CN113114161A - Electromechanical system signal filtering method for eliminating outliers by using minimum median method - Google Patents
Electromechanical system signal filtering method for eliminating outliers by using minimum median method Download PDFInfo
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Abstract
The invention discloses a signal filtering method of an electromechanical system for eliminating outliers by using a minimum median method. For discrete signals of an electromechanical system, firstly solving a linear model, calculating the square of deviation again and solving a median; obtaining threshold value parameter M for wild value discrimination through median and current optimal model parameteri(ii) a Putting the points with deviation squares smaller than threshold parameters of wild value judgment into an inner point set; and obtaining the nearest L data points after the outlier is corrected, and obtaining a final output value through a digital filter on the basis of the nearest L data points. The invention overcomes the problems that the existing method of the electromechanical system depends on threshold values and continuous misjudgment.
Description
Technical Field
The invention relates to the field of electromechanical systems, in particular to a signal filtering method for an electromechanical system, which is used for eliminating outliers by using a minimum median method.
Background
When designing an electromechanical servo system, it is common to deal with disturbances and noise present in the system. For continuous signal interference, such as power frequency interference, we generally suppress the interference through digital filtering. But if the interference occurs only at certain times and deviates significantly from normal, the normal digital filtering would be a one-handled two-edged sword: to smooth out these sporadic large jumps, the bandwidth of the digital filter is continuously pushed down, which results in a degradation of the performance of the entire electromechanical servo system. These sporadic hopping values are generally referred to as outliers, and are generally generated by unreliable communications in engineering practice. For example, two machines which are not synchronized with a clock may have repeated reading or missed reading data on a receiving side when transmitting signals, and if the read data needs to be subjected to differential operation subsequently, a large jump value may occur, which may seriously affect the performance of the electromechanical servo system. For outliers present in such discrete signals, two methods of processing are currently commonly employed.
The first method is to select the maximum variation amplitude of the signal under normal conditions according to experience, and then regard the point with the variation amplitude larger than the threshold value at the last moment as the outlier for interpolation. If the signal itself changes rapidly, it is difficult to correctly detect the outlier by this fixed threshold method.
To solve this problem, a second method, prediction and detection, is developed. Assuming that the signal change speed is kept unchanged in a short time, firstly, a predicted value at the current time is obtained by linear extrapolation according to data points at the previous two times, then, whether the current value is a outlier or not is judged according to the difference between the current value and the predicted value, and finally, possible outliers are interpolated. The second method can adjust the condition of the discrimination threshold to some extent in response to the change of the signal, but still needs to provide the discrimination threshold. In fact, the first method can be considered as prediction using zero-order extrapolation, and the second method only raises the order of extrapolation to one order, both methods requiring a fixed threshold to be specified in advance. If the threshold is not properly selected, false or even continuous false positives may result. If the normal value at the current moment is judged as the outlier and the outlier is interpolated, the current value is replaced by the interpolated value, so that the next moment is likely to be misjudged, and a chain reaction is caused to cause a series of misjudgments.
Disclosure of Invention
The invention provides an electromechanical system signal filtering method for eliminating outliers by using a minimum median method, which considers both real-time performance and accuracy and solves the problems that the existing method depends on a threshold value and continuous misjudgment.
The invention is realized by the following technical scheme:
a filtering method for eliminating outliers by using a minimum median method for signals of an electromechanical system specifically comprises the following steps:
step 1: for discrete signals r (n) of an electromechanical system, a fixed-length queue with the length of L is used for storing recent historical data which is recorded as a sequence ynR (k-L + n), n 1, L, where k is the current time;
step 2: number series { ynAll two groups with m index difference in the middle are combined into { y }i,y i+m1,2, (L-m), i.e., { y ═ m1,ym+1},{y2,ym+2},...,{yL-m,yL}；
And step 3: for each combination in the step 2, firstly solving a linear model, and then calculating the square of the deviation and solving the median;
and 4, step 4: obtained by the operation of step 3 to (k)i,bi,Mi) And i is 1, 2., (L-M), and a threshold parameter M for wild value judgment is obtained through a median and the current optimal model parameteri；
And 5: traverse the sequence of step 2 { ynSolving the deviation square of the ith point, and putting the point with the deviation square smaller than the threshold parameter judged by the wild value into the internal point set;
step 6: performing least square straight line fitting on the internal point set in the step 5, and replacing the optimal model parameter in the step 4 with the result
And 7: iterating step 5 and step 6, if the iteration frequency is not more than the input parameter K, or the number of elements in the inner point set obtained in step 5 is increased, continuing iteration; if the iteration times are larger than the input parameter K, or the number of elements in the inner point set obtained in the step 5 is not increased any more, exiting the iteration and entering a step 8;
and 8: if there is no interior point on the left side of the outlier point, go to step 9; if no interior point exists on the right side of the outlier point, the step 10 is executed; if there are interior points on both sides of the outlier point, go to step 11;
and step 9: correcting the value of the right nearest inner point;
step 10: correcting to the value of the inner point nearest to the left side;
step 11: using two nearest inner points at two sides to do linear interpolation for correction;
step 12: and obtaining the latest L data points after the outlier correction according to the step 9-11, and obtaining a final output value through a digital filter on the basis of the latest L data points.
