A frequency domain signal-to-noise ratio-based spectrum splicing method

Abstract

The application discloses a spectrum splicing method based on frequency domain signal-to-noise ratio, which comprises the following steps: designing a plurality of groups of excitation signals for an object to be identified, performing a plurality of experiments and recording corresponding experimental data; calculating weight coefficients for spectrum splicing according to excitation signal sequences and noise response sequences of the plurality of experiments and taking optimal frequency domain signal-to-noise ratio as a criterion; calculating Fourier transforms of the excitation signal sequences and excitation response sequences of the plurality of experiments and a frequency domain numerical model, and splicing the spectra according to the weight coefficients. The application has intuitiveness and easy implementation, provides an intuitive solution for the problem of fusing effective information of a plurality of groups of identification data, and does not need too complex calculation.

Description

Technical Field

[0001] This invention relates to the field of system identification technology, and in particular to a spectrum stitching method based on frequency domain signal-to-noise ratio. Background Technology

[0002] Frequency domain signal-to-noise ratio (SNR) is a key factor affecting the reliability of system identification results. Real-world systems often contain noise. For control systems, noise can be divided into external noise and internal noise. External noise is usually external disturbances, such as friction and cogging forces experienced by a motor at the output. Internal noise typically includes sensor zero drift and quantization noise caused by sampling. The input signal in the identification experiment is also called the excitation signal. The frequency domain SNR is the ratio of the self-power spectral density of the excitation signal to the self-power spectral density of the noise signal. A higher SNR means that the excitation signal is dominant relative to the noise signal, thus making the system identification more reflective of the system's true characteristics. In other words, improving the frequency domain SNR of the signal in the identification experiment enhances the effectiveness of the identification results.

[0003] Currently, commonly used excitation signals include pseudo-random signals, swept-frequency signals, and step signals. The self-power spectral density of pseudo-random signals is relatively uniformly distributed across a wide frequency band, gradually decreasing with increasing frequency; the bandwidth can be adjusted by designing signal parameters. Sweeped-frequency signals have a relatively wide self-power spectral density distribution across a broad frequency band, and their bandwidth distribution can be designed according to requirements. The power spectral density of step signals is mainly distributed in the low-frequency band. Using these excitation signals, common identification methods include Hankel identification based on impulse response, least squares identification, and step response identification. However, these methods often use only one type of excitation signal, and the design of the excitation signal needs to consider the safety of system operation; the signal amplitude cannot be too large. Therefore, it is difficult to guarantee sufficient frequency domain signal-to-noise ratio (SNR) across different frequency bands during the identification process, making it difficult to guarantee the accuracy of model estimation in low SNR frequency bands. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings and deficiencies of the prior art and provide a spectrum stitching method based on frequency domain signal-to-noise ratio. This invention solves the problem of insufficient frequency domain signal-to-noise ratio in some frequency bands caused by the use of a single excitation signal in existing identification methods;

[0005] This invention uses multiple sets of excitation signals with different frequency characteristics to conduct identification experiments, then calculates the numerical frequency characteristics of each set of experiments, and splices the spectrum using the frequency domain signal-to-noise ratio as the optimization criterion. Finally, it obtains a numerical frequency model with a high frequency domain signal-to-noise ratio in different frequency bands, providing effective data for subsequent system identification.

[0006] This invention is achieved through the following technical solution:

[0007] A spectrum stitching method based on frequency domain signal-to-noise ratio includes the following steps:

[0008] S1. Design multiple sets of excitation signals for the object to be identified, conduct multiple sets of experiments and record the corresponding experimental data;

[0009] S2. Calculate the weighting coefficients for spectrum splicing based on the excitation signal sequence and noise response sequence of multiple sets of experiments, using the optimal frequency domain signal-to-noise ratio as the criterion;

[0010] S3. Calculate the Fourier transforms and frequency domain numerical models of multiple sets of experimental excitation signal sequences and excitation response sequences, and splice their spectra according to weighting coefficients.

