Jet reactor multi-scale phase space correlation dimension analysis method under negative pressure condition

Abstract

The invention discloses a multi-scale phase space correlation dimension analysis method for a jet reactor under a negative pressure condition, and systematic research is carried out on nonlinear dynamic characteristics of an internal flow field of a jet impinging reactor by introducing a phase space reconstruction and attractor analysis method, namely a correlation dimension method. According to the phase space reconstruction technology, time sequence data are reconstructed into a track in a high-dimensional phase space through a delay embedding method, so that internal dynamic behaviors of the system are revealed. The attractors serve as geometric structures in the phase space and reflect the long-term dynamic characteristics of the system, and the shapes and distribution of the attractors can provide important clues for understanding the complexity of the flow field. Chaotic behaviors, fractal features and geometric structures of attractors in a flow field can be recognized through phase-space reconstruction attractor analysis, and then theoretical support is provided for optimization of reactor design and operation conditions.

Description

Technical Field

[0001] The present invention relates to the technical field of jet reactors, and in particular to a method for analyzing the multi-scale phase space correlation dimension of a jet reactor under negative pressure conditions. Background Art

[0002] The flow field within a jet impact reactor exhibits significant nonlinear and chaotic characteristics, and the motion of the fluid exhibits complex periodic and aperiodic behavior. In recent years, with the development of nonlinear dynamics theory, phase space reconstruction and attractor analysis have become powerful tools for studying the characteristics of complex flow fields. Through phase space reconstruction, one-dimensional pressure signal data can be mapped into a high-dimensional phase space, thereby revealing the periodicity and stability of the flow field. In a jet impact reactor, the complexity of the flow field is mainly reflected in phenomena such as the multi-scale structure of turbulence, the generation and evolution of vortices, and the periodic oscillations of the fluid. Through phase space reconstruction and attractor analysis, nonlinear mechanisms in the flow field of a jet impact reactor can be identified, providing theoretical support for the design and operation of the reactor. However, there is currently little research on jet impact under negative pressure conditions. Summary of the Invention

[0003] The present invention provides a multi-scale phase space correlation dimension analysis method for a jet reactor under negative pressure conditions, so as to systematically study the nonlinear dynamic characteristics of the internal flow field of the jet impact reactor. By reconstructing the attractor image in phase space and analyzing the correlation dimension, the nonlinear characteristics and dynamic behavior of the pressure signal under different negative pressure conditions are fully revealed.

[0004] According to the first aspect, an embodiment provides a method for analyzing the multi-scale phase space correlation dimension of a jet reactor under negative pressure conditions, the method comprising: The time series pressure signal of the negative pressure jet reactor is collected under different negative pressure conditions; The collected pressure signal is decomposed into multiple scales based on the wavelet transform method to obtain a multi-scale pressure signal; Based on the phase space reconstruction method, the phase space reconstructed attractor of the multi-scale pressure signal under different negative pressure conditions is performed to obtain the phase space reconstructed attractor images at different scales; The nonlinear characteristics and dynamic behaviors of the flow field under different negative pressure conditions are obtained through phase space reconstruction attractor image comparison and correlation dimension analysis.

[0005] Furthermore, the time series pressure signal acquisition of the negative pressure jet reactor under different negative pressure conditions specifically includes: Pressure signal collection ports are set in the negative pressure separation area and the slow flow area; the pressure signals of the negative pressure area and the slow flow area are collected respectively under different negative pressure values ​​at the top.

[0006] Furthermore, the collected pressure signal is decomposed into multiple scales based on the wavelet transform method to obtain a multi-scale pressure signal, which specifically includes: Symlet7 wavelet transform is used to perform multi-scale decomposition of the collected pressure signal. The decomposition process is based on scaling function and wavelet function to decompose the signal.

[0007] Furthermore, based on the phase space reconstruction method, the phase space reconstructed attractor of the multi-scale pressure signal under different negative pressure conditions is performed to obtain the phase space reconstructed attractor images at different scales, specifically including: Based on the mutual information method, the optimal time delay is determined by quantifying the dependence of two time series at different time delays; Determine the saturated embedding dimension of time series based on Cao algorithm; Phase space reconstruction is performed based on the obtained optimal time delay and saturation embedding dimension.

[0008] Furthermore, based on the mutual information method, the optimal time delay is determined by quantifying the dependency between the two time series at different time delays. Specifically, Given a time series and , calculate different delays Delayed mutual information under ,in Indicates at a point in time on At the time point on Mutual information between Plotting Delayed Mutual Information Follow The change curve of is used to find the first local minimum point, and the delay τ corresponding to the corresponding point is the optimal time delay.

[0009] Furthermore, the saturated embedding dimension of the time series is determined based on the Cao algorithm, specifically including: For the embedding dimension Phase space, defining statistics :

[0010]

[0011]

[0012] in, is the length of the time series, is the optimal time delay calculated according to the mutual information method, is the time series forecast value obtained by local linear fitting, is the embedding dimension, is the length of the time series; By calculating the different embedding dimensions d and ,when and Initial Increase and become larger, and in a certain If the values ​​of That is, it is the saturated embedding dimension m.

