A Prior Filtering Iterative Demodulation Method and System for Electrical Tomography

Abstract

The present invention relates to a prior filtering iterative demodulation method and system for electrical tomography. The system includes a signal excitation module, a high-speed data acquisition module, a prior filtering iterative demodulation module, and a data upload module. The signal excitation module generates a sinusoidal signal with a certain frequency as the voltage excitation of the electrical tomography system and applies it to the excitation electrodes of the sensor. The signals of the measurement electrodes are measured and sampled by the high-speed data acquisition module. The sampled signals are subjected to prior filtering iterative demodulation in the on-chip data processing unit to obtain the amplitude and phase of the sinusoidal signal of the frequency of interest, and the demodulation results are transmitted to the host computer through the data upload module for signal post-processing to obtain the electrical parameter distribution information of the measured field area. The feature of the present invention is that the prior filtering iterative demodulation method is used to demodulate the sinusoidal signal of the frequency of interest. While ensuring the demodulation accuracy, demodulation is achieved within one signal period, improving the demodulation speed of the sinusoidal signal. This method has broad application prospects in the field of electrical tomography parameter measurement.

Description

Technical Field

[0001] The present invention relates to a prior filtering iterative demodulation method and system for electrical tomography, belonging to the field of distributed parameter measurement. Background Art

[0002] Since the 1980s, process tomography technology has been widely developed and applied because it can realize the visualization of process monitoring. According to different detection environments and requirements, there are different process tomography methods, including X-ray tomography, gamma-ray tomography, ultrasonic imaging, microwave imaging, and electrical tomography, etc. Electrical Tomography (ET) technology is a tomography technology based on the electromagnetic field sensitive mechanism. According to different media having different electrical properties (conductivity / permittivity / permeability of magnetic field), by acquiring the measurement data at the sensitive field boundary and using an appropriate image reconstruction algorithm, the distribution of electrical parameters in the sensitive area is inversely calculated. It has the advantages of no radiation, non-invasive, portability, fast response speed, low price, etc., and has been widely applied to many aspects such as industrial process flow pattern identification, oil and gas pipeline condition detection, combustion field dynamic monitoring, etc., and has important application prospects in the fields of industry, chemistry, and medicine (Wang Huaxiang. Electrical Tomography Technology [J]. Process Automation Instrumentation, 2017, 38(5): 1-6.). The typical structure of an electrical tomography system includes three parts: a sensor, a multi-channel data acquisition system, and an image reconstruction method, where the multi-channel data acquisition system is used to measure the sensitive field boundary signal. To obtain better measurement signal-to-noise ratio, linearity, and resolution and reduce the difficulty of hardware design, the multi-channel data acquisition system often uses a sine signal as the excitation source, applies the excitation signal to the sensor electrode through a shielded wire, then obtains the signal of the measured port through a measurement circuit, and obtains the sensitive field boundary impedance information by demodulating the sine signal and uses it for the reconstruction of the electrical parameter distribution. Among them, the high-speed and high-precision demodulation method for sine signals has become one of the key technologies affecting electrical tomography systems.

[0003] Traditional electrical capacitance tomography (ECT) data acquisition systems use analog demodulation methods. Such methods have good filtering effects, high demodulation accuracy, and a wide measurement bandwidth, making it convenient to achieve high-frequency measurements. However, the demodulation speed is limited by the response time of high-order low-pass filters, and the circuit structure is relatively complex. In 1994, Yang proposed multiplying the measurement signal by a reference signal of the same frequency and using a low-pass filter to filter the sine signal to demodulate its amplitude and phase in the article "High frequency and high-resolution capacitance measuring circuit for process tomography" published on pages 215-219 of Volume 141, Issue 3 of "IEE Proceedings - Circuits, Devices and Systems". Chen used the analog demodulation method to achieve the demodulation of dual-frequency sine signals in the article "Design of Impedance Measuring Circuits Based on Phase-Sensitive Demodulation Technique" published on pages 1276-1282 of Volume 60, Issue 4 of "IEEE Transactions on Instrumentation and Measurement" in 2011. Analog demodulation is based on the principle of phase-sensitive demodulation. Along with the development of various analog filter theories, it has a quite mature theoretical basis and has the measurement advantages of high accuracy and wide bandwidth. It was once widely used as a typical demodulation method in many fields. However, the demodulation speed of this method is limited by the relatively long response time of the filter, and the circuit structure is relatively complex. Therefore, more and more scholars are researching digital demodulation methods.

