Gas-liquid two-phase spiral flow pattern identification method and system based on pressure signal statistical characteristics

Abstract

The invention discloses a gas-liquid two-phase spiral flow pattern identification method and system based on pressure signal statistical characteristics, and belongs to the technical field of multiphase flow. The method comprises the following steps: denoising a pressure signal through a sliding window method, calculating a mean value and a standard deviation in a window, setting a dynamic threshold value, and replacing an abnormal value with a median; generating a differential pressure signal to eliminate baseline drift; the method comprises the following steps: adaptively selecting a bandwidth based on a Silverman criterion, drawing a kernel density estimation (KDE) curve by adopting an Epanechnikov kernel function, and extracting morphological characteristics; in combination with four time domain parameters of standard deviation, skewness coefficient, variation coefficient and kurtosis, abnormal values are eliminated through a box plot, and a threshold interval is determined; and meanwhile, a flow pattern database is constructed, and flow pattern features are enhanced by using an image sharpening and slice splicing technology. And finally, realizing high-precision flow pattern identification through a KDE curve form and time domain parameter combined criterion. The method has the advantages of being high in signal stability, high in feature identification degree and good in identification robustness, and is suitable for automatic detection and control of complex gas-liquid two-phase spiral flow.

Description

Technical Field

[0001] The present invention belongs to the field of multiphase flow technology, and in particular relates to a method and system for identifying the flow pattern of a gas-liquid two-phase spiral flow based on statistical characteristics of a pressure signal. Background Art

[0002] Gas-liquid two-phase spiral flow is a complex flow process that is widely present in the fields of nuclear energy, petroleum, and chemical industry, and is particularly important in cyclone separators. To improve the performance of cyclone separators, it is necessary to consider the impact of the gas-liquid spiral flow pattern transition on the separation efficiency (Yue T, Chen J, Song J, et al. Experimental and numerical study of Upper Swirling Liquid Film (USLF) among Gas-Liquid Cylindrical Cyclones (GLCC) [J]. Chemical Engineering Journal, 2019, 358: 806-20.). Therefore, accurately identifying the gas-liquid two-phase spiral flow pattern not only helps to control the flow pattern in the separation chamber to be in a stable state for a long time, achieving stable operation and efficient separation of the separator, but also helps to reduce energy consumption and improve production efficiency and economic benefits in related industrial production.

[0003] In existing technologies, databases of different flow patterns are often established based on visualization experiments. The time-domain characteristics of two-phase fluids are extracted by measuring pressure pulsation signals or cross-sectional gas fraction signals. Probability density function (PDF) statistical analysis methods are then used to determine flow pattern criteria (Sun Qingming. Research on Flow Pattern Analysis Methods for Gas-Liquid Two-Phase Flow Based on Complex Networks [D], 2015). Traditional PDF methods are sensitive to noise and have difficulty capturing multimodal distribution characteristics. This limits their application in flow pattern identification and makes it difficult to meet high-precision identification requirements. Furthermore, a single time-domain characteristic statistical parameter (such as standard deviation) cannot accurately quantify the critical state of flow pattern transitions (Li X, Li L, Ma W, et al. Two-phase flow pattern identification in porous media using feature extraction and SVM [J]. International Journal of Multiphase Flow, 2022, 156:104-222). Therefore, it is necessary to use reasonable methods to improve the impact of noise, effectively present the useful signal part of the signal, and intuitively reflect the peak characteristics of the time domain signal statistical curves of different flow types, thereby improving the accuracy of flow type identification.

[0004] The Kernel Density Estimation (KDE) method is a non-parametric method in statistics used to estimate the probability density function of random variables. Compared with the traditional PDF, it can estimate the probability density function of data more smoothly and accurately. The KDE method can analyze the non-stationary characteristics of fluids and is suitable for processing complex gas-liquid flows. The KDE curve can capture subtle changes in the fluid state, especially when the two-phase flow mode switches. This characteristic enables it to effectively identify different flow types. By using the KDE method to extract the characteristics of the pressure signal in the time domain, the overall shape of the data set distribution can be accurately captured, providing a feasible optimization approach for solving the problem of noise sensitivity. Summary of the Invention

[0005] The purpose of the present invention is to provide a method and system for identifying the flow pattern of gas-liquid two-phase spiral flow based on the statistical characteristics of pressure signals, and to use the KDE statistical analysis method and multi-statistical parameter criterion to jointly perform high-precision identification of the gas-liquid two-phase spiral flow pattern.

