JPH0769185B2 - Data smoothing method and apparatus - Google Patents

Description

TECHNICAL FIELD The present invention relates to a data smoothing method used for measuring a true value from a large number of data including noise and stochastic variation, and a method for implementing the same. Regarding the device.

[Prior Art] As typified by the state observation of a system such as a plant, due to noise and stochastic variations, it is necessary to accurately grasp or measure the state of the system and the tendency of the state change from the observed values themselves. There are many cases where you cannot do it. Even in such a case, if the mathematical model of the system can be accurately described and the statistical property of noise is known, the state estimation can be performed by the Kalman filter.

However, many systems that actually exist cannot be described by mathematical models.
It is difficult to perform objective state estimation like the Kalman filter.

For example, as shown in FIG. 14, for observed values disturbed by non-stationary noise, the observed values themselves cannot be treated as the state of the system or the tendency of state change. In this case, in the conventional technique, analysis is performed by a statistical method such as a regression line or moving average.However, as shown in Fig. 15, when exceptionally large noise is added, Highly reliable state estimation is not possible with the statistical method of. Therefore, in order to remove such exceptional noise (spot noise), another method (for example, differentiation) must be used.

[Problems to be Solved by the Invention] As described above, actual system state observation values include noise as shown in FIG. 14 or FIG. In order to remove the noise, it is necessary to use different methods depending on the type of noise, and it is not possible to properly process data in which noises of different types are mixed by one method.

On the other hand, human beings can easily remove noise by subjective judgment and perform state estimation with relatively high reliability. A thick solid line in FIGS. 14 and 15 shows an example in which noise is excluded by human subjective judgment and data is smoothed (smoothed) to have a true value. this is,
It was obtained as a result of flattening the graph by ambiguous knowledge and judgment when analyzing the graph of observation data, and it does not necessarily perform accurate state estimation. It is a very important and effective data processing technology for displaying the observed values of or for predictive control.

Therefore, an object of the present invention is to provide a data smoothing method and apparatus for automatically performing a smoothing process, which is performed by humans, on data including noise as described above.

[Means for Solving the Problems] In order to achieve the above-mentioned object, the present invention uses a fuzzy theory to linearize the above-mentioned point sequence when a point sequence of data having noise or stochastic variation exists on a coordinate plane. Is calculated and the angle is calculated to reduce the components of noise and variations and output a smooth line of data.
That is, in the data smoothing method of the present invention, for data represented by a plurality of points distributed on the coordinate plane, a point sequence in which the center of an ellipse of a predetermined ellipse membership function is selected from the plurality of points. To a point near the center of the ellipse, and the ellipse is rotated about that point, and the sum of the goodness of fit by the ellipse membership function of each point at any rotation angle and each point are projected on the major axis of the ellipse. The ratio of the points to the sum of the goodness of fit by the ellipse membership function is calculated, and the ratio is used as the linearity evaluation value of the point sequence, and the angle of the major axis of the ellipse that maximizes the linearity evaluation value is measured. When measuring the angle of, draw a line that passes through the center of the ellipse at that time and has that angle up to near the center between the center of the ellipse and the center of the ellipse in the next angle measurement, and then obtain the value obtained by the previous angle measurement. Line of It is characterized in that a line obtained by smoothing the data is obtained by sequentially repeating the operation of drawing a straight line from the end point to the end point of the line obtained by the angle measurement at that time.

In the above method, as the end point of the line obtained by measuring the angle at a certain point, a line passing through the center of the ellipse at that time and having the angle is defined as the center of the ellipse at that time and the center of the ellipse at the next angle measurement. It will be the end point when it is pulled to near the middle of. Alternatively, the end point of the line obtained by the previous angle measurement starting from the end point of the line and having the angle at that time to near the middle of the center of the ellipse at that time and the center of the ellipse at the next angle measurement. Can be

In the data smoothing device of the present invention, when data represented by a plurality of points distributed on a coordinate plane is input, a point sequence in which the center of an ellipse of a predetermined ellipse membership function is selected from the plurality of points. To a point near the center of the ellipse, rotate the ellipse about that point, and project the points on the major axis of the ellipse and the sum of goodness of fit of the ellipse membership function at each point at any rotation angle. The ratio between the point and the sum of goodness of fit by the ellipse membership function is calculated, and the ratio is used as the linearity evaluation value of the point sequence to measure the angle of the major axis of the ellipse that maximizes the linearity evaluation value, At the time of the first angle measurement, draw a line that passes through the center of the ellipse at that time and has that angle to near the middle of the center of the ellipse and the center of the ellipse at the next angle measurement, and then obtain it by the previous angle measurement. Of the line drawn By repeating the operation to draw a straight line from a point to the end point of the line obtained by angle measurement at that time sequentially, comprising a calculation means for outputting a line obtained by smoothing the data.

