Signal analysis device, signal analysis method, and signal analysis program

Abstract

A signal analysis device (100) comprises: a complex extension unit (20) that generates a complex time-series signal (22) by frequency analysis that extends a measurement signal (14) obtained by a sensor into the complex domain; and a complex inharmonic analysis unit (24) that calculates the amplitude of a complex sinusoidal model signal, which is an ideal waveform, on the basis of correlation between the complex time-series signal and the complex sinusoidal model signal in which the frequency of the complex sinusoidal model signal and the initial phase of the complex sinusoidal model signal are substituted, each of the frequency and the initial phase being calculated using a linear equation optimization problem that minimizes the average of the square of the difference between the phase of the complex time-series signal and the phase of the complex sinusoidal model signal.

Description

Signal analysis device, signal analysis method, and signal analysis program

[0001] This disclosure relates to a signal analysis device, a signal analysis method, and a signal analysis program.

[0002] In recent years, signal analysis has been performed to diagnose abnormalities in equipment and other devices based on waveforms obtained by analyzing signals measured by vibration sensors and the like.

[0003] Patent Document 1 discloses an invention for a signal analysis method that performs frequency analysis of an input asynchronous signal.

[0004] The invention described in Patent Document 1 is characterized by converging to the optimal solution of a nonlinear equation for each of the parameters of the sinusoidal model signal, namely frequency f', phase φ', and amplitude A', such that the sum of the squares of the differences between the signal under analysis and the sinusoidal model signal representing the ideal waveform is minimized.

[0005] Patent No. 5590547

[0006] However, the technology described in Patent Document 1 has the problem that, in order to find the optimal solution to the nonlinear equation, it is necessary to provide appropriate initial values ​​in advance, the solution is always an approximate solution, and furthermore, it requires iterative calculations, which increases the computational cost.

[0007] This disclosure aims to provide a signal analysis device, a signal analysis method, and a signal analysis program that do not require the input of initial values ​​and can reduce computational costs.

[0008] The signal analysis device of this disclosure is characterized by comprising: a complex extension unit that generates a complex time series signal by frequency analysis that extends a measurement signal obtained by a sensor into the complex domain; and a complex anharmonic analysis unit that calculates the amplitude of the complex sine wave model signal by the correlation between the complex time series signal and the complex time series signal, with the frequency of the complex sine wave model signal and the initial phase of the complex sine wave model signal respectively calculated by a linear equation optimization problem that minimizes the mean of the square of the difference between the phase of the complex time series signal and the phase of a complex sine wave model signal which is an ideal waveform, and the complex time series signal.

[0009] The signal analysis method of this disclosure is a signal analysis method performed by a computer, comprising the steps of: generating a complex time series signal by frequency analysis that extends a measurement signal obtained by a sensor to the complex domain; and calculating the amplitude of the complex sine wave model signal by the correlation between the complex time series signal and the complex time series signal, with the frequency of the complex sine wave model signal and the initial phase of the complex sine wave model signal respectively calculated by a linear equation optimization problem that minimizes the mean of the square of the difference between the phase of the complex time series signal and the phase of a complex sine wave model signal which is an ideal waveform, and the initial phase of the complex sine wave model signal.

[0010] The signal analysis program of this disclosure causes a computer to perform the following steps: generate a complex time series signal by frequency analysis that extends a measurement signal obtained by a sensor into the complex domain; and calculate the amplitude of the complex sine wave model signal by the correlation between the complex time series signal and the complex time series signal, with the frequency of the complex sine wave model signal and the initial phase of the complex sine wave model signal, respectively, calculated by a linear equation optimization problem that minimizes the mean of the squared difference between the phase of the complex time series signal and the phase of the complex sine wave model signal, which is an ideal waveform.

[0011] According to this disclosure, it is possible to provide a signal analysis device, a signal analysis method, and a signal analysis program that do not require input of initial values ​​and can reduce computational costs by calculating the optimal solution to a linear equation.

