Fiber asphalt bond slip prediction method based on innovation-first fractional order accumulation

Abstract

The invention relates to the technical field of civil engineering materials, in particular to a fiber asphalt bond slip prediction method based on innovation-first fractional order accumulation, which comprises the following steps: firstly, selecting bond slip values obtained by performing monofilament drawing on basalt fibers in an asphalt matrix as a database, and constructing a non-negative original sequence as the input of a model; secondly, an innovation priority and fractional order accumulation operator is introduced when the model is constructed; then, a genetic algorithm is adopted to seek an optimal parameter in an innovation priority fractional order accumulation operator; and finally, applying the improved grey generalized Verhulst model to the bond slip curve prediction of the basalt fiber. According to the method, the interface performance evolution rule of the basalt fiber in the asphalt matrix can be well predicted, the influence of physical characteristics such as fiber modulus and surface morphology on interface stress transmission can be reflected, and a more reliable theoretical method is provided for predicting the interface performance of the fiber asphalt concrete.

Description

Technical Field

[0001] This invention relates to the field of civil engineering materials technology, and in particular to a fiber-reinforced bitumen bond slip prediction method based on the prioritization of information fractional-order accumulation. Background Technology

[0002] Fiber-reinforced asphalt concrete has become a core material in road engineering due to its excellent crack resistance. Accurate characterization of its interfacial bond-slip behavior is crucial for revealing the material's deformation resistance mechanism. Currently, interfacial mechanical data from single-filament pull-out tests exhibit small sample sizes and strong nonlinear characteristics, leading to vague quantitative descriptions of the interface and insufficient mechanistic analysis. Traditional bond-slip models (such as the Popovics model) and the grey Verhulst model suffer from insufficient prediction accuracy and distorted physical meaning. Summary of the Invention

[0003] The purpose of this invention is to address the shortcomings of existing technologies by proposing a fiber-reinforced asphalt bond slip prediction method based on innovation priority fractional-order accumulation. This method has a good predictive ability for the evolution of interfacial properties of basalt fibers in asphalt matrix, and can reflect the influence of physical properties such as fiber modulus and surface morphology on interfacial stress transmission, thus providing a more reliable theoretical method for predicting the interfacial properties of fiber-reinforced asphalt concrete.

[0004] To achieve the above objectives, the present invention adopts the following technical solution:

[0005] A fiber-reinforced bitumen bond-slip prediction method based on innovation-priority fractional-order accumulation includes the following steps:

[0006] Step S1: Select the bond slip values ​​obtained by monofilament pull-out of basalt fibers in a bitumen matrix as a database to construct a non-negative primitive sequence. ;

[0007] Step S2: Based on the non-negative original sequence Calculate the information priority fractional-order cumulative generation sequence Neighboring mean generation sequence ;

[0008] Step S3: Construct the new information priority fractional-order cumulative grey generalized Verhulst model (NIPGGVM) and the whitening differential equation;

[0009] Step S4: Generate a sequence based on the new information priority fractional order accumulation. Neighboring mean generation sequence Constructing a matrix and The parameter vector of the gray model NIPGGVM is estimated using the least squares method.

[0010] Step S5: By discrimination The size of the parameter vector and its initial values ​​are determined by selecting the model's fitted and restored values. Substituting the corresponding time response function yields the time response sequence, and the fitted sequence of the model is obtained by cumulative subtraction. MAPE, or fitness function, is calculated based on the true and fitted values.

[0011] Step S6: While ensuring the best prediction result, with the goal of minimizing the MAPE value, use a genetic algorithm to find the optimal fractional-order cumulative order. and new information priority accumulation operator And repeat steps S2~S5 to obtain the bond slip prediction sequence of basalt fiber pull-out in the asphalt matrix;

[0012] Step S7: Calculate the evaluation metrics for the NIPGGVM model and the comparison model, including: relative error, average relative error, root mean square error ratio, small error probability, and coefficient of determination.

[0013] Preferably, in step S1, let The database consists of a matrix sequence constructed using the bond-slip values ​​obtained from monofilament pull-out of basalt fibers in a pitch matrix.

