Multi-scale phase space correlation dimension analysis method for jet reactors under negative pressure conditions

Abstract

This invention discloses a multi-scale phase space correlation dimension analysis method for jet reactors under negative pressure conditions. By introducing phase space reconstruction and attractor analysis methods (i.e., the correlation dimension method), the nonlinear dynamic characteristics of the internal flow field of the jet impacting the reactor are systematically studied. Phase space reconstruction technology reconstructs time-series data into trajectories in a high-dimensional phase space using a delayed embedding method, thereby revealing the system's intrinsic dynamic behavior. Attractors, as geometric structures in phase space, reflect the long-term dynamic characteristics of the system; their shape and distribution can provide important clues for understanding the complexity of the flow field. Through phase space reconstruction and attractor analysis, chaotic behavior, fractal characteristics, and the geometric structure of attractors in the flow field can be identified, thus providing theoretical support for optimizing reactor design and operating conditions.

Description

Technical Field

[0001] This invention relates to the field of jet reactor technology, and more specifically to a method for multi-scale phase space correlation dimension analysis of jet reactors under negative pressure conditions. Background Technology

[0002] The flow field inside a jet impact reactor exhibits significant nonlinear and chaotic characteristics, with fluid motion displaying complex periodic and non-periodic behaviors. In recent years, with the development of nonlinear dynamics theory, phase space reconstruction and attractor analysis have gradually become powerful tools for studying the characteristics of complex flow fields. Phase space reconstruction allows mapping one-dimensional pressure signal data into a high-dimensional phase space, thereby revealing the periodicity and stability of the flow field. In jet impact reactors, the complexity of the flow field is mainly manifested in the multi-scale structure of turbulence, the generation and evolution of vortices, and the periodic oscillations of the fluid. Phase space reconstruction and attractor analysis can identify nonlinear mechanisms in the flow field of jet impact reactors and provide theoretical support for reactor design and operation. However, research on jet impact under negative pressure conditions is currently limited. Summary of the Invention

[0003] This invention provides a multi-scale phase space correlation dimension analysis method for jet reactors under negative pressure conditions 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 performing correlation dimension analysis, the nonlinear characteristics and dynamic behavior of pressure signals under different negative pressure conditions are fully revealed.

[0004] According to the first aspect, one embodiment provides a method for multi-scale phase space correlation dimension analysis of a jet reactor under negative pressure conditions, the method comprising:

[0005] Time-series pressure signals were acquired from the negative pressure jet reactor under different negative pressure conditions.

[0006] The collected pressure signal is decomposed into multi-scale pressure signals based on wavelet transform.

[0007] Based on the phase space reconstruction method, phase space reconstruction attractors are performed on multi-scale pressure signals under different negative pressure conditions to obtain phase space reconstruction attractor images at different scales.

[0008] By comparing attractor images reconstructed in phase space and performing correlation dimension analysis, the nonlinear characteristics and dynamic behavior of the flow field under different negative pressure conditions were obtained.

[0009] Furthermore, time-series pressure signal acquisition was performed on the negative pressure jet reactor under different negative pressure conditions, specifically including:

[0010] Pressure signal acquisition ports are set up in the negative pressure separation zone and the slow flow zone; pressure signals in the negative pressure zone and the slow flow zone are collected under different negative pressure values ​​at the top.

[0011] Furthermore, the acquired pressure signal is decomposed into multi-scale signals based on wavelet transform, specifically including:

[0012] The acquired pressure signal was decomposed into multiple scales using Symlet7 wavelet transform. The decomposition process was based on scaling functions and wavelet functions to decompose the signal.

[0013] Furthermore, based on the phase space reconstruction method, phase space reconstruction attractors are performed on multi-scale pressure signals under different negative pressure conditions to obtain phase space reconstruction attractor images at different scales, specifically including:

[0014] Based on the mutual information method, the optimal time delay is determined by quantifying the dependency relationship between two time series at different time delays.

[0015] Determining the saturated embedding dimension of time series based on the Cao algorithm;

[0016] Phase space reconstruction is performed based on the obtained optimal time delay and saturated embedding dimension.

[0017] Furthermore, based on the mutual information method, the optimal time delay is determined by quantifying the dependency between two time series at different time delays, specifically including:

[0018] Given a time series and Calculate different delays Delayed mutual information ,in Indicates a point in time On At a certain point in time On Mutual information between them;

[0019] Drawing delayed mutual information Follow Find the first local minimum point by observing the curve of change. The delay τ corresponding to the point is the optimal time delay.

[0020] Furthermore, the saturated embedding dimension of the time series is determined based on the Cao algorithm, specifically including:

[0021] For embedding dimension is The phase space, defining statistics :

[0022]

[0023]

[0024]

[0025] in, It is the length of the time series. The optimal time delay is calculated based on the mutual information method. These are time series predictions obtained through local linear fitting. For the embedding dimension, It is the length of the time series;

[0026] By calculating different embedding dimensions d and ,when and Initial random Increase and grow, and at a certain If the values ​​at each location no longer change significantly and tend to stabilize, then the corresponding... That is, the saturated embedding dimension m.

