JP2019074350A - Analyzer and analysis method - Google Patents

Abstract

To analyze the higher harmonics of a periodic signal having a high fundamental frequency with high accuracy.SOLUTION: An analyzer of the present invention comprises: a sampling unit 12 for acquiring the instantaneous value of a periodic signal S at sampling points of a sampling period; an analysis unit 17 for analyzing the higher harmonics of the periodic signal S on the basis of the instantaneous value; a zero-cross detection unit 14 for detecting the zero-cross of the periodic signal S; a fundamental period specification unit 15 for specifying the fundamental period of the periodic signal S on the basis of the zero-cross detection result; and a processing unit 16 for aggregating the sampling points included in a plurality of fundamental periods into one fundamental period so that the first time interval of two adjacent sampling points is reduced to be shorter than the sampling period. The analysis unit 17 executes a process of developing the periodic signal S into a Fourier series on the basis of the instantaneous value at each aggregated sampling point and calculating the Fourier coefficient of each term in the Fourier series by numerical integration and a process of calculating the absolute value of the Fourier coefficient and the value of a deviation angle as the result of higher harmonics analysis.SELECTED DRAWING: Figure 1

Description

  The present invention relates to an analysis apparatus and an analysis method for analyzing harmonics of a periodic signal.

  As an apparatus of this type, an AC signal measuring apparatus disclosed by the applicant in Patent Document 1 below is known. This AC signal measuring apparatus includes an input unit, a filter unit, a detection signal generation unit, a frequency measurement unit, a frequency calculation unit, a clock generation unit, an A / D conversion unit, and a signal processing unit, and receives an input AC signal (periodic signal). Measure the characteristic data of In this case, the filter unit removes the noise component contained in the AC signal input through the input unit, and the detection signal generation unit detects the zero cross of the AC signal and outputs a detection signal. The frequency measurement unit measures the time from the detection signal indicating the beginning (start time) of each cycle of the AC signal to the detection signal indicating the end (end time), and measures the frequency of the AC signal based on that time. Output frequency data. The frequency calculation unit calculates the sampling frequency based on the frequency data and outputs setting data indicating the sampling frequency. The clock generation unit generates a sampling clock of a frequency indicated by the setting data. The A / D converter samples the AC signal in synchronization with the sampling clock and outputs digital data indicating an instantaneous value of the AC signal. The signal processing unit performs analysis of the alternating current signal (calculation of characteristics of the alternating current signal) by performing FFT arithmetic processing on the digital data.

JP-A-2005-337980 (pages 4-6, FIGS. 1-2)

  However, the above-mentioned AC signal measuring apparatus has the following problems to be improved. Specifically, in the above-described alternating current signal measuring apparatus, analysis of the alternating current signal is performed by subjecting digital data obtained by sampling the alternating current signal to FFT arithmetic processing. In this case, it is preferable that the number of instantaneous values in one basic period of the alternating current signal be the number of powers of 2 in order to accurately analyze the alternating current signal by the FFT operation. For this reason, in this type of device, an interpolation equation representing the waveform of the AC signal is specified based on the instantaneous value of one fundamental cycle of the AC signal obtained by sampling, and the instantaneous value of the number of powers of 2 is determined from the interpolation equation. The interpolation process is performed to obtain However, the higher the fundamental frequency of the AC signal (the shorter the basic cycle) or the higher the harmonic to be analyzed, the lower the number of sampling points per cycle, and the lower the accuracy of the interpolation process. For this reason, in the above-mentioned AC signal measuring apparatus, there is a problem that the analysis accuracy of the AC signal having a high frequency is lowered by the accuracy of the interpolation processing being lowered in the AC signal having a high frequency. ing.

  The present invention has been made in view of the problem to be improved, and has as its main object to provide an analysis apparatus and analysis method capable of analyzing harmonics of a high frequency periodic signal with high accuracy.

  In order to achieve the above object, the analysis device according to claim 1 is characterized in that the sampling unit acquires an instantaneous value of the periodic signal at a sampling point of a predetermined sampling period, and the above-mentioned instantaneous value at a plurality of sampling points. An analysis apparatus comprising: an analysis unit that executes analysis processing for analyzing harmonics of a periodic signal, the detection unit detecting a zero cross of the periodic signal, and the basic of the periodic signal based on the detection result of the zero cross Each of the basic cycles specified in a plurality of the basic cycles such that a basic cycle specifying unit for specifying a cycle and a first time interval of each time of two adjacent sampling points in time are shorter than the sampling cycle. Aggregated data indicating the instantaneous value at each sampling point by aggregating the sampling points into one basic period A processing unit for executing an aggregation process to be generated, the analysis unit expanding the periodic signal into a Fourier series based on the instantaneous value at each of the sampling points aggregated by the aggregation process in the analysis process A process of calculating the Fourier coefficient of each term in the Fourier series by numerical integration, and a process of calculating the absolute value of the Fourier coefficient and the value of the argument as the analysis result of the harmonics are executed.