[0004] With the development and maturity of integrated circuits, the digital demodulation method for sine signals has become increasingly mature. The digital demodulation method has the advantages of high-speed and high-precision demodulation, and is convenient and fast for data transmission, post-processing, and transplantation. However, it is restricted by the sampling theorem, resulting in a limited measurement bandwidth. Currently, there are various digital demodulation methods used in ECT systems, which are suitable for different sine signal demodulation scenarios.

[0005] The full-cycle digital multiplication demodulation method has the advantages of clear and distinct basic theory and high demodulation accuracy. However, full-cycle demodulation results in limited demodulation speed, and the multiplication operation requires a relatively high demand for digital processing units. For example, Smith proposed a phase-sensitive demodulator based on the principle of matched filtering in the article "Design of a phase-sensitive detector to maximize signal-to-noise ratio in the presence of Gaussian wideband noise" published in Measurement Science and Technology, Vol. 3, No. 11, pp. 1054-1062 in 1992. The discrete sine sampling signal of one cycle is multiplied by the sine reference signal orthogonal to the same frequency and then summed to obtain the demodulation results of amplitude and phase, realizing digital quadrature demodulation. Cui realized on-chip digital quadrature demodulation in the article "A high-performance digital system for electrical capacitance tomography" published in Measurement Science and Technology, Vol. 22, No. 5 in 2011, improving the operation speed of the data acquisition system and reducing the burden of high-speed data transmission. This on-chip digital quadrature demodulation has gradually become a common demodulation method for electrical capacitance tomography data acquisition systems. The digital quadrature demodulation method and the traditional analog quadrature demodulation method are essentially phase-sensitive demodulation. Demodulation requires measuring the full cycle of the signal, resulting in limited demodulation speed, and both involve multiplication operations in the operation process, consuming a large amount of resources. It is difficult to implement for some processors without multipliers. Therefore, it is necessary to further develop demodulation methods to save hardware resources.

[0006] The low-power full-cycle digital multiplication demodulation method is used in the occasion where there is no multiplier in the digital processing unit, which has the advantages of high precision and low power consumption. However, the demodulation speed is limited, and the demodulation accuracy is affected by the tiny DC component and high-frequency noise existing in the measurement circuit. For example, Zhou proposed a rectification demodulation method that only requires addition and subtraction in the article titled "A complex programmable logic device-based high-precision electrical capacitance tomography system" published in Measurement Science and Technology, Vol. 24, No. 7, 2013. However, the rectification demodulation method can only obtain the amplitude information of the sine signal, resulting in the loss of phase information. Therefore, Xu proposed a digital switching demodulation method in the article titled "A Digital Switching Demodulator for Electrical Capacitance Tomography" published in IEEE Transactions on Instrumentation and Measurement, Vol. 62, No. 5, pp. 1025-1033, 2013. The demodulation process only involves addition and subtraction operations, reducing the resource occupancy rate. However, the square wave signal will introduce high-frequency noise. Therefore, when this method is implemented on an FPGA under the same conditions, the signal-to-noise ratio of the demodulation result is slightly lower than that of the digital quadrature demodulation result. In addition, the synchronous sampling demodulation method can be used to simplify the demodulation difficulty. For example, when sampling at four times the excitation frequency, when the frequency and phase of the carrier signal and the frequency of the measured signal are accurately known, there is a simple linear combination relationship between the amplitude and phase of the demodulated sine signal and the sampling signal. In 1993, Areny applied synchronous sampling demodulation to bioimpedance measurement in the article titled "Bioelectric impedance measurements using synchronous sampling" published in IEEE Transactions on Biomedical Engineering, Vol. 40, No. 8, pp. 824-829.

