Model-data fusion asphalt mixture optimal time threshold determination method and system and computer readable storage medium

Abstract

The invention discloses a model-data fused asphalt mixture optimal time threshold determination method, and belongs to the technical field of asphalt mixture linear viscoelasticity evaluation. Dynamic modulus test data of various asphalt mixtures are obtained, and the optimal time threshold of the asphalt mixtures is determined based on the obtained data; determining parameters of a complex modulus main curve model and a time-temperature displacement equation in combination with a fitting target error equation, obtaining a continuous relaxation time spectrum expression according to the parameters, further calculating a relaxation time threshold lower / upper limit value according to a relationship between relaxation intensity and relaxation time, and calculating the relaxation time threshold lower / upper limit value in combination with the upper / lower limit value of the asphalt mixture main curve reduction frequency. And determining characteristic values of an upper limit value and a lower limit value of the relaxation time threshold, and determining an optimal relaxation time threshold according to the relaxation time threshold characteristic values and the main curve reduction frequency. The problems that an existing method is low in calculation speed and low in efficiency in solving the time threshold parameter of the asphalt mixture are solved. The invention further discloses a system based on the method and a computer readable storage medium.

Description

Technical Field

[0001] The present invention belongs to the technical field of linear viscoelastic performance evaluation of asphalt mixtures, and specifically relates to a method, system and computer-readable storage medium for determining an optimal time threshold of an asphalt mixture by model-data fusion. Background Art

[0002] As a viscoelastic material with excellent performance, asphalt mixture is widely used in the construction of highway pavements at all levels. When subjected to vehicle loads, the strain generated inside the asphalt mixture is relatively small, and its mechanical state is generally considered to remain within the linear viscoelastic range. Therefore, when conducting response analysis and design of pavement structures, the industry generally uses linear viscoelastic constitutive models to describe the mechanical properties of asphalt mixtures. Among the many constitutive models that describe linear viscoelasticity, the generalized Maxwell model has become the preferred model for characterizing the relaxation behavior of asphalt mixtures due to its clear physical meaning and high computational efficiency. The generalized Maxwell model is not only widely used in the field of scientific research, but is also a built-in linear viscoelastic model in most mainstream finite element software. The research on the generalized Maxwell model has played a key role in promoting the development of related technologies.

[0003] When using the generalized Maxwell model to characterize the linear viscoelastic mechanical properties of asphalt mixtures, it is crucial to accurately determine the model parameters. The generalized Maxwell model mainly includes relaxation time parameters and relaxation strength parameters. Studies have shown that the relaxation strength parameters are related to the relaxation time parameters. Once the relaxation time parameters are determined, the corresponding relaxation strength parameters can be calculated through theoretical relationships. Unfortunately, the current related fields still face challenges in quickly and accurately determining these time parameters, which mainly rely on the subjective experience of the operator. This dependence not only limits the promotion and application of the generalized Maxwell model, but also affects the accurate evaluation of the mechanical behavior and service performance of asphalt mixtures to a certain extent.

[0004] In order to overcome this problem, researchers have proposed a method for determining the parameters of the Prony series model of asphalt mixtures based on the optimal relaxation time domain (CN201910155265.1). This method calculates the characteristic relaxation time range by the number of characteristic items and center points of the trial calculation group, thereby getting rid of the reliance on the subjective experience of the operator and showing good scientificity. However, in practical applications, this method still needs to be solved separately for each asphalt mixture sample, resulting in slow calculation speed and low efficiency, especially when performing batch analysis, its limitations are particularly obvious.

[0005] In view of the above background, the present invention aims to propose a more efficient and accurate method for determining the optimal time threshold of asphalt mixture, so as to further promote the application of generalized Maxwell model in the mechanical behavior analysis of asphalt mixture. Summary of the invention

[0006] 1. Technical issues to be resolved

[0007] In view of this, the purpose of the present invention is to solve the following problems: ① The existing method needs to solve each asphalt mixture sample separately, resulting in slow calculation speed and low efficiency, especially when performing batch analysis, its limitations are particularly obvious. ② The lack of a complete calculation system and program limits the application of the Maxwell model in the mechanical behavior analysis of asphalt mixtures.

