CN116108763A - Method for predicting bubble collapse critical point of foaming material based on temperature - Google Patents
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Abstract
The invention provides a temperature-based foam material bubble collapse critical point prediction method, which comprises the steps of selecting a sample space to predict bubble collapse critical points in a future time range, obtaining foam material bubble volume data, and substituting the foam material bubble volume data into a logarithmic period power law model; adding the historical data of the temperature change into a logarithmic period power law model, and constructing a new logarithmic period power law model; estimating all nonlinear parameters in the new log periodic power law model by adopting a plurality of group genetic algorithms; obtaining all linear parameters in a new log periodic power law model by adopting a least square method; performing Lomb periodic chart analysis, and adopting a sliding window method to obtain
The value predicts the final interval. The invention obtainsAnd a prediction foaming material bubble breaking critical point model for fusing temperature and bubble volume data enables prediction to be more in line with the actual situation, and model prediction accuracy is improved.
Description
Technical Field
The invention relates to the technical field of foaming materials, in particular to a temperature-based method for predicting bubble collapse critical points of a foaming material.
Background
By introducing a large number of micro bubbles into the polymer material in a physical or chemical way, the characteristics of the polymer and the characteristics of the micro bubbles are combined together in an optimized way, the material performance is obviously improved or the brand-new characteristics which the original polymer does not have are endowed, the polymer material has become one of the important directions of developing and applying the polymer material at present, and compared with the common plastic products, the structure has a plurality of excellent performances such as small weight, high strength, good toughness, stable size and the like, so the microporous polymer material is also self-evident as a 21 st century novel material. Although the foaming material has the advantages, the prior foaming process conditions and the selection of the foaming agent have limitations, so that the foam cells of the foaming material are large in size and uneven in distribution, and the large and uneven foam cells easily become crack sources under the action of large stress, so that the mechanical property of the material is reduced.
Chinese patent application publication No. CN114818519a discloses a method, system and computer readable medium for predicting bubble collapse of a foaming material, the method comprising: selecting a sample space to predict bubble collapse threshold points over a future time horizon; further dividing the selected sample space into a plurality of subintervals; for each subinterval, fitting parameters in a Logarithmic Periodic Power Law (LPPL) model by adopting a Particle Swarm Optimization (PSO), establishing the LPPL model, and obtaining critical points; and verifying whether the curve fitted by the LPPL model and the critical point are valid or not by using the Lomb periodic chart according to the LPPL model fitting result of each subinterval, wherein the turning point verified by the Lomb periodic chart is the bubble breaking critical point. The method can accurately predict bubble cracking in advance, thereby controlling the bubble cracking process of the foaming material and effectively improving the mechanical property of the foaming material.
Temperature is one of the main factors affecting the size and distribution of the bubbles of the foaming material, and has an effect on the surface tension of the polymer melt, the solubility of the gas in the polymer melt, the diffusion coefficient and the like. By adding the temperature as an exogenous variable to the bubble volume prediction, the study of the bubble collapse proximity zone has important practical significance for improving the mechanical properties of the foaming material, and the temperature factors are not considered in the scheme.
Disclosure of Invention
The purpose of the invention is that: aiming at the defects in the background technology, a bubble collapse critical point prediction method is provided, the temperature is added into a log periodic power law model, a new log periodic power law model (XLPP) is constructed, a multi-population genetic algorithm is used for estimating nonlinear parameters in the new log periodic power law model, and finally, interval prediction is used for replacing point prediction, so that bubble collapse prediction accuracy is improved.