[0007] The multi-frequency sine signal digital demodulation method is used for the frequency-domain analysis of the electrical properties of the medium in the measured sensitive field, which has the advantage of high precision. However, the demodulation requires demodulating the amplitudes and phases of multiple sine signals within one or more measurement signal periods, resulting in limited demodulation speed. For example, in 2007, Min published an article titled "Synchronous Sampling and Demodulation in an Instrument for Multifrequency Bioimpedance Measurement" in the IEEE Transactions on Instrumentation and Measurement, Vol. 56, No. 4, pp. 1365-1372, proposing to use the synchronous sampling demodulation method to achieve multi-frequency signal demodulation and reduce the computational complexity. In 2000, Yoo published an article titled "An Electrochemical Impedance Measurement Technique Employing Fourier Transform" in Analytical Chemistry, Vol. 72, No. 9, pp. 2035-2041, proposing a method for multi-frequency demodulation based on discrete Fourier transform impedance demodulation. In 2014, Sanchez published an article titled "An FPGA-based frequency response analyzer for multiline and stepped sine measurements on stationary and time-varying impedance" in Measurement Science and Technology, Vol. 25, No. 1, developing and evaluating the performance of a new frequency response analyzer for measuring the frequency response function of stationary and time-varying impedance. The excitation control is implemented using FPGA and digital signal processing based on fast Fourier transform to achieve impedance measurement in the range of 610.4 mHz to 12.5 MHz for the frequency response function.

[0008] The iterative digital demodulation method can break through the speed bottleneck that traditional demodulation methods require one or more full periods of measurement signals. It has the advantage of fast demodulation speed, but the demodulation program is relatively complex and requires more preprocessing processes. The demodulation accuracy is limited when the number of sampling points is small. For example, in 2013, Xu published an article titled "A recursive least squares-based demodulator for electrical tomography" in Review of Scientific Instruments, Vol. 84, No. 4, which proposed a recursive demodulation method based on the least squares method. Impedance demodulation can be performed using at least two sampling points, significantly improving the impedance measurement speed. In 2014, Sun published an article titled "A high-speed electrical impedance measurement circuit based on information-filtering demodulation" in IEEE Transactions on Instrumentation and Measurement, Vol. 25, No. 7, which proposed a high-speed impedance measurement circuit based on information-filtering demodulation. Similarly, it does not require full-period sampling points for demodulation. Its computational complexity is reduced, the resource occupancy rate is decreased, the signal-to-noise ratio is higher than 75 dB, and the phase angle standard deviation is less than 0.012 degrees. In 2017, Sun published an article titled "Digital Recursive Demodulator Based on Kalman Filter" on pages 3138-3147 in IEEE Transactions on Instrumentation and Measurement, Vol. 66, No. 12, which proposed a recursive demodulation method based on the Kalman filter. Compared with the previous two iterative demodulation methods, it has fewer multiplication calculations, less resource consumption, and comparable accuracy.To obtain more impedance spectra, in 2018, Sun published an article titled "A Recursive Demodulator for Real-Time Measurement of Multiple Sinusoids" in the IEEE Sensors Journal, Volume 18, Issue 15, pages 6281-6289, which proposed a demodulation method based on Kalman filtering to achieve synchronous recursive demodulation of the amplitude and phase of multi-frequency sinusoidal signals.

[0009] The above iterative digital demodulation method can process the random noise in the measured signal, achieve high-precision demodulation with less than the integer cycle sampling points of the measured signal, improve the demodulation speed, and ensure the demodulation accuracy. However, such demodulation methods are often effective in processing the random noise existing in the signal to be demodulated, but have limited ability to process the noise signals with specific spectra. In the electrical tomography system, the measured signal includes not only the sine signal of the interested frequency, but also the sine signals of other frequencies, the random noise signals with a wide spectrum range, and the specific spectrum harmonic signals caused by the DC power supply and circuit nonlinear components. These signals all cause great interference to the demodulation accuracy. Specifically, in order to improve the available information of the measured sensitive field, the medium of the measured field can be subjected to spectrum analysis, that is, in the form of multi-frequency excitation, the signal excitation module generates a signal mixed with multiple-frequency sine signals as the excitation signal of the electrical tomography system. By demodulating the measured electrode signals at different frequencies respectively, the action results at multiple frequencies can be obtained synchronously, improving the demodulation speed and increasing the dimension of the available information of the sensitive field. However, when demodulating a sine signal of a certain interested frequency, the other frequency components will have a certain impact on the demodulation speed and accuracy. In addition, the power supply will also cause frequency domain interference to the measured signal. The multi-channel data acquisition system uses a DC power supply to supply power to each circuit board. The common DC power supplies include linear power supplies and switching power supplies. The linear power supply has the characteristics of high-precision voltage regulation and small noise ripple, but its efficiency is low, the heat generation is large, and a large radiator needs to be added. The switching power supply has the advantages of high efficiency, small volume and good flexibility. However, a large ripple will be superimposed on the DC output of the switching power supply, and the purity of the power supply is poor (Wang Sicong. Review of the basic principle and technology development of switching power supplies [J]. Value Engineering, 2018, 37(14): 269-271.). Based on the development trend of miniaturization of multi-channel data acquisition systems, more and more acquisition systems use switching power supplies as the DC power supply form. Although currently, switching power supplies with a required power consumption greater than 75W must have a power factor correction circuit to improve the power factor of the system and reduce harmonic pollution. However, the power required by the acquisition system is often lower than 75W, and the influence of the high-frequency harmonic signals existing in the power supply on the circuit cannot be ignored (Diao Mingjun. Review of the research and development of switching power supplies [J]. Communication Power Technology, 2018, 35(7): 89-93). To solve the interference of other frequency harmonics and Gaussian noise during the demodulation of the sine signal of the interested frequency and ensure the demodulation speed and accuracy, it is necessary to study the fast demodulation method and system under such conditions.

