A method for inverse analysis of pavement temperature field parameters and data fusion

Abstract

This invention discloses a method for inverting pavement temperature field parameters and fusing data. Based on heat conduction theory, a partial differential equation for the pavement temperature field is established. An interpolation algorithm is used to characterize the initial conditions, boundary conditions, and measurement point temperatures of the pavement temperature field. The solution domain is normalized, and random sampling is used to generate sampling point coordinates within the pavement temperature solution domain and at its boundaries. These coordinates are used as input variables for a deep neural network. Based on the sampling point coordinates, a deep neural network and an automatic differentiation algorithm are combined to obtain normalized operator values for the sampling points. The measured temperature data is integrated with the initial and boundary conditions, and a total loss function for the deep neural network is constructed using a weighted summation method. The deep neural network is trained using gradient descent and the total loss function, and adaptive sampling is performed based on the partial differential equation loss of the current neural network, ultimately achieving pavement temperature field prediction. This invention achieves high-precision prediction of the pavement temperature field.

Description

Technical Field

[0001] The invention relates to the technical field of road engineering research, and in particular discloses a road surface temperature field parameter inversion and data fusion method. Background Art

[0002] The temperature field is a prerequisite for evaluating pavement performance. On the one hand, temperature causes thermal expansion and contraction of the material, leading to thermal cracking. On the other hand, asphalt concrete is a viscoelastic-plastic material, which can develop rutting or cracking under the influence of temperature and vehicle load. Furthermore, road surface temperature is correlated with the urban heat island effect and pavement skid resistance. Therefore, predicting the pavement temperature field is crucial for mitigating the summer urban heat island effect and improving winter driving safety.

[0003] Currently, pavement temperature field prediction methods mainly fall into two categories: physics-driven methods and data-driven methods. Physics-driven methods are based on the heat conduction equation and do not require internal pavement temperature data. They mainly include analytical and numerical methods. Analytical methods use the separation of variables and integral transformation methods to solve the pavement heat conduction equation. These methods require the introduction of empirical coefficients to account for nonlinear boundary conditions. Numerical methods use the finite element method (FEM), finite difference method (FDM), and finite volume method (FVM) to solve the pavement heat conduction equation. These methods can account for nonlinear boundary conditions and are widely used in pavement temperature prediction. However, both analytical and numerical methods ignore the discrepancy between physical laws and reality, resulting in limited prediction accuracy.

[0004] Data-driven methods primarily include empirical formulas and big data artificial intelligence (AI) methods. The empirical formula method expresses pavement temperature as a function of depth, latitude, and air temperature. The empirical formula method does not account for the effects of solar radiation or the thermophysical properties of road materials. Consequently, its generalization ability is limited, requiring regular recalibration, and it struggles to accurately predict abnormal temperature events. Big data AI methods primarily include support vector regression (SVR), regression trees (RT), Gaussian process regression (GPR), random forests (RF), fully connected neural networks (FNN), convolutional neural networks (CNN), gated recurrent units (CRU), recurrent neural networks (RNN), and ensemble deep learning (EDL). While big data AI methods significantly improve prediction accuracy in specific areas compared to empirical formula methods, they rely on large amounts of observational data and ignore the influence of pavement structure combinations and the thermophysical properties of road materials. Consequently, their accuracy is dependent on the size of the dataset, and they struggle to balance interpolation and extrapolation accuracy.

[0005] In summary, the physical-driven approach, based on the heat conduction equation, does not require actual measurements of the internal pavement temperature, making it highly universal but with limited prediction accuracy. The data-driven approach offers high accuracy in specific regions, but it ignores the influence of pavement structure combinations and the thermophysical properties of road materials. Its accuracy depends on the size of the dataset, its generalization is limited, and it is not suitable for sparse datasets.

[0006] Therefore, it is urgent to propose a new method to integrate the heat conduction equation and measured data to predict the pavement temperature field. Summary of the Invention

[0007] The present invention provides a pavement temperature field parameter inversion and data fusion method, which aims to solve at least one defect existing in the above-mentioned existing pavement temperature field prediction method.

[0008] The present invention relates to a pavement temperature field parameter inversion and data fusion method, comprising the following steps:

[0009] Based on the heat conduction theory, the road surface temperature field is established to solve the partial differential equation;

[0010] Based on the interpolation algorithm, the initial conditions, boundary conditions and measurement point temperatures of the road surface temperature field are characterized;

[0011] Normalize the solution domain and generate sampling point coordinates in the road surface temperature solution domain and at the boundary based on the random sampling method. The sampling point coordinates are used as input variables of the deep neural network.

[0012] Based on the coordinates of the sampling points, the normalized operator values of the sampling points are obtained by combining a deep neural network and an automatic differentiation algorithm. The total loss function of the deep neural network is constructed by combining the initial and boundary conditions and integrating the measured temperature data through a weighted summation method.

[0013] Based on gradient descent and total loss function, deep neural network training is carried out, and adaptive sampling is performed according to the partial differential equation loss of the current neural network to finally realize the road surface temperature field prediction.

