CN117408095B - Method for predicting fatigue life of asphalt at different temperatures - Google Patents
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Abstract
The invention provides a method for predicting fatigue life of asphalt at different temperatures, which relates to the technical field of asphalt testing and comprises the following steps: setting a test temperature, and obtaining composite modulus actual measurement data and fatigue life actual measurement data of asphalt; establishing a prediction model, wherein the prediction model comprises model parameters, and dividing the model parameters into two types, namely a first model parameter and a second model parameter; iteratively optimizing the first model parameters according to a first optimization method to obtain optimized first model parameters; iteratively optimizing the second model parameters according to a second optimization method to obtain optimized second model parameters; updating the prediction model by using the optimized first model parameter and the optimized second model parameter to obtain a final prediction model, and obtaining a prediction result of the fatigue life by using the final prediction model. The prediction model is simple in form and high in practicability, model parameters are optimized in batches through two optimization methods, and the accuracy of model prediction can be improved.
Description
Technical Field
The invention relates to the technical field of asphalt testing, in particular to a method for predicting fatigue life of asphalt at different temperatures.
Background
The fatigue life is an important index for measuring the durability of asphalt pavement, and the selection and design of pavement materials, construction process and later pavement maintenance and management can be optimized by accurately predicting the fatigue life of asphalt, so that scientific decision support is provided.
Under the background, the research and the application of the asphalt fatigue life estimation model are particularly important. The asphalt fatigue life prediction model can guide engineers to conduct more scientific pavement design and material selection, so that the durability and economic benefit of a pavement structure are improved. Meanwhile, by means of the fatigue life prediction model, engineers can realize effective maintenance opportunity judgment and life prediction, and safety and functional continuity of a road are ensured.
At present, a laboratory mostly adopts a dynamic shear rheological test to directly test the fatigue life of asphalt, and a great deal of test cost and time are required to test the fatigue life at different temperatures. Therefore, development of a prediction model capable of effectively predicting the fatigue life of asphalt under different environmental conditions is an important research direction in the current pavement engineering field.
The invention patent with the Chinese application number of 202310163323.1 discloses a rapid acquisition method of an asphalt strain-fatigue life curve, which predicts the fatigue life of asphalt at different strain levels through the strain-fatigue life curve, and solves the problem that the testing time of the asphalt fatigue resistance is long, so that the accuracy and the precision are limited, and the testing of the asphalt fatigue resistance at different testing temperatures cannot be dealt with.
Disclosure of Invention
In view of the above, the invention provides a prediction method for fatigue life of asphalt at different temperatures, and the prediction model is simple in form and higher in practicability, model parameters are optimized in batches by two optimization methods, and accuracy of model prediction can be improved.
The technical purpose of the invention is realized as follows:
the invention provides a method for predicting fatigue life of asphalt at different temperatures, which comprises the following steps:
s1, setting an experimental temperature, wherein the experimental temperature comprises a test temperature and a prediction temperature, acquiring composite modulus of asphalt at the experimental temperature, obtaining composite modulus actual measurement data of the asphalt, and performing a linear amplitude scanning test on the asphalt at the test temperature to obtain fatigue life actual measurement data of the asphalt;
s2, establishing a prediction model, wherein the prediction model comprises model parameters, and dividing the model parameters into two types, namely a first model parameter and a second model parameter;
in step S2, the representation function of the prediction model is:
；
in the method, in the process of the invention,for fatigue life prediction data, < >>Is a first model parameter describing the complex modulus of asphalt at different temperatures, +.>Is a second model parameter describing fatigue life of asphalt at different temperatures, +.>For external strain->To reduce the frequency;
s3, selecting a reference temperature from experimental temperatures, obtaining a composite modulus main curve at the reference temperature and a reduced frequency at other experimental temperatures based on a time-temperature equivalent principle by utilizing composite modulus measured data, and iteratively optimizing first model parameters according to a first optimization method based on the composite modulus measured data, the composite modulus main curve at the reference temperature and the reduced frequency at other experimental temperatures to obtain optimized first model parameters, wherein the first optimization method is an optimization method based on a least square method principle;
s4, iteratively optimizing second model parameters based on fatigue life actual measurement data according to a second optimization method to obtain optimized second model parameters, wherein the second optimization method is an optimization method based on a difference-by-difference method principle;
and S5, updating the prediction model by using the optimized first model parameter and the optimized second model parameter to obtain a final prediction model, and predicting asphalt at a prediction temperature by using the final prediction model to obtain a prediction result of fatigue life.
