CN116482767A - Multi-frequency SPWM high-precision frequency domain electromagnetic sounding excitation method - Google Patents
Multi-frequency SPWM high-precision frequency domain electromagnetic sounding excitation method Download PDFInfo
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Abstract
The invention belongs to the field of electromagnetic detection of magnetic source frequency domain in geophysical detection, in particular to a multi-frequency SPWM high-precision frequency domain electromagnetic sounding excitation method, which designs frequency spectrum, amplitude spectrum and phase spectrum of a multi-frequency SPWM excitation signal and a multi-frequency excitation current signal and determines a multi-frequency sinusoidal modulation signal u m Based on a regular sampling method, the signal u is modulated by multi-frequency sine m For bipolar triangular carrier u c The drive control circuit outputs a drive control signal s of the H-bridge transmitting circuit 1 Sum s 2 The method comprises the steps of carrying out a first treatment on the surface of the In the drive control signal s 1 Sum s 2 Under the action of the device, the transmitting voltage of the H-bridge transmitting circuit is a multi-frequency SPWM excitation signal, the transmitting current in the transmitting coil is a multi-frequency excitation current signal, and the transmitting current comprises all required main frequency points, so that the high-precision electromagnetic sounding of the investigation target area can be finished, and the defects of fixed main frequency point interval and low detection efficiency of the multi-frequency pseudo-random excitation signal are overcome, therebyAnd the disadvantage that the electromagnetic sounding excitation signal based on SHEPWM has large calculated amount and cannot be controlled in real time on the exploration site.
Description
Technical Field
The invention belongs to the field of electromagnetic detection of a magnetic source frequency domain of geophysical detection, and particularly relates to a multi-frequency SPWM high-precision frequency domain electromagnetic sounding excitation method suitable for electromagnetic sounding of a high-precision magnetic source frequency domain.
Background
With the continuous development of energy and mineral resources, the resources which are easy to be picked and detected are reduced year by year, and a high-efficiency and high-precision detection method aiming at extremely severe environments has become an important research direction in the field of geophysical exploration. The magnetic source frequency domain electromagnetic method is an important geophysical detection method and is widely applied to aspects such as geological investigation, environmental evaluation and the like in China. In the detection experiment, a high-frequency excitation current signal is injected into a transmitting coil through a transmitting system to serve as an excitation source, and an electromagnetic field response signal is induced to the ground according to an electromagnetic induction principle and is collected by a receiving system. According to the electromagnetic response signal generated by the specific excitation signal source, the earth resistivity distribution can be obtained by analyzing the earth, so that the geological structure can be deduced and the position of the abnormal body can be determined. As a source of electromagnetic method detection, the waveform quality of the excitation signal plays a vital role in detecting whether an experiment is successful or not. According to the frequency domain electromagnetic detection principle and the skin effect, the excitation current signals with different frequencies can detect the electrical information of the stratum with different depths, and the electromagnetic detection in the depth range corresponding to the earth can be completed by transmitting the excitation current signals with different frequencies in a certain range. In a high-precision electromagnetic sounding experiment, in order to ensure high longitudinal detection resolution of a detection target area, the frequency spectrum design of an excitation current signal needs to be completed, so that all main frequency points of the excitation signal are distributed in an effective frequency band corresponding to the depth range of the detection target area, and the expected frequency point distribution is met. In addition, on the premise that the total energy of the excitation signal is certain, the energy is concentrated on the effective main frequency points, the energy among the main frequency points is uniformly distributed, and the resolution capability of an abnormal body is improved.
In a high-precision frequency domain electromagnetic sounding experiment, a traditional detection method adopts a single-frequency excitation current signal as an excitation source, and the test of frequency points required in an effective frequency band one by one is completed in a sweep frequency mode. However, multiple experimental tests can reduce the detection efficiency and improve the detection cost, and the magnetotelluric characteristics and the environmental noise can be different due to different test time of different frequency points, so that the detection precision is reduced. The multi-frequency electromagnetic excitation method can effectively solve the problem of low detection efficiency of a single-frequency point frequency sweeping mode, and the multi-frequency pseudo-random method proposed by the university of south China He Jishan institution is most commonly adopted in China. The multi-frequency pseudo-random signal comprises a plurality of available frequency points with higher energy, all the frequency points are uniformly distributed on a logarithmic coordinate, the frequency points are fixed at intervals, and the ground electric response information of a plurality of effective main frequency points can be obtained by transmitting an excitation signal once during detection, so that the detection efficiency is improved. In a high-precision electromagnetic sounding experiment, resistivity imaging is required to be performed on a longitudinal section of a specific depth range of a investigation target area, main emission frequency points are required to be distributed in an effective narrow frequency band and are distributed specifically, main frequency points of the multi-frequency pseudorandom signals are at fixed intervals, in order to completely cover all required frequency points in the narrow frequency band, multiple experiments are usually required to be performed by setting different pseudorandom signal fundamental frequencies, and detection efficiency is low. In addition, low-order harmonics exist near each main frequency point in the pseudo-random signal, so that analysis and processing difficulties of later-stage electric response information are increased. In the CN108427145A patent, a SHEPWM-based earth-space frequency domain electromagnetic sounding excitation method is provided, and the multi-frequency excitation voltage signal containing expected main frequency is obtained by calculating the switching time of each switching device in a transmitting circuit, so that the random distribution of the frequency, amplitude and phase parameters of each main frequency point is realized, and the flexibility is high. However, since a complex nonlinear transcendental equation set needs to be solved by a computer, a lot of time is consumed, and when the required main frequency parameter changes, recalculation is required. Because the method cannot be realized in a singlechip controller, in a field exploration site, parameters of all main frequency points cannot be adjusted in real time according to detection environments, and the method is difficult to adapt to severe exploration environments with time-varying ground electric parameters such as medium resistivity and the like, and has certain limitation on practicality.
Disclosure of Invention
The technical problem to be solved by the invention is to provide the multi-frequency SPWM high-precision frequency domain electromagnetic sounding excitation method, wherein the multi-frequency SPWM excitation signal comprises a plurality of effective frequency points, and the random setting of the number, the amplitude and the distribution of the main frequency points in a specific frequency band can be realized. The calculated amount is small, and the main frequency point parameters can be adjusted in the controller in real time aiming at the changed environment in the field exploration experiment, so that the electromagnetic sounding experiment with high efficiency and high precision is realized. The defects that the main frequency point interval of the multi-frequency pseudo-random excitation signal is fixed, the detection efficiency is low, and the electromagnetic sounding excitation signal based on SHEPWM has large calculated amount and cannot be controlled in real time on the exploration site are overcome.