[0014] Furthermore, based on the heat conduction theory, in the step of establishing the road surface temperature field to solve the partial differential equation, the solution of the road surface temperature field is simplified to a one-dimensional heat conduction problem. The one-dimensional heat conduction partial differential equation is as follows:

[0015]

[0016] Among them, T i is the temperature of the i-th layer; t is the time; z is the coordinate of the calculation point, representing the vertical distance between the calculation point and the road surface; z i and z i+1 are the coordinates of the top and bottom of the i-th layer respectively; α i is the thermal conductivity of the i-th layer.

[0017] Furthermore, based on the heat conduction theory, in the step of establishing the road surface temperature field to solve the partial differential equation, the bottom boundary condition of the road surface temperature field is:

[0018]

[0019] Where Tn is the temperature at the bottom of the road surface temperature field; t is time; z is the coordinate of the calculation point, representing the vertical distance from the calculation point to the road surface; z n+1 is the bottom coordinate of the pavement structure;

[0020] The top boundary condition of the pavement temperature field is:

[0021]

[0022] Where T1 is the temperature at the bottom of the road surface temperature field; t is time; z is the coordinate of the calculation point, representing the vertical distance from the calculation point to the road surface; q c is the heat flux related to convection; q ns and q nl are the net solar radiation and net longwave radiation of the road surface respectively; h c is the convective heat transfer coefficient; V W is the wind speed; σ is the Stefan-Boltzmann constant, ε is the surface emissivity, Ta and T0 are the air temperature and absolute zero, respectively.

[0023] Furthermore, based on the interpolation algorithm, in the step of characterizing the initial conditions, boundary conditions, and measurement point temperatures of the road surface temperature field, triangular interpolation is used to characterize the road surface boundary conditions and measurement point temperatures. The interpolation results of air temperature and net solar radiation are:

[0024]

[0025] Among them, h (t) is the interpolation function, a0 is the interpolation coefficient, a m is the interpolation coefficient, k is the cumulative coefficient (representing the kth term in the summation symbol), l is the cumulative coefficient (representing the lth term in the summation symbol), and m is half the number of segment intervals; t a is the analysis time; h l is the endpoint function value of the lth subinterval; a k and b k is the interpolation coefficient; is the intermediate variable and π is the ratio of circumference to circumference.

[0026] Furthermore, the solution domain is normalized, and sampling point coordinates are generated in the road surface temperature solution domain and at the boundary based on the random sampling method. In the step of using the sampling point coordinates as input variables of the deep neural network, the generated sampling point coordinates are:

[0027]

[0028] Among them, z' ij and t' ij are the normalized sampling point coordinates and time respectively; and are the coordinates of the bottom and top of the i-th layer respectively; t a and z a Total analysis time and total depth of pavement structure respectively; Representatives in and Generate n uniformly distributed random numbers between 0 and 1; rand(0,1,n) represents generating n uniformly distributed random numbers between 0 and 1; z' i and t' i are the n-dimensional normalized sampling point coordinates and time series of the i-th layer of road surface; z'(j) and t'(j) represent the time series from z' i and t' i Select the jth element from .

[0029] Furthermore, the total loss function includes the partial differential equation loss term Initial condition loss term Boundary condition loss term Observation point loss and interface loss term Based on the sampling point coordinates, the deep neural network and automatic differentiation algorithm are combined to obtain the normalized operator value of the sampling point. In the step of constructing the total loss function of the deep neural network through the weighted summation method by combining the initial conditions and boundary conditions and integrating the measured temperature data, the total loss function is calculated by the following formula:

[0030]

[0031] Among them, MSE tol is the total loss function, is the loss term of the partial differential equation, is the boundary condition loss term, is the initial condition loss term, is the interface loss term, is the observation point loss term, They are and The weight in the i-th layer of pavement structure; m is the total number of pavement structure layers.

[0032] Furthermore, the partial differential equation loss term Calculated by the following formula:

[0033]

[0034] in, is the number of sampling points of the partial differential equation corresponding to the i-th layer of the pavement structure, F(T(z ij ,t ij θ i )) is the partial differential equation operator of the output variable of the deep neural network; f(z ij ,t ij ) is the partial differential equation operator satisfied by the theoretical solution of the road surface temperature field; θ i =(W i ,b i ), is the parameter of the deep neural network of the i-th layer of pavement structure; T(z ij ,t ij ) is the theoretical solution of the road surface temperature field; T(z ij ,t ij θ i ) is the output of the deep neural network.

[0035] Furthermore, the initial condition loss term and boundary condition loss terms Calculated by the following formula:

[0036]

[0037] in, is the number of sampling points of initial conditions in the i-th layer of pavement structure; T(z ij ,t ij θ i ) is the output of the deep neural network, T(z ij ,t ij ) is the theoretical solution of the road surface temperature field, θ i =(W i ,b i ), is the parameter of the deep neural network of the i-th layer of pavement structure; G(T(z ij ,t;θ i )) is the boundary condition operator of the output variable of the deep neural network; g(z ij ,t ij ) is the boundary condition operator satisfied by the theoretical solution of the pavement temperature field.