[0008] (II) Technical solution

[0009] In order to solve the technical problem ①, the present invention provides a method for determining the optimal time threshold of asphalt mixture by model-data fusion, which is characterized by comprising the following steps:

[0010] S1. Obtain all asphalt mixture dynamic modulus test data, by asphalt mixture type They are denoted as A1, A2, A3, ..., Az respectively;

[0011] S2. Select the appropriate complex modulus master curve model and time-temperature displacement equation, and determine them one by one according to the fitting target error equation The parameters of the complex modulus master curve model and the time-temperature displacement equation are determined one by one Storage modulus master curve and loss modulus master curve;

[0012] S3. Count all asphalt mixtures The upper and lower limits of the master curve reduction frequency;

[0013] S4. Determine one by one using the relationship between the complex modulus and the continuous relaxation time spectrum The relaxation time spectrum function expression of ;

[0014] S5, determining the relationship between relaxation intensity and relaxation time by using the approximate relationship satisfied between the continuous relaxation time spectrum and the discrete relaxation time spectrum;

[0015] S6. Derivative the continuous relaxation time spectrum function and determine The relaxation time point corresponding to the peak point of the continuous relaxation time spectrum curve;

[0016] S7. Determine all asphalt mixtures The lower and upper limits of relaxation time threshold;

[0017] S8. Calculate asphalt mixture one by one The difference between the upper / lower limit of the master curve reduction frequency and the lower / upper limit of the relaxation time threshold;

[0018] S9. Determine the relaxation time threshold characteristic value of the asphalt mixture, and then calculate and determine the optimal relaxation time threshold.

[0019] As a further description of the technical solution of the present invention:

[0020] The complex modulus (E * (ω r )) The master curve model is shown in formula (1), where the storage modulus (E′(ω r ))Master curve model and loss modulus (E″(ω r )) The master curve models are shown in equations (2) and (3) respectively; the time-temperature displacement equation is the WLF equation, as shown in equation (4):

[0021]

[0022] in:

[0023]

[0024] Where: E e =Minimum dynamic modulus, MPa; E g = Maximum value of dynamic modulus, MPa; ω r = reduction frequency, rad / s; i = imaginary unit; α, β, h, τ0, k = complex modulus master curve shape parameters; α T = time-temperature equivalence factor; T = test temperature, °C; T r = reference temperature, °C; C1 = model parameter; C2 = model parameter, °C.

[0025] As a further description of the technical solution of the present invention:

[0026] In step S2, a suitable temperature is selected as the reference temperature, and the equation shown in formula (7) is used as the fitting target error equation. The parameters of the master curve model and the WLF equation are determined with the help of the EXCEL planning and solving function.

[0027]

[0028] Where: N = the number of measured data points; Storage modulus calculated based on the master curve model, MPa; E n ' ,测 = storage modulus obtained from the nth test, MPa; Loss modulus calculated based on the master curve model, MPa; En ″ ,测 = loss modulus obtained from the nth test, MPa.

[0029] As a further description of the technical solution of the present invention:

[0030] The relationship between the complex modulus and the continuous relaxation time spectrum in S4 is shown in equation (8), and the relaxation time spectrum function expression is shown in equation (9).

[0031] H(τ)=±π -1 I E * (τ -1 e ±iπ ) (8)

[0032]

[0033] in:

[0034]

[0035] Where: H(τ) = continuous relaxation time spectrum, MPa; τ = relaxation time, s; Im = imaginary part of the function.

[0036] As a further description of the technical solution of the present invention:

[0037] The approximate relationship between the continuous relaxation time spectrum and the discrete relaxation time spectrum in S5 is as shown in equations (12) and (13), and the relationship between relaxation intensity and relaxation time is as shown in equation (14).

[0038]

[0039] E s =H(τ s )·Δlnτ=H(τ s )·(ln10)·Δlgτ (14)

[0040] Where: S = the number of discrete relaxation time parameters; E s =s relaxation strength parameter, MPa; τ s = the sth relaxation time parameter, s; ω = loading frequency, rad / s; Δlgτ = the distance between relaxation times on a logarithmic scale to base 10.