[0012] This is a block diagram schematically showing the configuration and processing flow of the signal analysis device according to this embodiment. This is a block diagram schematically showing the hardware configuration of the signal analysis device in this embodiment. This is a flowchart showing an example of the processing of the signal analysis device according to this embodiment. (A) is a schematic diagram showing an example of the analysis result of a human pulse wave by FFT, and (B) is a schematic diagram showing an example of the result of analyzing a human pulse wave using the signal analysis method according to this embodiment.

[0013] The following describes a signal analysis device, signal analysis method, and signal analysis program according to an embodiment, with reference to the drawings. The following embodiment is merely an example, and the embodiment can be modified as appropriate.

[0014] Figure 1 is a block diagram schematically showing the configuration and processing flow of the signal analysis device 100 according to this embodiment. The signal analysis device 100 includes a data measurement unit 12 that measures data using a sensor and passes the measured signal to a downsampling unit 16, a downsampling unit 16 that downsamples the measured signal with respect to the analysis target frequency within a range that satisfies the Nyquist theorem, a complex extension unit 20 that extends the signal into the complex domain, and a complex anharmonic analysis unit 24 that extracts a frequency spectrum 26 and a phase spectrum 28 from the signal extended into the complex domain.

[0015] The following describes the processing flow in the signal analysis device 100. The data measurement unit 12 measures time-series signals 10 such as vibrations of the object to be measured using a sensor, or acquires time-series signals 10 that have been measured in advance and stored in storage or the like. The data measurement unit 12 passes the measured or acquired time-series signals as measurement signals 14 to the subsequent downsampling unit 16.

[0016] The downsampling unit 16 downsamples the measurement signal 14 with respect to the analysis target frequency within a range that satisfies the Nyquist theorem, where the sampling frequency is twice the maximum value of the analysis target frequency. In this embodiment, the Nyquist theorem is an absolute requirement, and in order to perform a better analysis, the sampling frequency is set to three times or more the analysis target frequency. In this embodiment, downsampling by the downsampling unit 16 can significantly reduce the computational cost of subsequent processes. However, the downsampling process by the downsampling unit 16 is not essential, so this process does not have to be performed. Through downsampling, the measurement signal 14 becomes a real time-series signal (s(n)) 18.

[0017] The complex extension unit 20 reconstructs the imaginary component of the real time series signal 18 into a waveform using known complex extension methods through frequency analysis, thereby extending the signal into the complex domain. Suitable complex extension methods in frequency analysis include, for example, applying a Hilbert transform, or applying a complex wavelet transform followed by an inverse complex wavelet transform. As a result of the frequency analysis by the complex extension unit 20, the real time series signal 18 is extended into the complex domain as shown in equation (1) below, becoming a complex time series signal (c(n)) 22. A in equation (1) ｎ θ represents the amplitude of the complex time series signal 22, ｎ This indicates the phase of the complex time series signal 22.

[0018] Furthermore, the complex extension unit 20 obtains the amplitude and phase of the complex time-series signal 22, which is the complex-extended signal. The provisional values ​​of the amplitude and phase of the complex-extended signal can be obtained by taking the mean square root of the sum of squares of the complex-extended signal for the amplitude, and by taking the arctangent of the complex-extended signal for the phase. In this embodiment, an unwrapping process is performed to restore the continuous original phase value by adding an appropriate multiple of 2π to the obtained phase.

[0019] The complex anharmonic analysis unit 24 performs a fitting of equation (1), which represents the generated complex time series signal 22, to equation (2), which represents the complex sinusoidal wave model signal, which is the ideal waveform. In equation (2), A' represents the amplitude of the complex sinusoidal wave model signal, and x ｎ φ' represents the signal to be analyzed, f' represents the frequency of the complex sinusoidal model signal, and φ' represents the initial phase of the complex sinusoidal model signal.