[0038] Furthermore, the observation point loss term and interface loss term Calculated by the following formula:

[0039]

[0040] in, is the number of interface loss points in the corresponding i-th layer of pavement structure; is the number of lost observation points in the pavement structure of the corresponding layer i; L(T(z ij ,t ij θ i ))、Q(T(z ij ,t ij θ i )) are the interface operator and observation point operator of the deep neural network output variable respectively; l(z ij ,t ij )、q(z ij ,t ij ) are the interface operator and observation point operator satisfied by the theoretical solution of the pavement temperature field.

[0041] Furthermore, based on gradient descent and total loss function, deep neural network training is carried out, and adaptive sampling is performed according to the partial differential equation loss of the current neural network. Finally, in the step of realizing the road surface temperature field prediction, adaptive sampling is performed according to the partial differential equation residual of the neural network. The partial differential equation residual is:

[0042] R ij =F(T(z ij ,t ij θ i ))-f(z ij ,t ij )

[0043] Among them, R ij is the residual of the jth sampling point on the i-th road surface, F(T(z ij ,t ij θ i )) is the partial differential equation operator of the output variable of the deep neural network; f(z ij ,t ij ) is the partial differential equation operator satisfied by the theoretical solution of the road surface temperature field;

[0044] Adaptive sampling is:

[0045]

[0046] Among them, k and c are sampling hyperparameters, R k (z, t) is the residual of the partial differential equation calculated by the neural network; P(z, t) is the probability density function proportional to the residual of the partial differential equation; E is R k The expectation of (z,t), is the sampling probability in region S.

[0047] The beneficial effects achieved by the present invention are:

[0048] The present invention provides a method for inverting and fusion of pavement temperature field parameters. Based on heat conduction theory, a pavement temperature field is established to solve partial differential equations. Based on an interpolation algorithm, the initial conditions, boundary conditions, and measurement point temperatures of the pavement temperature field are characterized. The solution domain is normalized. Based on a random sampling method, sampling point coordinates are generated in the pavement temperature solution domain and at the boundary, and the sampling point coordinates are used as input variables of a deep neural network. Based on the sampling point coordinates, a deep neural network and an automatic differentiation algorithm are combined to obtain normalized operator values of the sampling points. Combined with the initial conditions and the boundary conditions, the measured temperature data is fused, and a total loss function of the deep neural network is constructed by a weighted summation method. Based on gradient descent and the total loss function, deep neural network training is carried out, and adaptive sampling is performed according to the partial differential equation loss of the current neural network, ultimately achieving pavement temperature field prediction. The pavement temperature field parameter inversion and data fusion method provided by the present invention has the following advantages over the physical-driven method and data-driven method used in traditional pavement temperature field prediction:

[0049] (1) The physical driven method uses analytical or numerical methods to solve the heat conduction equation, which cannot integrate the measured temperature data and ignores the differences between physical laws and actual conditions. Therefore, the prediction accuracy is limited.

[0050] (2) Data-driven methods use empirical formulas or big data artificial intelligence methods to predict pavement temperature fields, ignoring the influence of pavement structure combinations and the thermal physical properties of road materials. Their accuracy depends on the size of the dataset, their generalization ability is limited, and they are not suitable for sparse datasets.

[0051] (3) By integrating the heat conduction equation with measured temperature data, the present invention can achieve pavement temperature field prediction with higher accuracy than physical-driven models by integrating measured temperature data of any scale. Furthermore, due to the integration of the heat conduction equation, the pavement temperature field parameter inversion and data fusion method provided by the present invention has higher generalization capabilities than data-driven methods, enabling high-precision prediction of pavement temperature fields with sparse datasets.

[0052] (4) Compared with the physical-driven and data-driven methods, the pavement temperature field parameter inversion and data fusion method provided by the present invention can invert the missing parameters when some parameters are missing, and achieve high-precision prediction of the pavement temperature field. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 A schematic flow chart of an embodiment of a method for inverting and fusion of pavement temperature field parameters provided by the present invention;

[0054] Figure 2 This is a diagram of the temperature measurement and interpolation results in the pavement temperature field parameter inversion and data fusion method provided by the present invention;

[0055] Figure 3 This is a diagram of the net solar radiation measurement and interpolation results in the pavement temperature field parameter inversion and data fusion method provided by the present invention;

[0056] Figure 4 This is a schematic diagram of the structure of the first deep neural network architecture in the pavement temperature field parameter inversion and data fusion method provided by the present invention;

[0057] Figure 5 This is a structural diagram of the second deep neural network architecture in the pavement temperature field parameter inversion and data fusion method provided by the present invention;

[0058] Figure 6 This is a structural diagram of the third deep neural network architecture in the pavement temperature field parameter inversion and data fusion method provided by the present invention;

[0059] Figure 7 The temperature field diagram of the first working condition in the pavement temperature field parameter inversion and data fusion method provided by the present invention;

