CN112923847B - Local sine auxiliary grating ruler measurement error adaptive compensation method - Google Patents
Local sine auxiliary grating ruler measurement error adaptive compensation method Download PDFInfo
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Abstract
The application discloses a grating ruler measurement error self-adaptive compensation method assisted by local sine, wherein a sine signal is superposed to an original measurement error signal of a grating ruler to reconstruct the measurement error signal of the grating ruler, so that a mode aliasing phenomenon is inhibited. The method comprises the steps of obtaining a plurality of IMF components through empirical mode decomposition, carrying out threshold transformation based on preset self-adaptive IMF screening conditions after singular value decomposition is carried out on the IMF components, selecting the IMF components meeting the conditions as trend error components, and then obtaining the total trend error components to compensate the grating ruler, so that the basic trend of the measurement error of the grating ruler is eliminated, the measurement precision of the grating ruler is effectively improved, and the accuracy of measurement error compensation is improved.
Description
Technical Field
The application relates to the technical field of grating scales, in particular to a local sine auxiliary grating scale measurement error self-adaptive compensation method.
Background
The noun explains:
empirical mode decomposition: the Empical Mode Decomposition, abbreviated as EMD, is an algorithm for signal analysis and processing, and the idea of the algorithm is as follows: decomposing the complex signal into finite Intrinsic Mode Function (IMF) components, wherein each IMF component contains local characteristic signals of the original signal at different time scales;
IMF: intrinsic Mode Function;
the grating ruler is a high-precision position sensor, and the measurement precision of the grating ruler directly influences the machining precision of the numerical control machine tool. However, the grating ruler has various error factors such as photoelectric system error, vibration error, installation error and temperature error, and the measurement accuracy of the grating ruler is affected.
Specifically, in the error of the photoelectric system, two paths of orthogonal sinusoidal signals are subdivided to achieve the purpose of precision measurement, but the fringe signal of the photoelectric system has error components caused by direct current level, high-frequency noise, unequal amplitude, waveform distortion, phase offset and the like; in the vibration error, the error value of the grating ruler fluctuates in a certain range of the true value, once an error code occurs in the code reading of the image acquisition absolute grating ruler, the phenomenon of error decoding of the point reading can be directly caused, and the numerical value deviation has no reference value. Due to the influence of a series of error factors, the area with data exception has uncertainty, and various uncertainties may also occur due to the coupling effect of various error factors, and meanwhile, the measurement error of the grating ruler is nonlinear and non-stable due to a series of environmental factors.
Trend analysis of the time series shows that the measurement error is composed of an inherent component and a random component, wherein the inherent component is caused by the accumulation process of vibration and temperature change, and the random component is a random error reflecting other uncertain factors. The inherent component of the measurement error of the grating ruler is mainly reflected in the low-frequency component, while the distribution condition of different extreme values has certain influence on the low-frequency component, and the distribution of the low-frequency component may be influenced due to error factors and data abnormality, so that a mode aliasing phenomenon is generated. The mode aliasing is mainly caused by the intermittent phenomenon, and the intermittent phenomenon is often caused by abnormal events, such as intermittent signals, impulse interference, noise and the like. The influence of different degrees causes the abnormal event of the measurement error of the grating ruler, and it is not easy to find out the area where the data abnormality may occur. In order to inhibit data abnormity of error data, the accuracy of measurement errors can be kept, and error compensation is one of effective means for improving the measurement precision of the grating ruler.
In 2017, Mechanical Systems and Signal Processing journal discloses an absolute optical encoder error compensation method based on empirical mode decomposition, the method decomposes a grating ruler measurement error into a plurality of IMF components with different frequencies by using empirical mode decomposition, and because the HMS of the IMF components gives the whole energy distribution in the whole frequency range, the IMF components can be determined by using the local energy distribution of frequency subspans. The total frequency span of the HMS of the IMF component is averagely divided into three subspans, namely a low-frequency subspan, a medium-frequency subspan and a high-frequency subspan, the local energy distribution of the low-frequency subspan is used for dominating, the selected IMF component can be identified as a low-frequency signal, a trend component is constructed, and then error compensation is carried out. Although the grating ruler measurement error is decomposed by empirical mode decomposition, so that the grating ruler error compensation is realized, due to the comprehensive influence of various error factors, the measurement error data can cause data abnormity in partial regions, the inherent components of the measurement error are influenced, the IMF component can generate a mode aliasing phenomenon, the extraction of a trend component is influenced, and the accuracy of the error compensation is influenced.
