A coriolis mass flowmeter phase difference measurement method, medium and apparatus based on an adaptive strong tracking algorithm

Abstract

This invention discloses a method, medium, and device for measuring phase difference in a Coriolis mass flow meter based on an adaptive strong tracking algorithm, belonging to the field of signal processing and flow measurement of Coriolis mass flow meters. The method includes: data acquisition and discretization; establishing a signal state-space model; performing time updates using an adaptive strong tracking filter; calculating the covariance matrix of the residual and the actual output residual; dynamically adjusting the weakening factor to make the residual and the weakening factor positively correlated; calculating the fading factor and correcting the prior error covariance matrix; updating the state estimate and the error covariance matrix; and extracting the phase state vector to complete the phase difference measurement. This method dynamically adjusts the weakening factor according to system mutations, making the residual and the weakening factor positively correlated at the current time. After calculating the fading factor based on the weakening factor, the prior error covariance matrix is ​​corrected using the fading factor, thereby achieving accurate calculation of the fading factor to cope with abnormal fluctuations caused by system mutations and improving the accuracy of phase difference measurement.

Description

Technical Field

[0001] This application relates to the field of signal processing and flow measurement technology for Coriolis mass flow meters, and in particular to a method, medium, and device for measuring the phase difference of a Coriolis mass flow meter based on an adaptive strong tracking algorithm. Background Technology

[0002] Coriolis mass flowmeters (CMFs) have become indispensable core metering instruments in industrial process control due to their ability to achieve high-precision direct mass flow measurement and their insensitivity to changes in fluid properties such as density and viscosity. As industrial production becomes increasingly sophisticated, higher demands are placed on the dynamic response characteristics and real-time tracking capabilities of flowmeters for applications such as instantaneous flow, batch filling, and proportioning control. However, traditional signal processing and parameter estimation algorithms often face significant challenges in complex operating conditions such as gas-liquid two-phase flow, non-Newtonian fluids, or batch flows with frequent start-stop cycles.

[0003] Currently, the industry widely employs digital signal processing-based methods to extract the phase difference (i.e., flow signal) from Coriolis flowmeters. Among these, Discrete Wavelet Transform (DWT), due to its excellent localization characteristics in the time-frequency domain, is often used to filter out high-frequency noise from sensor output and restore the true flow characteristics. However, as a static analysis tool, wavelet transform requires pre-setting parameters such as the number of decomposition levels and threshold selection, making it difficult to achieve optimal adaptive noise reduction in dynamic processes with rapidly changing flow rates. This can easily lead to signal distortion or phase tracking lag. Furthermore, traditional estimation algorithms based on Minimum Mean Square Error (MMSE) often assume absolute accuracy of the system model and that noise follows an ideal statistical distribution when dealing with such nonlinear, strongly coupled systems, which is difficult to apply in engineering practice.

[0004] To address the aforementioned limitations, adaptive filtering algorithms based on state-space models have been introduced into the field of flow measurement. Among these, the Kalman filter (KF) and its extended version (EKF) can effectively estimate the parameters of nonlinear systems in real time by establishing the system's state-space equations. However, when faced with sudden system changes (such as step changes in flow), the standard Kalman filter suffers from slow dynamic response and is prone to large phase lag errors due to its over-reliance on prior state prediction models. To overcome this deficiency, the Strong Tracking Filter (STF) was developed. It introduces a fading factor to force the residual sequences to remain orthogonal, thereby rapidly adjusting the filter gain when sudden system changes occur, improving the ability to track the true state.

[0005] Although existing adaptive strong tracking filtering algorithms have made some progress in dynamic performance, when applied to the signal processing of Coriolis flowmeters with high noise and strong interference, there are still technical problems such as inaccurate calculation of the fading factor, which leads to untimely or excessive amplification of the filter gain when the flow rate fluctuates drastically, thus introducing measurement noise.

[0006] Therefore, how to accurately calculate the fading factor during the phase difference measurement process of a Coriolis mass flow meter in order to cope with abnormal fluctuations caused by sudden changes in the system and thus improve the measurement accuracy has become a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0007] Therefore, it is necessary to provide a method, medium, and device for measuring the phase difference of a Coriolis mass flow meter based on an adaptive strong tracking algorithm to address the aforementioned technical problems.

[0008] The following technical solution is adopted in this specification: This manual provides a method for measuring the phase difference of a Coriolis mass flow meter based on an adaptive strong tracking algorithm, specifically including: The output signal of the Coriolis mass flow meter is acquired and discretized into a sequence of sampled signals.