[0041] As a further description of the technical solution of the present invention:

[0042] The relaxation time point in step S6 is τ peak , the calculation method is shown in formula (15):

[0043]

[0044] As a further description of the technical solution of the present invention:

[0045] The steps for determining the relaxation time lower threshold value in step S7 are as follows:

[0046] S711, set the relaxation time threshold upper limit and relaxation time interval: lgτ max =60, andΔlgτ=0.05;

[0047] S712, set the initial value of the lower limit of the relaxation time to: logτ min,0 =logτ peak , calculate the storage modulus and loss modulus according to formula (12) and formula (13) respectively, and calculate the model error Error according to formula (7) j (j=0,1,2,L);

[0048] S713, setting the lower limit of relaxation time logτ min,j+1 =logτ min,j -0.05 and repeat step S712;

[0049] S714. Calculate the iterative error variation parameter V1 according to formula (16):

[0050]

[0051] S715. If V1≤0.01%, the calculation is terminated and the lower limit of the relaxation time threshold is determined to be lgτ min,j+1 ; Otherwise, repeat steps S713 and S714 until the lower limit of the relaxation time is determined;

[0052] The steps for determining the upper limit of the relaxation time threshold in step S7 are as follows:

[0053] S721, set the relaxation time lower threshold value and relaxation time interval: lgτ min = -60, Δlgτ = 0.05;

[0054] S722, set the initial value of the relaxation time upper limit to: logτ max,0 =logτ peak , calculate the storage modulus and loss modulus according to formula (12) and formula (13) respectively, and calculate the model error Error according to formula (7) l (l=0,1,2,L);

[0055] S723, setting the relaxation time upper limit logτ max,l+1 =logτ max,l +0.05 and repeat step S722;

[0056] S724. Calculate the iterative error variation parameter V2 according to formula (17):

[0057]

[0058] S725. If V2≤0.01%, the calculation is terminated and the upper limit of the relaxation time threshold is determined to be lgτ. max,l+1 ; Otherwise, repeat steps S723 and S724 until the upper limit value of the relaxation time is determined.

[0059] As a further description of the technical solution of the present invention:

[0060] Asphalt mixture in step S8 The difference between the upper limit of the master curve reduction frequency and the lower limit of the relaxation time threshold As shown in formula (18); Asphalt mixture The difference between the lower limit of the master curve reduction frequency and the upper limit of the relaxation time threshold As shown in formula (19),

[0061]

[0062] Will Arrange them in order from largest to smallest, with sequence number k min =[95%z] ([95%z] means 95%z is rounded up) is Δ min The eigenvalue of Will Arrange in ascending order, with sequence number k max = Δ corresponding to [95% z] ([95% z] means 95% z is rounded up) max,kmax is Δ max The eigenvalue of

[0063] Asphalt mixture The relaxation time threshold characteristic value and the master curve reduction frequency are substituted into equations (18) and (19) to determine the optimal relaxation time threshold. The master curve model parameters and the optimal relaxation time threshold are substituted into equation (14) to determine the relaxation intensity.

[0064] In order to solve technical problem ②, the present invention provides a model-data fusion asphalt mixture optimal time threshold determination system, which is characterized by executing the above-mentioned model-data fusion asphalt mixture optimal time threshold determination method.

[0065] The present invention also provides a computer-readable storage medium for storing the above-mentioned model-data fusion asphalt mixture optimal time threshold determination system, characterized in that a computer program is stored on the computer-readable storage medium, and when the computer program is executed by a processor, it can implement the above-mentioned model-data fusion asphalt mixture optimal time threshold determination method.

[0066] (III) Beneficial effects

[0067] Compared with the prior art, the present invention has the following beneficial effects:

[0068] (1) The traditional time parameter determination method heavily relies on the operator's experience and judgment. In contrast, the time domain determination method proposed in the present invention is based on the mathematical relationship between the discrete relaxation time spectrum and the continuous relaxation time spectrum and has a clear physical meaning.