[0010] Based on the above background, the present invention proposes a prior filtering iterative demodulation method and system for electrical tomography, which combines the advantages of frequency domain processing of linear time-invariant filtering systems and the advantages of random noise signal processing of information filtering methods, and uses an iterative demodulation method to achieve fast and high-precision demodulation of sine signals under random noise and specific frequency domain noise conditions. Summary of the Invention

[0011] The object of the present invention is to provide a priori filtering iterative demodulation method and system for electrical tomography, to realize the frequency-domain processing of the measurement signal of electrical tomography, reduce or eliminate the influence of the remaining frequency signals other than the interested frequency, and suppress the existing random noise by combining the information filtering method, so as to obtain a high-precision demodulation result within a time less than one period of the measured signal, and as the number of sampling points substituted into the iterative process increases, the anti-noise ability of the demodulation result is further enhanced.

[0012] A priori filtering iterative demodulation method and system for an electrical tomography system provided by the present invention includes the following steps:

[0013] Step 1: A signal excitation module generates a sine signal with a frequency including f as the voltage excitation of the electrical tomography system, and applies it to the excitation electrode of the sensor.

[0014] Step 2: Use a high-speed data acquisition module to start measuring the voltage signal on the measurement electrode of the sensor at the moment when the phase of the excitation signal is zero, and sample it into the on-chip data processing unit. The mathematical format of the sampled signal x[k] is:

[0015]

[0016] where k is the sampling point sequence; A, and Ω = 2πf / f s are respectively the amplitude, phase and angular frequency of the sine signal of the interested frequency; f and f s represent the interested frequency and the sampling frequency respectively; Δ represents the DC component existing in the measurement signal; ε represents the noise signal, which contains signal components other than the interested frequency, such as white noise and other sine harmonic signals existing in the signal.

[0017] Step 3: Initialize the iterative process using the a priori filtering iterative demodulation initialization formula, and its mathematical format is:

[0018]

[0019] where K1 and P1 respectively represent the initialization results of the information matrix and the innovation matrix; V1 represents a constant vector determined by the interested frequency and the sampling frequency, H1 represents the filtering matrix of the adopted linear time-invariant system, and X1 represents the initial sampling signal. The mathematical formats of V1, H1 and X1 are:

[0020]

[0021] Step 4: Use the updated sampling data and combine it with the prior filtering iterative demodulation recurrence formula for demodulation. The mathematical format of the recursive demodulation is as follows:

[0022]

[0023] where k is the sampling point ordinal number, and k ≥ 1; K k+1 and P k+1 represent the updated information matrix and innovation matrix respectively; Z k+1 represents the updated demodulation impedance matrix; X k represents the measurement signal column vector; h k represents the filtering matrix row vector of the adopted linear time-invariant system, which is uniquely determined by the selected filtering system; V k represents a constant vector uniquely determined by the frequency of interest and the sampling frequency. The specific mathematical format is as follows:

[0024]

[0025] h k = [h k,1 h k,2 … h k,k (6)

[0026]

[0027] Step 5: Use the calculated demodulation impedance matrix Z k+1 to solve for the amplitude A and phase θ of the sine signal at the frequency of interest. The mathematical format is as follows:

[0028]

[0029] Judge whether the amplitude and phase of the sine signal at the frequency of interest obtained by demodulation meet the system accuracy requirements. If not, return to Step 4 and continue the iterative demodulation process. If so, stop the iteration and transmit the demodulation result through the data upload module.

