A method for characterizing flow patterns of a gas-solid fluidized bed based on statistical characteristics of pressure drop

Abstract

The application discloses a kind of gas-solid fluidized bed flow mode characterization method based on pressure drop statistical characteristics, including by regular lift gas velocity, let bed layer experience different fluidization state, obtain the dynamic pressure difference signal of bed layer side wall multiple points;Low-pass filtering is carried out to the bed layer side wall pressure difference signal obtained in real time;Meanwhile, the data after low-pass filtering noise reduction is normalized to obtain normalized pressure difference time series signal;Characteristic parameters of normalized pressure difference time series signal are extracted using time-frequency domain statistical analysis method;The time-space matrix of multi-dimension characteristic parameters is constructed using statistical characteristics, and the transition of bed layer flow mode is quantitatively and cooperatively represented;For the time-space matrix flow pattern cluster formed under different superficial gas velocities, principal component analysis and K-means clustering analysis are carried out on it in characteristic space.The application avoids the disadvantages of immersion measurement and single-point measurement modeling characterization technology, and provides technical reserves for air dense medium fluidized bed flow pattern transition and fluidization state monitoring.

Description

Technical Field

[0001] This invention relates to the field of dry separation technology for gas-solid fluidized beds, specifically to a method for characterizing flow patterns in gas-solid fluidized beds based on statistical characteristics of pressure drop. Background Technology

[0002] Air-heavy media fluidized beds play a crucial role in the efficient and clean upgrading of low-quality coal and are one of the most effective methods in dry separation technology. Their separation performance strongly depends on the uniformity and dynamic stability of the bed density under bubbling fluidization conditions. The spatiotemporal fluidization state of the bed is one of the most important influencing factors, especially the rational setting of various thresholds in the monitoring system and the intelligent control of the separation process.

[0003] The separation performance of air-heavy media fluidized beds strongly depends on the uniformity and dynamic stability of bed density under bubbling fluidization conditions. Understanding the spatiotemporal fluidization characteristics of air-heavy media fluidized beds is crucial for real-time monitoring and control, especially for efficient and clean separation and process modeling. Visual observation and personal experience lack a quantitative or objective description of air-heavy media fluidized beds under different flow modes, particularly when exploring optimal sorting fluidization states. Each fluidization state of an air-heavy media fluidized bed possesses unique spatiotemporal characteristics and can be used to handle specific types of gas-solid reaction processes in various industries. To fully utilize the advantages of air-heavy media fluidized beds in microbubble fluidization states for mineral sorting and to promote the application of bed fluidization state monitoring and intelligent control, bed flow mode switching must be a priority. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention proposes a method for characterizing the flow pattern of a gas-solid fluidized bed based on statistical characteristics of pressure drop. It utilizes local pressure difference information obtained through non-immersion measurements to jointly and quantitatively characterize the more detailed spatiotemporal dynamic behavior of an air-heavy medium fluidized bed under different flow regimes and during flow regime transitions. Based on non-immersion multi-point measurements, a spatiotemporal matrix of characteristic parameters is constructed according to the statistical characteristic parameters of the normalized pressure drop signal time series. This allows for understanding and characterizing the temporal and spatial differences in pressure difference signals under different fluidization states from multiple characteristic parameter dimensions. To achieve the above technical objectives, this invention adopts the following technical solution:

[0005] A method for characterizing gas-solid fluidized bed flow patterns based on pressure drop statistical characteristics includes the following steps:

[0006] S1: By regularly increasing the gas velocity, the bed undergoes different fluidization states, and synchronous dynamic differential pressure signals at multiple points on the sidewall of the bed are acquired in real time.

[0007] S2: Low-pass filtering is performed on the real-time acquired bed sidewall pressure difference signal; at the same time, the data after low-pass filtering and noise reduction is normalized to obtain the normalized pressure difference time series signal;

[0008] S3: Use time-frequency domain statistical analysis methods to extract the characteristic parameters of the normalized differential pressure time series signal;

[0009] S4: Construct a spatiotemporal matrix of multi-dimensional feature parameters using statistical features to quantitatively and collaboratively characterize the transformation of bed flow patterns;

[0010] S5: For the spatiotemporal matrix manifold clusters formed under different apparent gas velocities, principal component analysis and K-means cluster analysis are performed on them in the feature space.