[Operation] According to the method and apparatus of the present invention, for a plurality of data points distributed on the coordinate plane, the center of the ellipse of the predetermined ellipse membership function is set as the angle measurement target of the data. Move to a point near the center of the column and rotate the ellipse about that point. Then, when the ratio of the sum of the goodness of fit by the ellipse membership function of each point at an arbitrary rotation angle and the sum of the goodness of fit by the ellipse membership function of the points projecting each point on the major axis of the ellipse is calculated, The obtained value becomes the linearity evaluation value of the point sequence. When the angle of the major axis of the ellipse that maximizes this linearity evaluation value is obtained, the angle between the point sequence and the reference coordinate axis is obtained.

The above procedure is the angle measuring method of the point sequence of the measuring object used in the present invention, but at the time of the first angle measurement, a line passing through the center of the ellipse at that time and having the angle is defined as follows. Draw up to near the center of the ellipse in the angle measurement. After that, the operation of drawing a straight line from the end point of the line obtained by the previous angle measurement to the end point of the line obtained by the angle measurement at that time is sequentially repeated. As a result, it is possible to obtain a smoothed line of the data obtained by observation, and data smoothing close to human's sensory judgment is realized.

[Embodiment] Hereinafter, as an embodiment of the present invention, a principle of measuring an angle of a line connecting point sequences using a three-dimensional elliptic membership function that defines a fuzzy set will be described.

In general, the linear relationship (correlation) between two variables is often displayed in the form of a distribution chart in which the two variables are plotted on the horizontal axis and the vertical axis and individual data are plotted on the coordinates.

On the other hand, if the bivariate normal distribution data has an elliptical contour, the human judgment on the correlation between the two variables should be based on the elliptical contour (ratio of the minor axis to the major axis of the elliptical contour). It has been known.

Based on this, in the embodiment, in order to evaluate the linearity of a straight line of a linear sequence of points, that is, a linearly plotted sequence of points, an elliptical "measurement" is set on the coordinate space, and the length of the ellipse is set. An algorithm of superimposing the axis and the data point sequence of the measurement target is used.

First, 3 consisting of xy Cartesian coordinates and goodness of fit of fuzzy operation
A dimensional space is defined, and a series of points P ₁ (x ₁ , y ₁ ), P ₂ (x ₂ , y ₂ ), ..., P _n (x _n , y) linearly plotted on the xy plane
_n ).

The fact that the data of bivariate normal distribution has an elliptic contour means that the product of two bell-shaped membership functions (represented by the function isomorphic to the normal distribution) forms a three-dimensional elliptic membership function. And have the same mathematical meaning. Based on this, a three-dimensional elliptic membership function represented by the following equation (1) is set for linearity evaluation of the point sequence. Here, the major axis of the ellipse is placed on the x-axis and the minor axis of the ellipse is placed on the y-axis.

t = exp [- {(x / a x) 2 + (y / a y) 2}] (1) Next, the center of the ellipse, it should be emphasis on evaluation of the most linear in the point sequence Move to. Normally, the point near the middle of the n points to be measured is matched. The coordinates of the center of the ellipse at this time are (A, B), and the ellipse is rotated around this point. When the rotation angle at this time is θ, the three-dimensional elliptic membership function is as follows.

t = M (x, y, θ) = exp [- {(X / a x) 2 + (Y / a y) 2}] (2) where, X = (x-A) cosθ + (y-B) sin θ (3) Y = − (x−A) sin θ + (y−B) cos θ (4) The above equation is represented in the figure as shown in FIG. 1. In this case,
The center of the ellipse is the point P ₄ , and FIGS. 9A and 9B show the ellipse rotated by angles θ and θ ′, respectively.

The linearity evaluation of the point sequence P _i (i = 1, 2, ...) In this case is referred to as “type 1”.