Chinese patent publication No. CN106091925A discloses a multi-interference-factor-coupled grating scale error compensation method, which includes obtaining action strength values of multiple interference factors by using multiple sensors during grating scale measurement, matching the action strength values with an error compensation database to obtain an optimal error compensation amount corresponding to the action strength values, and compensating a grating scale system by using the optimal error compensation amount. However, the method cannot process the basic characteristics of the measurement error data of the sensor, and cannot fundamentally improve the measurement precision, thereby affecting the accuracy of error compensation.
Disclosure of Invention
The application provides a local sine auxiliary grating ruler measurement error self-adaptive compensation method, which is used for solving the technical problem of poor accuracy of error compensation.
In view of this, the present application provides a local sine assisted grating scale measurement error adaptive compensation method, which includes the following steps:
s101: based on instrument errors and background environment interference factors generated by considering a grating ruler, a preset sinusoidal signal is superposed to an original measurement error signal of the grating ruler, so that a measurement error signal of the grating ruler is reconstructed;
s102: decomposing the reconstructed measurement error signal into a plurality of IMF components by adopting an empirical mode decomposition algorithm;
s103: performing singular value decomposition on each IMF component to obtain a non-zero singular value corresponding to each IMF component;
s104: performing threshold value transformation based on a preset adaptive IMF screening condition, thereby screening an IMF component which meets the preset adaptive IMF screening condition as a trend error component;
s105: accumulating IMF components corresponding to the trend error components to be used as total trend error components of the original measurement error signals of the grating ruler;
s106: and compensating the grating ruler by taking the total trend error component as an error compensation signal.
Preferably, the step S101 includes, before:
s1001: and linear interpolation is adopted to carry out linear interpolation processing on the original measurement error signal of the grating ruler.
Preferably, after the step S1001, the step S101 includes:
s1101: judging whether the amplitude variation of two adjacent original measurement error signals of the grating ruler is smaller than a preset multiple of the extreme value difference of the extreme value areas corresponding to the two adjacent original measurement error signals, if so, judging that the original measurement error signals corresponding to the extreme value areas have data abnormal sections.
Preferably, the step S101 specifically includes:
and adding a single-period sinusoidal signal with a preset amplitude value to the data abnormal section, so as to locally adjust the extreme value distribution condition of the original data and further construct a reconstruction measurement error of the grating ruler.
Preferably, the preset amplitude value is 0.3.
Preferably, the step S102 specifically includes:
decomposing the reconstructed measurement error signal of the grating ruler into a plurality of IMF components by adopting an empirical mode decomposition algorithm according to the following formula 1:
in formula 1, X (t) is the reconstruction measurement error, i is a natural number, n is the total number of decomposed IMF components, ci(t) is the ith IMF component after empirical mode decomposition, and when i is equal to n, c isi(t) is a residual component.
Preferably, the step S103 specifically includes:
s1031: constructing a corresponding reconstruction matrix for each IMF component according to equation 2 below:
in the formula 2, DiThe reconstruction matrix constructed for the ith IMF component, L being the total length of data for that IMF component, IMFi(k) The amplitude of the kth data point in the ith IMF component, k being 1,2,3.., L;
s1032: performing singular value decomposition on the reconstruction matrix according to the following formula 3 to obtain a group of non-zero singular values:
in equation 3, U, V are all orthogonal matrices, Σ is a diagonal matrix, and the diagonal element is DiThe non-zero singular values of (a) are sorted in a non-negative descending order, and H is a conjugate transpose of a matrix;
s1033: and reconstructing by using the non-zero singular value to obtain a reconstructed error signal component.