Based on the above technical solution, preferably, step S3 includes:
s31, selecting a reference temperature from experimental temperatures, and acquiring composite modulus measured data at the reference temperature, wherein the data comprise the change of loss modulus and storage modulus along with loading frequency;
s32, processing and analyzing the composite modulus measured data at the reference temperature to obtain a fitting curve of the loss modulus and the storage modulus along with the change of the loading frequency, namely a composite modulus main curve at the reference temperature;
s33, according to a time-temperature equivalent principle, converting a composite modulus main curve at a reference temperature into other experimental temperatures to acquire equivalent data, and obtaining a reduced frequency at the other experimental temperatures;
and S34, carrying out iterative optimization on the first model parameters by adopting a first optimization method based on the measured data of the composite modulus, the main curve of the composite modulus at the reference temperature and the reduction frequency at other experimental temperatures to obtain the optimized first model parameters.
Based on the above technical solution, preferably, step S34 includes:
s341 defines a first objective function and initializes a first model parameter;
s342, calculating a first objective function value under the current first model parameter according to the actual measurement data of the composite modulus;
s343, calculating a sensitive matrix of the first objective function on the first model parameter, and calculating an adjustment parameter of the first model parameter according to the sensitive matrix and the gradient of the first objective function value;
s344, superposing the calculated adjustment parameters to the current first model parameters to update the current first model parameters;
s345 calculates a new first objective function value by using the updated first model parameters;
s346 judges whether or not the new first objective function value converges:
if the first model parameters are converged, stopping iteration, and outputting the first model parameters obtained through final optimization as optimized first model parameters;
if not, the parameters of the sensitive matrix are adjusted according to the change condition of the first objective function value, and the step S343 is proceeded.
On the basis of the above technical solution, it is preferable that the first objective function is:
；
in the method, in the process of the invention,for the first objective function value, < >>Is the predicted data of complex modulus, +.>Is the measured data of the composite modulus, and N is the number of data points.
Based on the above technical solution, preferably, step S343 includes:
for each first model parameter, calculating the partial derivative of the first objective function on the single first model parameter to obtain a sensitive matrixJ；
Computing gradients of a first objective function using gradient operators；
Based on a sensitivity matrixJAnd gradientCalculating an adjustment parameter:
；
in the method, in the process of the invention,in order to adjust the parameters of the device,Jis a sensitive matrix->Transpose of sensitive matrix +.>As a parameter of the matrix,Iis a unitary matrix->Is a gradient.
Based on the above technical solution, preferably, step S4 includes:
s41 defining a second objective functionInitializing second model parameters;
s42, setting the maximum iteration times and the adjustment step length;
s43, selecting a second model parameter as a target parameter;
s44, superposing the current value of the target parameter with an adjustment step length to obtain an adjustment value of the target parameter;
s45, according to the actual measurement data of the fatigue life, calculating corresponding second objective function values by using the current value of the objective parameter and the adjustment value of the objective parameterAnd->；
S46 comparisonAnd->Determining the current value of the target parameter and the adjustment step length of the next iteration, and turning to the step S44 until reaching the convergence condition or the maximum iteration times;
s47, repeating the steps S43-S46, and optimizing each second model parameter to obtain optimized second model parameters.
Based on the above technical solution, preferably, the second objective function is:
；
in the method, in the process of the invention,for the second objective function value, < >>For fatigue life measured data, < >>For the average of fatigue life measured data, +.>For fatigue life prediction data, < >>Is the average of the fatigue life prediction data.
