CN109543324B - Determination method of thermal mechanical analysis curve turning point based on Pearson correlation coefficient - Google Patents
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Abstract
The invention discloses a method for measuring a turning point of a thermomechanical analysis curve based on a Pearson correlation coefficient, and aims to solve the problem that the turning point of the thermomechanical analysis curve of an existing asphalt mixture is difficult to determine. The determination method comprises the following steps: firstly, measuring thermomechanical parameters changing along with temperature, and establishing a temperature array and a thermomechanical parameter array; secondly, establishing a temperature-thermomechanical parameter data set; calculating the square of the Pearson correlation coefficient of the temperature data set and the thermal mechanical parameter data set based on the temperature-thermal mechanical parameter data set to obtain R 2 Data set with T as abscissa and R 2 For ordinate, R is plotted 2 -a T-plot; fourthly, with R 2 More than or equal to 0.995 as the defining condition of the turning point of the temperature stress curve, then R 2 The corresponding temperature is taken as the measured turning point temperature T T . The method takes the Pearson correlation coefficient as an index, and accurately determines the turning point of the thermal mechanical analysis curve of the asphalt mixture by analyzing and calculating the correlation coefficient between the thermal mechanical analysis parameter and the temperature data point.
Description
Technical Field
The invention belongs to the technical field of evaluation methods of low-temperature performance of asphalt mixtures, and particularly relates to a method for measuring a turning point of a thermomechanical analysis curve.
Background
The asphalt mixture is a composite material formed by combining asphalt, aggregate, admixture and the like according to a certain proportion, and due to the existence of viscoelastic material asphalt, the property of the asphalt mixture shows viscoelasticity, namely the property is related to temperature, and under characteristic temperature, the property of the asphalt mixture can be changed obviously, and the characteristic values are very critical for researching the performance of the asphalt mixture, especially for researching the low-temperature cracking problem of an asphalt pavement. The problem of low-temperature shrinkage cracking of the asphalt pavement is a difficult problem which puzzles experts at home and abroad at present. Asphalt pavements in more than half of China are damaged by temperature cracks. The low-temperature performance of the asphalt mixture directly reflects the temperature shrinkage cracking resistance of the asphalt mixture, so that the characteristic point, namely the turning point, on the thermomechanical analysis curve of the asphalt mixture is particularly important to obtain.
The methods currently used to determine the turning point on the thermomechanical analysis curve can be summarized in two ways: a direct slope calculation method and a staged curve fitting method, wherein the direct slope calculation method is sensitive to the fluctuation of experimental data, so that the determined turning point is deviated or is not unique; the staged curve fitting method can cause the condition that the determined turning points are not unique due to different adopted fitting models, and the fitting models are mostly pure mathematical models and cannot represent the real performance of the asphalt mixture. The definition of the turning point of the thermomechanical analysis curve of the asphalt mixture lacks a strong criterion.
Disclosure of Invention
The invention aims to solve the problem that the turning point of the thermomechanical analysis curve of the existing asphalt mixture is difficult to determine, and provides a method for determining the turning point of the thermomechanical analysis curve of the asphalt mixture based on the Pearson correlation coefficient, which is used for researching the low-temperature performance of the asphalt mixture.