[0013] Furthermore, the phase space is reconstructed based on the obtained optimal time delay and saturation embedding dimension, specifically including: For one One-dimensional scalar time series of chaotic attractors , n is the length of the time series, if the embedding dimension satisfy , then the attractor equivalent to the original system topology is reconstructed by delay embedding method; Reconstruct the phase space based on the obtained optimal time delay and saturation embedding dimension:

[0014] in, is the saturated embedding dimension, is the optimal delay time.

[0015] Furthermore, through phase space reconstruction attractor image comparison and correlation dimension analysis, the nonlinear characteristics and dynamic behaviors of the flow field under different negative pressure conditions are obtained, including: In MATLAB, the correlationDimension function is used to calculate the correlation dimension of the time series. , based on the Grassberger-Procaccia algorithm; Correlation dimension It is through fitting and The slope of the linear part is:

[0016] Among them, the correlation integral It represents the probability that the distance between point pairs in the phase space is less than r, where r is the preset distance threshold between point pairs.

[0017] According to the second aspect, an embodiment provides a multi-scale phase space correlation dimension analysis system for a negative pressure jet reactor, the system comprising: A pressure signal acquisition module is used to acquire time series pressure signals of the negative pressure jet reactor under different negative pressure conditions; A multi-scale decomposition module is used to perform multi-scale decomposition on the collected pressure signal based on the wavelet transform method to obtain a multi-scale pressure signal; The phase space reconstruction module is used to reconstruct the phase space attractor of the multi-scale pressure signals under different negative pressure conditions based on the phase space reconstruction method, and obtain the phase space reconstructed attractor images at different scales; The analysis module is used to obtain the nonlinear characteristics and dynamic behaviors of the flow field under different negative pressure conditions through phase space reconstruction attractor image comparison and correlation dimension analysis.

[0018] According to a third aspect, an embodiment provides an electronic device, the device comprising: a processor and a memory; The memory is used to store one or more program instructions; The processor is used to run one or more program instructions to execute the steps of the multi-scale phase space correlation dimension analysis method of a jet reactor under negative pressure conditions as described in any of the above items.

[0019] The present invention provides a multi-scale phase space correlation dimension analysis method for a jet reactor under negative pressure conditions. By introducing phase space reconstruction and attractor analysis methods, namely the correlation dimension method, a systematic study is conducted on the nonlinear dynamic characteristics of the internal flow field of a jet impact reactor. Phase space reconstruction technology reconstructs time series data into trajectories in a high-dimensional phase space through a delayed embedding method, thereby revealing the intrinsic dynamic behavior of the system. Attractors, as geometric structures in the phase space, reflect the long-term dynamic characteristics of the system, and their shape and distribution can provide important clues for understanding the complexity of the flow field. Through phase space reconstruction attractor analysis, chaotic behavior, fractal characteristics and the geometric structure of attractors in the flow field can be identified, thereby providing theoretical support for optimizing reactor design and operating conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 A flowchart of a method for analyzing the multi-scale phase space correlation dimension of a jet reactor under negative pressure conditions provided by one embodiment of the present invention; Figure 2 A schematic diagram of pressure signal measurement in a multi-scale phase space correlation dimension analysis method for a jet reactor under negative pressure conditions provided by one embodiment of the present invention; Figure 3 The pressure signal (negative pressure value 10000Pa) of position 1 of the Sym7 multi-scale decomposition in the multi-scale phase space correlation dimension analysis method of a jet reactor under negative pressure conditions provided by one embodiment of the present invention; Figure 4A schematic diagram of the time delay for mutual information calculation in a multi-scale phase space correlation dimension analysis method for a jet reactor under negative pressure provided by one embodiment of the present invention (the fifth scale of the pressure signal at one position under a negative pressure value of 10,000 Pa); Figure 5 A schematic diagram of the Cao algorithm for calculating the embedding dimension in a multi-scale phase space correlation dimension analysis method for a jet reactor under negative pressure conditions provided by one embodiment of the present invention; FIG6 is an attractor image of the phase reconstruction of the pressure signal in the slow flow zone under different negative pressure conditions in a multi-scale phase space correlation dimension analysis method of a jet reactor under negative pressure conditions provided by one embodiment of the present invention; FIG7 is an attractor image of the phase reconstruction of the pressure signal of the negative pressure area under different negative pressure conditions in a multi-scale phase space correlation dimension analysis method of a jet reactor under negative pressure conditions provided by one embodiment of the present invention; Figure 8 A schematic diagram of calculating the correlation dimension using the correlationDimension function in a multi-scale phase space correlation dimension analysis method for a jet reactor under negative pressure provided by one embodiment of the present invention; Figure 9 The correlation dimension of the pressure signal in the slow flow zone under different pressure conditions in a multi-scale phase space correlation dimension analysis method of a jet reactor under negative pressure provided by one embodiment of the present invention; Figure 10 The correlation dimension of the pressure signal in the negative pressure zone under different pressure conditions in a multi-scale phase space correlation dimension analysis method for a jet reactor under negative pressure conditions provided by one embodiment of the present invention; Figure 11 is a comparison of correlation dimension data of the same vertical boundary signal measurement port of the slow flow zone and the negative pressure zone under different negative pressure conditions in a multi-scale phase space correlation dimension analysis method of a jet reactor under negative pressure conditions provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0021] The present invention will be further described in detail below by means of specific embodiments in conjunction with the accompanying drawings. Similar elements in different embodiments are numbered with associated similar elements. In the following embodiments, many detailed descriptions are provided to enable the present invention to be better understood. However, those skilled in the art will readily appreciate that some of the features may be omitted under different circumstances, or may be replaced by other elements, materials, or methods. In some cases, some operations related to the present invention are not shown or described in the specification. This is to avoid the core of the present invention being overwhelmed by excessive descriptions, and for those skilled in the art, it is not necessary to describe these related operations in detail. They can fully understand the related operations based on the description in the specification and the general technical knowledge in the art.