Based on the above technical solution, preferably, in step S46, the comparison is performedAnd->Determining a new current value of the target parameter for the next iteration, comprising:
if it isTaking the adjustment value of the target parameter as the current value of the target parameter of the next iteration, and keeping the adjustment step length unchanged;
if it isAnd keeping the current value of the target parameter unchanged, and subtracting a step difference item from the adjustment step length to serve as a new adjustment step length of the next iteration.
Based on the above technical solution, preferably, step S1 further includes:
defining a fatigue failure criterion according to the composite modulus and the phase angle, and calculating to obtain fatigue life actual measurement data according to the result of the linear amplitude scanning test and the fatigue failure criterion;
wherein the fatigue failure criterion is that the fatigue failure reaches 35% of the initial fatigue factor, the fatigue failure is that the asphalt sample has cracks or breaks, and the initial fatigue factor is that，/>Is complex shear modulus>Is the phase angle.
Compared with the prior art, the method has the following beneficial effects:
(1) According to the invention, the measured data of the asphalt fatigue life at the test temperature is obtained through a linear amplitude scanning test, and the asphalt fatigue life prediction model at different temperatures is established based on a linear viscoelastic theory;
(2) The asphalt fatigue life model of the invention has 6 model parameters:、/>wherein->For describing the complex modulus of bitumen at different temperatures, < >>The model is used for describing the fatigue life of asphalt at different temperatures, and the fatigue life of asphalt at different temperatures can be predicted by the presentation of the model;
(3) According to the method, the first model parameter and the second model parameter are optimized respectively by adopting two optimization methods, and corresponding optimization modes are set according to the respective data characteristics of the composite modulus and the fatigue life, so that the first model parameter and the second model parameter can be obtained to the greatest extent, and the prediction precision of the prediction model is improved.
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In order to more clearly illustrate the embodiments of the invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, it being obvious that the drawings in the following description are only some embodiments of the invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a method according to an embodiment of the present invention;
FIG. 2 is a main curve of the composite modulus at the reference temperature in the first embodiment of the present invention;
FIG. 3 is a correlation of measured fatigue life to predicted fatigue life for a first embodiment of the present invention;
FIG. 4 is a correlation of measured fatigue life to predicted fatigue life for a second embodiment of the present invention;
FIG. 5 is a correlation of measured fatigue life and predicted fatigue life for a third embodiment of the present invention.
Detailed Description
The following description of the embodiments of the present invention will clearly and fully describe the technical aspects of the embodiments of the present invention, and it is apparent that the described embodiments are only some embodiments of the present invention, not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the present invention without making any inventive effort, are intended to fall within the scope of the present invention.
As shown in FIG. 1, the invention provides a method for predicting fatigue life of asphalt at different temperatures, which comprises the following steps:
s1, setting an experimental temperature, wherein the experimental temperature comprises a test temperature and a prediction temperature, acquiring composite modulus of asphalt at the experimental temperature, obtaining composite modulus actual measurement data of the asphalt, and performing a linear amplitude scanning test on the asphalt at the test temperature to obtain fatigue life actual measurement data of the asphalt;
s2, establishing a prediction model, wherein the prediction model comprises model parameters, and dividing the model parameters into two types, namely a first model parameter and a second model parameter;
s3, selecting a reference temperature from experimental temperatures, obtaining a composite modulus main curve at the reference temperature and a reduced frequency at other experimental temperatures based on a time-temperature equivalent principle by utilizing composite modulus measured data, and iteratively optimizing first model parameters according to a first optimization method based on the composite modulus measured data, the composite modulus main curve at the reference temperature and the reduced frequency at other experimental temperatures to obtain optimized first model parameters, wherein the first optimization method is an optimization method based on a least square method principle;
s4, iteratively optimizing second model parameters based on fatigue life actual measurement data according to a second optimization method to obtain optimized second model parameters, wherein the second optimization method is an optimization method based on a difference-by-difference method principle;
and S5, updating the prediction model by using the optimized first model parameter and the optimized second model parameter to obtain a final prediction model, and predicting asphalt at a prediction temperature by using the final prediction model to obtain a prediction result of fatigue life.
