Frequency spectrum splicing method based on frequency domain signal-to-noise ratio

Abstract

The invention discloses a frequency spectrum splicing method based on a frequency domain signal-to-noise ratio, and the method comprises the steps: designing a plurality of groups of excitation signals for an object needing to be identified, carrying out a plurality of groups of experiments, and recording corresponding experimental data; according to the excitation signal sequences and the noise response sequences of the multiple groups of experiments, calculating a weight coefficient for spectrum splicing by taking an optimal frequency domain signal-to-noise ratio as a criterion; fourier transform and frequency domain numerical models of the multiple groups of experiment excitation signal sequences and excitation response sequences are calculated, and frequency spectrums are spliced according to weight coefficients. The method is intuitive and easy to implement, an intuitive solution is provided for fusing effective information of multiple groups of identification data, and meanwhile too complex calculation is not needed.

Description

Technical Field

[0001] The present invention relates to the technical field of system identification, and in particular to a spectrum splicing method based on the signal-to-noise ratio in the frequency domain. Background Art

[0002] The signal-to-noise ratio in the frequency domain is a key factor affecting the credibility of system identification results. In real systems, there is often noise. For control systems, noise can be divided into external noise and internal noise. External noise is usually external disturbances, such as the disturbances of friction and cogging force on the output end of the motor; internal noise usually includes zero drift of sensors, quantization noise caused by sampling, etc. The input signal in the identification experiment is also called the excitation signal. The signal-to-noise ratio in the frequency domain is the ratio of the auto-power spectral density of the excitation signal to the auto-power spectral density of the noise signal. The larger the signal-to-noise ratio, it means that the excitation signal dominates relative to the noise signal, so that the system identification can better reflect the true characteristics of the system. That is to say, improving the signal-to-noise ratio in the frequency domain of the signal in the identification experiment can enhance the effectiveness of the identification results.

[0003] Currently, commonly used excitation signals include pseudo-random signals, swept-frequency signals, step signals, etc. The auto-power spectral density of pseudo-random signals is relatively evenly distributed over a wide frequency band. As the frequency increases, the power spectral density gradually decreases, and the frequency band width can be adjusted by designing signal parameters; the auto-power spectral density of swept-frequency signals is distributed over a relatively wide frequency band, and its frequency band distribution can be designed according to requirements; the power spectral density of step signals is mainly distributed in the low-frequency band. Using the above excitation signals, currently common identification methods include Hankel identification based on impulse response, least squares identification, step response identification, etc. However, the above identification methods often only use a certain kind of excitation signal, and the design of the excitation signal needs to consider the safety problem of system operation, and the amplitude of the signal cannot be too large. Therefore, it is difficult to ensure that there is sufficient signal-to-noise ratio in the frequency domain in different frequency bands during the identification process, making it difficult to guarantee the accuracy of model estimation in the frequency bands with low signal-to-noise ratio. Summary of the Invention

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

[0005] The present invention conducts identification experiments by using multiple groups of excitation signals with different frequency characteristics respectively, then calculates the numerical frequency characteristics of each group of experiments, and performs spectrum splicing with the signal-to-noise ratio in the frequency domain as the optimization criterion, and finally obtains a numerical frequency model with a high signal-to-noise ratio in the frequency domain in different frequency bands, providing effective data for subsequent system identification.

[0006] The present invention is realized by the following technical solutions:

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

[0008] S1. For the object to be identified, design multiple groups of excitation signals, conduct multiple groups of experiments and record the corresponding experimental data;

[0009] S2. Calculate the weight coefficients for spectrum splicing based on the excitation signal sequences and noise response sequences of multiple groups of experiments with the optimal frequency-domain signal-to-noise ratio as the criterion;

[0010] S3. Calculate the Fourier transforms and frequency-domain numerical models of the excitation signal sequences and excitation response sequences of multiple groups of experiments, and splice their spectra according to the weight coefficients.