Next, if the x-axis parameter is a parameter that does not affect the variation of the point sequence (for example, when the x-axis is the time axis and the time is accurately measured), the linearity described below is used. We must make the evaluation value dependent only on the value of y. That is, only the major axis of the ellipse should be rotated, the minor axis should remain vertical, and the shape of the membership function of the ellipse projected on the x-axis should not change due to the rotation of the ellipse. Is. In this case, the three-dimensional elliptic membership function is as follows.

t = M (x, y, θ) = exp [− {(X / a _x ′) ² + (Y / a _y ) ² }] (5) where X = (x−A) / cos θ (6) Y = - (x-a) tanθ + (y-B) (7) a x '= a x / cosθ (8) expressed in figure equation for this case, so that the second view. In the figure, (A) and (B) show the case where the ellipse is rotated by angles θ and θ ′, respectively. The linearity evaluation in this case is referred to as "type 2".

As described above, rotating the three-dimensional elliptic membership function corresponds to an operation of superimposing an elliptical "measurement" that allows ambiguity of an ambiguous line on a point sequence.

Therefore, the total sum T (θ) of the goodness of fits t ₁ , t ₂ , ..., T _n by the three-dimensional elliptic membership function of each measurement target point when the ellipse “measurement” is adjusted to an arbitrary angle θ, As shown in FIGS. 3 (A) and (B), the sum of the goodness of fit t _S1 , t _S2 , ..., T _Sn by the three-dimensional elliptic membership function of the points obtained by projecting each measurement target point on the major axis of the ellipse. The ratio with S (θ) is defined as the linearity evaluation value E (θ), and the major axis angle Ψ that maximizes this value is adopted as the angle of the ambiguous line. That is, the following calculation is performed.

E (Ψ) = max {E (θ), −π / 2 <θ <π / 2} (9) If a satisfactory evaluation value is not obtained at this time, the position of the center of the ellipse can be moved. It is valid. Normally,
An efficient method is to roughly evaluate linearity in advance for several points near the center of the point to be measured, and to evaluate in detail the central point where the highest linearity is obtained.

This method can be adapted to human senses by changing the lengths of the major axis and the minor axis of the ellipse.

Further, in the elliptical "measurement" method, the linearity evaluation value E at the angle Ψ obtained by the above equation (9) is obtained.
(Ψ) is the certainty factor of the linearity of the ambiguous line of the measurement target, and is also given as the certainty factor CF with respect to the angle by being normalized to a value in the range of 0 to 1. E
As is clear from the definition of (Ψ), the confidence factor CF has a maximum value of 1 when the point sequences are perfectly aligned.

Next, in the data smoothing based on the angle measurement as described above, basically, the angle measurement by the three-dimensional elliptic membership function is repeatedly performed in order from the end with respect to the point sequence to be smoothed. Normally, 5 to 7 points are picked up and the angle is measured. Depending on what kind of line (a line with reduced noise etc.) drawn based on the angle and certainty obtained at that time, It can be divided into three modes.

The smoothing and procedure for each mode will be described below.

Mode 1 (Figs. 4 to 6) First, in the first angle measurement, the center point of the ellipse (A ₁ , B
Draw a line passing through ₁ ) with an angle of Ψ ₁ near the center of the ellipse. Here, the end point of this line (Ex ₁ , Ey ₁ ) is the center point of the current ellipse (A ₁ , B ₁ ) and the center point of the ellipse in the next angle measurement [strictly speaking, the point to be the center. ] (A ₂ , B ₂ ) Select near the midpoint.

As an example, in Fig. 4, the left side 5 points (P1 to P5) are picked up from the 15 points of the smoothing target point sequence as the first angle measurement, and these 5 point sequences are selected. The case where the middle point, that is, the position of the third point P3 from the left is selected as the center of the ellipse, the angle is measured, and a line is drawn is shown. Furthermore, in this example, a line is drawn with the fifth point P5 from the left as the center point (point to be the center) of the ellipse in the next angle measurement.

From the next angle measurement, the procedure is as follows.

First, the line of the angle Ψ _i that passes through the center point (A _i , B _i ) of the ellipse (i = 2,3, ...) is taken as the center point of the current ellipse and the center point of the ellipse (A _{i + 1} , B _{i + 1} ) is assumed to be a line drawn near the middle, and the end point of this point is (Ex _i , Ey _i ). Normally, Is the end point. Then, a line is drawn with the end point (Ex _i-1 , Ey _i-1 ) of the line obtained by the previous angle measurement as the start point and the end point (Ex _i , Ey _i ) as the end point.