Specifically, step S1 further includes:
defining a fatigue failure criterion according to the composite modulus and the phase angle, and calculating to obtain fatigue life actual measurement data according to the result of the linear amplitude scanning test and the fatigue failure criterion;
wherein the fatigue failure criterion is that the fatigue failure reaches 35% of the initial fatigue factor, the fatigue failure is that the asphalt sample has cracks or breaks, and the initial fatigue factor is that，/>Is complex shear modulus>Is the phase angle.
In the embodiment of the invention, the actual measurement data of the composite modulus is data at all experimental temperatures, and can be obtained by directly testing, or can be obtained by firstly measuring the actual measurement data of the composite modulus at the test temperature, then selecting one temperature from the test temperature as a target temperature, and calculating the actual measurement data of the composite modulus at the predicted temperature based on the composite modulus at the target temperature according to a time-temperature equivalent principle.
Specifically, in the embodiment of the present invention, the prediction model representation function in step S2 is:
；
in the method, in the process of the invention,for fatigue life prediction data, < >>Is a first model parameter describing the complex modulus of asphalt at different temperatures, +.>Is a second model parameter describing fatigue life of asphalt at different temperatures, +.>For external strain->To reduce the frequency.
In this embodiment, the asphalt fatigue life prediction model has 6 model parameters:、wherein->For describing the complex modulus of bitumen at different temperatures, < >>For describing the fatigue life of asphalt at different temperatures, the model is presented to be able to predict the fatigue life of asphalt at different temperatures.
Specifically, step S3 includes:
s31, selecting a reference temperature from experimental temperatures, and acquiring composite modulus measured data at the reference temperature, wherein the data comprise the change of loss modulus and storage modulus along with loading frequency;
s32, processing and analyzing the composite modulus measured data at the reference temperature to obtain a fitting curve of the loss modulus and the storage modulus along with the change of the loading frequency, namely a composite modulus main curve at the reference temperature;
s33, according to a time-temperature equivalent principle, converting a composite modulus main curve at a reference temperature into other experimental temperatures to acquire equivalent data, and obtaining a reduced frequency at the other experimental temperatures;
and S34, carrying out iterative optimization on the first model parameters by adopting a first optimization method based on the measured data of the composite modulus, the main curve of the composite modulus at the reference temperature and the reduction frequency at other experimental temperatures to obtain the optimized first model parameters.
Wherein, step S34 includes:
s341 defines a first objective function and initializes a first model parameter;
the first objective function is:
；
in the method, in the process of the invention,for the first objective function value, < >>Is the predicted data of complex modulus, +.>Is the measured data of the composite modulus, and N is the number of data points.
S342, calculating a first objective function value under the current first model parameter according to the actual measurement data of the composite modulus;
s343, calculating a sensitive matrix of the first objective function on the first model parameter, and calculating an adjustment parameter of the first model parameter according to the sensitive matrix and the gradient of the first objective function value;
for each first model parameter, calculating the partial derivative of the first objective function on the single first model parameter to obtain a sensitive matrixJ；
Computing gradients of a first objective function using gradient operators；
Based on a sensitivity matrixJAnd gradientCalculating an adjustment parameter:
；
in the method, in the process of the invention,in order to adjust the parameters of the device,Jis a sensitive matrix->Transpose of sensitive matrix +.>As a parameter of the matrix,Iis a unitary matrix->Is a gradient.
S344, superposing the calculated adjustment parameters to the current first model parameters to update the current first model parameters;
s345 calculates a new first objective function value by using the updated first model parameters;
s346 judges whether or not the new first objective function value converges:
if the first model parameters are converged, stopping iteration, and outputting the first model parameters obtained through final optimization as optimized first model parameters;
if not, the parameters of the sensitive matrix are adjusted according to the change condition of the first objective function value, and the step S343 is proceeded.