In order to achieve the above object, the present invention provides a method for predicting bubble collapse critical point of a foaming material based on temperature, comprising the steps of:
s1, selecting a sample space to predict a bubble collapse critical point in a future time range, acquiring bubble volume data of a foaming material by extracting characteristic parameters of the area, equivalent diameter, geometric center, speed and acceleration of the bubble, and substituting the bubble volume data into a logarithmic period power law model;
s2, adding historical data of temperature change into a log periodic power law model, and constructing a new log periodic power law model;
s3, estimating all nonlinear parameters in the new log periodic power law model by adopting a plurality of group genetic algorithms;
wherein, the form of the logarithmic cycle power law model of bubble collapse of the foaming material is as follows:
wherein ,
for the bubble volume of the determined bubble breaking point critical point, +.>
For the initial time of the bubble measurement,
the critical point time for bubble collapse, i.e., the time for bubble to collapse; />
Is bubble acceleration; />
For logarithmic periodic vibration frequency, +.>
For the phase +.>
Are all amplitude +.>
Corresponding to the initial value of the volume of the bubble, < >>
Corresponding to bubble velocity, +.>
Is the diameter difference before and after bubble growth; />
Indicating the time to reach the bubble close to collapse +.>
When (I)>
The values that can be achieved, and +.>
，/>
Representing an upward acceleration +.>
Super-exponential characterization of the sequence of bubble volumes
Periodic oscillations of bubble volume are described;
setting up
，/>
Is->
The log periodic power law model is abbreviated as follows:
wherein ,
the historical data of temperature change is added into a logarithmic periodic power law model, and a new logarithmic periodic power law model is abbreviated as the following modes:
wherein ,
，/>
also amplitude and is a linear parameter, +.>
Is the historical data of temperature change;
s4, obtaining all linear parameters in a new log periodic power law model by adopting a least square method;
s5, performing Lomb periodic graph analysis to obtain a new log periodic power law model
Carrying out statistical test on the values, wherein the turning points which are statistically verified by the Lomb periodic chart are bubble breaking points of the XLPP model;
s6, adopting a sliding window method to obtain
The value predicts the final interval.
Further, S3 specifically includes the following sub-steps:
s31, randomly generating U initial populations, randomly generating W chromosomes in each population, wherein the chromosome individuals form a population, and each chromosome represents a feasible solution consisting of all nonlinear parameters of a log-periodic power law model;
s32, calculating the fitness, wherein the fitness represents the possibility of an individual living in the environment, and the higher the fitness is, the higher the probability that the individual is inherited to the next generation is;
s33, selecting the optimal individuals in the current generation of the population;
s34, obtaining new individuals through gene crossover of individuals in the generation population to obtain a new generation population, wherein the individuals in the new generation population inherit part of gene fragments in the father according to probability, and part of characteristics of the father are reserved;
s35, randomly changing a certain gene fragment on an individual through a preset gene mutation probability to obtain a new individual;
s36, reinserting the child population generated by evolution into the parent population;
s37, immigrating, wherein a plurality of independent populations are combined into a unified whole;
s38, carrying out iterative computation and judgment, and outputting a final chromosome to obtain all optimized nonlinear parameters.
Further, the plurality of genetic algorithms in S32 are calculated by
Bubble volume at time->
The sum of squares of residuals between fitting results with the new log periodic power law model evaluates fitness values for each chromosome: />
Further, use of the first in S37
The fitness value in each population is minimum +.>
Chromosome substitution of (c) in the (u+1) th population, fitness value max +.>
To combine separate populations into a unified whole.
Further, if the minimum fitness value of the new population is in S38
The minimum fitness value of the population in the last iteration process is smaller than the minimum fitness value of the population, and the record is updated; otherwise, the original record of the population remains unchanged; if the minimum fitness value of all the populations is not changed or the upper limit of the iteration times is reached, the calculation is terminated, and the minimum fitness value of all the populations and the corresponding chromosomes thereof after the last iteration is ended are the outputs of a plurality of genetic algorithms.