[0027] Furthermore, phase space reconstruction is performed based on the obtained optimal time delay and saturation embedding dimension, specifically including:

[0028] For a One-dimensional scalar time series of chaotic attractors , where n is the length of the time series, and if the embedding dimension is... satisfy Then, an attractor that is topologically equivalent to the original system can be reconstructed using the delayed embedding method;

[0029] Reconstruct the phase space based on the obtained optimal time delay and saturated embedding dimension:

[0030]

[0031] in, It is the saturation embedding dimension. This is the optimal delay time.

[0032] Furthermore, through phase space reconstruction attractor image comparison and correlation dimension analysis, the nonlinear characteristics and dynamic behavior of the flow field under different negative pressure conditions are obtained, specifically including:

[0033] In MATLAB, the correlationDimension function is used to calculate the correlation dimension of a time series. It is implemented based on the Grassberger-Procaccia algorithm;

[0034] Correlation dimension Through fitting and The slope obtained from the linear part:

[0035]

[0036] Among them, the correlation integral This represents the probability that the distance between a pair of points in phase space is less than r, where r is a preset threshold for the distance between pairs of points.

[0037] According to a second aspect, one embodiment provides a multi-scale phase space correlation dimension analysis system for a negative pressure jet reactor, the system comprising:

[0038] The pressure signal acquisition module is used to acquire time-series pressure signals of the negative pressure jet reactor under different negative pressure conditions.

[0039] The multi-scale decomposition module is used to perform multi-scale decomposition on the acquired pressure signal based on the wavelet transform method to obtain a multi-scale pressure signal.

[0040] The phase space reconstruction module is used to perform phase space reconstruction attractor on multi-scale pressure signals under different negative pressure conditions based on the phase space reconstruction method, and obtain phase space reconstruction attractor images at different scales.

[0041] The analysis module is used to obtain the nonlinear characteristics and dynamic behavior of the flow field under different negative pressure conditions by comparing and correlating attractor images reconstructed in phase space and performing correlation dimension analysis.

[0042] According to a third aspect, one embodiment provides an electronic device, the device comprising: a processor and a memory;

[0043] The memory is used to store one or more program instructions;

[0044] The processor is configured to run one or more program instructions to perform 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 preceding claims.

[0045] This invention provides a multi-scale phase space correlation dimension analysis method for jet reactors under negative pressure conditions. By introducing phase space reconstruction and attractor analysis methods (i.e., the correlation dimension method), the nonlinear dynamic characteristics of the internal flow field of the jet impacting the reactor are systematically studied. Phase space reconstruction technology reconstructs time-series data into trajectories in a high-dimensional phase space using a delayed embedding method, thereby revealing the system's intrinsic dynamic behavior. Attractors, as geometric structures in phase space, reflect the long-term dynamic characteristics of the system; their shape and distribution can provide important clues for understanding the complexity of the flow field. Through phase space reconstruction and attractor analysis, chaotic behavior, fractal characteristics, and attractor geometry in the flow field can be identified, thus providing theoretical support for optimizing reactor design and operating conditions. Attached Figure Description

[0046] Figure 1 A flowchart illustrating a method for multi-scale phase space correlation dimension analysis of a jet reactor under negative pressure conditions, provided in one embodiment of the present invention;

[0047] Figure 2 This is 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 in one embodiment of the present invention.

[0048] Figure 3 This invention provides a Sym7 multi-scale decomposition of the pressure signal at position 1 (negative pressure value 10000 Pa) in a multi-scale phase space correlation dimension analysis method for a jet reactor under negative pressure conditions, as an embodiment of the present invention.

[0049] Figure 4 A schematic diagram of the time delay in mutual information calculation in a multi-scale phase space correlation dimension analysis method for a jet reactor under negative pressure conditions, provided in an embodiment of the present invention (the fifth scale of the pressure signal at position 1 under a negative pressure value of 10000 Pa).

[0050] Figure 5 This is 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 in one embodiment of the present invention.

[0051] Figure 6 shows the phase reconstruction attractor images of pressure signals in the slow-flow zone under different negative pressure conditions in a multi-scale phase space correlation dimension analysis method for a jet reactor under negative pressure conditions provided in an embodiment of the present invention.

[0052] Figure 7 shows the phase reconstruction attractor images of pressure signals in the negative pressure zone under different negative pressure conditions in a multi-scale phase space correlation dimension analysis method for a jet reactor under negative pressure conditions provided in an embodiment of the present invention.

[0053] Figure 8This is a schematic diagram illustrating the calculation of the correlation dimension using the correlationDimension function in a multi-scale phase space correlation dimension analysis method for a jet reactor under negative pressure conditions, provided in one embodiment of the present invention.

[0054] Figure 9 This invention provides a method for analyzing the correlation dimension of pressure signals in a slow-flow zone under different pressure conditions in a multi-scale phase space correlation dimension analysis of a jet reactor under negative pressure conditions, as an embodiment of the present invention.

[0055] Figure 10 This invention provides a method for analyzing the correlation dimension of pressure signals in a jet reactor under negative pressure conditions at different pressure levels, based on an embodiment of the present invention.