In this embodiment, the first optimization method is an optimization method based on the principle of least squares, which is a method commonly used in statistics and mathematics for fitting a set of data points to a functional model. It is based on the following principle: for a given data point, the least squares method determines the best fit model parameters by minimizing the sum of squares residuals of the data point to model predictions. In other words, it finds a functional model such that the sum of squares of the residuals of the data points to the model predictions is minimized. The purpose of this is to enable the fitted model to best describe the relationship between the data points. The first optimization method of the embodiment is based on the principle of least square, introduces a sensitive matrix, and iteratively optimizes the first model parameters based on gradient descent and the sensitive matrix.
In this embodiment, through iterative optimization, the first model parameters can be continuously adjusted, so that the prediction result is more consistent with the measured data, and the accuracy and reliability of the model are improved. The sensitivity matrix and the gradient are utilized to calculate the adjustment parameters, so that the adjustment process of the first model parameters can be accelerated, and the optimization efficiency and the convergence speed are improved. By setting proper convergence judgment conditions, the automation of the optimization process can be realized, and the manual intervention is reduced.
Specifically, step S4 includes:
s41 defining a second objective functionInitializing second model parameters;
the second objective function is:
；
in the method, in the process of the invention,for the second objective function value, < >>For fatigue life measured data, < >>For the average of fatigue life measured data, +.>For fatigue life prediction data, < >>Is the average of the fatigue life prediction data.
S42, setting the maximum iteration times and the adjustment step length;
s43, selecting a second model parameter as a target parameter;
s44, superposing the current value of the target parameter with an adjustment step length to obtain an adjustment value of the target parameter;
s45, according to the actual measurement data of the fatigue life, calculating corresponding second objective function values by using the current value of the objective parameter and the adjustment value of the objective parameterAnd->；
S46 comparisonAnd->Determining the current value of the target parameter and the adjustment step length of the next iteration, and turning to the step S44 until reaching the convergence condition or the maximum iteration times;
the method specifically comprises the following steps:
if it isTaking the adjustment value of the target parameter as the current value of the target parameter of the next iteration, and keeping the adjustment step length unchanged;
if it isAnd keeping the current value of the target parameter unchanged, and subtracting a step difference item from the adjustment step length to serve as a new adjustment step length of the next iteration.
S47, repeating the steps S43-S46, and optimizing each second model parameter to obtain optimized second model parameters.
In this embodiment, the second optimization method is an optimization method based on the principle of a difference-by-difference method, which is a method for numerical approximation differential equation solution. The basic idea is to transform the differential equation into a differential equation by approximating the derivative in the differential equation differentially, and then perform numerical calculation using the differential equation. In the embodiment, the idea of the difference-by-difference method is introduced into the optimization process of the second model parameters, namely, the concepts of the adjustment step length and the adjustment value are introduced, and the updating mode of the adjustment step length is provided, so that the optimal solution is approximated by a gradual iteration mode, and in the iteration process, the second model parameters are continuously updated towards the direction of the optimal solution, and the mode can increase the generalization capability of the model, accelerate the convergence speed, ensure that the optimization process is more stable, and improve the optimization precision.
The validity of the prediction model is verified through three specific embodiments:
example 1
In this example, the PAV aged asphalt was subjected to linear amplitude sweep test according to AASHTO TP 101-12 standard, and four kinds of asphalt selected were tested, PG 58-28#1, PG 58-28#2, PG 58-28#3, PG 58-28#4, # representing different batches, at 13℃and 31℃and predicted temperatures of 19℃and 25 ℃. The results of the fatigue life calculations for the four asphalts under different applied strains are shown in Table 1, based on the test data.