Preferably, the step S104 specifically includes:
s1041: obtaining a series of corresponding optimal effective ranks by transforming correlation coefficient threshold values of screening conditions based on the screening conditions of the following formulas 4-8 before and after singular value decomposition according to each IMF component, wherein the optimal effective rank is defined as ropt：
roptR formula 4
s.t.Cr(ci(t),Si,r) Epsilon formula 5
DCr＝Cr+1-CrR-1, R-1 formula 6
DCr-1＜ε1Formula 7
DCr＜ε1Formula 8
In the above formulas 4-8, r is the number of non-zero singular values selected by the reconstruction error signal component; crReconstructing correlation coefficients of the error signal components for the IMF components using different non-zero singular values; c. Ci(t) is the ith IMF component after empirical mode decomposition; si,rReconstructing error signal components reconstructed using r singular values for the ith IMF component; epsilon is a correlation coefficient threshold value of the IMF component and the error signal component reconstructed by using different non-zero singular values; r is the total number of non-zero singular values; DC (direct current)rIncreasing the correlation coefficient increment of the reconstructed error signal component along with the number r of the singular values; DC (direct current)r-1Increment of correlation coefficient corresponding to the r-1 th singular value; epsilon1Increasing a threshold value for the influence of the preset effective rank of the non-zero singular value on a correlation coefficient;
s1042: averagely dividing the step length of the correlation coefficient threshold into a plurality of sections, and when the minimum value of the optimal effective rank corresponding to the correlation coefficient threshold of each section is equal to the average effective rank corresponding to the correlation coefficient threshold of the corresponding section, obtaining the minimum value in the optimal effective ranks corresponding to the correlation coefficient thresholds of the plurality of sections as the minimum optimal singular value effective rank of the current IMF component by comparing the optimal effective ranks corresponding to the correlation coefficient thresholds of the plurality of sections;
s1043: calculating to obtain an important factor corresponding to the IMF component according to the following formula 9, judging whether the important factor is larger than a preset important factor threshold value, and if so, judging that the IMF component is a trend error component:
in formula 9, P is an important factor, εmaxIs a preset maximum correlation threshold value with the value of 0.99, rmaxIs a singular optimal effective grade r 'corresponding to a preset maximum correlation threshold value'optIs the minimum optimal singular value effective rank, and epsilon 'is r'optA respective maximum correlation coefficient threshold;
s1044: and obtaining all IMF components meeting the screening condition through the step S043, thereby determining the IMF components corresponding to all trend error components.
Preferably, the step S105 specifically includes:
and according to the following formula 10, accumulating all the trend error components to be used as the total trend error component of the original measurement error signal of the grating scale:
Γ(t)＝∑c'i(t) formula 10
In expression 10, Γ (t) is a trend error component, c'iAnd (t) is an IMF component corresponding to the trend error component.
Preferably, the step S106 specifically includes:
compensating the grating scale by using the total trend error component as an error compensation signal according to the following formula 11:
y (t) ═ y (t) - Γ (t) formula 11
In equation 11, y (t) is the compensated measurement value of the grating ruler, y (t) is the original measurement error signal after linear interpolation, and Γ (t) is the total trend error component.
According to the technical scheme, the embodiment of the application has the following advantages:
the embodiment of the application provides a grating ruler measurement error self-adaptive compensation method assisted by local sine, and the method is characterized in that a sine signal is superposed to an original measurement error signal of a grating ruler to reconstruct the measurement error signal of the grating ruler, so that the modal aliasing phenomenon is inhibited. The method comprises the steps of obtaining a plurality of IMF components through empirical mode decomposition, carrying out threshold transformation based on preset self-adaptive IMF screening conditions after singular value decomposition is carried out on the IMF components, selecting the IMF components meeting the conditions as trend error components, and then obtaining the total trend error components to compensate the grating ruler, so that the basic trend of the measurement error of the grating ruler is eliminated, the measurement precision of the grating ruler is effectively improved, and the accuracy of measurement error compensation is improved.
Drawings
Fig. 1 is a flowchart of a local sine assisted grating scale measurement error adaptive compensation method according to an embodiment of the present application.
Detailed Description
In order to make the technical solutions of the present application better understood, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are only a part of the embodiments of the present application, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application.
For easy understanding, please refer to fig. 1, the present application provides a method for adaptively compensating a measurement error of a grating ruler with local sine assistance, including the following steps:
s101: based on the consideration of instrument errors and background environment interference factors generated by the grating ruler, a preset sinusoidal signal is superposed to an original measurement error signal of the grating ruler, so that the measurement error signal of the grating ruler is reconstructed.