[0011] Further, in step S1, the sampling frequency determines the upper limit of the observable frequency in the experiment. Then, according to the characteristics of the object to be identified, select the frequency band to be concerned about, select the working point of identification, and design multiple groups of excitation signals. For example, pseudo-random signals, whose auto-power spectral density is relatively uniformly distributed in a wide frequency band and gradually decreases with the increase of frequency, are suitable for exciting the characteristics of the middle and high frequency bands of the object; and swept-frequency signals can be selected, whose auto-power spectral density is distributed in a relatively wide frequency band and the frequency band distribution can be designed according to requirements. After setting the swept frequency band of this signal to the low frequency band, it is suitable for exciting the characteristics of the low frequency band of the object. Suppose a total of M groups of excitation signals are designed, and accordingly M groups of identification experiments are to be done to obtain the data of each group of experiments. The data of the l-th group of experiments includes the step response steady-state segment sequence y sl (i), the noise response sequence y nl (i), the excitation response sequence y ul (i) and the excitation signal sequence u l (i), where represents the discrete time, l represents the data of the l-th group of experiments, and l = 1, 2,..., M. The noise response sequence y ml (i) is obtained by acquiring the data of the step response steady-state segment sequence y sl (i) and removing its steady-state mean. For subsequent calculations, it is required that the lengths of y nl (i), y ul (i) and u l (i) are the same and all are K.

[0012] Further, in step S2, process the data of the l-th group of experiments, and calculate the discrete Fourier transforms of y nl (i) and u l (i) and Taking as an example, its calculation formula is:

[0013]

[0014] Further, calculate y nl (i) and u l (i) respectively to obtain the auto-power spectral density of and Taking as an example, its calculation formula is as follows:

[0015]

[0016] The vector composed of weight coefficients is W(k) = [W 1 (k), W 2 (k), …, W M (k)] T , and the calculation formula of W l (k) is as follows:

[0017]

[0018] where Φ l (k) is the evaluation function of the l-th group of experimental data. Since the noise signal is difficult to observe or estimate, the auto-power spectral density of the noise response is used to replace the auto-power spectral density of the noise. Thus, the evaluation function is defined as:

[0019]

[0020] Further, in step S3, process the data of the l-th group of experiments, and calculate the discrete Fourier transform of y ul (i) respectively

[0021] Further, the numerical frequency model of the object is calculated by the following formula:

[0022]

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

[0024]

[0025] The present invention has the following advantages and effects compared with the prior art:

[0026] Without injecting excessive energy, compared with using a single excitation signal, the spectrum splicing method of the present invention can have a higher signal-to-noise ratio in the concerned frequency band, avoid inaccurate identification results caused by insufficient frequency-domain signal-to-noise ratio in some frequency bands, effectively avoid the negative impact of low-power data on the identification results, and thus effectively improve the accuracy of the identification results.

[0027] The present invention has intuitiveness and easy implementation, provides an intuitive solution to the problem of integrating the effective information of multiple groups of identification data, and does not require overly complex calculations.

[0028] The spectrum splicing method of the present invention has simple and easy technical means, is more intuitive and has less computational complexity compared with the prior art. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 It is a schematic flowchart of the spectrum splicing method.

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

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

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

[0033] Figure 5 It is a module diagram of the Simulink open-loop simulation.

[0034] Figure 6 It is a frequency-domain numerical model of the open-loop object under each group of excitation signals.

[0035] Figure 7 It is a frequency-domain numerical model of the open-loop object after spectrum splicing and the theoretical open-loop object model. DETAILED DESCRIPTION OF THE EMBODIMENTS

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

[0037] Embodiment 1

[0038] As Figure 1 shown, the present invention discloses a spectrum splicing method, which can be realized through the following steps:

[0039] S1: For the object to be identified, design multiple groups of excitation signals, conduct multiple groups of experiments and record the corresponding experimental data;

[0040] S2: Calculate the weight coefficients for spectrum splicing based on the excitation signal sequences and noise response sequences of multiple groups of experiments with the optimal frequency-domain signal-to-noise ratio as the criterion;

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

[0042] Please refer to Figure 2 , this example is a spectrum splicing and closed-loop identification experiment carried out on a motor servo system.