  According to a second aspect of the invention, in the analysis device according to the first aspect, the processing unit is configured to calculate start times of the plurality of basic periods and times of the respective sampling points included in the respective basic periods. The second time interval is specified, and the process of generating the consolidated data by arranging the sampling points in order of the length of the second time interval is executed as the aggregation process.

  In the analysis device according to claim 3, in the analysis device according to claim 1 or 2, the processing unit is configured to determine the upper limit number and the lower limit number at which the number of sampling points to be integrated in the one basic period is predetermined. The number of basic cycles falling within the range of is defined as the number of processing targets, and the aggregation process is performed on each of the sampling points included in the basic cycles of the number of processing target.

  In the analysis device according to a fourth aspect of the present invention, in the analysis device according to the third aspect, the processing unit determines a predetermined number based on processing efficiency when the analysis unit calculates the Fourier coefficient in the analysis processing. The upper limit number is a number determined in advance based on the number of sampling points required to calculate the Fourier coefficient corresponding to the harmonic of the maximum frequency that can be analyzed by the analysis unit in the analysis process. The processing target number is defined as the lower limit number.

  Further, in the analysis device according to claim 5, in the analysis device according to claim 3 or 4, the processing unit is the one at the end time of the basic period among the sampling points included in one basic period. The process of calculating the third time interval between the time of the close sampling point and the end time is executed for a number of basic cycles greater than the number to be processed, and arranged in order of the length of the third time interval The basic cycles of the number to be processed are selected from the basic cycles, and the aggregation process is performed on each of the sampling points included in the basic cycles of the number to be processed.

  In the analysis apparatus according to claim 6, in the analysis apparatus according to claim 5, the processing unit is configured to calculate the number of the processing targets among the basic cycles arranged in order of the length of the third time interval. The basic cycle is selected every predetermined number defined in advance.

  Further, in the analysis device according to claim 7, in the analysis device according to claim 3 or 4, the processing unit targets each of the sampling points included in the basic cycles of the number of the processing targets continuous in time series. The aggregation process is performed.

In the analysis method according to claim 8, an instantaneous value of the periodic signal is acquired at a sampling point of a predetermined sampling period, and harmonics of the periodic signal are analyzed based on the instantaneous values at a plurality of the sampling points. Analysis method for executing the analysis processing
The zero crossing of the periodic signal is detected, the basic period of the periodic signal is specified based on the detection result of the zero crossing, and the first time interval of each time of two adjacent sampling points in time is the sampling period. The aggregation process is performed to aggregate each of the sampling points included in a plurality of the basic cycles into one basic cycle so as to be shorter than the basic cycle and generate aggregated data indicating the instantaneous value at each sampling point, A process of expanding the periodic signal into a Fourier series based on the instantaneous value at each of the sampling points aggregated by the aggregation process and calculating a Fourier coefficient of each term in the Fourier series by numerical integration in the analysis process; Calculate the absolute value of the Fourier coefficient and the value of the argument as the analysis result of the harmonic The processing and to be executed.

  In the analysis device according to claim 1 and the analysis method according to claim 8, each sampling point included in a plurality of basic periods in the periodic signal is aggregated into one basic period and aggregated data indicating an instantaneous value at each sampling point Executing an aggregation process of generating the periodic signal, expanding the periodic signal into a Fourier series based on the instantaneous value at each sampling point aggregated by the aggregation process, and calculating a Fourier coefficient of each term in the Fourier series by numerical integration; And a process of calculating the absolute value of the Fourier coefficient and the value of the argument as an analysis result of the harmonics of the periodic signal. For this reason, according to this analysis device and analysis method, even when the fundamental frequency of the periodic signal is high (the fundamental period is short), a sufficient number of sampling points are included in one fundamental period by executing the aggregation process. As a result, the harmonics of the periodic signal can be analyzed with sufficiently high accuracy using the instantaneous values at those sampling points. Further, according to this analysis apparatus and analysis method, the periodic signal is expanded into a Fourier series based on the instantaneous value at each sampling point, and the absolute value of the Fourier coefficient and the value of the argument calculated by numerical integration are harmonics of the periodic signal. Unlike the FFT operation processing in which the calculation accuracy decreases when the sampling points are not equally spaced by calculating as the analysis result of the wave, the Fourier coefficients are also obtained when the sampling points become unequal intervals due to the aggregation processing. Can be accurately calculated to analyze harmonics with high accuracy.

  Further, in the analysis device according to claim 2, the second time interval between each start time of the plurality of basic cycles and the time of each sampling point included in each basic cycle is specified, and the length of the second time interval is determined. A process of arranging each sampling point in order and generating aggregated data is executed as an aggregation process. Therefore, according to this analysis apparatus, sampling points in a plurality of basic cycles can be consolidated into one basic cycle by simple processing, and as a result, the processing efficiency of the consolidation process can be sufficiently improved.