The present invention has been achieved in such a way that,
a multi-frequency SPWM high-precision frequency domain electromagnetic sounding excitation method comprises the following steps:
step 1: determining a multi-frequency SPWM excitation signal expression according to a multi-frequency SPWM electromagnetic sounding emission system structure and a multi-frequency sinusoidal pulse width modulation principle;
step 2: depth range D according to investigation target region H ～D L And determining the frequency band range f of the effective main frequency point of the multi-frequency excitation current signal by a skin depth formula L ～f H According to the requirement of longitudinal detection resolution of the investigation target area, determining the number N of main frequencies of the emission current and the distribution of main frequency points, and completing the frequency spectrum design of the multi-frequency SPWM excitation signals and the multi-frequency excitation current signals;
step 3: make each main frequency point amplitude B of multi-frequency excitation current i Equal, combining the energy conservation law and the requirement of electromagnetic sounding experiment on the signal to noise ratio, calculating the amplitude A of each component of the multi-frequency sinusoidal synthesis signal i Determining the amplitude MEA of each main frequency point of the multi-frequency SPWM excitation signal i And the amplitude B of each main frequency point of the multi-frequency excitation current signal i Completing the amplitude spectrum design of the multi-frequency SPWM excitation signal and the multi-frequency excitation current signal;
step 4: based on the determined frequency spectrum and amplitude spectrum of the multi-frequency excitation current signalPhase combination θ= [ θ ] of sinusoidal components of frequency excitation current 1 θ 2 … θ N ] T As an independent variable, the optimal solution theta '= [ theta ] of the phase combination is determined by an iteration method with the aim of minimizing the crest factor CF of the multi-frequency excitation current signal' 1 θ′ 2 … θ′ N ] T Calculating the phase of each required main frequency point of the multi-frequency SPWM excitation signalCompleting the phase spectrum design of the multi-frequency SPWM excitation signal and the multi-frequency excitation current signal;
step 5: according to the frequency spectrum f of the multi-frequency SPWM excitation signal 1 ,f 2 ,…,f N Amplitude spectrum MEA 1 ,MEA 2 ,…,MEA N And phase spectrumDetermining a multi-frequency sinusoidal modulation signal u m An expression;
step 6: inside the drive control circuit, based on a regular sampling method, the signal u is modulated by a multi-frequency sine m For bipolar triangular carrier u c The drive control circuit outputs a drive control signal s of the H-bridge transmitting circuit 1 Sum s 2 ；
Step 7: in the drive control signal s 1 Sum s 2 Under the action of the electromagnetic sounding device, the transmitting voltage of the H-bridge transmitting circuit is a multi-frequency SPWM excitation signal, the transmitting current in the transmitting coil is a multi-frequency excitation current signal, and the transmitting current comprises all required main frequency points, so that the high-precision electromagnetic sounding of the investigation target area can be completed.
Further, step 2 specifically includes: according to the depth range of the investigation target area, determining the frequency band range of the effective main frequency point of the multi-frequency excitation current signal by using a skin depth formula (1):
where δ represents the depth of investigation, ρ represents the measured area medium resistivity, f represents the excitation signal frequency,
let the depth range of the investigation target be the shallow depth D L To depth D of deep layer H According to the skin depth formula, shallow depth D L Corresponding to the high frequency point f H Shallow depth D H Corresponding to the low frequency point f L The effective frequency band required by the exploration target area is f L ～f H And combining the requirement of the investigation target area on the longitudinal detection resolution, and determining the number N of required main frequencies and the distribution of main frequency points in an effective frequency band.
Further, the step 3 specifically includes:
after applying a multi-frequency SPWM excitation voltage signal across the transmit coil, a multi-frequency excitation current is generated in the coil. The transmission coil equivalent impedance expression is:
Z(ω)＝R+jωL
wherein R and L are respectively equivalent resistance and equivalent inductance of the transmitting coil;
transmitting a voltage U in the frequency domain out And emission current I out The relation of (2) is:
the time domain expression of the multi-frequency excitation current signal is:
wherein B is i And theta i The amplitude and the phase of the ith main frequency component in the multi-frequency excitation current signal are respectively, and the amplitude B i And phase theta i The expressions of (2) are respectively:
make moreAmplitude B of each main frequency point of the frequency excitation current i Are all equal, i.e. B 1 ＝B 2 ＝…＝B N The amplitudes of the sinusoidal components in the multi-frequency sinusoidal composite signal satisfy:
for the ith dominant frequency point in the multi-frequency excitation current signal, if omega i L is more than or equal to 10R, the main frequency point is considered to be high frequency, and the high frequency angular frequency omega is recorded H When ω is =10r/L i ≥ω H When the impedance of the transmitting coil is equal to the inductive reactance omega i L plays a main role, the impedance of the transmitting coil ignores the resistance R; when omega i ＜ω H When the resistance R in the impedance of the transmitting coil plays a main role, the impedance of the transmitting coil can neglect the inductance omega i L, combining the formula of the amplitude of each sinusoidal component in the multi-frequency sinusoidal synthesis signal, wherein the amplitude relation of each sinusoidal component in the multi-frequency sinusoidal synthesis signal is expressed as
According to the condition that the amplitude of each main frequency voltage in the multi-frequency SPWM excitation signal should meet and the multi-frequency sinusoidal synthesis signal u s The amplitude of each sinusoidal component in the multi-frequency sinusoidal synthesis signal meets the constraint condition and the detection precision requirement of the electromagnetic sounding experiment, and the amplitude A of each sinusoidal component in the multi-frequency sinusoidal synthesis signal is determined i At this time, the expression of the signal is excited by the multi-frequency SPWMAnd a multi-frequency sinusoidal synthesis signal u s The amplitude value MEA of each main frequency point of the multi-frequency SPWM excitation signal can be determined by meeting constraint conditions i Amplitude B of each main frequency point of multi-frequency excitation current i
Further, the method comprises the steps of,
step 4, solving the phase combination theta by adopting an iteration method, wherein the solving target is that the crest factor CF is minimum, and firstly, the phase combination theta is calculated in [0,2 pi ]]N angle values are taken as initial values of phase combination theta at equal intervalsSolving a phase combination by using fminesearch function in Matlab to obtain a phase combination initial value of theta (0) Optimal solution at timeSum crest factor CF (1) The phase combination theta after once solving (1) As a new initial value, the fminesearch function is called again to solve the phase combination, so that the phase combination theta is solved iteratively in this way, and after S fminesearch functions are called, the phase combination +.>Sum crest factor CF (S) When the number S of times of calling fminesearch function is greater than 50 or the crest factor CF (S) When the value is equal to or smaller than the set value, the optimal solution θ '= [ θ ]' 1 θ′ 2 … θ′ N ] T For the final solution result, θ ' = [ θ ' ] is combined according to the phase ' 1 θ′ 2 … θ′ N ] T Combined with phase theta i The expression of (2) can be used for dividing the phase of each main frequency point of the multi-frequency SPWM excitation signal>And completing the phase spectrum design of the multi-frequency SPWM excitation signal and the multi-frequency excitation current signal.
