Fourier transform device

Abstract

To provide a Fourier transformation device capable of efficiently performing Fourier transformation.SOLUTION: A Fourier transformation device 10 includes: a measurement unit 12A configured to output the amount of change in a measurement object Mt as a measurement value X; a sample value holding unit 11A configured with a ring buffer 30 having a plurality of holding parts 11D that hold the measurement value X as a sample value; a successive Fourier transformation unit 12B configured to obtain Fourier coefficients; a Fourier basis holding unit 11B configured to hold Fourier basis calculation results; a Fourier coefficient holding unit 11C configured to hold the Fourier coefficients; a power spectrum calculation unit 12C configured to calculate a power spectrum based on the Fourier coefficients; and a display section 12E configured to display the power spectrum. The successive Fourier transformation unit 12B designates the position of a holding part 11D in the sample value holding unit 11A, and obtains Fourier coefficients by multiplying the value of the Fourier basis with a difference value between the measurement value X and the sample value held in the designated holding part 11D each time the measurement value X is obtained from the measurement unit 12A.SELECTED DRAWING: Figure 3

Description

Technical Field

[0001] The present invention relates to a Fourier transform device.

Background Art

[0002] In the process of maintaining and managing a structure, sensors are installed on the target structure, various response values are measured, and by continuously monitoring this, the state of the target structure is grasped. For example, Patent Document 1 discloses a configuration in which a plurality of detection units (sensors) are attached to the lower surface of a plurality of PC girders in a beam portion to detect cracks on the lower surface of the girder. In recent years, with the development of information and communication equipment including measurement devices and processing devices that process measurement values obtained from measurement devices, it has become possible to provide an observer with the time history waveform of the response value during measurement in real time by means of a so-called waveform monitor or the like. An observer can obtain various information from this waveform monitor, not only the magnitude of the amplitude. For example, in the case of a vibration phenomenon, information on the occurrence and attenuation of vibration and whether a plurality of frequencies are included can be obtained. Also, in the case of strain measurement, information such as whether the response waveform is due to the deflection of the main girder, the response waveform due to the floor assembly, or the influence of vibration can be obtained.

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0004] The inventor considered that if the frequency characteristics could be sequentially displayed in the same way as such waveform monitors, it would provide useful information to the observer, and thus examined the processing method. As an assumed method, sample values are obtained from the measuring instrument at a predetermined sampling interval and discrete Fourier transform is performed, and based on this, the power spectrum is updated and displayed as a "frequency monitor" at the same timing as the waveform monitor. Here, it can also be considered that the same information can be obtained by performing Fourier transform after measuring for a predetermined time without performing real-time processing. However, observing the time history waveform that changes moment by moment and the corresponding power spectrum on the spot at that time is considered an important factor in simple inspections and diagnoses of structures and experiments / observations in the field of education.

[0005] As calculation methods for discrete Fourier transform, methods such as the Tukey-Cooley method and the calculation method called Fast Fourier Transform (FFT) are generally well used. However, these calculation methods are not suitable for sequential calculations as considered this time. For example, considering an "observation window" that always holds the observed values of a certain number of samples, when a new observed value is obtained, the oldest observed value is discarded and the other observed values are retained. Using FFT in such a situation would result in calculating the unchanged sample values over the entire set, except for the one updated sample value, which would be a waste of calculation. Here, in order not to waste the calculation amount, it might seem that the calculation of FFT and the update of the display screen could be performed after all the sample values in the observation window are updated. However, with this approach, there is a possibility that sequential time changes like those of a waveform monitor cannot be expressed.

[0006] Regarding the number of calculations at the time of update, it is considered to be the optimal method for implementing the frequency monitor as it requires fewer calculations compared to FFT that processes the entire observation window.

[0007] The present invention aims to implement a "frequency monitor" that can display the power spectrum in real time, and by utilizing the properties of a ring buffer that holds data circularly and the periodicity of Fourier bases, it executes a "sequential Fourier transform", which is a method of sequentially calculating the difference in the Fourier spectrum accompanying the update of one piece of data in the ring buffer, and aims to provide a Fourier transform device that can efficiently obtain Fourier coefficients.

Means for Solving the Problems

[0008] The Fourier transform device of the present invention includes: a measurement unit that outputs, as a measurement value, a changing amount that changes over time in a measurement target; a sample value holding unit configured by a ring buffer having a plurality of holding units that hold the measurement value as a sample value; a sequential Fourier transform unit that obtains Fourier coefficients each time the measurement value is acquired; a Fourier basis holding unit that holds the calculation result of the Fourier basis calculated in the sequential Fourier transform unit; a Fourier coefficient holding unit that holds the Fourier coefficients calculated in the sequential Fourier transform unit; a power spectrum calculation unit that calculates a power spectrum based on the Fourier coefficients; a display unit that displays the power spectrum; and is provided with: The sequential Fourier transform unit: designates the position of the holding unit in the sample value holding unit, and each time the measurement value is acquired from the measurement unit, multiplies the difference value between the sample value held in the designated holding unit and the measurement value by the value of the Fourier basis held in the Fourier basis holding unit to obtain the Fourier coefficients.