Further, in S4
wherein ,
，/>
in time units +.>
All linear parameters in the new log periodic power law model are calculated for the total time unit using the following equation:
further, in S5, the Lomb periodic chart is used for testing the periodic frequency of a new log periodic power law model obtained by a plurality of group genetic algorithms
and />
Whether or not continuous to determine whether the curve and critical points to which the model fits are valid;
the Lomb periodic chart first presets a frequency sequence
, wherein ,/>
Is the length of a predetermined frequency sequence; for a given frequency f, workRate spectral Density->
Analysis by Lomb periodogram is calculated as follows:
wherein ,
periodic oscillations of logarithmic volume, +.>
Denoted as->
Mean, time offset->
The calculation is as follows: />
Then from the generated
I.e. deletion of invalid values in the power spectral density sequence, if +.>
If no valid value exists in the series, the Lomb periodic chart refuses the original assumption, and XLPP is ineffective in calculating the critical point.
Further, invalid values include the following:
Further, in S6, the request is executed on an array or character string of a predetermined window size, the sliding window is moved in a predetermined direction, the window size is fixed or variable, and the array is composed of
Value composition->
The window size is constant +.>
The window is made of->
Initially, the window is slid backwards continuously when it reaches +.>
Stop at time, then select the inclusion +.>
The window with the highest value is taken as the final prediction interval.
The scheme of the invention has the following beneficial effects:
according to the temperature-based foam material bubble collapse critical point prediction method, the temperature is added into the LPPL model to obtain a foam material bubble collapse near point model which is fused with temperature and bubble volume data, so that the prediction method is more in line with the actual situation, and meanwhile, nonlinear parameters are calculated by adopting various group genetic algorithms, so that the prediction accuracy of the model is further improved; in addition, a method for estimating the alternative points by using interval estimation is adopted, so that the problems of randomness and dispersibility of the point estimation can be effectively solved.
Other advantageous effects of the present invention will be described in detail in the detailed description section which follows.
Drawings
FIG. 1 is a block diagram of a process flow according to the present invention;
FIG. 2 is a flow chart of a plurality of genetic algorithms according to the present invention;
FIG. 3 is a diagram illustrating an exemplary sliding window method according to the present invention;
FIG. 4 is a Lomb periodic chart of the present invention verifying bubble collapse threshold;
fig. 5 is a Lomb periodic chart of oscillations within the bubble collapse prediction interval of the present invention.
Detailed Description
Other advantages and effects of the present disclosure will become readily apparent to those skilled in the art from the following disclosure, which describes embodiments of the present disclosure by way of specific examples. It will be apparent that the described embodiments are merely some, but not all embodiments of the present disclosure. The disclosure may be embodied or practiced in other different specific embodiments, and details within the subject specification may be modified or changed from various points of view and applications without departing from the spirit of the disclosure. It should be noted that the following embodiments and features in the embodiments may be combined with each other without conflict. All other embodiments, which can be made by one of ordinary skill in the art without inventive effort, based on the embodiments in this disclosure are intended to be within the scope of this disclosure.
It is noted that various aspects of the embodiments are described below within the scope of the following claims. It should be apparent that the aspects described herein may be embodied in a wide variety of forms and that any specific structure and/or function described herein is merely illustrative. Based on the present disclosure, one skilled in the art will appreciate that one aspect described herein may be implemented independently of any other aspect, and that two or more of these aspects may be combined in various ways. For example, an apparatus may be implemented and/or a method practiced using any number of the aspects set forth herein. In addition, such apparatus may be implemented and/or such methods practiced using other structure and/or functionality in addition to one or more of the aspects set forth herein.
It should also be noted that the illustrations provided in the following embodiments merely illustrate the basic concepts of the disclosure by way of illustration, and only the components related to the disclosure are shown in the drawings and are not drawn according to the number, shape and size of the components in actual implementation, and the form, number and proportion of the components in actual implementation may be arbitrarily changed, and the layout of the components may be more complicated. In addition, in the following description, specific details are provided in order to provide a thorough understanding of the examples. However, it will be understood by those skilled in the art that the aspects may be practiced without these specific details.