[0020] The complex anharmonic analysis unit 24 calculates the frequency f' and initial phase φ' from the amplitude A', frequency f', and initial phase φ' in the fitting using equations (1) and (2) by the linear equation optimization problem of equation (3) below. Equation (3) below is the phase θ of the complex time series signal 22. ｎ And the phase of the complex sinusoidal wave model signal is 2πf'x ｎIt is configured to calculate the average of the squares of the differences with +φ'. In equation (3) below, N is the number of samples. Unlike when finding the optimal solution to the nonlinear equation, an initial value is not required when calculating the minimum value of equation (3) below. Also, when the right-hand side of equation (3) below is minimized, the frequency f' becomes an approximation of the frequency of the complex time series signal 22 shown in equation (1), and the initial phase φ' becomes an approximation of the initial phase of the complex time series signal 22. For example, when the right-hand side of equation (3) below is close to 0, the frequency f' approximates the frequency of the complex time series signal 22, and the initial phase φ' approximates the initial phase of the complex time series signal 22 with good accuracy. Conventionally, the frequency f' and initial phase φ' were calculated by finding the optimal solution to the nonlinear equation, but the obtained frequency f' and initial phase φ' are approximations. The accuracy of the frequency and initial phase values ​​of the complex time series signal 22, which are further approximations of such an approximate solution, will be even lower than the frequency and initial phase of the complex time series signal 22 calculated by the linear equation optimization problem according to this embodiment.

[0021] The complex anharmonic analysis unit 24 correlates the complex sinusoidal wave model signal of equation (2), where the amplitude is 1 (A'=1) at the frequency f' and initial phase φ' that minimize the right-hand side of equation (3), with equation (1) to calculate the amplitude A'. Specifically, for example, the amplitude is calculated by performing a Fourier transform on the difference between equation (2) and equation (1) after substituting the frequency f', initial phase φ', and amplitude A'=1 that minimize the right-hand side of equation (3), respectively. Each of the complex time series signal 22 and the complex sinusoidal wave model signal can be separated into a real part and an imaginary part according to Euler's formula, as shown in equations (4) and (5) below. Therefore, calculating the difference between equation (2) and equation (1) means calculating the difference between the real parts and the difference between the imaginary parts of the complex time series signal 22 and the complex sinusoidal wave model signal. Furthermore, the Fourier transform of the difference between equation (2) and equation (1), where amplitude A' = 1, gives the amplitude A for amplitude A' (= 1). ｎ(≠1) is extracted as the amplitude A' to be found in the complex time series signal 22. Alternatively, when calculating the amplitude A', the problem of minimizing the difference between equation (2), obtained by substituting the frequency f' and initial phase φ' that minimize the right-hand side of equation (3) above, and equation (1) may be solved by nonlinear equation optimization.

[0022]

[0023]

[0024] The complex anharmonic analysis unit 24 outputs the frequency f' and initial phase φ' as a phase spectrum 28 and the amplitude A' and frequency f' as a frequency spectrum 26 by fitting using equations (1) and (2). As described above, the frequency f' and initial phase φ' are approximate values ​​of the frequency and initial phase in the complex time series signal 22 shown in equation (1), and the amplitude A' is the amplitude to be determined in the complex time series signal 22. Therefore, the frequency spectrum 26 is the frequency spectrum 26 relating to the complex time series signal 22 and the measurement signal, and the phase spectrum 28 is the phase spectrum 28 relating to the complex time series signal 22 and the measurement signal.

[0025] The signal analysis device 100 can be implemented by a computer such as the PC (Personal Computer) 110 shown in Figure 2. The PC 110 may consist of multiple computers connected via a network, or it may consist of a processing circuit as dedicated hardware such as a single circuit or a composite circuit.

[0026] The PC110 includes a storage device 30 such as an HDD (Hard Disk Drive) or SSD (Solid State Drive), a memory 32, a processor 34 such as a CPU (Central Processing Unit), a sensor 36 for detecting vibrations of an object to be measured, a connection interface 38 to which input / output devices such as a keyboard, mouse, and display are connected, and a communication interface 40 such as a NIC (Network Interface Card). The storage device 30, memory 32, processor 34, sensor 36, connection interface 38, and communication interface 40 are each connected to a bus 42.

[0027] The data measurement unit 12, downsampling unit 16, complex extension unit 20, and complex anharmonic analysis unit 24 can be realized by loading a signal analysis program stored in storage 30 into memory 32, and having the processor 34 execute the signal analysis program. As a result, a signal analysis method is realized that includes the steps of measuring data using a sensor and passing the measurement signal to the downsampling unit, downsampling the measurement signal with respect to the analysis target frequency within a range that satisfies the Nyquist theorem, extending the signal into the complex domain, and extracting a frequency spectrum 26 and a phase spectrum 28 from the signal extended into the elementary domain.