[0011] Further, in step S1, the sampling frequency determines the upper limit of the observable frequency in the experiment. Then, based on the characteristics of the object to be identified, the desired frequency band is selected, the operating point for identification is chosen, and multiple sets of excitation signals are designed. For example, a pseudo-random signal, whose power spectral density is relatively uniformly distributed over a wide frequency band, gradually decreasing with increasing frequency, is suitable for the mid-to-high frequency characteristics of the object being excited. Alternatively, a swept-frequency signal can be selected, whose power spectral density is distributed over a relatively wide frequency band, and its frequency band distribution can be designed according to requirements. Setting the swept-frequency band of this signal to a low-frequency band is suitable for the low-frequency characteristics of the object being excited. Assuming a total of M sets of excitation signals are designed, M sets of identification experiments are performed accordingly, and data from each set of experiments are obtained. The data from the l-th set of experiments includes the step response steady-state sequence y. sl (i) Noise response sequence y nl (i) Excitation response sequence y ul (i) and the excitation signal sequence u l (i), where represents discrete time intervals, l represents the data from the l-th experimental group, l = 1, 2, ..., M. Noise response sequence y ml (i) is achieved by obtaining the steady-state sequence y of the step response. sl (i) The data is obtained by removing its steady-state mean. For subsequent calculations, y is required to... nl (i), y ul (i) and u l (i) have the same length and are all K.

[0012] Further, in step S2, the data from the l-th experiment are processed, and y is calculated respectively. nl (i) and u l Discrete Fourier Transform of (i) and by For example, the calculation formula is as follows:

[0013]

[0014] Further, calculate y separately. nl (i) and u l The self-power spectral density of (i) is obtained and by For example, the calculation formula is as follows:

[0015]

[0016] The vector consisting of the weight coefficients is W(k) = [W1(k), W2(k), ..., W... M (k)] T W l The formula for calculating (k) is as follows:

[0017]

[0018] Where Φ l (k) is the evaluation function for the l-th experimental data. Since the noise signal is difficult to observe or estimate, the self-power spectral density of the noise response is used instead of the self-power spectral density of the noise. Therefore, the evaluation function is defined as follows:

[0019]

[0020] Furthermore, in step S3, the data from the l-th experiment are processed, and y is calculated respectively. ul Discrete Fourier Transform of (i)

[0021] Furthermore, the numerical frequency model of the object Calculated using the following formula:

[0022]

[0023] Furthermore, after processing and splicing the spectra of the M sets of experimental data, the numerical frequency model of the object is as follows: The discrete Fourier transforms of the excitation response and the excitation signal are respectively and The formula for calculating spectrum splicing is as follows:

[0024]

[0025] Compared with the prior art, the present invention has the following advantages and effects:

[0026] Without injecting excessive energy, compared to using a single excitation signal, the spectrum stitching method of this invention can achieve a higher signal-to-noise ratio in the frequency band of interest, avoiding inaccurate identification results due to insufficient frequency domain signal-to-noise ratio in some frequency bands, effectively avoiding the negative impact of low-power data on the identification results, thereby effectively improving the accuracy of the identification results.

[0027] This invention is intuitive and easy to implement, providing an intuitive solution to the problem of integrating effective information from multiple sets of identification data, without requiring overly complex calculations.

[0028] The spectrum splicing method of this invention is simple and easy to implement, and is more intuitive and computationally less complex than existing technologies. Attached Figure Description

[0029] Figure 1 This is a flowchart illustrating the spectrum splicing method.

[0030] Figure 2 This is a system block diagram for the spectrum splicing and closed-loop identification experiment.

[0031] Figure 3 This is the frequency domain numerical model of the closed-loop system under each set of excitation signals.

[0032] Figure 4 This is the frequency domain numerical model of the closed-loop system after spectrum splicing.

[0033] Figure 5 The module diagram for Simulink open-loop simulation.

[0034] Figure 6 This provides a frequency domain numerical model of the open-loop object under each set of excitation signals.

[0035] Figure 7 This provides the frequency domain numerical model and theoretical open-loop object model for the spliced ​​spectrum. Detailed Implementation

[0036] The present invention will now be described in further detail with reference to specific embodiments.