[0030] The advantages of the present invention compared with the prior art are as follows: The measurement signal is processed from the frequency domain perspective to eliminate the information of the remaining frequency components outside the frequency of interest, and the information filtering method is combined to eliminate the random noise in the full frequency spectrum range, reducing the influence of the noise signal on the measured signal. It can achieve high-precision demodulation using fewer than one cycle of sampling points, reduce oscillations, and improve the convergence speed. Under noise-free conditions, this method can obtain accurate demodulation results without using the sampling points of a complete signal cycle. Under noisy conditions, it can also obtain high-precision demodulation results using fewer than the sampling points of a complete cycle, and the demodulation accuracy and anti-noise ability can be improved by increasing the number of sampling points. The iterative process of this method can be started without initial information, and the iterative form is simple. Description of the Drawings

[0031] Figure 1 It is a flowchart of a priori filtering iterative demodulation method for electrical tomography.

[0032] Figure 2 It is a device diagram of a priori filtering iterative demodulation system for electrical tomography.

[0033] Figure 3 It is the simulation result of amplitude demodulation of multiple demodulation methods.

[0034] Figure 4 It is the simulation result of phase demodulation of multiple demodulation methods. Detailed Implementation Manner

[0035] The present invention, namely a priori filtering iterative demodulation method and system for an electrical tomography system, includes the following steps:

[0036] Step 1: A signal excitation module generates a sine signal with a frequency including f as the voltage excitation of the electrical tomography system, and applies it to the excitation electrodes of the sensor;

[0037] Step 2: Use a high-speed data acquisition module to start measuring the voltage signal on the measurement electrodes of the sensor at the moment when the phase of the excitation signal is zero, and sample it into the on-chip data processing unit. According to the interested frequency f and the sampling frequency f s Establish the initial equation and recurrence equation of the a priori filtering iterative demodulation method;

[0038] Assume that the sampled signal is x[k], and its mathematical format is:

[0039]

[0040] where k is the sampling point sequence; A, and Ω = 2πf / f s are respectively the amplitude, phase and angular frequency of the interested sine signal; Δ represents the DC component existing in the measurement signal, and ε represents the noise signal, which includes Gaussian noise and any signal other than the interested frequency;

[0041] Using Euler's formula, represent the measurement signal as:

[0042]

[0043] Simplify Equation (10) to:

[0044] X N = V N Z + ε N (11)

[0045] The frequency-domain processing of the measurement signal is carried out using a digital filter to filter out the remaining spectral components outside the frequency of interest; the time-domain characteristics of a linear time-invariant discrete system are expressed in the form of an R-order difference equation:

[0046]

[0047] where y[n] represents the output of the linear time-invariant filter, a m and b r are the coefficients of the difference equation of the digital filter, both of which are constants; R represents the order of the difference equation; M represents the order of the input delay;

[0048] In the actual sampling process, the number of measurement signals is limited, that is

[0049]

[0050] To achieve real-time spectral processing of the measurement signal and meet the requirements of iterative demodulation, Equation (12) is further constrained as:

[0051]

[0052] Expanding Equation (14) into matrix form gives

[0053]

[0054] where

[0055]

[0056] and

[0057]

[0058] Assuming that the noise signal tends to 0 after being processed by the filtering system, and this system also has a certain impact on the measured signal, substituting Equation (10) into Equation (15) gives:

[0059]

[0060] Simplifying the mathematical form of Equation (18) gives:

[0061] H N X N = H N V N Z (19)

[0062] Let Y N = H N X N , U N = H N V N, Equation (19) becomes a typical linear equation solving format:

[0063] Y N = U N Z (20)

[0064] There are three unknowns in Equation (20). In theory, only three independent equations are needed for solving. However, in reality, a linear time-invariant system cannot remove the signals other than the frequency of interest, and there will still be some residual noise signals affecting demodulation. Moreover, since U N does not have an inverse matrix, the least squares method is used to estimate the parameter Z, that is:

[0065]

[0066] where, (·) T represents the matrix conjugate transpose operation.