Further, the expression of the multifrequency SPWM excitation signal is:
wherein u is out For the transmitting voltage, M is the modulation depth, E is the DC power supply voltage, A i Amplitude of each component of the multi-frequency sinusoidal synthesis signal, f i For the frequency of the components of the multi-frequency sinusoidal synthesis signal, < >>The phases of the components of the signal are synthesized for the multi-frequency sinusoids.
Further, a multi-frequency sinusoidal modulation signal u m The expression is:
compared with the prior art, the invention has the beneficial effects that: the invention provides a multi-frequency SPWM electromagnetic sounding excitation method based on sinusoidal pulse width modulation (Sinusoidal pulse width modulation, SPWM) technology. The multi-frequency SPWM excitation signal comprises a plurality of effective frequency points, and can realize any setting of the number, the amplitude and the distribution of the main frequency points in a specific frequency band. The calculated amount is small, and the main frequency point parameters can be adjusted in the controller in real time aiming at the changed environment in the field exploration experiment, so that the electromagnetic sounding experiment with high efficiency and high precision is realized. The defects of fixed frequency interval and low detection efficiency of the multi-frequency pseudo-random excitation signal and the defect that the electromagnetic sounding excitation signal based on SHEPWM has large calculated amount and cannot be controlled in real time on the exploration site are overcome.
Drawings
FIG. 1 is a schematic diagram of a multi-frequency SPWM electromagnetic sounding emission system according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a principle of multi-frequency sinusoidal pulse width modulation according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of a symmetric rule sampling method for multi-frequency sinusoidal modulation according to an embodiment of the present invention;
FIG. 4 is a model of a double-resistance anomaly even ground provided by an embodiment of the present invention;
FIG. 5a is a graph of a multi-frequency sinusoidal modulation wave versus a triangular carrier wave; FIG. 5b drive control signal s 1 A waveform diagram; FIG. 5c drive control signal s 2 A waveform diagram;
FIG. 6a Multi-frequency SPWM excitation signal time domain information; FIG. 6b is a plot of the time domain information of the multi-frequency excitation current signal; fig. 6c frequency domain information of a multi-frequency excitation current signal.
Detailed Description
The present invention will be described in further detail with reference to the following examples in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
A multi-frequency SPWM high-precision frequency domain electromagnetic sounding excitation method comprises the following steps:
step 1: determining a multi-frequency SPWM excitation signal expression according to a multi-frequency SPWM electromagnetic sounding emission system structure and a multi-frequency sinusoidal pulse width modulation principle;
step 2: depth range D according to investigation target region H ～D L And determining the frequency band range f of the effective main frequency point of the multi-frequency excitation current signal by a skin depth formula L ～f H According to the requirement of longitudinal detection resolution of the investigation target area, determining the number N of main frequencies of the emission current and the distribution of main frequency points, and completing the frequency spectrum design of the multi-frequency SPWM excitation signals and the multi-frequency excitation current signals;
step 3: make each main frequency point amplitude B of multi-frequency excitation current i Equal, combining the energy conservation law and the requirement of electromagnetic sounding experiment on the signal to noise ratio, calculating the amplitude A of each component of the multi-frequency sinusoidal synthesis signal i Determining the amplitude MEA of each main frequency point of the multi-frequency SPWM excitation signal i And the amplitude B of each main frequency point of the multi-frequency excitation current signal i Completing the amplitude spectrum design of the multi-frequency SPWM excitation signal and the multi-frequency excitation current signal;
step 4: combining θ= [ θ ] with the phases of sinusoidal components of the multi-frequency excitation current according to the determined frequency spectrum and amplitude spectrum of the multi-frequency excitation current signal 1 θ 2 … θ N ] T As an independent variable, the optimal solution theta '= [ theta ] of the phase combination is determined by an iteration method with the aim of minimizing the crest factor CF of the multi-frequency excitation current signal' 1 θ′ 2 … θ′ N ] T Calculating the phase of each required main frequency point of the multi-frequency SPWM excitation signalCompleting the phase spectrum design of the multi-frequency SPWM excitation signal and the multi-frequency excitation current signal;
step 5: according to the frequency spectrum f of the multi-frequency SPWM excitation signal 1 ,f 2 ,…,f N Amplitude spectrum MEA 1 ,MEA 2 ,…,MEA N And phase spectrumDetermining a multi-frequency sinusoidal modulation signal u m An expression;
step 6: inside the drive control circuit, based on a regular sampling method, the signal u is modulated by a multi-frequency sine m For bipolar triangular carrier u c The drive control circuit outputs a drive control signal s of the H-bridge transmitting circuit 1 Sum s 2 ；
Step 7: in the drive control signal s 1 Sum s 2 Under the action of the electromagnetic sounding device, the transmitting voltage of the H-bridge transmitting circuit is a multi-frequency SPWM excitation signal, the transmitting current in the transmitting coil is a multi-frequency excitation current signal, and the transmitting current comprises all required main frequency points, so that the high-precision electromagnetic sounding of the investigation target area can be completed.
Wherein, step 1: the structure schematic diagram of the multi-frequency SPWM electromagnetic sounding transmitting system is shown in fig. 1, and the system comprises a direct-current power supply, an H-bridge transmitting circuit, a transmitting coil and a driving control circuit. The voltage of the direct current power supply is E, which is responsible for supplying power to the transmitting circuit. The H-bridge transmitting circuit comprises two bridge arms, and a left bridge arm comprises a switching device V 1 And V 2 The right bridge arm comprises a switching device V 3 And V 4 . Left bridge arm middle switch device V 1 And V 2 Is U, the switching device V in the right bridge arm 3 And V 4 Is V, the transmitting voltage u of the transmitting circuit out The difference between the potentials at points U and V. The transmitting coil is connected in series with an equivalent inductance L and an equivalent resistance R, and the current in the transmitting coil is the transmitting current. Set the emission voltage u out And emission current i out All of which are marked as positive directions from U to V. The driving control circuit is responsible for generating a driving control signal s which can control each switching device of the H-bridge transmitting circuit to work normally 1 Sum s 2 . Switching device V 1 And V 4 Is s as the drive control signal of 1 Switching device V 2 And V 3 Is s as the drive control signal of 2 . Drive control signal s 1 Sum s 2 As complementary signals (without taking into account dead time), when driving the control signal s 1 ＝1，s 2 When=0, switching device V 1 And V 4 On, switching device V 2 And V 3 Turn off, emission voltage u out Is +E; when driving the control signal s 1 ＝0，s 2 When=1, switching device V 1 And V 4 Turn-off, switching device V 2 And V 3 Conduction, emission voltage u out is-E. Inside the drive control circuit, the drive control signal s is generated after the multi-frequency sinusoidal modulation signal and the triangular carrier wave pass through the multi-frequency sinusoidal modulation drive circuit 1 Sum s 2 . In the drive control signal s 1 Sum s 2 Under the action of the voltage u emitted by the output end of the H-bridge emitting circuit out For a multi-frequency SPWM excitation signal, a multi-frequency excitation current is generated in the transmit coil. Let the frequencies required for the electromagnetic sounding experiments of the investigation target area be f respectively 1 ,f 2 ,…,f N . Defining a multi-frequency sinusoidal synthesis signal u s For the combination of the sinusoidal signals of the N frequencies, the expression is:
wherein A is i 、f i 、ω i Amplitude, frequency, phase and angular frequency of the ith component in the multi-frequency sinusoidal composite signal, angular frequency omega i ＝2πf i T is a time variable.