[0006] The purpose of the present invention is achieved through the following technical solutions:

[0007] A method for identifying gas-liquid two-phase spiral flow patterns based on the statistical characteristics of pressure signals, the specific steps are as follows:

[0008] Step 1: Collect the pressure signal of the gas-liquid two-phase spiral flow, obtain the pressure signal sample points and perform denoising processing;

[0009] Using the sliding window method, the current pressure signal sample point and its two adjacent points before and after it are used as a window. The mean μ and standard deviation σ1 of the pressure signal within the window are calculated. Upper and lower thresholds are set. If the sample point exceeds the threshold range, the current sample value is replaced by the median within the window to obtain the threshold coefficient ρ. The threshold setting coefficient ρ is adjusted to optimize the smoothness of the denoised signal.

[0010] Step 2: Extract the denoised pressure signal;

[0011] Calculate the mean m of the denoised pressure signal sample points, subtract each pressure signal sample point from its mean, and obtain a pressure difference signal with the same number of original data samples, and use it to replace the original pressure signal sample points;

[0012] Step 3: Perform kernel density estimation (KDE) analysis based on the adaptive bandwidth selection method;

[0013] The bandwidth h is calculated according to the Silverman criterion, and the Epanechnikov kernel function is used to draw the KDE curve and perform probability density estimation;

[0014] Step 4: Extract the KDE curve morphological features of different flow patterns, including the number of peaks, width, symmetry, and curve tail performance characteristics, and match them with the features in the flow pattern database;

[0015] Step 5: Based on the flow pattern database, calculate the time domain characteristic parameters of the denoised pressure signal samples for different flow patterns, and introduce the standard deviation σ2 and skewness coefficient S after denoising. k , coefficient of variation CV and kurtosis K, for all-round flow pattern identification based on time domain characteristics;

[0016] Step 6: Eliminate outliers of time domain parameters based on the box plot and determine the threshold range of each parameter;

[0017] Step 7: Combine the KDE curve morphological characteristics and the time domain parameter threshold interval to jointly judge and identify the gas-liquid two-phase spiral flow pattern.

[0018] Furthermore, the step 1 is specifically as follows:

[0019] Step 1.1: From the third pressure signal sample point to the third-to-last pressure signal sample point, define the two points before and after each sample point as its adjacent values, and define the pressure signal sample point and its four adjacent values as a group; calculate the mean and standard deviation of the pressure signal values within the group of each pressure signal sample point in all data. For n pressure signal sample points, the calculation method is as follows:

[0020]

[0021]

[0022] Among them, x i is the original pressure signal sample point, μ is the mean of the original pressure signal sample points within a group, and σ1 is the standard deviation of the original pressure signal sample points within a group;

[0023] Step 1.2: Set the upper and lower thresholds as follows:

[0024] U=μ+ρ*σ1

[0025] L=μ-ρ*σ1

[0026] Among them, U is the upper limit of the signal threshold, L is the lower limit of the signal threshold, ρ is the threshold setting coefficient, and the initial value is 0.5;

[0027] Step 1.3: Plot a comparison chart of the original signal and the denoised signal to observe the denoising effect. If the denoised signal curve is still too rough or too smooth, adjust the threshold setting coefficient ρ until a more satisfactory effect is achieved.

[0028] Furthermore, in step 2, for n pressure signal sample points, the calculation formula for the mean m of the denoised pressure signal sample points is as follows:

[0029]

[0030] Among them, x i is the pressure signal sample point after denoising, and n is the number of pressure signal sample points.

[0031] At the same time, the standard deviation of the denoised pressure signal is calculated using the following formula:

[0032]

[0033] Among them, x i is the pressure signal sample point after denoising, and m is the mean of the pressure signal sample points after denoising.

[0034] Furthermore, the formula for the bandwidth h in step 3 is:

[0035]

[0036] Where, IQR(X) is the interquartile range of the sample;

[0037] Let x1,x2,···,x n For n sample points with independent and identical distribution of unit variable X, the kernel density estimation formula of probability density function is as follows:

[0038]

[0039] Among them, K(u) is the kernel function, and its mathematical expression is as follows:

[0040]

[0041] The integral of the kernel function is equal to 1 within its domain, which satisfies:

[0042]

[0043] Furthermore, the establishment of the flow pattern database in step 4 includes sharpening the visualized flow pattern image, extracting fixed pixel slices and vertically splicing them to generate a feature-enhanced image.

