CN111611714B - Supersonic mixed layer order reduction method and system - Google Patents
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Abstract
The invention discloses a method and a system for reducing the rank of a supersonic mixed layer, wherein the method comprises the following steps: collecting a plurality of flow field snapshots to form an observation sample set; performing cluster analysis on the observation samples according to flow field characteristics to obtain a plurality of subsets gathered around respective cluster centers; predicting the flow field evolution by analyzing the conversion relation and the conversion time among various types to construct a network model; and verifying the prediction result by adopting the autocorrelation function, respectively calculating and comparing the autocorrelation functions of the sample set and the prediction result, adjusting the parameters of the network model when the autocorrelation functions of the sample set and the prediction result are not consistent, and repeating the steps until the autocorrelation functions of the sample set and the prediction result are consistent. The method is used for solving the problems that the modal effective resolution ratio is low, the obtained flow field modal is greatly different from the actual flow field modal and the like in the prior art, and the supersonic mixing layer with high Reynolds number can be analyzed by a small amount of modes, so that the flow field modal closer to the physical actual flow field is obtained, and the corresponding physical significance is easy to explain.
Description
Technical Field
The invention relates to the technical field of turbulence order reduction analysis, in particular to an order reduction method for an ultrasonic mixing layer based on cluster analysis and a network model. The method can also be applied to reduced-order modeling of other flow models.
Background
Supersonic mixed layer flow is a very typical flow model in engineering application, and widely exists in practical problems such as rapid mixing of fuel and oxidant in a combined cycle engine, aerodynamic noise of a tail nozzle, aerodynamic optical effect in missile image navigation and the like. Supersonic mixing layers are commonly characterized by multi-scale turbulence and high-dimensional non-linearity. In addition, the interplay of the hybrid layer with shock waves and chemical reactions increases the complexity of the hybrid layer flow mechanism.
The research on the mixed layer starts under the condition of low speed and no compressibility and is gradually popularized to the supersonic speed field. A great deal of literature research focuses on pseudo-sequence vortex structures, turbulence statistical analysis, the influence of compression effect on the growth rate, characteristic flow field structures of mixed layers under periodic excitation and the like. But few reports are made on the study of the dynamics and evolution of the mixed layer. The development of high-precision experimental testing means and high-precision numerical simulation technology provides powerful means for the research of the mixed layer. But also with a large amount of data. Studying the potential kinetic characteristics of large data remains a powerful challenge.
Intrinsic orthogonal decomposition (POD) is a widely used turbulence reduction model, and the POD method is applied to a mixed layer flow analysis by Qin Yang et al (Qin, Yang, Song, et al. analysis of flow structures in super sonic plane mixing the POD method [ J ]. Science in China Series G, 2008) and Laizer et al (Laizer S, Lardeau S, Lambalais E.direct numerical simulation of a mixed layer down flow a piezoelectric layer and an incompressible layer, 2010,22(1): 015104), respectively. Firstly, the mixed layer flow contains a multi-scale quasi-sequential vortex structure, the spectrum range is wide, and the turbulence energy is difficult to be completely analyzed by a small number of POD modes. Furthermore, the POD mode corresponds to the orthonormal basis of the eigenvalue problem, and does not correspond to the true flow characteristic state, so that the physical meaning of the flow field structure corresponding to the POD mode is difficult to interpret.
The recent rise of artificial intelligence and machine learning techniques provides many effective mathematical means for big data analysis and is gradually applied to fluid mechanics research. And extracting effective information from the big data by adopting a machine learning method, and establishing a reduced order model of turbulence dynamics.
Disclosure of Invention
The invention provides a method and a system for reducing orders of supersonic mixing layers, which are used for overcoming the defects that the modal effective resolution ratio is low, the obtained flow field mode has larger difference with the actual flow field mode and the like in the prior art, realizing that the turbulent kinetic energy of the supersonic mixing layer with high Reynolds number can be analyzed by using a small number of modes (clustering centers), obtaining the flow field mode closer to the physical reality, and being easy to explain the corresponding physical significance.