[0056] Figure 11 shows a comparison of the correlation dimension data of the same vertical boundary signal measurement port in the slow flow zone and the negative pressure zone under different negative pressure conditions in a multi-scale phase space correlation dimension analysis method for a jet reactor under negative pressure conditions according to an embodiment of the present invention. Detailed Implementation

[0057] The present invention will now be described in further detail with reference to specific embodiments and accompanying drawings. Similar elements in different embodiments are referred to by associated similar element reference numerals. In the following embodiments, many details are described to facilitate a better understanding of the invention. However, those skilled in the art will readily recognize that some features may be omitted in different situations, or may be replaced by other elements, materials, or methods. In some cases, certain operations related to the present invention are not shown or described in the specification. This is to avoid obscuring the core parts of the invention with excessive description. For those skilled in the art, detailed description of these related operations is not necessary; they can fully understand the related operations based on the description in the specification and general technical knowledge in the art.

[0058] Furthermore, the features, operations, or characteristics described in the specification can be combined in any suitable manner to form various embodiments. At the same time, the steps or actions in the method description can be rearranged or adjusted in a manner obvious to those skilled in the art. Therefore, the various orders in the specification and drawings are only for the clear description of a particular embodiment and do not imply a necessary order, unless otherwise stated that a particular order must be followed.

[0059] The first embodiment of this invention provides a method for multi-scale phase space correlation dimension analysis of a jet reactor under negative pressure conditions. The following is a combination of... Figure 1 Please provide a detailed explanation.

[0060] like Figure 1As shown, in step S100, time-series pressure signals are acquired for the negative pressure jet reactor under different negative pressure conditions.

[0061] The above steps specifically include:

[0062] S110, pressure signal acquisition ports are set in the negative pressure separation zone and the slow flow zone; the pressure signals of the negative pressure zone and the slow flow zone are acquired separately under different negative pressure values ​​at the top.

[0063] The jet impact process is transient, exhibiting significant changes over time. Therefore, analyzing the time-series pressure signals of the device, utilizing the time-frequency information of the one-dimensional signal, can better explore the internal flow field characteristics and flow pattern distribution within the porous jet impact reactor. Figure 2 As shown, in this embodiment, pressure signal acquisition ports are mainly set at two locations: the negative pressure separation zone and the slow flow zone. There are two ports 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 conditions of negative pressure values ​​of 5000 Pa, 10000 Pa, 15000 Pa, and 20000 Pa.

[0064] 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.

[0065] The above steps specifically include:

[0066] S210 uses Symlet7 wavelet transform to perform multi-scale decomposition on the acquired pressure signal. The decomposition process is based on scaling function and wavelet function to decompose the signal.

[0067] Because jet impact pressure signals are non-stationary and nonlinear, feature extraction is difficult. Therefore, wavelets are used to process the signal.

[0068] Wavelet transform is a time-frequency analysis method that analyzes the local characteristics of a signal by decomposing it into wavelet functions at different scales and locations. It was found that Sym7 wavelets are a good fit for pressure signals measured by devices, and the Sym7 wavelet is a wavelet basis with good symmetry, commonly used for multi-scale decomposition in signal processing. For Sym7 wavelets, the decomposition process is based on two functions: a scaling function and a wavelet function, to decompose the signal.

[0069] The Sym7 multiscale decomposition formula for a discrete signal f(x) can be expressed as:

[0070]

[0071] in In scale The approximation coefficients below, In scale The detail factor is below. It is the initial scale. It is the largest decomposition scale.

[0072] It is a scaling function used to represent an approximate part of a signal. It varies at different scales. The representation under translation k is:

[0073]

[0074] in, The scale is represented by k, and the translation is represented by k.

[0075] This is a wavelet function used to represent the detailed parts of a signal. Its representation at different scales j and translations k is as follows:

[0076]

[0077] The relationship between the wavelet function and the scaling function is expressed as follows:

[0078]

[0079] in, These are wavelet function coefficients.

[0080] Scale Approximation coefficients This can be expressed by the formula:

[0081]

[0082] in, These are low-pass filter coefficients, used to calculate approximation coefficients. .

[0083] In scale Detail coefficient This can be expressed by the formula:

[0084]

[0085] in, These are high-pass filter coefficients, used to calculate detail coefficients. .

[0086] Sym7 wavelet reconstruction reconstructs the signal by recombining the decomposed coefficients to obtain the original signal, as expressed by the formula:

[0087]

[0088] The Sym7 wavelet reconstructing process utilizes inverse filter coefficients, as expressed in the following formula:

[0089]

[0090] Sym7 wavelet decomposes a signal into approximate and detail parts at different scales using scaling and wavelet functions, thus achieving multi-scale decomposition. Approximate coefficients are calculated using low-pass filter coefficients, and detail coefficients are calculated using high-pass filter coefficients. The calculation of decomposition coefficients is based on the filter coefficients, and signal reconstruction is achieved by recombining the decomposed coefficients to obtain the original signal.