[0009] According to this configuration, Fourier coefficients can be obtained efficiently.

Brief Description of the Drawings

[0010]

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

Figure 10

Figure 11

Figure 12

Figure 13

Figure 14

Embodiments for Carrying Out the Invention

[0011] Preferred embodiments of the present invention will be described.

[0012] In the Fourier transform device of the present invention, a band-pass filter unit is further provided that performs inverse Fourier transform on the sample values at positions a predetermined distance away from the latest sample value in the sample value holding unit and recombines them, and the display unit can display the recombined values. In this case, the filtering process can be performed in a form that suppresses the influence of the discontinuous portion as the time history waveform in the sample value holding unit.

[0013] The measurement unit of the Fourier transform device of the present invention is attached to a plurality of measurement objects, and the sequential Fourier transform unit can obtain Fourier coefficients corresponding to each measurement unit every time it acquires measurement values based on the measurement values from each measurement unit. Also, the values after the filtering process by the inverse Fourier transform can be obtained. In this case, based on the dominance situation of the frequencies at a plurality of positions of the measurement object and the differences in the values after the filtering process, the state of the measurement object can be grasped more precisely.

[0014] Next, Example 1 in which the Fourier transform device of the present invention is embodied will be described with reference to the drawings.

[0015] <Example 1> [Outline of Sequential Fourier Transform] As shown in Equation 1, it is assumed that N sample values measured at a constant sampling interval Δt are obtained.

[0016] [Equation]

[0017] Here, xi represents a collection of sample values, and i is used for the notation of the sample value numbers. Hereinafter, if there is no notation, i = 0, 1, 2,..., N - 1. When writing the Fourier transform of discrete data in the real form, it is expressed as in Equation 2.

[0018] [Equation]

[0019] Here, let j be used to denote the number of the basis function. Hereinafter, if not otherwise specified, let j = 0, 1, 2, …, N - 1. Also, Aj and Bj are Fourier coefficients. The discrete Fourier transform corresponds to obtaining the coefficients for each period when the measurement data is regarded as a sum of periodic signals, and the obtained group of Fourier coefficients is the Fourier spectrum.

[0020] Here, consider the case where the sample values are continuously measured and the Fourier transform is performed each time one sample value is updated. When the oldest data is held at the head of the observation window (ring buffer) (i.e., i = 0), it is necessary to rearrange the data each time a sample value is updated. However, here, consider using the ring buffer 30 as a method of storing the latest N measured sample values (see FIG. 1). The ring buffer 30 has a plurality of holding units 31 for holding sample values. Similar to Equation 1, let the variable for storing the sample values be denoted as xi, but due to the nature of the ring buffer 30, the number i is called the address indicating the address of the holding unit 31 in the ring buffer 30. ct is a pointer indicating the address of the holding unit 31 that holds the latest sample value. When a new sample value is obtained, the value obtained is overwritten and stored at the address of the holding unit 31 specified by the pointer ct. This operation is called the update of the sample value. After updating the sample value, add 1 to the pointer ct to move the storage position of the latest sample value in the ring buffer 30. When the value of the pointer ct becomes N after the update, set the pointer ct = 0 to return the value of the pointer ct to the head address in the ring buffer 30.

[0021] Consider the Fourier transform of the sample values stored in the ring buffer 30. When the state of the ring buffer 30 is as shown in FIG. 2(A), in order to arrange the sample values stored in the ring buffer 30 in the formal order as shown in FIG. 2(B) (i.e., storing the oldest data, the head value, in x0, and then storing the data in address order), it is necessary to rearrange the sample values in the two address intervals (i.e., from i = 0 to ct and from i = ct + 1 to N - 1) separated by the pointer ct.

[0022] However, the waveform considered in the discrete Fourier transform is regarded as a waveform in which the sequence of sample values continues infinitely. Then, as can be seen from the comparison between FIGS. 2(A) and 2(B), the group of sample values as the object of the discrete Fourier transform is essentially the same whether arranged in the correct time order or rearranged in the formal order within the ring buffer 30, and the Fourier spectra in each of these are also essentially the same.

[0023] If there is a difference, as shown in FIGS. 2(A) and 2(B), it is the difference between taking the pointer position (ct + 1) as the head or taking the 0th address in the ring buffer 30 as the head. This exists as the difference between the basis function of each frequency component and the phase of the sample value in the Fourier spectrum. Considering continuous observation, if rearrangement is performed, the phase difference between the start of observation and the current value will change each time, but if rearrangement is not performed, the phase difference between the start of observation and the current value will be permanently maintained. Therefore, it is more convenient to obtain the spectrum by performing the Fourier transform on the sequence of sample values stored in the ring buffer as it is, rather than rearranging the sample values in the ring buffer in the formal order to obtain the Fourier spectrum, so that the observation including the phase can be continued.

