JP2024019830A - Time series data analysis system - Google Patents

Abstract

An object of the present invention is to provide a data analysis system and a time-series data analysis method that enable more effective data analysis even for data containing a lot of noise. A time series data analysis system includes a bandpass filter processing section 16, a moving average processing section 18, a differentiation processing section 20, an integral difference processing section 22, a subtraction processing section 24, a pulse generation processing section 26, and a threshold processing section 28. , a dividing point search processing section 30, and a range setting processing section 32. By applying and executing various types of processing to the time series data in each of these processing units, it is possible to find inflection points in the time series data, that is, points at which the trend changes, with high accuracy. The range setting processing unit 32 executes, for example, a process in which the user directly sets a range on the time axis. Furthermore, the dividing point search processing section finds an approximate curve that fits well to the time series data through processing with less load on the computer. [Selection diagram] Figure 1

Description

The present invention relates to a time-series data analysis system and a time-series data analysis method for analyzing time-series data output from various measuring devices, various sensors, and the like.

At production sites in the manufacturing industry, various types of data are acquired by various measuring devices and sensors, and it is essential to analyze this data in order to maintain and improve product quality. As conventional methods for such data analysis, methods that capture the characteristics of the entire waveform, such as the MT method, have so far been mainstream.

However, actual data contains a lot of noise, and for data that contains a lot of noise, conventional MT methods cannot extract the "specific shape" contained in the waveform by calculation. was difficult.

SUMMARY OF THE INVENTION Therefore, an object of the present invention is to provide a data analysis system and a time-series data analysis method that make it possible to more effectively analyze data even when the data contains a lot of noise.

In order to solve the above problems, the time series data analysis system according to the present invention,
a time differentiation processing means for performing time differentiation on time series data and displaying a waveform diagram of the time series data after time differentiation as necessary;
a range setting processing section that sets a time range on a time axis when the time differentiation processing section executes time differentiation processing on time series data to be processed;
a peak position detection unit that detects a position where the time series data to be processed has a peak in the time range set by the range setting processing unit;
(first invention).

In the above first invention, the range setting processing section allows the user to directly set at least one boundary of the time range on the time axis of time series data (second invention).

In the first aspect of the invention, the range setting processing unit is capable of allowing the user to set a specific value on the vertical axis, and to set the corresponding value on the time axis as at least one boundary of the time range. 3 inventions).

In the first invention, the range setting processing unit searches for a peak value on the vertical axis of the time series data detected by the peak position detection unit, and calculates a value on the time axis corresponding to the peak value at the time. It can be one boundary of the range (fourth invention).

In the first invention, the moving average processing section further includes, as a noise removal means, a moving average processing unit that executes moving average processing on the time series data and displays a waveform diagram of the time series data after the moving average processing, if necessary; and an integral difference processing unit that executes integral difference processing on the time series data and displays a waveform diagram of the time series data after the integral difference processing as necessary. It is possible (fifth invention).

The first invention described above may further include a band-pass filter processing section that performs band-pass filter processing on time-series data (sixth invention).

The fifth invention described above may further include a user input processing section through which the user inputs user data (seventh invention).

The fifth invention described above may further include a data input section for importing time-series data into the system from the outside (eighth invention).

In order to solve the above problems, the time series data analysis system according to the present invention,
a time differentiation processing means for performing time differentiation on time series data and displaying a waveform diagram of the time series data after time differentiation as necessary;
For time series data, the first pulse waveform has a pulse width that is the length of time that the value is continuously positive, a pulse height that is the length of time that the value is continuously positive, and a first pulse waveform that has a continuous positive value. and a second pulse waveform in which the length of time in which the pulse is negative is the pulse width, and the length of time in which the pulse is continuously negative is the pulse height. a pulse generation unit that displays a waveform diagram of both or one of the pulse waveforms;
a subtraction processing unit that executes subtraction processing between a plurality of time series data or between a plurality of pulse waveforms, and displays the time series data or pulse waveform after the subtraction as necessary;
a threshold processing unit that compares the value of the pulse waveform with a prespecified threshold and selects a pulse larger or smaller than the threshold;
(9th invention).

In the above ninth invention, the moving average processing section further includes, as a noise removal means, a moving average processing unit that executes moving average processing on the time series data and displays a waveform diagram of the time series data after the moving average processing, if necessary; and an integral difference processing unit that executes integral difference processing on the time series data and displays a waveform diagram of the time series data after the integral difference processing as necessary. It is possible (10th invention).

The ninth invention described above may further include a bandpass filter processing section that performs bandpass filter processing on the time series data (eleventh invention).

The ninth invention described above may further include a user input processing section through which the user inputs user data (twelfth invention).

The ninth invention described above may further include a data input section for importing time series data into the system from the outside (the thirteenth invention).

In order to solve the above problem, the method for finding the inflection point of time series data imported into a time series data analysis system is as follows.
A first step of performing time differentiation three times on the captured first time series data by a differentiation processing unit included in the time series data analysis system to obtain second time series data;
The pulse generation unit included in the time series data analysis system defines the length of time during which the second time series data is continuously positive as a pulse width, and the length of time during which the second time series data is continuously positive as a pulse height. a first pulse waveform in which the length of time during which the fourth time series data is continuously negative is the pulse width, and the length of time during which the fourth time series data is continuously negative is the pulse height. A second step to find
A third step of subtracting the first pulse waveform and the second pulse waveform by a subtraction processing unit included in the time series data analysis system to obtain a third pulse waveform;
a fourth step of performing time differentiation on the third pulse waveform by the differentiation processing unit to obtain a fourth pulse waveform;
A threshold processing unit included in the time series data analysis system performs threshold processing on the fourth pulse waveform, selects only pulses exceeding a predetermined threshold, and determines the inflection point of the first time series data. a fifth step,
(14th invention).

In the fourteenth invention described above, in the first step, the third time differentiation is performed after noise is removed by performing integral difference on the time series data obtained by performing the second time differentiation. This can be used as second time series data (fifteenth invention).

In order to solve the above problems, the time series data analysis method in the present invention includes:
A time series data analysis method for analyzing time series data by obtaining an approximate curve of a waveform diagram of the time series data, the method comprising:
provisionally arranging from a first dividing point to an nth dividing point (n is an integer of 2 or more) on the time series data between a prespecified starting point and an ending point;
When the first dividing point is moved from the starting point to the second dividing point, the point where the first straight line connecting the starting point and the first dividing point best fits the time series data in that range is determined as the position of the first dividing point. decided,
When the second dividing point is moved from the first dividing point to the third dividing point, the second straight line connecting the first dividing point and the second dividing point best fits the time series data within that range. a step of determining the position of the two-parting point;
Continue the same procedure below, and when you move the nth dividing point from the n-1st dividing point to the end point, the nth straight line connecting the n-1st dividing point and the second dividing point will be chronologically in that range. determining the point that best fits the data as the position of the n-th division point;
Connecting the starting point, the first division point, ... the nth division point, and the end point in this order by a straight line and using a curve obtained as an approximate curve of the time series data;
(16th invention).