  Further, in the analysis device according to claim 3, the number of basic cycles in which the number of sampling points to be collected in one basic cycle falls within the range of the upper limit number and the lower limit number determined in advance is defined as the processing target number An aggregation process is performed on each sampling point included in the basic cycle of the target number. For this reason, according to this analysis apparatus, it is possible to calculate Fourier coefficients accurately and efficiently by determining the upper limit number and the lower limit number in advance as appropriate numbers.

  Further, according to the analysis device of the fourth aspect, the number determined in advance from the processing efficiency at the time of calculating the Fourier coefficient in the analysis processing is the upper limit number, and the harmonic of the maximum frequency that can be analyzed in the analysis processing By defining the number of processing targets with the lower limit number determined in advance based on the number of sampling points required to calculate the corresponding Fourier coefficient, the Fourier coefficients for harmonics of all frequencies that can be analyzed in analysis processing Can be calculated reliably.

  Also, in the analysis device according to claim 5, the processing of calculating the third time interval between the time of the sampling point closest to the end time of the basic cycle and the end time is executed for a number of basic cycles larger than the number to be processed. Select the basic cycles of the number to be processed from among the basic cycles arranged in order of the third time interval length, and execute the aggregation process on each sampling point included in the basic cycles of the number to be processed . For this reason, according to this analysis apparatus, for example, when the aggregation process is performed on each sampling point included in the basic cycles of the number of continuous processing targets in time series, each sampling point after consolidation is within the basic cycle. Even if it is difficult to accurately analyze the harmonics without being uniformly distributed, by selecting the number of basic cycles to be processed so that each sampling point after aggregation becomes uniform within the basic cycle, The harmonics can be analyzed accurately.

  Further, according to the analysis device of the sixth aspect, by selecting the basic cycles of the number of processing targets from among the basic cycles arranged in the order of the length of the third time interval, every predetermined number defined in advance. By defining the defined number to an appropriate number, the basic cycles of the number of processing targets can be efficiently selected by a simple process so that each sampling point after aggregation becomes uniform within the basic cycle.

  Further, according to the analysis device of the seventh aspect, by executing the aggregation process on each sampling point included in the basic cycle of the number of continuous processing targets in time series, the number of basics greater in number than the number of processing targets Since the process of selecting the number of basic cycles to be processed from the cycles is unnecessary, the processing efficiency of the aggregation process can be further improved.

FIG. 2 is a configuration diagram showing a configuration of an analysis device 1; 5 is a signal waveform diagram of a periodic signal S. FIG. It is an explanatory view explaining sampling processing. 7 is a flowchart of an aggregation process 50. FIG. 7 is a first explanatory view illustrating an aggregation process 50; FIG. 10 is a second explanatory view illustrating the aggregation process 50. FIG. 18 is a third explanatory view illustrating the aggregation process 50. It is the 4th explanatory view which explains intensive processing 50. FIG. 18 is a fifth explanatory diagram illustrating the aggregation process 50. FIG. 16 is a sixth explanatory diagram illustrating the aggregation process 50. FIG. 18 is a seventh explanatory diagram illustrating the aggregation process 50. FIG. 18 is an eighth explanatory diagram illustrating the aggregation process 50. FIG. 18 is a ninth explanatory diagram illustrating the aggregation process 50. 7 is a flowchart of analysis processing 60. It is a 1st explanatory view explaining other forms of intensive processing. It is a 2nd explanatory view explaining other forms of intensive processing.

  Hereinafter, embodiments of an analysis device and an analysis method will be described with reference to the attached drawings.

  First, the configuration of the analysis device 1 shown in FIG. 1 will be described. The analysis device 1 is an example of an analysis device, and is configured to be able to analyze harmonics (specify the level and phase of harmonics) of the input periodic signal (as an example, the periodic signal S shown in FIG. 2). . Specifically, as shown in FIG. 1, the analysis apparatus 1 includes a signal input unit 11, a sampling unit 12, a storage unit 13, a zero cross detection unit 14, a basic cycle identification unit 15, a processing unit 16, an analysis unit 17 and a display. A unit 18 is configured.

  The signal input unit 11 executes processing (anti-aliasing filter processing) for removing noise components included in the periodic signal S input through the signal cable.

The sampling unit 12 includes a sampling clock generation circuit and a sampling circuit (both not shown), and executes sampling processing (fixed sampling processing). In this case, the sampling clock generation circuit generates a sampling clock of a predetermined sampling period Ta (see FIG. 3). In addition, the sampling circuit acquires the instantaneous value Vi (see the same figure) of the periodic signal S at the sampling point P (see the same figure) of the sampling period Ta in synchronization with the sampling clock, and obtains sampling data Ds indicating the instantaneous value Vi. Output. In the figure, the sampling period Ta is illustrated to be longer than the actual length (about 10 ⁴ times the actual length), and in the figure and FIGS. 5 to 8 described later, the number of sampling points P is It is illustrated less (in the order of 10 ^-4 times the actual number) than the actual number.

