-21 | 中国科学院沈阳计算技术研究所有限公司 | Spline curve interpolation method based on secant method |
| CN103559563A (en) * | 2013-11-20 | 2014-02-05 | 国家电网公司 | Method for predicting wind speed of wind power plant at short term |
| CN103617548A (en) * | 2013-12-06 | 2014-03-05 | 李敬泉 | Medium and long term demand forecasting method for tendency and periodicity commodities |
| US20160336154A1 (en) * | 2015-05-12 | 2016-11-17 | Hitachi High-Technologies Corporation | Plasma processing apparatus, data processing apparatus and data processing method |
| CN105761489A (en) * | 2016-04-13 | 2016-07-13 | 南京邮电大学 | Cubic exponential smoothing optimal method of traffic flow prediction |
| CN107239849A (en) * | 2017-04-17 | 2017-10-10 | 西安电子科技大学 | One kind is based on improved exponential smoothing gray model Methods of electric load forecasting |
| CN107527118A (en) * | 2017-08-31 | 2017-12-29 | 佛山科学技术学院 | A kind of self-adapted tolerance exponential smoothing forecasting procedure |
| CN108038040A (en) * | 2017-12-08 | 2018-05-15 | 上海市信息网络有限公司 | Computer cluster performance indicator detection method, electronic equipment and storage medium |
| CN107942139A (en) * | 2017-12-28 | 2018-04-20 | 哈尔滨工业大学 | A kind of novel electric power harmonic parameters synchronous sampling by software method |
| CN109116716A (en) * | 2018-08-27 | 2019-01-01 | 中国人民解放军空军工程大学 | Based on the clock deviation forecasting procedure for improving exponential smoothing |
Non-Patent Citations (5)
| Title |
|---|
| LIJIE YAN ET AL.: "The predicted load balancing algorithm based on the dynamic exponential smoothing", 《OPEN PHYSICS》 * |
| TONG NIU ET AL.: "An improved prediction model combining inverse exponential smoothing and Markov chain", 《MATHEMATICAL PROBLEMS IN ENGINEERING》 * |
| 史永等: "一种实用的短期负荷组合预测方法", 《现代电力》 * |
| 杨济瑞等: "改进的三次指数平滑法及其在车联网中的应用", 《计算机技术与发展》 * |
| 沈海迪等: "基于指数平滑法的动态预测机制", 《计算机技术与发展》 * |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN115223365A (en) * | 2022-07-15 | 2022-10-21 | 北京市智慧交通发展中心(北京市机动车调控管理事务中心) | Road network speed prediction and anomaly identification method based on damping Holt model |
| CN115223365B (en) * | 2022-07-15 | 2023-09-29 | 北京市智慧交通发展中心(北京市机动车调控管理事务中心) | Road network speed prediction and anomaly identification method based on damping Holt model |
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