In Fig. 5, as the second angle measurement, the position of the fifth point P5 from the left is selected as the center point of the ellipse, and the five points (P3
~ P7) is an example in which a line is drawn by pulling up, and as the third angle measurement, the position of the seventh point P7 from the left is selected as the center point of the ellipse, and the five points around it (P5 ~ P9 ) Is picked up and a line is drawn.

By repeating the above procedure, as shown by the solid line in FIG. 6, a smoothed line (a line with reduced noise etc.)
Is obtained.

In the smoothing of mode 1 described above, the end point of the line obtained in the angle measurement at a certain point is the line of the angle Ψ _i passing through the center point (A _i , B _i ) of the ellipse at that time and the center point of the ellipse at that time. (A _i , B _i ) and the center point of the ellipse (A
_{i + 1} , B _{i + 1} ) and the end point (Ex _i , Ey)
_i ), and the information obtained by past angle measurement is not added to the coordinates of this end point at all. This focuses on making sure that the actually obtained line (the line to be smoothed) and the smoothed line are not too far apart from each other, and is focused on drawing a smoother line. Not not. Therefore, if the angle measurement with low confidence continues, the smoothing effect becomes less effective.

Mode 2 (FIGS. 4, 7, and 8) First, in the first angle measurement, the angle Ψ ₁ is passed through the center point (A ₁ , B ₁ ) of the ellipse as in the case of Mode _1. Draw a line near the center of the ellipse. Where the end of this line (Ex ₁ , E
y _1), the intermediate of the center point of the current of the ellipse and (A _1, B ₁₎ [Strictly speaking, the point that will become the center] next center point of the ellipse in the angular measurements and (A _2, B ₂₎ Try to choose near the point.

Therefore, also in this case, as shown in FIG. 4, five points on the left side (P1 to P5) are picked up from the 15 points in the smoothing target point sequence as the first angle measurement, and these 5 points are picked up.
Select the center point of the point sequence, that is, the position of the third point P3 from the left as the center of the ellipse, measure the angle, and draw a line. Also, a line is drawn with the fifth point P5 from the left as the center point (point to be the center) of the ellipse in the next angle measurement.

From the next angle measurement, the procedure is as follows.

First, the angle Ψ _i is obtained, and a line of the angle Ψ _i is drawn starting from the end point (Ex _i−1 , Ey _i−1 ) of the line obtained in the previous angle measurement. The end point of this line is the center point of the current ellipse (A _i , B _i ).
And a point (Ex _i , Ey _i ) near the center of the ellipse (A _{i + 1} , B _{i + 1} ) in the next angle measurement. Normally, Is the end point.

In Fig. 7, as the second angle measurement, the position of the fifth point P5 from the left is selected as the center point of the ellipse, and the five points (P3
~ P7) picked up a line and drawn as a third angle measurement. Select the 7th point P7 from the left as the center point of the ellipse and select 5 points (P5 ~ P9) around it. An example of picking up and drawing a line is shown.

By repeating the above procedure, as shown by the solid line in FIG. 8, smoothed lines (lines with reduced noise etc.)
Is obtained.

In smoothing of mode 2, the coordinates of the end point (Ex _i , Ey _i ) obtained in the angle measurement at a certain point depend on the end points (Ex _i-1 , Ey _i-1 ) obtained up to the previous angle measurement. However, the coordinates (A _i , B _i ) of the center point of the ellipse at that time are not taken into consideration. This does not focus on ensuring that the actually obtained line (the line to be smoothed) and the smoothed line do not separate, but on the faithful representation of the angle at each point. There is something. Therefore, if the angle measurement with low confidence continues, the line actually obtained and the smoothed line may be gradually separated. However, since a line that is much smoother than that in Mode 1 can be obtained, it is best if the method of picking up the angle measurement target point and the size of the ellipse can be adjusted so that the lines before and after smoothing do not separate in Mode 2.

Mode 3 (FIGS. 4, 9, and 10) First, in the first angle measurement, the angle Ψ ₁ is passed through the center points (A ₁ , B ₁ ) of the ellipse, as in the case of Mode _1. Draw a line near the center of the ellipse. Where the end of this line (Ex ₁ , E
y _1), the intermediate of the center point of the current of the ellipse and (A _1, B ₁₎ [Strictly speaking, the point that will become the center] next center point of the ellipse in the angular measurements and (A _2, B ₂₎ Try to choose near the point.