[0037] Example 1

[0038] like Figure 1 As shown, this invention discloses a spectrum stitching method, which can be implemented through the following steps:

[0039] S1: Design multiple sets of excitation signals for the object to be identified, conduct multiple sets of experiments and record the corresponding experimental data.

[0040] S2: Calculate the weighting coefficients for spectrum splicing based on the excitation signal sequence and noise response sequence of multiple sets of experiments, using the optimal frequency domain signal-to-noise ratio as the criterion;

[0041] S3: Calculate the Fourier transforms and frequency domain numerical models of multiple sets of experimental excitation signal sequences and excitation response sequences, and splice their spectra according to weighting coefficients.

[0042] Please see Figure 2 This example is a spectrum splicing and closed-loop identification experiment performed on a motor servo system.

[0043] Specifically, in step S1, the object to be identified is the current loop of the servo driver and its driven motor-driven system. The motor-driven system consists of a pair of permanent magnet synchronous motors. The control unit is the speed loop controller in the servo, the actuator is the permanent magnet synchronous motor, and the feedback measurement mechanism is a rotary encoder. Together, they form a closed-loop control system. The reference signal of the closed-loop control system is r(i), the excitation signal u(i) is injected from the output of the control unit, and the output signal y(i) is the estimated motor rotation speed. The sampling frequency of the system is set to 2000Hz, and r(i) is a step signal sequence with an amplitude of A = 250rpm, meaning the operating point of this identification experiment is at 250rpm. The continuous model of the servo speed loop controller is C(s), and...

[0044]

[0045] After discretization using the bilinear method, it is implemented on a server. Furthermore, the discrete transfer function of the closed-loop system from u(i) to y(i) is defined as G(e^(i-1)). jω ), C(e jω G0(e) is the discrete transfer function of the controller. jω G(e) is the discrete transfer function of the object to be identified. jω ), G0(e jω ) and C(e jω The relationship is as follows:

[0046]

[0047] Based on the system characteristics and sampling frequency, the main focus is on the 1Hz-1000Hz frequency band. Therefore, multiple sets of excitation signals with different self-power spectral densities need to be designed to ensure that the frequency domain numerical model of the closed-loop system after spectrum splicing has a good signal-to-noise ratio in the focus frequency band. Thus, three sets of logarithmic sweep frequency signal sequences and one set of pseudo-random signal sequences were designed for u(i). The detailed settings of these four sets of signals are as follows:

[0048] 1) Pseudo-random signal sequence: 11 levels, 2047 single-cycle length, and 0.15A amplitude.

[0049] 2) Logarithmic sweep frequency signal sequence 1: The sweep frequency band is 1Hz-150Hz, the single cycle length is 2047, and the amplitude is 0.15A.

[0050] 3) Logarithmic sweep frequency signal sequence 2: The sweep frequency band is 150Hz-300Hz, the single cycle length is 2047, and the amplitude is 0.15A.

[0051] 4) Logarithmic sweep frequency signal sequence 3: The sweep frequency band is 300Hz-450Hz, the single cycle length is 2047, and the amplitude is 0.15A.

[0052] The operating point of the above excitation signals is 250 rpm. In order to reduce the impact of spectrum leakage, the excitation signals need to be maintained for two cycles.

[0053] In order to obtain the steady-state gain and noise response signals of the system, a step response experiment was added to each set of identification experiments. The amplitude of the step signal was 250 rpm, and the length of the step signal was the same as that of the excitation signal.