Further, in step 1, specifically, the queue length L is data required for enabling the queue to cover subsequent digital filtering, and the signal does not fluctuate dramatically in the covered time interval.
Further, in the step 2, specifically, the selection criterion of m is that the subscript difference of at least one pair of non-outliers in the queue is m, and in addition, m should be as small as possible under the condition of guaranteeing timeliness.
Further, the step 3 is to record a certain combination as { yi,yi+mRepresents two points (i, y) having a difference of m in numberi) And (i + m, y)i+m) Then, a straight line model y obtained by the two points is determined as kix+bi(ii) a For { ynCalculating the deviation square and solving for median at the rest (L-2) points; the specific steps are that a certain point is recorded as yjIt corresponds to a deviation squared of
The (L-2) squares are sorted to find the median Mi；(ki,bi,Mi) Namely the result obtained by the operation.
Further, the linear model y in step 3 is kix+biThe specific formula of (a) is as follows,
the algorithm for the median of the (L-2) deviation squares is a half bubble sort.
The half bubble sorting is that firstly, the (L-2) numbers are arranged in a row from left to right, two adjacent numbers are respectively compared from right to left, the leftmost number is the smallest of all the numbers, and then the same operation is carried out on the remaining numbers, so that the second number from the left is the second smallest of all the numbers; iterating the operation for k times to obtain the kth number from the left, namely the kth small number; iteration (L-2)/2 times can obtain the median M of the group of numbers;
further, the step 4 is specifically to find out the corresponding combination (k) when the median is the minimumi,bi,Mi) Will (k)i,bi) Record as the current best model parameter
Will MiAnd recording as threshold parameter M for wild value discrimination.
Further, in the step 5, a deviation square of the ith point is obtained
And putting the points with deviation square smaller than M into the inner point set I.
Further, in the step 7, specifically, the L data points are divided into two, which are an inlier set and a non-inlier set, respectively, and elements in the non-inlier set are regarded as outliers.
Further, if the iteration is performed only once, i.e. step 4 is followed by steps 5 and 6 only once, the resulting set of inliers will contain only about L/2 elements, since M is a median; iterating the fifth step and the sixth step for multiple times, fitting the existing interior points by using least square, and growing new interior points;
the concrete formula for updating the linear model parameters by using the least square in the step 6 is as follows; if there are N inner points, the corresponding sequence numbers of the inner points are from small to largen1,n2,...,nNThen the interior point is available
Represents; obtained according to the least square method
Where the summation operations are all from 1 to N through all interior points.
Further, the step 12 is specifically to assume that the outlier point is ynIts two nearest interior points are yiAnd yjAnd if i < n < j, the value is corrected to
The outlier is modified in the historical data ynThe historical data forbids modification, which is done on the copy of the page, and the original value must be maintained.
The invention has the beneficial effects that:
the invention can be directly combined with a digital filtering algorithm, and because the wild points are preprocessed, the bandwidth does not need to be depressed to inhibit large-amplitude jumping, the lag of signals is reduced, and the performance of an electromechanical servo system is improved.
Drawings
FIG. 1 is a schematic structural view of the present invention.
FIG. 2 shows an example of selecting two points to estimate a straight line model and calculating the median squared deviation in the present invention.
FIG. 3 is an example of the present invention in which interior points are screened using the minimum median as an adaptive threshold and fitted to a least squares line.
FIG. 4 is an example of correcting the detected outliers in the present invention.
FIG. 5 is the result of the multi-point differencing of sinusoidal commands with repeat and missing numbers of the present invention, and comparison with the conventional multi-point differencing result.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, 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 invention.