[0024] Next, consider updating the Fourier spectrum when updating the sample values stored in the ring buffer. First, the basis functions (Fourier bases) Ci,j and Si,j are expressed as shown in Equation 3.

[0025]

Equation

[0026] Also, each element in the sum of Equation 2 is replaced as shown in Equation 4.

[0027]

Equation

[0028] Then, the Fourier spectrum can be expressed as shown in Equation 5.

[0029]

Number

[0030] However, the sample value number i is not the time-ordered number but the address in the ring buffer. Equation 5 is the sum of each element of the Fourier coefficients calculated for each individual sample value. When a new sample value is obtained, the changing element is only the element of the Fourier coefficient at the latest position, that is, the position of i = ct. Therefore, by subtracting the element of the Fourier spectrum of the old sample value (the sample value before update at the position of i = ct) from the Fourier coefficients and adding the element of the Fourier coefficients for the new sample value at the position of i = ct to the Fourier coefficients, the Fourier spectrum can be updated. Let the old sample value before update at the position of i = ct be xct, and the new sample value be

[0031]

Number

[0032] Denoted as, the elements of the old and new Fourier coefficients can be expressed as shown in Equation 6 respectively.

[0033]

Number

[0034] Since the sample values are held in the ring buffer, the component values of the Fourier basis multiplied by the old and new sample values are the same values Cct,j, Sct,j. Considering the difference at the time of update from Equations 5 and 6, the new Fourier coefficients can be updated by the mathematical formula shown in Equation 7.

[0035]

Number

[0036] Here, the symbol with a horizontal line above Aj indicates the updated value of the Fourier coefficient Aj (i.e., the new Fourier coefficient). The symbol with a horizontal line above Bj indicates the updated value of the Fourier coefficient Bj (i.e., the new Fourier coefficient). Note that if the Fourier coefficients Aj and Bj in Equation 5 are multiplied by N and held in the form of the mathematical formula shown in Equation 8 below, the recurrence formula for updating the Fourier coefficients can be expressed as shown in Equation 9, and the calculation becomes even simpler.

[0037]

Number

[0038]

Number

[0039] Note that although the data from before the measurement start time does not actually exist, as can be seen from Equation 9, until all of the ring buffer is initially filled with sample values from the start of the measurement, spectra are sequentially calculated with the sample values before the measurement start set to 0.

[0040] The calculation method described above will be called the Sequential Fourier Transform (SFT). The sequential Fourier transform utilizes the properties of the ring buffer to sequentially calculate the difference in spectra associated with the update of one piece of data within the ring buffer. The number of multiplications involved in updating the spectrum is actually N because for N / 2 periodic components, one multiplication is performed for sin and cos.

[0041] This results in a significant reduction in the number of multiplications compared to NLog2N times, which is the number of multiplications when obtaining the Fourier spectrum using FFT for the entire ring buffer. Also, considering implementation in a program, the number of memory accesses can be reduced compared to FFT that requires sorting across all data, so the processing time is considered to be even shorter compared to FFT. Therefore, when sequentially acquiring sample values and observing the change in the spectrum each time, this method can process in a shorter processing time compared to using FFT. This method can achieve a nice decimal frequency resolution compared to FFT where the frequency resolution becomes binary due to no constraint on the number of samples. The frequency fj of each frequency component of the discrete Fourier transform can be represented by the mathematical formula shown in Equation 10. According to this, the frequency resolution is 1 / NΔt.

[0042]

Number

[0043] Since the number of samples N is arbitrary, by determining an appropriate number of data together with the sampling interval Δt, a decimal numerical frequency resolution can be obtained. For example, in sampling with Δt = 5 ms and the number of samples N = 2000, as shown in Equation 11, the frequency resolution Δf becomes 0.1 Hz.

[0044]

Number

[0045] As shown in Equation 9, the sequential Fourier transform subtracts the old sample values associated with the update of the sample values from the Fourier coefficients. Here, consider continuing to accumulate the elements of the Fourier coefficients Aj and Bj without performing this subtraction even when the number of measurements exceeds the size of the ring buffer. Represented in a programming notation, it is represented by the mathematical formula shown in Equation 12, and it is to continue the calculation of this mathematical formula.

[0046]

Number

[0047] Here, assume that the cumulative calculation is terminated when twice the number of samples N, that is, when the ring buffer has been looped twice. Considering Equation 5, if the Fourier coefficients Aj and Bj at this time are divided by the number of samples 2N, the spectrum of the average of the sample value group for two loops can be obtained. However, considering the average spectrum, it is considered that it is not necessary to be a multiple of the number of samples N of the ring buffer. Note that even the spectrum obtained in this way retains the phase information from the measurement start point. That is, if the same operation is performed on the sample values obtained at two measurement points, it is considered that the average phase difference between the two measurement points can also be obtained. This calculation method is considered effective for the analysis of vibration characteristics based on long-term observation data such as the constant micro-vibration in a structure.