1 is a diagram illustrating functional blocks of a time-series data analysis system according to an embodiment of the present invention. This is time-series data of the output of a pressure sensor that measures changes in pressure from when resin is poured until it solidifies during injection molding. 3 is a waveform diagram in which a part of the waveform diagram of FIG. 2 is expanded in the time direction. FIG. FIG. 3 is a waveform diagram showing an example of time series data obtained by time-differentiating time series data. FIG. 3 is a waveform diagram showing an example of time series data obtained by taking a moving average of time series data. FIG. 3 is a diagram for explaining an integral difference with respect to time series data. FIG. 3 is a diagram for explaining an integral difference with respect to time series data. FIG. 3 is a diagram illustrating a problem when determining the time point when passing through zero by threshold processing. FIG. 4 is a waveform diagram showing the operation of a pulse generation section that generates pulses based on a waveform diagram obtained by differentiation. FIG. 7 is a waveform diagram showing an example of performing various processes on time series data to obtain an inflection point of the original time series data. 10 is a waveform diagram illustrating that threshold processing is performed on the refraction points obtained in FIG. 9 to select pulses that are equal to or greater than a predetermined threshold; FIG. FIG. 3 is a waveform diagram showing a method for correctly determining a peak point from a waveform diagram containing a lot of noise. FIG. 6 is a waveform diagram showing an example of a method for finding one refraction point of an original waveform diagram. FIG. 6 is a waveform diagram showing an example of a method for finding one refraction point of an original waveform diagram. FIG. 2 is a diagram summarizing processes that can be executed by a system according to an embodiment of the present invention. FIG. 1 is a diagram showing a user interface of a system according to an embodiment of the present invention. FIG. 2 is a diagram illustrating a problem when difference processing is performed on the entire time series data. FIG. 3 is a diagram illustrating that noise can be reduced by increasing the degree of moving average. FIG. 3 is a diagram illustrating problems caused by increasing the number of moving average points. FIG. 6 is a diagram illustrating a case where an operator manually sets a time range. FIG. 3 is a diagram illustrating a method of determining a range by focusing on a value range on the vertical axis. FIG. 6 is a diagram illustrating a method of setting a search range based on characteristics of feature points. FIG. 3 is a diagram illustrating a method of setting a range based on the maximum point of speed data. FIG. 3 is a diagram illustrating a process of setting a processing range based on the mutual relationship of a plurality of time series data. FIG. 3 is a diagram illustrating a specific method of actually setting a processing range for time-series data. FIG. 3 is a diagram illustrating a specific method of actually setting a processing range for time-series data. FIG. 3 is a diagram illustrating a specific method of actually setting a processing range for time-series data. FIG. 3 is a diagram for explaining a method for obtaining an approximate curve of original time series data. FIG. 3 is a diagram for explaining a method for obtaining an approximate curve of original time series data. FIG. 3 is a diagram for explaining a method for obtaining an approximate curve of original time series data.

FIG. 1 is a functional block diagram of main parts of a time-series data analysis system according to an embodiment of the present invention. Each processing unit shown in FIG. 1 includes a processor in a general computer including a personal computer, a temporary storage device such as a DRAM, a non-temporary storage device such as an HDD device, a keyboard and mouse as data input means, a display device, etc. Various types of processing are performed by a combination of hardware and software such as a computer program read from a storage device and executed by a processor.

In FIG. 1, a data input processing section 10 performs a process of importing time-series data from measurement devices, various sensors, etc. into the system. Here, time-series data refers to data that is captured at regular time intervals, or data that has undergone some processing on time-series data that has already been captured into the system. The user input processing unit 12 performs a process of importing data input by a user from a keyboard, mouse, etc. into the system. The image output processing unit 14 performs processing for outputting a user interface including characters, graphics, etc., actual time-series waveform data, etc. to a display or, if necessary, to an output device such as a printer.

The band-pass filter processing unit 16 performs band-pass filter processing on time-series data that has been imported into the system, or on time-series data that has already been imported into the system and has undergone some processing, and performs band-pass filter processing as necessary. Display the waveform diagram obtained. Note that the band-pass filter processing unit 16 not only directly performs band-pass filter processing on time-series data, but also performs fast Fourier transform as necessary, performs band-pass filter processing in frequency space, and then performs inverse processing. It is also possible to perform fast Fourier transform to return to time and space. The moving average processing unit 18 averages the time series data taken into the system, or the time series data that has already been taken into the system and has undergone some processing, at a predetermined number of adjacent time positions. Execute processing. For this predetermined number, the default setting may be used as is, or a value set by the user via a user interface to be described later may be used.

The differential processing unit 20 performs a time differential operation on the time series data taken into the system or on the time series data that has already undergone some processing in the system, and generates the obtained waveform as necessary. Show diagram. For example, if the time interval (reciprocal of the sampling frequency) for capturing time series data is 1/1000th of a second, then the difference between two adjacent data values at this 1/1000th of a second interval is expressed as 1/1000th of a second. By dividing, we get the time derivative. However, it is also possible to execute the differentiation process by widening the time interval, such as every other or every second time interval, for each time series. Taking time differentiation at finite time intervals in this way is also called difference. The integral difference processing unit 22 performs an integral operation on the time series data taken into the system or on the time series data that has already undergone some processing in the system, and further performs an integral operation on the obtained integral data. On the other hand, difference processing is executed, and the obtained waveform diagram is displayed as necessary.

The subtraction processing unit 24 executes subtraction processing between two certain waveform data, and displays the obtained waveform diagram as necessary. The pulse generation unit 26 generates a first pulse waveform for the time series data, in which the length of time during which the value is continuously positive is the pulse width, and the length of time during which the value is continuously positive is the pulse height. and a second pulse waveform whose pulse width is the length of time during which the value is continuously negative and whose pulse height is the length of time during which the value is continuously negative. A waveform diagram of both or one of the pulse waveform and the second pulse waveform is displayed. The threshold processing unit 28 executes a process of selecting a pulse that exceeds or is below the threshold from among a plurality of pulses by setting a threshold by the user, and selects the selected pulse as necessary. indicate. When the division point search processing unit 30 approximates a range from a certain start point to an end point of a certain time series data with a curve made of straight lines connecting several points (dividing points) included in the range, Processing is performed to determine the positions of these division points so that a sufficient approximation can be made to judge the characteristics of the time series data.