Example 1
A filtering method for eliminating outliers by using a minimum median method for signals of an electromechanical system specifically comprises the following steps:
step 1: for discrete signals r (n) of an electromechanical system, a fixed-length queue with the length of L is used for storing recent historical data which is recorded as a sequence ynR (k-L + n), n 1, L, where k is the current time;
step 2: number series { ynAll two groups with m index difference in the middle are combined into { y }i,y i+m1,2, (L-m), i.e., { y ═ m1,ym+1},{y2,ym+2},...,{yL-m,yL}；
And step 3: for each combination in the step 2, firstly solving a linear model, and then calculating the square of the deviation and solving the median;
and 4, step 4: obtained by the operation of step 3 to (k)i,bi,Mi) And i is 1, 2., (L-M), and a threshold parameter M for wild value judgment is obtained through a median and the current optimal model parameteri；
And 5: traverse the sequence of step 2 { ynSolving the deviation square of the ith point, and putting the point with the deviation square smaller than the threshold parameter judged by the wild value into the internal point set;
step 6: performing least square straight line fitting on the internal point set in the step 5, and replacing the optimal model parameter in the step 4 with the result
And 7: iterating step 5 and step 6, if the iteration frequency is not more than the input parameter K, or the number of elements in the inner point set obtained in step 5 is increased, continuing iteration; if the iteration times are larger than the input parameter K, or the number of elements in the inner point set obtained in the step 5 is not increased any more, exiting the iteration and entering a step 8;
and 8: if there is no interior point on the left side of the outlier point, go to step 9; if no interior point exists on the right side of the outlier point, the step 10 is executed; if there are interior points on both sides of the outlier point, go to step 11;
and step 9: correcting the value of the right nearest inner point;
step 10: correcting to the value of the inner point nearest to the left side;
step 11: using two nearest inner points at two sides to do linear interpolation for correction;
step 12: and obtaining the latest L data points after the outlier correction according to the step 9-11, and obtaining a final output value through a digital filter on the basis of the latest L data points.
Further, in the step 1, specifically, the queue length L is data required for enabling the queue to cover subsequent digital filtering, for example, if filtering is performed by using multipoint averaging, the queue length needs to be greater than the total number of points; in addition, it is also necessary to ensure that there is no drastic fluctuation of the signal during the covered time interval. In order to optimize the performance of the algorithm, the queue length should be as large as possible while satisfying the above conditions.
Further, in the step 2, specifically, the selection criterion of m is that the subscript difference of at least one pair of non-outliers in the queue is m, and in addition, m should be as small as possible under the condition of guaranteeing timeliness.
Further, the step 3 is to record a certain combination as { yi,yi+mRepresents two points (i, y) having a difference of m in numberi) And (i + m, y)i+m) Then, a straight line model y obtained by the two points is determined as kix+bi(ii) a For { ynCalculating the deviation square and solving for median at the rest (L-2) points; the specific steps are that a certain point is recorded as yjIt corresponds to a deviation squared of
The (L-2) squares are sorted to find the median Mi；(ki,bi,Mi) Namely the result obtained by the operation.
Further, the linear model y in step 3 is kix+biThe specific formula of (a) is as follows,
the algorithm for the median of the (L-2) deviation squares is a half bubble sort.
The half bubble sorting is that firstly, the (L-2) numbers are arranged into a row from left to right, two adjacent numbers are respectively compared from right to left, and if the number on the left side is larger than the number on the right side, the positions of the two numbers are exchanged; after the operation, the leftmost number is the smallest of all the numbers, and the second number from the left is the second smallest of all the numbers by performing the same operation on the remaining numbers; iterating the operation for k times to obtain the kth number from the left, namely the kth small number; iteration (L-2)/2 times can obtain the median M of the group of numbers; the algorithm of the optimal straight line model parameters is a least square median algorithm LMedS.
Further, the step 4 is specifically to find out the corresponding combination (k) when the median is the minimumi,bi,Mi) Will (k)i,bi) Record as the current best model parameter
Threshold parameter M for outlier determinationi. The algorithm of the optimal straight line model parameters is a least square median algorithm LMedS.
Further, in the step 5, a deviation square of the ith point is obtained
1, ·, L; and putting the points with deviation square smaller than M into the inner point set I.
Further, in the step 7, specifically, the L data points are divided into two, which are an inlier set and a non-inlier set, respectively, and elements in the non-inlier set are regarded as outliers. It can be proved that the wild value number is less than L/2.