[0043] Specifically, in step S1, the object to be identified is the current loop of the servo driver and the motor counter-rotation system it drives. The motor counter-rotation 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 the rotary encoder. They jointly 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 end of the control unit, the output signal y(i) is the estimated motor rotation speed, the sampling frequency of the system is set to 2000 Hz, r(i) is a step signal sequence with an amplitude of A = 250 rpm, that is, the operating point of this identification experiment is at 250 rpm. The continuous model of the servo speed loop controller is C(s) and,

[0044]

[0045] After discretization by the bilinear method, it is implemented on the servo. In addition, the discrete transfer function of the closed-loop system from u(i) to y(i) is defined as G(e jω ), C(e jω ) is the discrete transfer function of the controller, and G 0 (e jω ) is the discrete transfer function of the object to be identified. The relationships among G(e jω ), G 0 (e jω ) and C(e jω ) are as follows:

[0046]

[0047] According to the characteristics of the system and the sampling frequency, the main frequency band of concern is 1 Hz - 1000 Hz. Therefore, multiple groups of excitation signals with different auto-power spectral densities need to be designed so that the frequency-domain numerical model of the closed-loop system after spectrum splicing has a good signal-to-noise ratio in the frequency band of concern. Therefore, three groups of logarithmic sweep signal sequences and one group of pseudo-random signal sequences are designed for u(i). The following are the detailed settings of these four groups of signals:

[0048] 1) Pseudo-random signal sequence: The number of series is 11, the single-period length is 2047, and the amplitude is 0.15 A

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

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

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

[0052] The operating point of the above excitation signals is 250 rpm. At the same time, in order to reduce the influence of spectral leakage, the excitation signals need to maintain two cycles.

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

[0054] After completing four groups of step - response experiments and identification experiments and collecting the step - response, u(i) and y(i), the excitation signal sequence and output signal sequence of the l - th group of identification experiments are respectively denoted as u l (i) and y l (i). Process the data of the l - th group of experiments:

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

[0056] b) Calculate the mean value of y sl (i) as the mean value y mean_l ;

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

[0058] d) Take the data of the second - cycle part of y l (i), subtract y mean_l from it, and the obtained result is approximately the excitation response y ul (i);

[0059] e) Take the data of the second - cycle part of u l (i) as the excitation signal sequence U l (i)

[0060] In step S2, process the data of the l - th group of experiments, and calculate y nl (i) and u l(i) discrete Fourier transform and Taking as an example, its calculation formula is:

[0061]

[0062] Furthermore, calculate the auto-power spectral density of y nl (i) and u l (i) respectively to obtain and Taking as an example, its calculation formula is as follows:

[0063]

[0064] The vector composed of weight coefficients is W(k) = [W 1 (k), W 2 (k), …, W M (k)] T , and the calculation formula of W l (k) is as follows:

[0065]

[0066] where Φ l (k) is the evaluation function of the l-th group of experimental data. Since the noise signal is difficult to observe or estimate, the auto-power spectral density of the noise response is used to replace the auto-power spectral density of the noise. Thus, the evaluation function is defined as:

[0067]

[0068] In step S3, process the data of the l-th group of experiments, and calculate the discrete Fourier transform of y ul (i) respectively

[0069] Furthermore, the numerical frequency model of the object is calculated by the following formula:

[0070]

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

[0072]

[0073] When identifying using an excitation signal with a low DC component, the obtained results often do not have sufficient signal-to-noise ratio at 0 Hz. Therefore, a step signal needs to be used as the excitation signal to estimate the system gain, that is, the numerical value of the system numerical model at zero hertz. Calculate the mean value y of mean_1 y mean_2 … y mean_M . For the step response experiment, R(e mean ) is the discrete Fourier transform of r(i), and Y(e jω ) is the discrete Fourier transform of y(i). The relationship between the two is as follows: jω Y(e jω )=R(e jω )C(e jω )G(e jω )

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

[0076]

[0077] Approximate as y mean , then the numerical value of the closed-loop system numerical frequency model at 0 Hz can be estimated by the following formula

[0078]

[0079] Because the DC components of the swept-frequency signal and the pseudo-random signal are very small, needs to be used to replace

[0080] and and

[0081] at k = 0. The replacement calculation is as follows:

[0082] Figure 4 For the closed-loop system frequency-domain numerical model after spectrum splicing, please refer to

[0083] . Subsequently, the system parameters can be identified according to the frequency-domain numerical model of the closed-loop system.