The processing range setting processing unit 32 does not process the entire time series data that has been imported into the system or has already undergone some processing within the system, but rather sets a time range based on certain rules. , and execute processing that targets only time-series data within the set time range. The specific contents of the processing performed by the processing range setting processing section 32 will be described in detail later.

The moving average processing section 18 and the integral difference processing section 22 shown in FIG. 1 perform noise removal processing, and are not necessarily required as part of the system configuration. Either one of them may be used as necessary. Systems can be configured to include one or both. Furthermore, it is not the case that the present invention cannot be realized unless all the processing units shown in FIG. 1 are included. For example, if only the differential processing section 20, range setting processing section 32, and peak position detection section 34 are included, it is possible to construct a system that performs the minimum necessary processing on time series data, and the differential processing section 20, Even if only the pulse generation section 26, the subtraction processing section 24, and the threshold processing section 28 are included, it is possible to construct a system that performs the minimum necessary processing on time series data. After that, the system can be constructed by adding other processing units shown in FIG. 1 according to actual processing needs.

Figure 2 shows how the pressure applied during injection molding (vertical axis) changes over time (horizontal axis) from when the resin is poured into the mold until it solidifies, and shows an actual pressure sensor. Shows output time series data. Incorporation of such data into the time series data analysis system is performed by the data input processing section 10 in FIG.

In FIG. 2, circles 10a, 10b, 10c, and 10d are shown at four locations superimposed on the signal waveform. In the signal waveform shown in FIG. 2, the leftmost circle 10a is the point at which the pressure starts to rapidly increase from almost zero, and shows the moment just before the resin spreads throughout the inside of the mold. Then, the pressure increases rapidly from point 10a and reaches the peak of circle 10b. This peak corresponds to the point when the entire mold is filled with resin and resin pouring is stopped. When the resin pouring is stopped, the pressure rapidly decreases, and the pressure remains constant for a while from the point of circle 10c. This constant pressure period corresponds to a period during which the temperature of the resin is cooled. Then, when the resin is sufficiently cooled and solidified, the pressure rapidly decreases again from the point of circle 10d.

The way the pressure inside the mold changes over time as shown in FIG. 2 varies depending on the size and type of the mold, the composition of the resin, etc. Therefore, by capturing the points in time (inflection points) at which characteristic changes corresponding to circles 10a, 10b, 10c, and 10d in FIG. You can know about problems etc. That is, the injection molding operation itself and the condition of the molded product can be monitored using the pressure sensor.

By the way, when monitoring an injection molding operation or a steel plate cutting operation using a pressure sensor or a weight sensor, a large amount of data is obtained. In order to accurately extract the above-mentioned characteristic inflection points from such a large amount of data, rapid processing is required, so faster processing is required, and the load on the computer increases accordingly. Therefore, in this embodiment, the following data processing is performed.

In the example of injection molding described above, if the changes before and after the moment when the resin spreads throughout the inside of the mold (circle 10a in FIG. 2) are extended significantly, the result will be as shown in FIG. 3(a). The pressure starts to rise from the point at which the resin is distributed throughout the interior of the mold, as indicated by the circle 11a in FIG. 3(a). In other words, this point becomes the inflection point. When you want to know the point of inflection, first take the time derivative of the graph shown in FIG. 3(a) using the differential processing unit 20 shown in FIG. A curve is obtained. If the change in FIG. 3(a) is considered as displacement, the waveform in FIG. 3(b) corresponds to velocity. When the curve shown in FIG. 3(b) is further differentiated by the differential processing section 20, the curve shown in FIG. 3(c) is obtained. This corresponds to acceleration. If a maximum point like the circle 11b is found in the curve of FIG. 3(c), it can be determined that that point is the bending point at the moment when the resin has spread throughout the inside of the mold.

Therefore, the differential processing section 20 performs time differentiation one more time on the curve of FIG. 4(a), which is the same as that of FIG. 3(c), to obtain the curve of FIG. 4(b). If we know the point at which the curve in Fig. 4(b) passes through zero (indicated by an upward arrow), this point will be the maximum point of the curve in Fig. 4(a), that is, the point at which the resin has spread throughout the inside of the mold. It can be determined that there is. However, the curve shown in Figure 3(a) is only a curve that assumes the change in pressure when the resin is spread throughout the inside of the mold, and the signal waveform of the actual pressure sensor does not follow such a smooth graph. Instead, it is output with considerable noise added to it.

FIG. 5 shows a problem when trying to find a local maximum point from time series data that contains a lot of noise. FIG. 5(a) shows an example of a signal waveform corresponding to FIG. 4(a) for which the maximum point is to be determined, and it contains considerable noise when compared with the curve in FIG. 4(a). . Therefore, first, the moving average processing unit 18 of FIG. 1 takes a moving average. The waveform in FIG. 5(b) is a 49-point moving average of the signal waveform in FIG. 5(a), and the waveform in FIG. 5(c) is a 99-point moving average. The waveform in FIG. 5(d) is obtained by taking a 199-point moving average. Here, the multiple-point moving average corresponds to step difference, that is, performing differentiation, but in general, the more points the moving average has, the more the noise decreases.

The waveforms in (b), (c), and (d) in Figure 5 are obtained by taking moving averages at different points, and the waveforms in (b), (c), and (d) each pass through zero. The time points t _b , t _c , and t _d do not coincide, but are slightly shifted back and forth. This shows that the point at which the obtained waveform passes through zero changes depending on how the data is processed, that is, in this case, depending on how many points the moving average process is performed on. Therefore, with the method shown in FIG. 4 of taking the differential (difference) with respect to acceleration, it is not possible to accurately determine the point in time when the trend changes from the output signal containing noise.

という計算を実行する。 Therefore, in order to improve the above problem, in this embodiment, a process called integral difference is executed. That is, for a waveform whose point in time passing through zero is desired to be determined, it is integrated at certain equal intervals, and the difference is calculated with respect to this integrated value. in particular,

Perform the calculation.

The above integral difference equation will be explained with reference to FIGS. 6A and 6B. First, in the waveform (a) of FIGS. 6A and 6B (same as the waveform of FIG. 5(a)), if the point of interest is i and the range of integration is w, then the right side of the above equation The first term corresponds to the integrated value of waveform a from i to i+w, that is, the area under the curve of a from i to i+w (indicated by hatching). Similarly, the second term on the right side corresponds to the sum of the values of waveform a from iw to i, that is, the area under the curve from iw to i (shown in pear pattern). Therefore, the integral difference represents the difference between the area to the right of i and the area to the left of i. Here, if w is 99, it is called a 99-point integral difference, and if w is 199, it is called a 199-point integral difference.