[0054] After completing four sets of step response experiments and identification experiments and collecting step responses u(i) and y(i), the excitation signal sequence and output signal sequence of the l-th identification experiment are represented as u l (i) and y l (i) Processing the experimental data of the l-th group:

[0055] a) Take the steady-state data of the step response and denote it as y. sl (i);

[0056] b) Calculate y sl The mean of (i) is used as the mean y of the steady-state response of the closed-loop system. mean_l ;

[0057] c) y sl (i) Subtract y mean_l The result obtained is approximately the noise response y. nl (i);

[0058] d) Take y l (i) The data from the second period, minus y mean_l The result obtained is approximately the excitation response y ul (i);

[0059] e) Take u l (i) The data from the second period portion serves as the excitation signal sequence U for identification calculations. l (i)

[0060] In step S2, the data from the l-th experiment are processed, and y is calculated respectively. nl (i) and u l Discrete Fourier Transform of (i) and by For example, the calculation formula is as follows:

[0061]

[0062] Further, calculate y separately. nl (i) and u l The self-power spectral density of (i) is obtained and by For example, the calculation formula is as follows:

[0063]

[0064] The vector consisting of the weight coefficients is W(k) = [W1(k), W2(k), ..., W... M (k)] T W l The formula for calculating (k) is as follows:

[0065]

[0066] Where Φ l (k) is the evaluation function for the l-th experimental data. Since the noise signal is difficult to observe or estimate, the self-power spectral density of the noise response is used instead of the self-power spectral density of the noise. Therefore, the evaluation function is defined as follows:

[0067]

[0068] In step S3, the data from the l-th experiment are processed, and y is calculated respectively. ul Discrete Fourier Transform of (i)

[0069] Furthermore, the numerical frequency model of the object Calculated using the following formula:

[0070]

[0071] Furthermore, after processing and splicing the spectra of the M sets of experimental data, the numerical frequency model of the object is as follows: The discrete Fourier transforms of the excitation response and the excitation signal are respectively and The formula for calculating spectrum splicing is as follows:

[0072]

[0073] When using an excitation signal with a low DC component for identification, the result often lacks a sufficient signal-to-noise ratio at 0 Hz. Therefore, a step signal is needed as the excitation signal to estimate the system gain, i.e., the numerical model of the system at zero Hz. Calculate [y mean_1 y mean_2… y mean_M The mean y mean For the step response experiment, R(e jω Y(e) is the discrete Fourier transform of r(i). jω Let y(i) be the discrete Fourier transform of y(i), and the relationship between the two is as follows:

[0074] Y(e jω )=R(e jω )C(e jω )G(e jω )

[0075] According to the final value theorem of the z-transform:

[0076]

[0077] Will Approximately y mean Therefore, the numerical frequency model of the closed-loop system at 0 Hz can be estimated using the following formula.

[0078]

[0079] Because the DC components of both the frequency sweep signal and the pseudo-random signal are very small, it is necessary to use... Alternative

[0080] and The values ​​at k=0 are calculated using the following substitution method:

[0081]

[0082] Please refer to the frequency domain numerical model of the closed-loop system after spectrum splicing. Figure 4 The system parameters can then be identified based on the frequency domain numerical model of the closed-loop system.

[0083] Example 2

[0084] like Figure 1 As shown, this invention discloses a spectrum stitching method, which can be implemented through the following steps:

[0085] S11: For the object to be identified, design multiple sets of excitation signals, conduct multiple sets of experiments, and record the corresponding experimental data.

[0086] S12: Calculate the weighting coefficients for spectrum splicing based on the excitation signal sequence and noise response sequence of multiple sets of experiments, using the optimal frequency domain signal-to-noise ratio as the criterion;

[0087] S13: Calculate the Fourier transforms and frequency domain numerical models of multiple sets of experimental excitation signal sequences and excitation response sequences, and splice their spectra according to weighting coefficients.

[0088] Please see Figure 5 This example is a simulation of spectrum stitching and open-loop identification performed in Simulink.

[0089] Specifically, in step S11, the object to be identified is G(z), the input signal u(i) is injected from the input terminal of the object, the output signal y(i) is the output terminal signal of the object, the sampling frequency of the system is set to 2000Hz, and G(z) is set as follows in the simulation:

[0090]

[0091] Based on the system characteristics and sampling frequency, the main focus is on the 1Hz-1000Hz frequency band. Therefore, multiple sets of excitation signals with different self-power spectral densities need to be designed to ensure that the frequency domain numerical model of the closed-loop system after spectrum splicing has a good frequency domain signal-to-noise ratio in the focus frequency band. Thus, three sets of logarithmic sweep frequency signal sequences and one set of pseudo-random signal sequences were designed for u(i). The detailed settings of these four sets of signals are as follows:

[0092] 1) Pseudo-random signal sequence: number of levels 11, single period length 2047, amplitude 1

[0093] 2) Logarithmic sweep frequency signal sequence 1: The sweep frequency band is 1Hz-150Hz, the single cycle length is 2047, and the amplitude is 1.