[0060] Figure 8 The temperature map of the first working condition measuring point in the pavement temperature field parameter inversion and data fusion method provided by the present invention;

[0061] Figure 9 The temperature field diagram of the second working condition in the pavement temperature field parameter inversion and data fusion method provided by the present invention;

[0062] Figure 10 The temperature map of the second working condition measuring point in the pavement temperature field parameter inversion and data fusion method provided by the present invention;

[0063] Figure 11 The temperature field diagram of the third working condition in the pavement temperature field parameter inversion and data fusion method provided by the present invention;

[0064] Figure 12 The temperature map of the third working condition measuring point in the pavement temperature field parameter inversion and data fusion method provided by the present invention;

[0065] Figure 13 This is a convergence curve diagram of the convective heat transfer coefficient in the pavement temperature field parameter inversion and data fusion method provided by the present invention. DETAILED DESCRIPTION

[0066] In order to better understand the above technical solution, the above technical solution will be described in detail below with reference to the accompanying drawings and specific implementation methods.

[0067] like Figure 1 As shown, the first embodiment of the present invention proposes a road surface temperature field parameter inversion and data fusion method, including the following steps:

[0068] Step S100: Based on the heat conduction theory, a road surface temperature field is established to solve the partial differential equation.

[0069] Based on the heat conduction equation, the assumption of continuity of interlayer temperature and heat flow, and the pavement temperature boundary conditions, the partial differential equation for solving the pavement temperature field and the boundary conditions are established.

[0070] Step S200: Characterize the initial conditions, boundary conditions and measurement point temperatures of the road surface temperature field based on an interpolation algorithm.

[0071] Based on triangular interpolation, Chebyshev interpolation or piecewise interpolation algorithms, the initial conditions of the road surface temperature field, boundary conditions (solar radiation and air temperature) and temperature characterization of measuring points are realized.

[0072] Step S300: Normalize the solution domain, generate sampling point coordinates in the road surface temperature solution domain and at the boundary based on a random sampling method, and use the sampling point coordinates as input variables of the deep neural network.

[0073] Normalize the solution domain, generate sampling point coordinates in the road surface temperature solution domain and at the boundary based on the random sampling method, and use the sampling point coordinates as input variables of the deep neural network.

[0074] Step S400: Based on the sampling point coordinates, a deep neural network and an automatic differentiation algorithm are combined to obtain the normalized operator value of the sampling point; combined with the initial conditions and boundary conditions, the measured temperature data are integrated, and the total loss function of the deep neural network is constructed by the weighted summation method.

[0075] Based on the sampling point coordinates and normalization operator obtained in step S300, a deep neural network and automatic differentiation algorithm are combined to obtain the sampling point normalization operator value. On this basis, combined with the initial conditions and boundary conditions in step 2, the measured temperature data is integrated, and the total loss function of the deep neural network is constructed through a weighted summation method. This includes the partial differential equation loss term, the initial condition loss term, the boundary condition loss term, the observation point loss term, and the interface loss term.

[0076] Step S500: Based on gradient descent and the total loss function, deep neural network training is carried out, and adaptive sampling is performed according to the partial differential equation loss of the current neural network, so as to finally realize the road surface temperature field prediction.

[0077] Based on the total loss function established in step S400, deep neural network training is carried out based on gradient descent, and adaptive sampling is performed according to the partial differential equation loss of the current neural network, ultimately achieving road surface temperature field prediction.

[0078] Further, see Figures 1 to 13This embodiment provides a method for inverting road surface temperature field parameters and fusing data. In step S100, the road surface temperature field solution is simplified to a one-dimensional heat conduction problem. The one-dimensional heat conduction partial differential equation is as follows:

[0079]

[0080] In formula (1), T i is the temperature of the i-th layer, in °C; t is the time, in h; z is the coordinate of the calculation point, representing the vertical distance from the calculation point to the road surface, in m; z i and z i+1 are the coordinates of the top and bottom of the i-th layer respectively; α i is the thermal conductivity of the i-th layer, α i The unit is m 2 / h.

[0081]

[0082] In formula (2), z i is the coordinate of the junction between the i-th layer and the i+1-th layer, in meters; is the bottom temperature of the i-th layer; is the top temperature of the i+1th layer; k i is the thermal conductivity of the i-th layer, in W / (m·℃); k i+1 is the thermal conductivity of the i+1th layer, in W / (m·℃).

[0083] This embodiment assumes that the bottom temperature gradient can be ignored, and the bottom boundary condition of the road surface temperature field is:

[0084]

[0085] In formula (3), Tn is the temperature at the bottom of the road surface temperature field; t is time; z is the coordinate of the calculation point, which represents the vertical distance from the calculation point to the road surface; z n+1 is the bottom coordinate of the pavement structure;

[0086] In this embodiment, the top boundary condition of the road surface temperature field is:

[0087]

[0088] In formula (4), T1 is the temperature at the bottom of the road surface temperature field; t is time; z is the coordinate of the calculation point, representing the vertical distance from the calculation point to the road surface; q c is the heat flux related to convection, in W / m 2 ;q ns and q nl They are the net solar radiation and net longwave radiation of the road surface, respectively, in W / m 2;h c is the convection heat transfer coefficient, the unit is W / (m 2 ℃); V W is the wind speed in m / s; σ is the Stefan-Boltzmann constant, ε is the surface emissivity, Ta and T0 are the air temperature and absolute zero, respectively. In this embodiment, ε = 0.85; T0 = 273.15°C.

