A pavement performance prediction algorithm quantifying data and model uncertainty

Abstract

The application discloses a pavement performance prediction algorithm for quantifying data and model uncertainty, comprising the following steps: constructing a pavement performance change database; constructing a Bayesian neural network model f; constructing a loss function; performing model training; performing model prediction; and based on the prediction results of the model, performing maintenance opportunity and decision judgment. The application uses the prediction value output by the model as the expectation of the pavement detection index after maintenance, avoiding the emergence of extreme outlier prediction results; the data uncertainty output by the model can quantitatively evaluate the objectively existing measurement error in the real data, provide possible and poor pavement conditions under a certain confidence, and avoid the delay of the maintenance opportunity; the model uncertainty output by the model can quantify the abnormal degree of the prediction value, provide a kind of early warning for the road element that may have an abnormal pavement detection index before maintenance, avoid the wrong judgment of the maintenance scheme, and thus avoid the waste of maintenance resources while ensuring the good pavement service performance.

Description

Technical Field

[0001] This invention belongs to the field of road engineering inspection and maintenance, and specifically relates to a pavement performance prediction algorithm that quantifies data and model uncertainties. Background Technology

[0002] Making decisions and judgments about the timing of maintenance for different roads within a road network can greatly improve the effectiveness of maintenance projects and extend the service life of roads. Predicting pavement performance is extremely important for making these decisions, and providing comprehensive and reliable pavement performance predictions is crucial for road maintenance.

[0003] In recent years, with the gradual application of artificial intelligence (AI) technology in road inspection and maintenance, AI models that automatically mine data patterns from pavement performance change databases and use them for pavement performance prediction have gained attention. Currently, existing pavement performance prediction models mainly focus on predicting more performance aspects or making more accurate predictions, rarely considering the evaluation of uncertainties. However, in the real world, pavement performance inspection indicators suffer from data uncertainty caused by objective limitations in inspection technology and model uncertainty caused by limitations in model knowledge. A single prediction result cannot assess the objective error of the current prediction, ignoring the potential for a poor lower limit of pavement inspection indicators after maintenance, which may lead to delayed consideration of maintenance timing. Secondly, a single prediction result cannot provide a reliable quantitative evaluation indicator that the prediction result is within the scope of the model's knowledge, which may lead to an incorrect judgment of maintenance timing.

[0004] Therefore, it is necessary to research and develop a pavement performance prediction algorithm that quantifies the uncertainty of data and models. Summary of the Invention

[0005] Based on the aforementioned background and addressing the shortcomings of existing technologies, this invention proposes a road performance prediction algorithm that quantifies data and model uncertainties. This algorithm establishes a Bayesian neural network model by adding a Dropout layer after each hidden layer of the neural network. The loss function of this model is constructed using a variational method, and the Bayesian neural network model is solved using the gradient descent algorithm. A Monte Carlo simulation with 1000 iterations is then used to evaluate the prediction results, data uncertainty, and model uncertainty. Using the prediction algorithm proposed in this invention, the objective error and reliability of the prediction results can be quantitatively evaluated.

[0006] Technical solution: To achieve the above-mentioned objectives, the technical solution adopted by this invention is as follows:

[0007] A pavement performance prediction algorithm that quantifies data and model uncertainties includes the following steps:

[0008] Step 1: Construct a pavement performance change database, which includes the following steps:

[0009] Step 1.1: Collect all maintenance history data for the road segment whose pavement performance needs to be predicted. Divide the road segment into R road elements according to standard length. Based on the pavement inspection indicators specified in the "Highway Technical Condition Assessment Standard" (JTG 5210-2018), select the pavement inspection indicators from the maintenance history and construct the inspection information tensor for each road element over the years. Where F represents the number of test indicators that meet the maintenance standards during the maintenance history;

[0010] Step 1.2: Collect and organize the maintenance plans of each road element over the years in the maintenance history, and compile them into a road element performance change sample in the form of "pre-maintenance test indicators - maintenance plan - post-maintenance test indicators". Specifically, merge the test information of the year before the implementation of the maintenance plan, the actual maintenance plan, and the test information of the year after the implementation of the maintenance plan to generate a pavement performance change database.

[0011] Step 2: Construct a Bayesian neural network model f: Construct a fully connected neural network model based on samples from a pavement performance change database; after adding a Dropout layer after each hidden layer of the fully connected neural network, this fully connected neural network is equivalent to a Bayesian neural network whose model parameters follow a certain normal distribution; the inputs to the Bayesian neural network model f are the pre-maintenance detection information tensor x and the maintenance plan e. i The output of the Bayesian neural network model f is the predicted value of the tensor of pavement inspection information after maintenance. Data uncertainty and model uncertainty σ e Among them, data uncertainty With model uncertainty σ e Expressed in terms of standard deviation;

[0012] Step 3: Construct the loss function: Construct a loss function that approximates the Bayesian optimization function based on the variational method, and solve for the parameter M' of the posterior distribution of the parameters of the Bayesian neural network model f.