The method for measuring the turning point of the thermomechanical analysis curve based on the Pearson correlation coefficient is realized according to the following steps:
first, measure the thermomechanical change with temperatureParameter, establishing a temperature array T [i] ,i∈[1,N]And thermomechanical parameter array Y [i] ,i∈[1,N]；
Secondly, sorting the temperature array and the thermomechanical parameter array obtained in the step one in ascending order according to the size of the temperature measurement value, and recording the sorted data as a temperature-thermomechanical parameter data set { T } j ,Y j J ═ 1,2, …, N), where T j-1 ＜T j ＜T j+1 Drawing a temperature-thermomechanical parameter relation curve by taking the temperature T as an abscissa and the thermomechanical parameter Y as an ordinate;
thirdly, based on the temperature-thermomechanical parameter data set in the second step, calculating the square of the Pearson correlation coefficient of the temperature data set and the thermomechanical parameter data set according to the formula (1) to obtain a data set R [j] 2 ,j∈[2,N]With T as the abscissa and R as the ordinate 2 For the ordinate, R is plotted 2 -a T-plot;
IV, in R 2 In the graph of-T, with R 2 More than or equal to 0.995 as the defining condition of the turning point of the temperature stress curve, then R 2 The corresponding temperature is taken as the measured turning point temperature T T 。
The invention takes the Pearson correlation coefficient as an index, calculates the correlation coefficient between the thermomechanical analysis parameter and the temperature data point through analysis, and accurately determines the turning point of the thermomechanical analysis curve of the asphalt mixture. As can be seen from the statistical theorem, if R is X, the pearson correlation coefficient of Y has: (1) r 2 ≤1；(2)R 2 An adequate condition of 1 is that P (Y ═ a + bX) ═ 1, and a and b are constants. According to the theorem, when R 2 When 1, there is a linear relationship between Y and X, and R 2 The closer to 1, the more nearly linear relationship Y is to X. The correlation coefficient R between X and Y is a numerical feature that assesses the degree of linear correlation between X and Y. Compared with the prior art for calculating the slopeThe method is based on directly measured data points, is a direct characterization quantity of the actually measured data relation, and can accurately characterize the degree of data deviation from a straight line, thereby determining the turning point of a thermomechanical analysis curve of the asphalt mixture.
Drawings
FIG. 1 is a graph of the temperature-stress relationship obtained in step two of the first embodiment, wherein the arrows represent the temperature reduction process;
FIG. 2 shows R obtained in step three of example I 2 -a T-plot;
FIG. 3 is a graph of the loss shear modulus versus temperature obtained in step two of example two;
FIG. 4 shows R obtained in step three of example two 2 -T plot.
Detailed Description
The first embodiment is as follows: the method for measuring the turning point of the thermomechanical analysis curve based on the Pearson correlation coefficient is implemented according to the following steps:
firstly, measuring thermomechanical parameters changing along with temperature and establishing a temperature array T [i] ,i∈[1,N]And thermomechanical parameter array Y [i] ,i∈[1,N]；
Secondly, sorting the temperature array and the thermomechanical parameter array obtained in the first step in an ascending order according to the size of the temperature measurement value, and recording the sorted data as a temperature-thermomechanical parameter data set { T } j ,Y j J ═ 1,2, …, N), where T j-1 ＜T j ＜T j+1 Drawing a temperature-thermomechanical parameter relation curve by taking the temperature T as an abscissa and the thermomechanical parameter Y as an ordinate;
thirdly, based on the temperature-thermomechanical parameter data set in the second step, calculating the square of the Pearson correlation coefficient of the temperature data set and the thermomechanical parameter data set according to the formula (1) to obtain a data set R [j] 2 ,j∈[2,N]With T as the abscissa and R as the ordinate 2 For ordinate, R is plotted 2 -a T-plot;
IV, in R 2 In the graph of-T, with R 2 More than or equal to 0.995 as the defining condition of the turning point of the temperature stress curve, then R 2 The corresponding temperature is taken as the measured turning point temperature T T 。
The embodiment is used as a determination method for determining the turning point of the thermomechanical analysis curve of the asphalt mixture, has very key significance for researching the low-temperature performance of the asphalt mixture, and the performance of the asphalt mixture is obviously changed before and after the turning point of the curve. For example, the turning point temperature in the temperature stress variation process curve divides the temperature stress curve into two parts, when the temperature is lower than the turning point temperature, the temperature stress increases rapidly along with the temperature reduction, and basically no stress relaxation exists in the temperature range, and when the temperature is higher than the turning point temperature, the temperature stress increases slowly along with the temperature reduction, and the part reflects the stress relaxation performance of the asphalt mixture.
The second embodiment is as follows: the difference between the present embodiment and the first embodiment is that the thermomechanical parameters in the first step are stress value, loss shear modulus or temperature shrinkage strain.
The third concrete implementation mode: the second difference between the embodiment and the specific embodiment is that when the thermomechanical parameter is a stress value, a low-temperature freeze-breaking experimental device is adopted to perform a test piece temperature stress test on an asphalt mixture test piece, initial temperature and cooling rate are set, then a program is started to acquire and record temperature data and stress data in the test process, and temperature arrays T are respectively obtained [i] ,i∈[1,N]Sum stress array σ [i] ,i∈[1,N]And when the test piece is frozen off, the test is finished.