Therefore, also in this case, as shown in FIG. 4, five points on the left side (P1 to P5) are picked up from the 15 points in the smoothing target point sequence as the first angle measurement, and these 5 points are picked up.
Select the center point of the point sequence, that is, the position of the third point P3 from the left as the center of the ellipse, measure the angle, and draw a line. Also, a line is drawn with the fifth point P5 from the left as the center point (point to be the center) of the ellipse in the next angle measurement.

From the next angle measurement, the procedure is as follows. It basically corresponds to a compromise between mode 1 and mode 2.

First, the line of the angle Ψ _i that passes through the center point (A _i , B _i ) of the ellipse (i = 2,3, ...) is taken as the center point of the current ellipse and the center point of the ellipse (A _{i + 1, B i + 1} ) line when drawn to a nearly intermediate assume with, the end point of the line (Ex1 _i, Ey1 _i)
And Normally, Is the end point.

Next, the end point of the line obtained by the previous angle measurement (Ex _i-1 , Ey
_i-1 ) is used as a starting point, and a line of an angle Ψ _i is drawn. The end point of this line is (E _i , B _i ), which is near the midpoint between the current ellipse center point (A _i , B _i ) and the ellipse center point (A _{i + 1} , B _{i + 1} ) in the next angle measurement.
x2 _i , Ey2 _i ). That is, it is a point near (Ex1 _i , Ey1 _i ) above, and usually And the point. Then, an appropriate synthesis ratio α (0 <α <
Select 1), find the point (Ex _i , Ey _i ) such that Ex _i = αEx1 _i + (1-α) Ex2 _i Ey _i = αEy1 _i + (1-α) Ey2 _i, and obtain it at the previous angle A line is drawn with the end point (Ex _i-1 , Ey _i-1 ) of the line thus obtained as the start point and the end point (Ex _i , Ey _i ) as the end point.

The optimum value of α basically depends on the level of variation of the smoothing target point sequence, etc., so it will be determined by trial and error according to it, but the best value in the range obtained at this stage is the best. The means are as shown below.

Normally, when the confidence factor CF at the time of angle measurement is large (0.9 or more when the number of measurement target points is 5 or more on a trial basis), the center position of the ellipse at that time is the measurement target point sequence. It can be regarded as the central position of the distribution of. Further, a large value of the confidence factor CF means that the point sequences to be measured are arranged in a straight line, so that a smooth line can be obtained by the smoothing in mode 1.

For the above reason, when the confidence factor CF _i is a large value, the smoothing of the mode 1 is prioritized to increase the value of α, and when the confidence factor CF _i is a small value, the smoothing of the mode 2 is performed. And the value of α is also reduced. At this time, if the value of α suddenly increases or decreases suddenly while the angle measurement is sequentially repeated, a smooth line cannot be obtained as a result. Therefore, when the value of α is determined, α is calculated by the following equation using the confidence factor CF _i-1 at the time of the previous angle measurement.

Fig. 9 shows the position of the fifth point P5 from the left as the center point of the ellipse for the second angle measurement, and the surrounding five points (P3
~ P7) picked up a line and drawn as a third angle measurement. Select the 7th point P7 from the left as the center point of the ellipse and select 5 points (P5 ~ P9) around it. An example of picking up and drawing a line is shown.

By repeating the above procedure, as shown in FIG.
A smoothed line (a line with reduced noise etc.) is obtained.

The coordinates on which the data to be smoothed in the present invention are plotted are not limited to the orthogonal xy coordinates, but polar coordinates and other appropriate coordinates can be used.

Next, as a smoothing device for carrying out the method of the present invention, for example, as shown in FIG.
A computer configured by connecting a display 13 such as an RT and connecting interfaces 14 and 15 to the input side and the output side of the CPU 11 is used.

In this case, the CPU 11 constitutes the calculation means in the present invention. That is, when the data represented by the above point sequence is input through the input side interface 14, the CPU 11 selects the center of the ellipse of the above three-dimensional elliptic membership function from a plurality of points. To a point near the center of
The ellipse is rotated about that point, and the sum T (θ) of the goodness of fit of each point by the three-dimensional elliptic membership function at any rotation angle and the three-dimensional point projected onto the major axis of the ellipse. Sum of goodness of fit S by elliptic membership function
The ratio with (θ) is calculated and used as the linearity evaluation value E (θ) of the point sequence, and the angle Ψ of the major axis that maximizes this evaluation value is determined. A line that passes through the center of the ellipse and has the angle is drawn to near the middle of the center of the ellipse and the center of the ellipse in the next angle measurement, and then the angle from the end point of the line obtained by the previous angle measurement to that point. The smoothed line of the data is programmed to be output through the output side interface 15 by sequentially repeating the operation of drawing a straight line to the end point of the line obtained by the measurement. At this time, the memory 12 stores the data necessary for the above calculation.