[0091] 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) length is maintained at 100,000 to ensure good frequency resolution. As Sym7 decomposes the pressure signal across multiple scales, the signal characteristics become more clearly displayed with each scale, resulting in a total decomposition into 12 scales (d1-d12). Since frequency domain resolution is only related to the sampling time, the longer the sampling time, the higher the frequency domain resolution. The Sym7 wavelet basis decomposes the signal into different time and frequency scales, effectively demonstrating the characteristics and structure of the pressure signal from the jet impact reactor.

[0092] like Figure 1 As shown, in step S300, phase space reconstruction attractors are performed on multi-scale pressure signals under different negative pressure conditions based on the phase space reconstruction method to obtain phase space reconstruction attractor images at different scales.

[0093] The above steps specifically include:

[0094] S310, based on the mutual information method, determines the optimal time delay by quantifying the dependency relationship between two time series under different time delays.

[0095] Specifically, given a time series and Calculate different delays Delayed mutual information ,in Indicates a point in time On At a certain point in time On Mutual information between them; plotting delayed mutual information Follow Find the first local minimum point by observing the curve of change. The delay τ corresponding to the point is the optimal time delay.

[0096] Mutual information method for calculating time delay: Its core is to determine the optimal time delay τ by quantifying the dependency between two time series under different time delays. The following are the mathematical formulas and calculation steps for calculating time delay using the mutual information method:

[0097] (1) For a known and definite time series and Assuming and The range of values ​​for are respectively and .Will and The range of values ​​for is divided into several intervals. Assume that... The range of values ​​is divided into Each interval, The range of values ​​is divided into Each interval. (Note: The original text appears to be incomplete and contains several errors. A more accurate translation would require the full context. The The intervals are , The The intervals are For each time point ,statistics and The frequency of all values ​​falling within a certain interval. (Note: The original text contains a typo and can be omitted.) for Falling in intervals and Falling in The frequency of each interval, for Falling in The frequency of each interval, for Falling in Frequency of each interval.

[0098] (2) Based on the joint frequency and total sample size Calculate the joint probability :

[0099]

[0100] Specifically, it is ensured that the sum of all joint probabilities is 1, that is:

[0101]

[0102] calculate Marginal probability distribution and Marginal probability distribution .

[0103] Based on frequency N i Given the total sample size N, calculate X. t marginal probability :

[0104]

[0105] Similarly, according to the frequency M j Given the total number of samples N, calculate Y. t+τ marginal probability

[0106]

[0107] (3) For two discrete random variables and mutual information Defined as:

[0108]

[0109] in, yes and The joint probability distribution, and yes and Separate marginal probability distributions.

[0110] At the same time, mutual information can also be expressed as the difference in entropy:

[0111]

[0112] in, and They are and entropy, It is the joint entropy.

[0113] Calculate different delays using the definition formula of mutual information. Below To determine the optimal time delay, it is typically necessary to calculate the mutual information of delays under different delays and find the first local minimum point. For example... Figure 4 The figure shows the time series Calculate different delays Below Draw delayed mutual information Follow By analyzing the curve of change, we can find the first local minimum point. The delay τ corresponding to this point is the optimal time delay. Figure 4 The time delay shown is 11.

[0114] S320, based on the Cao algorithm, determines the saturated embedding dimension of a time series.

[0115] Specifically, for embedding dimension of The phase space, defining statistics :

[0116]

[0117]

[0118]

[0119] in, It is the length of the time series. The optimal time delay is calculated based on the mutual information method. These are time series predictions obtained through local linear fitting. For the embedding dimension, It refers to 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 establish a local linear model in the reconstructed phase space using the neighboring points of the target point, and then use this model for prediction.

[0120] By calculating different embedding dimensions d and ,when and Initial random Increase and grow, and at a certain If the values ​​at each location no longer change significantly and tend to stabilize, then the corresponding... That is, the saturation embedding dimension m. For example... Figure 5 As shown, Follow When the number of embeddings increases and then stabilizes, it indicates that the embedding dimension is sufficient. exist The time-space relationship no longer changes significantly. Therefore, the calculated saturation embedding dimension is 4.

[0121] S330 performs phase space reconstruction based on the obtained optimal time delay and saturated embedding dimension.

[0122] Because pressure signals exhibit fractal structures at different scales, and calculations show that single-fractals and bifractals at different scales exhibit self-similarity across scales, pressure signals possess chaotic attractors. Therefore, this embodiment employs the phase space reconstruction method to reconstruct the attractors in the phase space of multi-scale pressure signals under different negative pressure conditions.

[0123] Phase space reconstruction attractor: Phase space reconstruction is one of the important methods for studying nonlinear dynamical systems. Its core is to reconstruct the phase space of the system through 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*.

[0124] Specifically, for a One-dimensional scalar time series of chaotic attractors , where n is the length of the time series, and if the embedding dimension is... satisfy Then, an attractor that is topologically equivalent to the original system can be reconstructed using the delayed embedding method;

[0125] Reconstruct the phase space based on the obtained optimal time delay and saturated embedding dimension:

[0126]

[0127] in, It is the saturation embedding dimension. This is the optimal delay time.