[0069] (2) The model-data fusion method for determining the optimal time threshold of asphalt mixture proposed in the present invention analyzes the relationship between the reduced frequency range and the relaxation time range of the master curve of a large number of asphalt mixtures when calculating the optimal time threshold of the asphalt mixture, and then obtains the statistical characteristic parameters between the relaxation time range and the reduced frequency range. The statistical characteristic parameters have strong robustness and generalization ability.

[0070] (3) When applying the model-data fusion asphalt mixture optimal time threshold determination method proposed in the present invention to calculate the optimal time threshold of the asphalt mixture, it is only necessary to obtain the main curve reduction frequency range, and then perform simple addition and subtraction operations with the statistical characteristic parameters. The calculation process is simple and easy to apply and promote. At the same time, the proposed system and computer-readable storage medium perform calculations through computers, which greatly improves the calculation efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 It is the overall logical thinking diagram of the present invention;

[0072] Figure 2 This is a storage modulus data diagram of asphalt mixture A1 in an embodiment of the present invention;

[0073] Figure 3 This is a data diagram of the loss modulus of asphalt mixture A1 in an embodiment of the present invention;

[0074] Figure 4 The storage modulus main curve of asphalt mixture A1 in the embodiment of the present invention (reference temperature: 20°C);

[0075] Figure 5 is the main curve of the loss modulus of the asphalt mixture A1 in the embodiment of the present invention (reference temperature: 20°C);

[0076] Figure 6 It is a diagram of the upper and lower limits of the frequency domain of the master curve of all asphalt mixtures in the embodiments of the present invention;

[0077] Figure 7 It is a curve diagram of continuous relaxation time spectrum of asphalt mixture A1 in the embodiment of the present invention;

[0078] Figure 8 is the lower limit of the relaxation time domain of all asphalt mixtures in the embodiments of the present invention;

[0079] Fig. 9 is the upper limit of the relaxation time domain of all asphalt mixtures in the embodiments of the present invention;

[0080] Fig.10 It is a statistical parameter diagram of relaxation time threshold of all asphalt mixtures in the embodiment of the present invention;

[0081] Fig.11 Calculation results of the generalized Maxwell model parameters for asphalt mixture A1 in the embodiment of the present invention. DETAILED DESCRIPTION

[0082] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0083] Embodiment 1: The present invention provides a method for determining the optimal time threshold of asphalt mixture by model-data fusion, using a generalized Maxwell model, and determining the optimal relaxation time threshold according to Figure 1 The logic shown is carried out, and the specific steps are as follows:

[0084] 1. Obtaining dynamic modulus test data of asphalt mixture

[0085] There are many ways to obtain dynamic modulus test data of asphalt mixtures. It can be obtained through experiments. The most direct and effective way is to obtain it through literature retrieval. When obtaining, select data from articles published in high-quality journals to ensure the accuracy of the data as much as possible. When obtaining, it is necessary to obtain all the dynamic modulus test data of asphalt mixtures that can be retrieved. The test data includes test temperature, loading frequency, storage modulus and loss modulus, etc., and according to the type of asphalt mixture, They are denoted as A1, A2, A3,…, Az respectively.

[0086] In a preferred example, it is necessary to first draw a storage modulus data graph with the loading frequency as the horizontal axis and the storage modulus as the vertical axis, and draw a loss modulus data graph with the loading frequency as the horizontal axis and the loss modulus as the vertical axis. In actual calculation, it is necessary to calculate the storage modulus data of all asphalt mixtures. Taking one asphalt mixture (referred to as asphalt mixture A1) as an example, the storage modulus data is shown in Figure 2 As shown, the loss modulus data is shown in Figure 3 By observing the data distribution, we can determine whether the data is abnormal. If the data is obviously abnormal, we can abandon the data or choose alternative data.

[0087] 2. Select the master curve model of viscoelastic parameters and the time-temperature displacement equation

[0088] There are many types of viscoelastic parameter master curve models, such as Sigmoidal model, HN model, 2S2P1D model, etc., which have the same functions. The present invention uses the 2S2P1D model as the preferred one.

[0089] Similarly, the time-temperature displacement equation can be the WLF equation, the Arrhenius equation, the SOP equation, etc. The WLF equation is preferred in the present invention.