As shown in fig. 1, an embodiment of the present invention provides a method for predicting bubble collapse critical point of a foaming material based on temperature, which specifically includes the following steps:
s1, selecting a sample space to predict a bubble collapse critical point in a future time range, acquiring bubble volume data of the foaming material by extracting characteristic parameters of the area, equivalent diameter, geometric center, speed and acceleration of the bubble, and substituting the data into a Log Periodic Power Law (LPPL) model.
It should be noted that, the data in the sample space uses a bubble volume, and a specific method for acquiring the bubble volume is consistent with the disclosure in the background art, which is not described herein.
S2, adding the historical data of the temperature change into a Log Periodic Power Law (LPPL) model, and constructing a new log periodic power law (XLPP) model.
Wherein, the form of the logarithmic cycle power law model of bubble collapse of the foaming material is as follows:
wherein ,
bubble volume, which is the critical point for the bubble breaking point, is +.>
For the initial time of bubble measurement, +.>
The critical point time for bubble collapse, i.e., the time for bubble to collapse; />
Is bubble acceleration; />
For logarithmic periodic vibration frequency, +.>
For the phase +.>
Are all amplitude +.>
Corresponding to the initial value of the volume of the bubble, < >>
In correspondence with the velocity of the gas bubbles,
is the difference in diameter between before and after bubble growth. Wherein (1)>
Indicating the time to reach the bubble close to collapse +.>
When (I)>
The values that can be achieved, and +.>
，/>
Representing an upward acceleration +.>
Super-exponential characterization of the sequence of bubble volumes
Periodic oscillations of the bubble volume are described.
In the actual fitting, the settings are set
，/>
Is->
. The model can also be abbreviated as follows:
wherein ,
the history data of temperature change is added to the LPPL model, and the xlpl model can be abbreviated as the following modes:
wherein ,
，/>
and->
Are all amplitude and linear parameters, +.>
Is warmHistorical data of degree changes.
S3, estimating 4 nonlinear parameters in the XLPP model by adopting a plurality of group genetic algorithms (MPGA).
Meanwhile, as shown in fig. 2, S3 specifically includes the following steps:
s31, randomly generating
And (3) initial populations.
Wherein each population randomly generates
Chromosome number, this->
Individual chromosomes constitute a population, each chromosome representing a feasible solution consisting of four nonlinear parameters of a log periodic power law model.
S32, calculating the fitness.
Where fitness represents the likelihood of an individual to survive in the environment, the greater the fitness of an individual, the greater the chance that the individual will be inherited to the next generation. The genetic algorithm of multiple populations is calculated
Bubble volume at time->
Sum of squares Residual (RSS) between fitting results with xlpl model evaluates fitness values for each chromosome (i.e., four non-linear parameters):
S33, selecting and selecting the optimal individuals in the current generation of the population, so that the individuals are inherited into the next generation with high probability.
S34, obtaining new individuals by crossing individual genes in the generation population, thereby obtaining a new generation population, wherein the individuals in the new generation population inherit part of gene fragments in the father according to probability, and part of characteristics of the father are reserved.
S35, obtaining a new individual by randomly changing a certain gene fragment on the individual with a certain gene mutation probability. In the genetic algorithm, mutation probability of the gene fragment can be increased and occurrence positions are increased through setting mutation parameters.
S36, reinserting the child population generated by evolution into the parent population, wherein the insertion principle can be selected to be uniform random insertion, or insertion based on individual fitness can be selected, and the effect of retaining elite individuals to the next generation can be realized based on individual fitness insertion.
S37, immigrating.
By the first
The fitness value in each population is minimum +.>
Chromosome substitution of (c) u+1thMaximum fitness value in population>
To combine separate populations into a unified whole.