[0128] like Figure 1 As shown, in step S400, the nonlinear characteristics and dynamic behavior of the flow field under different negative pressure conditions are obtained by comparing the phase space reconstructed attractor images and performing correlation dimension analysis.

[0129] S410, Comparative analysis of attractor images.

[0130] 1. Attractor analysis in slow-flow regions

[0131] Figures 6(a) and 6(b) show the phase reconstruction attractor images of pressure signals in the slow-flow region under different negative pressure conditions. The area size of the attractor can intuitively reflect the complexity and chaos of the system. As the pressure signal is decomposed by wavelet multi-scale decomposition, the attractor corresponding to the pressure signal gradually becomes clearer in three-dimensional space. The attractors reconstructed from the multi-scale pressure signals under different negative pressure conditions show obvious differences. As the scale of the wavelet-decomposed signal increases, the shape of the attractor becomes more and more obvious, indicating that wavelet multi-scale denoising exhibits good characteristics for pressure signals. The 7th and 8th scales show complete and clear attractor patterns. The higher the scale of the pressure signal, the clearer the attractor image becomes with the increase of scale, indicating that signal denoising is beneficial to the display of chaotic attractors, that is, the system has a strong sensitivity to noise.

[0132] Figure 6(a) shows that the area of ​​the chaotic attractor image at scale 8 decreases significantly with increasing top negative pressure, indicating that the complexity and chaos at position 1 gradually decrease with increasing negative pressure. Figure 6(b) shows that the area of ​​the chaotic attractor image at scale 8 increases significantly with increasing top negative pressure, reflecting that the complexity and chaos at position 2 gradually increase with increasing negative pressure. The top negative pressure shows opposite trends for the dynamic characteristics at positions 1 and 2 in the slow flow region. Figure 6(a) shows that a two-dimensional attractor image appears at scale 12 when the top negative pressure is 10000 Pa and 15000 Pa, indicating that the dynamic behavior of the system under this pressure condition has a certain degree of stability and predictability, or that the system is closer to a periodic or quasi-periodic state under this pressure condition. Figure 6(b) shows that a two-dimensional attractor image appears at higher scales when the top negative pressure is 10000 Pa, 15000 Pa, and 20000 Pa. Compared with signal measurement port 1, signal measurement port 2 has stronger stability and predictability under pressure changes.

[0133] 2. Negative pressure region attractor analysis

[0134] Figures 7(a) and 7(b) show the reconstructed attractor images of the pressure signal in the negative pressure region under different negative pressure conditions. Since the attractor size can visually indicate the chaotic state of the system, Figure 7(a) shows the attractor reconstructed from the pressure signal at the 5-signal measurement port. The attractor size at different scales shows significant differences as the pressure increases. Based on the system's sensitivity to noise, the pressure signal exhibits 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 show smaller areas at 15000 Pa, indicating that the system at the 5-signal measurement port exhibits lower complexity at a top negative pressure of 15000 Pa. Meanwhile, Figure 7(a) shows that at top negative pressures of 5000 Pa, 10000 Pa, and 20000 Pa, the system exhibits a two-dimensional attractor at the 12th scale, indicating that the system has good periodicity or predictability in this state.

[0135] Figure 7(b) shows that the area of ​​the chaotic attractor at the 8th scale gradually decreases with increasing top negative pressure, indicating that the randomness of the system near the 6-signal measurement port decreases while its predictability and stability increase with increasing top negative pressure. Simultaneously, Figure 7(b) shows that a two-dimensional attractor appears at the 11th scale when the top negative pressure is 15000 Pa and 20000 Pa, meaning that the periodicity and predictability of the system improve with increasing top negative pressure. The 6-signal measurement port has fewer two-dimensional attractors than the 5-signal measurement port, indicating that the system at the 6-signal measurement port has lower periodicity and stability, meaning that different dynamic trajectories exist at non-axisymmetric positions on the same plane.

[0136] S420 calculates the correlation dimension to analyze dynamic complexity.

[0137] In MATLAB, the correlationDimension function is used to calculate the correlation dimension of a time series. It is based on the Grassberger-Procaccia algorithm. The correlationDimension function fits the line by selecting an appropriate radius range (MinRadius and MaxRadius).

[0138] Correlation dimension Through fitting and The slope obtained from the linear part:

[0139]

[0140] Among them, the correlation integral The probability that the distance between a pair of points in phase space is less than a preset radius r is defined as:

[0141]

[0142] Where: N is the number of points in the phase space. and It is the reconstructed phase space vector. It is the Heaviside step function, when The value is 1 if it is true, and 0 otherwise.

[0143] The correlation dimension function is computed by using r values ​​that are uniformly distributed on a logarithmic scale. Figure 8 This shows a diagram illustrating how the correlationDimension function calculates the correlation dimension. and In a double logarithmic plot, the linear portion is selected for fitting, and its slope is the correlation dimension. .