It should be noted that, according to the basic features of the measurement error data of the grating scale and factors affecting the measurement error, the inherent component of the measurement error of the grating scale is mainly embodied in the low-frequency component, and the distribution of different extrema will have a certain influence on the low-frequency component, which may cause the distribution of the low-frequency component to be affected due to the error factor and data abnormality, and cause the mode aliasing phenomenon to mainly be the intermittent phenomenon, and often cause the intermittent phenomenon to be abnormal events, such as intermittent signals, impulse interference, noise, and the like. In the error of the photoelectric system, two paths of orthogonal sinusoidal signals are subdivided to achieve the purpose of precision measurement, but fringe signals of the photoelectric system have error components caused by direct current level, high-frequency noise, unequal amplitude, waveform distortion, phase offset and the like. In the vibration error, the error value fluctuates in a certain range of the true value, once an error code occurs in the code reading of the image acquisition absolute grating ruler, the phenomenon of error decoding of the point reading can be directly caused, and the numerical value deviation has no reference value. Therefore, instrument error factors and background environment interference factors generated by the grating ruler need to be considered, and a preset sinusoidal signal is superposed into an original measurement error signal of the grating ruler, so that the measurement error signal of the grating ruler is reconstructed, and the aliasing phenomenon can be inhibited.
In this embodiment, step S101 includes, before:
s1101: and judging whether the amplitude variation of two adjacent original measurement error signals of the grating ruler is smaller than a preset multiple of the extreme value difference of the extreme value areas corresponding to the two adjacent original measurement error signals, if so, judging that the corresponding original data between the two extreme values has a data abnormal section.
It can be understood that the two extreme values are respectively a maximum extreme value and a minimum extreme value, in the original data, a plurality of data segments should be arranged between the two extreme values, wherein when the increasing amplitude of the ordinate of one data segment is smaller than the preset multiple of the amplitude between the two current extreme values, the data segment is a data abnormal segment, the line segment is a region to which the sinusoidal signal is added, and the region is abnormal due to the instrument error of the grating ruler or the external environment factor, so that the distribution condition of the extreme values is changed. Specifically, when the original measurement error exists between the ith extreme point and the (i +1) th extreme point in the original data, the existence of the data abnormal segment is judged by satisfying the following formula:
|x(j+1)-x(j)|＜n×|e(i+1)-e(i)| ；
in the above formula, x (j) is the jth original measurement error, x (j) is the jth +1 th original measurement error, n is a preset multiple, in this embodiment, the preset multiple is 0.3 times, e (i) is the ith extreme point, e (i +1) is the (i +1) th extreme point, where x (j), x (j +1) is e (i: i + 1).
After the data abnormity is judged for the original data, the original data of the grating ruler is preprocessed based on the instrument error factor generated by the grating ruler, so that the larger influence of the abnormal data area on the compensation of the measurement error of the grating ruler is avoided, and the accuracy of the measurement error data is improved.
S102: decomposing the reconstructed measurement error into a plurality of IMF components by adopting an empirical mode decomposition algorithm;
s103: performing singular value decomposition on each IMF component to obtain a non-zero singular value corresponding to each IMF component;
s104: performing threshold transformation based on a preset adaptive IMF screening condition, thereby screening an IMF component which meets the preset adaptive IMF screening condition as a trend error component;
s105: accumulating IMF components corresponding to the trend error components to be used as the total trend error components of original measurement error signals of the grating ruler;
s106: and compensating the grating ruler by using the total trend error component as an error compensation signal.
In the embodiment, the sinusoidal signal is superposed into the original measurement error signal of the grating ruler to reconstruct the measurement error signal of the grating ruler, so that the modal aliasing phenomenon is suppressed. The method comprises the steps of obtaining a plurality of IMF components through empirical mode decomposition, carrying out threshold transformation based on preset self-adaptive IMF screening conditions after singular value decomposition is carried out on the IMF components, selecting the IMF components meeting the conditions as trend error components, and then obtaining the total trend error components to compensate the grating ruler, so that the basic trend of the measurement error of the grating ruler is eliminated, the measurement precision of the grating ruler is effectively improved, and the accuracy of measurement error compensation is improved.
The following is a detailed description of an embodiment of the local sine assisted grating scale measurement error adaptive compensation method provided by the present invention.
S201: and linear interpolation is adopted to carry out linear interpolation processing on the original measurement error signal of the grating ruler.
It should be noted that the linear interpolation has the function of ensuring that the original data can be inserted into an undistorted sinusoidal signal. During linear interpolation, the measurement error data is expanded, and the basic characteristics of the original data, the maximum value, the minimum value and the extreme value of the basic characteristics are kept.