[0067] To reduce the computational complexity, an iterative format is used for solving. The iterative format of the estimated value of parameter Z is:

[0068]

[0069] where,

[0070]

[0071] The format of the information matrix is defined as:

[0072] K = U T U (24)

[0073] The iterative format of the information matrix is defined as:

[0074]

[0075] Substituting Equations (19) and (20) into (25) gives:

[0076]

[0077] where,

[0078] h k = [h k,1 h k,2 …h k,k (27)

[0079]

[0080] When the frequency of interest and the sampling frequency are determined, the information matrix can be calculated in advance; then the iterative format of parameter Z is:

[0081]

[0082] Define the iterative format of the innovation matrix as:

[0083]

[0084] Substitute Eqs. (19) and (20) into Eq. (30) and combine them to obtain

[0085]

[0086] Then, the iterative format of Z is:

[0087]

[0088] Set the initial conditions of the iterative demodulation as:

[0089]

[0090] Substitute Eqs. (19) and (20) into (33) to obtain:

[0091]

[0092] where K1 and P1 represent the initialization results of the information matrix and the innovation matrix respectively; V1 represents the constant vector determined by the frequency of interest and the sampling frequency, H1 represents the filtering matrix of the adopted linear time-invariant system, and X1 represents the initial sampling signal. The mathematical formats of V1, H1, and X1 are:

[0093]

[0094] Step 3: Take the moment when the phase of the excitation signal is zero as the measurement starting position, and use the measurement values X1, the linear time-invariant system filtering matrix H1, and the constant vector V1 starting from the starting position to initialize the information matrix K1 and the innovation matrix P1 according to the initial equations in Step 2;

[0095] Step 4: Substitute the calculated information matrix K k , innovation matrix P k and the updated sampling signal X k into the recurrence equations in Step 2, and gradually calculate the updated information matrix K k+1 , innovation matrix P k+1 and the demodulation impedance matrix Z k+1 values;

[0096] Step 5: Use the calculated demodulation impedance matrix Z k+1 to solve the amplitude A and phase θ of the sinusoidal signal at the frequency of interest, and their mathematical formats are:

[0097]

[0098] Determine whether the amplitude and phase of the sine signal at the frequency of interest after demodulation meet the system accuracy requirements. If not, return to step four and continue the iterative demodulation process. If so, stop the iteration and transmit the demodulation result through the data upload module.

[0099] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0100] An excitation signal is generated by the 101 signal excitation module, where the excitation signal includes a sine signal at the frequency of interest, other high-frequency sine signals, and noise signals. Specifically, the signal at the frequency of interest is an ideal cosine signal with an amplitude of 1, a phase of 60°, and a frequency of 100 kHz; a cosine signal with an amplitude of 0.01, a phase of 30°, and a frequency of 10 MHz is superimposed to simulate the aliased high-frequency noise signal. On the basis of the above two signals, 1% Gaussian white noise is added to simulate the measurement signal with a signal-to-noise ratio of 40 - 60 dB. The excitation signal is applied to the excitation electrode of the 102 sensor placed around the 103 sensitive area to be measured. The measurement electrode signal is sampled by the 104 high-speed data acquisition module at a sampling frequency of 40 MHz, and each period of the signal at the frequency of interest contains 400 sampling points. Then, the sampled signal is input into the 105 prior filtering iterative demodulation module to demodulate the amplitude and phase of the sine signal at the frequency of interest. When the demodulation result meets the system accuracy requirements, the demodulation result is transmitted to the 107 computer through the 106 data upload module for post-processing, realizing the inversion of the electrical parameter distribution of the measured sensitive area.

[0101] In the simulation experiment, the prior filtering iterative demodulation method proposed in this patent is compared with the information filtering iterative demodulation method and quadrature demodulation, and the demodulation effects of various demodulation methods are calculated 1000 times. It can be seen from the simulation results that under the above noise conditions, the prior filtering iterative demodulation method proposed in the present invention can obtain a relatively satisfactory demodulation result within a time less than one period of the sine signal at the frequency of interest, and the closeness of the demodulation result to the true value gradually increases with the increase of the number of iterations. The method proposed in this patent can achieve non-integer period demodulation compared with the traditional quadrature demodulation method, improving the demodulation speed while ensuring the demodulation accuracy; compared with the information filtering demodulation method, the proposed result method in this patent has no obvious oscillation in the iterative process, and the convergence speed of the demodulation process is faster, and higher-speed demodulation can be achieved while ensuring the demodulation accuracy. The simulation experiment verifies the good effect of the prior filtering iterative demodulation method proposed in the present invention.