[0028] The above signal analysis program may be input to storage 30 from a recording medium (not shown) via a reader / writer (not shown), or downloaded to storage 30 via a network through a communication interface 40, and then loaded onto memory 32 and executed by processor 34. Alternatively, it may be loaded directly onto memory 32 from a recording medium (not shown) via a reader / writer, or from a network via a communication interface 40, and then executed by processor 34. In other words, the signal analysis program may be provided as a program product such as a recording medium.

[0029] Figure 3 is a flowchart showing an example of the processing of the signal analysis device 100 according to this embodiment. In step S1, the data measurement unit 12 measures data using the sensor 36 and passes the measurement signal to the downsampling unit 16.

[0030] In step S2, the downsampling unit 16 performs downsampling of the measurement signal with respect to the analysis target frequency within a range that satisfies the Nyquist theorem. The downsampling unit 16 considers the Nyquist theorem an absolute requirement and sets the sampling frequency to a frequency at least three times the analysis target frequency in order to perform a better analysis.

[0031] In step S3, the complex extension unit 20 acquires a real-valued time-series signal 18, which is the signal after downsampling.

[0032] In step S4, the complex extension unit 20 performs a complex extension that extends the real-time series signal 18 into the complex domain.

[0033] In step S5, the complex non-harmonic analysis unit 24 acquires the complex time series signal 22, which is the complex signal obtained by the complex extension.

[0034] In step S6, the complex non-harmonic analysis unit 24 calculates the frequency f´, the initial phase φ´, and the amplitude A´ by performing a complex non-harmonic analysis in which the complex time series signal 22 shown in formula (1) is fitted with the complex sine wave model signal shown in formula (2), which is an ideal waveform.

[0035] In step S7, the complex non-harmonic analysis unit 24 obtains the amplitude A´ and the frequency f´ as the frequency spectrum 26.

[0036] In step S8, the complex non-harmonic analysis unit 24 obtains the frequency f´ and the initial phase φ´ as the phase spectrum 28.

[0037] In step S9, the complex non-harmonic analysis unit 24 determines whether to obtain the next frequency spectrum 26 and phase spectrum 28. If the complex non-harmonic analysis unit 24 is to obtain the next frequency spectrum 26 and phase spectrum 28, the procedure proceeds to step S10. If not, the process ends.

[0038] In step S10, in order for the complex non-harmonic analysis unit 24 to remove the signal that has undergone complex non-harmonic analysis from the complex time series signal 22 before complex non-harmonic analysis, the difference between the complex time series signal 22 and the complex sine wave model signal is taken to calculate the residual complex signal. Since each of the complex time series signal 22 and the complex sine wave model signal can be separated into a real part and an imaginary part as in formulas (4) and (5) above, calculating the difference between the complex time series signal 22 and the complex sine wave model signal means calculating the difference between the real parts and the difference between the imaginary parts in the complex time series signal 22 and the complex sine wave model signal.

[0039] The complex non-harmonic analysis unit 24 calculates the difference between the complex time-series signal 22 and the complex sine wave model signal in step S10, then proceeds to step S5, and executes the procedures of steps S5 to S9 to calculate the next frequency spectrum 26 and phase spectrum 28. The complex non-harmonic analysis unit 24 holds the difference between the complex time-series signal 22 calculated in step S10 and the complex sine wave model signal in the memory 32 or the storage 30. In the subsequent procedures of steps S5 to S9, the complex non-harmonic analysis unit 24 performs fitting using the difference and the complex sine wave model signal to calculate the next frequency spectrum 26 and phase spectrum 28.

[0040] After calculating the next frequency spectrum 26 and phase spectrum 28, when further calculating the next frequency spectrum 26 and phase spectrum 28, in step S10, the complex non-harmonic analysis unit 24 calculates the difference between the difference held in the memory 32 or the storage 30 and the complex sine wave model signal, and holds the newly calculated difference in the memory 32 or the storage 30 instead of the difference that has been held in the memory 32 or the storage 30. Then, in the subsequent procedures of steps S5 to S9, fitting is performed using the difference and the complex sine wave model signal to calculate the further next frequency spectrum 26 and phase spectrum 28.