S202: and judging whether the amplitude variation of two adjacent original measurement error signals of the grating ruler is smaller than a preset multiple of the extreme value difference of the extreme value areas corresponding to the two adjacent original measurement error signals, if so, judging that the original measurement error signals corresponding to the extreme value areas have data abnormal sections.
It should be noted that this step is identical to step S1101 described above, and is not described again here.
S203: and adding a single-period sinusoidal signal with a preset amplitude value to the abnormal data section, so as to locally adjust the extreme value distribution condition of the original data and further construct the reconstruction measurement error of the grating ruler.
It should be noted that, the reconstruction measurement error of the grating ruler is,
S(t)＝θ×|e(i+1)-e(i)|×sin(t) ；
in the above equation, s (t) is the reconstructed measurement error, θ is the predetermined amplitude value, in this embodiment, θ is 0.3, and sin (t) is a single-period sinusoidal signal.
S204: the new measurement error is decomposed into a plurality of IMF components using an empirical mode decomposition algorithm according to equation 1 below:
in formula 1, X (t) is the reconstruction measurement error, i is a natural number, n is the total number of decomposed IMF components, ci(t) is the ith IMF component after empirical mode decomposition, and when i is equal to n, c isi(t) is a residual component.
It should be noted that a series of environmental factors cause the measurement error of the grating ruler to be nonlinear and non-stationary, and the empirical mode decomposition algorithm can well process the nonlinear and non-stationary signal, thereby improving the accuracy of error compensation.
S205: constructing a corresponding reconstruction matrix for each IMF component according to equation 2 below:
in the formula 2, DiThe reconstruction matrix constructed for the ith IMF component, L being the total length of data for that IMF component, IMFi(k) The amplitude of the kth data point in the ith IMF component, k being 1,2,3.., L;
it will be appreciated that the IMF components are composed of both the desired signal and noise, and the matrix D is theniThe method is also a matrix consisting of useful signals and noise, and singular values in the matrix can reflect the concentration of signal and noise energy.
S206: performing singular value decomposition on the reconstruction matrix according to the following formula 3 to obtain a group of non-zero singular values:
in equation 3, U, V are all orthogonal matrices, Σ is a diagonal matrix, and the diagonal element is DiThe non-zero singular values of (a) are sorted in a non-negative descending order, and H is a conjugate transpose of a matrix;
s207: and reconstructing by using the non-zero singular value to obtain a reconstructed error signal component.
It will be appreciated that the error signal components are reconstructed by choosing the number of significant singular values in the diagonal matrix Σ.
S208: obtaining a series of corresponding optimal effective ranks by transforming threshold values of screening conditions based on the screening conditions of the following formulas 4-8 before and after singular value decomposition according to each IMF component, wherein the optimal effective rank is defined as ropt：
roptR formula 4
s.t.Cr(ci(t),Si,r) Epsilon formula 5
DCr＝Cr+1-CrR-1, R-1 formula 6
DCr-1＜ε1Formula 7
DCr＜ε1Formula 8
In the above formulas 4 to 8, r is selected as a component of the reconstructed error signalThe number of non-zero singular values; crReconstructing correlation coefficients of the error signal components for the IMF components using different non-zero singular values; c. Ci(t) is the ith IMF component after empirical mode decomposition; si,rReconstructing error signal components reconstructed using r singular values for the ith IMF component; epsilon is a correlation coefficient threshold value of the IMF component by utilizing different non-zero singular values to reconstruct an error signal component; r is the total number of non-zero singular values; DC (direct current)rIncreasing the correlation coefficient increment of the reconstructed error signal component along with the number r of the singular values; DC (direct current)r-1Increment of correlation coefficient corresponding to the r-1 th singular value; epsilon1The threshold for the influence of the predetermined non-zero singular value on the correlation coefficient is increased for a predetermined effective rank, in this embodiment, epsilon1Taking 0.01;
s209: and averagely dividing the step length of the correlation coefficient threshold into a plurality of sections, and when the minimum value of the optimal effective rank corresponding to the correlation coefficient threshold of each section is equal to the average effective rank corresponding to the correlation coefficient threshold of the corresponding section, obtaining the minimum value in the optimal effective ranks corresponding to the correlation coefficient thresholds of the plurality of sections as the minimum optimal singular value effective rank of the current IMF component by comparing the optimal effective ranks corresponding to the correlation coefficient thresholds of the plurality of sections.
It should be noted that the step size of the correlation coefficient threshold is [0,1], and in a specific embodiment, the step size is divided into 5 segments.