  The storage unit 13 stores the sampling data Ds output from the sampling unit 12 and the later-described aggregated data Da generated by the processing unit 16 according to the control of the processing unit 16.

  The zero cross detection unit 14 low-pass-filters the waveform specified by the sampling data Ds, and detects the time (start time Ts and end time Tt shown in FIG. 3) at which the waveform after low-pass filter processing crosses zero (crosses 0V). To detect.

  The basic cycle specifying unit 15 specifies a basic cycle T (see FIG. 3) of the periodic signal S based on the time (the detection result of the zero crossing) of the zero crossing detected by the zero crossing detection unit 14.

  The processing unit 16 stores the sampling data Ds output from the sampling unit 12 in the storage unit 13. In addition, the processing unit 16 sets the time interval Ia (first time) of the time of the two sampling points P adjacent (that is, temporally adjacent) in the time axis direction (the left and right direction shown in FIG. 3) of the periodic signal S. Interval: The aggregation process 50 (see FIG. 4) of aggregating each sampling point P included in a plurality of basic periods T into one basic period T is performed so that the sampling period Ta is shorter than the sampling period Ta). .

  The analysis unit 17 executes an analysis process 60 (see FIG. 14) for analyzing harmonics included in the periodic signal S based on the instantaneous values Vi of the periodic signal S at a plurality of sampling points P. In this case, the analysis unit 17 converts the periodic signal S into a Fourier series based on each instantaneous value Vi of the periodic signal S at each sampling point P aggregated by the aggregation processing 50 executed by the processing unit 16 in the analysis processing 60. A process of expanding and calculating Fourier coefficients of each term in the Fourier series (Fourier coefficients corresponding to each order of harmonics) by numerical integration, absolute value of each Fourier coefficient (level of each harmonic) and value of argument And (a process of calculating (phase of each harmonic) as an analysis result of the harmonics. In addition, the analysis unit 17 causes the display unit 18 to display the calculated absolute values of the respective Fourier coefficients and the values of the declination.

  Next, an analysis method using the analysis device 1 and an operation of the analysis device 1 at that time will be described with reference to the drawings.

  In this analysis device 1, when the operation of instructing the start of analysis to the operation unit (not shown) is performed, the signal input unit 11 removes the noise component of the periodic signal S input through the signal cable. , And outputs the processed periodic signal S to the sampling unit 12.

  Next, the sampling unit 12 performs sampling processing. In this sampling process, the sampling clock generation circuit of the sampling unit 12 generates a sampling clock of a predetermined sampling period Ta (see FIG. 3). Further, the sampling circuit of the sampling unit 12 acquires the instantaneous value Vi of the periodic signal S at the sampling point P of the sampling period Ta in synchronization with the sampling clock (see the same figure), and outputs sampling data Ds indicating the instantaneous value Vi Do.

  Subsequently, the processing unit 16 causes the storage unit 13 to store the sampling data Ds output from the sampling unit 12.

  Next, the zero cross detection unit 14 low-pass-filters the waveform specified by the sampling data Ds, and specifies times when the waveform after low-pass filter processing crosses zero (for example, start time Ts and end time Tt shown in FIG. 3). .

  Subsequently, the basic cycle specifying unit 15 specifies the basic cycle T (see FIG. 3) of the periodic signal S based on the time of the zero crossing detected by the zero cross detection unit 14. Specifically, for example, the basic cycle specifying unit 15 measures the time from the time of the rising zero cross (start time Ts shown in the figure) to the time of the next falling zero cross (end time Tt shown in the figure). It is specified as a basic cycle T.

  Next, the processing unit 16 executes the aggregation process 50 shown in FIG. In the aggregation process 50, the processing unit 16 determines the time axis direction of the periodic signal S in order to obtain the number of sampling points P necessary to execute analysis processing 60 (see FIG. 14) described later accurately and efficiently. The time interval Ia (first time interval) of each time of two sampling points P adjacent (that is, temporally adjacent) in the (left and right direction shown in FIG. 13) is shorter than the sampling period Ta Each sampling point P included in a plurality of basic cycles T is integrated into one basic cycle T.