[0013] Step 4: Train the model.

[0014] Based on steps 1-3, the gradient descent algorithm is used to solve for the parameter M' of the posterior distribution of the parameters of the Bayesian neural network model f. The parameter that minimizes the loss function is taken as the final parameter of the posterior distribution of the parameters of the Bayesian neural network model f in step 2, thus obtaining the trained Bayesian neural network model f.

[0015] Step 5: Perform model predictions:

[0016] Given a tensor x containing pavement detection information before maintenance for one of the road elements.n Maintenance plan As input to the trained Bayesian neural network model f, a Monte Carlo simulation with 1000 sampling iterations is performed on the model with input parameters, and the expected prediction result is output. Data uncertainty of predicted values Model uncertainty of predicted values

[0017] Step 6: Based on the model's prediction results, determine the timing and decision-making for maintenance.

[0018] In a preferred embodiment, the Bayesian neural network model f includes multiple hidden layers, and a Dropout layer is added after each hidden layer;

[0019] During the training and prediction process of the Bayesian neural network f, each Dropout layer remains active.

[0020] In a preferred embodiment, the fully connected neural network with added Dropout layers is equivalent to a Bayesian neural network in the following principle:

[0021] Let M denote the model parameters of a neuron in a hidden layer of a fully connected neural network, and p denote the probability of the neuron being retained in the Dropout layer following the neuron. The random variable z follows this Bernoulli distribution, as expressed below:

[0022] P(z=x)=p x (1-p) 1-x ,x∈{0,1}, (1)

[0023] Let the random variable ∈ follow a standard normal distribution N(0,1), and let σ>0 represent a positive number. Construct the following random variable:

[0024] w=z(M+σ∈)+(1-z)σ∈, (2)

[0025] In summary, w is a function that follows N(M,σ) 2 ) and N(0,σ 2 Weighted mixture normal distribution:

[0026] P(w)=pN(M,σ 2 )+(1-p)N(0,σ 2 (3)

[0027] Let w be a random variable parameter of a Bayesian neural network model f with the same structure as a fully connected neural network model; let σ approach 0, the parameter w is approximately as follows:

[0028] w≈zM, (4)

[0029] M represents the parameters of the fully connected neural network model, and z represents the random variable of whether or not the Dropout layer of the fully connected neural network model is retained. The approximate result of the parameter w means that adding the Dropout layer to the fully connected neural network is equivalent to a Bayesian neural network. Solving for the parameters M of the fully connected neural network model is equivalent to solving for the posterior distribution of the parameters w of a Bayesian neural network model f.

[0030] In a preferred embodiment, the input and output terms of the Bayesian neural network f satisfy the following conditions:

[0031] Input items:

[0032] Output items:

[0033] Where F represents the number of test indicators that meet the maintenance specifications during the maintenance history; for input e i "1" appears at the i-th position, n2 represents the types of maintenance schemes in the pavement performance change database, and K represents the number of types of pavement inspection indicators after maintenance in the pavement performance change database.

[0034] In the preferred embodiment, the specific steps for constructing the loss function in step 3 are as follows:

[0035] Step 3.1: Construct the Bayesian optimization function: Let Ω represent all random variable parameters of a conventional Bayesian neural network model, i.e., w∈Ω. The posterior distribution of Ω is solved through Bayesian optimization:

[0036]

[0037] In the formula, P(Ω) represents the prior distribution of the model parameters; P(Ω|x,y) represents the posterior distribution of the model parameters; P(y|Ω,x) is the likelihood; P(y|x) is the marginal likelihood; x and y are the input value and the true value, respectively. It is the predicted value of y;

[0038] Step 3.2, Variational Function:

[0039] Let q(Ω) denote a distribution of the posterior distribution of the approximate model parameters, whose form is consistent with the distribution of the model parameters w. Based on the Kullback-Leibler (KL) divergence, a variational function is constructed to quantitatively represent the degree of difference between q(Ω) and P(Ω|x,y), as shown in the following expression:

[0040]

[0041] In the formula, Let represent the divergence between q(Ω) and P(Ω|x,y), and log(·) be the logarithmic function. The constructed variational function is considered as the degree of difference between the distributions q(Ω) and P(Ω|x,y); when When q(Ω) equals 0, it indicates that q(Ω) is equal to the posterior distribution P(Ω|x,y), and the two distributions are identical. In this case, obtaining the posterior distribution is equivalent to finding a distribution such that... The smallest q(Ω), i.e. It is a loss function that needs to be minimized continuously.

[0042] In the preferred embodiment, equation (6) is simplified through the following steps:

[0043] Assuming that the predicted values ​​of each test index after maintenance are independent of each other, the likelihood function in the second term of equation (6) can be written as:

[0044]

[0045] In the formula, N represents the sample size, y n,k This represents the detection index of the nth sample after the kth maintenance.