[0089] The initial temperature of the road surface in this embodiment is expressed as follows:

[0090] T i (z,0)=F i (z)z i ≤z <z i+1 (5)

[0091] In formula (5), T i(z,0) is the initial temperature of the i-th layer of pavement, Fi(z) is the function expression satisfied by the initial temperature of the i-th layer of pavement, z i and z i+1 are the coordinates of the top and bottom of the i-th layer respectively.

[0092] Further, see Figures 1 to 13 This embodiment provides a method for inverting road surface temperature field parameters and fusion of data. In step S200, triangular interpolation is used to represent the road surface boundary conditions (solar radiation and air temperature) and the temperature of the measuring point. The interpolation results of air temperature and net solar radiation are:

[0093]

[0094] In formula (6), h (t) is the interpolation function, a0 is the interpolation coefficient, a m is the interpolation coefficient, k is the cumulative coefficient (representing the kth term in the summation symbol), l is the cumulative coefficient (representing the lth term in the summation symbol), and m is half the number of segment intervals; t a is the analysis time; h l is the endpoint function value of the lth subinterval; a k and b k is the interpolation coefficient; is the intermediate variable and π is the ratio of circumference to circumference.

[0095] Preferably, see Figures 1 to 13 This embodiment provides a method for inverting road surface temperature field parameters and fusion of data. In step S200, monotone piecewise cubic interpolation as shown in the following formula is used to achieve the initial road surface temperature representation.

[0096] h(t)=a0+a1(tt s )+a2(tt s )2 +a3(tt s) 3 (7)

[0097]

[0098] In formulas (7) and (8), a0, a1, a2, and a3 are interpolation coefficients; t s and t e is the start and end time of the interpolation subinterval; h s and h e is the function value at the start and end of the interpolation subinterval; h' s is the derivative value of the function at the starting moment of the interpolation subinterval.

[0099] The derivative of the function at the beginning of the first and last interpolation subintervals can be calculated as follows:

[0100]

[0101] In formula (9), h0 and h1 represent the function values at the start and end of the first interval respectively; t0 and t1 represent the start and end of the first interval respectively; h n-1 and h n Represent the function values at the start and end of the first interval respectively; t n-1 and t n Represent the start and end time of the first interval respectively.

[0102] The derivative value of the function at the beginning of the intermediate interpolation subinterval can be calculated as follows:

[0103]

[0104] In formula (10), h' k+1 is the derivative value of the function at the starting time of the k+1th interval; w1 and w2 are the weight coefficients calculated by formula (11); b min and b max is an intermediate variable, whose value is calculated by formula (12); Δ is the forward difference quotient operator. k is the forward difference quotient of the function at the starting time of the kth subinterval, Δh k+1 is the forward difference quotient of the function at the starting time of the k+1th subinterval.

[0105]

[0106] In formulas (11) and (12), d k is the width of the kth subinterval, d k =t k+1 -t k , tk+1 is the end time of the kth subinterval, t k is the starting time of the kth subinterval; d k+1 is the width of the k+1th subinterval, w1 and w2 are weight coefficients; b min and b max is the intermediate variable; l k is the intermediate variable, Δh k is the forward difference quotient of the function at the starting time of the kth subinterval, Δh k+1 is the forward difference quotient of the function at the starting time of the k+1th subinterval.

[0107] Further, see Figures 1 to 13 This embodiment provides a method for inverting and fusion of pavement temperature field parameters. In step S300, the coordinates are normalized according to formula (13):

[0108]

[0109] In formula (13), t' and z' are normalized time and coordinate respectively; t a and z a are the total analysis time and the total depth of the pavement structure, respectively. t is the time in h; z is the coordinate of the calculation point, representing the vertical distance from the calculation point to the road surface in m.

[0110] Normalize the differential operator according to formula (14):

[0111]

[0112] In formula (14), T is temperature, t is time, and the unit is h; z is the coordinate of the calculation point, which represents the vertical distance from the calculation point to the road surface, and the unit is m; z a is the total depth of the pavement structure, t a is the total analysis time, t' is the normalized time, and z' is the normalized calculation point coordinate.

[0113] The normalized sampling point coordinates generated by formula (15) are:

[0114]

[0115] In formula (15), z' ij and t' ij are the normalized sampling point coordinates and time respectively; and are the coordinates of the bottom and top of the i-th layer respectively; t a and z a Total analysis time and total depth of pavement structure respectively; Representatives in and Generate n uniformly distributed random numbers between 0 and 1; rand(0,1,n) represents generating n uniformly distributed random numbers between 0 and 1; z' i and t' i are the n-dimensional normalized sampling point coordinates and time series of the i-th layer of road surface; z'(j) and t'(j) represent the time series from z' i and t' i Select the jth element from .