[0014] (1.1)

[0015] In the formula, This is a non-negative primitive sequence constructed based on bond slip data from basalt fiber monofilament pull-out tests. For the first in the original sequence Data points ( ), indicating the first The bond slip value measured in the second measurement; This is the index for the data points, with values ​​1, 2, ... ; This represents the number of samples (total number of data points) in the original sequence.

[0016] Preferably, in step S2, the original matrix sequence New information priority fractional-order cumulative generation sequence Represented as:

[0017] (1.2)

[0018] In the formula, For the original sequence The generated sequence obtained after performing a fractional-order accumulation of the new information priority; To generate the first in the sequence Data points ( ); For fractional order, the cumulative order is 1. The new information priority accumulation operator.

[0019] (1.3)

[0020] In the formula, For the first in the original sequence There are 10 data points. Among them, .

[0021] Then the nearest mean generates the sequence for:

[0022] (1.4)

[0023] In the formula, To generate a sequence based on the innovation priority fractional-order cumulative generation The constructed nearest neighbor mean sequence, The first in the nearest mean sequence There are 1 data points, and the calculation formula is: .

[0024] Preferably, in step S3, the NIPGGVM model expression is:

[0025] (1.5)

[0026] In the formula, , These are the first fractional-order cumulative generation sequences of the new information priority generation sequence. and the -1 data point, ; The first in the nearest mean sequence One data point; The development coefficient; The amount of gray action; This is a constant term.

[0027] The whitening differential equation of the NIPGGVM model is:

[0028] (1.6)

[0029] In the formula, a, b, and c are the development coefficient, gray action quantity, and constant term, respectively.

[0030] Preferably, in step S4, the least squares parameter estimation vector of the grey model is represented as:

[0031] (1.7)

[0032] Its satisfaction ,in, To generate a sequence based on the new information priority fractional order cumulative generation. Neighboring mean generation sequence The constructed matrix.

[0033] Among them, matrix for An ordinal matrix, represented as:

[0034] (1.8)

[0035] In the formula, The first in the nearest mean sequence Data points .

[0036] Among them, matrix for An ordinal matrix, represented as:

[0037] (1.9)

[0038] In the formula, ( ) is the first-order difference of the information priority fractional-order cumulative generation sequence.

[0039] Preferably, in step S5, the time response expression of the NIPGGVM model is:

[0040] (1) When hour

[0041] (1.10)

[0042] In the formula, For the model, the cumulative generated sequence is the first... Predicted values ​​for each data point; represents the initial value of the original sequence; tan(⋅) and arctan(⋅) are the tangent and arctangent functions, respectively; It is the square root of the discriminant (used to distinguish different response forms).

[0043] (2) When hour

[0044] like

[0045] (1.11)

[0046] In the formula, For the model, the cumulative generated sequence is the first... Predicted values ​​for each data point; These are the initial values ​​for the original sequence; It is the square root of the discriminant (used to distinguish different response forms).

[0047] like

[0048] (1.12)

[0049] In the formula, For the model, the cumulative generated sequence is the first... Predicted values ​​for each data point; These are the initial values ​​for the original sequence; It is the square root of the discriminant (used to distinguish different response forms).

[0050] (3) When hour

[0051] like

[0052] (1.13)

[0053] In the formula, For the model, the cumulative generated sequence is the first... Predicted values ​​for each data point; These are the initial values ​​for the original sequence; It is the square root of the discriminant (used to distinguish different response forms).

[0054] like

[0055] (1.14)

[0056] In the formula, For the model, the cumulative generated sequence is the first... Predicted values ​​for each data point; These are the initial values ​​for the original sequence; It is the square root of the discriminant (used to distinguish different response forms).

[0057] After repeated subtraction and restoration, the predicted values ​​of the original sequence obtained by the NIPGGVM model are:

[0058] (1.15)

[0059] In the formula, The original sequence obtained after restoration Predicted values ​​for each data point; These are the initial values ​​for the original sequence; , For the cumulative generation sequence, the first... and the -1 predicted value.