[0102] The above description of the present invention and its implementation manners is not limited thereto. What is shown in the drawings is only one of the implementation manners of the present invention. Without departing from the gist of the present invention, structures or embodiments similar to this technical solution designed without creativity all fall within the protection scope of the present invention.

Claims

1. A prior filtering iterative demodulation method and system for electrical tomography, the system comprising a signal excitation module, a high-speed data acquisition module, a prior filtering iterative demodulation module, and a data uploading module; The signal excitation module generates a sinusoidal signal with a frequency of Ω as the voltage excitation of the electrical resistance tomography system and applies it to the excitation electrodes of the sensor. The sensor is placed around the measured sensitive field. The high-speed data acquisition module measures the signals on the measurement electrodes of the sensor and samples them into the on-chip data processing unit. In the on-chip data processing unit, the sampled signals are subjected to prior filtering and iterative demodulation to obtain the amplitude and phase of the sinusoidal signal at the frequency of interest within less than one measurement signal period. Then, the demodulated amplitude and phase are transmitted to the host computer through the data upload module. On the host computer, an image reconstruction algorithm is used to invert the distribution information of the electrical parameters of the measured field domain; The signal excitation module of the electrical resistance tomography system generates a sinusoidal signal with a frequency of Ω as the excitation signal, and the high-speed data acquisition module acquires the signals on the measurement electrodes and samples them into the on-chip data processing unit. The sampled signal is x[k], and its mathematical form is: where, k is the sampling point sequence; A, and Ω = 2πf / f s are respectively the amplitude, phase and angular frequency of the sine signal at the frequency of interest; f and f s respectively represent the frequency of interest and the sampling frequency; Δ represents the DC component present in the measured signal; ε represents the noise signal, which contains signal components with any frequencies other than the frequency of interest; Using Euler's formula, the measurement signal is expressed as: Equation (2) is simplified to: X N = V N Z + ε N (3) where, N represents the number of signals; the measurement signals are processed by a linear time-invariant system to filter out the frequency components other than the frequency of interest, and its mathematical form after the operation is: H N X N = H N V N Z (4) Among them, H N represents the filtering matrix of a linear time-invariant system, and each element is a constant. Its mathematical format is: Let Y N = H N X N , U N = H N V N , Equation (4) becomes a typical linear equation system solving format: Y N = U N Z (6) To reduce the computational complexity, an iterative method based on the least squares is used to solve for the parameter Z, and its mathematical form is: where (·) T denotes the conjugate transpose operation of a matrix, and The iterative format of the information matrix K is defined as: where, h k = [h k,1 h k,2 …h k,k (10) When the frequency of interest f and the sampling frequency f s are determined, the information matrix is calculated in advance; then the iterative formula for the parameter Z is as follows: The iterative format of the innovation matrix P is defined as: Then, the iterative format of Z is updated to: The initial conditions of the iterative format are set as: where, K1 and P1 represent the initialization results of the information matrix and the innovation matrix respectively; V1 represents the constant vector determined by the frequency of interest and the sampling frequency, H1 represents the filtering matrix of the linear time-invariant system used, and X1 represents the initial sampled signal. The mathematical forms of V1, H1, and X1 are: Using the calculated demodulation impedance matrix Z k+1 Solve for the amplitude A and phase θ of the sinusoidal signal at the frequency of interest, in the mathematical form of: Judge whether the amplitude and phase of the sinusoidal signal at the frequency of interest obtained by demodulation meet the system accuracy requirements. If not, continue the iterative demodulation process; if so, stop the iteration and transmit the demodulation results through the data upload module.

2. The prior filtering iterative demodulation method and system for electrical tomography according to claim 1, wherein The sampled signals of the high-speed data acquisition system are filtered by a linear time-invariant system to filter out the frequency components other than the frequency of interest; the time-domain characteristics of any linear time-invariant discrete system are expressed in the form of a difference equation, and its mathematical form is: where y represents the output of a linear time-invariant system; a m and b r are the coefficients of the difference equation of the digital filter, both of which are constants; R represents the order of the difference equation; M represents the order of input delay; To meet the iterative requirements and the realistic condition of the limited number of sampled signals, Equation (18) is expressed in matrix form as: where, and, Substituting Equation (2) into Equation (19) gives H N X N = H N V N Z (22) where N represents the number of signals, and H N represents the filtering matrix of the linear time-invariant system.

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