[0048] The fact that spectra are obtained sequentially means that inverse Fourier transform can be performed sequentially. Utilizing this, consider applying a simple frequency filter to the signal sequentially. The inverse discrete Fourier transform can be expressed as shown in Equation 13 using the values Ci,j and Si,j of the basis functions in Equation 3 and the Fourier coefficients Aj and Bj in Equation 8.

[0049]

Equation

[0050] Here, i is not the time number but the address indicating the position in the ring buffer. Equation 13 can be applied to all the addresses of the ring buffer when the latest value is obtained and the Fourier coefficients Aj and Bj are obtained. Among these, the sample value xct (the latest observed value) at the position of the pointer ct is represented by the mathematical formula shown in Equation 14.

[0051]

Equation

[0052] Since Equation 14 is a mathematical formula for obtaining the sum of each frequency component, just looking at the formula, it seems that by extracting only the components in a specific frequency band from this sum formula, sequential filtering can be performed in real time on the latest sample values. However, the latest position (pointer ct) and the oldest position (pointer ct + 1) of the ring buffer are not temporally continuous. For this reason, it is conceivable that a large difference in values will occur between these two positions (ct and ct + 1) depending on the timing. In such a case, the Fourier spectrum is required to reproduce the existence of this discontinuous part (ct and ct + 1), and this discontinuous part (ct and ct + 1) becomes a step function and thus contains components in a wide band. Therefore, the filtering process in this discontinuous part is considered inappropriate.

[0053] On the other hand, except for the start and end points (discontinuous parts) of the ring buffer, since the signal is originally temporally continuous, it is considered that a similar effect to the filtering process by the general inverse Fourier transform can be obtained at a position that is a certain distance away from the position indicated by the pointer ct. The sample value xct-γ held at a position offset by a predetermined distance γ before the position indicated by the pointer ct can be expressed as shown in Equation 15 using the inverse Fourier transform.

[0054]

Number

[0055] The Fourier coefficients Aj and Bj in Equation 15 are obtained for the latest sample value xct. That is, using the Fourier coefficients Aj and Bj obtained for the latest sample value xct, the sample value xct-γ at a position (offset) a predetermined distance γ before the time when the latest sample value xct was obtained is resynthesized. Note that the subscript ct-γ in Equation 15 indicates a position offset by a predetermined distance γ before the position indicated by the pointer ct, and is the address of the holding part in the ring buffer. Equation 15 is the sum of all frequency components (i.e., from j = 0 to N-1), but if only the necessary frequency components are extracted, it becomes a frequency filter.

[0056] It is also conceivable to perform processing such as subtracting only the components in a certain predetermined frequency band from the original observed value or multiplying by a coefficient to emphasize it. For example, by setting the range of j in Equation 15 to the frequency number fL of the band lower limit to the frequency number fH of the band upper limit, it is conceivable to extract the spectrum of the frequency in the band from the frequency number fL to fH. In this method, since only one sample value needs to be filtered for each update of the spectrum, the maximum number of multiplications required for the filtering process is N times per update. Regarding how far the pointer ct needs to be away from the indicated position so that the influence of the discontinuous part is reduced, it is considered to depend on the nature of the observed waveform, but the value of γ is preferably set to N / 10 to N / 2. When the pointer ct is farthest from the indicated position, the value of γ is half of the number of samples (half of the total number of holding parts), that is, N / 2.

[0057] [Overview of Fourier Transform Device] Next, an example of a Fourier transform device that executes the above-described sequential Fourier transform will be described. As shown in FIG. 3, the Fourier transform device 10 includes a data holding device 11 and an arithmetic display device 12. The data holding device 11 has a sample value holding unit 11A, a Fourier basis holding unit 11B, a Fourier coefficient holding unit 11C, and a filter processing value holding unit 11E. The arithmetic display device 12 has a measurement unit 12A, a sequential Fourier transform unit 12B, a power spectrum calculation unit 12C, a bandpass filter unit 12D, and a display unit 12E.

[0058] The Fourier transform device 10 can be configured by, for example, a single circuit, a composite circuit, a programmed processor, a parallel-programmed processor, or the like. Further, the Fourier transform device 10 may be configured by software, firmware, or the like. The software or firmware is stored in the memory of a computer. The computer means hardware that executes a program, and for example, a CPU, a microprocessor, a microcomputer, or the like is applicable.

[0059] The sample value holding unit 11A is configured, for example, as the above-described ring buffer 30. The sample value holding unit 11A has a plurality of holding units 11D that hold the measurement value X measured by the measurement unit 12A described later as a sample value. The number of the holding units 11D is N. The plurality of sample values held in the sample value holding unit 11A are represented as xi shown in Equation 1.