[0144] 1. Correlation dimension analysis of slow-flow zone

[0145] Figure 9The correlation dimension of the pressure signal in the slow-flow region under different negative pressure conditions is shown. As the scale increases, the correlation dimension decreases, indicating that the complexity of the pressure signal gradually decreases during multi-scale changes, and high-frequency and low-frequency components are eliminated. The variation ranges of the pressure signal at signal measurement port 1 in the slow-flow region under different negative pressure conditions are 423.49%, 425.70%, 504.52%, and 420.43%, respectively. The variation ranges of the pressure signal at signal measurement port 2 in the slow-flow region under different negative pressure conditions are 463.35%, 447.57%, 448.36%, and 374.71%, respectively. This indicates that the pressure signal in the slow-flow region exhibits significant heterogeneity or diversity at different scales, implying a more complex interaction or feedback mechanism within the system. Compared to signal measurement port 1, the correlation dimension variation range at signal measurement port 2 is larger, indicating that the system near the location of signal measurement port 2 on the same plane has stronger nonlinear characteristics, and the pressure signal has a more complex structure.

[0146] Meanwhile, comparing the correlation dimensions at the same scale under different negative pressure conditions, it can be seen that the correlation dimension of signal measurement port 1 exhibits similar values ​​at scales of 8-12, ranging from 3.31% to 5.71%, with the range decreasing as the scale increases. The correlation dimension of signal measurement port 2 exhibits similar values ​​at scales of 9-12, ranging from 5.84% to 19.11%. Compared to signal measurement port 1, the correlation dimension of pressure signals at signal measurement port 2 shows more significant fluctuations. Pressure signals typically reflect the macroscopic characteristics of the interaction between the gas and solid phases as a whole, and may also include mesoscopic characteristics resulting from the coupling of microscopic and macroscopic characteristics. Under high-scale conditions, the main dynamic behaviors of the system are concentrated at the macroscopic level. The correlation dimensions of pressure signals in the slow-flow region are relatively similar at high scales, indicating that the dynamic behavior in the slow-flow region does not differ significantly macroscopically under different negative pressure conditions. The pressure signals in the slow-flow region show significant differences at low scales, with the differences at low scales being the main factor. This indicates that the negative pressure at the top has a significant impact at the microscopic level. As the pressure signal changes across multiple scales, the complexity at the microscopic level is simplified to some extent.

[0147] 2. Correlation dimension analysis of negative pressure zone

[0148] Figure 10The correlation dimension of the pressure signal at two measurement ports in the negative pressure zone under different pressure conditions is shown. During wavelet multi-scale denoising, the correlation dimension of the chaotic attractor of the pressure signal generally decreases, with local increases. The multi-scale variation ranges of the pressure signal at 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 multi-scale variation ranges of the pressure signal at 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 multi-scale variation process is a denoising process; therefore, it is evident that the correlation dimension changes significantly when the top negative pressure is 10000 Pa and 20000 Pa, indicating that these two negative pressure conditions generate more high-frequency signals and have a greater impact on the microscopic changes within the system.

[0149] Comparing the correlation dimensions under different negative pressure conditions at the same scale, the correlation dimension of the 5-signal measuring port shows similar values ​​at scales 11-12, with a variation range of 1.26%-4.06%. The larger the scale, the smaller the difference in correlation dimension, indicating that at the macroscopic scale, the influence of the top negative pressure on the flow characteristics of the 5-signal measuring port is similar. The correlation dimension of the 6-signal measuring port shows similar values ​​at scales 10-12, with a variation range of 2.78%-6.3%. Compared to the 5-signal measuring port showing the smallest difference at scale 12, the 6-signal measuring port shows the smallest difference at scale 11. Furthermore, comparing the values ​​shows that the macroscopic influence of the top negative pressure on the 6-signal measuring port is greater than that on the 5-signal measuring port.

[0150] 3. Comparison of correlation dimensions between the slow-flow zone and the negative pressure zone

[0151] Figures 11(a) and 11(b) show a comparison of the correlation dimension data of 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 pressure signal correlation dimension of the 1-position signal measurement port and the 5-position signal measurement port. The pressure signal correlation dimension of the 1-position signal measurement port is 1.6%, 0.9%, 5.4%, and 0.2% higher than that of the 5-position signal measurement port at the top negative pressure of 5000 Pa, 10000 Pa, 15000 Pa, and 20000 Pa, respectively, and there is a larger difference at the top negative pressure of 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.

[0152] Figure 11(b) shows a multi-scale comparison of the pressure signal correlation dimension between the 2-position and 6-position signal measuring ports. The pressure signal correlation dimension of the 2-position port is 0.22%, 0.35%, 0.13%, and -0.16% higher than that of the 6-position port at the top negative pressure of 5000 Pa, 10000 Pa, 15000 Pa, and 20000 Pa, respectively. Compared to the difference between the 1-position and 5-position signal measuring ports, the data from the 2-position and 6-position ports are relatively close, indicating that the nonlinear characteristic complexity of these two positions is relatively consistent. However, Figure 11(b) shows significant differences in local variations between the 2-position and 6-position signal measuring ports, suggesting that at the microscopic level, the two positions should have different nonlinear characteristics.