[0009] A signal state-space model is established based on the sampled signal sequence.

[0010] An initialized adaptive strong tracking filter is used in conjunction with the aforementioned signal state model. Time updates are performed to predict the current state variables and prior error covariance matrix.

[0011] Calculate the covariance matrix of the current residual and the actual output residual.

[0012] Based on the current residual, the weakening factor is dynamically adjusted to make the current residual and the weakening factor positively correlated.

[0013] The fading factor is calculated based on the weakening factor, and the prior error covariance matrix is ​​corrected based on the fading factor.

[0014] The Kalman gain matrix is ​​calculated based on the corrected prior error covariance matrix, and the current state estimate and error covariance matrix are updated based on the Kalman gain and the current time residual.

[0015] Based on the updated state estimate for the current moment, the phase state vector is extracted to complete the phase difference measurement of the Coriolis mass flow meter at the current moment.

[0016] Furthermore, the step of discretizing the output signal into a sequence of sampled signals... Specifically, it includes: ; in, For the first The signal amplitude at each sampling point For the first The signal angular frequency at each sampling point The sampling period is For the first The signal phase at each sampling point For the first Gaussian white noise at each sampling point.

[0017] Furthermore, the signal state-space model includes state transition equations. and measurement equations ; ; ; in, This is the state transition matrix; For state variables, Signal amplitude The corresponding signal amplitude state quantity, For signal phase The corresponding signal phase state quantity, Signal angular frequency The corresponding signal frequency state quantity; For process noise, For measuring noise.

[0018] Furthermore, the initialized adaptive strong tracking filter, combined with the signal state model, performs time updates to predict the current moment. state variables and prior error covariance matrix Specifically, it includes: ; ; in, Here is the state transition matrix. For the previous moment Predicted values ​​of state variables, For the previous moment of, Let be the process noise covariance matrix.

[0019] Furthermore, the calculation of the residual at the current time... and the actual output residual covariance matrix Specifically, it includes: ; ; in, For measurement equations nonlinear functions, The sampled value at the current moment. For the previous moment The residual, Forgetting factor, For the previous moment The residual covariance matrix, This is for transpose calculation.

[0020] Furthermore, the weakening factor is dynamically adjusted based on the residual at the current time. Specifically, making the current residual and the weakening factor positively correlated includes: ; in, As the initial value of the weakening factor, This is the weighting factor that decreases as the residual increases.

[0021] Furthermore, the step of calculating the fading factor based on the weakening factor... The correction of the prior error covariance matrix based on the fading factor specifically includes: ; ; in, This is the residual volatility ratio. The trace of the matrix; To predict residual covariance, To measure the Jacobian matrix of the equation, Here is the noise covariance matrix; To correct the residual covariance, This is the corrected prior error covariance matrix.

[0022] Furthermore, the calculation of the Kalman gain matrix based on the corrected prior error covariance matrix... The state estimate at the current time is updated based on the Kalman gain and the current time residual. And error covariance matrix Specifically, it includes: ; ; ; in, It is an identity matrix.

[0023] This specification provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method described above.

[0024] This specification provides a computer device including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the method described above.

[0025] The beneficial effects of this invention are as follows: Compared with the prior art, this invention dynamically adjusts the weakening factor according to the system mutation, so that the residual at the current time and the weakening factor are positively correlated, and after calculating the fading factor according to the weakening factor, the prior error covariance matrix is ​​corrected by the fading factor, thereby realizing the accurate calculation of the fading factor to cope with the abnormal fluctuations caused by the system mutation and improving the phase difference measurement accuracy. Attached Figure Description

[0026] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings:

[0027] Figure 1 This is a schematic diagram of the process of the present invention; Figure 2 This is a schematic diagram of the mutation signal model according to an embodiment of the present invention; Figure 3 The images show the time-domain waveforms of the original signal (blue) and the signal filtered by the Mallat algorithm (red) in this embodiment of the invention. Figure 4 The spectrum diagrams are of the original signal (blue) and the signal filtered by the Mallat algorithm (red) in this embodiment of the invention. Figure 5 This is a comparison chart of the phase difference abrupt change estimation results in an embodiment of the present invention; Figure 6 This is a comparison chart of estimation results after both frequency and phase difference abruptly change in an embodiment of the present invention. Detailed Implementation

[0028] To make the objectives, technical solutions, and advantages of this specification clearer, the technical solutions of this application will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments in this specification without creative effort are within the scope of protection of this application.