Multi-frequency sinusoidal synthesis signal u s Is satisfied by the amplitude of (a) satisfying the constraint
|u s (t)|≤1 (2)
Multi-frequency sinusoidal modulation signal u m Is a modulation depth M and a multi-frequency sinusoidal synthesis signal u s The product of (a), u m ＝Mu s . The modulation depth M ranges from 0 to 1. The multi-frequency sinusoidal modulation signal u can be adjusted by varying the modulation depth M m Is a function of the amplitude of (a).
Triangular carrier u c Is that the positive peak value is 1, the negative peak value is-1,angular frequency omega c Is a bipolar isosceles triangle wave. To ensure the waveform quality of the multi-frequency excitation current signal, the carrier angular frequency omega c To meet omega c ≥10ω i Where i=1, 2, …, N.
A schematic diagram of the principle of multi-frequency sinusoidal pulse width modulation is shown in fig. 2. In the multi-frequency sine pulse width modulation, a multi-frequency sine modulation signal u m For triangular carrier u c Bipolar modulation is performed. Based on symmetrical rule sampling method, in each carrier period T c In, the multi-frequency sine modulation signal u is at the negative peak time of the triangular carrier m Sampling, namely, taking a sampling value of a multi-frequency sinusoidal modulation signal as a center to guide a horizontal line, intersecting with triangular carriers at two sides, and taking left and right intersection points as primary carrier periods T respectively c Internal drive control signal s 1 Front and rear edges of square wave pulse, for driving control signal s 1 Waveform inversion can obtain driving control signal s 2 At this time, the driving control signal s of the H-bridge transmitting circuit can be obtained in the time domain 1 Sum s 2 . In the drive control signal s 1 Sum s 2 Under the action of the voltage u emitted by the output end of the H-bridge emitting circuit out For a multi-frequency SPWM excitation signal, a transmit current i is generated in the transmit coil out Is a multi-frequency excitation current. By modulating the signal u m The design of (2) can obtain the multi-frequency SPWM excitation signal and multi-frequency excitation current containing the required main frequency information.
And carrying out Fourier analysis on the output voltage in a multi-frequency sinusoidal modulation mode. A schematic diagram of the principle of the multi-frequency sinusoidal modulation symmetric rule sampling method is shown in fig. 3. To simplify the analysis, a sampling point time omega is set c t=0, in one sampling period T s In, alpha 1 And alpha 2 For multi-frequency sinusoidal modulation wave u m Abscissa of horizontal line where sampling value is located and right and left intersection points of triangular carrier, intersection point alpha 1 And alpha 2 The expression of (2) is
In one sampling period T s In, emission voltage u out The expression of (2) is
In accordance with the definition of the Fourier transform formula, the Fourier transform is defined as [ -pi, pi]In, at the angular frequency omega of triangular carrier c As a reference, the emission voltage u out The Fourier series expansion of (2) is as follows
Wherein n is the carrier angular frequency omega c Harmonic order of a 0 ，a n And b n Fourier coefficients for the fundamental and n-th harmonics. According to the definition of the Fourier coefficient and the formula (4), the Fourier coefficient of each subharmonic can be obtained as
Synthesizing a multi-frequency sinusoidal signal u s Expression (1) of (2), intersection point alpha 1 And alpha 2 Substituting the expression (3) of (2) into the fourier coefficient expression (6) can be obtained:
further, the transmission voltage u can be obtained by substituting the Fourier coefficient expression (7) into the Fourier series expression (5) out Further reduction of Fourier series expansion into
In the formula (8), the 1 st item on the right side of the equation is a main frequency component, and comprises all expected main frequency points; the 2 nd harmonic component is generated by modulating the triangular carrier with the multi-frequency sinusoidal modulation signal, and is denoted by the expression H. Expanding H can obtain the following expression
(1) Cos (npi/2) =0 when the carrier harmonic order n is odd, i.e., n=1, 3,5, …. H can be converted into
The identity (11) is obtainable according to the Bessel function of the first kind
Wherein x and beta are variables, J is an imaginary unit, J m The first class of Bessel functions is m times, and m is an integer.
Substituting the multi-frequency sinusoidal synthesis signal expression (1) into the identity (11) can obtain
According to the property of the Bessel function, when m is an integer order, the Bessel function J of the first class is m times m Satisfy the following requirements
J -m (x)＝(-1) m J m (x) (13)
Thus the formula (12) can be converted into
From Euler identity, we can obtain
The combination formula (14) and the formula (15) are that the real part and the imaginary part of the two ends of the formula are respectively equal, and the formula is substituted into the formula (10), the phase of each subharmonic is ignored, and the high-frequency harmonic expression H can be further simplified
Wherein n=1, 3,5, …, k i ＝0,2,4,…，k i Is the kth harmonic of the ith desired dominant frequency bin.