[0022] In addition, the features, operations, or characteristics described in the specification may be combined in any appropriate manner to form various embodiments. Furthermore, the steps or actions in the method description may be reordered or adjusted in a manner readily apparent to those skilled in the art. Therefore, the various sequences in the specification and drawings are provided solely for the purpose of clearly describing a particular embodiment and are not intended to be mandatory, unless otherwise specified.

[0023] The first embodiment of the present invention provides a method for analyzing the multi-scale phase space correlation dimension of a jet reactor under negative pressure conditions. Figure 1 Provide detailed explanation.

[0024] like Figure 1 As shown, in step S100, time series pressure signals of the negative pressure jet reactor are collected under different negative pressure conditions.

[0025] The above steps specifically include: S110, setting pressure signal collection ports in the negative pressure separation area and the slow flow area; collecting pressure signals of the negative pressure area and the slow flow area respectively under different negative pressure values ​​at the top.

[0026] The jet impact process is instantaneous and has obvious changes on the time scale. Therefore, by analyzing the time series pressure signal of the device and using the time-frequency information of the one-dimensional signal, we can better explore the internal flow field characteristics and flow pattern distribution inside the porous jet impact reactor. Figure 2 As shown, the sampling areas of this embodiment are primarily located in the negative pressure separation zone and the slow flow zone, with pressure signal acquisition ports set up. Two ports are located in each of the negative pressure separation zone and the slow flow zone, symmetrically distributed at 90°. Pressure signals from the negative pressure zone and the slow flow zone were collected under top negative pressure values ​​of 5000 Pa, 10000 Pa, 15000 Pa, and 20000 Pa, respectively.

[0027] like Figure 1 As shown, in step S200, the collected pressure signal is decomposed into multiple scales based on the wavelet transform method to obtain a multi-scale pressure signal.

[0028] The above steps specifically include: S210, using Symlet7 wavelet transform to perform multi-scale decomposition on the collected pressure signal, wherein the decomposition process decomposes the signal based on a scale function and a wavelet function.

[0029] Since the jet impact pressure signal has non-stationary and nonlinear characteristics, it is difficult to extract the characteristics of the pressure signal. Therefore, wavelet is used to process the signal.

[0030] The wavelet transform (Wavelet Transform) is a time-frequency analysis method that analyzes the local characteristics of a signal by decomposing it into wavelet functions of varying scales and locations. Sym7 was found to be highly consistent with the pressure signal measured by the device. The Sym7 (Symlet 7) wavelet is a well-symmetric wavelet basis and is commonly used for multi-scale decomposition in signal processing. The Sym7 wavelet decomposition process is based on two functions: a scale function and a wavelet function.

[0031] Sym7 multi-scale decomposition of a discrete signal f(x) can be expressed as:

[0032] in It is on scale The approximate coefficients under It is on scale The detail coefficient under is the initial scale, is the maximum decomposition scale.

[0033] Is a scaling function, used to represent the approximate part of the signal. The expression under translation k is:

[0034] in, represents the scale and k represents the translation.

[0035] is a wavelet function used to represent the details of the signal. Its representation at different scales j and translations k is:

[0036] The relationship between the wavelet function and the scaling function is expressed as:

[0037] in, are the wavelet function coefficients.

[0038] Under scale The approximate coefficient of It can be expressed as:

[0039] in, is the low-pass filter coefficient, used to calculate the approximate coefficient .

[0040] In scale The detail coefficient under It can be expressed as:

[0041] in, is the high-pass filter coefficient, used to calculate the detail coefficient .

[0042] Sym7 wavelet reconstructs the signal by recombining the decomposed coefficients to obtain the original signal. The formula is:

[0043] The signal reconstruction process of Sym7 wavelet is expressed as follows using the inverse filter coefficients:

[0044] Sym7 wavelet decomposes the signal into approximate and detailed components at different scales using scaling and wavelet functions, thus completing multi-scale decomposition of the signal. Approximate coefficients are calculated using low-pass filter coefficients, while detail coefficients are calculated using high-pass filter coefficients. The decomposition coefficients are calculated based on the filter coefficients, and signal reconstruction is achieved by recombining the decomposed coefficients to obtain the original signal.