  Specifically, as shown in FIG. 4, the processing unit 16 first defines the number of basic cycles T targeted by the aggregation process 50 (hereinafter, this number is also referred to as “the number of processing targets B”) (see FIG. 4) Step 51). In this case, the processing unit 16 sets the upper limit number Nmax at which the number of sampling points P (this number is also referred to as a “prescribed number N”) to be consolidated into one basic cycle T (target of consolidation processing 50) is predetermined. The number of basic cycles T within the range of the lower limit number Nmin is defined as the number B to be processed. Further, in the analysis device 1, the processing unit 16 sets the number determined in advance from the processing efficiency when the analysis unit 17 calculates the Fourier coefficient C described later in the analysis processing 60 as the upper limit number Nmax and analyzes The lower limit number Nmin is the number determined in advance based on the number of sampling points P required to accurately calculate the Fourier coefficient C corresponding to the harmonic of the maximum frequency fmax that can be analyzed by the unit 17. Define the number B of objects to be processed.

  As an example, assuming that the sampling frequency is 5 MHz (sampling period Ta is 5 MS / s), the fundamental frequency f (reciprocal of basic period T) is a 2.4 MHz harmonic which is the eighth harmonic of the periodic signal S of 300 kHz. It shall analyze as a harmonic of maximum frequency fmax. In this case, if the number of sampling points P to be processed in the Fourier series expansion is too large, the operation processing time will be longer (processing efficiency will be reduced). I assume. Also, in this case, since the 2.4 MHz waveform is sampled at 5 MHz, the number of sampling points P per waveform is two to three. On the other hand, assuming that it is preferable that the number of sampling points P per waveform is 10 or more in order to accurately analyze the harmonics, the number of sampling points P per waveform at 2.4 MHz should be 10 or more. It is necessary to integrate at least five waves of sampling points P as waveform data of one wave. Therefore, the lower limit number Nmin is 5M / 300k × 5 ≒ 84, which is the number of sampling points P for five waves of the 300 kHz waveform. Therefore, in this example, 5M / 300 k × 5 ≒ 84 (lower limit number Nmin) <N (specified number) <N (specified number) in order to sufficiently increase the calculation accuracy (the accuracy of analysis) while satisfying the restriction of the calculation processing time. For example, 450 pieces satisfying the condition 480 (upper limit number Nmax) can be defined as the specified number N, and 27 pieces calculated by 450 / (5M / 300k) can be defined as the number B to be processed. In order to facilitate understanding of the invention, an example in which the number of processing targets B is defined to four will be described below.

  Subsequently, the processing unit 16 reads the sampling data Ds from the storage unit 13 (step 52). Next, the processing unit 16 executes a time interval specifying process using the sampling data Ds (step 53). In this time interval specifying process, the processing unit 16 calculates the time of the sampling point P closest to the end time Tt (see FIG. 5) of the basic cycle T among the sampling points P included in one basic cycle T. The process of calculating the time interval Ic (third time interval: see the same figure) from the end time Tt is a number twice as many as the number B to be processed (for example, four being the number B to be processed) In this example, eight basic cycles T (hereinafter, each basic cycle T is also referred to as “basic cycles Ta to Th” in time series) are executed.

  Subsequently, the processing unit 16 executes the rearrangement process (step 54). In this rearrangement process, as shown in FIG. 6, the processing unit 16 arranges the eight basic cycles Ta to Th targeted in the above-described time interval specifying process in ascending order of the time interval Ic (an example of the order of lengths). Rearrange. In this case, in this example, the processing unit 16 rearranges each basic cycle T in the order of the basic cycles Td, Th, Ta, Te, Tb, Tf, Tc, and Tg, as shown in the figure.

  Next, the processing unit 16 executes a selection process (step 55). In this selection process, as shown in FIG. 7, the processing unit 16 selects, from among the basic cycles T rearranged in the above-described rearrangement process, basic cycles T of the number B (four in this example) to be processed. Choose In this case, as an example, as shown in the figure, the processing unit 16 includes four basic cycles Td, Ta, Tb every other (every prescribed number defined in advance), including the basic cycle Td at the beginning. , Tc. In the same figure, the selected basic periods Td, Ta, Tb, and Tc are illustrated by solid lines.

  Subsequently, the processing unit 16 consolidates each sampling point P included in the four basic cycles Td, Ta, Tb, Tc selected in the above selection process into one basic cycle T (step 56). In this case, as shown in FIGS. 8 to 11, the processing unit 16 selects each sampling point included in each of the start time Ts and the basic cycles Td, Ta, Tb, and Tc in the basic cycles Td, Ta, Tb, and Tc. A time interval Ib (second time interval) from the time of P is specified, and processing of arranging the sampling points P in ascending order of the time interval Ib (an example in order of length) is performed.

  By performing this process, as shown conceptually in FIGS. 12 and 13, each basic cycle Td, Ta, Tb, and Tc is obtained such that the start times Ts of the basic cycles Td, Ta, Tb, and Tc coincide with each other. The partial waveforms are superimposed, whereby each sampling point P included in each of the basic periods Td, Ta, Tb, and Tc is aggregated into one basic period T. Further, by consolidating each sampling point P included in a plurality of basic cycles T into one basic cycle T in this manner, as shown in FIG. The time interval Ia (first time interval) of the time is shorter than the sampling period Ta.