[0029] This invention provides a phase difference measurement method for Coriolis mass flow meters based on an adaptive strong tracking algorithm. The method comprises eight steps: data acquisition and discretization; establishing a signal state-space model; performing time updates using an initialized adaptive strong tracking filter; calculating the covariance matrix of the current residual and the actual output residual; dynamically adjusting the weakening factor to ensure a positive correlation between the current residual and the weakening factor; calculating the fading factor and correcting the prior error covariance matrix; updating the current state estimate and the error covariance matrix; and extracting the phase state vector to complete the phase difference measurement. This method dynamically adjusts the weakening factor based on system mutations to ensure a positive correlation between the current residual and the weakening factor. After calculating the fading factor based on the weakening factor, the prior error covariance matrix is ​​corrected using the fading factor, thereby achieving accurate calculation of the fading factor to cope with abnormal fluctuations caused by system mutations and improving the accuracy of phase difference measurement.

[0030] The technical solutions provided by the various embodiments of this application are described in detail below with reference to the accompanying drawings.

[0031] A method for measuring phase difference in a Coriolis mass flow meter based on an adaptive strong tracking algorithm, such as Figure 1 As shown, it specifically includes: Step 1: Obtain the output signal of the Coriolis mass flow meter and discretize the output signal into a sequence of sampled signals.

[0032] Preferably, the output signal is discretized into a sequence of sampled signals. Specifically, it includes: ; in, For the first The signal amplitude at each sampling point For the first The signal angular frequency at each sampling point The sampling period is For the first The signal phase at each sampling point For the first Gaussian white noise at each sampling point.

[0033] Step 2: Establish a signal state-space model based on the sampled signal sequence.

[0034] Preferably, the signal state-space model includes state transition equations. and measurement equations ; ; ; in, This is the state transition matrix; For state variables, Signal amplitude The corresponding signal amplitude state quantity, For signal phase The corresponding signal phase state quantity, Signal angular frequency The corresponding signal frequency state quantity; For process noise, For measuring noise.

[0035] Step 3: Using the initialized adaptive strong tracking filter and combining it with the signal state model, perform time updates to predict the current state variables and prior error covariance matrix.

[0036] Preferably, an initialized adaptive strong tracking filter is used in conjunction with a signal state model to perform time updates and predict the current time. state variables and prior error covariance matrix Specifically, it includes: ; ; in, Here is the state transition matrix. For the previous moment Predicted values ​​of state variables, For the previous moment of, Let be the process noise covariance matrix.

[0037] Step 4: Calculate the covariance matrix of the current residual and the actual output residual.

[0038] Preferably, the residual at the current time is calculated. and the actual output residual covariance matrix Specifically, it includes: ; ; in, For measurement equations nonlinear functions, The sampled value at the current moment. For the previous moment The residual, Forgetting factor, For the previous moment The residual covariance matrix, This is for transpose calculation.

[0039] Step 5: Based on the current residual, dynamically adjust the weakening factor to make the current residual and the weakening factor positively correlated.

[0040] Preferably, the weakening factor is dynamically adjusted based on the residual at the current time. Specifically, making the current residual and the weakening factor positively correlated includes: ; in, As the initial value of the weakening factor, This is the weighting factor that decreases as the residual increases.

[0041] Step 6: Calculate the fading factor based on the weakening factor, and correct the prior error covariance matrix based on the fading factor.

[0042] Preferably, the fading factor is calculated based on the weakening factor. The prior error covariance matrix is ​​corrected based on the fading factor, specifically including: ; ; in, This is the residual volatility ratio. The trace of the matrix; To predict residual covariance, To measure the Jacobian matrix of the equation, Here is the noise covariance matrix; To correct the residual covariance, This is the corrected prior error covariance matrix.

[0043] Step 7: Calculate the Kalman gain matrix based on the corrected prior error covariance matrix, and update the current state estimate and error covariance matrix based on the Kalman gain and the current time residual.

[0044] Preferably, the Kalman gain matrix is ​​calculated based on the corrected prior error covariance matrix. The state estimate at the current time step is updated based on the Kalman gain and the residual at the current time step. And error covariance matrix Specifically, it includes: ; ; ; in, It is an identity matrix.

[0045] Step 8: Extract the phase state vector from the updated current state estimate and complete the phase difference measurement of the Coriolis mass flow meter at the current moment.

[0046] Example When Coriolis mass flow meters are used for measuring stable single-phase flow, the two output signals are usually considered to be sinusoidal signals with constant amplitude and frequency. However, in actual measurements, it has been found that in addition to the sensor's operating frequency, there are also second harmonic, third harmonic, and random signals in the signals.