(2) When the carrier harmonic order n is even, i.e., n=2, 4,6, …, sin (npi/2) =0. Neglecting the phase of each subharmonic, the high frequency harmonic expression H can be expressed as
Where n=2, 4,6, …, k i ＝1,3,5,…。
According to the formulas (8), (16) and (17), the angular frequency of each high-frequency harmonic generated by modulating the triangular carrier with the multi-frequency sinusoidal modulation signal isAmplitude is +.>When n=1, 3,5, …, k i =0, 2,4, …; when n=2, 4,6, …, k i ＝1,3,5,…。
According to the Fourier series expansion (8) and the high-frequency harmonic expression (16) and the expression (17) of the multi-frequency SPWM excitation signal, the multi-frequency SPWM excitation signal contains various expected main frequency points. In the effective frequency band corresponding to the detection target area, the amplitudes of the other frequency components are 0 except for each expected main frequency point, and low-order harmonic waves near each expected main frequency point are eliminated through multi-frequency sinusoidal modulation, so that the longitudinal resolution of an electromagnetic sounding experiment can be improved. High-frequency harmonics generated by modulating the carrier wave by the multi-frequency sinusoidal modulation signal are distributed over upper and lower frequency bands at and near the odd-multiple carrier frequency. The frequency of the high frequency harmonic component is high and the amplitude is low compared with the required dominant frequency point. The transmitting coil is inductive, so that the high-frequency harmonic wave has a good inhibition effect, and the influence of the high-frequency harmonic wave on an electromagnetic sounding experiment is almost negligible, so that the expression of the multi-frequency SPWM excitation signal can be simplified into
According to (18), the phase of each main frequency point in the multi-frequency SPWM excitation signalThe voltage amplitude of each main frequency point is MEA (membrane electrode assembly) as same as that of the multi-frequency sinusoidal modulation signal i 。
According to the law of conservation of energy, the total energy of the multi-frequency SPWM excitation signal is the sum of the energy of each main frequency point and the energy of high-frequency harmonic waves. Therefore, the amplitude of each main frequency voltage in the multi-frequency SPWM excitation signal should satisfy
Under the premise of meeting the formula (19) and the constraint condition (2), in the electromagnetic sounding experiment, the amplitude A of each component of the DC power supply voltage E, the modulation depth M and the multi-frequency sinusoidal synthesized signal can be increased according to the detection precision requirement i The energy of each main frequency point of the multi-frequency SPWM excitation signal is improved, and the signal to noise ratio is further improved.
Step 2: in an electromagnetic sounding experiment, a skin depth formula (20) is utilized to determine the frequency band range of the effective main frequency point of the multi-frequency excitation current signal according to the depth range of a survey target area
Where δ represents the depth of investigation, ρ represents the measured area medium resistivity, and f represents the excitation signal frequency.
Let the depth range of the investigation target be the shallow depth D L To depth D of deep layer H According to the skin depth formula, shallow depth D L Corresponding to the high frequency point f H Shallow depth D H Corresponding to the low frequency point f L Desired for exploration of the target areaIs f L ～f H . The number N of the required main frequencies and the distribution of the main frequency points in the effective frequency band can be determined by combining the requirement of the investigation target area on the longitudinal detection resolution.
Step 3:
after applying a multi-frequency SPWM excitation voltage signal across the transmit coil, a multi-frequency excitation current is generated in the transmit coil. The transmission coil equivalent impedance expression is:
Z(ω)＝R+jωL (21)
wherein R and L are the equivalent resistance and the equivalent inductance of the transmitting coil respectively.
Transmitting a voltage U in the frequency domain out And emission current I out Is as follows
According to equation (22), the multi-frequency excitation current is the same as each main frequency point in the multi-frequency SPWM excitation signal in frequency, and the amplitude and phase are different. Thus, the time domain expression of the multi-frequency excitation current signal is
Wherein B is i And theta i The amplitude and the phase of the ith main frequency component in the multi-frequency excitation current signal are respectively. Amplitude B i And phase theta i The expressions of (a) are respectively
According to equation (24), when each main frequency point voltage amplitude MEA in the multi-frequency SPWM excitation signal i At the same time, angular frequency omega i Higher current amplitude B of the dominant frequency component i Lower angular frequency omega i Lower levelCurrent amplitude B of the dominant frequency component of (2) i Higher. It can be seen that the transmitting coil suppresses the high frequency components due to the inductive nature of the transmitting coil. In order to accurately measure the ground electric response information of each required main frequency point, ensure the detection precision of each main frequency point to be the same, the current amplitude B of each expected main frequency point of the multi-frequency excitation current signal needs to be controlled i Approximately equal, so that the energy distribution among the main frequency points of the multi-frequency excitation current signal in the frequency domain is more uniform.
Make each main frequency point amplitude B of multi-frequency excitation current i Are all equal, i.e. B 1 ＝B 2 ＝…＝B N . Combining equation (21) and equation (22) yields a multi-frequency sinusoidal composite signal having sinusoidal components of sufficient amplitude
For the ith dominant frequency point in the multi-frequency excitation current signal, if omega i L is more than or equal to 10R, the main frequency point is considered to be high frequency, and the high frequency angular frequency omega is recorded H =10r/L. When omega i ≥ω H When the impedance of the transmitting coil is equal to the inductive reactance omega i L plays a main role, and the impedance of the transmitting coil can be ignored as the resistance R; when omega i ＜ω H When the resistance R in the impedance of the transmitting coil plays a main role, the impedance of the transmitting coil can neglect the inductance omega i L. In combination (26), the amplitude relationship of the sinusoidal components in the multi-frequency sinusoidal composite signal may be expressed as
According to the requirements of the equation (2) and the equation (19) and the electromagnetic sounding experiment on the detection precision, the amplitude A of each sinusoidal component in the multi-frequency sinusoidal composite signal can be determined i . At this time, the amplitude MEA of each main frequency point of the multi-frequency SPWM excitation signal can be determined by the formulas (18) and (24) i Amplitude B of each main frequency point of multi-frequency excitation current i Thus, the amplitude spectrum design of the multi-frequency SPWM excitation signal and the multi-frequency excitation current signal is completed.
Step 4: in order to avoid the detection precision reduction caused by the aliasing of the ground electric response signals generated by the excitation of a plurality of main frequency points and reduce the requirement of a receiving system on the ground electric response signal acquisition precision, the multi-frequency excitation current signals are uniform in amplitude distribution in a time domain and have few peak pulse numbers. The uniformity of the amplitude distribution of the multi-frequency excitation current signal is measured by a Crest Factor (CF), which is defined as
Wherein i is max 、i min Respectively the emission currents i out Maximum and minimum of (I) eff For transmitting current i out Is effective. The lower crest factor CF indicates that the more uniform the amplitude distribution of the multi-frequency excitation current signal is, the signal to noise ratio can be effectively improved.
Due to the frequency spectrum f of the multifrequency excitation current signal 1 ,f 2 ,…,f N Sum amplitude spectrum B 1 ,B 2 ,…,B N It has been determined that, according to equations (23) and (28), the crest factor CF is calculated by phase combining θ= [ θ ] at each principal frequency point of the multi-frequency excitation current signal 1 θ 2 … θ N ] T As a function of the argument. The invention adopts an iteration method to solve the phase combination theta, and the solving target is that the crest factor CF is minimum. First, at [0,2 pi ]]N angle values are taken as initial values of phase combination theta at equal intervalsAccording to the formulas (23) and (28), solving the phase combination by using the fminesearch function in Matlab to obtain the initial value of the phase combination of theta (0) Optimal solution->Sum crest factor CF (1) . Since the use of fminesearch function may result in a locally optimal solution, the phase after solution is combined with θ (1) As a new initial value, the fminesearch function is called again to solve the phase combination, in this way iteratively solving the phase combination theta,after invoking the fminearch function S times, the phase combination can be obtained>Sum crest factor CF (S) . When the number S of times of calling fminesearch function is greater than 50 or the crest factor CF (S) When the value is equal to or smaller than the set value, the optimal solution θ '= [ θ ]' 1 θ′ 2 … θ′ N ] T In order to finally solve the result, the crest factor of the multi-frequency excitation current signal is low, the current amplitude is uniformly distributed in the time domain, and the signal to noise ratio is improved. According to the phase combination θ '= [ θ ]' 1 θ′ 2 … θ′ N ] T The phase of each main frequency point of the multi-frequency SPWM excitation signal can be combined with (25)>The phase spectrum design of the multi-frequency SPWM excitation signal and the multi-frequency excitation current signal is completed.
