Pavement temperature field parameter inversion and data fusion method

Abstract

The invention discloses a pavement temperature field parameter inversion and data fusion method, and the method comprises the steps: building a pavement temperature field solving partial differential equation based on a heat conduction theory; representing an initial condition, a boundary condition and a measuring point temperature of a pavement temperature field based on an interpolation algorithm; normalizing the solution domain, generating sampling point coordinates at the pavement temperature solution domain and the boundary based on a random sampling method, and taking the sampling point coordinates as input variables of the deep neural network; based on the coordinates of the sampling points, a normalized operator value of the sampling points is obtained in combination with a deep neural network and an automatic differential algorithm; combining initial conditions and boundary conditions, fusing actually measured temperature data, and constructing a total loss function of the deep neural network through a weighted summation method; and based on gradient descent and a total loss function, deep neural network training is carried out, adaptive sampling is carried out according to partial differential equation loss of the current neural network, and finally pavement temperature field prediction is realized. According to the invention, high-precision prediction of the pavement temperature field is realized.

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] Temperature field is a prerequisite for evaluating the performance of pavement. On the one hand, temperature will cause thermal expansion and contraction of materials, resulting in temperature cracks; on the other hand, asphalt concrete is a viscoelastic-plastic material, which will cause rutting or cracking under the action of temperature and vehicle load. In addition, road surface temperature is related to the urban heat island effect and pavement anti-skid performance. Therefore, predicting the pavement temperature field is of great significance to alleviate the urban heat island effect in summer and improve driving safety in winter.

[0003] At present, the pavement temperature field prediction methods mainly include two categories: physical-driven methods and data-driven methods. The physical-driven method is based on the heat conduction equation and does not require the use of internal pavement temperature data. It mainly includes analytical methods and numerical methods. The analytical method uses the separation of variables method and integral transformation method to solve the pavement heat conduction equation. When calculating, empirical coefficients need to be introduced to consider nonlinear boundary conditions. The numerical method uses the finite element method (FEM), finite difference method (FDM) and finite volume method (FVM) to solve the pavement heat conduction equation. Nonlinear boundary conditions can be considered during calculation and are widely used in pavement temperature prediction. However, both analytical and numerical methods ignore the differences between physical laws and actual conditions, and the prediction accuracy is limited.

[0004] Data-driven methods mainly include empirical formula method and big data artificial intelligence method. The empirical formula method expresses the road surface temperature as a function of depth, latitude and air temperature. The empirical formula method does not consider the influence of solar radiation or the thermophysical properties of road materials, so its generalization ability is limited, it needs to be recalibrated regularly, and it is difficult to accurately predict abnormal temperature events. Big data artificial intelligence methods mainly include: support vector regression (SVR), regression tree (RT), Gaussian process regression (GPR), random forest (RF), fully connected neural network (FNN), convolutional neural network (CNN), gated recurrent unit (CRU), recurrent neural network (RNN) and ensemble deep learning (EDL). Compared with the empirical formula method, the prediction accuracy of big data artificial intelligence method in specific areas has been greatly improved, but it requires a large amount of observation data and ignores the influence of pavement structure combination and thermophysical properties of road materials. Therefore, its accuracy depends on the size of the data set, and it is difficult to balance the accuracy of interpolation and extension.

[0005] In summary, the physical-driven method is established with the help of the heat conduction equation, and does not require the actual measurement of the internal temperature of the road surface. It has strong universality, but the prediction accuracy is limited. The data-driven method has high accuracy in specific areas, but it ignores the influence of the pavement structure combination and the thermal physical properties of road materials. The accuracy depends on the size of the data set, the generalization ability is limited, and it is not suitable for sparse data sets.

[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, aiming to solve at least one defect existing in the above-mentioned existing pavement temperature field prediction method.