Table 1 fatigue life of four asphalts at different strain levels
According to the prediction model provided by the invention, based on the step S3, the composite modulus main curve at the reference temperature of the embodiment is obtained, as shown in FIG. 2, the data points respectively represented by triangles, circles and diamonds are the existing experimental data of the composite modulus at 19 ℃, 25 ℃ and 31 ℃, the data points represented by forks are the composite modulus main curve at the reference temperature of 25 ℃, and the main curve can obtain the reduction frequency at any temperature。
In this embodiment, a first model parameter obtained by a first optimization method is usedAs shown in table 2 below:
table 2 first model parameters of fatigue life prediction models for four asphalts
In this embodiment, the second model parameters obtained by the second optimization method are usedAs shown in table 3 below:
table 3 second model parameters of fatigue life prediction models for four asphalts
Reducing frequencies of the first model parameter and the second model parameter of the optimized prediction model at the temperature (19 ℃ and 25 ℃) which needs to be predictedSubstituting the fatigue life into a representation function of the prediction model to obtain the fatigue life at the predicted temperature.
In this example, in order to verify the accuracy of the prediction model, fatigue life was measured at 19℃and 25℃for PG 58-28#1, PG 58-28#2, PG 58-28#3 and PG 58-28#4. The correlation of the measured fatigue life and the predicted fatigue life for the four asphalts at 19℃and 25℃is shown in FIG. 3. The data points represented by circles in fig. 3 are model predictions at two measured temperatures, while the data points represented by triangles are measured results from two intermediate temperatures, the model being able to accurately predict fatigue life at different temperatures with good agreement between the simulated predictions and the measured values.
Example 2
In this example, the PAV aged asphalt was subjected to linear amplitude sweep test according to AASHTO TP 101-12 standard, and four kinds of asphalt selected were tested, PG 64-22#1, PG 64-22#2, PG 64-22#3, PG 64-22#4, # representing different batches, at 19℃and 37℃and predicted temperatures of 25℃and 31 ℃. The results of the fatigue life calculations for the four asphalts under different applied strains are shown in Table 4, based on the test data.
Table 4 fatigue life of four asphalts at different strain levels
Based on the time-temperature equivalent principle, the composite modulus main curve at the reference temperature and the reduction frequency at any temperature are obtained by utilizing the test data of the existing composite modulus。
In this embodiment, a first model parameter obtained by a first optimization method is usedAs shown in table 5 below:
table 5 fatigue life prediction model parameters for four asphalts
In this embodiment, the second model parameters obtained by the second optimization method are usedAs shown in table 6 below:
table 6 fatigue life prediction model parameters for four asphalts
Reducing frequencies of the first model parameter and the second model parameter of the optimized prediction model at the temperature (25 ℃ and 31 ℃) which needs to be predictedSubstituting the fatigue life into a representation function of the prediction model to obtain the fatigue life at the predicted temperature.
In order to verify the accuracy of the model, fatigue life measurements at 25℃and 31℃were performed on PG 64-22#1, PG 64-22#2, PG 64-22#3, and PG 64-22#4. The correlation of the measured fatigue life and the predicted fatigue life for the four asphalts at 25℃and 31℃is shown in FIG. 4. The data points represented by circles in fig. 4 are model predictions at two measured temperatures, while the data points represented by triangles are measured results from two intermediate temperatures, the model being able to accurately predict fatigue life at different temperatures with good agreement between the simulated predictions and the measured values.
Example 3
In this example, the PAV aged asphalt was subjected to linear amplitude sweep test according to AASHTO TP 101-12 standard, and four kinds of asphalt selected were tested, PG 70-22#1, PG 70-22#2, PG 70-22#R1, PG 70-22#R2, # representing different batches, R representing modified asphalt at 25℃and 43℃and predicted at 31℃and 37 ℃. From the test data, the results of asphalt fatigue life calculations for four asphalts under different applied strains are shown in Table 7.