In order to achieve the purpose, the invention provides a supersonic mixed layer order reducing method which comprises the following steps:
and 4, verifying the prediction result by adopting an autocorrelation function, respectively calculating and comparing the autocorrelation functions of the sample set and the prediction result, adjusting network model parameters when the autocorrelation functions of the sample set and the prediction result are not consistent, and repeating the steps 1-3 until the autocorrelation function of the prediction result is consistent with the autocorrelation function of the sample set.
In order to achieve the above object, the present invention further provides a supersonic hybrid layer order reduction system, which includes a processor and a memory, where the memory stores a supersonic hybrid layer order reduction program, and the processor executes the steps of the method when running the supersonic hybrid layer order reduction program.
The invention provides a supersonic mixed layer order-reducing method and a system, wherein a plurality of snapshot samples are gathered into one class by clustering and analyzing speed field snapshots collected from experiments or numerical simulation, a plurality of classes with the quantity far smaller than that of the snapshot samples are finally obtained, a clustering center is taken as a characteristic state representing a certain class (characteristic state of a plurality of sample snapshots contained in a corresponding class), a representative flow field structure is obtained after clustering and analyzing the conversion relation among the classes and the corresponding conversion time from the angle of statistical probability by using a network model; simulating a random process by using the obtained conversion relation and conversion time among various types to obtain an evolution process of the supersonic mixed layer power system; according to the scheme, order reduction is realized through pure data driven clustering analysis, and prediction of flow field evolution of the supersonic mixing layer power system is realized through fusion of a model network and the clustering analysis in two dimensions of conversion probability and conversion time.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the structures shown in the drawings without creative efforts.
Fig. 1 is a flowchart of a turbulence order reduction model based on cluster analysis in a supersonic velocity mixing layer order reduction method according to an embodiment of the present invention;
FIG. 2 is a schematic view of a flow model of a large-vortex simulation supersonic velocity mixing layer in a simulation test;
FIG. 3 is a transverse pulsating velocity cloud plot of a cluster center obtained by cluster analysis of velocity field snapshots obtained in the numerical simulation process by the flow model of FIG. 2;
fig. 4 is a transverse pulsation velocity cloud chart of the first 10-order POD mode obtained by analyzing a velocity field snapshot obtained in the numerical simulation process by the flow model of fig. 2 by a conventional POD method;
FIG. 5 is a clustering index function obtained by the order reduction method according to the first embodiment;
FIG. 6a is a transition probability matrix obtained by the order reduction method according to the first embodiment;
FIG. 6b is the average transition time matrix obtained by the order reduction method according to the first embodiment;
fig. 7 is a comparison of autocorrelation functions of velocity field evolution (solid line) obtained by simulation using the order-reducing method proposed by the present invention and velocity field evolution (dotted line) obtained by simulation using large vortices.
The implementation, functional features and advantages of the objects of the present invention will be further explained with reference to the accompanying drawings.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It should be noted that all the directional indicators (such as up, down, left, right, front, and rear … …) in the embodiment of the present invention are only used to explain the relative position relationship between the components, the movement situation, etc. in a specific posture (as shown in the drawing), and if the specific posture is changed, the directional indicator is changed accordingly.
In addition, the descriptions related to "first", "second", etc. in the present invention are only for descriptive purposes and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of the present invention, "a plurality" means at least two, e.g., two, three, etc., unless specifically limited otherwise.
In the present invention, unless otherwise expressly stated or limited, the terms "connected," "secured," and the like are to be construed broadly, and for example, "secured" may be a fixed connection, a removable connection, or an integral part; the connection can be mechanical connection, electrical connection, physical connection or wireless communication connection; they may be directly connected or indirectly connected through intervening media, or they may be connected internally or in any other suitable relationship, unless expressly stated otherwise. The specific meanings of the above terms in the present invention can be understood by those skilled in the art according to specific situations.