[0045] Figure 3 A schematic diagram of the pressure signal measured at position 1 using sym7 multi-scale decomposition is shown. The measured signal (original signal) is kept at 100,000 characters to ensure good frequency resolution. As sym7 decomposes the pressure signal at multiple scales, the signal's characteristics become more distinct with each scale, resulting in a total of 12 decompositions (d1-d12). Since frequency domain resolution is solely dependent on the sampling time, a longer sampling time yields higher frequency domain resolution. The Sym7 wavelet decomposition of the signal into different time and frequency scales effectively illustrates the characteristics and structure of the pressure signal from the jet impact reactor.

[0046] like Figure 1 As shown, in step S300, the phase space reconstruction attractor is performed on the multi-scale pressure signals under different negative pressure conditions based on the phase space reconstruction method to obtain the phase space reconstruction attractor images at different scales.

[0047] The above steps specifically include: S310 , based on a mutual information method, determines an optimal time delay by quantifying the dependency between two time series at different time delays.

[0048] Specifically, given a time series and , calculate different delays Delayed mutual information under ,in Indicates at a point in time on At the time point on Mutual information between ; plotting delayed mutual information Follow The change curve of is used to find the first local minimum point, and the delay τ corresponding to the corresponding point is the optimal time delay.

[0049] The mutual information method calculates time delay: Its core is to determine the optimal time delay τ by quantifying the dependence of two time series at different time delays. The following is the mathematical formula and calculation steps for calculating time delay using the mutual information method: (1) For a known fixed time series and , assuming and The value ranges are and .Will and The value range of is divided into several intervals. Assume that The value range is divided into interval, will The value range is divided into intervals. No. The interval is , No. The interval is For each time point ,statistics and The frequency of falling within a certain interval at the same time. for Falling in intervals and Falling in The frequency of the interval, for Falling in The frequency of the interval, for Falling in The frequency of an interval.

[0050] (2) Based on joint frequency and the total number of samples , calculate the joint probability :

[0051] Among them, ensure that the sum of all joint probabilities is 1, that is:

[0052] calculate The marginal probability distribution of and The marginal probability distribution of .

[0053] According to the frequency N i And the total number of samples N, calculate X t The marginal probability :

[0054] Similarly, according to the frequency M j And the total number of samples N, calculate Y t+τ The marginal probability

[0055]

[0056] (3) For two discrete random variables and , mutual information Defined as:

[0057] in, yes and The joint probability distribution of and yes and The marginal probability distributions are respectively.

[0058] At the same time, mutual information can also be expressed as the difference in entropy:

[0059] in, and They are and The entropy of is the joint entropy.

[0060] Calculate different delays using the definition formula of mutual information Next In order to determine the optimal time delay, it is usually necessary to calculate the delay mutual information under different delays and find the first local minimum point. Figure 4 As shown for time series , calculate different delays Next , plotting the delayed mutual information Follow The change curve of the local minimum point is found, and the delay τ corresponding to this point is the optimal time delay. Figure 4 The time delay shown is 11.

[0061] S320: Determine the saturated embedding dimension of the time series based on the Cao algorithm.

[0062] Specifically, for the embedding dimension Phase space, defining statistics :

[0063]

[0064]

[0065] in, is the length of the time series, is the optimal time delay calculated according to the mutual information method, is the time series forecast value obtained by local linear fitting, is the embedding dimension, is the length of the time series. Local linear fitting is a time series prediction method based on phase space reconstruction. Its core idea is to use the neighboring points of the target point in the reconstructed phase space to build a local linear model, and then use this model for prediction.

[0066] By calculating the different embedding dimensions d and ,when and Initial Increase and become larger, and in a certain If the values ​​of That is, as the saturated embedding dimension m. Figure 5 As shown, Follow When it increases and tends to be stable, it indicates that the embedding dimension is sufficient. exist Therefore, the calculated saturated embedding dimension is 4.

[0067] S330 , performing phase space reconstruction according to the obtained optimal time delay and saturation embedding dimension.

[0068] Since the pressure signal has a fractal structure at different scales, and the measured single and bifractals at different scales show self-similarity in scale, the pressure signal has a chaotic attractor. Therefore, this embodiment uses the phase space reconstruction method to reconstruct the attractor of the multi-scale pressure signal under different negative pressure conditions.

[0069] Phase space reconstruction attractor: Phase space reconstruction is an important method for studying nonlinear dynamical systems. Its core is to reconstruct the system's phase space from time series, thereby revealing the system's dynamic characteristics. The theoretical basis of the phase space reconstruction attractor is Takens' embedding theorem. The phase space is reconstructed using the embedding dimension m and the time delay τ.

[0070] Specifically, for a One-dimensional scalar time series of chaotic attractors , n is the length of the time series, if the embedding dimension satisfy , then the attractor equivalent to the original system topology is reconstructed by delay embedding method; Reconstruct the phase space based on the obtained optimal time delay and saturation embedding dimension:

[0071] in, is the saturated embedding dimension, is the optimal delay time.