[0090] Taking the 2S2P1D model as the complex modulus (E * (ω r )) master curve model, as shown in formula (1), where the storage modulus (E′(ω r ))Master curve model and loss modulus (E″(ω r )) The master curve models are shown in equations (2) and (3) respectively; the WLF equation is used as the time-temperature displacement equation, as shown in equation (4).

[0091]

[0092] in:

[0093]

[0094] Where: E e =Minimum dynamic modulus, MPa; E g = Maximum value of dynamic modulus, MPa; ω r = reduction frequency, rad / s; i = imaginary unit; α, β, h, τ0, k = complex modulus master curve shape parameters; α T = time-temperature equivalence factor; T = test temperature, °C; T r = reference temperature, °C; C1 = model parameter; C2 = model parameter, °C.

[0095] 3. Determine the parameters of the master curve model and the time-temperature displacement equation

[0096] The equation shown in formula (7) is used as the fitting target error equation, and the parameters of the master curve model and the WLF equation are determined with the help of the EXCEL planning and solving function. Taking asphalt mixture A1 as an example, 20℃ is selected as the reference temperature, and the determined parameters are shown in Table 1. The determined storage modulus master curve and loss modulus master curve are shown in Figure 4 and Figure 5 shown.

[0097]

[0098] Where: N = the number of measured data points; Storage modulus calculated based on the master curve model, MPa; E n ' ,测 = storage modulus obtained from the nth test, MPa; Loss modulus calculated based on the master curve model, MPa; E n ″ ,测 = loss modulus obtained from the nth test, MPa.

[0099] Table 1 Parameter fitting results

[0100]

[0101]

[0102] Complete all asphalt mixtures in the same way Parameter fitting and determination of all asphalt mixtures Storage modulus master curve and loss modulus master curve.

[0103] 4. Count all asphalt mixtures The upper and lower limits of the master curve reduction frequency

[0104] According to all asphalt mixture The storage modulus master curve and loss modulus master curve of all asphalt mixtures are statistically analyzed. The upper and lower limits of the master curve reduction frequency are as follows Figure 6 shown.

[0105] 5. Determine the relaxation time spectrum function expression

[0106] The relationship between the complex modulus and the continuous relaxation time spectrum (as shown in formula (8)) is used to determine the relaxation time spectrum function expression (as shown in formula (9)). Taking asphalt mixture A1 as an example, the parameter values ​​listed in Table 1 are substituted into the continuous relaxation time spectrum function to obtain the continuous relaxation time spectrum expression. The continuous relaxation time spectrum curve is shown in Figure 7 shown.

[0107] H(τ)=±π -1 I E * (τ -1 e ±iπ ) (27)

[0108]

[0109] in:

[0110]

[0111] Where: H(τ) = continuous relaxation time spectrum, MPa; τ = relaxation time, s; Im = imaginary part of the function.

[0112] In the same way, all asphalt mixtures The fitting parameter values ​​are substituted into the continuous relaxation time spectrum function to obtain the corresponding continuous relaxation time spectrum expression, and the corresponding continuous relaxation time spectrum curve is plotted.

[0113] 6. Determine the relationship between relaxation intensity and relaxation time

[0114] The relationship between relaxation intensity and relaxation time (as shown in equation (14)) is determined by using the approximate relationship between the continuous relaxation time spectrum and the discrete relaxation time spectrum (as shown in equation (12) and equation (13)).

[0115]

[0116] Where: S = the number of discrete relaxation time parameters; E s =s relaxation strength parameter, MPa; τ s =s relaxation time parameter, s; ω=loading frequency, rad / s; Δlgτ=the distance between relaxation times on a logarithmic scale with base 10, usually 0.5, and 0.5 in the present invention.

[0117] 7. Determine the relaxation time point corresponding to the peak point of the continuous relaxation time spectrum curve

[0118] Take the derivative of the continuous relaxation time spectrum function and determine the relaxation time point τ corresponding to the peak point of the continuous relaxation time spectrum curve peak , the calculation method is shown in formula (15):

[0119]

[0120] The τ of asphalt mixture A1 calculated using formula (11) peak For 10 -2.12 s. The same is true for all asphalt mixtures. relaxation time point.