  Next, the processing unit 16 generates aggregated data Da indicating the instantaneous value Vi at each of the collected sampling points P, stores the data in the storage unit 13 (step 57), and ends the aggregation processing 50.

  Subsequently, the analysis unit 17 executes an analysis process 60 shown in FIG. In the analysis process 60, the analysis unit 17 reads the consolidated data Da from the storage unit 13 (step 61). Next, the analysis unit 17 performs Fourier series expansion of the periodic signal S based on the instantaneous value Vi at each sampling point P indicated by the read consolidated data Da (step 62).

Here, when the periodic signal S to be analyzed is a function χ (t) of time t, a complex Fourier series (complex exponential type Fourier series) of χ (t) is given by the following equation (1) Given.
χ (t) = Σ [n = −∞, ∞] C _n · exp (j · 2πnf · t) (1)
In the above equation (1), n (n is an integer of 1 or more) is the harmonic order, C _n is the Fourier coefficient C of the n-th harmonic, j is the imaginary unit, f is the fundamental frequency (basic period T (Reciprocal of) is respectively shown (the same in each of the formulas described below).

Subsequently, the analysis unit 17 calculates the Fourier coefficient C of each n-th harmonic. In this case, C _n in the above equation (1) is given by the following equation (2).
C _n = 2 / T · ∫ [0, T] χ (t) · exp (−j · 2πnf · t) dt (2)
In the above equation (2), T represents a basic cycle T (the same applies to the equations described below).

Further, the right side (numerical integration) of the above equation (2) can be approximated by a trapezoidal formula (trapezoidal integration) represented by the right side of the following equation (3).
C _n = 2 / T · ∫ [0, T] χ (t) · exp (−j · 2πnf · t) dt = 1 / TΣ [k = 1, N] {χ (t _k ) · exp (−j · 2π n f · t _k ) + χ (t _k ) · exp (-j · 2 π n f · t _{k + 1} )} · (t _{k + 1-} t _k ) Formula (3)
In the above equation (3), N represents the specified number N of sampling points P described in the above aggregation process 50.
Therefore, it is possible to calculate each Fourier coefficient C by substituting each instantaneous value Vi of each sampling point P included in the consolidated data Da into χ (t _k ) of the above equation (3).

  The analysis unit 17 calculates the Fourier coefficient C of the n-th harmonic of each periodic signal S according to this calculation method (step 63). In this case, in the analysis device 1, each sampling point P included in a plurality of basic cycles T is integrated into one basic cycle T, so that one basic cycle T includes a sufficiently large number of sampling points P. There is. For this reason, in this analysis device 1, it is possible to accurately calculate the Fourier coefficient C.

Next, the analysis unit 17 calculates the absolute value (the level of the n-th harmonic) and the argument (the phase of the n-th harmonic) of each Fourier coefficient C as an analysis result of each n-th harmonic (step 64). In this case, assuming that the real part of the Fourier coefficient C is a and the imaginary part is b, C = a + bj, and the absolute value of the Fourier coefficient C is calculated by | C | = √ (a ² + b ² ) The value of the argument of the Fourier coefficient C is calculated by ArgC = arctan (b / a) (where −π <ArgC <π).

  In this case, in the method of performing Fourier series expansion of the function χ (t) of the periodic signal S and calculating each Fourier coefficient C in the Fourier series based on the instantaneous value Vi of each sampling point P, the interval of each sampling point P is The Fourier coefficient C can be accurately calculated even when the intervals are not equal (in the case of unequal intervals). For this reason, in this analysis device 1, unlike the FFT operation processing in which the calculation accuracy is lowered when the sampling points P are at unequal intervals, the Fourier processing is performed even when the sampling points P become unequal intervals by the aggregation process. It is possible to calculate the coefficient C accurately and analyze the harmonics with high accuracy.

  Subsequently, the analysis unit 17 causes the display unit 18 to display the calculated absolute value and argument value of the Fourier coefficient C (step 65), and ends the analysis processing 60.

  Thus, in this analysis device 1 and analysis method, each sampling point P included in a plurality of basic periods T in the periodic signal S is aggregated into one basic period T, and an aggregation indicating the instantaneous value Vi at each sampling point P is performed. Execute aggregation processing to generate data Da, expand periodic signal S into Fourier series based on instantaneous value Vi at each sampling point P aggregated by aggregation processing, and numerically integrate Fourier coefficient C of each term in the Fourier series And the process of calculating the absolute value of the Fourier coefficient C and the value of the argument as an analysis result of the harmonics of the periodic signal S. For this reason, according to this analysis apparatus 1 and the analysis method, even when the fundamental frequency f of the periodic signal S is high (the fundamental period T is short), one basic period T is sufficiently large by executing the aggregation process. As a result of the inclusion of sampling points P, it is possible to analyze the harmonics of the periodic signal S with sufficiently high accuracy using the instantaneous values Vi at those sampling points P. Further, according to the analysis apparatus 1 and the analysis method, the periodic signal S is expanded into a Fourier series based on the instantaneous value Vi at each sampling point P, and the absolute value of the Fourier coefficient C calculated by numerical integration and the value of the declination Unlike the FFT operation processing in which the calculation accuracy decreases when the sampling points P are at unequal intervals by calculating as an analysis result of the harmonics of the periodic signal S, the aggregation processing causes the sampling points P to be uneven Even in this case, analysis of harmonics can be performed with high accuracy by accurately calculating the Fourier coefficient C.