In addition, the technical solutions in the embodiments of the present invention may be combined with each other, but it must be based on the realization of those skilled in the art, and when the technical solutions are contradictory or cannot be realized, such a combination of technical solutions should not be considered to exist, and is not within the protection scope of the present invention.
Example one
As shown in fig. 1, a supersonic hybrid layer order reduction method includes the following steps:
step S1, collecting a plurality of speed field snapshots to form an observation sample set;
collecting flow field snapshots in a fixed region omega in experiments or numerical simulation, wherein the collection time step is delta t; the following describes a specific order reduction method by taking a speed field snapshot in the acquisition process as an example: the method comprises the steps of acquiring speed field snapshots on a fixed area of an experiment or numerical simulation, wherein the fixed area refers to the condition that each acquisition of the speed field snapshots is performed in a two-dimensional plane area or a three-dimensional volume area of the same fixed range, and the plane area or the three-dimensional volume is marked as omega.
Acquiring time step satisfying delta t less than or equal to 1/f, namely acquiring the main characteristic that the acquired speed field snapshot should capture the flow field, wherein f is the dominant frequency of the supersonic mixed layer; at tmThe snapshot of the flow field at time is denoted u (x, t)m) Wherein M is 1, … …, M, where x is an area position vector, that is, it means that all the acquired velocity field snapshots are located in the same area; the M speed field snapshots at least cover the characteristic period of 1000 mixed layers, namely M multiplied by delta t is less than or equal to 1000/f; the collected speed field snapshots are grouped into a set A ═ u in time seriesm(x):＝u(x,tm) And M is 1, …, M }. And the region position vector represents that all the acquired M speed field snapshots are located in the fixed region omega.
Step S2, carrying out cluster analysis on the observation samples according to the similarity of the speed field characteristics to obtain cluster centers and various subsets gathered around the respective cluster centers; the step S2 includes:
step S21, determining the optimal clustering number as K by using an elbow method;
step S22, the speed field characteristic of each class is determined by the clustering center ck(x) And characterizing, wherein a clustering index function characterizes the mapping relation between each speed field snapshot and the nearest clustering center:
wherein x is a position vector; t is tmM × Δ t represents a time series, which is a discrete quantity; u is a velocity field snapshot; c. CiRepresenting the clustering centers of the ith class, and the nearest equivalence of each speed field snapshot and the corresponding clustering center is that the Euclidean distance between the speed field snapshots and the corresponding clustering centers is the minimum.
Step S23, adopting k-means + + algorithm to snapshot the M speed fields um(x) And performing clustering analysis to obtain K types. Clustering Analysis was performed using the k-means + + algorithm, which was first presented in the literature (Macqueen J. Some Methods for Classification and Analysis of multivariable occlusions [ C ]]//Proc of Berkeley Symposium on Mathematical Statistics&Probability.1965.). The process is as follows:
step S231, randomly initializing K clustering centers
From velocity field snapshot um(x) The mean variance measure between the corresponding nearest cluster center, also called the within-class variance:
wherein x is an area position vector, i.e. it means that all the acquired M velocity field snapshots are located in the same area Ω, ckDenotes the k-th cluster center, ck(m)Representing the mth range-velocity field snapshot um(x) The nearest cluster center;
step S232, dividing each speed field snapshot as a sample point into classes with the shortest distance according to the Euclidean distance minimum principle;
step S233, recalculating the clustering centers, and repeating the steps S221 and S222 until a group of optimal clustering centers is obtained
So that the intra-class variance V is sufficiently small:
the cluster center is the average of all velocity field snapshot feature values in the corresponding class:
Nkthe number of all speed field snapshot sample points contained in the kth class is shown, wherein m is the serial number of the flow field snapshot characteristic value sample points and is an integer; ckIs the state space of class k.
