CN104794313A - Method and device for obtaining frequency response function of system to be identified - Google Patents
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Abstract
The invention provides a method and a device for obtaining a frequency response function of a system to be identified. The method comprises the following steps: triggering a linear feedback shift register to generate an input signal through a clock signal and triggering a software program to generate a reference signal according to the time sequence period and sampling rate of the input signal, wherein both the input signal and the reference signal are invert-repeated m-sequence and the periods of the signals are even times a power frequency period; inputting the input signal to the system to be identified and acquiring an output signal output by the system to be identified; and applying a cross-correlation theory to the reference signal, the input signal and the output signal to obtain the frequency response function of the system to be identified. The input signal is multi-period invert-repeated m-sequence and the frequency spectrum of the input signal contains a plurality of discrete frequencies to avoid the sequential input of a plurality of single-frequency signals, so that the efficiency of obtaining the frequency response function is improved. The reference signal is added, so that the identification precision of obtaining the frequency response function is high; the periods of the input signal and the reference signal are even times the power frequency period, so that the power frequency interference can be effectively suppressed.
Description
Technical Field
The invention relates to the field of signal acquisition and processing, the field of system identification and the field of geophysical electromagnetic prospecting, in particular to a method and a device for acquiring a frequency response function of a system to be identified.
Background
At present, in order to know the system characteristics of the system to be identified, it is often necessary to obtain the frequency response function of the system to be identified, and the system to be identified may be a circuit system, an observation instrument system, or a ground system to be detected. For example, in order to determine the geological distribution of the earth system to be surveyed, and thus to survey the ore body in the earth system to be surveyed, it is necessary to obtain the electromagnetic frequency response function of the earth system to be surveyed.
Currently, the prior art provides a method for obtaining a frequency response function of a system to be identified, which includes: exciting the system to be identified by using an input signal with a certain frequency, and collecting the response of the system to be identified to the input signal and outputting the response as an output signal. And then changing the frequency of the input signal, exciting the system to be identified by using the input signal with changed frequency, and collecting an output signal output by the system to be identified. Thus, input signals with different frequencies are sequentially input to the system to be identified according to the method, and output signals corresponding to each input signal are respectively collected. And analyzing and processing each input signal and the corresponding output signal to obtain a frequency response function of the system to be identified.
In the process of implementing the invention, the inventor finds that at least the following problems exist in the prior art:
a large amount of time is required to input a plurality of input signals to the system to be identified and to acquire an output signal in sequence, which results in low efficiency of acquiring the frequency response function. In addition, the industrial alternating current electromagnetic field widely existing in the modern society can affect input signals and output signals, so that in a region with serious power frequency interference, the frequency response function of a system is difficult to accurately obtain.
Disclosure of Invention
In view of this, an object of the embodiments of the present invention is to provide a method and an apparatus for obtaining a frequency response function of a system to be identified, so as to improve efficiency of obtaining the frequency response function and improve accuracy of obtaining the frequency response function.
In a first aspect, an embodiment of the present invention provides a method for obtaining a frequency response function of a system to be identified, where the method includes:
triggering a linear feedback shift register through a clock signal to generate an input signal, and triggering a software program to generate a reference signal according to the time sequence period and the sampling rate of the input signal, wherein the input signal and the reference signal are both inverse repetitive M sequences, and the periods of the input signal and the reference signal are both even multiples of a power frequency period;
inputting the input signal to a system to be identified, and collecting an output signal output by the system to be identified;
and applying a cross-correlation theory to the reference signal, the input signal and the output signal to obtain a frequency response function of the system to be identified.
With reference to the first aspect, an embodiment of the present invention provides a first possible implementation manner of the first aspect, where the obtaining a frequency response function of the system to be identified by applying a cross-correlation theory to the reference signal, the input signal, and the output signal includes:
performing circular cross correlation on the output signal and the input signal with the reference signal respectively to obtain a cross correlation time sequence corresponding to the output signal and a cross correlation time sequence corresponding to the input signal;
performing fast Fourier transform on the cross-correlation time sequence corresponding to the output signal and the cross-correlation time sequence corresponding to the input signal respectively to obtain a cross-power spectrum of the output signal and a cross-power spectrum of the input signal;
and acquiring a frequency response function of the system to be identified according to the cross-power spectrum of the output signal and the cross-power spectrum of the input signal.
With reference to the first possible implementation manner of the first aspect, an embodiment of the present invention provides a second possible implementation manner of the first aspect, where the obtaining a frequency response function of the system to be identified according to a cross-power spectrum of the output signal and a cross-power spectrum of the input signal includes:
acquiring an output spectral line peak value and a frequency value corresponding to the output spectral line peak value from the cross-power spectrum of the output signal, and acquiring an input spectral line peak value and a frequency value corresponding to the input spectral line peak value from the cross-power spectrum of the input signal;
screening an output spectral line peak value and an input spectral line peak value with the same frequency value from the obtained output spectral line peak value and the obtained input spectral line peak value, and calculating the ratio of the output spectral line peak value and the input spectral line peak value with the same frequency value through the following formula (1) to obtain a frequency response function of the system to be identified;
wherein in the formula (1), ω is a frequency value,is the peak value of the output spectral line corresponding to the frequency value omega,is the peak value of the input spectral line corresponding to the frequency value omega, and H (omega) is the frequency response function of the system to be identified.
With reference to the first possible implementation manner of the first aspect, an embodiment of the present invention provides a third possible implementation manner of the first aspect, where the inputting the input signal to the system to be recognized and acquiring the output signal output by the system to be recognized includes:
inputting the input signal to the system to be identified, and acquiring an output signal output by the system to be identified in a synchronous mode or an asynchronous mode;
correspondingly, the applying a cross-correlation theory to the reference signal, the input signal and the output signal to obtain a frequency response function of the system to be identified includes:
when the output signal is acquired in the asynchronous mode, acquiring a frequency response function of the system to be identified according to the cross-power spectrum of the output signal and the cross-power spectrum of the input signal, wherein the frequency response function comprises an amplitude spectrum;
when the output signals are acquired in the synchronous mode, acquiring a frequency response function of the system to be identified according to the cross-power spectrum of the output signals and the cross-power spectrum of the input signals, wherein the frequency response function comprises a phase spectrum and a magnitude spectrum, and acquiring the phase spectrum of the frequency response function of the system to be identified through the following formula (2);
wherein in formula (2), mod is the modulo operator,the phase of the cross-power spectrum of the output signal corresponding to frequency omega,the phase of the cross-power spectrum of the input signal corresponding to frequency omega,is the phase spectrum of the frequency response function of the system to be identified.