S210: calculating to obtain an important factor corresponding to the IMF component through the following formula 9, judging whether the important factor is greater than a preset important factor threshold value, and if so, judging that the IMF component is a trend error component:
in formula 9, P is an important factor, εmaxIs a preset maximum correlation threshold value with the value of 0.99, rmaxIs a singular optimal effective grade r 'corresponding to a preset maximum correlation threshold value'optIs the minimum optimal singular value effective rank, and epsilon 'is r'optCorresponding bestA large correlation coefficient threshold;
it can be understood that the maximum correlation coefficient threshold epsilon' is the maximum value of the correlation coefficient threshold epsilon that satisfies the above equations 4-8 and can correspond to the minimum optimal singular value effective rank.
It should be noted that, after the correlation coefficient threshold epsilon in the screening condition is changed, a series of optimal effective ranks r corresponding to the IMF components can be obtainedoptAccording to the formula 9, the corresponding importance factor P can be obtained, and the larger the importance factor P is, the more signal components are included in the corresponding IMF component, and the less noise components are included. If the importance factor P corresponding to the IMF component is greater than the preset importance factor threshold, the IMF component is a trend error component, and in this embodiment, the preset importance factor threshold is 0.9.
S211: all the IMF components that meet the screening condition are obtained through step S210, and thus the IMF components corresponding to all the trend error components are determined.
S212: and accumulating all the trend error components to be used as the total trend error component of the original measurement error signal of the grating ruler according to the following formula 10:
Γ(t)＝∑c'i(t) formula 10
In expression 10, Γ (t) is a trend error component, c'iAnd (t) is an IMF component corresponding to the trend error component.
S213: the grating scale is compensated for the total trend error component as an error compensation signal according to equation 11 below:
y (t) ═ y (t) - Γ (t) formula 11
In equation 11, y (t) is the compensated measurement value of the grating ruler, y (t) is the original measurement error signal after linear interpolation, and Γ (t) is the total trend error component.
The above embodiments are only used to illustrate the technical solutions of the present application, and not to limit the same; although the present application has been described in detail with reference to the foregoing embodiments, it should be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions in the embodiments of the present application.
Claims (7)
1. A self-adaptive compensation method for measurement errors of a grating ruler assisted by local sine is characterized by comprising the following steps:
s101: based on instrument errors and background environment interference factors generated by considering a grating ruler, a preset sinusoidal signal is superposed to an original measurement error signal of the grating ruler, so that a measurement error signal of the grating ruler is reconstructed;
s102: decomposing the reconstructed measurement error signal into a plurality of IMF components by adopting an empirical mode decomposition algorithm;
s103: performing singular value decomposition on each IMF component to obtain a non-zero singular value corresponding to each IMF component;
s104: performing threshold value transformation based on a preset adaptive IMF screening condition, thereby screening an IMF component which meets the preset adaptive IMF screening condition as a trend error component;
s105: accumulating IMF components corresponding to the trend error components to be used as total trend error components of the original measurement error signals of the grating ruler;
s106: compensating the grating ruler by taking the total trend error component as an error compensation signal;
the step S101 comprises:
s1101: judging whether the amplitude variation of two adjacent original measurement error signals of the grating ruler is smaller than a preset multiple of the extreme value difference of the extreme value areas corresponding to the two adjacent original measurement error signals, if so, judging that the original measurement error signals corresponding to the extreme value areas have data abnormal sections;
the step S101 specifically includes:
adding a single-period sinusoidal signal with a preset amplitude value to the data abnormal section, so as to locally adjust the extreme value distribution condition of the original data and further construct a reconstruction measurement error of the grating ruler;
the step S104 specifically includes:
s1041: obtaining a series of corresponding optimal effective ranks by transforming correlation coefficient threshold values of screening conditions based on the screening conditions of the following formulas 4-8 before and after singular value decomposition according to each IMF component, wherein the optimal effective rank is defined as ropt：
roptR formula 4
s.t.Cr(ci(t),Si,r) Epsilon formula 5
DCr＝Cr+1-CrR-1, R-1 formula 6
DCr-1＜ε1Formula 7
DCr＜ε1Formula 8