The above-described data smoothing device can be used, for example, as means for obtaining a smooth graph in which noise and variations are removed from plant observation data in plant control, and displaying it on a display.

Finally, an example of noise removal and smoothing by the data smoothing of the present invention will be shown.

FIG. 12 shows an example of noise removal, which uses “type 2” for linearity evaluation by a three-dimensional membership function and “mode 3” for smoothing. In the figure, the broken line is the noise removal target, and the solid line is the line obtained by the present invention.

FIG. 13 shows an example of smoothing, the linearity evaluation by the three-dimensional membership function is “type 2”, smoothing is “mode 1” in FIG. 13A, “mode 2” in (B), and (C).
Use "mode 3" respectively. In the figure, the broken line is the smoothing target, and the solid line is the line obtained by the present invention.

[Effect of the Invention] As described above, according to the present invention, noise reduction of a signal from a system that cannot be described by a mathematical model is realized. As a result, the state of the system or the tendency of the state change can be obtained with higher accuracy than in the prior art, and the effect that the data can be automatically and accurately smoothed in various control fields is obtained.

[Brief description of drawings]

FIG. 1 is a diagram showing a state in which the ellipse of the ellipse membership function of the embodiment is rotated, and FIG. 2 is a diagram of the ellipse of the ellipse membership function of the embodiment in which only the major axis is rotated and the minor axis is kept vertical. FIG. 3 is a diagram showing the case of rotation, FIG. 3 is an explanatory diagram when a plurality of points are projected on the major axis of an ellipse, and FIGS. 4 to 10 show the principle of data smoothing based on linearity evaluation according to the present invention. FIG. 11, FIG. 11 is a block diagram showing the configuration of a computer used for implementing the present invention, FIGS. 12 and 13 are diagrams showing an example of noise removal and smoothing according to the present invention, FIGS. 14 and 15 FIG. 6 is a diagram showing an example in which data disturbed by non-stationary noise and exceptional noise is smoothed by human judgment. 11 …… CPU, 12 …… memory, 13 …… display, 14,15 …… interface.

Claims (2)

[Claims] 1. For data represented by a plurality of points distributed on a coordinate plane, a point near the center of a point sequence in which the center of an ellipse of a predetermined ellipse membership function is selected from the plurality of points. , And rotate the ellipse about that point, and the sum of goodness of fit by the elliptic membership function of each point at an arbitrary rotation angle, and the elliptic membership of each point projected on the major axis of the ellipse. The ratio with the sum of the goodness of fit by the function is calculated, and the ratio is used as the linearity evaluation value of the point sequence to measure the angle of the major axis of the ellipse that maximizes the linearity evaluation value, and at the time of the first angle measurement, A line passing through the center of the ellipse at that time and having the angle is drawn to near the middle of the center of the ellipse and the center of the ellipse in the next angle measurement, and then from the end point of the line obtained by the previous angle measurement. According to the angle measurement at that time By sequentially repeating the operation to draw a straight line to the end of the obtained line data smoothing method characterized by obtaining a line obtained by smoothing the data. 2. When data represented by a plurality of points distributed on a coordinate plane is inputted, the center of an ellipse of a predetermined ellipse membership function is near the center of a point sequence selected from the plurality of points. , The ellipse is rotated about that point, and the sum of goodness of fit by the ellipse membership function of each point at any rotation angle and the point projected on the long axis of the ellipse. The ratio with the sum of the goodness of fit by the ellipse membership function is calculated, and the ratio is used as the linearity evaluation value of the point sequence to measure the angle of the major axis of the ellipse that maximizes the linearity evaluation value, and the first angle At the time of measurement, draw a line passing through the center of the ellipse at that time and having the angle to about the middle of the center of the ellipse and the center of the ellipse in the next angle measurement,
After that, an arithmetic means for outputting a line obtained by smoothing the data by sequentially repeating the operation of drawing a straight line from the end point of the line obtained by the previous angle measurement to the end point of the line obtained by the angle measurement at that time is provided. A data smoothing device characterized in that