[0116] The relationship between the normalized sampling point coordinates and time and the sampling point coordinates and time is as follows:

[0117]

[0118] In formula (16), z' ij and t' ij is the normalized sampling point coordinate and time; z ij and z ij is the sampling point coordinate and time, z a is the total depth of the pavement structure, t a is the total analysis time.

[0119] Based on the sampling point coordinates and normalization operator obtained in step S300, use Figure 4 、 Figure 5 or Figure 6 The deep neural network shown in the figure is combined with the automatic differentiation algorithm to obtain the differential operator value of the sampling point (this embodiment uses Figure 3 The neural network shown has 4 layers and 40 neurons in each layer. On this basis, combined with the initial conditions and boundary conditions in step S200, the measured temperature data is integrated and the total loss function of the deep neural network shown in formula (17) is constructed by weighted summation method. The total loss function includes the partial differential equation loss term Initial condition loss term Boundary condition loss term Observation point loss and interface loss term The total loss function is calculated by the following formula:

[0120]

[0121] In formula (17), MSE tol is the total loss function, is the loss term of the partial differential equation, is the boundary condition loss term, is the initial condition loss term, is the interface loss term, is the observation point loss term, They are and The weight of the i-th pavement structure. m is the total number of pavement structure layers.

[0122] Furthermore, the partial differential equation loss term Calculated by the following formula:

[0123]

[0124] In formula (18), is the number of sampling points of the partial differential equation corresponding to the i-th layer of the pavement structure, F(T(z ij ,t ij θ i )) is the partial differential equation operator of the output variable of the deep neural network; f(z ij ,t ij ) is the partial differential equation operator satisfied by the theoretical solution of the road surface temperature field; θ i =(W i ,b i ), is the parameter of the deep neural network of the i-th layer of pavement structure; T(z ij ,t ij ) is the theoretical solution of the road surface temperature field; T(z ij ,t ij θ i ) is the output of the deep neural network.

[0125] Furthermore, the initial condition loss term and boundary condition loss terms Calculated by the following formula:

[0126]

[0127] In formulas (19) and (20), is the number of sampling points of initial conditions in the i-th layer of pavement structure; T(z ij ,t ij θ i ) is the output of the deep neural network, T(z ij ,t ij ) is the theoretical solution of the road surface temperature field, θ i =(W i ,b i ), is the parameter of the deep neural network of the i-th layer of pavement structure; G(T(z ij ,t;θ i )) is the boundary condition operator of the output variable of the deep neural network; g(z ij ,t ij ) is the boundary condition operator satisfied by the theoretical solution of the pavement temperature field.

[0128] Furthermore, the observation point loss term and interface loss term Calculated by the following formula:

[0129]

[0130] In formulas (21) and (22), is the number of interface loss points in the corresponding i-th layer of pavement structure; is the number of lost observation points in the pavement structure of the corresponding layer i; L(T(z ij ,t ij θ i ))、Q(T(z ij ,t ij θ i )) are the interface operator and observation point operator of the deep neural network output variable respectively; l(z ij ,t ij )、q(z ij ,t ij ) are the interface operator and observation point operator satisfied by the theoretical solution of the pavement temperature field.

[0131] Furthermore, in step S500, based on the total loss function established in step S400, the neural network is trained for several rounds based on the Adam algorithm (set to 20,000 rounds in this embodiment). On this basis, adaptive sampling is performed according to formula (24) based on the partial differential equation residual of the neural network (formula (23)). During adaptive sampling, the neural network is trained for every m1 rounds (m1=10,000 in this embodiment), and m2 sampling points are added (m2=600 in this embodiment), and a total of m3 rounds are trained (m3=100,000 in this embodiment). Finally, the BFGS algorithm is used to train for m4 rounds (m4=50,000 in this embodiment), and the road surface temperature field under different working conditions is obtained as shown in Table 2. Figure 7 As shown in (predicted value is represented by "pre", observed value is represented by "obs"), the inversion curve of convective heat transfer coefficient is as follows Figure 8 The results show that when the convective heat transfer coefficient is unknown, regardless of the data size, this method can achieve high-precision prediction of road surface temperature, R 2 The above steps require adaptive sampling based on the residual of the partial differential equation of the neural network, which is:

[0132] R ij =|F(T(z ij ,t ij θ i ))-f(z ij ,tij )| (23)

[0133] In formula (23), R ij is the residual of the jth sampling point on the i-th road surface, F(T(z ij ,t ij θ i )) is the partial differential equation operator of the output variable of the deep neural network; f(z ij ,t ij ) is the partial differential equation operator satisfied by the theoretical solution of the road surface temperature field;

[0134] Adaptive sampling is:

[0135]

[0136] In formula (24), k and c are sampling hyperparameters. In this embodiment, k = 2, c = 0; R k (z, t) is the residual of the partial differential equation calculated by the neural network; P(z, t) is the probability density function proportional to the residual of the partial differential equation; E is R k The expectation of (z, t) can be solved by Monte Carlo integration; is the sampling probability in region S.