S38, if the minimum fitness value of the new population
Less than the corresponding record of the last iteration process (i.e., the minimum fitness value of the population in the last iteration process), the record is updated; otherwise, the original record of the population remains unchanged. Minimum fitness value of all populations +.>
And the corresponding chromosome recordings are also processed in the same manner. If the minimum fitness value of all populations has not changed or reaches the upper limit of the iteration times, the algorithm is terminated, and the minimum fitness value of all populations and the corresponding chromosome ∈thereof after the last iteration is ended>
Is the output of a plurality of genetic algorithms. Multiple swarm genetic algorithm optimizing nonlinear parameters +.>
The specific flow of (2) is shown in figure 2.
S4, obtaining 4 linear parameters in the XLPP model by adopting a least square method.
wherein ,
，/>
in time units +.>
The linear parameter may be calculated as the total time unit using the following equation:
s5, performing Lomb periodic chart analysis to obtain XLPP model
The values were statistically tested and the statistically verified inflection points were considered as bubble breaking points of xlpl model by Lomb periodogram analysis.
Testing periodic frequency of XLPP model obtained by multiple genetic algorithms by using Lomb periodic chart
And
whether it is continuous or not to determine whether the curve and critical points to which the model fits are valid or not.
The Lomb periodic chart first presets a frequency sequence
, wherein ,/>
Is the length of a predetermined frequency sequence; for a given frequency->
Power spectral density->
The following can be calculated by Lomb periodogram analysis:
wherein ,
periodic oscillations of logarithmic volume, +.>
Denoted as->
Mean, time offset->
The calculation is as follows:
then from the generated
I.e. deletion of invalid values in the power spectral density sequence, if +.>
If no valid value exists in the series, the Lomb periodic chart refuses the original assumption, and XLPP is ineffective in calculating the critical point.
Wherein the invalid value includes the following:
The critical point statistically verified by Lomb periodogram analysis is considered as the bubble collapse critical point of the foamed material.
S6, adopting a sliding window method to obtain
The value predicts the final interval.
The critical points obtained after Lomb periodogram analysis are not one but a plurality of, the sliding window method is established on a plurality of critical points, and from the first critical point, the window moves backwards until one exists
Value minus 15 positions, within the selection window +.>
The interval with the highest value is the final prediction interval.
Also, as shown in fig. 3, the sliding window method refers to performing a desired operation on an array or string given a specific window size, wherein sliding means that the window is moved in a certain direction, and the window size may be fixed or variable. In the method, the array is composed of
Value composition->
The window size is 15, the window is made up of +.>
Initially, the window is slid backwards continuously when it reaches +.>
Stop at time, then select the inclusion +.>
The window with the highest value is the final prediction interval. Taking fig. 3 as an example, the window size in this figure is 15, since the last window contains +.>
The most significant, the last window is chosen as the prediction interval.
Finally, determining a bubble breaking zone according to the bubble breaking critical point to obtain the most possible bubble breaking zone, so as to optimize and improve the mechanical property of the foaming material.
The effect of the process is further illustrated by the specific examples below, in which the polymer microcellular foam material is selected to be a material having a cell size of less than 100. Mu.m, and a cell density of greater than 1.0X106 cells/cm 3 Is a polymer porous foam material. A major concern is one where it is desirable to check the behavior of the flow field and the shape of the bubbles before they disappear (i.e., before the mold is filled). In particular, it may be important to know the position of the bubble vanishing point in advance to prevent unwanted bubbles from occurring in the mold. When the bubbles are close to the breaking point, the dimensional change of the bubbles in the growth movement process is observed, the bubbles are found to be hemispherical under the action of surface tension in the orifice growth process, and the bubbles stretch upwards along with continuous injection of the gas, the neck begins to sink inwards, and finally the bubbles are separated from the orifice after the volume is expanded to a certain value. The speed of the bubbles in the rising process is increased and then tends to be stable, and meanwhile, the bubbles are developed into ellipsoids from the initial spherical shape, and the aspect ratio is obviously reduced. The change in growth process with steep increase of bubbles corresponds to critical behavior and is typical of logarithmic cycle oscillations and power law growth.