Table 7 fatigue life of four asphalts at different strain levels
Based on the time-temperature equivalent principle, the composite modulus main curve at the reference temperature and the reduction frequency at any temperature are obtained by utilizing the test data of the existing composite modulus。
In this embodiment, a first model parameter obtained by a first optimization method is usedAs shown in table 8 below:
table 8 fatigue life prediction model parameters for four asphalts
In this embodiment, the second model parameters obtained by the second optimization method are usedAs shown in table 9 below:
table 9 fatigue life prediction model parameters for four asphalts
Reducing frequencies of the first model parameter and the second model parameter of the optimized prediction model at the temperature (31 ℃ and 37 ℃) needing predictionSubstituting into the representation function of the prediction model to obtainFatigue life at temperature is predicted.
In order to verify the accuracy of the model, fatigue life measurements at 31℃and 37℃were performed on PG 70-22#1, PG 70-22#2, PG 70-22#R1, PG 70-22#R2. The correlation of the measured fatigue life and the predicted fatigue life for the four asphalts at 31℃and 37℃is shown in FIG. 5. The data points represented by circles in fig. 5 are model predictions at two measured temperatures, while the data points represented by triangles are measured results from two intermediate temperatures, the model being able to accurately predict fatigue life at different temperatures with good agreement between the simulated predictions and the measured values.
The foregoing description of the preferred embodiments of the invention is not intended to be limiting, but rather is intended to cover all modifications, equivalents, alternatives, and improvements that fall within the spirit and scope of the invention.
Claims (9)
1. The method for predicting the fatigue life of asphalt at different temperatures is characterized by comprising the following steps:
s1, setting an experimental temperature, wherein the experimental temperature comprises a test temperature and a prediction temperature, acquiring composite modulus of asphalt at the experimental temperature, obtaining composite modulus actual measurement data of the asphalt, and performing a linear amplitude scanning test on the asphalt at the test temperature to obtain fatigue life actual measurement data of the asphalt;
s2, establishing a prediction model, wherein the prediction model comprises model parameters, and dividing the model parameters into two types, namely a first model parameter and a second model parameter;
in step S2, the representation function of the prediction model is:
；
in the method, in the process of the invention,for fatigue life prediction data, < >>Is a first model parameter describing the complex modulus of asphalt at different temperatures, +.>Is a second model parameter describing fatigue life of asphalt at different temperatures, +.>For external strain->To reduce the frequency;
s3, selecting a reference temperature from experimental temperatures, obtaining a composite modulus main curve at the reference temperature and a reduced frequency at other experimental temperatures based on a time-temperature equivalent principle by utilizing composite modulus measured data, and iteratively optimizing first model parameters according to a first optimization method based on the composite modulus measured data, the composite modulus main curve at the reference temperature and the reduced frequency at other experimental temperatures to obtain optimized first model parameters, wherein the first optimization method is an optimization method based on a least square method principle;
s4, iteratively optimizing second model parameters based on fatigue life actual measurement data according to a second optimization method to obtain optimized second model parameters, wherein the second optimization method is an optimization method based on a difference-by-difference method principle;
and S5, updating the prediction model by using the optimized first model parameter and the optimized second model parameter to obtain a final prediction model, and predicting asphalt at a prediction temperature by using the final prediction model to obtain a prediction result of fatigue life.
2. A method for predicting fatigue life of asphalt at different temperatures as defined in claim 1, wherein step S3 comprises:
s31, selecting a reference temperature from experimental temperatures, and acquiring composite modulus measured data at the reference temperature, wherein the data comprise the change of loss modulus and storage modulus along with loading frequency;
s32, processing and analyzing the composite modulus measured data at the reference temperature to obtain a fitting curve of the loss modulus and the storage modulus along with the change of the loading frequency, namely a composite modulus main curve at the reference temperature;
s33, according to a time-temperature equivalent principle, converting a composite modulus main curve at a reference temperature into other experimental temperatures to acquire equivalent data, and obtaining a reduced frequency at the other experimental temperatures;
and S34, carrying out iterative optimization on the first model parameters by adopting a first optimization method based on the measured data of the composite modulus, the main curve of the composite modulus at the reference temperature and the reduction frequency at other experimental temperatures to obtain the optimized first model parameters.