With reference to the first aspect, an embodiment of the present invention provides a fourth possible implementation manner of the first aspect, where after the obtaining a frequency response function of the system to be identified, the method further includes:
and when the system to be identified is the earth system to be detected, carrying out inversion calculation on the frequency response function to obtain the earth electric section of the earth system to be detected, and calculating the electromagnetic exploration parameters of the earth system to be detected according to the frequency response function, wherein the electromagnetic exploration parameters comprise step response, complex resistivity, percentage frequency effect and late apparent resistivity.
In a second aspect, a device for obtaining a frequency response function of a system to be identified comprises:
the generating module is used for triggering the linear feedback shift register through a clock signal to generate an input signal, and triggering a software program to generate a reference signal according to the time sequence period and the sampling rate of the input signal, wherein the input signal and the reference signal are both inverse repeated M sequences, and the same period is even times of a power frequency period;
the acquisition module is used for inputting the input signal to a system to be identified and acquiring an output signal output by the system to be identified;
and the acquisition module is used for applying a cross-correlation theory to the reference signal, the input signal and the output signal to acquire a frequency response function of the system to be identified.
With reference to the second aspect, an embodiment of the present invention provides a first possible implementation manner of the second aspect, where the obtaining module includes:
a circular cross-correlation unit, configured to perform circular cross-correlation on the output signal and the input signal with the reference signal, respectively, to obtain a cross-correlation time sequence corresponding to the output signal and a cross-correlation time sequence corresponding to the input signal;
a fast fourier transform unit, configured to perform fast fourier transform on the cross-correlation time sequence corresponding to the output signal and the cross-correlation time sequence corresponding to the input signal, respectively, to obtain a cross-power spectrum of the output signal and a cross-power spectrum of the input signal;
and the first acquisition unit is used for acquiring the frequency response function of the system to be identified according to the cross-power spectrum of the output signal and the cross-power spectrum of the input signal.
With reference to the first possible implementation manner of the second aspect, an embodiment of the present invention provides a second possible implementation manner of the second aspect, where the first obtaining unit includes:
the acquisition subunit is used for acquiring an output spectral line peak value and a frequency value corresponding to the output spectral line peak value from the cross-power spectrum of the output signal, and acquiring an input spectral line peak value and a frequency value corresponding to the input spectral line peak value from the cross-power spectrum of the input signal;
the calculating subunit is used for screening an output spectral line peak value and an input spectral line peak value with the same frequency value from the obtained output spectral line peak value and the obtained input spectral line peak value, and calculating a ratio between the output spectral line peak value and the input spectral line peak value with the same frequency value through a formula (1) to obtain a frequency response function of the system to be identified;
wherein in the formula (1), ω is a frequency value,is the peak value of the output spectral line corresponding to the frequency value omega,is the peak value of the input spectral line corresponding to the frequency value omega, and H (omega) is the frequency response function of the system to be identified.
With reference to the first possible implementation manner of the second aspect, an embodiment of the present invention provides a third possible implementation manner of the second aspect, where the acquisition module is configured to input the input signal to the system to be identified, and acquire an output signal output by the system to be identified in a synchronous manner or an asynchronous manner;
correspondingly, the obtaining module comprises:
the second acquisition unit is used for acquiring a frequency response function of the system to be identified according to the cross-power spectrum of the output signal and the cross-power spectrum of the input signal when the output signal is acquired in the asynchronous mode, wherein the frequency response function comprises a magnitude spectrum;
a third obtaining unit, configured to, when the output signal is collected in the synchronous manner, obtain a frequency response function of the system to be identified according to a cross-power spectrum of the output signal and a cross-power spectrum of the input signal, where the frequency response function includes a phase spectrum and a magnitude spectrum, and obtain a phase spectrum of the frequency response function of the system to be identified by using the following formula (2);
wherein in formula (2), mod is the modulo operator,the phase of the cross-power spectrum of the output signal corresponding to frequency omega,the phase of the cross-power spectrum of the input signal corresponding to frequency omega,is the phase spectrum of the frequency response function of the system to be identified.
With reference to the second aspect, an embodiment of the present invention provides a fourth possible implementation manner of the second aspect, where the apparatus further includes:
and the calculating module is used for performing inversion calculation on the frequency response function when the system to be identified is a to-be-detected geodetic system, acquiring the geodetic section of the to-be-detected geodetic system, and calculating the electromagnetic exploration parameters of the to-be-detected geodetic system according to the frequency response function, wherein the electromagnetic exploration parameters comprise step response, complex resistivity, percentage frequency effect and late apparent resistivity.
In the embodiment of the invention, because the input signal is an inverse repetition M sequence, the frequency spectrum of the input signal comprises a plurality of discrete frequency signals, and the amplitudes of the plurality of discrete frequency signals are approximately equal in the main frequency band, the condition that a plurality of single frequency signals are sequentially input to the system to be identified is avoided, and the efficiency of acquiring the frequency response function is improved. In addition, the precision of obtaining the frequency response function through a cross-correlation method according to the reference signal, the output signal and the input signal is very high, the period of the input signal and the reference signal is even times of the power frequency period, and power frequency interference can be effectively suppressed.
In order to make the aforementioned and other objects, features and advantages of the present invention comprehensible, preferred embodiments accompanied with figures are described in detail below.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the embodiments will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present invention and therefore should not be considered as limiting the scope, and for those skilled in the art, other related drawings can be obtained according to the drawings without inventive efforts.