[0121] 8. Determine the lower limit of relaxation time

[0122] The steps to determine are as follows:

[0123] (1) Set the upper limit of the relaxation time threshold and the relaxation time interval: lgτ max =60,andΔlgτ=0.05;

[0124] (2) Set the initial value of the lower limit of the relaxation time to: logτ min,0 =logτ peak , calculate the storage modulus and loss modulus according to formula (12) and formula (13) respectively, and calculate the model error Error according to formula (7) j (j=0,1,2,L);

[0125] (3) Set the lower limit of relaxation time logτ min,j+1 =logτ min,j -0.05 and repeat step (2);

[0126] (4) Calculate the iterative error change parameter V1 according to formula (16):

[0127]

[0128] (5) If V1≤0.01%, the calculation is terminated and the lower limit of the relaxation time threshold is determined to be lgτ min,j+1 ; Otherwise, repeat steps (3) and (4) until the lower limit of the relaxation time is determined.

[0129] Complete all asphalt mixtures through the above steps The calculation result of the relaxation time lower threshold is as follows: Figure 8 shown.

[0130] 9. Determine the upper limit of relaxation time threshold

[0131] (1) Set the relaxation time lower threshold and relaxation time interval: lgτ min = -60, Δlgτ = 0.05;

[0132] (2) Set the initial value of the relaxation time upper limit to: logτ max,0 =logτ peak , calculate the storage modulus and loss modulus according to formula (12) and formula (13) respectively, and calculate the model error Error according to formula (7) l (l=0,1,2,L);

[0133] (3) Set the upper limit of relaxation time logτ max,l+1 =logτ max,l +0.05 and repeat step (2);

[0134] (4) Calculate the iterative error change parameter V2 according to formula (17):

[0135]

[0136] (5) If V2≤0.01%, the calculation is terminated and the upper limit of the relaxation time threshold is determined to be lgτ max,l+1 ; Otherwise, repeat steps (3) and (4) until the upper limit of the relaxation time is determined.

[0137] Complete all asphalt mixtures through the above steps The calculation result of the relaxation time threshold upper limit is as follows: Fig. 9 shown.

[0138] 10. Calculation of asphalt mixture The difference between the upper / lower limit value of the master curve reduction frequency and the lower / upper limit value of the relaxation time threshold is used to calculate the asphalt mixture The difference between the upper limit of the master curve reduction frequency (determined by step 4) and the lower limit of the relaxation time threshold (determined by step 8) As shown in formula (18). Calculate asphalt mixture The difference between the lower limit of the master curve reduction frequency (determined by step 4) and the upper limit of the relaxation time threshold (determined by step 9) As shown in formula (19). and The calculation results are as follows Fig.10 shown.

[0139]

[0140] 11. Determine the relaxation time threshold characteristic value of asphalt mixture

[0141] Will Arrange them in order from largest to smallest, with sequence number k min =[95%z] ([95%z] means 95%z is rounded up) is Δ min The eigenvalue of Will Arrange in ascending order, with sequence number k max =[95%z] ([95%z] means 95%z is rounded up) is Δ max The eigenvalue of The calculation results are listed in Table 2.

[0142] Table 2 Characteristic values ​​of the upper and lower limits of relaxation time threshold

[0143]

[0144] 12. Determine the optimal relaxation time threshold

[0145] Substitute the relaxation time threshold characteristic value of the asphalt mixture and the master curve reduction frequency into equations (18) and (19) to determine the optimal relaxation time threshold, and substitute the master curve model parameters and the optimal relaxation time threshold into equation (14) to determine the relaxation strength. Taking asphalt mixture A1 as an example, this application uses the relaxation time parameters and relaxation strength parameters in the generalized Maxwell model to calculate the results as follows: Fig.11 shown.

[0146] All the same parameters in the formulas of the present invention have the same definitions in different formulas, and therefore are only described when they appear for the first time without repeated description.