[0011] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0012] This method acquires synchronous dynamic differential pressure signals at multiple points on the bed sidewall using a non-immersion measurement approach. It then employs statistical analysis to extract characteristic parameters from the time-series differential pressure signals, proposing a method to quantitatively characterize the real-time fluidization state of the bed using these multi-point differential pressure fluctuation characteristic parameters. Based on this, a spatiotemporal matrix of multi-dimensional characteristic parameters is constructed to quantitatively and collaboratively characterize the transformation of bed flow patterns. Cluster analysis of the spatiotemporal matrix flow pattern clusters in the characteristic space demonstrates that classifying three typical flow pattern transitions is feasible and effective. This invention avoids the drawbacks of immersion measurement and single-point measurement modeling techniques, providing a technical reserve for monitoring flow pattern transformation and fluidization state in air-heavy medium fluidized beds. It also has certain reference value for equipment scale-up, operating system upgrades, and intelligent control of air-heavy medium fluidized beds. Attached Figure Description

[0013] To more clearly illustrate the technical solutions of the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0014] Figure 1 This is a schematic diagram of the gas-solid fluidized bed flow mode characterization system.

[0015] Figure 2 A half-violin plot showing the distribution of pressure drop data at nine apparent gas velocities acquired synchronously.

[0016] Figure 3 This is a data distribution map showing the time-domain statistical characteristics and apparent gas velocity in different measurement areas.

[0017] Figure 4This is a data distribution diagram showing the frequency domain statistical characteristics and apparent gas velocity in different measurement areas.

[0018] Figure 5 Radar plot of eigenvectors of the characteristic parameter matrix under different apparent air velocities.

[0019] Figure 6 The image shows the spatial cluster diagrams of PCs for samples under three fluidization states.

[0020] Figure 7 This is a cluster distribution diagram of sample data for the initial fluidized state and the microbubble fluidized state.

[0021] In the diagram: 1. Blower; 2. Air receiver; 3. Solenoid valve; 4. Flow meter; 5. Pre-distribution air chamber; 6. Bed; 7. Differential pressure sensor; 8. Data acquisition instrument; 9. Computer; 10. Exhaust hood; 11. Dust collector; 12. Exhaust fan. Detailed Implementation

[0022] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0023] like Figure 1As shown, the gas-solid fluidized bed flow mode characterization system includes a bed body 6, with a pre-distribution air chamber 5 located below the bed body 6. An air receiver 2 is connected to the pre-distribution air chamber 5 via pipelines, which include a solenoid valve 3 and a flow meter 4. The air receiver 2 is connected to a blower 1 via pipelines. A dust collector 11 is located above the air receiver 2, with one end connected to an induced draft fan 12 and the other end connected to an induced draft hood 10. The induced draft hood 10 is positioned above the bed body 6. Six non-immersion pressure measuring ports are evenly spaced along the centerline of the side wall of the bed body 6 from bottom to top. A differential pressure sensor 7 is installed between two adjacent non-immersion pressure measuring ports. The differential pressure sensors 7 are numbered DP1, DP2, DP3, DP4, and DP5 from bottom to top. The differential pressure sensors 7 are connected to a data acquisition instrument 8, which is connected to a computer 9. The dynamic differential pressure signal of each differential pressure sensor 7 is measured at both ends, i.e., a two-point differential pressure. Nine apparent gas velocities were set, with operating ranges of 0.60, 0.70, 0.80, 0.90, 1.00, 1.15, 1.25, 1.35, and 1.45 times the minimum fluidizing gas velocity (Umf). By regularly increasing the gas velocity, air was delivered from blower 1 and air receiver 2 into the pre-distribution air chamber 5 at the bottom of the bed 6, and then evenly distributed through the gas distributor before fluidizing the medium particles upwards. DP1, DP2, DP3, DP4, and DP5 synchronously collected local pressure drop signals at 5, 10, 15, 20, 25, and 30 cm above the air distributor in real time.