[0060] Preferably, in step S6, in order to better satisfy the grey exponent law and the innovation-first principle in the innovation-first fractional-order cumulative grey generalized Verhulst model, it is necessary to determine the optimal fractional-order cumulative order. Sum of weights This is to improve the smoothness of the preprocessed data, thereby achieving optimal fitting and prediction results. Here, the fractional-order cumulative order is used. Sum of weights The optimal selection can be achieved by establishing a nonlinear optimization model consisting of the objective function shown in equation (1.16) and the constraints shown in equation (1.17):

[0061] (1.16)

[0062] In the formula, MAPE is the mean absolute percentage error (used to evaluate model accuracy). The fractional-order accumulation order and the innovation-first accumulation operator to be optimized; The original sequence obtained after restoration Predicted values ​​for each data point; For the original sequence The actual value of each data point ( =1,2,⋯,i).

[0063] (1.17)

[0064] In the formula, For the model, the cumulative generated sequence is the first... Predicted values ​​for each data point; The original sequence obtained after restoration Predicted values ​​for each data point.

[0065] By employing a genetic algorithm to solve the aforementioned nonlinear optimization problem, the optimal fractional-order cumulative order is obtained. and new information priority accumulation operator Repeat steps S2 to S5 to obtain the predicted sequence of bond slip of basalt fibers pulled out of the asphalt matrix.

[0066] Preferably, in step S7, for the gray model and all contrast models, the following applies:

[0067] Relative error calculation formula:

[0068] (1.18)

[0069] In the formula, For the first The relative error of each data point , The predicted and actual values ​​of the k-th data point.

[0070] Formula for calculating average relative error:

[0071] (1.19)

[0072] In the formula, MAPE is the mean relative error (the average of the relative errors of all data points).

[0073] Formula for calculating the mean squared error ratio:

[0074] (1.20)

[0075] In the formula, , These are the mean square errors of the original sequence and the residual sequence, respectively. This is the average value of the original sequence; This represents the average value of the residual sequence.

[0076] Formula for calculating the probability of small error:

[0077] (1.21)

[0078] In the formula, P is the probability of small error (an indicator for evaluating model accuracy). For the first The relative error of each data point; This represents the average value of the residual sequence; denoted as the mean squared error of the original sequence.

[0079] Formula for calculating the coefficient of determination:

[0080] (1.22)

[0081] In the formula, The coefficient of determination (measures the goodness of fit of the model; the closer the value is to 1, the better the fit). , No. Predicted and actual values ​​for each data point; This represents the average value of the original sequence.

[0082] Compared with the prior art, the present invention has the following beneficial effects:

[0083] 1. This invention, by introducing an innovation-first fractional-order accumulation operator, constructs the NIPFGGVM model, achieving first-order accuracy in predicting the bond slip of basalt fibers. The average relative error of basalt fibers is reduced by 66.18% compared to the Popovics model, with a goodness-of-fit R0. 2With a maximum value of 0.9850, it can accurately capture the elastic phase, peak point, and attenuation characteristics of interfacial bonding and slippage.

[0084] 2. This invention addresses the characteristics of small sample size and strong nonlinearity in interfacial mechanical data during monofilament pull-out tests. The model effectively handles the uncertainty of the data through an innovation-priority fractional-order accumulation operator, and has a good predictive ability for the evolution of interfacial properties of basalt fibers in asphalt matrix. It can reflect the influence of physical properties such as fiber modulus and surface morphology on interfacial stress transmission.

[0085] 3. Compared with traditional grey Verhulst model (GVM) and grey generalized Verhulst model (GGVM), the NIPFGGVM has a lower root mean square error ratio and a higher probability of small errors. It avoids the problems of insufficient fit in the nonlinear segment and "drift" of prediction results in traditional models, and provides a more reliable theoretical method for predicting the interface performance of fiber-reinforced asphalt concrete. Attached Figure Description

[0086] Figure 1 This is a graph showing the comparison between the fitted values ​​and actual values ​​of the six prediction models of this invention;

[0087] Figure 2 This is a distribution diagram of the relative error results of the six models of this invention;

[0088] Figure 3 The six models R of this invention 2 picture. Detailed Implementation

[0089] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings, so that those skilled in the art can better understand the advantages and features of the present invention, thereby making a clearer definition of the scope of protection of the present invention. The embodiments described in this invention are only some embodiments of the present invention, not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0090] Example:

[0091] This implementation case selects literature ( https: / / doi.org / 10.1016 / j.conbuildmat.2024.134873 The pull-out test data of basalt fiber asphalt concrete composite material were used to verify the results. This literature provides slip-bond stress data at a loading rate of 1 mm / min and a temperature of 25 degrees Celsius, covering the elastic stage, peak point, and decay stage, and exhibiting typical nonlinear characteristics.