3. A method for predicting fatigue life of asphalt at different temperatures as defined in claim 2, wherein step S34 comprises:
s341 defines a first objective function and initializes a first model parameter;
s342, calculating a value of a first objective function under the current first model parameter according to the actual measurement data of the composite modulus;
s343, calculating a sensitive matrix of the first objective function to the first model parameter, and calculating an adjustment parameter of the first model parameter according to the sensitive matrix and the gradient of the value of the first objective function;
s344, superposing the calculated adjustment parameters to the current first model parameters to update the current first model parameters;
s345 calculates a new value of the first objective function by using the updated first model parameters;
s346 judges whether or not the value of the new first objective function converges:
if the first model parameters are converged, stopping iteration, and outputting the first model parameters obtained through final optimization as optimized first model parameters;
if not, the parameters of the sensitive matrix are adjusted according to the change condition of the value of the first objective function, and the step S343 is proceeded.
4. A method for predicting fatigue life of asphalt at different temperatures as defined in claim 3, wherein the first objective function is:
；
in the method, in the process of the invention,for the value of the first objective function, +.>Is the predicted data of complex modulus, +.>Is the measured data of the composite modulus, and N is the number of data points.
5. The method of claim 4, wherein step S343 comprises:
for each first model parameter, calculating the partial derivative of the first objective function on the single first model parameter to obtain a sensitive matrixJ；
Computing gradients of a first objective function using gradient operators；
Based on a sensitivity matrixJAnd gradientCalculating an adjustment parameter:
；
in the method, in the process of the invention,in order to adjust the parameters of the device,Jis a sensitive matrix->Transpose of sensitive matrix +.>As a parameter of the matrix,Iis a matrix of units which is a matrix of units,is a gradient.
6. A method for predicting fatigue life of asphalt at different temperatures as defined in claim 1, wherein step S4 comprises:
s41 defining a second objective functionInitializing second model parameters;
s42, setting the maximum iteration times and the adjustment step length;
s43, selecting a second model parameter as a target parameter;
s44, superposing the current value of the target parameter with an adjustment step length to obtain an adjustment value of the target parameter;
s45, according to the actual measurement data of the fatigue life, calculating corresponding second objective function values by using the current value of the objective parameter and the adjustment value of the objective parameterAnd->；
S46 comparisonAnd->To determine the size of the next iterationThe current value of the target parameter and the adjustment step length are transferred to the step S44 until reaching the convergence condition or reaching the maximum iteration times;
s47, repeating the steps S43-S46, and optimizing each second model parameter to obtain optimized second model parameters.
7. A method of predicting fatigue life of asphalt at different temperatures as recited in claim 6, wherein the second objective function is:
；
in the method, in the process of the invention,for the second objective function value, < >>For fatigue life measured data, < >>For the average of fatigue life measured data, +.>For fatigue life prediction data, < >>Is the average of the fatigue life prediction data.
8. The method for predicting fatigue life of asphalt at different temperatures as defined in claim 6, wherein in step S46, the comparison is madeAnd->To determine the size of the next stepNew current values of the target parameters of the generation, including:
if it isTaking the adjustment value of the target parameter as the current value of the target parameter of the next iteration, and keeping the adjustment step length unchanged;
if it isAnd keeping the current value of the target parameter unchanged, and subtracting a step difference item from the adjustment step length to serve as a new adjustment step length of the next iteration.
9. The method for predicting fatigue life of asphalt at different temperatures as defined in claim 6, wherein step S1 further comprises:
defining a fatigue failure criterion according to the composite modulus and the phase angle, and calculating to obtain fatigue life actual measurement data according to the result of the linear amplitude scanning test and the fatigue failure criterion;
wherein the fatigue failure criterion is that the fatigue failure reaches 35% of the initial fatigue factor, the fatigue failure is that the asphalt sample has cracks or breaks, and the initial fatigue factor is that，/>Is complex shear modulus>Is the phase angle.
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