Step S3, calculating a conversion probability matrix and average conversion time to obtain a network model; a network model is constructed by analyzing the conversion relation and the conversion time among various types to predict the evolution of the velocity field;
calculating various conversion probability matrixes and average conversion time of each type of speed field characteristics by taking a clustering center as a representative to obtain a network model, analyzing conversion relations and conversion time among various types according to the network model, and constructing various unified motion models among adjacent time points to predict speed field evolution;
the step S3 includes:
step S31, according to the clustering index function k (t)m) Calculating a conversion probability matrix and an average conversion time matrix to obtain a network model;
step S32, according to the transition probability matrix PijAnd average transition time matrix TijThe velocity field evolution is predicted. According to conversion summaryObtaining a conversion path between any two clustering centers by a rate matrix simulation random process, obtaining the time of conversion from the corresponding position of an average conversion time matrix according to the conversion path, constructing a motion model by taking the motion of any two clustering centers between adjacent time sequences as linearity, and predicting the flow field evolution by accessing the motion track of each clustering center on the conversion path on a discrete time sequence;
the step S31 includes:
recording the time point of conversion as tnAnd satisfies the following conditions: k (t)n-ε)≠k(tn+ epsilon), where epsilon is any small amount satisfying epsilon < 1 × 10-5. The formula shows that at the switching time tnBefore and after, the flow field snapshots belong to different classes; in the time interval (t)n，tn+1) In this example, assume that the characteristic state of class k is at the midpoint of the time interval, i.e., (t)n+tn+1) 2; the residence time in this class is defined as: tau isn＝tn+1-tn；
Defining j and i as transition time points tnAnd tn+1The subsequent clustering index; the transition time from class i to class j is defined as the time between two feature states:
transition probability matrix PijComprises the following steps:
wherein n isijIs from cjTo ciThe number of transitions of (1), njIs from cjStarting to number of other classes, which includes nijThe average of all possible transition times is taken as the average transition time in the model:
Tij＝<τij> (7)
formulas (6) and (7) are network models;
step S32 includes: set at an initial time t0State space k-like when 00Then the time passes
Class k0Conversion to class k1At the moment of
By analogy, class k1Conversion to class k2At the moment of
Simulating random walk by the conversion probability matrix to obtain a conversion path; wherein the conversion path is from class k0To class k1Go to class k2The random process can be obtained by simulating a random process according to the conversion probability matrix; converting the time elapsed
And
obtained from the corresponding position of the average transition time matrix according to the transition path. Therefore, the velocity field evolution is predicted by accessing representative characteristic velocity fields (cluster centers) over a discrete time series:
the movement of any two cluster centers between two adjacent time points is set to be linear, namely in a time region t1∈[tn,tn+1]The velocity field is:
wherein the linearity coefficient is:
and repeating the process to obtain corresponding speed fields on all continuous time points to complete the prediction of the speed field evolution.
And step S4, verifying the prediction result by adopting an autocorrelation function, respectively calculating and comparing the autocorrelation functions of the sample set and the prediction result, adjusting the parameters of the network model when the autocorrelation functions of the sample set and the prediction result are not consistent, and repeating the steps S1-S3 until the autocorrelation functions of the prediction result are consistent with the autocorrelation functions of the sample set.
The method specifically comprises the following steps: when the prediction result does not match the autocorrelation function of the sample set, the number M of velocity field snapshots or the number K of clusters needs to be adjusted, and the above steps S1-S3 are repeated until the autocorrelation function matches.
Wherein the autocorrelation function of the sample set in step S4 is defined as:
respectively calculating autocorrelation functions by adopting numerical simulation results or time series velocity field snapshots obtained by experiments and prediction results carried out by adopting the network model based on the cluster analysis, comparing, if the autocorrelation functions of the two are consistent well with the evolution of time, indicating that the model processing and application are correct, otherwise, adjusting relevant parameters and data, and repeating the steps S1-S3.
The scheme has the following technical effects:
1. compared with the traditional order reduction method such as intrinsic orthogonal decomposition (POD), the ultrasonic mixed layer order reduction method based on cluster analysis and network model provided by the invention can analyze the turbulent kinetic energy of the ultrasonic mixed layer with high Reynolds number only by using a small number of modes (cluster centers). The present invention is an effective alternative to POD.