Fig. 1 is a flowchart illustrating a method for obtaining a frequency response function of a system to be identified according to embodiment 1 of the present invention;
fig. 2A is a flowchart illustrating a method for obtaining a frequency response function of a system to be identified according to embodiment 2 of the present invention;
FIG. 2B is a schematic diagram showing a time domain waveform of an inverted M-sequence according to embodiment 2 of the present invention;
FIG. 2C is a schematic diagram showing a power spectrum of an inverted repeat M sequence provided in embodiment 2 of the present invention;
FIG. 2D is a diagram illustrating an autocorrelation function curve of an inversely repeated M sequence provided in embodiment 2 of the present invention;
fig. 2E is a schematic diagram illustrating a cross-power spectrum of an output signal and a reference signal provided in embodiment 2 of the present invention;
fig. 3 is a flowchart illustrating a method for obtaining a frequency response function of a system to be identified according to embodiment 3 of the present invention;
fig. 4 is a schematic structural diagram illustrating an apparatus for obtaining a frequency response function of a system to be identified according to embodiment 4 of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. The components of embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations. Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present invention without making any creative effort, shall fall within the protection scope of the present invention.
In consideration of the fact that in the prior art, a large amount of time is required for inputting a plurality of input signals to a system to be identified and collecting output signals in sequence, and the efficiency of obtaining a frequency response function is low. And the frequency of the input signal is affected by the frequency of the industrial alternating current in the related art, so that the accuracy of the obtained frequency response function is low. Accordingly, the embodiment of the invention provides a method and a device for acquiring a frequency response function of a system to be identified. The following is described by way of example.
Example 1
Referring to fig. 1, an embodiment of the present invention provides a method for obtaining a frequency response function of a system to be identified, which may be performed by an apparatus for obtaining a frequency response function of a system to be identified. The method specifically comprises the following steps:
step 101: triggering a linear feedback shift register through a clock signal to generate an input signal, triggering a software program to generate a reference signal according to the time sequence period and the sampling rate of the input signal, wherein the input signal and the reference signal are both an inverse repetition M sequence, and the periods of the input signal and the reference signal are both even multiples of a power frequency period;
step 102: inputting the input signal to a system to be identified, and collecting an output signal output by the system to be identified;
step 103: and applying a cross-correlation theory to the reference signal, the input signal and the output signal to obtain a frequency response function of the system to be identified.
In the embodiment of the invention, because the input signal is an inverse repetition M sequence, the frequency spectrum of the input signal comprises a plurality of discrete frequency signals, and the amplitudes of the plurality of discrete frequency signals are approximately equal in the main frequency band, the condition that a plurality of single frequency signals are sequentially input to the system to be identified is avoided, and the efficiency of acquiring the frequency response function is improved. In addition, the precision of obtaining the frequency response function through a cross-correlation method according to the reference signal, the output signal and the input signal is very high, the period of the input signal and the reference signal is even times of the power frequency period, and power frequency interference can be effectively suppressed.
Example 2
The embodiment of the invention provides a method for acquiring a frequency response function of a system to be identified, which can be executed by a device for acquiring the frequency response function of the system to be identified.
The system to be identified is a circuit system, an observation instrument system or a ground system to be detected. Because the system to be identified comprises media with different conductivity and magnetic conductivity, the system to be identified is excited by the input signal, and the system to be identified responds to the input signal due to the electromagnetic induction. In the embodiment of the invention, the output signal output by the system to be identified is acquired in a synchronous mode, and the frequency response function of the system to be identified is acquired by the method provided by the embodiment of the invention.
Referring to fig. 2A, the method specifically includes the steps of:
step 201: triggering a linear feedback shift register through a clock signal to generate an input signal, wherein the input signal is an inverse repetition M sequence and has a period which is an even multiple of a power frequency period;
wherein, the input signal is a periodic pseudo-random inverse repeating M sequence.
The execution subject of the embodiment of the invention is a device for acquiring the frequency response function of the system to be identified, and the system to be identified can be a circuit system, an observation instrument system or a geodetic system to be detected and the like. The device is provided with an N +1 bit register, wherein N is an integer greater than or equal to 3. In the N +1 bit registers, a 1 bit register is used for generating a clock signal of a two-frequency division shift register, the rest N bit registers form a linear feedback shift register, the feedback bit of the linear feedback shift register is preset, and the N bit linear feedback shift register forms a maximum length pseudo-random m sequence generating circuit. And performing exclusive or operation on the clock signal of the other 1-bit register binary frequency linear feedback shift register and the pseudo-random M sequence generated by the N-bit linear feedback shift register to realize inversion of the separation of the pseudo-random M sequence and obtain an inverted repetitive M sequence. Presetting a sampling rate, sampling the time sequence of the inverted repetitive M sequence according to the sampling rate, and determining the time sequence signal obtained by sampling as an input signal, wherein the sampling rate is the frequency for acquiring the input signal. The input signal is a multi-period signal.
The period and frequency band of the reverse repeating M sequence are adjustable, and can be adjusted by selecting different linear feedback shift register bits and clock frequencies. The number of bits of the linear feedback shift register is typically 5, 6, 7, 8, 9 or 10 bits, and the clock frequency can be selected within the frequency interval 0.5Hz, 10 kHz. As shown in table 1, the period and the sequence bit length of the corresponding inverted repeat M sequence are different for different linear feedback shift register bit numbers and clock frequencies. The primitive polynomial in table 1 is a feedback bit expression for generating an inverted repeating M-sequence, the clock frequency is only schematically given in the corresponding table of the clock frequency and the period of the inverted repeating M-sequence, and the clock frequency can be selected within a frequency interval [0.5Hz, 10kHz ] in a specific operation.
TABLE 1
Wherein the period of the inversely repeated M-sequence is 2 times the period of the maximum linear feedback pseudorandom M-sequence. And taking the period of the inverse repetitive M sequence as even multiple of the power frequency period, namely the period of the input signal is the even multiple of the power frequency period. In a scene with more industrial electricity, the input signal is influenced by the industrial electricity. And the correlation peak value of the input signal shows that the periodic positive and negative alternately appear, so that the period of the input signal is taken as the even multiple of the power frequency period, the power frequency interference can be effectively suppressed, the influence of the power frequency interference on the input signal is weakened, and the accuracy of the obtained frequency response function is improved.
The power frequency is the frequency of an alternating current power supply used in industry, and is generally 50 Hz.