Further, if the iteration is performed only once, i.e. step 4 is followed by steps 5 and 6 only once, the resulting set of inliers will contain only about L/2 elements, since M is a median; if the outlier interpolation stage is entered immediately, half of the points will need to be corrected, which will cause some non-outlier points to be modified; in order to reduce the number of corrected points as much as possible and increase the accuracy of outlier detection, the fifth step and the sixth step are iterated for multiple times, and the existing interior points are fitted by using least squares and new interior points are grown;
the concrete formula for updating the linear model parameters by using the least square in the step 6 is as follows; if there are N inner points, the corresponding serial numbers of the inner points are N from small to large1,n2,...,nNThen the interior point is available
Represents; obtained according to the least square method
Where the summation operations are all from 1 to N through all interior points.
Further, the step 12 is specifically to assume that the outlier point is ynIts two nearest interior points are yiAnd yjAnd if i < n < j, the value is corrected to
The outlier is modified in the historical data ynThe historical data forbids modification, which is done on the copy of the page, and the original value must be maintained.
The first seven steps are performed on original historical data, but not on data processed at the previous moments, so as to ensure that the algorithm has no memory, namely, the outlier correction at the previous moment does not influence the outlier correction at the current moment.
Example 2
The queue designed in the step 1 for covering the data required by the subsequent filtering is characterized in that compared with the existing outlier detection algorithm, more historical information is utilized, and outliers can be detected more robustly.
The fixed-length sampling designed in step 2 is a variation of random sampling in robust regression. Different from randomly selecting data points to carry out model estimation, the fixed-length sampling grasps the characteristics of low signal dimension and interval existing in the appearance of field values. Random sampling can only ensure that sampling points at a certain time are all internal points under a certain probability, but if observation shows that the appearance intervals of field values are regular, fixed-length sampling can certainly cover the condition that two points are all internal points. Furthermore, the fixed-length sampling traverses a small number of times, corresponding to sampling only a fraction of all pairwise combinations, which is necessary in the real-time processing of high-frequency discrete signals.
The algorithm for solving the optimal straight line model parameters designed in the steps 3 and 4 is a least square median algorithm LMedS. Unlike least squares minimization of the sum of squared errors, median of least squares minimization of the median of the squared errors can reduce the effects of outliers in the data. The median of least squares method gives a good estimate of the model parameters when the percentage of outliers in the data is not more than 50%. In fact, other robust regression algorithms such as the median least squares method are widely used in the field of computer vision, which are dedicated to robustly estimating models from noisy data. The invention transfers the algorithm to the outlier detection of the discrete signal, takes a straight line as a model but not takes the straight line fitting as a purpose, and utilizes the algorithm to adaptively obtain the threshold M for distinguishing the outlier, thereby thoroughly solving the problem that the existing outlier detection method depends on the artificially given threshold.
The purpose of the algorithm for screening interior points designed in step 5, step 6 and step 7 is to maximize the number of interior points in a similar growing manner. If only one iteration is performed, i.e. step four followed by step five and step six, the resulting set of inliers will contain only about L/2 elements, since M is a median. Approximately half of the points would need to be corrected if the outlier interpolation stage were entered immediately, which may cause some non-outlier points to be modified. In order to reduce the number of corrected points as much as possible and increase the accuracy of wild value detection, the fifth step and the sixth step need to be iterated for multiple times, and the existing interior points are fitted and grown by using least squaresA new interior point is found. The concrete formula for updating the linear model parameters by using the least square in the step six is as follows. If there are N inner points, the corresponding serial numbers of the inner points are N from small to large1,n2,...,nNThen the interior point is available
And (4) showing. Obtained according to the least square method
Where the summation operations are all from 1 to N through all interior points.
The outlier interpolation algorithm designed in step 8 actually performs piecewise linear interpolation on outlier points by using the outlier set as an interpolation table. If the outlier point is ynIts two nearest interior points are yiAnd yjAnd if i < n < j, the value is corrected to
Note that the outlier modification is in the historical data ynThe historical data forbids modification, which is done on the copy of the page, and the original value must be maintained. The first seven steps are performed on original historical data, but not on data processed at the previous moments, so as to ensure that the algorithm has no memory, namely, the outlier correction at the previous moment does not influence the outlier correction at the current moment. The memory of the algorithm is eliminated, and the problem that continuous misjudgment can be caused by one-time misjudgment of the existing outlier detection algorithm is avoided.