[0047] This embodiment provides a method for measuring the phase difference of a Coriolis mass flow meter based on an adaptive strong tracking algorithm, specifically including: S1: Using wavelet preprocessing, the discrete form of the Coriolis mass flow meter output signal can be expressed as: ; in, It is a sampling index; It is the instantaneous sample value of the output signal; It is the signal amplitude; It is the signal phase; It is angular frequency; It is the sampling period; It is a filtered signal with a small amount of interference, and is white noise with zero mean.

[0048] The amplitude, phase, and frequency information of the signal are selected to establish the state variables. ,in It is an amplitude state quantity; It is a phase state quantity; This is a frequency state quantity.

[0049] The state transition equation for the CMF output signal is: ; in For process noise, Let be the state transition matrix.

[0050] The measurement equation describes the relationship between measurement and state. The measurement equation is:

[0051] ; in Noise measurement.

[0052] The CMF output signal model shown above can be represented by a unified nonlinear model as follows: ; ; in, It is a state vector. It is the state transition matrix. It is a measurement vector. It is a nonlinear measurement function. It has covariance. Process noise and with covariance Measurement noise It consists of uncorrelated zero-mean Gaussian white noise, and the noise particles are not correlated with each other.

[0053] S2: System initialization, setting state variables Initial error covariance matrix System noise covariance .

[0054] S3: Execution time update, predicting state variables The state equations are linear, so it is not necessary to calculate the Jacobian matrix.

[0055] .

[0056] S4: Calculate the residuals ,in, For measurement equations nonlinear functions, This is the sampled value at the current moment.

[0057] S5: Calculate the covariance matrix of the actual output residual sequence. ,in, For the previous moment The residual, Forgetting factor, For the previous moment The residual covariance matrix, This is for transpose calculation.

[0058] S6: Calculate the weakening factor And calculate the fading factor. .

[0059] ; ; in, As the initial value of the weakening factor, This is a weighting factor that decreases as the residual increases. This is the residual volatility ratio. The trace of the matrix; To predict residual covariance, To measure the Jacobian matrix of the equation, Here is the noise covariance matrix; To correct for residual covariance.

[0060] S7: Perform state error covariance prediction .

[0061] S8: Calculate the Kalman gain matrix .

[0062] S9: Update the state error covariance .

[0063] S10: Perform state variable update .

[0064] S11: Numerical Example Verification S11.1: In an ideal scenario, the two signals output by a Coriolis mass flow meter are sinusoidal signals with fixed amplitude and frequency. The phase difference between the two signals reflects the magnitude of the fluid mass flow rate. Under short-duration batch flow conditions, due to rapid changes in flow rate, the phase difference of the output signals will abruptly change during start-up and shutdown, while the frequency will change relatively slowly. Both parameters tend to stabilize after a short period of change. A U-shaped sensor with a 25 mm diameter is used as the research object. When the flow valve suddenly opens, the phase difference between the two sensor output signals will undergo an approximately step change from 0° to 2.6°, and the frequency will also decrease by approximately 0.08 Hz. The entire process of short-duration batch flow consists of an on-state phase, a stable phase, and a off-state phase. Because the on-state and off-state phases are symmetrical, the simulation model only considers the on-state and stable phases.

[0065] The catastrophe model used in this paper treats both the phase difference and frequency of the sensor output signal as step changes. The two sinusoidal signals generated by MATLAB are shown in the following equation:

[0066] ; in, The signal amplitude, For signal frequency, Sampling frequency, For signal phase, This is for superimposed noise.

[0067] To simulate the sensor output signal under short-time batch material flow conditions, the phase difference, frequency, and synthesized sine signal of the two signals are as follows: Figure 2 As shown.

[0068] S11.2: Case Analysis S11.2.1: Signal Preprocessing Coriolis mass flow meters are highly sensitive to noise, but in practical applications, they are inevitably affected by various noises in industrial environments. This noise intrusion during signal acquisition and output can cause the actual measurement accuracy to fall short of specified requirements. When the noise impact is severe, the performance of the Coriolis mass flow meter degrades significantly or even fails to function properly. Therefore, it is necessary to accurately extract the original signal from the contaminated signal affected by noise. This paper uses the Mallat algorithm for signal filtering preprocessing. The signal-to-noise ratio (SNR) of the analog signal is 19.6 dB. The Db40 wavelet function is used to decompose the CMF signal into five layers. The denoised signal is reconstructed based on the low-frequency coefficients of different frequency bands. Figure 2 and Figure 3 These represent the time-domain waveform and spectrum of the filtered signal, respectively. Figure 3 As can be seen, the method reaches stability after approximately 0.05 seconds. The filtered signal retains the characteristics of the original signal, with a signal-to-noise ratio of 34.3 dB. Figure 4 As shown, the Mallat algorithm provides good filtering effects for both harmonics and random noise.