Step 5: according to the designed frequency spectrum f of the multi-frequency SPWM excitation signal 1 ,f 2 ,…,f N Amplitude spectrum MEA 1 ,MEA 2 ,…,MEA N And phase spectrumCan determine a multi-frequency sinusoidal modulation signal
Step 7: inside the drive control circuit, based on the rule sampling method, the designed multi-frequency sine modulation signal u m For bipolar triangular carrier u c Bipolar modulation is carried out, and a drive control circuit outputs a drive control signal s of an H-bridge transmitting circuit 1 Sum s 2 。
In the drive control signal s 1 Sum s 2 Under the action of the voltage u emitted by the output end of the H-bridge emitting circuit out For a multi-frequency SPWM excitation signal, a transmit current i is generated in the transmit coil out Is a multi-frequency excitation current. Multi-frequency SPWM excitation signal fullA desired frequency spectrum, a magnitude spectrum, and a phase spectrum. The multi-frequency excitation current comprises all required main frequency points, current amplitude is uniformly distributed in a time domain, and energy among all main frequency points is very close, so that the longitudinal detection resolution of an electromagnetic sounding experiment is improved, and the normal implementation of the high-precision electromagnetic sounding experiment is ensured. When the detection requirement is changed, according to the number, the amplitude and the distribution of main frequency points required by actual detection, the corresponding modulation depth M and the amplitude A of the multi-frequency sinusoidal modulation signal can be adjusted in the singlechip controller i Frequency f i And phase ofParameters, the required multi-frequency SPWM excitation signals and multi-frequency excitation currents are obtained, the calculated amount is small, the parameters are easy to adjust, and real-time control of the exploration site can be realized.
Specific examples: in order to test the performance of the multi-frequency SPWM high-precision electromagnetic sounding excitation source, the invention selects a uniformly large double-anomaly model for simulation verification. The burial depths of the anomaly 1 and the anomaly 2 are 125m and 200m respectively, the sizes of anomaly bodies are 50m multiplied by 50m, and the resistivities are 300 omega-m. The resistivity was 50Ω·m in the region of 250m below the surface of the earth to be uniform.
The implementation method of the multi-frequency SPWM high-precision electromagnetic sounding excitation source comprises the following steps:
step 1: determining a multi-frequency SPWM excitation signal expression according to a multi-frequency SPWM electromagnetic sounding emission system structure and a multi-frequency sinusoidal pulse width modulation principle;
step 2: depth range D according to investigation target region H ～D L And determining the frequency band range f of the effective main frequency point of the multi-frequency excitation current signal by a skin depth formula L ～f H According to the requirement of longitudinal detection resolution of the investigation target area, determining the number N of main frequencies of the emission current and the distribution of main frequency points, and completing the frequency spectrum design of the multi-frequency SPWM excitation signals and the multi-frequency excitation current signals;
step 3: make each main frequency point amplitude B of multi-frequency excitation current i Equal, combining the energy conservation law and the requirement of electromagnetic sounding experiment on the signal to noise ratio, calculating each of the multi-frequency sinusoidal synthesis signalsComponent amplitude A i Determining the amplitude MEA of each main frequency point of the multi-frequency SPWM excitation signal i And the amplitude B of each main frequency point of the multi-frequency excitation current signal i Completing the amplitude spectrum design of the multi-frequency SPWM excitation signal and the multi-frequency excitation current signal;
step 4: combining θ= [ θ ] with the phases of sinusoidal components of the multi-frequency excitation current according to the determined frequency spectrum and amplitude spectrum of the multi-frequency excitation current signal 1 θ 2 … θ N ] T As an independent variable, the optimal solution theta '= [ theta ] of the phase combination is determined by an iteration method with the aim of minimizing the crest factor CF of the multi-frequency excitation current signal' 1 θ′ 2 … θ′ N ] T Calculating the phase of each required main frequency point of the multi-frequency SPWM excitation signalCompleting the phase spectrum design of the multi-frequency SPWM excitation signal and the multi-frequency excitation current signal;
step 5: according to the frequency spectrum f of the multi-frequency SPWM excitation signal 1 ,f 2 ,…,f N Amplitude spectrum MEA 1 ,MEA 2 ,…,MEA N And phase spectrumDetermining a multi-frequency sinusoidal modulation signal u m An expression;
step 6: inside the drive control circuit, based on a regular sampling method, the signal u is modulated by a multi-frequency sine m For bipolar triangular carrier u c Outputs a drive control signal s of an H-bridge transmitting circuit 1 Sum s 2 ；
Step 7: in the drive control signal s 1 Sum s 2 Under the action of the device, the transmitting voltage of the H-bridge transmitting circuit is a multi-frequency SPWM excitation signal, the transmitting current in the transmitting coil is a multi-frequency excitation current signal, the transmitting current comprises all required main frequency points, no low-frequency harmonic wave exists except the expected main frequency, the energy distribution among all main frequency points of the transmitting current is uniform, and the high-precision sounding experiment of the investigation target area can be completed.