The fourth concrete implementation mode: the third embodiment is different from the third embodiment in that the initial temperature is set to 10-18 ℃, and the cooling rate is set to 15-25 ℃/h.
The fifth concrete implementation mode is as follows: the fourth difference between this embodiment and the fourth embodiment is that the initial temperature is set to 16 ℃ and the cooling rate is set to 20 ℃/h.
The sixth specific implementation mode: the difference between the first embodiment and the fifth embodiment is that when the thermomechanical parameter is loss shear modulus, a Dynamic Shear Rheometer (DSR) is used to perform a temperature scanning test on an asphalt mixture test piece, a loading frequency and a test temperature are set, and temperature data and loss shear modulus data in the test process are respectively acquired.
The seventh embodiment: the sixth embodiment is different from the sixth embodiment in that the loading frequency is set to 0.5Hz, and the temperature range is-20 ℃ to 25 ℃.
The specific implementation mode is eight: the difference between this embodiment and one of the first to seventh embodiments is that R in step four 2 0.995 to 0.999.
The specific implementation method nine: this embodiment differs from the first to seventh embodiments in that R is the number of steps 2 The temperature stress curve turning point is defined as 0.998.
The first embodiment is as follows: the method for determining the turning point of the thermomechanical analysis curve based on the Pearson correlation coefficient is implemented by the following steps:
firstly, a low-temperature freezing-breaking experiment device is adopted to carry out a constrained specimen temperature stress test on an asphalt mixture (AC-13C) test specimen, the initial temperature is set to be 16 ℃, the cooling rate is 20 ℃/h, then a program is started to collect and record temperature data and stress data in the experiment process, and temperature arrays T are respectively obtained [i] ,i∈[1,N]Sum stress array σ [i] ,i∈[1,N]When the test piece is frozen off, the test is finished;
secondly, the temperature array and the stress array obtained in the first step are sorted in an ascending order according to the size of the temperature measurement value, and the sorted data are recorded as a temperature-stress data set { T } j ,σ j J ═ 1,2, …, N), in which T j-1 ＜T j ＜T j+1 And drawing a temperature-stress relation curve by taking the temperature T as an abscissa and the stress sigma as an ordinate, as shown in FIG. 1;
thirdly, based on the temperature-stress data set in the second step, calculating the square of the Pearson correlation coefficient of the temperature data set and the stress data set according to the following formula to obtain a data set R [j] 2 ,j∈[2,N]With T as abscissa and R as ordinate 2 For ordinate, R is plotted 2 -graph T, as shown in FIG. 2;
IV, in R 2 In the graph of-T, with R 2 When the temperature stress curve turning point is defined as 0.998, R is 2 The temperature corresponding to 0.998 was taken as the measured inflection point temperature T T 。
The stress inflection point temperature T of the asphalt mixture measured in this example T Is-14 ℃.
Example two: the method for determining the turning point of the thermomechanical analysis curve based on the Pearson correlation coefficient is implemented by the following steps:
firstly, a temperature scanning test is carried out on an asphalt mixture (AC-13C) test piece by adopting a Dynamic Shear Rheometer (DSR), the loading frequency is set to be 0.5Hz, the temperature range is-20-25 ℃, temperature data and loss shear modulus data in the experimental process are respectively collected, and a temperature array T is obtained [i] ,i∈[1,N]And loss shear modulus array G ″) [i] ,i∈[1,N]；
Secondly, sorting the data set obtained in the first step in an ascending order according to the size of the temperature measurement value, and recording the data after the ascending order as a temperature-loss shear modulus data set { T } j ,G″ j J ═ 1,2, …, N), where T j-1 ＜T j ＜T j+1 Drawing a loss shear modulus-temperature relation curve by taking the temperature T as an abscissa and the loss shear modulus G' as an ordinate, as shown in FIG. 3;
thirdly, based on the temperature-loss shear modulus data set, calculating the square of the Pearson correlation coefficient of the temperature and the loss shear modulus according to the following formula to obtain a data set R [j] 2 ,j∈[2,N]With T as the abscissa and R as the ordinate 2 For ordinate, R is plotted 2 -graph T, as shown in FIG. 4;
IV, in R 2 In the graph of-T, with R 2 When the temperature stress curve turning point is defined as 0.998, R is 2 The temperature corresponding to 0.998 was taken as the measured inflection point temperature T T 。
The loss shear modulus inflection point temperature T of the asphalt mixture measured in this example T Is-0.06 ℃.