[0069] S11.2.2: Comparison of Algorithm Convergence Time and Estimation Accuracy The performance of the SDTFT algorithm, Hilbert transform algorithm, STF algorithm, and the ASTF algorithm proposed in this embodiment under parameter abrupt changes was compared using MATLAB simulation software. Because EKF has poor robustness to model uncertainty and cannot track abrupt signals, it is not considered in the following analysis. The algorithm convergence time is measured in seconds, and the algorithm estimation accuracy is represented by the root mean squared error (RMSE) of the phase difference.

[0070] Analysis of abrupt phase difference changes To evaluate the performance of various signal processing methods in handling abrupt phase difference changes, the signal frequency was initially maintained at the fundamental frequency of 104 Hz, and the phase difference abruptly changed from 0° to 2.6° at 0.6 s. The simulation results for phase difference estimation are as follows: Figure 5 As shown. The algorithm is considered to have converged when the phase difference error is less than 2%. Figure 5 As shown in Table 1, the SDTFT algorithm, Hilbert transform algorithm, STF algorithm and the ASTF algorithm proposed in this paper can all track the phase difference after the abrupt change, requiring 31.8, 8.1, 3.7 and 2.4 ms respectively. It can be seen that the convergence speed of the ASTF algorithm is faster than the other three algorithms.

[0071] To evaluate the estimation accuracy of the algorithm, the root mean square error of the parameters is defined as... .

[0072] The RMSE of the estimated values ​​is calculated, and the results are shown in Table 1. It can be seen that the estimation accuracy of the ASTF algorithm is better than that of the other three algorithms. This shows that, with the frequency unchanged and the phase difference abruptly changed, the ASTF algorithm has a faster step response speed, smaller tracking error, and better step response performance.

[0073] Analysis of cases where both frequency and phase difference undergo abrupt changes The frequency abruptly changes from 104 Hz to 103.92 Hz at 0.6 s, and the phase difference abruptly changes from 0° to 2.6° at 0.6 s. The simulation results for phase difference estimation are as follows. Figure 6 As shown in the figure. The algorithm is considered to have converged when the phase difference error is less than 2%.

[0074] Because the SDTFTT algorithm requires prior knowledge of the signal frequency, and the accuracy of the signal frequency directly affects the accuracy of the phase difference calculation, a lattice adaptive filter is first used to track the signal frequency. However, when the signal frequency changes abruptly, the lattice adaptive filter must reconverge to a new stable frequency point, making it impossible to track and calculate the frequency in real time during frequency changes. Consequently, the phase difference estimation results of the SDTFT algorithm exhibit significant fluctuations, resulting in low phase difference estimation accuracy, which will not be compared here.

[0075] Hilbert's algorithm, STF algorithm, and ASTF algorithm do not rely on signal frequency preprocessing. Figure 6 It can be seen that the Hilbert algorithm, the STF algorithm, and the ASTF algorithm proposed in this paper can all track the phase difference parameter after both the frequency and phase difference change abruptly, requiring 12, 5.2, and 4.0 ms respectively.

[0076] While the Hilbert algorithm can track phase difference changes without knowing the signal frequency, it suffers from fly-through due to its inherent endpoint effect. Furthermore, the Hilbert algorithm has weak anti-interference capabilities, and its computational accuracy is significantly affected by noise. Calculating the RMSE of the estimated values ​​shows that the ASTF algorithm has better estimation accuracy than both the STF and Hilbert algorithms. This demonstrates that the ASTF algorithm can effectively estimate the phase difference after both frequency and phase difference undergo a step change.

[0077] To address the abrupt phase difference changes in short-duration batch flow, this embodiment proposes a phase difference measurement method for Coriolis mass flow meters based on an adaptive strong tracking algorithm, building upon the Kalman filter algorithm. Experimental results show that this method can adaptively adjust the weakening factor, eliminates the need to predict the frequency of the CMF output signal, and exhibits high anti-interference performance. Compared to the STF and Hilbert transform algorithms, this algorithm achieves a shorter convergence time to 98% steady-state output while improving estimation accuracy, effectively enhancing the dynamic characteristics of the Coriolis mass flow meter.