[0072] like Figure 1 As shown, in step S400, the nonlinear characteristics and dynamic behaviors of the flow field under different negative pressure conditions are obtained through phase space reconstruction attractor image comparison and correlation dimension analysis.

[0073] S410, comparing and analyzing attractor images.

[0074] 1. Analysis of attractors in slow flow areas Figures 6(a) and 6(b) show the attractor images reconstructed from the phase space of the pressure signal in the slow flow zone under different negative pressure conditions. The size of the attractor can intuitively reflect the complexity and degree of chaos of the system. As the pressure signal is decomposed using wavelet multiscale decomposition, the attractor corresponding to the pressure signal gradually becomes clearer in three-dimensional space. The attractors reconstructed using phase space using multiscale pressure signals under different negative pressure conditions show significant differences. As the scale of the wavelet decomposition signal increases, the attractor shape becomes more distinct, demonstrating that wavelet multiscale denoising exhibits good properties for pressure signals. The 7th and 8th scales show complete and clear attractor patterns. The attractor image becomes clearer with increasing scale of the pressure signal, indicating that signal denoising facilitates the visualization of chaotic attractors, indicating that the system is highly sensitive to noise.

[0075] Figure 6(a) shows that as the top negative pressure increases, the area of ​​the chaotic attractor image at the eighth scale decreases significantly, indicating that the complexity and chaos at position 1 gradually decrease with increasing negative pressure. Figure 6(b) shows that as the top negative pressure increases, the area of ​​the chaotic attractor image at the eighth scale increases significantly, indicating that the complexity and chaos at position 2 gradually increase with increasing negative pressure. The top negative pressure has opposite effects on the dynamic characteristics of positions 1 and 2 in the slow flow zone. Figure 6(a) shows that when the top negative pressure is 10,000 Pa and 15,000 Pa, a two-dimensional attractor image appears at the 12th scale, indicating that the system's dynamic behavior under these pressure conditions has a certain degree of stability and predictability, or in other words, the system is closer to a periodic or quasi-periodic state under these pressure conditions. Figure 6(b) shows that when the top negative pressure is 10,000 Pa, 15,000 Pa, and 20,000 Pa, two-dimensional attractor images appear at higher scales. Compared with the one-signal measurement port, the two-signal measurement port has greater stability and predictability under pressure changes.

[0076] 2. Analysis of attractors in negative pressure areas Figures 7(a) and 7(b) show the attractor images reconstructed from the pressure signals in the negative pressure zone under different negative pressure conditions. Because the size of the attractor can intuitively indicate the chaotic state of the system, Figure 7(a) shows the attractor images reconstructed from the pressure signals at the five signal measurement ports. As pressure increases, the attractor sizes at different scales show significant differences. Based on the system's sensitivity to noise, the pressure signals exhibit relatively complete attractor images at the 7th and 8th scales. As the top negative pressure increases, the chaotic attractors at the 7th and 8th scales become smaller at 15,000 Pa. Therefore, the system with five signal measurement ports exhibits lower complexity at a top negative pressure of 15,000 Pa. Furthermore, Figure 7(a) shows the emergence of a two-dimensional attractor at the 12th scale for top negative pressures of 5,000 Pa, 10,000 Pa, and 20,000 Pa, indicating that the system exhibits good periodicity or predictability in this state.

[0077] Figure 7(b) shows that as the top negative pressure increases, the area of ​​the chaotic attractor at the eighth scale decreases, indicating that as the top negative pressure increases near the six-signal measurement port, the system's randomness decreases, while its predictability and stability increase. Furthermore, Figure 7(b) shows that when the top negative pressure is 15,000 Pa and 20,000 Pa, the system develops a two-dimensional attractor at the eleventh scale, indicating that increasing the top negative pressure increases the system's periodicity and predictability. The six-signal measurement port has fewer two-dimensional attractors than the five-signal measurement port, indicating that the system has lower periodicity and stability, meaning that non-axisymmetric locations on the same plane have different dynamical trajectories.

[0078] S420, calculating the correlation dimension to analyze the dynamic complexity.

[0079] In MATLAB, the correlationDimension function is used to calculate the correlation dimension of the time series. , which is based on the Grassberger-Procaccia algorithm. The correlationDimension function fits the line by selecting the appropriate radius range (MinRadius and MaxRadius).

[0080] Correlation dimension It is through fitting and The slope of the linear part is:

[0081] Among them, the correlation integral It represents the probability that the distance between the point pairs in the phase space is less than the preset radius range r, which is defined as:

[0082] Where: N is the number of points in phase space, and is the reconstructed phase space vector, is the Heaviside step function, when The value is 1 when , otherwise it is 0.

[0083] The correlationDimension function computes the correlation integral using r values ​​that are evenly spaced on a logarithmic scale. Figure 8 Shows a schematic diagram of the correlationDimension function calculating the correlation dimension. and In the double logarithmic plot, the linear part is selected for fitting, and its slope is the correlation dimension .