[0137] This embodiment provides a method for inverting and fusion of pavement temperature field parameters. Compared with the existing technology, based on the heat conduction theory, a pavement temperature field is established to solve partial differential equations; based on the interpolation algorithm, the initial conditions, boundary conditions and measurement point temperatures of the pavement temperature field are characterized; the solution domain is normalized, and based on the random sampling method, sampling point coordinates are generated in the pavement temperature solution domain and at the boundary, and the sampling point coordinates are used as input variables of the deep neural network; based on the sampling point coordinates, the sampling point normalization operator value is obtained by combining the deep neural network and the automatic differentiation algorithm; combined with the initial conditions and the boundary conditions, the measured temperature data is fused, and the total loss function of the deep neural network is constructed by the weighted summation method; based on gradient descent and the total loss function, the deep neural network is trained, and adaptive sampling is performed according to the partial differential equation loss of the current neural network, ultimately realizing the pavement temperature field prediction. Compared with the physical-driven method and data-driven method used in traditional pavement temperature field prediction, the pavement temperature field parameter inversion and data fusion method provided by this embodiment has the following advantages:

[0138] (1) The physical driven method uses analytical or numerical methods to solve the heat conduction equation, which cannot integrate the measured temperature data and ignores the differences between physical laws and actual conditions. Therefore, the prediction accuracy is limited.

[0139] (2) Data-driven methods use empirical formulas or big data artificial intelligence methods to predict pavement temperature fields, ignoring the influence of pavement structure combinations and the thermal physical properties of road materials. Their accuracy depends on the size of the dataset, their generalization ability is limited, and they are not suitable for sparse datasets.

[0140] (3) This embodiment integrates the heat conduction equation and measured temperature data, enabling the prediction of road surface temperature fields with greater accuracy than physically driven models by integrating measured temperature data of any scale. Furthermore, due to the integration of the heat conduction equation, the road surface temperature field parameter inversion and data fusion method provided by this embodiment has greater generalization capabilities than data-driven methods, enabling high-precision prediction of road surface temperature fields with sparse datasets.

[0141] (4) Compared with the physical-driven and data-driven methods, the pavement temperature field parameter inversion and data fusion method provided in this embodiment can invert the missing parameters when some parameters are missing, and achieve high-precision prediction of the pavement temperature field.

[0142] Although preferred embodiments of the present invention have been described, those skilled in the art may make additional changes and modifications to these embodiments once they are aware of the basic inventive concepts. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the invention. Obviously, those skilled in the art may make various changes and modifications to the present invention without departing from the spirit and scope of the invention. Thus, the present invention is intended to include such changes and modifications as fall within the scope of the claims and their equivalents.

Claims

1. A pavement temperature field parameter inversion and data fusion method, characterized in that: The following steps are involved: Based on the heat conduction theory, the road surface temperature field is established to solve the partial differential equation; Based on the interpolation algorithm, the initial conditions, boundary conditions and measurement point temperatures of the road surface temperature field are characterized; Normalizing the solution domain, generating sampling point coordinates in the road surface temperature solution domain and at the boundary based on a random sampling method, and using the sampling point coordinates as input variables of the deep neural network; Based on the sampling point coordinates, a deep neural network and an automatic differentiation algorithm are combined to obtain a normalized operator value of the sampling point; combining the initial conditions and the boundary conditions, fusing the measured temperature data, and constructing a total loss function of the deep neural network through a weighted summation method; Based on gradient descent and the total loss function, deep neural network training is carried out, and adaptive sampling is performed according to the partial differential equation loss of the current neural network to ultimately achieve road surface temperature field prediction; The bottom boundary condition of the pavement temperature field is: Where Tn is the temperature at the bottom of the road surface temperature field; t is time; z is the coordinate of the calculation point, representing the vertical distance from the calculation point to the road surface; z n+1 is the bottom coordinate of the pavement structure; The top boundary condition of the pavement temperature field is: Where T1 is the temperature of the road surface; t is the time; z is the coordinate of the calculation point, which represents the vertical distance between the calculation point and the road surface; q c is the heat flux related to convection; q ns and q n1 are the net solar radiation and net longwave radiation of the road surface respectively; h c is the convection heat transfer coefficient; v W is the wind speed; σ is the Stefan-Boltzmann constant, ε is the surface emissivity, Ta and T0 are the air temperature and absolute zero, respectively; Triangular interpolation is used to represent the road surface boundary conditions and the temperature of the measuring points. The interpolation results of air temperature and net solar radiation are: Among them, h (t) is the interpolation function, a0 is the interpolation coefficient, a m is the interpolation coefficient, k is the cumulative coefficient, l is the cumulative coefficient, and m is half of the number of segment intervals; t a is the analysis time; h l is the endpoint function value of the lth subinterval; a k and b k is the interpolation coefficient; is an intermediate variable, π is the ratio of circumference to circle; The total loss function includes the partial differential equation loss term Initial condition loss term Boundary condition loss term Observation point loss and interface loss term Based on the sampling point coordinates, a deep neural network and an automatic differentiation algorithm are combined to obtain a normalized operator value of the sampling point; in the step of combining the initial conditions and the boundary conditions, integrating the measured temperature data, and constructing a total loss function of the deep neural network by a weighted summation method, the total loss function is calculated by the following formula: Among them, MSE tol is the total loss function, is the loss term of the partial differential equation, is the boundary condition loss term, is the initial condition loss term, is the interface loss term, is the observation point loss term, They are and The weight in the i-th pavement structure; m is the number of pavement structure layers.