The step 1 is that according to the multi-frequency SPWM modulation principle, the expression of the multi-frequency SPWM excitation signal is as follows
And step 2, as shown in fig. 4, determining the frequency band range, the number N of main frequencies and the distribution of the main frequency points of the effective main frequency points of the multi-frequency excitation current signals of the uniform ground double abnormal body model, and completing the frequency spectrum design of the multi-frequency SPWM excitation signals and the multi-frequency excitation current signals. The depth of the anomaly 1 is 125m, the depth of the anomaly 2 is 250m, and the frequency point of the emission current required for detecting the anomaly 1 is 400Hz (corresponding to the depth of 125 m) according to a skin depth formula; the frequency point of the required emission current is 128Hz (corresponding to the depth 225 m), and the effective frequency band range is 128 Hz-400 Hz. And combining the requirement of an electromagnetic sounding experiment on the longitudinal detection resolution, and determining the frequency point of the emission current required for distinguishing the anomaly 1 from the anomaly 2 to be 256Hz (the corresponding depth is 157 m). The number of main frequencies N is 3, and the expected main frequencies are f respectively 1 ＝128Hz、f 2 =256 Hz and f 3 ＝400Hz。
Step 3, according to the determined frequency spectrum of the multi-frequency excitation current signal, making each main frequency point amplitude B of the multi-frequency excitation current i And (3) equivalently, combining the energy conservation law and the requirement of an electromagnetic sounding experiment on the signal to noise ratio, and completing the amplitude spectrum design of the multi-frequency SPWM excitation signal and the multi-frequency excitation current signal. The impedance of the transmitting coil is Z (ω) =r+jωl, the coil equivalent inductance L is 2mH, and the equivalent resistance R is 0.02 Ω. For each desired dominant frequency point f 1 ＝128Hz、f 2 =256 Hz and f 3 =400 Hz, the inductive reactance of the transmitting coil being ω respectively 1 L＝1.61Ω，ω 2 L＝3.22Ω，ω 3 L=5.03 Ω, all having ω i L.gtoreq.10R=0.2Ω (i=1, 2, 3), inductive reactance ω in transmit coil impedance Z (ω) i L plays a major role and the resistance R can be ignored. In the multi-frequency sinusoidal composite signal, the amplitude relation of each sinusoidal component is that
The amplitude of each sinusoidal component satisfies the following energy conservation law
Combining the amplitude constraint of the multi-frequency sinusoidal synthesis signal and the requirement of the sounding experiment on the detection precision, taking the modulation depth M as 0.8, determining the amplitude of the main frequency of each sinusoidal component, A 1 ＝0.2057，A 2 ＝0.4115，A 3 = 0.6429. The direct-current power supply voltage E is 10V, and each main frequency amplitude value MEA of the multi-frequency SPWM excitation voltage signal is determined 1 ＝1.6459V，MEA 2 ＝3.2918V，MEA 3 5.1434V, the main frequency amplitude of each multi-frequency excitation current signal is B 1 ＝B 2 ＝B 3 ＝1.0232A。
Step 4: according to the determined frequency spectrum and amplitude spectrum of the multi-frequency excitation current signal, iteratively solving the phase combination theta= [ theta ] of each main frequency component of the multi-frequency excitation current with the aim of minimizing the crest factor CF of the multi-frequency excitation current 1 θ 2 θ 3 ] T . Let the initial value of phase combination be theta (0) ＝[0 2π/3 4π/3] T The phase combination obtained after 50 iterations or when the crest factor CF is smaller than 10 is taken as the optimal solution. Determining the phase θ of each dominant frequency component of a multi-frequency excitation current 1 ＝2.5133rad，θ 2 ＝6.2832rad，θ 3 = 5.0266rad. Determining the phase of each dominant frequency component of a multi-frequency SPWM excitation signal
Step 5: according to the frequency spectrum f of the multi-frequency SPWM excitation signal 1 ＝128Hz，f 2 ＝256Hz，f 3 =400 Hz; magnitude spectrum MEA 1 ＝1.6459V，MEA 2 ＝3.2918V，MEA 3 = 5.1434V; phase spectrumDetermining a multi-frequency sinusoidal modulation signal u m ：
u m (t)＝0.1646sin(256πt+4.0716)+0.3292sin(512πt+1.5646)+0.5143sin(800πt+0.3102)(33)
Step 6: FIG. 5a is a graph of a multi-frequency sinusoidal modulation wave versus a triangular carrier wave; FIG. 5b drive control signal s 1 A waveform diagram; FIG. 5c drive control signal s 2 Waveform diagram, based on regular sampling method, of multi-frequency sinusoidal modulation signal u m For bipolar triangular carrier u c Modulation is performed. Triangular carrier u c Is a bipolar isosceles triangle wave, the positive peak value is 1, the negative peak value is-1, and the carrier angular frequency omega c ＝20πrad·s -1 . The drive control circuit outputs a drive control signal s of the H-bridge transmitting circuit 1 Sum s 2 。
Step 7: FIG. 6a Multi-frequency SPWM excitation signal time domain information; FIG. 6b is a plot of the time domain information of the multi-frequency excitation current signal; FIG. 6c frequency domain information of the multifrequency excitation current signal, in the driving control signal s 1 Sum s 2 Under the control of the H bridge transmitting circuit, the transmitting voltage is a multi-frequency SPWM excitation signal waveform, the transmitting current is a multi-frequency excitation current waveform, and the current amplitude is uniformly distributed in the time domain. The multi-frequency excitation current comprises all required main frequency points in a frequency domain, the low-frequency harmonic component is 0 except the main frequency points, the energy distribution among the main frequency points is uniform, the frequency spectrum characteristic is good, and the detection precision can be effectively improved.
The foregoing description of the preferred embodiments of the invention is not intended to be limiting, but rather is intended to cover all modifications, equivalents, and alternatives falling within the spirit and principles of the invention.
Claims (7)
1. A multi-frequency SPWM high-precision frequency domain electromagnetic sounding excitation method is characterized by comprising the following steps:
step 1: determining a multi-frequency SPWM excitation signal expression according to a multi-frequency SPWM electromagnetic sounding emission system structure and a multi-frequency sinusoidal pulse width modulation principle;
step 2: depth range D according to investigation target region H ～D L Skin depth regulating bodyDetermining the frequency band range f of the effective main frequency point of the multi-frequency excitation current signal L ～f H According to the requirement of longitudinal detection resolution of the investigation target area, determining the number N of main frequencies of the emission current and the distribution of main frequency points, and completing the frequency spectrum design of the multi-frequency SPWM excitation signals and the multi-frequency excitation current signals;
step 3: make each main frequency point amplitude B of multi-frequency excitation current i Equal, combining the energy conservation law and the requirement of electromagnetic sounding experiment on the signal to noise ratio, calculating the amplitude A of each component of the multi-frequency sinusoidal synthesis signal i Determining the amplitude MEA of each main frequency point of the multi-frequency SPWM excitation signal i And the amplitude B of each main frequency point of the multi-frequency excitation current signal i Completing the amplitude spectrum design of the multi-frequency SPWM excitation signal and the multi-frequency excitation current signal;
step 4: combining θ= [ θ ] with the phases of sinusoidal components of the multi-frequency excitation current according to the determined frequency spectrum and amplitude spectrum of the multi-frequency excitation current signal 1 θ 2 … θ N ] T As an independent variable, the optimal solution theta '= [ theta ] of the phase combination is determined by an iteration method with the aim of minimizing the crest factor CF of the multi-frequency excitation current signal' 1 θ′ 2 … θ′ N ] T Calculating the phase of each required main frequency point of the multi-frequency SPWM excitation signalCompleting the phase spectrum design of the multi-frequency SPWM excitation signal and the multi-frequency excitation current signal;
step 5: according to the frequency spectrum f of the multi-frequency SPWM excitation signal 1 ,f 2 ,…,f N Amplitude spectrum MEA 1 ,MEA 2 ,…,MEA N And phase spectrumDetermining a multi-frequency sinusoidal modulation signal u m An expression;
step 6: inside the drive control circuit, based on a regular sampling method, the signal u is modulated by a multi-frequency sine m For bipolar triangular carrier u c Is used for driving the output of the control circuitDrive control signal s for H-bridge transmitting circuit 1 Sum s 2 ；
Step 7: in the drive control signal s 1 Sum s 2 Under the action of the electromagnetic sounding device, the transmitting voltage of the H-bridge transmitting circuit is a multi-frequency SPWM excitation signal, the transmitting current in the transmitting coil is a multi-frequency excitation current signal, and the transmitting current comprises all required main frequency points, so that the high-precision electromagnetic sounding of the investigation target area can be completed.