[0147] Of course, the present invention is not limited to determining the optimal relaxation time threshold, but can also determine the optimal delay time threshold. Another function can be achieved by only changing the input data from complex modulus data to complex compliance data, the complex modulus master curve model to the complex compliance master curve model, and the relaxation time spectrum to the delay time spectrum.

[0148] Example 2: The present invention also provides a system for determining the optimal time threshold of asphalt mixture based on the model-data fusion established based on the operating steps in Example 1. The system executes the method for determining the optimal time threshold of asphalt mixture based on the model-data fusion described in Example 1, making the calculation more convenient.

[0149] Embodiment 3: The present invention also provides a computer-readable storage medium storing the system for determining the optimal time threshold of asphalt mixture by model-data fusion described in Embodiment 2, on which a computer program is stored, and when the computer program is executed by a processor, the method for determining the optimal time threshold of asphalt mixture by model-data fusion described in Embodiment 1 can be implemented. By executing the budget by computer, the operation efficiency is greatly improved.

[0150] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for determining the optimal time threshold of asphalt mixture by model-data fusion, characterized in that The following steps are involved: S1. Obtain all asphalt mixture dynamic modulus test data, by asphalt mixture type They are denoted as A1, A2, A3, ..., Az respectively; S2. Select the appropriate complex modulus master curve model and time-temperature displacement equation, and determine them one by one according to the fitting target error equation The parameters of the complex modulus master curve model and the time-temperature displacement equation are determined one by one Storage modulus master curve and loss modulus master curve; S3. Count all asphalt mixtures The upper and lower limits of the master curve reduction frequency; S4. Determine one by one using the relationship between the complex modulus and the continuous relaxation time spectrum The relaxation time spectrum function expression of ; S5, determining the relationship between relaxation intensity and relaxation time by using the approximate relationship satisfied between the continuous relaxation time spectrum and the discrete relaxation time spectrum; S6. Derivative the continuous relaxation time spectrum function and determine The relaxation time point corresponding to the peak point of the continuous relaxation time spectrum curve; S7. Determine all asphalt mixtures The lower and upper limits of relaxation time threshold; S8. Calculate asphalt mixture one by one The difference between the upper / lower limit of the master curve reduction frequency and the lower / upper limit of the relaxation time threshold; S9. Determine the relaxation time threshold characteristic value of the asphalt mixture, and then calculate and determine the optimal relaxation time threshold.

2. The method for determining the optimal time threshold of asphalt mixture by model-data fusion according to claim 1, characterized in that: The complex modulus (E * (ω r )) The master curve model is shown in formula (1), where the storage modulus (E′(ω r ))Master curve model and loss modulus (E″(ω r )) The master curve models are shown in equations (2) and (3) respectively; the time-temperature displacement equation is the WLF equation, as shown in equation (4): in: Where: E e =Minimum dynamic modulus, MPa; E g = Maximum value of dynamic modulus, MPa; ω r = reduction frequency, rad / s; i = imaginary unit; α, β, h, τ0, k = complex modulus master curve shape parameters; α T = time-temperature equivalence factor; T = test temperature, °C; T r = reference temperature, °C; C1 = model parameter; C2 = model parameter, °C.

3. The method for determining the optimal time threshold of asphalt mixture by model-data fusion as claimed in claim 2, characterized in that: In step S2, a suitable temperature is selected as the reference temperature, and the equation shown in formula (7) is used as the fitting target error equation. The parameters of the master curve model and the WLF equation are determined with the help of the EXCEL planning and solving function. Where: N = the number of measured data points; MPa; E n ' ,测 = storage modulus obtained from the nth test, MPa; MPa; E″ n,测 = loss modulus obtained from the nth test, MPa.

4. The method for determining the optimal time threshold of asphalt mixture by model-data fusion as claimed in claim 3, characterized in that: The relationship between the complex modulus and the continuous relaxation time spectrum in S4 is shown in equation (8), and the relaxation time spectrum function expression is shown in equation (9). H(τ)=±π -1 ImE * (t -1 e ±iπ ) (8) in: Where: H(τ) = continuous relaxation time spectrum, MPa; τ = relaxation time, s; Im = imaginary part of the function.