[0092] A fiber-reinforced bitumen bond-slip prediction method based on innovation-priority fractional-order accumulation includes the following steps:

[0093] Step S1: Select the bond slip values ​​obtained by monofilament pull-out of basalt fibers in a bitumen matrix as a database to construct a non-negative primitive sequence. ;

[0094] Step S2: Based on the non-negative original sequence Calculate the information priority fractional-order cumulative generation sequence Neighboring mean generation sequence ;

[0095] Step S3: Construct the new information priority fractional-order cumulative grey generalized Verhulst model (NIPGGVM) and the whitening differential equation;

[0096] Step S4: Generate a sequence based on the new information priority fractional order accumulation. Neighboring mean generation sequence Constructing a matrix and The parameter vector of the gray model NIPGGVM is estimated using the least squares method.

[0097] Step S5: By discrimination The size of the parameter vector and its initial values ​​are determined by selecting the model's fitted and restored values. Substituting the corresponding time response function yields the time response sequence, and the fitted sequence of the model is obtained by cumulative subtraction. MAPE, or fitness function, is calculated based on the true and fitted values.

[0098] Step S6: While ensuring the best prediction result, with the goal of minimizing the MAPE value, use a genetic algorithm to find the optimal fractional-order cumulative order. and new information priority accumulation operator And repeat steps S2~S5 to obtain the bond slip prediction sequence of basalt fiber pull-out in the asphalt matrix;

[0099] Step S7: Calculate the evaluation metrics for the NIPGGVM model and the comparison model, including: relative error, average relative error, root mean square error ratio, small error probability, and coefficient of determination.

[0100] Preferably, in step S1, let The database consists of a matrix sequence constructed using the bond-slip values ​​obtained from monofilament pull-out of basalt fibers in a pitch matrix.

[0101] (1.1)

[0102] In the formula, This is a non-negative primitive sequence constructed based on bond slip data from basalt fiber monofilament pull-out tests. For the first in the original sequence Data points ( ), indicating the first The bond slip value measured in the second measurement; This is the index for the data points, with values ​​1, 2, ... ; This represents the number of samples (total number of data points) in the original sequence.

[0103] Preferably, in step S2, the original matrix sequence New information priority fractional-order cumulative generation sequence Represented as:

[0104] (1.2)

[0105] In the formula, For the original sequence The generated sequence obtained after performing a fractional-order accumulation of the new information priority; To generate the first in the sequence Data points ( ); For fractional order, the cumulative order is 1. The new information priority accumulation operator.

[0106] (1.3)

[0107] In the formula, For the first in the original sequence There are 10 data points. Among them, .

[0108] Then the nearest mean generates the sequence for:

[0109] (1.4)

[0110] In the formula, To generate a sequence based on the innovation priority fractional-order cumulative generation The constructed nearest neighbor mean sequence, The first in the nearest mean sequence There are 1 data points, and the calculation formula is: .

[0111] Preferably, in step S3, the NIPGGVM model expression is:

[0112] (1.5)

[0113] In the formula, , These are the first fractional-order cumulative generation sequences of the new information priority generation sequence. and the -1 data point, ; The first in the nearest mean sequence One data point; The development coefficient; The amount of gray action; This is a constant term.

[0114] The whitening differential equation of the NIPGGVM model is:

[0115] (1.6)

[0116] In the formula, a, b, and c are the development coefficient, gray action quantity, and constant term, respectively.

[0117] Preferably, in step S4, the least squares parameter estimation vector of the grey model is represented as:

[0118] (1.7)

[0119] Its satisfaction ,in, To generate a sequence based on the new information priority fractional order cumulative generation. Neighboring mean generation sequence The constructed matrix.

[0120] Among them, matrix for An ordinal matrix, represented as:

[0121] (1.8)

[0122] In the formula, The first in the nearest mean sequence Data points .

[0123] Among them, matrix for An ordinal matrix, represented as:

[0124] (1.9)

[0125] In the formula, ( ) is the first-order difference of the information priority fractional-order cumulative generation sequence.