The time domain waveform of the M-sequence is shown in fig. 2B, and the waveform of the M-sequence is random within 1 cycle. The power spectrum of the inverted repeat M sequence is shown in fig. 2C, which is a discrete line spectrum. The curve of the autocorrelation function of the inversely repeated M sequence, which is shown in fig. 2D, appears as alternating positive and negative spikes.
The input signal is an inverted M sequence, the inverted M sequence signal comprises a plurality of discrete frequency signals, and the amplitudes of the plurality of discrete frequency signals in the main frequency band are equal, so that a frequency response function is obtained according to the input signal, the condition that a plurality of single frequency signals are input to a system to be identified one by one can be avoided, and the efficiency of obtaining the frequency response function is improved.
After the input signal is generated through the operation of this step, the output signal of the system to be recognized needs to be acquired through the following operation of step 202.
Step 202: inputting the input signal to a system to be identified, and acquiring an output signal output by the system to be identified in a synchronous mode;
the synchronous mode refers to that output signals output after the system to be identified responds to the input signals are collected consistently through sampler actions with consistent performance according to the same sampling rate and sampling time as the input signals. The output signal may be an electrical signal or a magnetic signal.
The device for acquiring the frequency response function of the system to be identified can be a split type signal transmitting device and a signal receiving device, and can also be a transmitting and receiving integrated acquisition device. The signal sending device can comprise a high-power inverter and the like, an input signal is driven by the high-power inverter and is output to the system to be identified through an electric dipole, the signal receiving device receives electromagnetic response of the system to be identified through the electric dipole or a magnetic dipole, the electric dipole can be an electrically separated electrode and the like, and the magnetic dipole can be a magnetic probe and the like. The input signal is an electric signal, and the output signal has two types of electric signals and magnetic signals. The signal transmitting device transmits the input signal to the system to be identified through the electric dipole by using the inverter. When the output signals are collected, the output signals collected by the electric dipoles of the signal collection equipment are electric signals, and the output signals collected by the magnetic dipoles of the signal collection equipment are magnetic signals.
The step is specifically that the control signal sending equipment is connected to the system to be identified through the electric dipole, and the control signal acquisition equipment is used for connecting the electric dipole or the magnetic probe to the system to be identified. The control signal transmitting equipment inputs an input signal to the system to be identified through an electric dipole to excite the system to be identified, and meanwhile, the control signal collecting equipment collects the electromagnetic response of the system to be identified as an output signal through an electrode or a magnetic probe according to the same sampling rate and sampling time as those of the input signal.
In the embodiment of the invention, the electric field response or the magnetic field response of the system to be identified can be acquired through the electric dipole or the magnetic dipole of the signal acquisition equipment. In order to improve the accuracy of the obtained frequency response function, in the embodiment of the present invention, it is necessary to keep the system characteristics of the input signal collector and the output signal collector consistent.
In addition, the device for acquiring the frequency response function of the system to be identified is also provided with time synchronization equipment for controlling the time synchronization equipment to synchronize with the signal sending equipment and synchronize with the signal acquisition equipment, so that the signal acquisition equipment simultaneously acquires the output signal output by the system to be identified when the signal sending equipment excites the system to be identified. Furthermore, a sampling rate can be preset in the time synchronization device, and the time synchronization device controls the signal acquisition device to synchronously acquire the input signal and the output signal according to the preset sampling rate. The sampling rate is the frequency of the collected signals, that is, the amplitude of the input signal and the amplitude of the output signal are collected once every preset time period.
Furthermore, the signal acquisition equipment can also store the acquired input signals and output signals and transmit the acquired input signals and output signals to the processing equipment such as a computer, so that the processing equipment such as the computer can carry out deeper calculation processing on the acquired input signals and output signals.
After the input signal and the output signal are obtained through the operations of the above steps 201 and 202, the reference signal needs to be generated through the following operation of the step 203.
Step 203: triggering a software program to generate a reference signal according to the time sequence period and the sampling rate of the input signal;
wherein, the sequence length of the reference signal 1 period is the same as the sequence length of the input signal 1 period, and the initial state can be different from the input signal. The reference signal only needs 1 or 2 complete period of the reverse repeating M sequence, and the input signal is a multi-period reverse repeating M sequence with the period being an even multiple of the power frequency period. The reference signal may be generated in the same manner as the input signal. After the number of bits and the feedback bits of the linear feedback shift register generating the inverse repeating M sequence are set, the generated inverse repeating M sequence is fixed, only time delay exists among the inverse repeating M sequences generated in different initial states of the register, but the frequency spectrum distribution of the generated inverse repeating M sequence is the same.
In this step, parameters such as a clock frequency and a sampling rate required for generating the reference signal are the same as those for generating the input signal. Further, a skilled person may develop a software program for generating a reference signal in advance, set a clock frequency and the number of bits of the linear feedback shift register, trigger the software program in accordance with the time-series period and the sampling rate of the input signal to generate an inverted repeating M-sequence of 1 or 2 full periods, and determine the generated inverted repeating M-sequence as the reference signal.
The period of the reference signal is the same as that of the input signal and is even multiple of the power frequency period. And subsequently, the input signal and the output signal are subjected to circular cross-correlation processing according to the reference signal, so that power frequency interference can be effectively suppressed, and the precision of the obtained frequency response function is improved.
The operation of this step may also be performed simultaneously with the operation of step 201.
After the input signal, the output signal and the reference signal are acquired, the frequency response function of the system to be identified may be acquired through the following operation of step 204.
Step 204: applying a cross-correlation theory to the reference signal, the input signal and the output signal to obtain a frequency response function of the system to be identified;
the step can be realized through the following operations of S1-S4, specifically:
s1: respectively acquiring a cross-correlation time sequence corresponding to the input signal and a cross-correlation time sequence corresponding to the output signal according to the reference signal, the input signal and the output signal;
specifically, according to the reference signal and the input signal, the reference signal and the input signal are circularly cross-correlated by the following formula (3), and a cross-correlation time series corresponding to the input signal is obtained. And according to the reference signal and the output signal, performing cyclic cross correlation on the reference signal and the output signal through the following formula (4) to obtain a cross correlation time sequence corresponding to the output signal.