2. The pavement temperature field parameter inversion and data fusion method according to claim 1, characterized in that: In the step of establishing the road surface temperature field to solve the partial differential equation based on the heat conduction theory, the solution of the road surface temperature field is simplified to a one-dimensional heat conduction problem. The one-dimensional heat conduction partial differential equation is as follows: Among them, T i is the temperature of the i-th layer; t is the time; z is the coordinate of the calculation point, representing the vertical distance between the calculation point and the road surface; z i and z i+1 are the coordinates of the top and bottom of the i-th layer respectively; α i is the thermal conductivity of the i-th layer.

3. The pavement temperature field parameter inversion and data fusion method according to claim 1, characterized in that: In the step of normalizing the solution domain, generating sampling point coordinates in the road surface temperature solution domain and at the boundary based on a random sampling method, and using the sampling point coordinates as input variables of a deep neural network, the generated sampling point coordinates are: Among them, z′ ij and t′ ij are the normalized sampling point coordinates and time respectively; and are the coordinates of the bottom and top of the i-th layer respectively; t a and z a Total analysis time and total depth of pavement structure respectively; Representatives in and Generate n uniformly distributed random numbers between 0 and 1; rand(0,1,n) represents generating n uniformly distributed random numbers between 0 and 1; z' i and t' i are the n-dimensional normalized sampling point coordinates and time series of the i-th layer of road surface; z'(j) and t'(j) represent the time series from z' i and t' i Select the jth element from .

4. The pavement temperature field parameter inversion and data fusion method according to claim 1, characterized in that: The loss term of the partial differential equation Calculated by the following formula: in, is the number of sampling points of the partial differential equation corresponding to the i-th layer of the pavement structure, F(T(z ij ,t ij θ i )) is the partial differential equation operator of the output variable of the deep neural network; f(z ij ,t ij ) is the partial differential equation operator satisfied by the theoretical solution of the road surface temperature field; θ i =(W i ,b i ), is the parameter of the deep neural network of the i-th layer of pavement structure; T(z ij ,t ij ) is the theoretical solution of the road surface temperature field; T(z ij ,t ij θ i ) is the output of the deep neural network.

5. The pavement temperature field parameter inversion and data fusion method according to claim 1, characterized in that: The initial condition loss term and the boundary condition loss term Calculated by the following formula: in, is the number of sampling points of initial conditions in the i-th layer of pavement structure; T(z ij ,t ij θ i ) is the output of the deep neural network, T(z ij ,t ij ) is the theoretical solution of the road surface temperature field, θ i =(W i ,b i ), is the parameter of the deep neural network of the i-th layer of pavement structure; G(T(z ij ,t;θ i )) is the boundary condition operator of the output variable of the deep neural network; g(z ij ,t ij ) is the boundary condition operator satisfied by the theoretical solution of the pavement temperature field.

6. The pavement temperature field parameter inversion and data fusion method according to claim 1, characterized in that: The observation point loss term and the interface loss term Calculated by the following formula: in, is the number of interface loss points in the corresponding i-th layer of pavement structure; is the number of lost observation points in the pavement structure of the corresponding layer i; L(T(z ij ,t ij θ i ))、Q(T(z ij ,t ij θ i )) are the interface operator and observation point operator of the deep neural network output variable respectively; l(z ij ,t ij )、q(z ij ,t ij ) are the interface operator and observation point operator satisfied by the theoretical solution of the pavement temperature field.

7. The pavement temperature field parameter inversion and data fusion method according to claim 1, characterized in that: In the step of conducting deep neural network training based on gradient descent and the total loss function, and performing adaptive sampling according to the partial differential equation loss of the current neural network, and finally realizing the road surface temperature field prediction, adaptive sampling is performed according to the partial differential equation residual of the neural network, and the partial differential equation residual is: R ij =|F(T(z ij ,t ij ;θ i ))-f(z ij ,t ij )| Among them, R ij is the residual of the jth sampling point on the i-th road surface, F(T(z ij ,t ij θ i )) is the partial differential equation operator of the output variable of the deep neural network; f(z ij ,t ij ) is the partial differential equation operator satisfied by the theoretical solution of the road surface temperature field; The adaptive sampling is: Among them, k and c are sampling hyperparameters, R k (z, t) is the residual of the partial differential equation calculated by the neural network; P(z, t) is the probability density function proportional to the residual of the partial differential equation; E is R k The expectation of (z,t), is the sampling probability in region S.

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