In FIGS. 6A and 6B, the waveform in (b) shows a waveform diagram obtained by performing a 99-point integral difference on the waveform a in (a). 6A corresponds to the case where the value of the integral difference is zero, and FIG. 6B corresponds to the case where the difference between the first term and the second term on the right side is almost minimum. As can be seen from the waveform (b) in FIGS. 6A and 6B, the noise is reduced to the extent that it does not interfere with identifying the local maximum point, that is, the point in time when passing zero, without significantly losing the characteristics of the original waveform. You can see that it has been removed. Looking at the waveform in (a) of FIG. 6A, there is a point slightly to the left of point i when this waveform actually reaches its peak. If a person sees this peak, he or she can determine that the peak is caused by noise, but it is extremely difficult to have a computer make such a determination. On the other hand, looking at the waveform in FIG. 6A (b) obtained by performing the above integral difference processing, the point at which this waveform passes through zero is the entire waveform curve in FIG. 6A (a). It can be seen that this coincides with the maximum point.

Next, a specific method for using a computer to determine the point at which the waveform shown in FIG. 6A (b) passes through zero will be described. The waveform shown in FIG. 6A (b) is actually time series data plotted against discrete times (horizontal axis) and connected by curves. In FIGS. 7A and 7B, the upper waveform diagram corresponds to FIG. 6A (b), and the lower waveform diagram is obtained by time-differentiating the upper waveform diagram. Therefore, the point in time when the lower waveform diagram becomes zero is the point in time when the upper waveform diagram passes through zero. However, the lower waveform diagram is also plotted against discrete times, similar to the upper waveform diagram. Since the time resolution is thus limited, it is rare for the time series data shown at the bottom of FIGS. 7(a) and 7(b) to contain complete zeros.

When searching for a point where the data is zero, as shown in the waveform diagrams at the bottom of Figures 7(a) and (b), a threshold value of a constant width centered on zero on the vertical axis ( It is conceivable to set a band-shaped portion with a constant width centered on the time axis, and determine that data included in this range is zero. In the lower diagrams of FIGS. 7A and 7B, data within the threshold range is shown by lines parallel to the vertical axis for ease of understanding. In this case, if the threshold width is narrow as in (a), there may be no data that falls within the range where the curve changes significantly, and if the threshold width is wide as in (b), there may be no corresponding data. A situation may arise in which there is a large amount of data to search for and it is not possible to find the data that one originally wants to find. As described above, there is a problem in that it is not easy to set an appropriate threshold value for each application, and it is also inefficient. Another method is to search the time series data point by point and find the point at which the sign changes from plus to minus or from minus to plus. However, this method is inefficient because the processing is scalar processing.

Therefore, in this embodiment, the point at which the waveform diagram passes through zero is found in the following manner. FIG. 8(a) corresponds to the upper waveform diagram in FIGS. 7(a) and (b), and FIG. 8(b) corresponds to the lower waveform diagram in FIGS. 7(a) and (b). FIG. 8(b) is a waveform obtained by time-differentiating the waveform of FIG. 8(a). Regarding the waveform of FIG. 8(b), the pulse generating section 26 shown in FIG. 1 generates pulse waveforms as shown in FIGS. 8(c) and 8(d). The pulse waveform of FIG. 8(c) is derived from the waveform of FIG. 8(b) by deriving the length of time in which the pulse is continuously positive as the pulse width and the length of time in which the pulse is continuously positive as the pulse height. It is. For example, in the portion of FIG. 8(c) that corresponds to the time width of T ₁ in the central portion of FIG. 8(b) where the pulse changes greatly, a pulse having a height corresponding to the value of T ₁ is shown. On the other hand, in the pulse waveform of FIG. 8(d), the length of time when the pulse is continuously negative is the pulse width, and the length of the time when the pulse is continuously negative is the pulse height. It is something that For example, in the portion of FIG. 8(d) that corresponds to the time width of T ₂ in the central portion of FIG. 8(b) where the pulse changes greatly, a pulse having a height corresponding to the value of T ₂ is shown. (c) and (d) in FIG. 8 are staggered when viewed on the time axis, apart from the values on the vertical axis.

Next, as shown in FIG. 9 (FIGS. 9(a) to 9(d) correspond to FIGS. 8(a) to 8(d)), the subtraction processing unit 24 of FIG. By subtracting and taking the difference in Fig. 9(c), the waveform diagram in Fig. 9(e) is obtained, and by further performing time differentiation on the waveform diagram in Fig. 9(e), Fig. 9(f) is obtained. A waveform diagram as shown in which pulses remain only at the time of switching from positive to negative and the time of switching from negative to positive is obtained. Depending on whether this pulse is positive or negative, it can be determined whether the pulse has switched from positive to negative or from negative to positive. Each peak in the waveform diagram of FIG. 9(f) corresponds to the temporal position of the maximum point, and the height of each peak reflects the length in which each step difference continues with the same sign. Note that the processing up to this point is all vector processing, and there is no need to search each piece of data, so the computational processing load is significantly reduced.

Furthermore, when the above-mentioned integral step difference is performed on the waveform diagram of FIG. 9(f), the waveform diagram of FIG. 10(h) is obtained ((a) of FIG. 10 shows the pressure inside the mold detected. (b) to (g) correspond to (a) to (f) in FIG. 9). Here, if a certain threshold value is set by the threshold value processing unit 26 in FIG. 1 and only pulses exceeding this threshold value are selected, this time point becomes the inflection point of the time series data in FIG. 10(a), i.e. It can be seen that the trend has changed.

Next, an example of searching for an actual peak point from data containing noise will be described. In FIG. 11, (a) is the output data of a pressure sensor that detects the actual pressure inside the mold, and the maximum pressure point is determined from this data that includes considerable noise. In FIG. 11, the horizontal axis is time. A fast Fourier transform (FFT) is performed on the output data in FIG. This is the waveform shown in FIG. 11(b). Note that in FIG. 11(b), "0-40 Hz" means that waveforms with frequencies higher than 40 Hz are cut and only waveforms with frequencies between 0 and 40 Hz are extracted.