[0084] 1. Correlation dimension analysis of slow flow area Figure 9The correlation dimension of the pressure signal in the slow flow zone under different negative pressure conditions is shown. The correlation dimension decreases with increasing scale, indicating that as the pressure signal changes at multiple scales, its complexity decreases and high- and low-frequency components are eliminated. The range of variation of the pressure signal at signal port 1 in the slow flow zone under different negative pressure conditions is 423.49%, 425.70%, 504.52%, and 420.43%, respectively. The range of variation of the pressure signal at signal port 2 in the slow flow zone under different negative pressure conditions is 463.35%, 447.57%, 448.36%, and 374.71%, respectively. This indicates significant heterogeneity or diversity in the pressure signal at different scales in the slow flow zone, suggesting more complex interactions or feedback mechanisms within the system. Compared to signal port 1, the range of variation of the correlation dimension at signal port 2 is larger, indicating that the system near signal port 2 on the same plane has stronger nonlinear characteristics and a more complex pressure signal structure.

[0085] Furthermore, a comparison of the correlation dimensions at the same scale under different negative pressure conditions reveals that the correlation dimension for the 1-signal port exhibits similar values ​​at scales 8-12, ranging from 3.31% to 5.71%. The larger the scale, the smaller the variation. The correlation dimension for the 2-signal port exhibits similar values ​​at scales 9-12, ranging from 5.84% to 19.11%. Compared to the 1-signal port, the correlation dimension of the pressure signal at the 2-signal port exhibits more pronounced fluctuations. Pressure signals typically reflect the macroscopic properties of the interaction between the gas and solid phases, but may also include mesoscale properties resulting from the coupling of microscopic and macroscopic properties. Under high-scale conditions, the primary dynamic behavior of the system is concentrated at the macroscopic level. The correlation dimensions of the pressure signals in the slow-flow zone are relatively similar at high scales, indicating that the macroscopic differences in the dynamic behavior of the slow-flow zone are minimal under different negative pressure conditions. Under low-scale conditions, the pressure signals in the slow-flow area vary greatly, and the differences at low scales account for the majority of the differences, indicating that the top negative pressure has a greater impact at the microscopic level. As the pressure signal changes at multiple scales, the complexity at the microscopic level is simplified to a certain extent.

[0086] 2. Correlation Dimension Analysis of Negative Pressure Zone Figure 10The correlation dimensions of the pressure signal at two signal measurement ports in the negative pressure zone under different pressure conditions are shown. As wavelet multiscale denoising is performed, the correlation dimension of the chaotic attractor of the pressure signal shows an overall downward trend, with some increases. The multiscale variation ranges of the pressure signal at signal measurement port 5 in the negative pressure zone under different negative pressure conditions are 403.77%, 439.99%, 385.73%, and 447.64%, respectively. The multiscale variation ranges of the pressure signal at signal measurement port 6 in the negative pressure zone under different negative pressure conditions are 417.76%, 469.82%, 405.47%, and 439.86%, respectively. The multiscale variation process is a denoising process, which clearly shows that the correlation dimension shows significant changes when the top negative pressure is 10,000 Pa and 20,000 Pa, indicating that these two negative pressure conditions generate more high-frequency signals and have a significant impact on microscopic changes within the system.

[0087] Comparing the correlation dimensions under different negative pressure conditions at the same scale, the correlation dimension of the 5-signal measurement port exhibits similar values ​​at scales 11-12, with values ​​varying from 1.26% to 4.06%. The larger the scale, the smaller the difference in correlation dimension. This indicates that, at the macroscale, the top negative pressure has a similar effect on the flow characteristics of the 5-signal measurement port. The correlation dimension of the 6-signal measurement port exhibits similar values ​​at scales 10-12, with values ​​varying from 2.78% to 6.3%. Compared to the 5-signal measurement port, which exhibits the smallest difference at scale 12, the 6-signal measurement port exhibits the smallest difference at scale 11. This numerical comparison indicates that the top negative pressure has a greater macroscopic impact on the 6-signal measurement port than the 5-signal measurement port.

[0088] 3. Comparison of correlation dimensions between slow flow area and negative pressure area Figures 11(a) and 11(b) show a comparison of correlation dimension data for the same vertical boundary signal measurement port in the slow flow zone and the negative pressure zone under different negative pressure conditions. Figure 11(a) shows a multi-scale comparison of the correlation dimension of the pressure signals at the 1-position signal measurement port and the 5-position signal measurement port. The correlation dimension of the pressure signal at the 1-position signal measurement port is 1.6%, 0.9%, 5.4%, and 0.2% higher than that at the 5-position signal measurement port when the top negative pressure is 5000 Pa, 10000 Pa, 15000 Pa, and 20000 Pa, respectively. The difference is even greater when the top negative pressure is 15000 Pa. Therefore, compared with the 5-position signal measurement port, the 1-position signal measurement port has more nonlinear characteristics, which may indicate stronger turbulence or more complex fluid dynamics behavior.