[0024] This invention provides a method for characterizing gas-solid fluidized bed flow patterns based on pressure drop statistical characteristics, comprising the following steps:

[0025] S1: By regularly increasing the gas velocity, the bed undergoes different fluidization states, and synchronous dynamic differential pressure signals at multiple points on the bed sidewall are acquired in real time; the synchronous dynamic differential pressure signals at multiple points on the bed sidewall are acquired by pressure sensors in a non-immersion measurement method.

[0026] S2: The real-time acquired bed sidewall pressure difference signal is low-pass filtered with a cutoff frequency of 60Hz; at the same time, the data after low-pass filtering and noise reduction is normalized to obtain a normalized pressure difference time series signal; the data normalization process is to eliminate the dimensional influence between indicators.

[0027] The normalization formula is defined as follows:

[0028]

[0029] Where, p i These are the standardized values ​​of each variable. These are the original values ​​of each variable. and These are the maximum and minimum values ​​of each variable; for example... Figure 2As shown, the waveform differences of the probability density function of five pressure drop signals under different fluidization states are compared and analyzed. This indicates that the probability density function under different fluidization states contains a wealth of information about the changes in flow patterns. It is necessary to extract and analyze the representative time-domain and frequency-domain statistical features (feature parameters).

[0030] S3: Use time-frequency domain statistical analysis methods to extract the characteristic parameters of the normalized differential pressure time series signal; the characteristic parameters include: standard deviation, skewness, kurtosis, centroid frequency, and frequency standard deviation;

[0031] Standard deviation is a statistic that measures the variability or dispersion of a signal. It measures the difference between each data point in a set of signal samples and the mean of the dataset. The formula for calculating standard deviation is as follows:

[0032]

[0033] Where n is the number of signal samples, x i It is each sample value, x mean It is the average value of the signal;

[0034] Skewness is a statistical measure used to describe the distribution pattern of a signal. It measures the degree of asymmetry of signal data relative to its mean. Generally, a skewness in the range [-1, 1] can be considered relatively symmetrical, while an absolute value greater than 1 can be considered a significantly skewed distribution. The formula for calculating skewness is as follows:

[0035]

[0036] Where n is the number of signal samples, x i It is each sample value, x mean σ is the average value of the signal, and σ is the standard deviation of the signal.

[0037] Kurtosis is a statistical measure used to describe the distribution pattern of a signal. It measures the degree of peak or sharpness of signal data relative to its mean. A kurtosis greater than 3 indicates that the signal distribution has a sharper peak pattern than a normal distribution, and is called positive kurtosis. A kurtosis less than 3 indicates that the signal distribution is relatively flat-topped, and is called negative kurtosis. The formula for calculating kurtosis is as follows:

[0038]

[0039] Where n is the number of signal samples, x i It is each sample value, x mean σ is the average value of the signal, and σ is the standard deviation of the signal.

[0040] The centroid frequency is an index used to describe the energy distribution of a signal in the frequency domain. It represents the center position of the signal's power spectrum and can provide the average concentration point of the signal's frequency. The formula for calculating the centroid frequency is as follows:

[0041]

[0042] Where f represents frequency, and P(f) represents the power spectral density at frequency f;

[0043] Frequency standard deviation is a measure of the width of a signal's frequency distribution in the frequency domain. It represents the degree of dispersion or expansion of the frequency components in the power spectrum. In the calculation, frequency becomes the weight, used to represent the contribution of different frequencies to the overall power spectrum. The formula for calculating the frequency standard deviation is as follows:

[0044]

[0045] Where f represents frequency, f avg Let f represent the average frequency, and P(f) represent the power spectral density at frequency f.