Cus(t)＝cxcorr(u,SS)…(3)
Cys(t)＝cxcorr(yout,SS)…(4)
Wherein, in the formulas (3) and (4), u is an input signal, yout is an output signal, SS is a reference signal, t is time, Cus(t) is the cross-correlation time series corresponding to the input signal, Cys(t) is a cross-correlation time sequence corresponding to the output signal, cxcorr (u, SS) represents performing a circular cross-correlation operation on the input signal u and the reference signal SS, and cxcorr (yout, SS) represents performing a circular cross-correlation operation on the output signal yout and the reference signal SS.
S2: respectively acquiring a cross-power spectrum of the input signal and a cross-power spectrum of the output signal according to the cross-correlation time sequence corresponding to the input signal and the cross-correlation time sequence corresponding to the output signal;
specifically, the cross-power spectrum of the input signal is obtained by performing fast fourier transform on the cross-correlation time series corresponding to the input signal by the following formula (5). And performing fast Fourier transform on the cross-correlation time sequence corresponding to the output signal through the following formula (6) to obtain a cross-power spectrum of the output signal.
Wherein in the formulas (5) and (6), ω is a frequency value,for the cross-power spectrum of the input signal,for cross-power spectra of the output signals, FFT (C)us(t)) represents the cross-correlation time series C corresponding to the input signalus(t) performing a fast Fourier transform, FFT (C)ys(t)) represents the cross-correlation time series C corresponding to the output signalys(t) performing a fast Fourier transform.
The cross-power spectrum of the output signal and the reference signal is shown in fig. 2E, the output signal and the reference signal are circularly cross-correlated to obtain a cross-correlation time sequence corresponding to the output signal, and then the cross-correlation time sequence of the output signal is subjected to fast fourier transform to obtain the cross-power spectrum of the output signal. The cross-power spectrum shown in fig. 2E is the cross-power spectrum of the output signal.
After the cross-power spectrum of the input signal and the cross-power spectrum of the output signal are obtained through the operations of S1 and S2, the frequency response function of the system to be identified can be obtained according to the cross-power spectrum of the input signal and the cross-power spectrum of the output signal through the operations of S3 and S4.
S3: obtaining an input spectral line peak value and a frequency value corresponding to the input spectral line peak value from a cross power spectrum of the input signal, and obtaining an output spectral line peak value and a frequency value corresponding to the output spectral line peak value from a cross power spectrum of the output signal;
the input spectral line peak value is a cross-power spectral value of which the amplitude in the cross-power spectrum of the input signal is greater than a preset threshold value, and the output spectral line peak value is a cross-power spectral value of which the amplitude in the cross-power spectrum of the output signal is greater than the preset threshold value.
The method specifically comprises the steps of determining all spectral line maximum value points with the amplitude larger than a preset threshold value from spectral lines of a cross-power spectrum of an input signal, obtaining cross-power spectral values and frequency values corresponding to each determined maximum value point, determining the cross-power spectral values corresponding to the maximum value points as input spectral line peak values, and determining the frequency values corresponding to the maximum value points as frequency values corresponding to the input spectral line peak values. Similarly, determining all spectral line maximum points with the amplitude larger than a preset threshold value from spectral lines of the cross-power spectrum of the output signal, acquiring cross-power spectral values and frequency values corresponding to each determined maximum value, determining the cross-power spectral values corresponding to the maximum values as output spectral line peak values, and determining the frequency values corresponding to the maximum values as frequency values corresponding to the output spectral line peak values.
S4: and acquiring a frequency response function of the system to be identified according to the input spectral line peak value and the corresponding frequency value thereof, and the output spectral line peak value and the corresponding frequency value thereof.
Specifically, an input spectral line peak value and an output spectral line peak value with the same frequency value are screened out from the input spectral line peak value and the output spectral line peak value, and the ratio of the output spectral line peak value and the input spectral line peak value with the same frequency value is calculated through the following formula (1), so that the frequency response function of the system to be identified is obtained.
Wherein in the formula (1), ω is a frequency value,is the peak value of the output spectral line corresponding to the frequency value omega,is the peak value of the input spectral line corresponding to the frequency value omega, and H (omega) is the frequency response function of the system to be identified.
Wherein,the cross-power spectrum of the output signal here represents the cross-power spectrum value of the output signal corresponding to the frequency value ω, i.e. the peak value of the output spectral line corresponding to the frequency value ω.The cross-power spectrum of the input signal represents a cross-power spectrum value of the input signal corresponding to the frequency value ω, that is, a peak value of the input spectral line corresponding to the frequency value ω.
Because the periods of the input signal and the reference signal are even multiples of the power frequency period, the system to be identified is excited according to the input signal to obtain an output signal, and the input signal and the output signal are respectively subjected to circular cross-correlation with the reference signal, so that the obtained frequency response function is slightly influenced by power frequency interference, and the obtained frequency response function has high precision.
When the input signal and the output signal are acquired in a synchronous mode, the amplitude spectrum and the phase spectrum of the frequency response of the system to be identified can be simultaneously reflected in the acquired frequency response function. The amplitude spectrum of the frequency response reflects the intensity of the response of the system to be identified to the input signal, and the phase spectrum of the frequency response reflects the response of the system to be identified and the time delay of the input signal. The amplitude spectrum and the phase spectrum are included in the frequency response function obtained when the input signal and the output signal are acquired in a synchronous manner.
In the embodiment of the present invention, when the output signal of the system to be identified is acquired in a synchronous manner, the phase spectrum of the frequency response function of the system to be identified can be directly acquired through the following operation of step 205.
Step 205: acquiring a phase spectrum of a frequency response function of a system to be identified according to the cross-power spectrum of the input signal and the cross-power spectrum of the output signal;
wherein, the cross power spectrum of the input signal and the cross power spectrum of the output signal can be directly calculated from S1 and S2 in step 204.
Specifically, the phase spectrum of the frequency response function of the system to be identified is obtained through the following formula (2) according to the cross-power spectrum of the input signal and the cross-power spectrum of the output signal.
Wherein in formula (2), mod is the modulo operator,the phase of the cross-power spectrum of the output signal corresponding to frequency omega,the phase of the cross-power spectrum of the input signal corresponding to frequency omega,is the phase spectrum of the frequency response function of the system to be identified.