[0094] 3) Logarithmic sweep frequency signal sequence 2: The sweep frequency band is 150Hz-300Hz, the single cycle length is 2047, and the amplitude is 1.

[0095] 4) Logarithmic sweep frequency signal sequence 3: The sweep frequency band is 300Hz-450Hz, the single cycle length is 2047, and the amplitude is 1.

[0096] The operating point of all the above excitation signals is 500. In order to reduce the impact of spectrum leakage, the excitation signal needs to be maintained for two cycles.

[0097] In order to obtain the steady-state gain and noise response signal of the system, a step response experiment is added to each set of identification experiments. The amplitude of the step signal is A = 500, and the length of the step signal is the same as that of the excitation signal.

[0098] After completing four sets of step response experiments and identification experiments and collecting step responses u(i) and y(i), the excitation signal sequence and output signal sequence of the l-th identification experiment are represented as u l (i) and y l (i) Processing the experimental data of the l-th group:

[0099] a) Take the steady-state data of the step response and denote it as y. sl (i);

[0100] b) Calculate y sl The mean of (i) is used as the mean y of the steady-state response of the closed-loop system. mean_l ;

[0101] c) y sl (i) Subtract y mean_l The result obtained is approximately the noise response y. nl (i);

[0102] d) Take y l (i) The data from the second period, minus y mean_l The result obtained is approximately the excitation response y ul (i);

[0103] e) Take u l (i) The data from the second period portion serves as the excitation signal sequence U for identification calculations. l (i)

[0104] In step S12, the data from the l-th experiment are processed, and y is calculated respectively. nl (i) and u l Discrete (i)

[0105] The calculation formula is:

[0106]

[0107] Further, calculate y separately. nl (i) and u l The self-power spectral density of (i) is obtained and by For example, the calculation formula is as follows:

[0108]

[0109] The vector consisting of the weight coefficients is W(k) = [W1(k), W2(k), ..., W... M (k)] T W l The formula for calculating (k) is as follows:

[0110]

[0111] Where Φ l(k) is the evaluation function for the l-th experimental data. Since the noise signal is difficult to observe or estimate, the self-power spectral density of the noise response is used instead of the self-power spectral density of the noise. Therefore, the evaluation function is defined as follows:

[0112]

[0113] In step S13, the data from the l-th experiment are processed, and y is calculated respectively. ul Discrete Fourier Transform of (i)

[0114] Furthermore, the numerical frequency model of the object Calculated using the following formula:

[0115]

[0116] Furthermore, after processing and splicing the spectra of the M sets of experimental data, the numerical frequency model of the object is as follows: The discrete Fourier transforms of the excitation response and the excitation signal are respectively and The formula for calculating spectrum splicing is as follows:

[0117]

[0118]

[0119]

[0120] When using an excitation signal with a low DC component for identification, the result often lacks a sufficient signal-to-noise ratio at 0 Hz. Therefore, a step signal is needed as the excitation signal to estimate the system gain, i.e., the numerical model of the system at zero Hz. Calculate [y mean_1 y mean_2 … y mean_M The mean y mean For the step response experiment, u(i) is a step signal with amplitude A, U(e) jω Y(e) is the discrete Fourier transform of u(i), and Y(e) is the discrete Fourier transform of u(i). jω Let y(i) be the discrete Fourier transform of y(i), and the relationship between the two is as follows:

[0121] Y(e jω )=U(e jω )G(e jω )

[0122] According to the final value theorem of the z-transform:

[0123]

[0124] Will Approximately y mean Therefore, the numerical frequency model of the closed-loop system at 0 Hz can be estimated using the following formula.