The waveform shown in FIG. 11(c) is obtained by taking a nine-point moving average of the waveform shown in FIG. 11(b). The maximum point of the waveform in FIG. 11(c) can be considered to be the point of maximum pressure. By the way, when comparing the waveform in FIG. 11(a) and the waveform in FIG. 11(c), the actual peak position in FIG. 11(a) is shifted to the left side from the peak position in FIG. 11(c). . This is considered to be due to the influence of noise. Even if the peak position shifts due to noise, by performing the steps (a) → (b) → (c) in Figure 11, the influence of noise can be eliminated and the pressure can be maximized. You can find the point in time when The portion that performs the processing from (a) to (b) to (c) in FIG. 11 functionally corresponds to the peak position detection unit 34 shown in FIG. 1.

Next, find the point corresponding to circle 10c of the output waveform of the pressure sensor in Fig. 2, that is, immediately after the resin is filled and the pressure reaches its peak, the pressure suddenly decreases and then a nearly constant stable period begins. The process will be explained. In FIG. 12, (a) shows a state in which the output waveform of the pressure sensor shown in FIG. 2 is expanded in the direction of the time axis (horizontal axis). The waveform shown in FIG. 12(a) is subjected to band-pass filtering similar to that shown in FIG. 11(b) by the band-pass filter processing unit 16 shown in FIG. ) is the waveform shown.

The waveform shown in (c) is obtained by taking a nine-point moving average of the waveform in (b) by the moving average processing unit 18 of FIG. Furthermore, the waveform shown in (d) is obtained by time-differentiating the waveform in (c) by the differentiation processing unit 20, and the waveform (e) obtained by further performing time differentiation on this is obtained. ) is the waveform shown. In the waveform shown in (e), a peak can be seen slightly before the value of 600 on the horizontal axis, but if you compare it with the waveform in (a), this point is the start of a stable period. I understand.

Next, a process for finding the point corresponding to the circle 10d of the output waveform of the pressure sensor shown in FIG. 2, that is, the point at which the resin is sufficiently cooled and solidified and the pressure decreases, will be described. In FIG. 13, (a) shows the output waveform of the pressure sensor shown in FIG. 2 extended in the direction of the time axis (horizontal axis). This corresponds to the point at which the pressure decreases as it cools and solidifies. The waveform in FIG. 13(a) is subjected to band-pass filter processing similar to that in FIG. 11(b) by the band-pass filter processing unit 16 in FIG. 1, and the result is shown in FIG. 13(b). The waveform is shown in

The waveform shown in FIG. 13(c) is obtained by taking a nine-point moving average of the waveform shown in FIG. 13(b) by the moving average processing unit 18 of FIG. Furthermore, the waveform shown in (d) is obtained by subjecting the waveform in (c) to time differentiation by the differential processing section 20. Here, from the waveform shown in FIG. 13(d), it can be seen that the point in time when the value temporarily changes from a certain approximately constant positive value to a negative value corresponds to the portion shown by the circle in FIG. 13(a). Note that in this example, the waveform (e) obtained by further time-differentiating the waveform (d), that is, the waveform corresponding to acceleration, has a gradual downward movement, so this point can be successfully detected. It's difficult to do.

As explained so far, by applying and executing various types of processing to time-series data by each processing unit shown in Figure 1, the inflection point in the time-series data, that is, the trend, changes. It is possible to find the points with high accuracy. FIG. 14 is a diagram summarizing what can be done with the system of this embodiment. There are four basic processes that can be performed as data processing: band pass filter processing, moving average processing, difference integration processing, and differential processing, and by combining these, various data processing becomes possible. Then, for the processed data, one or more of the following are determined: the maximum value, the position of the maximum value (time), the position of the minimum value (time), threshold processing, and integral. It is possible to identify changing points in trends.

FIG. 15 shows an example of a user interface of the time series data analysis system shown in FIG. Utilizing such a user interface improves convenience when the user actually performs processing on time-series data. Through this user interface, the above-described processes can be executed on arbitrary time-series data, and the results of the processes can be visually viewed immediately. In the "Data source" column at the top left of this screen, the name of the time series data to be processed is listed, and in the "Raw data" column immediately to the right of this, the data to be processed, such as the output data of pressure sensors and weight sensors, is listed. The actual time series data input to the target computer will be displayed.

Furthermore, an "FFT spectrum" column is provided on the right side, and an FFT spectrum obtained by performing fast Fourier transform (FFT) on the waveform diagram displayed in the "Raw data" column is displayed here. This FFT processing can be performed on all input data displayed in the "Raw data" field, or the user can select whether or not to perform the FFT processing. Note that bandpass design is possible in this "FFT spectrum" column. Looking at the waveform in the "FFT spectrum" column of FIG. 15, it can be seen that the peaks are concentrated around 50 Hz on the horizontal axis. Therefore, 25 Hz is specified here as the upper limit of the bandpass (gray shading in the frequency portion higher than 25 Hz indicates this), and only waveforms below 25 Hz are extracted.

Further, in FIG. 15, a column for selecting a sampling rate is provided below the "data source" column. This sampling data corresponds to the time interval of adjacent individual data of the time series data, and here, "100Hz (1/100 second interval)", "1000Hz (1/1000 second interval)", It is possible to select one of "100 kHz (1/100,000 second interval)" (1000 Hz is selected in FIG. 15). In the "Detection mode" column below, you can select and display displacement, velocity, or acceleration for time-series data. Further below, in "Bandpass Lower Limit (Hz)" and "Bandpass Upper Limit (Hz)", the upper and lower limits of bandpass processing can be graphically set on the screen.

The "moving average range" column below is for setting the range for taking the moving average, that is, the number of consecutive time series data to take the average, and can be set in the range from 1 to 19. The "center" column below is a switch for selecting the center of the moving average. The "refraction point detection" column below is set by checking or not checking the check column to determine whether or not to perform refraction point detection. The "Peak Direction" column below is a column for selecting to detect either or both of an upward peak and a downward peak when detecting a peak. The "Peak Width" field is a field where, when detecting a peak, it is set so that only peaks with a width equal to or less than the width set here are detected. “Peak threshold (ratio to maximum peak)” is a field in which settings are made so that only those having a value exceeding the threshold set here are detected as peaks. In the widest area at the bottom right of FIG. 15, a waveform diagram obtained by processing input time-series data based on the contents set in each column so far is shown.