According to the method, on the premise of ensuring real-time performance, a robust regression algorithm in the model identification field is transferred to outlier detection of discrete signals, the actual optimization efficiency is accelerated by designing a self-adaptive threshold value method, the problem of continuous misjudgment is solved by removing the memory of the algorithm, and the fault tolerance of the algorithm is enhanced. The digital filter can be quickly embedded into the existing digital filter in engineering, and the adverse effect of large-amplitude fields appearing at intervals on the whole system is reduced.
Example 3
Abnormal sounds at fixed intervals can occur when a certain type of simulation turntable tracks a command signal, and the main reason for the occurrence of the abnormal sounds is found through investigation to be the problem that the command signal is repeated or lost in the transmission process. Since the feedforward control method adopted by the turntable requires differentiation of the command signal, the repetition and loss of the command signal are amplified to zero and double values of the differential signal. In order to solve the problem, the existing method utilizes multipoint difference to smooth the difference result as much as possible, but the signal has larger lag, and the positive effect of feedforward control is weakened; the simulation turntable is a research object.
And designing field value correction and smooth filtering of the command differential signal. The sampling frequency of the instruction signal is 1kHz, 10-point difference is adopted, and the typical input instruction is a sine wave with the frequency of 1Hz and the amplitude of 5 degrees. The ordinary 10-point difference needs to calculate the difference between 5 groups of points with serial number difference of 5, then average the 5 numbers and divide by 5 times of sampling period to obtain the speed value. The implementation method of the invention firstly corrects the outlier of 5 numbers of the interval point difference and then calculates the speed, and comprises the following specific steps:
(1) let discrete command signal be { cnThe current time k is more than 5, and a dot separation difference is defined as dk＝ck-ck-5. The values of the dot differences are stored in a queue of length 20 in chronological order, the queue having an available number yn＝dk-20+nAnd n is 1. The queue stores the data to be corrected, and the queue length parameter L in the algorithm is 20.
(2) Listing { y }nPoint pairs with sequence number difference m 2, i.e. y1,y3},{y2,y4},...,{y18,y20}
(3) Calculating a straight line formula of two points for the ith point in the previous step to obtain a model parameter ki、biAnd calculates the squared deviation of the 18 remaining points. The median M of the 18 numbers is obtained by using a half bubble algorithmi. Go through each pair of points in the previous step to get (k)i,bi,Mi),i＝1,...,18。
(4) Finding MiMinimum sizeIs corresponding to ki、biLet the current best model parameters
Let the wild value discrimination threshold M be Mi。
(5) Traverse { y }nWill be
And marking the corresponding points as interior points to obtain an interior point set I.
(6) Performing least square straight line fitting on all points in the inner point set, and replacing the result
(7) And (6) iterating (6) and (7), and if the iteration number is more than K-2, or the number of elements of the inner point set in (6) is not increased any more, entering the next step.
(8) All non-interior points are regarded as outlier points, each outlier point is subjected to piecewise linear interpolation correction by using an interpolation table consisting of the interior points, and the result is recorded as
(9) Calculating a current output speed value
Wherein the sampling period
A section of sinusoidal signals containing the problems of repetition and loss are respectively subjected to 2-point difference, 10-point difference and 60-point difference, and 10-point difference calculation speed signals are added. It can be found that the normal 10-point difference is greatly influenced by the outlier, the obvious 60-point difference with the outlier increases the smooth strength compared with the 10-point difference, the influence of the outlier is suppressed, but the signal has obvious lag. The 10-point difference added in the invention not only inhibits the influence of the outlier, but also does not introduce extra hysteresis, and can effectively improve the performance of the whole electromechanical system.