2. The method for reducing the rank of the supersonic mixing layer of the cluster analysis and network model, provided by the invention, obtains the average value of the velocity field snapshots contained in various types of flow field modes, and is closer to the physical reality, so that the flow field modes closer to the physical reality can be obtained, and the corresponding physical significance is easy to explain.
3. The method provided by the invention is used for carrying out evolution analysis on the power system of the supersonic velocity mixing layer, and can carry out automatic processing after the sample set and the clustering number K obtained by collection are given, so that the operation is simple, and the technical realization difficulty is low.
4. The method provided by the invention has wide application range, and can be widely applied to various turbulent flow models; the method can be applied to evolution and analysis of a speed field, and can also be applied to evolution and analysis of power systems such as pressure field, density field and flow field visualization. Within a certain time range, the evolution of various fields can be accurately predicted.
Next, a simulation test is performed on a specific flow field by the order reduction method of the first embodiment:
the invention provides a supersonic mixing layer order reduction method based on cluster analysis and a network model by combining machine learning and a network model algorithm. The model starts from a speed field snapshot, and extracts representative characteristic states in the speed field by adopting a cluster analysis method based on the similarity of the speed field snapshot. The transitions between the various feature states are modeled using a probabilistic network model. Referring to fig. 1, the method comprises the following steps:
step 1: determining dominant frequency f of the supersonic mixed layer in a natural state, selecting a proper speed field snapshot acquisition time step delta t by taking the frequency as a reference value, acquiring speed field snapshots from experiments or numerical simulation, and establishing a speed field snapshot set A in which the supersonic mixed layer is arranged in a time sequence.
Step 2: and carrying out cluster analysis on the speed field snapshot set A. Firstly, determining the optimal clustering number K, initializing a group of K clustering centers ckThe intra-class variance V (equation 2) of the velocity field of the set of cluster centers and the corresponding class is calculated. Iterative calculation is carried out by adopting a k-means + + method to determine a group of optimal clustering centers
So that the intra-class variance V is minimized (formula 3). Repeating the above calculation 30 times, selecting 30 times of calculation to obtain the minimum value pair of varianceA group of cluster centers is regarded as the optimal cluster analysis result
(FIG. 3). Respectively calculating Euclidean distance between each speed field snapshot and K cluster centers, taking the cluster center index corresponding to the minimum Euclidean distance as the cluster index of the speed field snapshot to obtain a cluster index function K (t)m) (equation 1, FIG. 5).
And step 3: indexing function k (t) from the clusterm) Starting from, determining a transition probability matrix PijAnd average transition time matrix Tij. Determining a transition time t for each class during time evolutionnThese transition points in time form a series of time intervals tn，tn+1]Determining the dwell time tau of the classnAnd setting the cluster center corresponding to the class to be positioned in the middle of the time interval. Taking half the dwell time of two different classes as the transition time τ between classesij(equation 5). Calculating the conversion time between each class in the time sequence according to the method, and averaging the conversion probability between classes of the same conversion path to obtain Tij(equation 7, FIG. 6 b).
Respectively calculating the number of transitions from class j (without considering the transition destination) and the number of transitions from class j to class i in the time series, and determining the transition probability matrix Pij(equation 6, FIG. 6 a). The transition probability matrix here resolves all possible transition paths between classes, here only two from the example, e.g. 1->2->3->4->5->6->7->1 or 1->9->6->7->1。
And 4, step 4: and simulating the velocity field evolution by adopting a transition probability matrix and an average transition time matrix. Firstly, the initial state of the velocity field is determined and can be represented by a certain cluster center, and which type of initialization the velocity field evolves from can be determined according to research needs. And simulating a random process according to the probability conversion matrix and the average conversion time matrix. I.e. class j will have a probability PijElapsed time TijTo class i, which will be converted to a different class in the same way as described above. At the time of each class conversionIn the sequence, the conversion destination from a certain class is determined by adopting a conversion probability simulation random process, the time consumption between conversion of various classes is determined by average conversion time, the characteristic state of each class is characterized by a cluster center, and the conversion from the certain class to another class is assumed to be linear motion (formula 8).