[0008] The present invention relates to a road surface 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, 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;

[0012] 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; combined with the initial conditions and boundary conditions, the measured temperature data is integrated, and the total loss function of the deep neural network is constructed through the 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 from the calculation point to 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 long-wave 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 temperature of the measuring point of the road surface temperature field, triangular interpolation is used to characterize the road surface boundary conditions and the temperature of the measuring point, and the interpolation results of the air temperature and the 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 function value of the endpoint of the lth subinterval; a k and b k is the interpolation coefficient; is the intermediate variable and π is the ratio of a circle to a circle.

[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 They are the total analysis time and the total depth of the pavement structure; Representatives 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 the 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 the 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 is integrated, and the total loss function of the deep neural network is constructed by the weighted summation method. 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 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 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 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 pavement structure; is the number of lost points at the observation point in the i-th pavement structure; 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 output variable of the deep neural network 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 the 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. In the step of finally 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 pavement, 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 inversion of pavement temperature field parameters and data fusion. 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 in combination with 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 the gradient descent and the total loss function, the deep neural network training is carried out, and adaptive sampling is performed according to the partial differential equation loss of the current neural network, and finally the pavement temperature field prediction is realized. The pavement temperature field parameter inversion and data fusion method provided by the present invention has the following advantages compared with the physical drive method and data drive method used in the traditional pavement temperature field prediction:

[0049] (1) The physical-driven method uses analytical or numerical methods to solve the heat conduction equation. It is unable to integrate the measured temperature data and ignores the difference 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 thermal physical properties of road materials. Their accuracy depends on the size of the data set, their generalization ability is limited, and they are not suitable for sparse data sets.

[0051] (3) The present invention integrates the heat conduction equation and the measured temperature data, and can integrate the measured temperature data of any scale to achieve the prediction of the road surface temperature field, with higher accuracy than the physical drive model. In addition, due to the integration of the heat conduction equation, the road surface temperature field parameter inversion and data fusion method provided by the present invention has a higher generalization ability than the data-driven method, and can achieve high-precision prediction of the road surface temperature field under sparse data sets.

[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 pavement temperature field parameter inversion and data fusion provided by the present invention;

[0054] Figure 2 A diagram showing the actual temperature measurement and interpolation results in the pavement temperature field parameter inversion and data fusion method provided by the present invention;

[0055] Figure 3 A diagram showing the measured and interpolated results of net solar radiation in the pavement temperature field parameter inversion and data fusion method provided by the present invention;

[0056] Figure 4 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 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 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 diagram of the first working condition measuring point in the pavement temperature field parameter inversion and data fusion method provided by the present invention;

[0061] Fig. 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] Fig.10 The temperature diagram of the second working condition measuring point in the pavement temperature field parameter inversion and data fusion method provided by the present invention;

[0063] Fig.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] Fig.12 The temperature diagram of the third working condition measuring point in the pavement temperature field parameter inversion and data fusion method provided by the present invention;

[0065] Fig.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 in conjunction with 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, comprising 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 pavement 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, the deep neural network and the 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 is 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, the sampling point normalization operator value is obtained by combining the deep neural network and the automatic differentiation algorithm. 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 by the weighted summation method, including 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 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 inversion and data fusion of road surface temperature field parameters. 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, representing 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 long-wave radiation of the road surface, 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 shown in the following formula:

[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 pavement layer, Fi(z) is the function expression satisfied by the initial temperature of the i-th pavement layer, 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 characterize 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 function value of the endpoint of the lth subinterval; a k and b k is the interpolation coefficient; is the intermediate variable and π is the ratio of a circle to a circle.

[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, the monotone piecewise cubic interpolation shown in the following formula is used to achieve the initial temperature characterization of the road surface.