  Further, in this analysis device 1 and analysis method, the time interval Ib between the start time Ts of the plurality of basic cycles T and the time of each sampling point P included in each basic cycle T is specified to increase the time interval Ib A process of arranging each sampling point P to generate aggregated data Da is executed as an aggregation process. Therefore, according to the analysis apparatus 1 and the analysis method, the sampling points P in a plurality of basic cycles T can be consolidated into one basic cycle T by a simple process, and as a result, the processing efficiency of the consolidation process is sufficiently improved. It can be done.

  Further, in the analysis device 1 and the analysis method, the number of basic cycles T in which the number of sampling points P to be integrated into one basic cycle T falls within a predetermined upper limit number Nmax and lower limit number Nmin B is defined as B, and aggregation processing is performed on each sampling point P included in the basic cycle T of the number B to be processed. For this reason, according to this analysis device 1, the Fourier coefficient C can be calculated accurately and efficiently by determining the upper limit number Nmax and the lower limit number Nmin in advance as appropriate numbers.

  Further, according to the analysis apparatus 1 and the analysis method, the number determined from the processing efficiency at the time of calculating the Fourier coefficient in the analysis processing is the upper limit number Nmax, and the harmonics of the maximum frequency fmax which can be analyzed in the analysis processing By defining the processing target number B as the lower limit number Nmin, with the number determined based on the number of sampling points P required to calculate the Fourier coefficient C corresponding to The Fourier coefficient C for the wave can be calculated reliably.

  Further, in this analysis device 1 and analysis method, the process of calculating the time interval Ic between the time of the sampling point P closest to the end time Tt of the basic cycle T and the end time Tt The basic cycle T of the number B to be processed is selected from the basic cycles T arranged in ascending order of the time interval Ic for the cycle T, and each sampling point P included in the basic cycle T of the number B to be processed is targeted Execute consolidation processing as Therefore, according to the analysis device 1 and the analysis method, for example, when the aggregation process is performed on each sampling point P included in the basic cycle T of the number B to be processed continuously in time series, Even if sampling points P are not uniformly dispersed within basic period T and accurate analysis of harmonics becomes difficult, processing is performed so that each sampling point P after aggregation becomes uniform within basic period T The harmonics can be accurately analyzed by selecting the basic period T of the number of objects B.

  Further, according to the analysis device 1 and the analysis method, the basic cycles T of the number B to be processed are selected every prescribed number defined in advance from among the basic cycles T arranged in ascending order of the time interval Ic. By defining the prescribed number as an appropriate number, the basic cycles T of the number B to be processed can be efficiently selected by a simple process so that each sampling point P after aggregation becomes uniform within the basic cycle T. it can.

  The analysis device and the analysis method are not limited to the above configurations and methods. For example, although the above describes the example in which the processing of arranging the sampling points P in the ascending order of the time interval Ib between the start time Ts of the basic cycle T and the time of the sampling point P has been described above as an aggregation process It is also possible to adopt a configuration and method in which the process of arranging the sampling points P in another example of the order is executed as an aggregation process.

  Also, although an example of selecting the basic cycle T of the number to be processed B from among the basic cycles T arranged in ascending order of the time interval Ic has been described above, arranging in the descending order of the time interval Ic (another example in order of length) It is also possible to adopt a configuration and a method of selecting the number of basic cycles T to be processed from each basic cycle T.

  In addition, although the basic cycle T of the number B to be processed is selected from the basic cycle T (basic cycle T to be selected) twice the number B to be processed as a number larger than the number B to be processed The number of basic cycles T to be selected is not limited to this, and can be defined to an arbitrary number one or more times the number B to be processed (for example, a number three or more times the number B to be processed) .

  Also, although the basic cycle T of the number of processing targets B is selected every other basic cycle T (number of predetermined numbers defined in advance) from among the basic cycles T of the number larger than the processing target number B, for example When the number of target basic cycles T is three or more times the number of processing targets B, a configuration and method are adopted to select the number of basic cycles T for processing target B every two or more from the basic cycles T to be selected. You can also

  Further, the basic cycle T of the number to be processed B is selected from among the basic cycles T having a number larger than the number to be processed B, and the aggregation processing is performed on sampling points P included in each selected basic cycle T As shown in FIG. 15, the sampling points P included in the basic cycles Ti to Tl of the number B (four in this example) of consecutive processing targets in time series are shown in FIG. It is also possible to adopt a configuration and method of executing an aggregation process of aggregating each sampling point P into one basic cycle T. According to this configuration and method, the process of selecting the basic cycle T of the number B to be processed from the basic cycles T of the number larger than the number B to be processed is not necessary. It can be improved.