And 5: and verifying the correctness of the velocity field evolution simulation result. Calculating an autocorrelation function (formula 9, fig. 7) by using the velocity field snapshot in the set A and the velocity field simulation result in the step 4, respectively, and simulating the velocity field evolution on the discrete time sequence; the velocity field evolution between two time points is determined using equation 8, so that the velocity field evolution is not discrete but becomes continuous. The time evolution of the velocity field is used to calculate the autocorrelation function (equation 9), and the results are analyzed by comparison. If the two corresponding autocorrelation functions are well matched, the established network model based on the cluster analysis correctly captures the evolution process of the velocity field, and the correctness of the calculation result and the reliability of the model are verified. And if the two corresponding cross-correlation functions are in a matching difference, adjusting the number of speed field snapshots or the number of clusters K, and repeating the steps 1-4 until the two corresponding cross-correlation functions are in a better matching state.
Example two
On the basis of the first embodiment, the present embodiment provides a supersonic mixed layer order reduction system, which includes a processor and a memory, where the memory stores a supersonic mixed layer order reduction program, and the processor executes the steps of the method of the first embodiment when running the supersonic mixed layer order reduction program.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention, and all modifications and equivalents of the present invention, which are made by the contents of the present specification and the accompanying drawings, or directly/indirectly applied to other related technical fields, are included in the scope of the present invention.
Claims (7)
1. A supersonic mixed layer order reduction method is characterized by comprising the following steps:
step 1, collecting a plurality of speed flow field snapshots to form an observation sample set;
step 2, performing cluster analysis on the observation sample set by taking the speed field characteristics as a cluster center to obtain a cluster index function k (t)m) And a plurality of subsets of clusters clustered around respective cluster centers;
step 3, according to the clustering index function k (t)m) Calculating a transition probability matrix PijAnd an average transition time matrix; average transition time T in the average transition time matrixijIs the average of all possible transition times from class i to class j;
according to the transition probability matrix PijConstructing a network model by the average conversion time matrix to predict the evolution of the speed field;
the step 3 specifically includes: according to the transition probability matrix PijSimulating a random process to obtain a conversion path between any two clustering centers, obtaining the time of conversion from the corresponding position of the average conversion time matrix according to the conversion path, constructing a motion model by taking the motion of any two clustering centers between adjacent time sequences as linearity, and predicting the flow field evolution by accessing the motion track of each clustering center on the conversion path on a discrete time sequence;
and 4, verifying the prediction result by adopting the autocorrelation function, respectively calculating and comparing the autocorrelation functions of the sample set and the prediction result, adjusting the parameters of the network model when the autocorrelation functions of the sample set and the prediction result are not consistent, and repeating the steps 1-3 until the autocorrelation function of the prediction result is consistent with the autocorrelation function of the sample set.
2. The hybrid layer order reduction method for supersonic velocity according to claim 1, wherein the step 1 comprises:
acquiring a speed field snapshot in a fixed region omega in an experiment or numerical simulation, wherein the acquisition time step is delta t; the acquisition time step satisfies that delta t is less than or equal to 1/f, wherein f is the dominant frequency of the supersonic mixed layer; at tmThe velocity field snapshot at time is denoted u (x, t)m) Wherein M is 1, … …, M, andthe foot MX delta t is less than or equal to 1000/f; the observation sample set is a set A ═ { u } composed in time seriesm(x)：＝u(x，tm) And M is 1, …, M, and x is a region position vector, which indicates that all the acquired M velocity field snapshots are located in the fixed region Ω.
3. The hybrid layer order reduction method for supersonic velocity according to claim 2, wherein the step 2 comprises:
step 21, determining the optimal clustering number as K by adopting an elbow method;
step 22, the velocity field characteristic of each type is determined by the cluster center ck(x) Characterizing, a cluster index function characterizes a mapping relationship between the velocity field and the nearest cluster center:
wherein u is represented at tmSnapshot of the velocity field of the moment; t is tmM × Δ t represents a time series, which is a discrete quantity; c. CiRepresenting the clustering center of the ith class, wherein x is a region position vector, and all acquired M speed field snapshots are located in a fixed region omega;
step 23, adopting k-means + + algorithm to snapshot the M speed fields um(x) And performing clustering analysis to obtain K types.