Claims (10)
1. A method for filtering signals of an electromechanical system by using a minimum median method to remove outliers is characterized by comprising the following steps:
step 1: for discrete signals r (n) of an electromechanical system, a fixed-length queue with the length of L is used for storing recent historical data which is recorded as a sequence ynR (k-L + n), n 1, L, where k is the current time;
step 2: number series { ynAll two groups with m index difference in the middle are combined into { y }i,yi+m1,2, (L-m), i.e., { y ═ m1,ym+1},{y2,ym+2},...,{yL-m,yL}；
And step 3: for { y1,ym+1},{y2,ym+2},...,{yL-m,yLSolving a linear model for each combination, calculating the square of the deviation and solving a median;
and 4, step 4: (k) obtained by step 3i,bi,Mi) And i is 1, 2., (L-M), and a threshold parameter M for wild value judgment is obtained through a median and the current optimal model parameteri；
And 5: traverse the sequence of step 2 { ynSolving the square of the deviation of the ith point, and judging whether the square of the deviation is smaller than a threshold parameter M of the wild valueiThe points of (2) are put into an inner point set;
step 6: performing least square straight line fitting on the internal point set in the step 5, and replacing the current optimal model parameter in the step 4 with the result;
and 7: iterating step 5 and step 6, if the iteration frequency is not more than the input parameter K, or the number of elements in the inner point set obtained in step 5 is increased, continuing iteration; if the iteration times are larger than the input parameter K, or the number of elements in the inner point set obtained in the step 5 is not increased any more, exiting the iteration and entering a step 8;
and 8: if there is no interior point on the left side of the outlier point, go to step 9; if no interior point exists on the right side of the outlier point, the step 10 is executed; if there are interior points on both sides of the outlier point, go to step 11;
and step 9: correcting the value of the right nearest inner point;
step 10: correcting to the value of the inner point nearest to the left side;
step 11: using two nearest inner points at two sides to do linear interpolation for correction;
step 12: and obtaining the latest L data points after the outlier correction according to the step 9-11, and obtaining a final output value through a digital filter on the basis of the latest L data points.
2. The electromechanical system signal filtering method for eliminating outliers by using a minimum median method as claimed in claim 1, wherein the step 1 is specifically that the queue length L is such that the queue can cover data required by subsequent digital filtering, and there is no sharp fluctuation of signals in the covered time interval.
3. The method as claimed in claim 1, wherein the step 2 is implemented by selecting m as a criterion that the index difference between at least one pair of non-outliers in the queue is m, and m should be as small as possible under the condition of time keeping.
4. The method as claimed in claim 1, wherein the step 3 is to take a certain combination as { y }i,yi+mRepresents two points (i, y) having a difference of m in numberi) And (i + m, y)i+m) Then, a straight line model y obtained by the two points is determined as kix+bi(ii) a For { ynCalculating the deviation square and solving for median at the rest (L-2) points; the specific steps are that a certain point is recorded as yjIt corresponds to a deviation squared of
The (L-2) squares are sorted to find the median Mi；(ki,bi,Mi) That is the exercise of this timeThe obtained results were obtained.
5. The method as claimed in claim 4, wherein the linear model in step 3 is k, and wherein the linear model is a linear model with a median value of kix+biThe specific formula of (a) is as follows,
the algorithm for the median of the (L-2) deviation squares is a half bubble sort.
The half bubble sorting is that firstly, the (L-2) numbers are arranged in a row from left to right, two adjacent numbers are respectively compared from right to left, the leftmost number is the smallest of all the numbers, and then the same operation is carried out on the remaining numbers, so that the second number from the left is the second smallest of all the numbers; iterating the operation for k times to obtain the kth number from the left, namely the kth small number; iteration (L-2)/2 can obtain the median M of the group of numbers.
6. The method as claimed in claim 1, wherein the step 4 is to find the corresponding combination (k) when the median is the minimumi,bi,Mi) Will (k)i,bi) Record as the current best model parameter
Threshold parameter M for outlier determinationi。
7. The method as claimed in claim 1, wherein the step 5 is to find the square deviation of the ith point
With deviation squared less than MThe points are placed in an inner set of points I.
8. The method as claimed in claim 1, wherein in step 7, the L data points are divided into two sets, i.e. an inlier set and a non-inlier set, and the elements in the non-inlier set are regarded as outliers.
9. The method according to claim 1, 7 or 8, wherein if the iteration is performed only once, i.e. only one step 5 and 6 is performed after step 4, the resulting inner point set will contain only about L/2 elements because M is the median; iterating the fifth step and the sixth step for multiple times, fitting the existing interior points by using least square, and growing new interior points;
the concrete formula for updating the linear model parameters by using the least square in the step 6 is as follows; if there are N inner points, the corresponding serial numbers of the inner points are N from small to large1,n2,...,nNThen the interior point is available (n)i,yni) 1, N represents; obtained according to the least square method
Where the summation operations are all from 1 to N through all interior points.
10. The method as claimed in claim 1, wherein the step 12 is implemented if the outlier point is ynIts two nearest interior points are yiAnd yjAnd if i < n < j, the value is corrected to
The outlier is modified in the historical data ynMade on a copy of the log, the historical data is prohibited from being modified and must be preservedHold the original value.
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