[0060] The Fourier basis holding unit 11B is configured by, for example, a RAM or the like that is a memory of a computer. The Fourier basis holding unit 11B has a function of holding the calculation results of the basis functions (Fourier bases) Ci,j and Si,j shown in Equation 3 in the sequential Fourier transform unit 12B described later.

[0061] The Fourier coefficient holding unit 11C is constituted by, for example, a RAM which is a memory of a computer. The Fourier coefficient holding unit 11C has a function of holding, as Fourier coefficients Aj and Bj, the calculation result of the mathematical formula shown in Equation 2 based on the value held in the Fourier basis holding unit 11B and the sample value held in the sample value holding unit 11A in the sequential Fourier transform unit 12B described later.

[0062] The filter processing value holding unit 11E is configured separately from the sample value holding unit 11A as, for example, the above-described ring buffer 30. The filter processing value holding unit 11E has a plurality of holding units 11F that hold a value obtained by inverse Fourier-transforming and resynthesizing the sample value xct-γ held in the holding unit 11D at a position γ before the current pointer ct from the holding unit 11D that holds the latest sample value xct specified by the current pointer ct in the band-pass filter unit 12D described later. Here, when ct-γ becomes negative (that is, when crossing the start and end points (discontinuous part) of the ring buffer), ct-γ is replaced with N+(ct-γ), whereby the holding unit 11D at a position γ before the predetermined distance can be appropriately specified. N is the number of holding units 11D in the ring buffer.

[0063] The measurement unit 12A uses, for example, sensors such as an accelerometer, a displacement meter, and a strain gauge that can measure changes in acceleration, displacement, strain, etc. that change over time in the measurement target. The measurement unit 12A is attached to the measurement target and is configured to be able to output a voltage value corresponding to the change amount as a measurement value X.

[0064] The sequential Fourier transform unit 12B is implemented using, for example, a CPU or the like. Each time the sequential Fourier transform unit 12B acquires the measurement value X from the measurement unit 12A, it calculates the basis functions Ci,j and Si,j shown in Equation 3 and stores them in the Fourier basis holding unit 11B. Based on the values stored in the Fourier basis holding unit 11B, the sample values xct stored in the sample value holding unit 11A, and the measurement value X acquired from the measurement unit 12A, the Fourier coefficients Aj and Bj are calculated and stored in the Fourier coefficient holding unit 11C. Thereafter, the measurement value X acquired from the measurement unit 12A is overwritten and stored in a predetermined holding unit 11D of the sample value holding unit 11A.

[0065] The power spectrum calculation unit 12C is implemented using, for example, a CPU or the like. The power spectrum calculation unit 12C calculates and obtains the power spectrum Pj based on the Fourier coefficients Aj and Bj stored in the Fourier coefficient holding unit 11C. Specifically, the power spectrum Pj is obtained by squaring and adding each of the Fourier coefficients Aj and Bj.

[0066] The band-pass filter unit 12D is implemented using, for example, a CPU or the like. The band-pass filter unit 12D performs the inverse Fourier transform shown in Equation 15 based on the Fourier coefficients Aj and Bj stored in the Fourier coefficient holding unit 11C and the values (basis functions Cct-γ,j and Sct-γ,j) stored in the Fourier basis holding unit 11B, and recombines the sample values stored in the holding unit 11D at a position γ away from the position of the holding unit 11D in the sample value holding unit 11A specified by the pointer ct to obtain the value xct-γ, which is then stored in the holding unit 11F of the filter processing value holding unit 11E. Here, the range of j is from the frequency number fL of the band lower limit to the frequency number fH of the band upper limit.

[0067] The display unit 12E is implemented using, for example, a known liquid crystal display or the like. The display unit 12E can display the power spectrum Pj obtained by the power spectrum calculation unit 12C, the value xct-γ recombined by performing the inverse Fourier transform in the band-pass filter unit 12D, and the like.

[0068] [An example of the operation of the Fourier transform device] The Fourier transform device 10 repeatedly executes calculations at predetermined intervals (for example, every sampling interval Δt). First, the measurement unit 12A measures the amount of change in the measurement target. Then, the sequential Fourier transform unit 12B designates the position of the holding unit 11D in the sample value holding unit 11A with a pointer ct. Then, the sequential Fourier transform unit 12B multiplies the difference value between the measured value X of the amount of change measured by the measurement unit 12A this time and the sample value xct already held in the holding unit 11D designated by the pointer ct by the values held in the Fourier basis holding unit 11B (the values of the Fourier bases (basis functions) Cct,j and Sct,j shown in Equation 3) to obtain Fourier coefficients Aj and Bj, and holds these Fourier coefficients Aj and Bj in the Fourier coefficient holding unit 11C.