  Also, although the above describes the example of calculating the Fourier coefficient C by trapezoidal integration (trapezoidal formula), the configuration and method of calculating the Fourier coefficient C by other numerical integration or approximation formula (for example, Simpson's formula or Gaussian quadrature) It can also be adopted.

Reference Signs List 1 analyzer 12 sampling unit 14 zero-cross detection unit 15 basic cycle identification unit 16 processing unit 50 analysis unit 50 aggregation processing 60 analysis processing B number of processing targets Ia time interval Ib time interval Ic time interval Nmax upper limit number Nmin lower limit number P sampling point S Periodic signal T, Ta to Th, Ti to Tl Basic period Ta Sampling period Tt End time Ts Start time Vi Instantaneous value

Claims (8)

A sampling unit that acquires an instantaneous value of a periodic signal at a sampling point of a predetermined sampling period, and an analysis unit that executes an analysis process that analyzes harmonics of the periodic signal based on the instantaneous values at a plurality of sampling points And an analyzer equipped with
A detection unit that detects a zero cross of the periodic signal, a basic period identification unit that specifies a basic period of the periodic signal based on the detection result of the zero cross, and a second of each of the two adjacent sampling points in time The sampling points included in the plurality of basic cycles are aggregated into one basic cycle so that one time interval is shorter than the sampling cycle, and consolidated data indicating the instantaneous value at each sampling point is generated. And a processing unit that executes an aggregation process to
The analysis unit expands the periodic signal into a Fourier series based on the instantaneous value at each of the sampling points aggregated by the aggregation process in the analysis process, and numerically integrates Fourier coefficients of respective terms in the Fourier series. An analysis apparatus that executes a process of calculating by the following equation and a process of calculating the absolute value of the Fourier coefficient and the value of the argument as an analysis result of the harmonic.   The processing unit specifies a second time interval between the start time of each of the plurality of basic cycles and the time of each of the sampling points included in each of the basic cycles, and arranges the second time intervals in order of length. The analysis apparatus according to claim 1, wherein the process of arranging the respective sampling points to generate the aggregated data is executed as the aggregation process.   The processing unit defines, as the number of processing targets, the number of basic cycles in which the number of sampling points to be collected in the one basic cycle falls within a predetermined upper limit number and a lower limit number. The analysis apparatus according to claim 1, wherein the aggregation process is performed on each of the sampling points included in the basic cycle of   The processing unit sets the number determined in advance from the processing efficiency when the analysis unit calculates the Fourier coefficient in the analysis process as the upper limit number, and the maximum frequency that can be analyzed by the analysis unit in the analysis process 4. The analyzer according to claim 3, wherein the number to be processed is defined with the number determined in advance based on the number of sampling points required to calculate the Fourier coefficient corresponding to the harmonics as the lower limit number.   The processing unit is configured to calculate a third time interval between the time of the sampling point closest to the end time of the basic cycle among the sampling points included in one basic cycle and the end time. The basic cycles of the number of processing targets are selected from among the basic cycles arranged in the order of the length of the third time interval, and the basic cycles of the number of processing targets are selected. 5. The analyzer according to claim 3, wherein the aggregation process is performed on each of the sampling points included in the basic cycle.   The analysis device according to claim 5, wherein the processing unit selects basic cycles of the number to be processed from among the basic cycles arranged in order of the length of the third time interval, every predetermined number defined in advance. .   The analysis device according to claim 3 or 4, wherein the processing unit executes the aggregation process on each of the sampling points included in the basic cycle of the number of the processing targets continuous in time series. An analysis method for acquiring an instantaneous value of a periodic signal at a sampling point of a predetermined sampling period, and performing an analysis process of analyzing harmonics of the periodic signal based on the instantaneous values at a plurality of the sampling points. ,
The zero crossing of the periodic signal is detected, and the basic period of the periodic signal is specified based on the detection result of the zero crossing;
The sampling points included in a plurality of basic periods are aggregated into one basic period so that the first time interval of each time of two adjacent sampling points in time is shorter than the sampling period Execute an aggregation process to generate aggregated data indicating the instantaneous value at each sampling point,
A process of expanding the periodic signal into a Fourier series based on the instantaneous values at the sampling points aggregated by the aggregation process in the analysis process, and calculating Fourier coefficients of respective terms in the Fourier series by numerical integration; And a process of calculating the absolute value of the Fourier coefficient and the value of the argument as an analysis result of the harmonic.

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