[0126] Preferably, in step S5, the time response expression of the NIPGGVM model is:

[0127] (1) When hour

[0128] (1.10)

[0129] In the formula, For the model, the cumulative generated sequence is the first... Predicted values ​​for each data point; represents the initial value of the original sequence; tan(⋅) and arctan(⋅) are the tangent and arctangent functions, respectively; It is the square root of the discriminant (used to distinguish different response forms).

[0130] (2) When hour

[0131] like

[0132] (1.11)

[0133] In the formula, For the model, the cumulative generated sequence is the first... Predicted values ​​for each data point; These are the initial values ​​for the original sequence; It is the square root of the discriminant (used to distinguish different response forms).

[0134] like

[0135] (1.12)

[0136] In the formula, For the model, the cumulative generated sequence is the first... Predicted values ​​for each data point; These are the initial values ​​for the original sequence; It is the square root of the discriminant (used to distinguish different response forms).

[0137] (3) When hour

[0138] like

[0139] (1.13)

[0140] In the formula, For the model, the cumulative generated sequence is the first... Predicted values ​​for each data point; These are the initial values ​​for the original sequence; It is the square root of the discriminant (used to distinguish different response forms).

[0141] like

[0142] (1.14)

[0143] In the formula, For the model, the cumulative generated sequence is the first... Predicted values ​​for each data point; These are the initial values ​​for the original sequence; It is the square root of the discriminant (used to distinguish different response forms).

[0144] After repeated subtraction and restoration, the predicted values ​​of the original sequence obtained by the NIPGGVM model are:

[0145] (1.15)

[0146] In the formula, The original sequence obtained after restoration Predicted values ​​for each data point; These are the initial values ​​for the original sequence; , For the cumulative generation sequence, the first... and the -1 predicted value.

[0147] Preferably, in step S6, in order to better satisfy the grey exponent law and the innovation-first principle in the innovation-first fractional-order cumulative grey generalized Verhulst model, it is necessary to determine the optimal fractional-order cumulative order. Sum of weights This is to improve the smoothness of the preprocessed data, thereby achieving optimal fitting and prediction results. Here, the fractional-order cumulative order is used. Sum of weights The optimal selection can be achieved by establishing a nonlinear optimization model consisting of the objective function shown in equation (1.16) and the constraints shown in equation (1.17):

[0148] (1.16)

[0149] In the formula, MAPE is the mean absolute percentage error (used to evaluate model accuracy). The parameters to be optimized are (fractional order of accumulation and innovation-first accumulation operator). The original sequence obtained after restoration Predicted values ​​for each data point; For the original sequence The actual value of each data point ( =1,2,⋯,i).

[0150] (1.17)

[0151] In the formula, For the model, the cumulative generated sequence is the first... Predicted values ​​for each data point; The original sequence obtained after restoration Predicted values ​​for each data point.

[0152] By employing a genetic algorithm to solve the aforementioned nonlinear optimization problem, the optimal fractional-order cumulative order is obtained. and new information priority accumulation operator Repeat steps S2 to S5 to obtain the predicted sequence of bond slip of basalt fibers pulled out of the asphalt matrix.

[0153] Preferably, in step S7, the comparison models include: the traditional grey Verhulst model (GVM), the grey generalized Verhulst model (GGVM), the fractional-order cumulative grey generalized Verhulst model (FGGVM), the innovation-first cumulative grey Verhulst model (NIPGGVM), and the literature ( https: / / doi.org / 10.1016 / j.conbuildmat.2024.134873 The Popovics empirical formula used is as follows: For the grey model and all contrast models, we have:

[0154] Relative error calculation formula:

[0155] (1.18)

[0156] In the formula, For the first The relative error of each data point , The predicted and actual values ​​of the k-th data point.

[0157] Formula for calculating average relative error:

[0158] (1.19)

[0159] In the formula, MAPE is the mean relative error (the average of the relative errors of all data points).

[0160] Formula for calculating the mean squared error ratio:

[0161] (1.20)

[0162] In the formula, , These are the mean square errors of the original sequence and the residual sequence, respectively. This is the average value of the original sequence; This represents the average value of the residual sequence.

[0163] Formula for calculating the probability of small error:

[0164] (1.21)

[0165] In the formula, P is the probability of small error (an indicator for evaluating model accuracy). For the first The relative error of each data point; This represents the average value of the residual sequence; denoted as the mean squared error of the original sequence.