[0069] Then, the measurement unit 12A overwrites and holds the measured value X measured this time in the holding unit 11D in which the sample value xct was held. When the Fourier transform device 10 performs calculations in the next cycle (after Δt), the sequential Fourier transform unit 12B designates the position of the holding unit 11D in the sample value holding unit 11A with a value obtained by adding 1 to the pointer ct, and multiplies the difference value between the measured value X measured next time (after Δt) and the sample value xct+1 already held in the holding unit 11D designated by the value obtained by adding 1 to the pointer ct by the values held in the Fourier basis holding unit 11B (the values of the Fourier bases Cct+1,j and Sct+1,j) to obtain Fourier coefficients Aj and Bj, and holds them in the holding unit 11D adjacent to the holding unit 11D that holds the measured value X this time. In this way, every time the sequential Fourier transform unit 12B acquires the measured value X from the measurement unit 12A, it obtains the Fourier coefficients Aj and Bj.

[0070] When the measured value X is held in all the holding units 11D of the sample value holding unit 11A, the sequential Fourier transform unit 12B sets the pointer ct to 0, designates the first holding unit 11D, and overwrites and holds the measured value X measured next time (after Δt) in the first holding unit 11D of the sample value holding unit 11A.

[0071] Next, the power spectrum calculation unit 12C squares and adds each of the Fourier coefficients Aj and Bj held in the Fourier coefficient holding unit 11C to obtain a power spectrum Pj.

[0072] Next, the band-pass filter unit 12D performs an inverse Fourier transform on the sample value xct-γ held in the holding unit 11D that is offset by a predetermined distance γ in front of the pointer ct indicating the address of the holding unit 11D that holds the measured value X measured this time, among the Fourier coefficients Aj and Bj held in the Fourier coefficient holding unit 11C and the Fourier basis held in the Fourier basis holding unit 11B, using the Fourier bases Cct-γ,j and Sct-γ,j at a position offset by a predetermined distance γ in front of the holding unit 11D that holds the measured value X measured this time, and recombines them. Then, the recombined sample value xct-γ is held in the filter processing value holding unit 11E. Here, the range of j can be from the frequency number fL of the lower band limit to the frequency number fH of the upper band limit.

[0073] Next, the power spectrum Pj obtained by the power spectrum calculation unit 12C and the sample value xct-γ obtained by performing an inverse Fourier transform in the band-pass filter unit 12D are output to the display unit 12E for display.

[0074] [Example of Implementing a Fourier Transform Device] Software for performing the above-described sequential Fourier transform process was created using Visual Basic on Microsoft Visual Studio 2019. As the measuring instrument for the measuring unit 12A, a dynamic strain measuring instrument DC-204R manufactured by Tokyo Sokki Kenkyujo Co., Ltd. was used. This measuring instrument can be attached to four different parts of the measurement target and measure the strain at the four different attached positions. That is, this measuring instrument has four channels from Ch1 to Ch4 and can be attached to multiple measurement targets. This software can acquire the measured value X via the USB terminal at a specified sampling interval Δt, perform a sequential Fourier transform, and display the waveform, the power spectrum Pj, and the waveform after filter processing (sample value xct-γ) on the display unit 12E in real time.

[0075] The configuration of the program is shown in Fig. 4. Since the sequential Fourier transform needs to be performed for each measurement sampling (every Δt), while the graph drawing is sufficient at time intervals about the refresh rate of the screen of the display unit 12E, it is processed by two asynchronous tasks. Each time the measurement task 20 updates the data, it copies the necessary array, and the drawing task 21 refers to it. In the measurement task 20, the acquisition of the measured value X is executed in the measurement unit 12A, the sequential Fourier transform is executed in the sequential Fourier transform unit 12B, and the inverse sequential Fourier transform is executed in the band-pass filter unit 12D. Here, each time the sequential Fourier transform unit 12B acquires the measured value X based on the measured values X from a plurality of measuring instruments attached to the measurement target, it can obtain the Fourier coefficients corresponding to each measuring instrument.

[0076] In the drawing task 21, the power spectrum calculation is executed in the power spectrum calculation unit 12C, and the graph drawing is executed in the display unit 12E. An example of the display screen that the software displays on the display unit 12E is shown in Fig. 5. The upper side in Fig. 5 is a window of the time history waveform, and the lower side is a window for displaying the power spectrum Pj. The power spectrum Pj is sequentially updated simultaneously with the scrolling display of the time history waveform, and the state in which the power spectrum Pj changes moment by moment according to the change of the waveform can be observed. Also, in this window, the time history waveforms of four channels (Ch1 to Ch4) acquired by the measuring instruments can be arranged side by side in the left-right direction and displayed.