[0046] The frequency domain statistical analysis method is the smoothed pseudo-Wigner-Ville distribution method. The smoothed pseudo-Wigner-Ville distribution is a commonly used method in time-frequency analysis and is an improved version of the Wigner-Ville distribution. Its calculation results can provide the local energy distribution of the signal in time and frequency, reflecting the time-frequency characteristics of the signal. The calculation formula is as follows:

[0047]

[0048] Where SPWVD(t,f) is a smoothed pseudo-Wignaville distribution, h(τ) and g(u-τ) are smoothing window functions, x(t) is the input signal, f is the frequency variable, t is the time variable, u is the frequency delay, τ is the time delay, * is the complex conjugate, and e -jfτ For the parameter factors of the Fourier transform;

[0049] By using time-frequency domain statistical analysis, characteristic parameters of the normalized pressure difference time series signal were extracted, and the data distribution and intrinsic relationship between the statistical characteristics and apparent gas velocity in different measurement areas were obtained. Figure 3 and Figure 4As shown, with the change in fluidization state, the pressure difference PDF in the five axial measurement regions extends from positive to negative skewness, with slightly different trends. Meanwhile, the change in fluidization state is mainly concentrated in the steep kurtosis range (K>3), and the PDF kurtosis in different axial measurement regions is most sensitive to the fully bubbling fluidization state. The frequency energy and energy spectrum waveform in the fully bubbling fluidization state are relatively sensitive to changes in fluidization state, mainly reflected in the distribution of the pressure difference signal power spectrum. During the transition of fluidization state, the distribution characteristics of the centroid frequency are similar in each measurement region, and the sensitivity to centroid frequency shifts and power spectrum fluctuations is low. The distribution characteristics of the frequency standard deviation are similar to those of the centroid frequency.

[0050] S4: Construct a spatiotemporal matrix of multi-dimensional feature parameters using statistical features, such as... Figure 5 As shown in the figure, the quantitative synergistic characterization of the bed flow pattern transformation reveals that the internal structural information of the characteristic parameter matrix exhibits different distribution patterns with increasing apparent gas velocity. Compared to the other two fluidization states, the internal structural information of the characteristic parameter matrix is ​​more prominent in the fully bubbling fluidization state, with clearer trends and outlines of matrix data and a more defined characteristic space. However, in the initial fluidization and microbubble fluidization states, the internal structural information of the characteristic parameter matrix shows a similar distribution, and the characteristic space is relatively ambiguous. Each matrix has its inherent characteristics, and the eigenvectors tend to reflect the differences between different matrices. Solving for the eigenvectors of the characteristic parameters is significant because it helps to identify the aspects in which the matrices produce greater differences, thereby reducing information overlap and retaining effective information. Five characteristic parameters of the pressure difference signal in the time and frequency domains are selected to characterize the fluidization state. These characteristic parameters are represented by eigenvectors in each measurement region, i.e., x = {t1, t2, t3, ..., t...}. p} T Where p = 5, t1 = σ, t2 = S, t3 = K, t4 = CF, t5 = FSD, the fluidization state of the bed layer under each apparent gas velocity can be characterized by a spatiotemporal matrix of multi-dimensional characteristic parameters, i.e., X = {x1, x2, ..., x N}, where N = 5, and N represents the longitudinal measurement area location;

[0051] S5: For the spatiotemporal matrix flow pattern clusters formed under different apparent gas velocities, principal component analysis and K-means cluster analysis are performed on them in the feature space; the clusters of characteristic parameters of the three typical fluidization states in different dimensional spaces are as follows: Figure 6 As shown, from a two-dimensional perspective, the fully bubbling fluidized state exhibits clear separation characteristics in the two-dimensional space (PC1, PC2) and is easily distinguishable. The other two fluidization states overlap in the space, resulting in blurred boundaries. Since the initial fluidized state and the microbubble fluidized state have blurred boundaries in the principal component space and are difficult to distinguish, another feature space needs to be constructed. Figure 7The cluster space of sample data for the initial fluidization state and the microbubble fluidization state based on K-means is displayed. The centroid between the initial fluidization state and the microbubble fluidization state represents the result calculated by the classification method. As can be seen from the figure, the K-means clustering algorithm can classify and identify the two fluidization states in the feature space with high discriminative performance. To further quantify the internal structure information of the spatiotemporal matrix of feature parameters under different fluidization states, principal component analysis is used to extract feature parameters under different fluidization states, and the sensitivity of feature parameters to fluidization state is quantitatively studied. The principal component analysis process is as follows:

[0052] Let x be an m-dimensional random variable, and let Σ be the covariance matrix. The eigenvalues ​​of Σ are λ1≥λ2≥...≥λ m ≥0, the unit vectors corresponding to the eigenvalues ​​are α1, α2, ... ≥α m Then the qth principal component of x is:

[0053]

[0054] The variance of the qth principal component of x is:

[0055]

[0056] That is, the covariance matrix Σ is the qth principal eigenvalue; the goal of principal component analysis is to find a new coordinate system in which the variance of the first principal component is maximized, the variance of the second principal component is next, and so on, until the variance of the last principal component is minimized. Each principal component is a linear combination of the original variables, and these principal components are orthogonal to each other.

[0057] Since the initial fluidization state and the microbubble fluidization state have blurred boundaries in the principal component space and are difficult to distinguish, it is necessary to use K-means clustering to construct another feature space for classification and representation. The K-means clustering process is as follows:

[0058] First, for a given center value (m1, m2, ..., m k Let k be the number of center values. Find a partition C that minimizes the objective function.

[0059]

[0060] Then, for a given partition C, find the center of each class (m1, m2, ..., m). k This minimizes the objective function.

[0061]

[0062] Given a defined partition, the solution is to minimize the sum of distances between a sample and the centers of its other classes. The result is obtained for each subset of n.l Class G of each sample l Update its mean m l :

[0063]

[0064] Repeat the above steps until the division no longer changes, and you will get the clustering results.

[0065] This invention utilizes local pressure difference information obtained through non-immersion measurements to jointly and quantitatively characterize the more detailed dynamic behavior of air-heavy medium fluidized beds under different flow regimes and during flow regime transitions. Based on non-immersion multi-point measurements, a spatiotemporal matrix of characteristic parameters is constructed according to the statistical characteristic parameters of the normalized pressure drop signal time series: standard deviation, skewness, kurtosis, centroid frequency, and frequency standard deviation. This quantitatively and collaboratively characterizes the transformation of bed flow patterns, understanding and characterizing the temporal and spatial differences in pressure difference signals under different fluidization states from multiple characteristic parameter dimensions. Simultaneously, considering the differences in the spatiotemporal matrices of different characteristic parameters in the characteristic space, principal component analysis and K-means clustering methods are used to characterize the K-means clustering analysis attributes of changes in fluidization states in the characteristic space, and their feasibility is demonstrated.

[0066] This invention acquires synchronous dynamic differential pressure signals at multiple points on the bed sidewall using a non-immersion measurement method. It then extracts characteristic parameters from the time-series differential pressure signals using statistical analysis, proposing a method to quantitatively characterize the real-time fluidization state of the bed using the combined characteristic parameters of multi-point differential pressure fluctuations. Based on this, a spatiotemporal matrix of multi-dimensional characteristic parameters is constructed to quantitatively and collaboratively characterize the transformation of bed flow patterns. Cluster analysis of the spatiotemporal matrix flow pattern clusters in the characteristic space demonstrates that classifying three typical flow pattern transformations is feasible and effective. This invention avoids the drawbacks of immersion measurement and single-point measurement modeling techniques, providing technical reserves for monitoring flow pattern transformation and fluidization state in air-heavy medium fluidized beds. It also has certain reference value for equipment scale-up, operating system upgrades, and intelligent control of air-heavy medium fluidized beds.