[0089] Figure 11(b) shows a multi-scale comparison of the correlation dimensions of the pressure signals at two and six signal measurement ports. The correlation dimensions of the pressure signals at two and six signal measurement ports are 0.22%, 0.35%, 0.13%, and -0.16% higher than those at six signal measurement ports at top negative pressures of 5000 Pa, 10000 Pa, 15000 Pa, and 20000 Pa, respectively. Compared to the difference between the pressure signals at one and five signal measurement ports, the data for the pressure signals at two and six are closer, indicating that the complexity of the nonlinear characteristics at these two locations is relatively consistent. However, Figure 11(b) shows significant differences in the local variations between the pressure signals at two and six, suggesting that at the microscopic level, the two locations should have different nonlinear characteristics.

[0090] As the scale increases, the high-frequency details in the pressure signals of the two pressure signal measurement ports are smoothed, and the complexity of the signals is reduced, which leads to a decrease in the correlation dimension. As a result, the difference in the correlation dimension under different negative pressure conditions at the two signal measurement ports decreases, indicating that the macroscopic changes at the two positions are relatively small, and therefore the effect of the top negative pressure is more reflected in the microscopic changes.

[0091] In summary, the present invention, through phase space reconstruction of attractor images and correlation dimension analysis, comprehensively reveals the nonlinear characteristics and dynamic behavior of pressure signals under different negative pressure conditions. These findings provide important insights into the dynamic behavior of complex fluid systems and offer theoretical support for further research into regional differences in fluid dynamics.

[0092] Corresponding to the above-disclosed method for analyzing the multi-scale phase space correlation dimension of a jet reactor under negative pressure conditions, an embodiment of the present invention further discloses a system for analyzing the multi-scale phase space correlation dimension of a negative pressure jet reactor, which specifically includes: A pressure signal acquisition module is used to acquire time series pressure signals of the negative pressure jet reactor under different negative pressure conditions; A multi-scale decomposition module is used to perform multi-scale decomposition on the collected pressure signal based on the wavelet transform method to obtain a multi-scale pressure signal; The phase space reconstruction module is used to reconstruct the phase space attractor of the multi-scale pressure signals under different negative pressure conditions based on the phase space reconstruction method, and obtain the phase space reconstructed attractor images at different scales; The analysis module is used to obtain the nonlinear characteristics and dynamic behaviors of the flow field under different negative pressure conditions through phase space reconstruction attractor image comparison and correlation dimension analysis.

[0093] It should be noted that for the detailed description of the multi-scale phase space correlation dimension analysis system of a negative pressure jet reactor provided in an embodiment of the present invention, reference can be made to the relevant description of the multi-scale phase space correlation dimension analysis method of a jet reactor under negative pressure conditions provided in an embodiment of the present application, which will not be repeated here.

[0094] In addition, an embodiment of the present invention also provides an electronic device, which includes: a processor and a memory; the memory is used to store one or more program instructions; the processor is used to run one or more program instructions to execute the steps of a multi-scale phase space correlation dimension analysis method for a jet reactor under negative pressure conditions as described in any of the above items.

[0095] It should be noted that for the detailed description of an electronic device provided in an embodiment of the present invention, reference can be made to the relevant description of a multi-scale phase space correlation dimension analysis method of a jet reactor under negative pressure conditions provided in an embodiment of the present application, which will not be repeated here.

[0096] In addition, an embodiment of the present invention also provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, it implements the steps of a multi-scale phase space correlation dimension analysis method of a jet reactor under negative pressure conditions as described in any of the above items.

[0097] It should be noted that for the detailed description of a computer-readable storage medium provided in an embodiment of the present invention, reference can be made to the relevant description of a multi-scale phase space correlation dimension analysis method of a jet reactor under negative pressure conditions provided in an embodiment of the present application, which will not be repeated here.

[0098] Those skilled in the art will appreciate that all or part of the functions of the various methods in the above embodiments can be implemented by hardware or by computer program. When all or part of the functions in the above embodiments are implemented by computer program, the program can be stored in a computer-readable storage medium, and the storage medium can include: read-only memory, random access memory, disk, optical disk, hard disk, etc., and the program is executed by a computer to implement the above functions. For example, the program is stored in the memory of the device, and when the program in the memory is executed by the processor, all or part of the above functions can be implemented. In addition, when all or part of the functions in the above embodiments are implemented by computer program, the program can also be stored in a storage medium such as a server, another computer, disk, optical disk, flash disk or mobile hard disk, and saved in the memory of the local device by downloading or copying, or the system of the local device is updated. When the program in the memory is executed by the processor, all or part of the functions in the above embodiments can be implemented.

[0099] The above examples are used to illustrate the present invention, which are only used to help understand the present invention and are not intended to limit the present invention. Those skilled in the art can make several simple deductions, modifications or substitutions based on the concept of the present invention.

Claims

1. A method for analyzing the multi-scale phase space correlation dimension of a jet reactor under negative pressure conditions, characterized in that: The method comprises: The time series pressure signal of the negative pressure jet reactor is collected under different negative pressure conditions; The collected pressure signal is decomposed into multiple scales based on the wavelet transform method to obtain a multi-scale pressure signal; Based on the phase space reconstruction method, the phase space reconstructed attractor of the multi-scale pressure signal under different negative pressure conditions is performed to obtain the phase space reconstructed attractor images at different scales; The nonlinear characteristics and dynamic behaviors of the flow field under different negative pressure conditions are obtained through phase space reconstruction attractor image comparison and correlation dimension analysis.