[0077] Also, by specifying the upper limit (fH) and the lower limit (fL) of the passband, the result of the real-time band filter by the sequential filter processing method is displayed in the waveform window. Furthermore, the measurement can be stopped at an arbitrary timing, and the waveform and the power spectrum at that time can be acquired as data. It was confirmed that this program operates for each of the four measurement points (Ch1 to Ch4) with a sample number N of about 2000 to 4000, a sampling interval Δt of 5 ms, and a screen update interval of 10 ms.

[0078] To verify the operating conditions, Table 1 shows the results of measuring the processing time required for one-time processing for each important processing item in the program. With a sampling interval Δt = 5 ms, four measurement points were used for a measurement operation for 60 seconds. Considering all data for all measurement points and the update of the display screen as one update, the average time per update for each process was obtained. The sample numbers N were 2000 and 4000, and for the filter processing, the passband was set to half of the full band.

[0079]

Table 1

[0080] The time required for drawing, such as the calculation of drawing coordinates and power spectrum, is the largest, but it is within the range of 50 Hz to 60 Hz, which is the update interval of a general PC monitor screen. The total time for data acquisition from the measuring instrument, Fourier transform, and inverse Fourier transform is about 1 ms to 2 ms, which can be processed. If the discrete Fourier transform of this program is to be performed by FFT, it is considered difficult to implement with a sampling interval Δt = 5 ms.

[0081] Using this measuring instrument, trial measurements of the vibration acceleration at four points were carried out on the steel plate girder bridge shown in Figures 6, 7, and 8. This steel plate girder bridge is the measurement target Mt. The sampling interval Δt was 5 ms, and the sample number N was 2000. The measured span was a simple steel plate girder with a width of 9.9 m, a span of 35 m, and five main girders for two lanes. Four accelerometers were installed at the mid-span position of the main girder, and the vertical vibration acceleration under the running of general vehicles in service was measured. An example of the observed result of the power spectrum in the measured vibration acceleration is shown in Figure 9. This observed result is data obtained after confirming a state that is considered to be in a free vibration state after the passage of large vehicles.

[0082] As shown in Fig. 9, in the waveforms from each measuring instrument, common peaks of each acceleration appear at 2.7 Hz and 3.8 Hz, and these are considered to indicate the natural frequencies of the first-order bending vibration and the first-order torsional vibration, respectively. Fig. 10 shows the power spectrum calculated from the average Fourier spectrum. The measurement time is about 12 minutes and 5 seconds, the total number of samples is 144,966, and considering the size of the ring buffer (2,000), it is the power spectrum obtained by accumulating waveforms for approximately 72 rounds of the ring buffer. The two peaks seen in this power spectrum are at 2.5 Hz and 3.7 Hz, and they appear at almost the same positions as the peaks shown in Fig. 9.

[0083] Based on these observation results, two bands, from 1.3 Hz to 2.9 Hz and from 2.9 Hz to 4.7 Hz, were set as the bands for real-time filter processing, and sequential filter processing was performed in real time. An example of the waveform of the filter processing in the band from 1.3 Hz to 2.9 Hz is shown in Fig. 11. This is, as before, a waveform obtained by confirming the free vibration state after a large vehicle passes. It can be read that the four measurement points from Ch1 to Ch4 vibrate in the same phase.

[0084] Fig. 12 shows a graph of the values of the four measurement points cut out at the times when the value of Ch1 shows maxima and minima in the waveform of Fig. 11. Although this figure is simple, it is considered to be a cross-sectional view of the first-order vibration mode of the bending vibration described above. Figs. 13 and 14 show the same results as Figs. 11 and 12 in the band from 2.9 Hz to 4.7 Hz. Here, the positions where Ch1 and 2 are installed and the positions where Ch3 and 4 are installed vibrate in opposite directions to each other, and it is considered that the first-order torsional vibration is extracted.

[0085] In this implementation, the result of the band filter in sequential filter processing was only displayed as a time history waveform. However, looking at the results of this trial, as shown in FIGS. 12 and 14, it is considered that a simple vibration mode can be displayed by displaying in real time the relationship between the position of the measurement point and the value after filtering at the measurement point. Specifically, the dominant frequency band common to all measurement points from Ch1 to Ch4 is grasped. Then, sequential filter processing is performed in that frequency band. In this way, the values after filter processing at each measurement point are displayed on the display unit 12E as a vibration mode.

[0086] Regarding the number of calculations at the time of update, the sequential Fourier transform requires fewer calculations compared to the FFT that processes the entire ring buffer, and is considered to be an optimal method when it is desired to monitor and display frequency characteristics in real time. Also, since this calculation method can arbitrarily determine the length of the ring buffer, that is, the number of samples, the desired frequency resolution can be obtained by adjusting the number of samples according to the sampling interval Δt. It can also be applied when it is desired to efficiently calculate the change in the Fourier spectrum or the average Fourier spectrum for long data. Furthermore, by utilizing the fact that the Fourier spectrum is obtained sequentially, it is also possible to sequentially apply a frequency filter to the signal.