[0041] FIG. 4(A) is a schematic diagram showing an example of the analysis result by FFT (Fast Fourier Transform) of the pulse wave of the human body detected by a pulse wave sensor or the like, and FIG. 4(B) is a schematic diagram showing an example of the result of analyzing the pulse wave of the human body detected by a pulse wave sensor or the like by the signal analysis method according to the present embodiment. The pulse wave sensor is a sensor that detects the volume change of blood vessels as a waveform.

[0042] As shown in FIG. 4(A), in the pulse wave analysis by FFT, although the boundary 50 between the vibration LF due to respiration and the vibration HF due to the pulse among the components of the pulse fluctuation can be identified, the frequency components other than the frequencies to be detected converge, and there is a difficulty in frequency resolution.

[0043] Increasing the frequency resolution of FFT requires measures such as increasing the sampling frequency, but this increases the computational cost. This increased computational cost is particularly serious in small devices such as wearable devices, leading to problems such as significant battery consumption.

[0044] As shown in Figure 4(B), the analysis results obtained by the signal analysis method according to this embodiment clearly identify the boundary 52 with the vibration HF due to the pulse, and because the frequency resolution is high, the frequency to be detected can be extracted with high accuracy. Furthermore, this embodiment reduces computational costs and suppresses battery consumption of wearable devices, etc., because it performs data downsampling within the range that satisfies the Nyquist theorem and calculates the frequency spectrum 26 and phase spectrum 28 using a linear equation optimization problem.

[0045] The signal analysis device, signal analysis method, and signal analysis program according to this embodiment can, in addition to pulse wave analysis as described above, measure the vibrations of rotating machinery such as electric motors and internal combustion engines using vibration sensors, and analyze the signals obtained from the measurements to detect abnormalities in the rotating machinery. Specifically, as an example, by analyzing the signals obtained from measuring the vibrations of a vehicle using vibration sensors, etc., using the signal analysis device, signal analysis method, and signal analysis program according to this embodiment, abnormalities in the vehicle can be detected quickly. Furthermore, by analyzing the vibrations of manufacturing equipment such as machine tools in factories, the operating status of the manufacturing equipment can be determined. The signal analysis device, signal analysis method, and signal analysis program according to this embodiment can reduce computational costs while performing analysis with higher resolution than FFT by downsampling the data to match the frequency band being analyzed, thereby achieving high accuracy in abnormality diagnosis.

[0046] The signal analysis device, signal analysis method, and signal analysis program according to this embodiment can be applied not only to the analysis of vibrations of devices but also to the detection of fine features in images. For example, as the state of a railway turnout, even if it is difficult to instantaneously determine with the naked eye whether it is in a state where it has completely switched in the direction in which the train is moving or in a state where the switching is incomplete due to some trouble, the signal analysis device, signal analysis method, and signal analysis program according to this embodiment can detect fine differences in image data and, for example, determine the state of the turnout.

[0047] As described above, in this embodiment, by complex-expanding the signal to be analyzed, the problem that has conventionally been treated as a non-linear equation optimization problem is replaced with a linear equation optimization problem, and by performing the calculation of the linear least squares method, an accurate solution can be obtained without an initial value.

[0048] Further, according to this embodiment, the linear equation optimization problem can suppress the calculation cost in iterative calculations compared to the non-linear equation optimization problem, and by performing downsampling of data within the range that satisfies the Nyquist theorem, the calculation cost can be further suppressed.

[0049] When analyzing data of the same data length, in FFT, it is necessary to increase the sampling frequency in order to increase the frequency resolution. However, according to this embodiment, a high frequency resolution can be achieved with a sampling frequency that satisfies the Nyquist theorem. As a result, according to this embodiment, when analyzing data of the same sampling frequency, it is possible to achieve a high frequency resolution in a shorter time length for the problem that it is necessary to increase the data length in FFT in order to increase the frequency resolution.