2. The multi-frequency SPWM high precision frequency domain electromagnetic sounding excitation method of claim 1, wherein step 2 specifically comprises: according to the depth range of the investigation target area, determining the frequency band range of the effective main frequency point of the multi-frequency excitation current signal by using a skin depth formula (1):
where δ represents the depth of investigation, ρ represents the measured area medium resistivity, f represents the excitation signal frequency,
let the depth range of the investigation target be the shallow depth D L To depth D of deep layer H According to the skin depth formula, shallow depth D L Corresponding to the high frequency point f H Shallow depth D H Corresponding to the low frequency point f L The effective frequency band required by the exploration target area is f L ～f H And combining the requirement of the investigation target area on the longitudinal detection resolution, and determining the number N of required main frequencies and the distribution of main frequency points in an effective frequency band.
3. The multi-frequency SPWM high precision frequency domain electromagnetic sounding excitation method of claim 1, wherein step 3 specifically comprises:
after applying a multi-frequency SPWM excitation voltage signal across the transmit coil, a multi-frequency excitation current is generated in the coil. The transmission coil equivalent impedance expression is:
Z(ω)＝R+jωL
wherein R and L are respectively equivalent resistance and equivalent inductance of the transmitting coil;
transmitting a voltage U in the frequency domain out And emission current I out The relation of (2) is:
the time domain expression of the multi-frequency excitation current signal is:
wherein B is i And theta i The amplitude and the phase of the ith main frequency component in the multi-frequency excitation current signal are respectively, and the amplitude B i And phase theta i The expressions of (2) are respectively:
make each main frequency point amplitude B of multi-frequency excitation current i Are all equal, i.e. B 1 ＝B 2 ＝…＝B N The amplitudes of the sinusoidal components in the multi-frequency sinusoidal composite signal satisfy:
for the ith dominant frequency point in the multi-frequency excitation current signal, if omega i L is more than or equal to 10R, the main frequency point is considered to be high frequency, and the high frequency angular frequency omega is recorded H When ω is =10r/L i ≥ω H When the impedance of the transmitting coil is equal to the inductive reactance omega i L plays a main role, the impedance of the transmitting coil ignores the resistance R; when omega i ＜ω H When the resistance R in the impedance of the transmitting coil plays a main role, the impedance of the transmitting coil can neglect the inductance omega i L, combining the formula of the amplitude of each sinusoidal component in the multi-frequency sinusoidal synthesis signal, wherein the amplitude relation of each sinusoidal component in the multi-frequency sinusoidal synthesis signal is expressed as
According to the condition that the amplitude of each main frequency voltage in the multi-frequency SPWM excitation signal should meet and the multi-frequency sinusoidal synthesis signal u s The amplitude of each sinusoidal component in the multi-frequency sinusoidal synthesis signal meets the constraint condition and the detection precision requirement of the electromagnetic sounding experiment, and the amplitude A of each sinusoidal component in the multi-frequency sinusoidal synthesis signal is determined i At this time, the expression of the signal is excited by the multi-frequency SPWMAnd a multi-frequency sinusoidal synthesis signal u s The amplitude value MEA of each main frequency point of the multi-frequency SPWM excitation signal can be determined by meeting constraint conditions i Amplitude B of each main frequency point of multi-frequency excitation current i 。
4. The multi-frequency SPWM high-precision frequency domain electromagnetic sounding excitation method of claim 3,
step 4, solving the phase combination theta by adopting an iteration method, wherein the solving target is that the crest factor CF is minimum, and firstly, the phase combination theta is calculated in [0,2 pi ]]N angle values are taken as initial values of phase combination theta at equal intervalsSolving a phase combination by using fminesearch function in Matlab to obtain a phase combination initial value of theta (0) Optimal solution at timeSum crest factor CF (1) The phase combination theta after once solving (1) As a new oneIn (2) calling the fminesearch function again to solve the phase combination, iteratively solving the phase combination theta in this way, and obtaining the phase combination +.>Sum crest factor CF (S) When the number S of times of calling fminesearch function is greater than 50 or the crest factor CF (S) When the value is equal to or smaller than the set value, the optimal solution θ '= [ θ ]' 1 θ′ 2 … θ′ N ] T For the final solution result, θ ' = [ θ ' ] is combined according to the phase ' 1 θ′ 2 … θ′ N ] T Combined with phase theta i The expression of (2) can be used for dividing the phase of each main frequency point of the multi-frequency SPWM excitation signal>And completing the phase spectrum design of the multi-frequency SPWM excitation signal and the multi-frequency excitation current signal.
5. The multi-frequency SPWM high precision frequency domain electromagnetic sounding excitation method of claim 1, wherein the multi-frequency SPWM excitation signal expression is:
wherein u is out For the transmitting voltage M to be the modulation depth, E to be the DC power supply voltage, A i Amplitude of each component of the multi-frequency sinusoidal synthesis signal, f i For the frequency of the components of the multi-frequency sinusoidal synthesis signal, < >>The phases of the components of the signal are synthesized for the multi-frequency sinusoids.
6. The method for electromagnetic sounding excitation in the high accuracy frequency domain of a multi-frequency SPWM of claim 5 wherein the multi-frequency sinusoidal modulation signal u m The expression is:
7. the method for electromagnetic sounding excitation in the high accuracy frequency domain of a multi-frequency SPWM according to claim 1, wherein the regular sampling method is for each carrier period T c In, the multi-frequency sine modulation signal u is at the negative peak time of the triangular carrier m Sampling, namely, taking a sampling value of a multi-frequency sinusoidal modulation signal as a center to guide a horizontal line, intersecting with triangular carriers at two sides, and taking left and right intersection points as primary carrier periods T respectively c Internal drive control signal s 1 The front and back edges of the square wave pulse.
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