[0153] As the scale increases, the high-frequency details in the pressure signals from the two pressure signal measuring ports are smoothed, the signal complexity is reduced, and the correlation dimension is reduced. This leads to a decrease in the correlation dimension difference between the two signal measuring ports under different negative pressure conditions, indicating that the macroscopic changes at the two locations are relatively small. Therefore, the effect of the negative pressure at the top is more reflected in the microscopic changes.

[0154] In summary, the embodiments of this invention comprehensively reveal the nonlinear characteristics and dynamic behavior of pressure signals under different negative pressure conditions through phase space reconstruction of attractor images and correlation dimension analysis. These findings provide important reference for understanding the dynamic behavior of complex fluid systems and offer theoretical support for further research on regional differences in fluid dynamics.

[0155] Corresponding to the above-disclosed method for multi-scale phase space correlation dimension analysis of a jet reactor under negative pressure conditions, this invention also discloses a system for multi-scale phase space correlation dimension analysis of a negative pressure jet reactor, which specifically includes:

[0156] The pressure signal acquisition module is used to acquire time-series pressure signals of the negative pressure jet reactor under different negative pressure conditions.

[0157] The multi-scale decomposition module is used to perform multi-scale decomposition on the acquired pressure signal based on the wavelet transform method to obtain a multi-scale pressure signal.

[0158] The phase space reconstruction module is used to perform phase space reconstruction attractor on multi-scale pressure signals under different negative pressure conditions based on the phase space reconstruction method, and obtain phase space reconstruction attractor images at different scales.

[0159] The analysis module is used to obtain the nonlinear characteristics and dynamic behavior of the flow field under different negative pressure conditions by comparing and correlating attractor images reconstructed in phase space and performing correlation dimension analysis.

[0160] It should be noted that for a detailed description of the multi-scale phase space correlation dimension analysis system for a negative pressure jet reactor provided in the embodiments of the present invention, please refer to the relevant description of the multi-scale phase space correlation dimension analysis method for a jet reactor under negative pressure conditions provided in the embodiments of this application, which will not be repeated here.

[0161] In addition, embodiments of the present invention also provide an electronic device, the device comprising: a processor and a memory; the memory being used to store one or more program instructions; the processor being used to execute one or more program instructions to perform 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 preceding embodiments.

[0162] It should be noted that for a detailed description of an electronic device provided in the embodiments of the present invention, please refer to the relevant description of a multi-scale phase space correlation dimension analysis method for a jet reactor under negative pressure conditions provided in the embodiments of this application, which will not be repeated here.

[0163] In addition, embodiments of the present invention also provide a computer-readable storage medium storing a computer program, which, when executed by a processor, implements 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 preceding embodiments.

[0164] It should be noted that for a detailed description of a computer-readable storage medium provided in the embodiments of the present invention, please refer to the relevant description of a multi-scale phase space correlation dimension analysis method for a jet reactor under negative pressure conditions provided in the embodiments of this application, which will not be repeated here.

[0165] Those skilled in the art will understand that all or part of the functions of the various methods in the above embodiments can be implemented by hardware or by computer programs. When all or part of the functions in the above embodiments are implemented by computer programs, the program can be stored in a computer-readable storage medium, which may include: read-only memory, random access memory, disk, optical disk, hard disk, etc., and the program is executed by a computer to achieve the above functions. For example, the program can be stored in the memory of a device, and when the program in the memory is executed by the processor, all or part of the above functions can be achieved. In addition, when all or part of the functions in the above embodiments are implemented by computer programs, the program can also be stored in a server, another computer, disk, optical disk, flash drive, or external hard drive, etc., and can be downloaded or copied to the memory of a local device, or the system of the local device can be updated. When the program in the memory is executed by the processor, all or part of the functions in the above embodiments can be achieved.

[0166] The above examples illustrate the present invention only to aid in understanding it and are not intended to limit the scope of the invention. Those skilled in the art can make various simple deductions, modifications, or substitutions based on the principles of this invention.

Claims

1. A method for multi-scale phase space correlation dimension analysis of a jet reactor under negative pressure conditions, characterized in that, The method includes: Time-series pressure signals were acquired from the negative pressure jet reactor under different negative pressure conditions. The collected pressure signal is decomposed into multi-scale pressure signals based on wavelet transform. The phase space reconstruction method is used to reconstruct the attractor in the phase space of multi-scale pressure signals under different negative pressure conditions, resulting in phase space reconstruction attractor images at different scales. Specifically, this includes: determining the optimal time delay by quantizing the dependency between two time series at different time delays using the mutual information method; determining the saturated embedding dimension of the time series using the Cao algorithm; and performing phase space reconstruction based on the obtained optimal time delay and saturated embedding dimension. By comparing phase space reconstructed attractor images and performing correlation dimension analysis, the nonlinear characteristics and dynamic behavior of the flow field under different negative pressure conditions are obtained. The phase space reconstruction, based on the obtained optimal time delay and saturated embedding dimension, specifically includes: For a One-dimensional scalar time series of chaotic attractors , where n is the length of the time series, and if the embedding dimension is... satisfy Then, an attractor that is topologically equivalent to the original system can be reconstructed using the delayed embedding method; Reconstruct the phase space based on the obtained optimal time delay and saturated embedding dimension: in, It is the saturation embedding dimension. It is the optimal delay time; By comparing phase space reconstructed attractor images and performing correlation dimension analysis, the nonlinear characteristics and dynamic behavior of the flow field under different negative pressure conditions are obtained, specifically including: In MATLAB, the correlationDimension function is used to calculate the correlation dimension of a time series. It is implemented based on the Grassberger-Procaccia algorithm; Correlation dimension Through fitting and The slope obtained from the linear part: Among them, the correlation integral This represents the probability that the distance between a pair of points in phase space is less than r, where r is a preset threshold for the distance between pairs of points.