[0166] Formula for calculating the coefficient of determination:

[0167] (1.22)

[0168] In the formula, The coefficient of determination (measures the goodness of fit of the model; the closer the value is to 1, the better the fit). , No. Predicted and actual values ​​for each data point; This represents the average value of the original sequence.

[0169] The performance comparison results of each model are shown in the table below:

[0170] Table 1 Model Performance Comparison Table

[0171]

[0172] In summary, this invention has a good predictive ability for the evolution of interfacial properties of basalt fibers in asphalt matrix, and can reflect the influence of physical properties such as fiber modulus and surface morphology on interfacial stress transmission, providing a more reliable theoretical method for predicting the interfacial properties of fiber-reinforced asphalt concrete.

[0173] The descriptions and practices disclosed in this invention are readily apparent and understandable to those skilled in the art, and various modifications and refinements can be made without departing from the principles of this invention. Therefore, any modifications or improvements made without departing from the spirit of this invention should also be considered within the scope of protection of this invention.

Claims

1. A fiber-reinforced bitumen bond-slip prediction method based on innovation-priority fractional-order accumulation, characterized in that, Includes the following steps: Step S1: Select the bond slip values ​​obtained by monofilament pull-out of basalt fibers in a bitumen matrix as a database to construct a non-negative primitive sequence. ; Step S2: Based on the non-negative original sequence Calculate the information priority fractional-order cumulative generation sequence Neighboring mean generation sequence ; Step S3: Construct the new information priority fractional-order cumulative grey generalized Verhulst model NIPGGVM and the whitening differential equation; Step S4: Generate a sequence based on the new information priority fractional order accumulation. Neighboring mean generation sequence Constructing a matrix and The parameter vector of the gray model NIPGGVM is estimated using the least squares method. Step S5: By discrimination The size of the parameter vector and its initial values ​​are determined by selecting the model's fitted and restored values. Substituting the corresponding time response function yields the time response sequence, and the fitted sequence of the model is obtained by cumulative subtraction. MAPE, or fitness function, is calculated based on the true and fitted values. Step S6: While ensuring the best prediction result, with the goal of minimizing the MAPE value, use a genetic algorithm to find the optimal fractional-order cumulative order. and new information priority accumulation operator And repeat steps S2~S5 to obtain the bond slip prediction sequence of basalt fiber pull-out in the asphalt matrix; Step S7: Calculate the evaluation metrics for the NIPGGVM model and the comparison model, including: relative error, average relative error, root mean square error ratio, small error probability, and coefficient of determination.

2. The fiber-reinforced bituminous bond-slip prediction method based on innovation priority fractional-order accumulation as described in claim 1, characterized in that, In step S1, let The database consists of a matrix sequence constructed using the bond-slip values ​​obtained from monofilament pull-out of basalt fibers in a pitch matrix. （1.2） In the formula, This is a non-negative primitive sequence constructed based on bond slip data from basalt fiber monofilament pull-out tests. For the first in the original sequence Data points, , indicating the first The bond slip value measured in the second measurement; This is the index for the data points, with values ​​1, 2, ... ; This represents the number of samples in the original sequence.

3. The fiber-reinforced bituminous bond-slip prediction method based on innovation priority fractional-order accumulation as described in claim 1, characterized in that, In step S2, the original matrix sequence New information priority fractional-order cumulative generation sequence Represented as: （1.2） In the formula, For the original sequence The generated sequence obtained after performing a fractional-order accumulation of the new information priority; To generate the first in the sequence Data points, ; For fractional order, the cumulative order is 1. For the new information priority accumulation operator; （1.3） In the formula, For the first in the original sequence There are data points, among which, ; Then the nearest mean generation sequence for: （1.4） In the formula, To generate a sequence based on the innovation priority fractional-order cumulative generation. The constructed nearest neighbor mean sequence, The first in the nearest mean sequence There are 1 data points, and the calculation formula is: .

4. The fiber-reinforced bituminous bond-slip prediction method based on innovation priority fractional-order accumulation as described in claim 1, characterized in that, In step S3, the NIPGGVM model expression is: （1.5） In the formula, , These are the first fractional-order cumulative generation sequences of the new information priority generation sequence. and the -1 data point, ; The first in the nearest mean sequence One data point; The development coefficient; The amount of gray action; For constant terms; The whitening differential equation of the NIPGGVM model is: （1.6） In the formula, a, b, and c are the development coefficient, gray action quantity, and constant term, respectively.