With the continuous increase of the temperature, bubbles can be formed in the foamed plastic product, characteristic parameters such as the area, equivalent diameter, speed and the like of bubbles with different diameters are respectively recorded, and the change condition of the temperature in the product is recorded.
Adding the historical data of temperature change into an LPPL model, constructing an XLPP model, estimating nonlinear parameters in the XLPP model by adopting an MPGA algorithm, and continuously comparing the minimum of a new population and the last recorded populationAnd updating the record when the minimum fitness of the new population is smaller than that of the last recorded population, and stopping the MPGA algorithm when the minimum fitness of all the populations is not updated or reaches the iteration upper limit, so as to obtain 4 nonlinear parameters. Substituting 4 nonlinear parameters into an XLPP model, estimating 4 linear parameters in the XLPL model by adopting a least square method, then obtaining bubble collapse critical points of the foaming material through analysis and statistical verification of a Lomb periodic chart, and obtaining bubble collapse critical intervals according to the bubble collapse critical points by adopting a sliding window algorithm. The bubble collapse critical section is shown in FIG. 4, and the specific values of the parameters simulated by the data are respectively
，/>
，/>
，/>
，/>
，/>
，/>
Therefore, the final prediction interval is [305,320 ]]Second.
The final collapse point of bubble collapse is the climax of log periodic oscillations, and it can be seen from fig. 5 that the Lomb periodic graph oscillating in this predicted interval has very significant frequency peaks, which represent that small bubble squeezing activity before large bubble collapse occurs is abnormally pronounced, i.e. large collapse is imminent. By the method, possible bubble cracking critical points can be known in advance, measures are taken to avoid, and the mechanical properties of the foaming material are improved.
While the foregoing is directed to the preferred embodiments of the present invention, it will be appreciated by those skilled in the art that various modifications and adaptations can be made without departing from the principles of the present invention, and such modifications and adaptations are intended to be comprehended within the scope of the present invention.
Claims (9)
1. A method for predicting bubble collapse critical point of a foaming material based on temperature, which is characterized by comprising the following steps:
s1, selecting a sample space to predict a bubble collapse critical point in a future time range, acquiring bubble volume data of a foaming material by extracting characteristic parameters of the area, equivalent diameter, geometric center, speed and acceleration of the bubble, and substituting the bubble volume data into a logarithmic period power law model;
s2, adding historical data of temperature change into a log periodic power law model, and constructing a new log periodic power law model;
s3, estimating all nonlinear parameters in the new log periodic power law model by adopting a plurality of group genetic algorithms;
wherein, the form of the logarithmic cycle power law model of bubble collapse of the foaming material is as follows:
wherein ,
for the bubble volume of the determined bubble breaking point critical point, +.>
For the initial time of bubble measurement, +.>
The critical point time for bubble collapse, i.e., the time for bubble to collapse; />
Is bubble acceleration; />
For logarithmic periodic vibration frequency, +.>
For the phase +.>
Are all amplitude +.>
Corresponding to the initial value of the volume of the bubble, < >>
Corresponding to bubble velocity, +.>
Is the diameter difference before and after bubble growth;
setting up
，/>
Is->
The log periodic power law model is abbreviated as follows:
wherein ,
the historical data of temperature change is added into a logarithmic periodic power law model, and a new logarithmic periodic power law model is abbreviated as the following modes:
wherein ,
，/>
is amplitude and is a linear parameter, ">
Is the historical data of temperature change;
s4, obtaining all linear parameters in a new log periodic power law model by adopting a least square method;
s5, performing Lomb periodic graph analysis to obtain a new log periodic power law model
Carrying out statistical test on the values, wherein turning points which are verified by the statistics of the Lomb periodic graph are bubble breaking points of a new logarithmic periodic power law model;
s6, adopting a sliding window method to obtain
The value predicts the final interval.