Claims

1. A method for characterizing gas-solid fluidized bed flow patterns based on pressure drop statistical characteristics, characterized in that, Includes the following steps: S1: By regularly increasing the gas velocity, the bed undergoes different fluidization states, and synchronous dynamic differential pressure signals at multiple points on the sidewall of the bed are acquired in real time. S2: Low-pass filtering is performed on the real-time acquired bed sidewall pressure difference signal; at the same time, the data after low-pass filtering and noise reduction is normalized to obtain the normalized pressure difference time series signal; S3: Use time-frequency domain statistical analysis methods to extract the characteristic parameters of the normalized differential pressure time series signal; the characteristic parameters include: standard deviation, skewness, kurtosis, centroid frequency, and frequency standard deviation; The formula for calculating standard deviation is as follows: in, It is the number of signal samples. It is each sample value. It is the average value of the signal; The formula for calculating skewness is as follows: in, It is the number of signal samples. It is each sample value. It is the average value of the signal. It is the standard deviation of the signal; The formula for calculating kurtosis is as follows: in, It is the number of signal samples. It is each sample value. It is the average value of the signal. It is the standard deviation of the signal; The formula for calculating the center of gravity frequency is as follows: in, Indicates frequency, Represents frequency Power spectral density at; The formula for calculating the standard deviation of frequency is as follows: in, Indicates frequency, Indicates the average frequency. Represents frequency The power spectral density at the specified location; the frequency domain statistical analysis method is the smoothed pseudo-Wigner-Vignerville distribution method, and the calculation formula is as follows: in, It is a smooth pseudo-Wignerville distribution. and It is a smoothing window function. It is the input signal. It is a frequency variable. It is a time variable. For frequency delay, For time delay, * represents complex conjugate. For the parameter factors of the Fourier transform; S4: Construct a spatiotemporal matrix of multi-dimensional feature parameters using statistical features to quantitatively and collaboratively characterize the transformation of bed flow patterns; S5: For the spatiotemporal matrix manifold clusters formed under different apparent gas velocities, principal component analysis and K-means cluster analysis are performed on them in the feature space.

2. The method for characterizing gas-solid fluidized bed flow patterns based on pressure drop statistical characteristics according to claim 1, characterized in that, In step S1, the synchronous dynamic differential pressure signals at multiple points on the bed sidewall are acquired by pressure sensors using a non-immersion measurement method.

3. The method for characterizing gas-solid fluidized bed flow patterns based on pressure drop statistical characteristics according to claim 1, characterized in that, In step S2, the normalization formula is defined as: in, These are the standardized values ​​of each variable. These are the original values ​​of each variable. and These are the maximum and minimum values ​​for each variable, respectively.

4. The method for characterizing gas-solid fluidized bed flow patterns based on pressure drop statistical characteristics according to claim 1, characterized in that, Step S4 includes: Five characteristic parameters of the differential pressure signal in the time and frequency domains are selected to characterize the fluidization state; these characteristic parameters are represented by eigenvectors in each measurement region, i.e. x ={t1,t2,t3,…,t p } T Where p=5, , , , , Thus, the overall fluidization state of the bed at each apparent gas velocity can be characterized by a spatiotemporal matrix of multi-dimensional characteristic parameters, i.e., X={ x 1, x 2,…, x N }, where N=5, and N represents the longitudinal measurement area location.

5. The method for characterizing gas-solid fluidized bed flow patterns based on pressure drop statistical characteristics according to claim 1, characterized in that, In step S5, the principal component analysis process is as follows: x Let be an m-dimensional random variable, Σ be the covariance matrix, and the eigenvalues ​​of Σ be respectively... The unit vectors corresponding to the eigenvalues ​​are respectively ,but x The q The principal components are: x The q The variance of the principal components is: That is, the covariance matrix Σ q The primary eigenvalue.

6. The method for characterizing gas-solid fluidized bed flow patterns based on pressure drop statistical characteristics according to claim 1, characterized in that, In step S5, the K-means clustering process is as follows: First, for a given center value ( m 1 ,m 2 ,…,m k ), k Given the number of center values, find a partition. C This minimizes the objective function: Then, for the given partition C Then find the center of each class ( m 1 ,m 2 ,…,m k This minimizes the objective function: Given a defined partition, the goal is to minimize the sum of distances between a sample and the centers of its other constituent classes. The solution is given for each included sample. n l Class of each sample G l Update its mean m l : Repeat the above steps until the division no longer changes, and you will get the clustering results.

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