[0044] Furthermore, the standard deviation σ2 and skewness coefficient S introduced in step 5 are k , coefficient of variation CV and kurtosis K, the calculation formula is:

[0045]

[0046] Furthermore, in step 7, when the KDE curve shape and the four time domain parameters simultaneously fall into the threshold interval of the corresponding flow type, it is determined to be a matching flow type.

[0047] A computer device / equipment / system includes a memory, a processor, and a computer program stored in the memory. The processor executes the computer program to implement the steps of a method for identifying the flow pattern of a gas-liquid two-phase spiral flow based on the statistical characteristics of a pressure signal.

[0048] The beneficial effects of the present invention are:

[0049] (1) Using the sliding window method, adaptive threshold setting is achieved by gradually calculating the mean and standard deviation. This can remove obvious abnormal fluctuations while retaining the original characteristics of the signal, effectively enhancing the signal stability. The operation method is simple and efficient, and plays a key role in presenting the morphological characteristics of the KDE statistical curve.

[0050] (2) Replacing the original pressure signal with the pressure difference signal can effectively quantify the relative change of the signal and eliminate the data instability caused by the baseline drift and other reasons of the original pressure signal, thereby focusing on analyzing the changes in the flow state and helping to identify the flow type more accurately;

[0051] (3) KDE curve drawing based on the Epanechnikov kernel function can improve the smoothness of the curve compared with the traditional PDF curve, effectively avoiding the hindrance of peak feature analysis caused by its sensitivity to noise. At the same time, based on adaptive bandwidth selection, it can achieve a balance between curve smoothness and data feature retention, and clearly reflect the probability density distribution of the pressure difference signal;

[0052] (4) Based on image processing technology, the flow pattern characteristics of different visualized gas-liquid spiral flows are extracted. Since the internal flow field of the two-phase spiral flow is complex and the phenomenon changes dramatically, compared with direct visual observation, this method can effectively reduce the influence of subjective factors to a certain extent and establish a more accurate flow pattern database;

[0053] (5) Combined with the flow pattern database, four non-dimensional parameters, namely standard deviation, skewness coefficient, coefficient of variation and kurtosis, are selected to quantitatively analyze the flow pattern. The threshold intervals of different time domain characteristic parameters are given, which reduces the impact of the randomness of various flow conditions on the data analysis results and improves the reliability of flow pattern identification with a standardized processing method.

[0054] (6) The KDE curve morphological characteristics and the dimensionless parameter threshold interval are used together as flow pattern identification criteria, so that it can also perform well for complex data distribution of unstable flow patterns. It not only has a wide coverage range and high recognition accuracy, but also has simple operation steps and strong feasibility, providing a repeatable and efficient flow pattern identification technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 The present invention is a flow chart of a method for identifying a gas-liquid two-phase spiral flow pattern based on statistical characteristics of a pressure signal in an embodiment. DETAILED DESCRIPTION

[0056] The present invention will be further described below with reference to the accompanying drawings.

[0057] The present invention provides a method and system for identifying the flow pattern of a gas-liquid two-phase spiral flow based on the statistical characteristics of a pressure signal, and solves the following technical problems: the traditional flow pattern identification method based on a pressure pulsation signal needs to eliminate noise interference in order to obtain a more accurate response signal. However, in the implementation process, the use of methods such as wavelet transform can only optimize the denoising effect to a certain extent, and the final probability density function curve will still have many peaks formed by noise, which will have an adverse effect on the judgment of the characteristics of different flow pattern curves, thereby affecting the flow pattern identification accuracy. At the same time, the existing method is also mainly based on a visual flow pattern database, combined with time domain characteristic parameters to assist in identifying flow patterns, but due to the complexity of the vortex flow pattern phenomenon, its transition boundary is difficult to accurately distinguish, resulting in the establishment of a flow pattern database. There may be large subjective errors, and the overlapping span of the characteristic parameter threshold interval under different flow patterns is large, resulting in a single statistical characteristic parameter being unable to accurately quantify the critical state of flow pattern identification.

[0058] like Figure 1 As shown, this embodiment provides a method for identifying the flow pattern of gas-liquid two-phase spiral flow based on the statistical characteristics of pressure signals, comprising the following steps:

[0059] S1: Obtain the pressure signal and perform denoising using a sliding window method. First, define a grouping method, calculate the mean and standard deviation of each pressure signal sample point within the group, set upper and lower thresholds based on the mean and standard deviation, and replace the signal portion exceeding the threshold with the median of the adjacent sample points to obtain a denoised signal consistent with the original number.