Claims (9)
1. The method for measuring the turning point of the thermomechanical analysis curve based on the Pearson correlation coefficient is characterized by comprising the following steps of:
firstly, measuring thermomechanical parameter changing with temperature, and establishing temperature array T [ 2 ] i ],i∈[1,N]And thermomechanical parameter array Y [i] ,i∈[1,N]；
Secondly, sorting the temperature array and the thermomechanical parameter array obtained in the step one in ascending order according to the size of the temperature measurement value, and recording the sorted data as a temperature-thermomechanical parameter data set { T } j ,Y j Where j is 1,2, …, N, T j-1 ＜T j ＜T j+1 Drawing a temperature-thermomechanical parameter relation curve by taking the temperature T as an abscissa and the thermomechanical parameter Y as an ordinate;
thirdly, based on the temperature-thermomechanical parameter data set in the second step, calculating the square of the Pearson correlation coefficient of the temperature data set and the Pearson correlation coefficient of the thermomechanical parameter data set according to the formula (1) to obtain a data set R [j] 2 With T as abscissa and R as ordinate 2 For the ordinate, R is plotted 2 -a T-plot;
IV, in R 2 In the graph of-T, with R 2 More than or equal to 0.995 is taken as the definition condition of the turning point of the temperature stress curve, then R 2 The corresponding temperature is taken as the measured turning point temperature T T 。
2. The method for determining the turning point of a thermo-mechanical analysis curve based on the pearson correlation coefficient as claimed in claim 1, wherein the thermo-mechanical parameter in the first step is a stress value, a loss shear modulus or a temperature shrinkage strain.
3. The method for determining the turning point of the thermal mechanical analysis curve based on the pearson correlation coefficient as claimed in claim 2, wherein when the thermal mechanical parameter is a stress value, a low temperature freeze-breaking experimental device is used to perform a constrained test piece temperature stress test on the asphalt mixture test piece, an initial temperature and a cooling rate are set, and then a program is started to collect and record temperature data and stress data in the test process to respectively obtain a temperature array T [i] ,i∈[1,N]Sum stress array σ [i] ,i∈[1,N]And when the test piece is frozen off, the test is finished.
4. The method for determining the turning point of the thermal mechanical analysis curve based on the pearson correlation coefficient as claimed in claim 3, wherein the initial temperature is set to 10-18 ℃ and the temperature decrease rate is set to 15-25 ℃/h.
5. The method for determining the turning point of a thermo-mechanical analysis curve based on the pearson correlation coefficient as claimed in claim 4, wherein the initial temperature is set to 16 ℃ and the temperature decrease rate is set to 20 ℃/h.
6. The method for determining the turning point of the thermal mechanical analysis curve based on the pearson correlation coefficient as claimed in claim 1, wherein when the thermal mechanical parameter is the loss shear modulus, a dynamic shear rheometer is used to perform a temperature sweep test on the asphalt mixture test piece, the loading frequency and the test temperature are set, and the temperature data and the loss shear modulus data during the test process are respectively collected.
7. The method for determining the inflection point of a curve for thermo-mechanical analysis based on the pearson correlation coefficient as claimed in claim 6, wherein the loading frequency is set to 0.5Hz and the temperature is set to range from-20 ℃ to 25 ℃.
8. The method for determining the inflection point of a curve based on the correlation coefficient of pearson as claimed in claim 1, wherein R is in step four 2 Is 0.995 to 0.999.
9. The method for determining the turning point of a thermo-mechanical analysis curve based on the Pearson's correlation coefficient as claimed in claim 8, wherein R is the number of the fourth step 2 The temperature stress curve turning point is defined as 0.998.
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