2. The method for analyzing the multi-scale phase space correlation dimension of a jet reactor under negative pressure conditions according to claim 1, characterized in that: The time series pressure signal acquisition of the negative pressure jet reactor under different negative pressure conditions includes: Pressure signal collection ports are set in the negative pressure separation area and the slow flow area; the pressure signals of the negative pressure area and the slow flow area are collected respectively under different negative pressure values ​​at the top.

3. The method for analyzing the multi-scale phase space correlation dimension of a jet reactor under negative pressure conditions according to claim 1, characterized in that: The collected pressure signal is decomposed into multiple scales based on the wavelet transform method to obtain a multi-scale pressure signal, which specifically includes: Symlet7 wavelet transform is used to perform multi-scale decomposition of the collected pressure signal. The decomposition process is based on scaling function and wavelet function to decompose the signal.

4. The method for analyzing the multi-scale phase space correlation dimension of a jet reactor under negative pressure conditions according to claim 1, characterized in that: Based on the phase space reconstruction method, the phase space reconstructed attractor of the multi-scale pressure signal under different negative pressure conditions is performed to obtain the phase space reconstructed attractor images at different scales, including: Based on the mutual information method, the optimal time delay is determined by quantifying the dependence of two time series at different time delays; Determine the saturated embedding dimension of time series based on Cao algorithm; Phase space reconstruction is performed based on the obtained optimal time delay and saturation embedding dimension.

5. The method for analyzing the multi-scale phase space correlation dimension of a jet reactor under negative pressure conditions according to claim 4, characterized in that: Based on the mutual information method, the optimal time delay is determined by quantifying the dependence of two time series at different time delays. Specifically, Given a time series and , calculate different delays Delayed mutual information under ,in Indicates at a point in time on At the time point on Mutual information between Plotting Delayed Mutual Information Follow The change curve of is used to find the first local minimum point, and the delay τ corresponding to the corresponding point is the optimal time delay.

6. The method for analyzing the multi-scale phase space correlation dimension of a jet reactor under negative pressure conditions according to claim 4, characterized in that: The saturated embedding dimension of the time series is determined based on the Cao algorithm, specifically including: For the embedding dimension Phase space, defining statistics : in, is the length of the time series, is the optimal time delay calculated according to the mutual information method, is the time series forecast value obtained by local linear fitting, is the embedding dimension, is the length of the time series; By calculating the different embedding dimensions d and ,when and Initial Increase and become larger, and in a certain If the values ​​of That is, it is the saturated embedding dimension m.

7. The method for analyzing the multi-scale phase space correlation dimension of a jet reactor under negative pressure conditions according to claim 4, characterized in that: The phase space is reconstructed based on the obtained optimal time delay and saturation embedding dimension, including: For one One-dimensional scalar time series of chaotic attractors , n is the length of the time series, if the embedding dimension satisfy , then the attractor equivalent to the original system topology is reconstructed by delay embedding method; Reconstruct the phase space based on the obtained optimal time delay and saturation embedding dimension: in, is the saturated embedding dimension, is the optimal delay time.

8. The method for analyzing the multi-scale phase space correlation dimension of a jet reactor under negative pressure conditions according to claim 1, characterized in that: Through phase space reconstruction attractor image comparison and correlation dimension analysis, the nonlinear characteristics and dynamic behaviors of the flow field under different negative pressure conditions are obtained, including: In MATLAB, the correlationDimension function is used to calculate the correlation dimension of the time series. , based on the Grassberger-Procaccia algorithm; Correlation dimension It is through fitting and The slope of the linear part is: Among them, the correlation integral It represents the probability that the distance between point pairs in the phase space is less than r, where r is the preset distance threshold between point pairs.

9. A multi-scale phase space correlation dimension analysis system for a negative pressure jet reactor, characterized in that: The system comprises: A pressure signal acquisition module is used to acquire time series pressure signals of the negative pressure jet reactor under different negative pressure conditions; A multi-scale decomposition module is used to perform multi-scale decomposition on the collected pressure signal based on the wavelet transform method to obtain a multi-scale pressure signal; The phase space reconstruction module is used to reconstruct the phase space attractor of the multi-scale pressure signals under different negative pressure conditions based on the phase space reconstruction method, and obtain the phase space reconstructed attractor images at different scales; The analysis module is used to obtain the nonlinear characteristics and dynamic behaviors of the flow field under different negative pressure conditions through phase space reconstruction attractor image comparison and correlation dimension analysis.

10. An electronic device, characterized in that: The device includes: a processor and a memory; The memory is used to store one or more program instructions; The processor is used to run one or more program instructions to execute the steps of the multi-scale phase space correlation dimension analysis method of a jet reactor under negative pressure conditions as described in any one of claims 1 to 8.

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