[0060] S2, based on the mean value of the denoised pressure signal, obtains a relative pressure signal that is consistent with the original quantity, i.e., the pressure difference signal;

[0061] S3, based on the processed pressure difference signal, the adaptive bandwidth selection method is used to draw the KDE curves under different gas-liquid two-phase spiral flow patterns, and the peak number, peak distribution characteristics and peak range of each curve are counted;

[0062] S4, establish a flow pattern database, use statistical methods to calculate the standard deviation, skewness coefficient, coefficient of variation and kurtosis of the pressure signal, four time domain characteristic parameters as flow pattern quantitative identification standards, obtain the threshold range of the characteristic parameters, and combine the characteristic parameter threshold with the KDE curve characteristics to jointly judge and identify the gas-liquid two-phase spiral flow pattern.

[0063] In one embodiment, a method for identifying a gas-liquid two-phase spiral flow pattern based on statistical characteristics of a pressure signal specifically includes the following steps:

[0064] (1) Obtain the pressure signal and perform denoising first. Perform sliding window processing on the signal, that is, from the third pressure signal sample point to the third-to-last pressure signal sample point, define the two points before and after each sample point as its adjacent values, and define the pressure signal sample point and its four adjacent values as a group. Calculate the mean and standard deviation of the pressure signal values in the group where each pressure signal sample point belongs in all the data. For n pressure signal sample points, the calculation method is as follows:

[0065]

[0066] Among them, x i is the original pressure signal sample point, μ is the mean of the original pressure signal sample points within a group, and σ1 is the standard deviation of the original pressure signal sample points within a group.

[0067] (2) Based on the mean and standard deviation, set upper and lower thresholds. If the signal exceeds the set upper and lower thresholds, the median of the pressure signal sample group is used to replace the current signal value, thereby realizing the detection and replacement of the pulse signal. This can effectively reduce the impact of outliers on the signal and maintain the overall trend of the signal. The method for setting the upper and lower thresholds is as follows:

[0068] U=μ+ρ*σ1

[0069] L=μ-ρ*σ1

[0070] Among them, U is the upper limit of the signal threshold, L is the lower limit of the signal threshold, μ is the mean of the original pressure signal within a group, σ1 is the standard deviation of the original pressure signal within a group, and ρ is the threshold setting coefficient, and the initial value can be 0.5.

[0071] (3) Draw a comparison chart of the original signal and the denoised signal to observe the denoising effect. If the denoised signal curve is still too rough or too smooth, readjust the threshold setting coefficient ρ until a more ideal effect is achieved.

[0072] (4) Extract the denoised pressure signal. First, calculate the mean of the pressure signal. Then, subtract each pressure signal sample point from its mean to obtain a pressure difference signal with the same number of original pressure signal samples, and use it to replace the original pressure signal. For n pressure signal sample points, the mean calculation formula is as follows:

[0073]

[0074] Among them, x iis the pressure signal sample point after denoising, and n is the number of pressure signal sample points.

[0075] At the same time, the standard deviation of the denoised pressure signal is calculated, which is needed in the subsequent bandwidth selection. The calculation formula is as follows:

[0076]

[0077] Among them, x i is the pressure signal sample point after denoising, and m is the mean of the pressure signal sample points after denoising.

[0078] (5) Improve the accuracy of the analysis through adaptive bandwidth selection (Silverman criterion), that is, set the bandwidth based on the standard deviation of the data to adapt to the distribution characteristics of the data. The choice of bandwidth affects the shape and characteristics of the kernel density estimate. In order to increase the smoothness of the curve while retaining certain data characteristics as much as possible. The bandwidth selection formula is as follows:

[0079]

[0080] Where IQR(X) is the interquartile range of the pressure signal samples.

[0081] The standard deviation is sensitive to changes in the overall data distribution, while the interquartile range is less affected by outliers, providing a more robust estimate when the data distribution is skewed or there are outliers. In the above bandwidth selection formula, the bandwidth is no longer fixed but instead adapts to the actual distribution characteristics of the data, effectively avoiding oversmoothing or undersmoothing the KDE curve, achieving a certain degree of balance.