[0084] Example 2 Figure 1 As

[0085] shown, the present invention discloses a spectrum splicing method, which can be realized through the following steps:

[0086] S11: For the object to be identified, design multiple groups of excitation signals, conduct multiple groups of experiments and record the corresponding experimental data;

[0087] S12: Calculate the weight coefficients for spectrum splicing based on the excitation signal sequences and noise response sequences of multiple groups of experiments with the optimal frequency-domain signal-to-noise ratio as the criterion;

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

[0088] Please refer to Figure 5 , this example is a spectrum splicing and open-loop identification simulation carried out on Simulink.

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

[0090]

[0091] According to the characteristics of the system and the sampling frequency, the main frequency band of concern is 1 Hz - 1000 Hz. Therefore, multiple groups of excitation signals with different auto-power spectral densities need to be designed so 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 frequency band of concern. So, three groups of logarithmic sweep signal sequences and one group of pseudo-random signal sequences are designed for u(i). The following are the detailed settings of these four groups of signals:

[0092] 1) Pseudo-random signal sequence: The number of series is 11, the single-cycle length is 2047, and the amplitude is 1

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

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

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

[0096] The operating point of the above excitation signals is 500. At the same time, in order to reduce the influence of spectrum leakage, the excitation signals need to maintain two cycles.

[0097] In order to obtain the steady-state gain and noise response signal of the system, an additional step response experiment is added to each group of identification experiments. The amplitude of the step signal is A = 500, and at the same time, 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 the step responses, u(i) and y(i), the excitation signal sequence and output signal sequence of the l-th identification experiment are respectively denoted as u l (i) and y l (i). Process the experimental data of the l-th group:

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

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

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

[0102] d) Take the data of the second cycle part of y l (i), subtract y mean_l from it. The obtained result is approximately the excitation response y ul (i);

[0103] e) Take the data of the second cycle part of u l (i) as the excitation signal sequence U l (i) for identification calculation

[0104] In step S12, process the data of the l-th group of experiments, and calculate the discrete nl of y l (i) and u . The calculation formula is:

[0106]

[0107] Furthermore, calculate the auto-power spectral density of y nl (i) and u l (i) to obtain and Taking as an example, its calculation formula is as follows:

[0108]

[0109] The vector composed of weight coefficients is W(k) = [W 1 (k), W 2 (k), …, W M (k)] T , and the calculation formula of W l (k) is as follows:

[0110]

[0111] where Φ l (k) is the evaluation function of the l-th group of experimental data. Since the noise signal is difficult to observe or estimate, the auto-power spectral density of the noise response is used to replace the auto-power spectral density of the noise. Thus, the evaluation function is defined as:

[0112]

[0113] In step S13, the data of the l-th group of experiments are processed, and the discrete Fourier transform of y ul (i) is calculated respectively

[0114] Furthermore, the numerical frequency model of the object is calculated by the following formula:

[0115]

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

[0117]

[0118]

[0119]

[0120] When identifying using an excitation signal with a low DC component, the obtained result often does not have sufficient signal-to-noise ratio at 0 Hz. Therefore, a step signal needs to be used as the excitation signal to estimate the system gain, that is, the value of the system numerical model at zero hertz. Calculate the mean value y mean_1 y mean_2 … y mean_M of [y mean . For the step response experiment, u(i) is a step signal with an amplitude of A, U(e jω ) is the discrete Fourier transform of u(i), Y(e jω ) is 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, there is:

[0123]

[0124] Approximate as y mean , so the numerical value of the closed-loop system numerical frequency model at 0 Hz can be estimated by the following formula

[0125]

[0126] Since the DC components of the frequency-sweeping signal and the pseudo-random signal are both very small, it is necessary to use to replace and the numerical values at k = 0, and the replacement calculation is as follows:

[0127]

[0128] For the frequency-domain numerical model of the open-loop object and the theoretical open-loop object model after spectrum splicing, please refer to Figure 7 . Subsequently, the system parameters can be identified according to 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 the present invention can have a higher signal-to-noise ratio in the concerned frequency band, avoid inaccurate identification results due to insufficient frequency-domain signal-to-noise ratio in some frequency bands, effectively avoid the negative impact of low-power data on the identification results, and thus effectively improve the accuracy of the identification results.