[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 beginning 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 time of the first interval respectively; t0 and t1 represent the start and end time 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 start 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. Δh k is the forward difference quotient of the function at the start 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 start 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 inversion and data fusion of road surface 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, the unit is h; z is the calculation point coordinate, representing the vertical distance from the calculation point to the road surface, the unit is 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 between the calculation point and 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 They are the total analysis time and the total depth of the pavement structure; Representatives 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 the 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 coordinates 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, Figure 4 , Figure 5 or Figure 6 The deep neural network shown in FIG. 1 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 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 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 pavement structure; is the number of lost points at the observation point in the i-th pavement structure; 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 output variable of the deep neural network 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, for every m1 rounds of training of the neural network (m1=10,000 in this embodiment), 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 m4 rounds (m4=50,000 in this embodiment), and the pavement 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 mean absolute percentage error (MAPE) is less than 1.9%. The above steps require adaptive sampling based on the residual of the partial differential equation of the neural network. The residual of the partial differential equation 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 pavement, 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 inversion of pavement temperature field parameters and data fusion. Compared with the prior art, 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 in combination with 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 the gradient descent and the total loss function, the deep neural network training is carried out, and adaptive sampling is performed according to the partial differential equation loss of the current neural network, and finally the pavement temperature field prediction is realized. Compared with the physical drive method and data drive method used in the traditional pavement temperature field prediction, the pavement temperature field parameter inversion and data fusion method provided in this embodiment has the following advantages:

[0138] (1) The physical-driven method uses analytical or numerical methods to solve the heat conduction equation. It is unable to integrate the measured temperature data and ignores the difference 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 thermal physical properties of road materials. Their accuracy depends on the size of the data set, their generalization ability is limited, and they are not suitable for sparse data sets.

[0140] (3) This embodiment integrates the heat conduction equation and the measured temperature data, and can integrate the measured temperature data of any scale to achieve the prediction of the road surface temperature field, with higher accuracy than the physical drive model. In addition, 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 a higher generalization ability than the data-driven method, and can achieve high-precision prediction of the road surface temperature field under sparse data sets.

[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, additional changes and modifications may be made to these embodiments by those skilled in the art once the basic inventive concepts are known. 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 present 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 present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. A method for inversion and data fusion of pavement temperature field parameters, 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, integrating 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 finally achieve road surface temperature field prediction.

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 from the calculation point to 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 establishing the road surface temperature field to solve the partial differential equation based on the heat conduction theory, the bottom boundary condition of the road surface 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, 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 long-wave 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.

4. The pavement temperature field parameter inversion and data fusion method according to claim 1, characterized in that: In the step of characterizing the initial conditions, boundary conditions and temperature of the measuring point of the road surface temperature field based on the interpolation algorithm, triangular interpolation is used to characterize the road surface boundary conditions and the temperature of the measuring point, and the interpolation results of the air temperature and the 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 function value of the endpoint of the lth subinterval; a k and b k is the interpolation coefficient; is the intermediate variable and π is the ratio of a circle to a circle.

5. The pavement temperature field parameter inversion and data fusion method according to claim 1, characterized in that: The normalized solution domain generates sampling point coordinates in the road surface temperature solution domain and at the boundary based on a random sampling method, and in the step of using the sampling point coordinates as input variables of a deep neural network, the generated sampling point coordinates are: Among them, z i ' j and t i ' j 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 They are the total analysis time and the total depth of the pavement structure; 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 the road surface; z'(j) and t'(j) represent the time series from z' i and t' i Select the jth element from .

6. The pavement temperature field parameter inversion and data fusion method according to claim 1, characterized in that: 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.

7. The pavement temperature field parameter inversion and data fusion method according to claim 6, characterized in that: The partial differential equation loss term Calculated by the following formula: in, is the number of sampling points of the partial differential equation corresponding to the i-th 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.

8. The pavement temperature field parameter inversion and data fusion method according to claim 6, 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 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.

9. The pavement temperature field parameter inversion and data fusion method according to claim 6, 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 pavement structure; is the number of lost points at the observation point in the i-th pavement structure; 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 output variable of the deep neural network 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.

10. 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 pavement, 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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