As understood from the above explanation, an inflection point where time-series data shows a characteristic change can be found as a peak in displacement, velocity, or acceleration. The actual method of determining velocity from displacement and acceleration from velocity is based on time differentiation, that is, taking the step difference. However, if the process of calculating the difference is performed on the entire input time series data, the long-term trend in the time series data will be lost. Loss of long-term trends emphasizes short-term fluctuations, that is, noise, and hinders the extraction of feature points. FIG. 16 is a diagram explaining this, in which (a) is time series data showing changes in a certain load, (b) is velocity data obtained by time differentiating the time series data in (a), ( c) shows acceleration data obtained by time-differentiating the velocity data in (b). As shown in FIG. 16(c), when the process of calculating the time differential for the entire time series data in (a) is performed continuously, the noise is emphasized and the trend indicated by the circle in (a) is It becomes difficult to find changed feature points.

Further, FIG. 17 shows that noise can be reduced by increasing the degree of moving average. Figure 17 (a) shows a 5-point moving average of velocity and acceleration, (b) a 9-point moving average, and (c) a 19-point moving average. ing. In these figures, the upward arrow shown at the bottom of the figure indicates the point at which it was determined to be a minutiae, but in (a) it is not the minutiae point where the load begins to decrease, but it is shifted to the right of that point. Time points are extracted as feature points. In (b), the noise is reduced compared to (a), and the feature points can be detected, but there is a high possibility that they were detected by chance, and there may be a problem with robustness. In (c), the noise has been considerably removed, and the noise has been further reduced and the feature has been detected.

However, when the number of moving average points is increased, a problem as shown in FIG. 18 may occur. In Figure 18, the solid line is the actual curve showing the load fluctuation, the dotted line is the curve obtained by taking a 19-point moving average of the original load data, and the dashed-dotted line is the curve obtained by moving 39 points relative to the original load data. Each averaged curve is shown. In Figure 18, for example, if you want to know the rise of the curve that indicates the beginning of load application, and you take a 39-point moving average, the curve will deviate significantly to the left (earlier side of time) from the actual rise. In this way, when the number of moving average points is increased, the waveform changes significantly from the original curve, and it becomes difficult to obtain accurate feature points simply by increasing the number of moving average points.

The top graph in Figure 19 shows how the pressure applied during injection molding (vertical axis) changes over time (horizontal axis) from when the resin is poured into the mold until it solidifies. It shows a graph of time series data of the output of the pressure sensor, and the second graph is a graph of time series data obtained by performing one differentiation on the top time series data to find the velocity. The bottom graph shows time-series data obtained by differentiating the acceleration once more. In the top graph, the value on the vertical axis rises rapidly when the value on the horizontal axis is around 250 (indicated by t ₁ ), and then reaches a peak and declines just after 300 (indicated by t ₂ ). At around a little over 400 (indicated by t ₃ ), the rate of decline rapidly decreases and then remains at a nearly constant value for a while. In this way, there are three major trend changes between 200 and 500 on the horizontal axis, each of which has a different meaning.

If the operator knows that the output from the pressure sensor behaves like the top graph in Figure 19, for example, an operator trying to extract the feature point at t ₃ would be able to calculate that the horizontal axis is slightly over 400. If the processes shown in FIGS. 3 to 13 are executed limited to an appropriate range before and after the area, the efficiency of the feature point extraction process can be improved, and the accuracy can also be improved. Therefore, in this embodiment, when performing feature point extraction processing on time series data such as that shown in FIG. 19, when the time series data shown in FIG. By manually directly setting the gray time width before and after the area, it is possible to instruct the system to perform the processing shown in FIGS. 3 to 13 only for that setting range.

FIG. 20 shows a method of determining the range by focusing on the value range on the vertical axis rather than the time axis on the horizontal axis. The graph shown in Figure 20 is the same as the graph shown in Figure 19, but in the speed graph shown second, a range in which the vertical axis value is less than -0.1 is set, and this setting range is This instructs the system to execute the processes shown in FIGS. 3 to 13 only. By doing this, it is possible to exclude from the feature point search process a portion where the acceleration changes significantly, where the horizontal axis is around 300. In this way, by specifying a threshold based on the value of the vertical axis and specifying a range where the original value is smaller or larger than the threshold, it is possible to reliably find the feature point that you really want to find.

FIG. 21 is the same graph as FIGS. 19 and 20, and here, an attempt is made to find the time point at which the acceleration is maximum before and after the time point corresponding to t ₃ in FIG. 19. Therefore, the system is instructed to execute the processes shown in FIGS. 3 to 13, limited to a certain range (in this case, a range of 150 points) before and after time _t3 . By setting the range to be searched based on the characteristics of the feature points in this manner, the efficiency of the feature point extraction process can be improved, and accuracy can also be improved.

FIG. 22 shows a search range between the minimum acceleration point and the maximum speed point in the graphs showing the temporal changes in the sensors shown in FIGS. 19 to 21, and the point where the acceleration is maximum within this range is searched. This is an example of instructing the system to execute the processes shown in FIGS. 3 to 13.

Next, a process of setting a processing range based on the mutual relationships of a plurality of time series data will be described. The upper graph in FIG. 23 shows three time series data captured simultaneously. These are graphs showing how the output from pressure sensors provided at three locations on an injection mold changes over time before and after resin is applied to the mold. Three channels of data are generated simultaneously from three pressure sensors and input into the system. As can be seen from the graph shown at the top of FIG. 23, even within the same mold, the pressure changes are not the same depending on the location, but the overall tendency of the changes is similar. Setting the range based on the relationship between the data from these three sensors will be explained.

Let us consider the case of finding the point at which the pressure starts to increase from the three-channel time series data shown in the upper part of FIG. 23. The graph shown at the bottom of Figure 23 shows the variance of the three data shown above (the difference between the average value at each time point of the three time-series data and each data is calculated, and each difference is squared and summed). something). Looking at the lower graph of FIG. 23, there is almost no change before the resin is filled. Since the positions where the pressure sensors are installed are different from each other, the times at which the pressures start to rise are different, so the dispersion becomes maximum just before the three pressures start to rise, and once the resin is filled, the output of the pressure sensor returns to similar behavior again. Therefore, in the example shown at the bottom of Figure 23, if the range from -50 to +10 points before and after the point where the variance first peaks is set as the search target, the rise points of the three pressure sensors can be set as the search range. I can do it.

Next, a specific method of actually setting a processing range for time-series data using DSL will be described with reference to FIGS. 24 to 26. FIG. 24 shows a graph of the time series data shown in FIG. 19 at the bottom, and an example of a DSL for data input for the operator to specify a processing range for the time series data below at the top. There is. This example shows a state in which the operator inputs "380" and "450" in parentheses to the right of "HORIZONTAL_LIMIT=" while looking at the time series data at the bottom of the figure. By this operation, a gray band is displayed in the time series data in the range from 350 to 450 on the horizontal axis (time axis), and this range is designated as the processing range. If you look at the width of this gray band and decide that it is not appropriate, you can set the appropriate range again by changing the number in parentheses to the right of "HORIZONTAL_LIMIT =". Furthermore, "ROLLING_MEAN = 5" indicates that the moving average score is "5", "VERTICAL_LIMIT = [None, None]" indicates that the vertical range is not specified, and " "TARGET = IDXMIN(ACC)" indicates that the command is to search for the position where the acceleration (ACC) is minimum.