5. The fiber-reinforced bituminous bond-slip prediction method based on innovation priority fractional-order accumulation as described in claim 1, characterized in that, In step S4, the least squares parameter estimation vector of the grey model is represented as: （1.7） Its satisfaction ,in, To generate a sequence based on the new information priority fractional order cumulative generation Neighboring mean generation sequence The constructed matrix; Among them, matrix for An ordinal matrix, represented as: （1.8） In the formula, The first in the nearest mean sequence Data points ; Among them, matrix for An ordinal matrix, represented as: （1.9） In the formula, , , is the first-order difference of the information priority fractional-order cumulative generation sequence.

6. The fiber-reinforced bituminous bond-slip prediction method based on innovation priority fractional-order accumulation as described in claim 1, characterized in that, In step S5, the time response of the NIPGGVM model is: (1) When hour （1.10） In the formula, For the model, the cumulative generated sequence is the first... Predicted values ​​for each data point; represents the initial value of the original sequence; tan(⋅) and arctan(⋅) are the tangent and arctangent functions, respectively; The square root of the discriminant; (2) When hour like （1.11） In the formula, For the model, the cumulative generated sequence is the first... Predicted values ​​for each data point; These are the initial values ​​for the original sequence; The square root of the discriminant; like （1.12） In the formula, For the model, the cumulative generated sequence is the first... Predicted values ​​for each data point; These are the initial values ​​for the original sequence; The square root of the discriminant; (3) When hour like （1.13） In the formula, For the model, the cumulative generated sequence is the first... Predicted values ​​for each data point; These are the initial values ​​for the original sequence; The square root of the discriminant; like （1.14） In the formula, For the model, the cumulative generated sequence is the first... Predicted values ​​for each data point; These are the initial values ​​for the original sequence; The square root of the discriminant; After repeated subtraction and restoration, the predicted values ​​of the original sequence obtained by the NIPGGVM model are: （1.15） In the formula, The original sequence obtained after restoration Predicted values ​​for each data point; These are the initial values ​​for the original sequence; , For the cumulative generation sequence, the first... and the -1 predicted value.

7. The fiber-reinforced bituminous bond-slip prediction method based on innovation priority fractional-order accumulation as described in claim 1, characterized in that, In step S6, the fractional order cumulative order is... Sum of weights The optimal selection can be achieved by establishing a nonlinear optimization model consisting of the objective function shown in equation (1.16) and the constraints shown in equation (1.17): （1.16） In the formula, MAPE is the mean absolute percentage error; The fractional-order accumulation order and the innovation-first accumulation operator to be optimized; The original sequence obtained after restoration Predicted values ​​for each data point; For the original sequence The actual value of each data point =1,2,⋯,i; （1.17） In the formula, For the model, the cumulative generated sequence is the first... Predicted values ​​for each data point; The original sequence obtained after restoration Predicted values ​​for each data point; By employing a genetic algorithm to solve the aforementioned nonlinear optimization problem, the optimal fractional-order cumulative order is obtained. and new information priority accumulation operator Repeat steps S2 to S5 to obtain the predicted sequence of bond slip of basalt fibers pulled out of the asphalt matrix.

8. The fiber-reinforced bituminous bond-slip prediction method based on innovation priority fractional-order accumulation as described in claim 1, characterized in that, In step S7, for the gray model and all contrast models, we have: Relative error calculation formula: （1.18） In the formula, For the first The relative error of each data point , The predicted and actual values ​​of the k-th data point; Formula for calculating average relative error: （1.19） In the formula, MAPE is the average relative error; Formula for calculating the mean squared error ratio: （1.20） In the formula, , These are the mean square errors of the original sequence and the residual sequence, respectively. This is the average value of the original sequence; This represents the average value of the residual sequence; Formula for calculating the probability of small error: （1.21） In the formula, P is the probability of a small error; For the first The relative error of each data point; This represents the average value of the residual sequence; The mean squared error of the original sequence; Formula for calculating the coefficient of determination: （1.22） In the formula, The coefficient of determination; , No. Predicted and actual values ​​for each data point; This represents the average value of the original sequence.

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