[0078] This specification also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described method.

[0079] This specification provides a computer device including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the method described above.

[0080] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the methods described above. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, or optical storage, etc. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc.

[0081] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

Claims

1. A method for measuring the phase difference of a Coriolis mass flow meter based on an adaptive strong tracking algorithm, characterized in that, include: Acquire the output signal of the Coriolis mass flow meter and discretize the output signal into a sequence of sampled signals; Based on the sampled signal sequence, a signal state space model is established; Using the initialized adaptive strong tracking filter and combining it with the signal state model, time updates are performed to predict the current state variables and prior error covariance matrix. Calculate the covariance matrix of the current residual and the actual output residual; Based on the current residual, the weakening factor is dynamically adjusted to make the current residual and the weakening factor positively correlated. The fading factor is calculated based on the weakening factor, and the prior error covariance matrix is ​​corrected based on the fading factor. The Kalman gain matrix is ​​calculated based on the corrected prior error covariance matrix, and the current state estimate and error covariance matrix are updated based on the Kalman gain and the current time residual. Based on the updated state estimate for the current moment, the phase state vector is extracted to complete the phase difference measurement of the Coriolis mass flow meter at the current moment.

2. The method for measuring phase difference of a Coriolis mass flow meter based on an adaptive strong tracking algorithm as described in claim 1, characterized in that, The output signal is discretized into a sampled signal sequence. Specifically, it includes: ； in, For the first The signal amplitude at each sampling point For the first The signal angular frequency at each sampling point The sampling period is For the first The signal phase at each sampling point For the first Gaussian white noise at each sampling point.

3. The method for measuring phase difference of a Coriolis mass flow meter based on an adaptive strong tracking algorithm as described in claim 2, characterized in that: The signal state-space model includes state transition equations. and measurement equations ; ； ； in, This is the state transition matrix; For state variables, Signal amplitude The corresponding signal amplitude state quantity, For signal phase The corresponding signal phase state quantity, Signal angular frequency The corresponding signal frequency state quantity; For process noise, For measuring noise.

4. The method for measuring phase difference of a Coriolis mass flow meter based on an adaptive strong tracking algorithm as described in claim 1, characterized in that, The initialized adaptive strong tracking filter, combined with the signal state model, is used to perform time updates and predict the current time. state variables and prior error covariance matrix Specifically, it includes: ； ； in, Here is the state transition matrix. For the previous moment Predicted values ​​of state variables, For the previous moment of, Let be the process noise covariance matrix.

5. The method for measuring phase difference of a Coriolis mass flow meter based on an adaptive strong tracking algorithm as described in claim 1, characterized in that, The calculation of the residual at the current time and the actual output residual covariance matrix Specifically, it includes: ； ； in, For measurement equations nonlinear functions, The sampled value at the current moment. For the previous moment The residual, Forgetting factor, For the previous moment The residual covariance matrix, This is for transpose calculation.

6. The method for measuring phase difference of a Coriolis mass flow meter based on an adaptive strong tracking algorithm as described in claim 1, characterized in that, The weakening factor is dynamically adjusted based on the residual at the current moment. Specifically, making the current residual and the weakening factor positively correlated includes: ； in, As the initial value of the weakening factor, This is the weighting factor that decreases as the residual increases.

7. The method for measuring phase difference of a Coriolis mass flow meter based on an adaptive strong tracking algorithm as described in claim 1, characterized in that, The fading factor is calculated based on the weakening factor. The correction of the prior error covariance matrix based on the fading factor specifically includes: ； ； in, This is the residual volatility ratio. The trace of the matrix; To predict residual covariance, To measure the Jacobian matrix of the equation, Here is the noise covariance matrix; To correct the residual covariance, This is the corrected prior error covariance matrix.

8. The method for measuring phase difference of a Coriolis mass flow meter based on an adaptive strong tracking algorithm as described in claim 1, characterized in that, The Kalman gain matrix is ​​calculated based on the corrected prior error covariance matrix. The state estimate at the current time is updated based on the Kalman gain and the current time residual. And error covariance matrix Specifically, it includes: ； ； ； in, It is an identity matrix.

9. A computer-readable storage medium, characterized in that, The storage medium stores a computer program, which, when executed by a processor, implements the method described in any one of claims 1 to 8.

10. A computer device, characterized in that, The method includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the method described in any one of claims 1 to 8.

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