FIG. 25 shows a specific method of setting a processing range using DSL for the time series data shown in FIG. 20, focusing on the range on the vertical axis. In Figure 25, "HORIZONTAL_LIMIT = [None, None]" is set, and no range is set for the horizontal axis, but instead, "VERTIAL_LIMIT = [None, -0.1, VCT]" is set, and the second This indicates that an instruction has been given to search for a range in which the value of the vertical axis of speed is -0.1 or less. Note that "ROLLING_MEAN = 5" indicates that the moving average score is "5", and "TARGET = IDXMAN(ACC)" indicates that the search is directed to the position where the acceleration is maximum. It shows.

The lower part of FIG. 26 shows how to set a processing range using DSL to search for the maximum acceleration point for the time series data shown in FIG. 22. In Figure 26, "HORIZONTAL_LIMIT = [IDXMAX(DST), IDXMAX(DST)+150]" means that the left end of the search range is the point where the range of the original waveform (DST) is maximum, and the vertical axis of the original waveform is This shows that the point where the value of is +150 is set as the right end of the search range. Furthermore, "TARGET = IDXMAX(ACC)" indicates that an instruction has been given to search for the position where the acceleration is maximum.

As described above, if the operator knows the characteristics of time series data, he can easily set the range according to the characteristics and use only a part of the set range instead of the entire time series data. It can be searched. By doing so, search processing efficiency and search accuracy can be improved, and the problems described in connection with FIG. 18 can be avoided.

Next, an embodiment will be described in which a small number of straight lines are connected to the time series data at dividing points to obtain an approximate curve that better fits the time series data. FIG. 27 shows the waveform of output data from a sensor called a strain gauge used during press working. By looking at the state of the waveform between the two peaks indicated by arrows x ₁ and x ₂ in the output data waveform of Fig. 27, it is possible to know whether the press working was successful or whether some problem has occurred. It is known from experience that this is possible. Therefore, in order to automatically determine whether or not the press work was successful, the best output is obtained by dividing the two peaks x ₁ and x ₂ into as few numbers as possible and connecting the dividing points with a straight line. An approximated curve that fits the data waveform is found, and the above-mentioned judgments are made based on this approximated curve. To this end, in this embodiment, the division point search processing unit 30 of the time series data analysis system shown in FIG. 1 executes the following processing.

Although the waveform shown in FIG. 28 is not the same as the waveform shown in FIG. 27, the general tendency is the same, so the division point search process will be explained using FIG. 28. In FIG. 28, three division points p ₁ , p ₂ , and p ₃ are temporarily placed on the waveform data between two peaks, the starting point x ₁ and the ending point x ₂ , and the points are connected by a straight line. The tentative positions of the division points p ₁ , p ₂ , and p ₃ can be arranged evenly between x ₁ and x ₂ by the division point search processing unit 24, but other temporary locations can be arranged by the user. can also be selected and set.

Once the initial positions of p ₁ , p ₂ , and p ₃ are determined, straight lines a connecting x ₁ and p ₁ , straight lines b connecting p ₁ and p ₂ , straight lines c and p connecting p ₂ and p ₃ , Four straight lines a, b, c, and d are obtained, a straight line d connecting ₃ and x ₂ . Since the dividing points p ₁ , p ₂ , and p ₃ are only temporarily placed points, the curve made up of the four straight lines a, b, c, and d at this point best represents the waveform of the output data in FIG. 27. Unlikely. However, even if the number of dividing points p ₁ , p ₂ , p ₃ is small, by moving them arbitrarily at all points between the two points x ₁ and x ₂ , a straight line can be drawn using the least squares method. Although the regression calculation approximated by , the algorithm itself is short, the amount of calculation increases significantly by combining multiple division points.

Therefore, consider moving the three dividing points p ₁ , p ₂ , p ₃ to obtain four curves a, b, c, and d that best represent the waveform of the output data in FIG. 27. FIG. 29 is a diagram for explaining how the positions of the three division points p ₁ , p ₂ , and p ₃ are finally determined. First, in FIG. 29(a), x ₁ and the tentatively determined position of p ₂ are fixed. On the scale of the horizontal axis in FIG. 29(a), x ₁ is located around 210, and p ₂ is located around 240. During this time, p ₁ is moved at predetermined intervals, for example, by 1 on the scale of the horizontal axis, and at each point, the straight line a connecting x ₁ and p ₁ best fits the waveform of the output data in the corresponding range. Determine the position of p ₁ as a point.

Here, the best-fitting point is determined, for example, as the point p ₁ where the regression error is minimized by performing a regression calculation to approximate the straight line a and the output data waveform by the method of least squares. The processing up to this point requires calculations at 30 points from 210 to 240 on the horizontal axis, but since there is only one division point _p1 , the loop processing only needs to be done once, and the load on the computer is not that large. .

Next, as shown in FIG. 29(b), p ₂ is moved by 1 between the determined p ₁ and the tentatively determined p ₃ , and a straight line b connecting p ₁ and p ₂ at each point. The position of p ₂ is determined as the point that best fits the waveform of the output data in the corresponding range. Furthermore, as shown in FIG. 29(c), p ₃ is moved by 1 between the determined p ₂ and x ₂ , and the straight line c connecting p ₂ and p ₃ at each point is The position of p ₃ is determined as the point that best fits the waveform of the output data. The approximate curve obtained by straight lines a, b, c, and d connecting p ₁ , p ₂ , and p ₃ determined as above is a curve that is approximated quite well compared to the waveform of the output data. . Thereby, it is possible to determine whether the press working was successful based on the approximate curve obtained by the straight lines a, b, c, and d. Moreover, since the processing described above only moves one point, the calculation load is not so high and it can be sufficiently executed by a normal personal computer.

In addition, if a sufficiently fitting curve cannot be obtained by performing the processing shown in FIGS. 28 and 29 only once, perform such processing multiple times to obtain the curve that minimizes the regression error. can also be adopted. Even in such a case, the load on the computer and the time required for one process are not large, so the overall load on the computer and the time required can be reduced.