[0050] This embodiment has been described for the one-dimensional case where the signal to be analyzed is x ｎ However, it is not limited to this. For example, like the complex model signal representing the ideal waveform expressed by the following formula (6) and the complex measurement signal obtained by expanding the measured signal into the complex domain expressed by the following formula (7), it can correspond to the two-dimensional case where x ｎ and y ｍ are the signals to be analyzed.

[0051]

[0052]

[0053] When the signal to be analyzed is two-dimensional, the frequency f ｘ ',f ｙ The initial phase φ and the initial phase ' are calculated using the linear equation optimization problem shown in equation (8) below.

[0054]

[0055] Then, the frequency f calculated using the linear equation optimization problem in equation (8) above ｘ ',f ｙ The amplitude spectrum is calculated by performing a Fourier transform on the difference between equation (6) and equation (7) obtained by substituting ' and the initial phase φ'.

[0056] As described above, the signal analysis device, signal analysis method, and signal analysis program according to this embodiment can handle cases where the signal to be analyzed is two-dimensional. Furthermore, the signal analysis device, signal analysis method, and signal analysis program according to this embodiment can also handle signals to be analyzed that are extended from two dimensions to n dimensions (where n is any natural number).

[0057] 10 Time series signal, 12 Data measurement unit, 14 Measurement signal, 16 Downsampling unit, 18 Real number time series signal, 20 Complex extension unit, 22 Complex time series signal, 24 Complex anharmonic analysis unit, 26 Frequency spectrum, 28 Phase spectrum, 30 Storage, 32 Memory, 34 Processor, 36 Sensor, 38 Connection I / F, 40 Communication I / F, 42 Bus, 50, 52 Boundary, 100 Signal analysis device, 110 PC.

Claims

1. A signal analysis device comprising: a complex extension unit that generates a complex time series signal by frequency analysis that extends a measurement signal obtained by a sensor into the complex domain; and a complex anharmonic analysis unit that calculates the amplitude of the complex sine wave model signal by the correlation between the complex time series signal and the complex time series signal, with the frequency of the complex sine wave model signal and the initial phase of the complex sine wave model signal, respectively, calculated by a linear equation optimization problem that minimizes the mean of the squared difference between the phase of the complex time series signal and the phase of a complex sine wave model signal which is an ideal waveform, and the complex time series signal.

2. The signal analysis device according to claim 1, wherein the complex anharmonic analysis unit calculates the amplitude of the complex sinusoidal wave model signal by performing a Fourier transform of the difference between the complex sinusoidal wave model signal and the complex time series signal, with the frequency of the complex sinusoidal wave model signal and the initial phase of the complex sinusoidal wave model signal substituted as the correlation.

3. The signal analysis device according to claim 1 or 2, further comprising a downsampling unit that outputs a real time series signal obtained by downsampling the measurement signal within a range that satisfies the Nyquist theorem to the complex extension unit, wherein the complex extension unit generates the complex time series signal by frequency analysis of the real time series signal.

4. The signal analysis device according to claim 3, wherein the complex anharmonic analysis unit outputs the frequency and the initial phase as a phase spectrum relating to the measurement signal, and the amplitude and the frequency as a frequency spectrum relating to the measurement signal.

5. A signal analysis method performed by a computer, comprising: a step of generating a complex time series signal by frequency analysis that extends a measurement signal obtained by a sensor into the complex domain; and a step of calculating the amplitude of the complex sine wave model signal by the correlation between the complex time series signal and the complex time series signal, with the frequency of the complex sine wave model signal and the initial phase of the complex sine wave model signal respectively calculated by a linear equation optimization problem that minimizes the mean of the squared difference between the phase of the complex time series signal and the phase of a complex sine wave model signal which is an ideal waveform, and the initial phase of the complex sine wave model signal.

6. A signal analysis program that causes a computer to perform the following steps: generate a complex time series signal by frequency analysis that extends a measurement signal obtained by a sensor into the complex domain; and calculate the amplitude of the complex sine wave model signal by the correlation between the complex time series signal and the complex time series signal, with the frequency of the complex sine wave model signal and the initial phase of the complex sine wave model signal respectively calculated by a linear equation optimization problem that minimizes the mean of the squared difference between the phase of the complex time series signal and the phase of the ideal waveform, a complex sine wave model signal.

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