2. The method for predicting bubble collapse critical point of a foam material based on temperature according to claim 1, wherein S3 specifically comprises the following sub-steps:
s31, randomly generating
A plurality of initial populations, each population randomly producing +.>
A population of individuals comprising chromosomes, each chromosome representing all non-lines of the log periodic power law modelFeasible solutions composed of sexual parameters;
s32, calculating the fitness, wherein the fitness represents the possibility of an individual living in the environment, and the higher the fitness is, the higher the probability that the individual is inherited to the next generation is;
s33, selecting the optimal individuals in the current generation of the population;
s34, obtaining new individuals through gene crossover of individuals in the generation population to obtain a new generation population, wherein the individuals in the new generation population inherit part of gene fragments in the father according to probability, and part of characteristics of the father are reserved;
s35, randomly changing a certain gene fragment on an individual through a preset gene mutation probability to obtain a new individual;
s36, reinserting the child population generated by evolution into the parent population;
s37, immigrating, wherein a plurality of independent populations are combined into a unified whole;
s38, carrying out iterative computation and judgment, and outputting a final chromosome to obtain all optimized nonlinear parameters.
3. The method for predicting bubble collapse threshold of temperature-based foam material as claimed in claim 2, wherein the plurality of genetic algorithms in S32 are calculated by calculation
Bubble volume at time->
The sum of squares of residuals between fitting results with the new log periodic power law model evaluates fitness values for each chromosome:
4. The method for predicting bubble collapse threshold of temperature-based foam material as claimed in claim 3, wherein the method of S37 is performed by using the first step of
The fitness value in each population is minimum +.>
Chromosome substitution of->
The maximum fitness value in the individual populations>
To combine separate populations into a unified whole.
5. The temperature-based foam bubble collapse of claim 4Method for boundary point prediction, characterized in that in S38 if the minimum fitness value of the new population is
The minimum fitness value of the population in the last iteration process is smaller than the minimum fitness value of the population, and the record is updated; otherwise, the original record of the population remains unchanged; if the minimum fitness value of all the populations is not changed or the upper limit of the iteration times is reached, the calculation is terminated, and the minimum fitness value of all the populations and the corresponding chromosomes thereof after the last iteration is ended are the outputs of a plurality of genetic algorithms.
6. The method for predicting bubble collapse threshold of a temperature-based foam material as recited in claim 5, wherein in S4
wherein ,
，/>
in time units +.>
All linear parameters in the new log periodic power law model are calculated for the total time unit using the following equation:
7. the method for predicting bubble collapse critical point of foam material based on temperature as claimed in claim 6, wherein the periodic frequency of new log periodic power law model obtained by testing multiple groups of genetic algorithms by using Lomb periodic chart in S5
and />
Whether or not continuous to determine whether the curve and critical points to which the model fits are valid;
the Lomb periodic chart first presets a frequency sequence
Wherein N is the length of a predetermined frequency sequence; for a given frequency->
Power spectral density->
Analysis by Lomb periodogram is calculated as follows:
then from the generated
Delete invalid value in (a) if->
If no valid value exists in the series, the Lomb periodic diagram refuses the original assumption, the new logarithmic periodic power law model is invalid to calculate the critical point, < ->
Is a sequence of power spectral densities.
8. The method of temperature-based foam bubble collapse threshold prediction according to claim 7, wherein the invalid value comprises:
9. The method for predicting bubble collapse threshold of a foamed material based on temperature as claimed in claim 1, wherein the step S6 is performed on an array or character string of a predetermined window size, the sliding indicating window moving in a predetermined direction, the array being composed of
Value composition->
The window size is constant F, the window is made of +.>
Initially, the window is slid backwards continuously when it reaches +.>
Stop at time, then select the inclusion +.>
The window with the highest value is taken as the final prediction interval. />
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