Prediction of the skid-resistance deterioration in asphalt pavement based on peephole–LSTM neural network

Figures & data

Figure 1. Lab testing instruments.

Table 1. Mixture gradation.

Mixture type	Pass rate through different apertures(mm)/%
	16	13.2	9.5	4.75	2.36	1.18	0.6	0.3	0.15	0.075
SMA-13	100	95	62.5	27	20.5	19	16	13	12	10

Figure 2. Box plot of friction.

Figure 3. Separation of pavement 3D texture.

Figure 4. Decay trend of pavement texture.

Figure 5. Structure of FrictionNet-II.

Figure 6. Structure of hidden cell of FrictionNet-II at moment t.

Table

$z_t$	is the value of input layer at moment t
$h_t$	is the value of hidden layer output at moment t
$C_t$	is the value of hidden layer cell state at moment t
$f_t$	is the forget gate matrix
$i_t$	is the input gate matrix
$o_t$	is the output gate matrix
$W_f$	is the weight matrix of forget gate
$W_i$	is the wight matrix of input gate
$W_i$	is the wight matrix of output gate
$\ast In$	is the input gate
$\ast For$	is the forget gate
$\ast Out$	is the output gate
${\tilde{C}}_t$	is the cell state correction
$\times$	is the pointwise multiplication operation
$+$	is the addition operation
$tanh$	is the hyperbolic tangent function using as activation function here
$\sigma$	is the sigmoid function using as activation function here

Table 2. Hyperparameter determination.

Parameters/Value	Explanation	Value
$\mathit{y}ita$	Learning rate	0.01
$\mathit{i}ter$	Iteration(number of training)	1000000
$\mathit{m}$	Number of neurons in hidden layer	12
$\mathit{t}rain\mathrm{\_}\mathit{n}um$	Data volume of train set	152
$\mathit{t}est\mathrm{\_}\mathit{n}um$	Data volume of test set	40
$\mathit{i}nput\mathrm{\_}\mathit{n}um$	Length of input data	8
$\mathit{o}utput\mathrm{\_}\mathit{n}um$	Length of output data	3

Table 3. Variables to be adjusted during training.

Variable	Explanation
${\mathit{W}}_{\mathit{i}}^{\mathit{h}}$	Weight matrix between input and hidden layer
${\mathit{W}}_{\mathit{h}}^{\mathit{o}}$	Weight matrix between hidden and output layer
${\mathit{W}}_{\mathit{h}}^{{\mathit{h}}^{\mathrm{\prime }}}$	Weight matrix between hidden layers (different times)
${\mathit{B}}_{\mathit{i}}^{\mathit{h}}$	Weight matrix between input and hidden layer
${\mathit{B}}_{\mathit{h}}^{\mathit{o}}$	Weight matrix between hidden and output layer
${\mathit{B}}_{\mathit{h}}^{{\mathit{h}}^{\mathrm{\prime }}}$	Weight matrix between hidden layers (different times)
${\mathit{W}}_{\mathit{f}}$	Weight matrix of forget gate
${\mathit{W}}_{\mathit{i}}$	Weight matrix of input gate
${\mathit{W}}_{\mathit{o}}$	Weight matrix of output gate
${\mathit{B}}_{\mathit{f}}$	Biased matrix of forget gate
${\mathit{B}}_{\mathit{i}}$	Biased matrix of input gate
${\mathit{B}}_{\mathit{o}}$	Biased matrix of output gate
${\mathit{h}}_{\mathit{t}}$	Hidden layer output at moment t
${\mathit{C}}_{\mathit{t}}$	Cell state of hidden layer at moment t

Figure 7. Error-iteration graph.

Figure 8. Testing result demonstration.

Table 4. Model evaluation results.

Indicators	160,000 wear cycles	180,000 wear cycles	200,000 wear cycles
$\mathit{R}MSE$	0.89	0.81	0.97
$\mathit{M}SE$	0.71	0.66	0.76
$\mathit{M}APE$	1.45%	1.34%	1.60%
${\mathit{R}}^2$	88%	90%	90%