2. The method for multi-scale phase space correlation dimension analysis of a jet reactor under negative pressure conditions as described in claim 1, characterized in that, Time-series pressure signal acquisition was performed on the negative pressure jet reactor under different negative pressure conditions, specifically including: Pressure signal acquisition ports are set up in the negative pressure separation zone and the slow flow zone; pressure signals in the negative pressure zone and the slow flow zone are collected under different negative pressure values ​​at the top.

3. The method for multi-scale phase space correlation dimension analysis of a jet reactor under negative pressure conditions as described in claim 1, characterized in that, The acquired pressure signal is decomposed into multiple scales based on wavelet transform to obtain a multi-scale pressure signal, specifically including: The acquired pressure signal was decomposed into multiple scales using Symlet7 wavelet transform. The decomposition process was based on scaling functions and wavelet functions to decompose the signal.

4. The method for multi-scale phase space correlation dimension analysis of a jet reactor under negative pressure conditions as described in claim 1, characterized in that, Based on mutual information, the optimal time delay is determined by quantifying the dependency between two time series at different time delays. Specifically, this includes: Given a time series and Calculate different delays Delayed mutual information ,in Indicates at a point in time On At a certain point in time On Mutual information between them; Drawing delayed mutual information Follow Find the first local minimum point by observing the curve of change. The delay τ corresponding to the point is the optimal time delay.

5. The method for multi-scale phase space correlation dimension analysis of a jet reactor under negative pressure conditions as described in claim 1, characterized in that, The saturated embedding dimension of a time series is determined based on the Cao algorithm, specifically including: For embedding dimension is The phase space, defining statistics : in, It is the length of the time series. The optimal time delay is calculated based on the mutual information method. These are time series predictions obtained through local linear fitting. For the embedding dimension, It is the length of the time series; By calculating different embedding dimensions d and ,when and Initial random Increase and grow, and at a certain If the values ​​at each location no longer change significantly and tend to stabilize, then the corresponding... That is, the saturated embedding dimension m.

6. A multi-scale phase space correlation dimension analysis system for a negative pressure jet reactor, characterized in that, The system includes: The pressure signal acquisition module is used to acquire time-series pressure signals of the negative pressure jet reactor under different negative pressure conditions. The multi-scale decomposition module is used to perform multi-scale decomposition on the acquired pressure signal based on the wavelet transform method to obtain a multi-scale pressure signal. The phase space reconstruction module is used to perform phase space reconstruction attractor on multi-scale pressure signals under different negative pressure conditions based on the phase space reconstruction method, and obtain phase space reconstruction attractor images at different scales. The phase space reconstruction method is used to reconstruct the attractor in the phase space of multi-scale pressure signals under different negative pressure conditions, resulting in phase space reconstruction attractor images at different scales. Specifically, this includes: determining the optimal time delay by quantizing the dependency between two time series at different time delays using the mutual information method; determining the saturated embedding dimension of the time series using the Cao algorithm; and performing phase space reconstruction based on the obtained optimal time delay and saturated embedding dimension. The analysis module is used to obtain the nonlinear characteristics and dynamic behavior of the flow field under different negative pressure conditions by comparing and correlating attractor images reconstructed in phase space and performing correlation dimension analysis. The phase space reconstruction, based on the obtained optimal time delay and saturated embedding dimension, specifically includes: For a One-dimensional scalar time series of chaotic attractors , where n is the length of the time series, and if the embedding dimension is... satisfy Then, an attractor that is topologically equivalent to the original system can be reconstructed using the delayed embedding method; Reconstruct the phase space based on the obtained optimal time delay and saturated embedding dimension: in, It is the saturation embedding dimension. It is the optimal delay time; By comparing phase space reconstructed attractor images and performing correlation dimension analysis, the nonlinear characteristics and dynamic behavior of the flow field under different negative pressure conditions are obtained, specifically including: In MATLAB, the correlationDimension function is used to calculate the correlation dimension of a time series. It is implemented based on the Grassberger-Procaccia algorithm; Correlation dimension Through fitting and The slope obtained from the linear part: Among them, the correlation integral This represents the probability that the distance between a pair of points in phase space is less than r, where r is a preset threshold for the distance between pairs of points.

7. 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 configured to run one or more program instructions to perform the steps of a multi-scale phase space correlation dimension analysis method for a jet reactor under negative pressure conditions as described in any one of claims 1 to 5.

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