[0082] (6) Select the Epanechnikov kernel function to draw the KDE curve. The horizontal axis of the curve is the sample value of the pressure difference signal, and the vertical axis is the probability density under the specific pressure signal sample value, which reflects the relative frequency of the data. Let x1, x2, ···, x n For n pressure signal sample points with independent and identical distribution of unit variable X, the kernel density estimation calculation formula of probability density function is as follows:

[0083]

[0084] Among them, K(u) is the kernel function, and its mathematical expression is as follows:

[0085]

[0086] The integral of the kernel function is equal to 1 within its domain, which satisfies:

[0087]

[0088] This property enables it to be used in kernel density estimation and can provide smooth probability density function estimates.

[0089] (7) Compare the KDE curve characteristics of different flow patterns. The peak value, width, symmetry, and tail performance of the KDE curves of different flow patterns are different. At the same time, the number and position distribution of peaks are also significantly different. The morphological characteristics of the KDE curves of different gas-liquid spiral flow patterns are extracted and summarized as the criteria for flow pattern identification.

[0090] (8) To obtain clear visual flow pattern images, first brighten and sharpen the different gas-liquid two-phase spiral flow pattern images. Then, sequentially extract fixed pixel-length sections of the image. These slices are vertically spliced together to form a complete image. This method can extract the most obvious features of each flow pattern at a certain axial position. By observing and classifying these synthesized images, a more accurate flow pattern database can be established.

[0091] (9) Based on the flow pattern database, the time domain characteristic parameters of the denoised pressure signal samples are calculated for different flow patterns. By introducing dimensionless time domain characteristic parameters, the signal distribution differences of different flow patterns can be quantified. Here, the standard deviation σ and skewness coefficient S are introduced. k Four dimensionless parameters, CV, and kurtosis K, are used to further identify the flow pattern, where σ reflects the discrete degree of the signal, S k It is used to measure the symmetry of signal distribution, CV reflects the relative fluctuation of the signal, and K is used to describe the flatness of the signal waveform. The specific calculation formulas for each parameter are as follows:

[0092]

[0093] (10) The temporal characteristic parameters under different flow patterns are represented in the form of box plots. This can stably depict the discrete distribution of the data without being affected by outliers. Data points beyond the upper and lower edges of the box plot are determined as outliers. The relevant outliers are eliminated, and the interval formed by the remaining data points is used as the threshold interval of the temporal characteristic parameters of different flow patterns.

[0094] (11) The KDE curve morphological characteristics are used as the basis for flow pattern identification, and the four time-domain characteristic parameter threshold intervals are combined as joint criteria for flow pattern identification, which are used together for flow pattern identification and judgment. Specifically, the KDE curve can effectively reflect the distribution characteristics and flow pattern changes of gas-liquid two-phase flow, while the time-domain characteristic parameters provide further quantitative analysis of signal volatility and distribution morphology, thereby improving the accuracy of flow pattern identification. This method does not require visualization of the internal flow state of the fluid, reduces dependence on sensors of complex equipment, and provides operational convenience, which is of great significance for the identification and control of gas-liquid two-phase spiral flow patterns.

[0095] The function of the gas-liquid two-phase spiral flow pattern identification system based on pressure signal statistical characteristics of the present invention can be explained by the aforementioned gas-liquid two-phase spiral flow pattern identification method based on pressure signal statistical characteristics, which will not be repeated here.

[0096] This flow pattern identification method was used to identify the gas-liquid two-phase spiral flow induced by a blade-type swirler in a vertical tube with a diameter of 50 mm. Considering the influence of spiral flow stability on identification, the comparative experiments were designed to include two typical spiral flow patterns with unique properties: spiral column flow and spiral intermittent flow. The experimental comparison data are shown in the table below. The experimental verification results show that compared with the traditional PDF method, the overall flow pattern identification efficiency of this method increased from 83.33% to 95.28%, with a significant improvement in the identification of stable flow patterns such as spiral column flow.