4. The hybrid layer order reduction method of claim 3, wherein the step 23 comprises:
step 231, randomly initializing K cluster centers
From velocity field snapshot um(x) The mean variance measure between the corresponding nearest cluster center, also called the within-class variance:
wherein x is an area position vector, i.e. it means that all the acquired M velocity field snapshots are located in the same area Ω, ckDenotes the k-th cluster center, ck(m)Representing the mth range-velocity field snapshot um(x) The nearest cluster center;
step 232, according to the Euclidean distance minimum principle, dividing each point into classes with the shortest distance;
step 233, recalculating the clustering centers, and repeating the above steps 231 and 232 until a group of optimal clustering centers is obtained
So that the intra-class variance V is sufficiently small:
the cluster center is now the average of all velocity field snapshots in the corresponding class:
wherein N iskThe number of all speed field snapshot sample points contained in the kth class is, and m is the number of the flow field snapshot characteristic value sample points and is an integer; ckIs the state space of class k.
5. The hybrid layer rank reduction method of claim 4, wherein k (t) is a function of the cluster indexm) Calculating a transition probability matrix PijAnd an average transition time matrix comprising:
recording the time point of conversion as tnAnd satisfies the following conditions: k (t)n-ε)≠k(tn+ ε), where ε is any minor amount; in the time interval (t)n，tn+1) In this example, assume that the characteristic state of class k is at the midpoint of the time interval, i.e., (t)n+tn+1) 2; the residence time in this class is defined as: tau isn＝tn+1-tn；
Defining j and i as transition time points tnAnd tn+1The subsequent clustering index; the transition time from class i to class j is defined as the time between two feature states:
transition probability matrix PijComprises the following steps:
wherein n isijIs from cjTo ciThe number of transitions of (1), njIs from cjStarting to number of other classes, which includes nijThe average of all possible transition times is taken as the average transition time in the model:
Tij＝<τij> (7)
according to the transition probability matrix PijAnd constructing a network model by the average conversion time matrix to predict the evolution of the speed field, wherein the prediction comprises the following steps:
set at an initial time t0State space k-like when 00Then the time passes
Class k0Conversion to class k1At the moment of
By analogy, class k1Conversion to class k2At the moment of
Simulating random walk by the conversion probability matrix to obtain a conversion path;
the movement between any two cluster centers is set to be linear, i.e. in the time region t1∈[tn，tn+1]The velocity field is:
wherein the linearity coefficient is:
6. the hybrid layer order reduction method for supersonic velocity according to claim 1, wherein the autocorrelation function in step 4 is defined as:
7. a supersonic hybrid layer order reduction system, comprising a processor and a memory, wherein the memory stores a supersonic hybrid layer order reduction program, and the processor executes the steps of the method according to any one of claims 1 to 6 when running the supersonic hybrid layer order reduction program.
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| CN102023079A (en) * | 2010-11-18 | 2011-04-20 | 中国人民解放军国防科学技术大学 | Supersonic free vortex mixing layer wind tunnel |
| CN105353412A (en) * | 2015-12-14 | 2016-02-24 | 中国石油大学(华东) | Calculating method and system of well-to-seismic integration average speed field |
| CN109581487A (en) * | 2018-12-17 | 2019-04-05 | 中国海洋石油集团有限公司 | A kind of lithosomic body waveform space structural analysis and body control Inverse modeling method |
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| CN105353412A (en) * | 2015-12-14 | 2016-02-24 | 中国石油大学(华东) | Calculating method and system of well-to-seismic integration average speed field |
| CN109581487A (en) * | 2018-12-17 | 2019-04-05 | 中国海洋石油集团有限公司 | A kind of lithosomic body waveform space structural analysis and body control Inverse modeling method |
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