After the amplitude spectrum and the phase spectrum of the frequency response function of the system to be identified are obtained through the operations of the above-mentioned step 201 and 205, the system characteristics, the medium composition, and the like of the system to be identified can be analyzed according to the frequency response function of the system to be identified. Because the precision of the amplitude spectrum and the phase spectrum of the frequency response function obtained in the embodiment of the invention is very high, the error of analyzing the system to be identified according to the frequency response function is very small.
In the embodiment of the invention, when the system to be identified is a to-be-detected ground system, the obtained frequency response function is an impedance spectrum of the ground, inversion calculation is carried out by using the impedance spectrum to obtain the ground electric section of the to-be-detected ground system, and the electromagnetic exploration parameters of the to-be-detected ground system are calculated according to the frequency response function, wherein the electromagnetic exploration parameters can be step response, complex resistivity, percentage frequency effect, late apparent resistivity and the like.
Specifically, the amplitude spectrum and the phase spectrum of the frequency response function of the earth system to be detected, which are identified, reflect impedance information of the earth system, and inversion calculation is performed by using the amplitude spectrum and the phase spectrum to obtain the earth electric section of the earth system to be detected. And deriving the complex resistivity of the earth system to be identified by the following formula (7), and deriving the percentage frequency effect of the earth system to be identified by the following formula (8). And calculating the step response of the earth system to be detected according to the frequency response function, and calculating the late apparent resistivity of the earth system to be identified according to the late progressive value of the step response.
ρ(ω)＝KZ(ω)…(7)
In formula (7), ρ (ω) is complex resistivity, K is device coefficient, and Z (ω) is magnitude spectrum of the earth system to be identified. In equation (8), PFE is the percentage frequency effect, Z (ω)L) For low frequency spot amplitude, Z (omega)H) Is the high frequency spot amplitude.
When the signal acquisition equipment receives the output signal of the system to be identified, the signal acquisition equipment also responds to the output signal, namely, the signal acquisition equipment also has frequency response, and the frequency response can reduce the accuracy of the acquired frequency response function of the system to be identified. Therefore, in the embodiment of the invention, the frequency response value of the signal acquisition equipment is always 1 by applying the technical method of the invention to the signal acquisition equipment for pre-calibration and debugging, so that the influence of the frequency response of the signal acquisition equipment is eliminated. Therefore, the frequency response obtained in the embodiment of the invention is only the frequency response of the system to be identified, the accuracy of the frequency response function is very high, and the frequency resolution is very high.
In the embodiment of the invention, because the input signal is an inverse repetition M sequence, the frequency spectrum of the input signal comprises a plurality of signals with discrete frequencies, the condition that a plurality of single-frequency signals are input in sequence is avoided, and the efficiency of acquiring the frequency response function is improved. The reference signal, the output signal and the input signal are respectively subjected to circular cross correlation, so that the precision of the frequency response function is high, the period of the input signal and the reference signal is even times of the power frequency period, and the power frequency interference can be effectively suppressed.
Example 3
The embodiment of the invention provides a method for acquiring a frequency response function of a system to be identified, which can be executed by a device for acquiring the frequency response function of the system to be identified.
The system to be identified is a circuit system, an observation instrument system or a ground system to be detected. Because the system to be identified comprises media with different conductivity and magnetic conductivity, an input signal is input into the system to be identified, and the system to be identified responds to the input signal due to the electromagnetic induction. In the embodiment of the invention, the output signal output by the system to be identified is acquired in an asynchronous mode, and the amplitude spectrum of the frequency response function of the system to be identified is acquired by the method provided by the embodiment of the invention.
Referring to fig. 3, the method specifically includes the following steps:
step 301: the operation is the same as that in step 201, and is not described herein again;
step 302: inputting the input signal to a system to be identified, and acquiring an output signal output by the system to be identified in an asynchronous mode;
the asynchronous mode is that the time points of the input signal and the output signal of the system to be identified can be different, but the sampling rate is the same.
Step 303: the operation is the same as that in step 203, and is not described herein again;
step 304: and applying a cross-correlation theory to the reference signal, the input signal and the output signal to obtain a frequency response function of the system to be identified.
The specific manner of obtaining the frequency response function is the same as the operations of S1-S4 in step 204. It should be noted that, when the input signal and the output signal are acquired in an asynchronous manner, the delay time between the acquisition of the output signal and the acquisition of the input signal is uncertain, and therefore, in the asynchronous manner, the acquired frequency response function cannot reflect the delay time between the response output of the system to be identified and the input signal, that is, the frequency response function acquired in the asynchronous manner only includes an amplitude spectrum and does not include a phase spectrum.
In the embodiment of the invention, because the input signal is an inverse repetition M sequence, the frequency spectrum of the input signal comprises a plurality of signals with discrete frequencies, the condition that a plurality of single-frequency signals are input in sequence is avoided, and the efficiency of acquiring the frequency response function is improved. The reference signal, the output signal and the input signal are respectively subjected to circular cross correlation, so that the precision of the frequency response function is high, the period of the input signal and the reference signal is even times of the power frequency period, and the power frequency interference can be effectively suppressed.
Example 4
Referring to fig. 4, an embodiment of the present invention provides an apparatus for obtaining a frequency response function of a system to be identified, where the apparatus is configured to perform the above method for obtaining a frequency response function of a system to be identified. The device specifically includes:
the generating module 401 is configured to trigger the linear feedback shift register to generate an input signal through a clock signal, and trigger a software program to generate a reference signal according to a time sequence period and a sampling rate of the input signal, where the input signal and the reference signal are both an inverse repeating M sequence, and the same period is even times of a power frequency period;
an acquisition module 402, configured to input the input signal to the system to be identified, and acquire an output signal output by the system to be identified;
an obtaining module 403, configured to apply a cross-correlation theory to the reference signal, the input signal, and the output signal, and obtain a frequency response function of the system to be identified.