5. The method for determining the optimal time threshold of asphalt mixture by model-data fusion as claimed in claim 4, characterized in that: The approximate relationship between the continuous relaxation time spectrum and the discrete relaxation time spectrum in S5 is as shown in equations (12) and (13), and the relationship between relaxation intensity and relaxation time is as shown in equation (14). E s =H(τ s )·Δlnτ=H(τ s )·(ln10)·Δlgτ (14) Where: S = the number of discrete relaxation time parameters; E s =s relaxation strength parameter, MPa; τ s = the sth relaxation time parameter, s; ω = loading frequency, rad / s; Δlgτ = the distance between relaxation times on a logarithmic scale to base 10.

6. The method for determining the optimal time threshold of asphalt mixture by model-data fusion as claimed in claim 5, characterized in that: The relaxation time point in step S6 is τ peak , the calculation method is shown in formula (15):

7. A method for determining the optimal time threshold of asphalt mixture by model-data fusion as claimed in claim 6, characterized in that: The steps for determining the relaxation time lower threshold value in step S7 are as follows: S711, set the relaxation time threshold upper limit and relaxation time interval: lgτ max =60, andΔlgτ=0.05; S712, set the initial value of the lower limit of the relaxation time to: logτ min,0 =logτ peak , calculate the storage modulus and loss modulus according to formula (12) and formula (13) respectively, and calculate the model error Error according to formula (7) j (j=0,1,2,L); S713, setting the lower limit of relaxation time logτ min,j+1 =logτ min,j -0.05 and repeat step S712; S714. Calculate the iterative error variation parameter V1 according to formula (16): S715. If V1≤0.01%, the calculation is terminated and the lower limit of the relaxation time threshold is determined to be lgτ min,j+1 ; Otherwise, repeat steps S713 and S714 until the lower limit of the relaxation time is determined; The steps for determining the upper limit of the relaxation time threshold in step S7 are as follows: S721, set the relaxation time lower threshold value and relaxation time interval: lgτ min = -60, Δlgτ = 0.05; S722, set the initial value of the relaxation time upper limit to: logτ max,0 =logτ peak , calculate the storage modulus and loss modulus according to formula (12) and formula (13) respectively, and calculate the model error Error according to formula (7) l (l=0,1,2,L); S723, setting the relaxation time upper limit logτ max,l+1 =logτ max,l +0.05 and repeat step S722; S724. Calculate the iterative error variation parameter V2 according to formula (17): S725. If V2≤0.01%, the calculation is terminated and the upper limit of the relaxation time threshold is determined to be lgτ. max,l+1 ; Otherwise, steps S723 and S724 are repeated until the upper limit value of the relaxation time is determined.

8. The method for determining the optimal time threshold of asphalt mixture by model-data fusion as claimed in claim 7, characterized in that: Asphalt mixture in step S8 The difference between the upper limit of the master curve reduction frequency and the lower limit of the relaxation time threshold As shown in formula (18); Asphalt mixture The difference between the lower limit of the master curve reduction frequency and the upper limit of the relaxation time threshold As shown in formula (19), Will Arrange them in order from largest to smallest, with sequence number k min =[95%z] ([95%z] means 95%z is rounded up) is Δ min The eigenvalue of Will Arrange in ascending order, with sequence number k max = Δ corresponding to [95% z] ([95% z] means 95% z is rounded up) max,kmax is Δ max The eigenvalue of The relaxation time threshold characteristic value of asphalt mixture and the master curve reduction frequency are substituted into equations (18) and (19) to determine the optimal relaxation time threshold. The master curve model parameters and the optimal relaxation time threshold are substituted into equation (14) to determine the relaxation intensity.

9. A model-data fusion asphalt mixture optimal time threshold determination system, characterized by A method for determining the optimal time threshold of asphalt mixture by implementing the model-data fusion described in any one of claims 1-8.

10. A computer-readable storage medium storing the model-data fusion asphalt mixture optimal time threshold determination system according to claim 9, characterized in that: The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, it can implement the method for determining the optimal time threshold of asphalt mixture by model-data fusion as described in any one of claims 1-8.

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