[0087] Next, the effects in the above embodiment will be described. The Fourier transform device 10 of the present invention includes a measurement unit 12A that outputs, as a measurement value X, a change amount that changes over time in a measurement target Mt, a sample value holding unit 11A configured by a ring buffer 30 having a plurality of holding units 11D that hold the measurement value X as a sample value, a sequential Fourier transform unit 12B that obtains Fourier coefficients Aj and Bj every time the measurement value X is acquired, a Fourier basis holding unit 11B that holds the calculation results of the Fourier bases Ci,j and Si,j calculated in the sequential Fourier transform unit 12B, a Fourier coefficient holding unit 11C that holds the Fourier coefficients Aj and Bj calculated in the sequential Fourier transform unit 12B, a power spectrum calculation unit 12C that calculates a power spectrum Pj based on the Fourier coefficients Aj and Bj, and a display unit 12E that displays the power spectrum Pj. The sequential Fourier transform unit 12B designates the position of the holding unit 11D in the sample value holding unit 11A by a pointer ct, and every time the measurement value X is acquired from the measurement unit 12A, the Fourier coefficients Aj and Bj are obtained by multiplying the difference value between the sample value xct held in the designated holding unit 11D and the measurement value X by the values of the Fourier bases Cct,j and Sct,j held in the Fourier basis holding unit 11B. According to this configuration, Fourier transform can be efficiently performed without using all the sample values.

[0088] In the Fourier transform device 10 of the present invention, a band-pass filter unit 12D is further provided that performs inverse Fourier transform and resynthesis on a sample value xct-γ at a position a predetermined distance γ away from the holding unit 11D that holds the latest sample value xct in the sample value holding unit 11A designated by the pointer ct, and the display unit 12E displays the resynthesized value xct-γ. In this case, the display unit 12E can display the result of filter processing in a form that suppresses the influence of the discontinuous portion as the time history waveform in the sample value holding unit 11A.

[0089] The measuring unit 12A of the Fourier transform device 10 of the present invention is attached to a plurality of measurement targets Mt, and each time the sequential Fourier transform unit 12B acquires the measurement value X based on the measurement value X from each measuring unit 12A, it obtains Fourier coefficients corresponding to each measuring unit 12A. In this case, based on the dominant situation of the vibration frequency at multiple positions of the measurement target Mt and the difference in the values after the filter processing, the state of the measurement target Mt can be grasped more precisely.

[0090] The present invention is not limited to the embodiment 1 described above and the drawings. For example, the following embodiments are also included in the technical scope of the present invention. (1) Different from the embodiment 1, the measuring unit may be configured to measure vibration, strain accompanying vibration, sound, pressure, etc. as the amount of change. (2) The number of measurement positions in the measuring instrument is not limited to the number in the embodiment 1. (3) The measurement target is not limited to bridges.

Explanation of reference numerals

[0091] 11A... Sample value holding unit 11B... Fourier basis holding unit 11C... Fourier coefficient holding unit 11D... Holding unit 12A... Measuring unit 12B... Sequential Fourier transform unit 12C... Power spectrum calculation unit 12D... Band-pass filter unit 12E... Display unit 30... Ring buffer Aj, Bj... Fourier coefficients Ci,j, Si,j... Fourier bases Mt... Measurement target Pj... Power spectrum xct... Latest sample value X... Measurement value γ... Predetermined distance

Claims

1. A measurement unit that outputs, as a measurement value, a change amount that changes over time in a measurement target; A sample value holding unit configured by a ring buffer having a plurality of holding units that hold the measurement value as a sample value; A sequential Fourier transform unit that obtains Fourier coefficients each time the measurement value is acquired; A Fourier basis holding unit that holds an operation result of a Fourier basis calculated by the sequential Fourier transform unit; A Fourier coefficient holding unit that holds the Fourier coefficients calculated by the sequential Fourier transform unit; A power spectrum calculation unit that calculates a power spectrum based on the Fourier coefficients; A display unit that displays the power spectrum; Comprising: The sequential Fourier transform unit: Specifies the position of the holding unit in the sample value holding unit, and Each time the measurement value is acquired from the measurement unit, multiplies the difference value between the sample value held in the specified holding unit and the measurement value by the value of the Fourier basis held in the Fourier basis holding unit to obtain the Fourier coefficients. A Fourier transform device.

2. Further comprising a band-pass filter unit that performs inverse Fourier transform and recombines the sample values at positions a predetermined distance away from the latest sample value in the sample value holding unit, The display unit displays the recombined value. The Fourier transform device according to claim 1.

3. The measurement unit is attached to the measurement target in plurality, The sequential Fourier transform unit obtains the Fourier coefficients corresponding to each measurement unit each time the measurement value is acquired based on the measurement values from each measurement unit. The Fourier transform device according to claim 1 or claim 2.

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