In the above formulas 4-8, r is the number of non-zero singular values selected by the reconstruction error signal component; crReconstructing correlation coefficients of the error signal components for the IMF components using different non-zero singular values; c. Ci(t) is the ith IMF component after empirical mode decomposition; si,rReconstructing error signal components reconstructed using r singular values for the ith IMF component; epsilon is a correlation coefficient threshold value of the IMF component and the error signal component reconstructed by using different non-zero singular values; r is the total number of non-zero singular values; DC (direct current)rIncreasing the correlation coefficient increment of the reconstructed error signal component along with the number r of the singular values; DC (direct current)r-1Increment of correlation coefficient corresponding to the r-1 th singular value; epsilon1Increasing a threshold value for the influence of the preset effective rank of the non-zero singular value on a correlation coefficient;
s1042: averagely dividing the step length of the correlation coefficient threshold into a plurality of sections, and when the minimum value of the optimal effective rank corresponding to the correlation coefficient threshold of each section is equal to the average effective rank corresponding to the correlation coefficient threshold of the corresponding section, obtaining the minimum value in the optimal effective ranks corresponding to the correlation coefficient thresholds of the plurality of sections as the minimum optimal singular value effective rank of the current IMF component by comparing the optimal effective ranks corresponding to the correlation coefficient thresholds of the plurality of sections;
s1043: calculating to obtain an important factor corresponding to the IMF component according to the following formula 9, judging whether the important factor is larger than a preset important factor threshold value, and if so, judging that the IMF component is a trend error component:
in formula 9, P is an important factor, εmaxIs a preset maximum correlation threshold value with the value of 0.99, rmaxIs a singular optimal effective grade r 'corresponding to a preset maximum correlation threshold value'optIs the minimum optimal singular value effective rank, and epsilon 'is r'optA respective maximum correlation coefficient threshold;
s1044: all the IMF components meeting the screening condition are obtained through the step S1043, so as to determine the IMF components corresponding to all the trend error components.
2. The method for adaptively compensating the measurement error of the grating scale assisted by the local sine according to claim 1, wherein the step S1101 is preceded by:
s1001: and linear interpolation is adopted to carry out linear interpolation processing on the original measurement error signal of the grating ruler.
3. The local sine assisted grating scale measurement error adaptive compensation method according to claim 1, wherein the preset amplitude value is 0.3.
4. The local sine assisted grating scale measurement error adaptive compensation method according to claim 1, wherein the step S102 specifically comprises:
decomposing the reconstructed measurement error signal of the grating ruler into a plurality of IMF components by adopting an empirical mode decomposition algorithm according to the following formula 1:
formula 1Where X (t) is the reconstruction measurement error, i is a natural number, n is the total number of decomposed IMF components, ci(t) is the ith IMF component after empirical mode decomposition, and when i is equal to n, c isi(t) is a residual component.
5. The local sine assisted grating scale measurement error adaptive compensation method according to claim 1, wherein the step S103 specifically comprises:
s1031: constructing a corresponding reconstruction matrix for each IMF component according to equation 2 below:
in the formula 2, DiThe reconstruction matrix constructed for the ith IMF component, L being the total length of data for that IMF component, IMFi(k) The amplitude of the kth data point in the ith IMF component, k being 1,2,3.., L;
s1032: performing singular value decomposition on the reconstruction matrix according to the following formula 3 to obtain a group of non-zero singular values
In equation 3, U, V are all orthogonal matrices, Σ is a diagonal matrix, and the diagonal element is DiThe non-zero singular values of (a) are sorted in a non-negative descending order, and H is a conjugate transpose of a matrix;
s1033: and reconstructing by using the non-zero singular value to obtain a reconstructed error signal component.
6. The local sine assisted grating scale measurement error adaptive compensation method according to claim 1, wherein the step S105 specifically comprises:
and according to the following formula 10, accumulating all the trend error components to be used as the total trend error component of the original measurement error signal of the grating ruler:
Γ(t)＝∑c'i(t) formula 10
In expression 10, Γ (t) is a trend error component, c'iAnd (t) is an IMF component corresponding to the trend error component.
7. The local sine assisted grating scale measurement error adaptive compensation method according to claim 6, wherein the step S106 specifically comprises:
compensating the grating scale by using the total trend error component as an error compensation signal according to the following formula 11:
y (t) ═ y (t) - Γ (t) formula 11
In equation 11, y (t) is the compensated measurement value of the grating ruler, y (t) is the original measurement error signal after linear interpolation, and Γ (t) is the total trend error component.
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