Wherein, the obtaining module 403 includes:
the cyclic cross-correlation unit is used for performing cyclic cross-correlation on the output signal and the input signal and the reference signal respectively to obtain a cross-correlation time sequence corresponding to the output signal and a cross-correlation time sequence corresponding to the input signal;
the fast Fourier transform unit is used for respectively carrying out fast Fourier transform on the cross-correlation time sequence corresponding to the output signal and the cross-correlation time sequence corresponding to the input signal to obtain a cross-power spectrum of the output signal and a cross-power spectrum of the input signal;
the first obtaining unit is used for obtaining a frequency response function of the system to be identified according to the cross-power spectrum of the output signal and the cross-power spectrum of the input signal.
Wherein, the first acquisition unit includes:
the acquisition subunit is used for acquiring an output spectral line peak value and a frequency value corresponding to the output spectral line peak value from the cross-power spectrum of the output signal, and acquiring an input spectral line peak value and a frequency value corresponding to the input spectral line peak value from the cross-power spectrum of the input signal;
the calculating subunit is used for screening an output spectral line peak value and an input spectral line peak value with the same frequency value from the obtained output spectral line peak value and the obtained input spectral line peak value, and calculating the ratio of the output spectral line peak value and the input spectral line peak value with the same frequency value through the following formula (1) to obtain a frequency response function of the system to be identified;
wherein in the formula (1), ω is a frequency value,is the peak value of the output spectral line corresponding to the frequency value omega,is the peak value of the input spectral line corresponding to the frequency value omega, and H (omega) is the frequency response function of the system to be identified.
The acquisition module 402 is configured to input an input signal to the system to be identified, and acquire an output signal output by the system to be identified in a synchronous manner or an asynchronous manner;
correspondingly, the obtaining module 403 includes:
the second acquisition unit is used for acquiring a frequency response function of the system to be identified according to the cross-power spectrum of the output signal and the cross-power spectrum of the input signal when the output signal is acquired in an asynchronous mode, wherein the frequency response function comprises an amplitude spectrum;
a third obtaining unit, configured to obtain, when the output signal is collected in a synchronous manner, a frequency response function of the system to be identified according to a cross-power spectrum of the output signal and a cross-power spectrum of the input signal, where the frequency response function includes a phase spectrum and a magnitude spectrum, and obtain a phase spectrum of the frequency response function of the system to be identified by using the following formula (2);
wherein in formula (2), mod is the modulo operator,the phase of the cross-power spectrum of the output signal corresponding to frequency omega,the phase of the cross-power spectrum of the input signal corresponding to frequency omega,is the phase spectrum of the frequency response function of the system to be identified.
Further, the apparatus further comprises:
the calculating module 404 is configured to perform inversion calculation on the frequency response function when the system to be identified is the geodetic system to be detected, obtain the geodetic section of the geodetic system to be detected, and calculate the electromagnetic exploration parameters of the geodetic system to be detected according to the frequency response function, where the electromagnetic exploration parameters include step response, complex resistivity, percentage frequency effect, and late apparent resistivity.
In the embodiment of the invention, because the input signal is an inverse repetition M sequence, the frequency spectrum of the input signal comprises a plurality of signals with discrete frequencies, the condition that a plurality of single-frequency signals are input in sequence is avoided, and the efficiency of acquiring the frequency response function is improved. The reference signal, the output signal and the input signal are respectively subjected to circular cross correlation, so that the precision of the frequency response function is high, the period of the input signal and the reference signal is even times of the power frequency period, and the power frequency interference can be effectively suppressed.
The device for acquiring the frequency response function of the system to be identified provided by the embodiment of the invention can be specific hardware on equipment or software or firmware installed on the equipment and the like. It will be clear to those skilled in the art that for convenience and brevity of description, the specific operations of the system, apparatus and unit described above may all refer to corresponding processes in the above described method embodiments.
In the several embodiments provided in the present application, it should be understood that the disclosed apparatus and method may be implemented in other ways. The above-described embodiments of the apparatus are merely illustrative, and for example, the division of the units is only one logical division, and there may be other divisions when actually implemented, and for example, a plurality of units or components may be combined or integrated into another system, or some features may be omitted, or not executed. In addition, the shown or discussed mutual coupling or direct coupling or communication connection may be an indirect coupling or communication connection of devices or units through some communication interfaces, and may be in an electrical, mechanical or other form.
The units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of the embodiment.
In addition, functional units in the embodiments of the present invention may be integrated into one processing unit, or each unit may exist alone physically, or two or more units are integrated into one unit.
The functions, if implemented in the form of software functional units and sold or used as a stand-alone product, may be stored in a computer readable storage medium. Based on such understanding, the technical solution of the present invention may be embodied in the form of a software product, which is stored in a storage medium and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk or an optical disk, and other various media capable of storing program codes.
The above description is only for the specific embodiments of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can easily conceive of the changes or substitutions within the technical scope of the present invention, and all the changes or substitutions should be covered within the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (10)
1. A method for obtaining a frequency response function of a system to be identified, the method comprising:
triggering a linear feedback shift register through a clock signal to generate an input signal, and triggering a software program to generate a reference signal according to the time sequence period and the sampling rate of the input signal, wherein the input signal and the reference signal are both inverse repetitive M sequences, and the periods of the input signal and the reference signal are both even multiples of a power frequency period;
inputting the input signal to a system to be identified, and collecting an output signal output by the system to be identified;
and applying a cross-correlation theory to the reference signal, the input signal and the output signal to obtain a frequency response function of the system to be identified.
2. The method of claim 1, wherein the applying cross-correlation theory to the reference signal, the input signal and the output signal to obtain the frequency response function of the system to be identified comprises:
performing circular cross correlation on the output signal and the input signal with the reference signal respectively to obtain a cross correlation time sequence corresponding to the output signal and a cross correlation time sequence corresponding to the input signal;
performing fast Fourier transform on the cross-correlation time sequence corresponding to the output signal and the cross-correlation time sequence corresponding to the input signal respectively to obtain a cross-power spectrum of the output signal and a cross-power spectrum of the input signal;
and acquiring a frequency response function of the system to be identified according to the cross-power spectrum of the output signal and the cross-power spectrum of the input signal.