[0097]

[0098] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. A method for identifying gas-liquid two-phase spiral flow patterns based on statistical characteristics of pressure signals, characterized by: The specific steps are as follows: Step 1: Collect the pressure signal of the gas-liquid two-phase spiral flow, obtain the pressure signal sample points and perform denoising processing; The sliding window method is used. The current pressure signal sample point and its two adjacent points before and after it are used as a window. The mean μ and standard deviation σ1 of the pressure signal in the window are calculated. The upper and lower thresholds are set. If the sample point exceeds the threshold range, the current sample value is replaced by the median in the window to obtain the threshold coefficient ρ. Adjust the threshold setting coefficient ρ to optimize the smoothness of the denoised signal; Step 2: Extract the denoised pressure signal; Calculate the mean m of the denoised pressure signal sample points, subtract each pressure signal sample point from its mean, and obtain a pressure difference signal with the same number of original data samples, and use it to replace the original pressure signal sample points; Step 3: Perform kernel density estimation (KDE) analysis based on the adaptive bandwidth selection method; The bandwidth h is calculated according to the Silverman criterion, and the Epanechnikov kernel function is used to draw the KDE curve and perform probability density estimation; Step 4: Extract the KDE curve morphological features of different flow patterns, including the number of peaks, width, symmetry, and curve tail performance characteristics, and match them with the features in the flow pattern database; Step 5: Based on the flow pattern database, calculate the time domain characteristic parameters of the denoised pressure signal samples for different flow patterns, and introduce the standard deviation σ2 and skewness coefficient S after denoising. k , coefficient of variation CV and kurtosis K, for all-round flow pattern identification based on time domain characteristics; Step 6: Eliminate outliers of time domain parameters based on the box plot and determine the threshold range of each parameter; Step 7: Combine the KDE curve morphological characteristics and the time domain parameter threshold interval to jointly judge and identify the gas-liquid two-phase spiral flow pattern.

2. The method for identifying gas-liquid two-phase spiral flow patterns based on pressure signal statistical characteristics according to claim 1, characterized in that: The step 1 is specifically as follows: Step 1.1: From the third pressure signal sample point to the third-to-last pressure signal sample point, define the two points before and after each sample point as its adjacent values, and define the pressure signal sample point and its four adjacent values as a group; calculate the mean and standard deviation of the pressure signal values within the group of each pressure signal sample point in all data. For n pressure signal sample points, the calculation method is as follows: Among them, x i is the original pressure signal sample point, μ is the mean of the original pressure signal sample points within a group, and σ1 is the standard deviation of the original pressure signal sample points within a group; Step 1.2: Set the upper and lower thresholds as follows: U=μ+ρ*σ1 L=μ-ρ*σ1 Among them, U is the upper limit of the signal threshold, L is the lower limit of the signal threshold, ρ is the threshold setting coefficient, and the initial value is 0.5; Step 1.3: Plot a comparison chart of the original signal and the denoised signal to observe the denoising effect. If the denoised signal curve is still too rough or too smooth, adjust the threshold setting coefficient ρ until a more satisfactory effect is achieved.

3. The method for identifying gas-liquid two-phase spiral flow patterns based on pressure signal statistical characteristics according to claim 1, characterized in that: In step 2, for n pressure signal sample points, the calculation formula for the mean m of the pressure signal sample points after denoising is as follows: Among them, x i is the pressure signal sample point after denoising, and n is the number of pressure signal sample points. At the same time, the standard deviation of the denoised pressure signal is calculated using the following formula: Among them, x i is the pressure signal sample point after denoising, and m is the mean of the pressure signal sample points after denoising.

4. The method for identifying gas-liquid two-phase spiral flow patterns based on pressure signal statistical characteristics according to claim 1, characterized in that: The formula for the bandwidth h in step 3 is: Where, IQR(X) is the interquartile range of the sample; Let x1,x2,···,x n For n sample points with independent and identical distribution of unit variable X, the kernel density estimation formula of probability density function is as follows: Among them, K(u) is the kernel function, and its mathematical expression is as follows: The integral of the kernel function is equal to 1 within its domain, which satisfies:

5. The method for identifying gas-liquid two-phase spiral flow patterns based on pressure signal statistical characteristics according to claim 1, characterized in that: The establishment of the flow pattern database in step 4 includes sharpening the visualized flow pattern image, extracting fixed pixel slices and vertically splicing them to generate a feature-enhanced image.

6. The method for identifying gas-liquid two-phase spiral flow patterns based on pressure signal statistical characteristics according to claim 1, characterized in that: The standard deviation σ2 and skewness coefficient S introduced in step 5 k , coefficient of variation CV and kurtosis K, the calculation formula is:

7. The method for identifying gas-liquid two-phase spiral flow patterns based on pressure signal statistical characteristics according to claim 1, characterized in that: In step 7, when the KDE curve shape and the four time domain parameters simultaneously fall into the threshold interval of the corresponding flow type, it is determined to be a matching flow type.

8. A computer device / apparatus / system comprising a memory, a processor, and a computer program stored in the memory, characterized in that: The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 6.

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