[0125]

[0126] Because the DC components of both the frequency sweep signal and the pseudo-random signal are very small, it is necessary to use... Alternative and The values ​​at k=0 are calculated using the following substitution method:

[0127]

[0128] Please refer to the frequency domain numerical model of the open-loop object after spectrum splicing and the theoretical open-loop object model. Figure 7 The system parameters can then be identified based on the frequency domain numerical model of the open-loop object.

[0129] As described above, without injecting too much energy, compared with using a single excitation signal, the spectrum splicing method of this invention can achieve a higher signal-to-noise ratio in the frequency band of interest, avoiding inaccurate identification results due to insufficient frequency domain signal-to-noise ratio in some frequency bands, effectively avoiding the negative impact of low-power data on the identification results, thereby effectively improving the accuracy of the identification results.

[0130] This invention is intuitive and easy to implement, providing an intuitive solution to the problem of integrating effective information from multiple sets of identification data, without requiring overly complex calculations.

[0131] The implementation of the present invention is not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A frequency domain signal-to-noise ratio based spectrum stitching method, characterized in that, The method comprises the following steps: S1: design multiple sets of excitation signals for the object to be identified, conduct multiple sets of experiments and record the corresponding experimental data; if M sets of excitation signals are designed, then M sets of identification experiments are correspondingly conducted to obtain the data of each set of experiments, wherein the data of the lth set of experiments includes a sequence of step response steady-state segments y sl (i), a sequence of noise response segments y nl (i), a sequence of excitation response segments y ul (i), and a sequence of excitation signals u l (i); Wherein i represents discrete time; L represents the data of the lth group of experiments; l＝1,2,…,M； the noise response sequence y nl (i) is obtained by taking the step response steady state segment sequence y sl (i) data removing its steady state mean; for subsequent calculations, it is required that y nl (i), y ul (i) and u l (i) are of the same length and are both K; S2: According to the excitation signal sequence and the noise response sequence of multiple groups of experiments, the weight coefficients for spectral splicing are calculated according to the optimal frequency domain signal-to-noise ratio as the criterion; S3: The Fourier transform of the excitation signal sequence and the excitation response sequence of multiple groups of experiments and the frequency domain numerical model are calculated, and the spectral splicing is performed according to the weight coefficients; In step S2, the data of the 1th experiment is processed to calculate y nl (i) and u l the discrete Fourier transform of (i) and The calculation formula is: The autocorrelation function y nl (i) and the autocorrelation function u l (i) are calculated as follows: and The calculation formula is as follows: The vector of weight coefficients is W(k) = [W(k)1, W(k)2,..., W(k)N]T M ] T , W(k) l The calculation formula of W(k) is as follows: where Φ(k) l is the evaluation function for the 1st set of experimental data, using the auto-power spectral density of the noise response in place of the auto-power spectral density of the noise, and the evaluation function is defined as: In step S3, the data of the 1st set of experiments is processed and y ul Discrete Fourier transform of (i) Numerical frequency model of an object is calculated by the formula: After the data processing of M group experiment and spectrum splicing, the numerical frequency model of the object is The discrete Fourier transform of the excitation response and the excitation signal are respectively and The spectrum splicing calculation formula is as follows:

2. The frequency domain signal-to-noise ratio based spectral splicing method of claim 1, wherein, In step S1, the sampling frequency determines the upper limit of the frequency that can be observed in the experiment, and then the frequency band that needs to be concerned is selected according to the characteristics of the object to be identified, the working point of identification is selected, and multiple excitation signals are designed.

3. The frequency domain signal-to-noise ratio based spectral splicing method of claim 2, wherein, In the process of designing multiple excitation signals, the pseudo-random signal has a relatively uniform distribution of self-power spectral density on a wide frequency band, and the power spectral density gradually decreases with the increase of frequency. This signal is suitable for exciting the medium and high frequency characteristics of the object; and the sweep signal is selected, the self-power spectral density of which is distributed on a wide frequency band, and the frequency band distribution is designed according to the demand. The sweep frequency band of the signal is set to the low frequency band, which is suitable for exciting the low frequency characteristics of the object.

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