3. The method of claim 2, wherein obtaining the frequency response function of the system to be identified according to the cross-power spectrum of the output signal and the cross-power spectrum of the input signal comprises:
acquiring an output spectral line peak value and a frequency value corresponding to the output spectral line peak value from the cross-power spectrum of the output signal, and acquiring an input spectral line peak value and a frequency value corresponding to the input spectral line peak value from the cross-power spectrum of the input signal;
screening an output spectral line peak value and an input spectral line peak value with the same frequency value from the obtained output spectral line peak value and the obtained input spectral line peak value, and calculating the ratio of the output spectral line peak value and the input spectral line peak value with the same frequency value through the following formula (1) to obtain a frequency response function of the system to be identified;
wherein in the formula (1), ω is a frequency value,is the peak value of the output spectral line corresponding to the frequency value omega,is the peak value of the input spectral line corresponding to the frequency value omega, and H (omega) is the frequency response function of the system to be identified.
4. The method of claim 2, wherein the inputting the input signal to the system to be recognized and the collecting the output signal output by the system to be recognized comprises:
inputting the input signal to the system to be identified, and acquiring an output signal output by the system to be identified in a synchronous mode or an asynchronous mode;
correspondingly, the applying a cross-correlation theory to the reference signal, the input signal and the output signal to obtain a frequency response function of the system to be identified includes:
when the output signal is acquired in the asynchronous mode, acquiring a frequency response function of the system to be identified according to the cross-power spectrum of the output signal and the cross-power spectrum of the input signal, wherein the frequency response function comprises an amplitude spectrum;
when the output signals are acquired in the synchronous mode, acquiring a frequency response function of the system to be identified according to the cross-power spectrum of the output signals and the cross-power spectrum of the input signals, wherein the frequency response function comprises a phase spectrum and a magnitude spectrum, and acquiring the phase spectrum of the frequency response function of the system to be identified through the following formula (2);
wherein in formula (2), mod is the modulo operator,the phase of the cross-power spectrum of the output signal corresponding to frequency omega,the phase of the cross-power spectrum of the input signal corresponding to frequency omega,is the phase spectrum of the frequency response function of the system to be identified.
5. The method according to any one of claims 1-4, wherein after obtaining the frequency response function of the system to be identified, the method further comprises:
and when the system to be identified is the earth system to be detected, carrying out inversion calculation on the frequency response function to obtain the earth electric section of the earth system to be detected, and calculating the electromagnetic exploration parameters of the earth system to be detected according to the frequency response function, wherein the electromagnetic exploration parameters comprise step response, complex resistivity, percentage frequency effect and late apparent resistivity.
6. An apparatus for obtaining a frequency response function of a system to be identified, the apparatus comprising:
the generating module is used for triggering the linear feedback shift register through a clock signal to generate an input signal, and triggering a software program to generate a reference signal according to the time sequence period and the sampling rate of the input signal, wherein the input signal and the reference signal are both inverse repeated M sequences, and the same period is even times of a power frequency period;
the acquisition module is used for inputting the input signal to a system to be identified and acquiring an output signal output by the system to be identified;
and the acquisition module is used for applying a cross-correlation theory to the reference signal, the input signal and the output signal to acquire a frequency response function of the system to be identified.
7. The apparatus of claim 6, wherein the obtaining module comprises:
a circular cross-correlation unit, configured to perform circular cross-correlation on the output signal and the input signal with the reference signal, respectively, to obtain a cross-correlation time sequence corresponding to the output signal and a cross-correlation time sequence corresponding to the input signal;
a fast fourier transform unit, configured to perform fast fourier transform on the cross-correlation time sequence corresponding to the output signal and the cross-correlation time sequence corresponding to the input signal, respectively, to obtain a cross-power spectrum of the output signal and a cross-power spectrum of the input signal;
and the first acquisition unit is used for acquiring the frequency response function of the system to be identified according to the cross-power spectrum of the output signal and the cross-power spectrum of the input signal.
8. The apparatus of claim 7, wherein the first obtaining unit comprises:
the acquisition subunit is used for acquiring an output spectral line peak value and a frequency value corresponding to the output spectral line peak value from the cross-power spectrum of the output signal, and acquiring an input spectral line peak value and a frequency value corresponding to the input spectral line peak value from the cross-power spectrum of the input signal;
the calculating subunit is used for screening an output spectral line peak value and an input spectral line peak value with the same frequency value from the obtained output spectral line peak value and the obtained input spectral line peak value, and calculating a ratio between the output spectral line peak value and the input spectral line peak value with the same frequency value through a formula (1) to obtain a frequency response function of the system to be identified;
wherein in the formula (1), ω is a frequency value,is the peak value of the output spectral line corresponding to the frequency value omega,is the peak value of the input spectral line corresponding to the frequency value omega, and H (omega) is the frequency response function of the system to be identified.
9. The device of claim 7, wherein the collecting module is configured to input the input signal to the system to be recognized and collect an output signal output by the system to be recognized in a synchronous manner or an asynchronous manner;
correspondingly, the obtaining module comprises:
the second acquisition unit is used for acquiring a frequency response function of the system to be identified according to the cross-power spectrum of the output signal and the cross-power spectrum of the input signal when the output signal is acquired in the asynchronous mode, wherein the frequency response function comprises a magnitude spectrum;
a third obtaining unit, configured to, when the output signal is collected in the synchronous manner, obtain a frequency response function of the system to be identified according to a cross-power spectrum of the output signal and a cross-power spectrum of the input signal, where the frequency response function includes a phase spectrum and a magnitude spectrum, and obtain a phase spectrum of the frequency response function of the system to be identified by using the following formula (2);
wherein in formula (2), mod is the modulo operator,the phase of the cross-power spectrum of the output signal corresponding to frequency omega,the phase of the cross-power spectrum of the input signal corresponding to frequency omega,is the phase spectrum of the frequency response function of the system to be identified.
10. The apparatus according to any one of claims 6-9, further comprising:
and the calculating module is used for performing inversion calculation on the frequency response function when the system to be identified is a to-be-detected geodetic system, acquiring the geodetic section of the to-be-detected geodetic system, and calculating the electromagnetic exploration parameters of the to-be-detected geodetic system according to the frequency response function, wherein the electromagnetic exploration parameters comprise step response, complex resistivity, percentage frequency effect and late apparent resistivity.
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