[0130] The present invention has intuitiveness and easy implementation, provides an intuitive solution to the problem of fusing the effective information of multiple groups of identification data, and does not require overly complex calculations.

[0131] The implementation manners of the present invention are not limited by the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications made without departing from the spirit and principle of the present invention shall be equivalent replacement manners and are all included in the protection scope of the present invention.

Claims

1. A spectrum splicing method based on frequency domain signal-to-noise ratio, characterized in that: The following steps are involved: S1: Design multiple sets of excitation signals for the objects to be identified, conduct multiple sets of experiments and record the corresponding experimental data; S2: Calculate the weight coefficient for spectrum splicing based on the excitation signal sequence and noise response sequence of multiple groups of experiments with the optimal frequency domain signal-to-noise ratio as the criterion; S3: Calculate the Fourier transform and frequency domain numerical model of multiple sets of experimental excitation signal sequences and excitation response sequences, and splice their spectra according to the weight coefficients.

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

3. The spectrum splicing method based on frequency domain signal-to-noise ratio according to claim 2, characterized in that: In the process of designing multiple groups of excitation signals, for example, a pseudo-random signal, whose power spectrum density is relatively evenly distributed over a wide frequency band, decreases gradually with increasing frequency, and is suitable for stimulating the medium and high frequency band characteristics of an object; and a frequency sweep signal, whose power spectrum density is distributed over a wider frequency band, and whose frequency band distribution can be designed according to demand, is suitable for stimulating the low frequency band characteristics of an object after the frequency sweep of the signal is set to a low frequency band; assuming that a total of M groups of excitation signals are designed, M groups of identification experiments are to be performed accordingly, and the data of each group of experiments are obtained, wherein the data of the first group of experiments include the step response steady-state segment sequence y sl (i) Noise response sequence y nl (i) stimulus response sequence y ul (i) and the excitation signal sequence u l (i); Where i represents a discrete moment; l represents the data of the lth group of experiments; l＝1，2，…，M； Noise response sequence y nl (i) is to obtain the step response steady-state segment sequence y sl (i) The data is then removed from its steady-state mean; for subsequent calculations, y is required nl (i) y ul (i) and u l (i) have the same length and are both K.

4. The spectrum splicing method based on frequency domain signal-to-noise ratio according to claim 3, characterized in that: In step 2), the data of the first group of experiments are processed to calculate y nl (i) and u l Discrete Fourier transform of (i) and by For example, the calculation formula is:

5. The spectrum splicing method based on frequency domain signal-to-noise ratio according to claim 4, characterized in that: Calculate y separately nl (i) and u l The autopower spectral density of (i) is obtained and by For example, the calculation formula is as follows: The vector of weight coefficients is W(k)=[W1(k), W2(k), …, W M (k)] T , W l The calculation formula of (k) is as follows: where Φ l (k) is the evaluation function of the first group of experimental data. The self-power spectrum density of the noise response is used to replace the self-power spectrum density of the noise. The evaluation function is defined as:

6. The spectrum splicing method based on frequency domain signal-to-noise ratio according to claim 1, characterized in that: In step 3), the data of the first group of experiments are processed to calculate y ul Discrete Fourier transform of (i) 7. The spectrum splicing method based on frequency domain signal-to-noise ratio according to claim 6, characterized in that: Numerical frequency model of the object Calculated by the following formula:

8. The spectrum splicing method based on frequency domain signal-to-noise ratio according to claim 7, characterized in that: After completing the processing of M groups of experimental data and spectral splicing, the numerical frequency model of the object is The discrete Fourier transforms of the stimulus response and the stimulus signal are and The spectrum splicing calculation formula is as follows:

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