For example, in injection molding, a pressure sensor is provided inside the mold to detect the internal pressure during actual injection molding, and the waveform of the output data can be obtained. The pressure inside the mold increases when liquid resin is injected, but as the resin injection ends and the resin inside cools and hardens, the pressure gradually decreases, and eventually the molded product leaves the mold. At the stage of extraction, the internal pressure decreases rapidly. Whether or not the injection molding process has been carried out properly can be confirmed by looking at the waveform of output data from such an output sensor. In such a case, the system of this embodiment can be utilized.

In the above example, the number of dividing points was three points p ₁ , p ₂ , and p ₃ , but if the characteristics of such pressure changes are known in advance, the number of dividing points can be increased or decreased based on that. The number can be adjusted to suit the application. Furthermore, this embodiment can be applied to any data as long as it is time-series data. For example, since the output data of the pressure sensor shown in Fig. 2 is also time series data, a fitting curve is obtained using an appropriate number of division points in the second embodiment, and the steel plate cutting operation is performed appropriately based on the fitting curve. The system of this embodiment can be used to determine whether or not a request has been made.

10 Data input section 12 User input processing section 14 Image output processing section 16 Band pass filter processing section 18 Moving average processing section 20 Differential processing section 22 Integral difference processing 24 Subtraction processing section 26 Pulse generation section 28 Threshold processing section 30 Division point search Processing unit 32 Range setting processing unit

Claims (16)

a time differentiation processing means for performing time differentiation on time series data and displaying a waveform diagram of the time series data after time differentiation as necessary;
a range setting processing section that sets a time range on a time axis when the time differentiation processing section executes time differentiation processing on time series data to be processed;
a peak position detection unit that detects a position where the time series data to be processed has a peak in the time range set by the range setting processing unit;
A time series data analysis system equipped with The time-series data analysis system according to claim 1, wherein the range setting processing unit allows a user to directly set at least one boundary of the time range on the time axis of the time-series data. The time series according to claim 1, wherein the range setting processing unit sets a specific value on the vertical axis by a user, and sets a corresponding value on the time axis as at least one boundary of the time range. Data analysis system. The range setting processing unit searches for a peak value on the vertical axis of the time series data detected by the peak position detection unit, and sets a value on the time axis corresponding to the peak value as one boundary of the time range. The time-series data analysis system according to claim 1, which is a time-series data analysis system. Furthermore, as a noise removal means, a moving average processing unit is provided which performs moving average processing on the time series data and displays a waveform diagram of the time series data after the moving average processing as necessary; 2. The time series according to claim 1, further comprising one or both of an integral difference processing section that executes integral difference processing and, if necessary, displays a waveform diagram of the time series data after the integral difference processing. Data analysis system. The time-series data analysis system according to claim 1, further comprising a band-pass filter processing unit that performs band-pass filter processing on the time-series data. The time-series data analysis system according to claim 5, further comprising a user input processing section through which a user inputs user data. The time-series data analysis system according to claim 5, further comprising a data input section for importing time-series data into the system from the outside. a time differentiation processing means for performing time differentiation on time series data and displaying a waveform diagram of the time series data after time differentiation as necessary;
For time series data, the first pulse waveform has a pulse width that is the length of time that the value is continuously positive, a pulse height that is the length of time that the value is continuously positive, and a first pulse waveform that has a continuous positive value. and a second pulse waveform in which the length of time in which the pulse is negative is the pulse width, and the length of time in which the pulse is continuously negative is the pulse height. a pulse generation unit that displays a waveform diagram of both or one of the pulse waveforms;
a subtraction processing unit that executes subtraction processing between a plurality of time series data or between a plurality of pulse waveforms, and displays the time series data or pulse waveform after the subtraction as necessary;
a threshold processing unit that compares the value of the pulse waveform with a prespecified threshold and selects a pulse larger or smaller than the threshold;
A time series data analysis system equipped with Furthermore, as a noise removal means, a moving average processing section is provided which executes moving average processing on the time series data and displays a waveform diagram of the time series data after the moving average processing as necessary; 10. The time series according to claim 9, further comprising one or both of an integral difference processing unit that executes integral difference processing and displays a waveform diagram of the time series data after the integral difference processing as necessary. Data analysis system. The time-series data analysis system according to claim 9, further comprising a band-pass filter processing unit that performs band-pass filter processing on the time-series data. The time series data analysis system according to claim 9, further comprising a user input processing section through which a user inputs user data. The time-series data analysis system according to claim 9, further comprising a data input unit for importing time-series data into the system from the outside. A method for finding an inflection point in time series data imported into a time series data analysis system, the method comprising:
A first step of performing time differentiation three times on the captured first time series data by a differentiation processing unit included in the time series data analysis system to obtain second time series data;
The pulse generation unit included in the time series data analysis system defines the length of time during which the second time series data is continuously positive as a pulse width, and the length of time during which the second time series data is continuously positive as a pulse height. a first pulse waveform in which the length of time during which the fourth time series data is continuously negative is the pulse width, and the length of time during which the fourth time series data is continuously negative is the pulse height. A second step to find
A third step of subtracting the first pulse waveform and the second pulse waveform by a subtraction processing unit included in the time series data analysis system to obtain a third pulse waveform;
a fourth step of performing time differentiation on the third pulse waveform by the differentiation processing unit to obtain a fourth pulse waveform;
A threshold processing unit included in the time series data analysis system performs threshold processing on the fourth pulse waveform, selects only pulses exceeding a predetermined threshold, and determines the inflection point of the first time series data. a fifth step,
time series data analysis methods, including In the first step, the time series data obtained by performing the second time differentiation is subjected to integral step difference to remove noise, and then the third time differentiation is performed to obtain the second time series data. The time series data analysis method according to claim 14. A time series data analysis method for analyzing time series data by obtaining an approximate curve of a waveform diagram of the time series data, the method comprising:
provisionally arranging from a first dividing point to an nth dividing point (n is an integer of 2 or more) on the time series data between a prespecified starting point and an ending point;
When the first dividing point is moved from the starting point to the second dividing point, the point where the first straight line connecting the starting point and the first dividing point best fits the time series data in that range is determined as the position of the first dividing point. decided,
When the second dividing point is moved from the first dividing point to the third dividing point, the second straight line connecting the first dividing point and the second dividing point best fits the time series data within that range. a step of determining the position of the two-parting point;
Continue the same procedure below, and when you move the nth dividing point from the n-1st dividing point to the end point, the nth straight line connecting the n-1st dividing point and the second dividing point will be chronologically in that range. determining the point that best fits the data as the position of the n-th division point;
Connecting the starting point, the first division point, ... the nth division point, and the end point in this order by a straight line and using a curve obtained as an approximate curve of the time series data;
Time series data analysis methods including.