[0046] In equation (7), P(y) n,k |x,Ω) is given by the mean of Standard deviation is Calculation of normal distribution:

[0047]

[0048] Through a first MCMC approximation The second item is:

[0049]

[0050] In the formula, and When the input is x, the Bayesian neural network model f samples its parameter Ω once and then performs a forward pass. This sampling is equivalent to performing Dropout once on the fully connected neural network established in step 2. The second term is essentially part of the loss function of the established fully connected neural network model.

[0051] The first term of equation (6) is equivalent to:

[0052]

[0053] In the formula, p' is the probability of the Dropout layer neuron dropping, and M... l With b lThese are the weight parameters and bias parameters of the l-th layer of the fully connected neural network model that is equivalent to the Bayesian neural network model f, respectively. L indicates that the model structure established in step 2 has L hidden layers, and C is a constant.

[0054] In summary, we obtain the final simplified form of equation (6):

[0055]

[0056] In a preferred embodiment, in step 4, the parameters of the posterior distribution of the parameters f of the Bayesian neural network model are obtained by reducing the loss function to 0 or when it converges using the gradient descent algorithm.

[0057] In a preferred embodiment, in step 5, when the given input parameter is the pavement inspection index x before road element maintenance... n Maintenance plan At that time, model f is based on x n and Each prediction is a sampling process, let j represent the j-th sampling;

[0058] The expected predicted values ​​of the road element maintenance post-inspection indicators, which are used as input parameters, and the standard deviations used to represent the uncertainty of the data and model are estimated through a Monte Carlo simulation with 1000 sampling times. The calculation method is as follows:

[0059]

[0060] In the formula, This indicates that the pre-maintenance detection index x is based on the nth sample. n Maintenance plan The expected prediction results obtained from Monte Carlo simulation, This indicates the uncertainty of the predicted value at this time. This indicates the model uncertainty of the predicted value at this time, f j () represents the j-th prediction of the model. and This represents the uncertainty of the predicted value obtained from the j-th prediction by the model compared to the data.

[0061] In the preferred embodiment, the processing in step 6 is as follows:

[0062] Preparation phase:

[0063] The lower bound of the prediction result with a certain confidence level is obtained by using the data uncertainty in step 5, which serves as the basis for judging the timing of maintenance under the worst possible road conditions in the future.

[0064] Based on step 5, the mean of the model uncertainty of the expected predicted values ​​of all road element post-maintenance detection indicators in the pavement performance change database of the road segment to be predicted is used as the threshold.

[0065] Decision-making stage:

[0066] Following the method in step 5, the expected predicted value of the road element's detection index and maintenance plan after maintenance is obtained. The model uncertainty and prediction uncertainty are compared with the threshold obtained in the preparation stage. If the model uncertainty of the predicted value of the corresponding road element to be detected is greater than the threshold, the prediction value is considered unreliable and the corresponding output prediction value is not used for the decision on maintenance timing. Conversely, the expected predicted value of the detection index and the data uncertainty are used to calibrate the lower limit of pavement performance for the judgment and decision on maintenance plan and maintenance timing.

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

[0068] The algorithm provided by this invention uses the predicted values ​​output by the model as the expected values ​​of pavement inspection indicators after maintenance, which can avoid the occurrence of extreme outlier prediction results. The data uncertainty output by the model can quantitatively evaluate the measurement errors that objectively exist in the real data, and can provide possible poor pavement conditions with a certain confidence level, thus avoiding delays in maintenance. The model uncertainty output by the model can quantify the degree of abnormality of the predicted values, thereby providing an early warning for pavement elements that may have abnormal pavement inspection indicators before maintenance, avoiding incorrect judgments on the timing of maintenance, and protecting maintenance resources from waste. Attached image description:

[0069] Figure 1 The flowchart shows the pavement performance prediction algorithm for quantifying uncertainty provided by this invention.

[0070] Figure 2 This is a comparison chart of the model parameters in this invention on the test set of the Yeats neural network model.

[0071] Figure 3 This is a comparison chart showing the results of the model parameters in this invention on the training set of the Yeesian neural network model.

[0072] Figure 4 This is a comparison chart showing the relationship between the test set, the abnormal dataset, and the threshold in this invention. Detailed implementation method:

[0073] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and specific examples.

[0074] like Figure 1As shown, a pavement performance prediction algorithm that quantifies data and model uncertainties specifically includes the following steps:

[0075] Step 1: Construct a pavement performance change database: Divide the road segment to be predicted into R road elements according to standard length. Based on the pavement inspection indicators specified in the "Highway Technical Condition Assessment Standard" (JTG 5210-2018), screen the pavement inspection indicators from the maintenance history and construct the inspection information tensor of each road element over the years. Where F represents the number of test indicators that meet the maintenance specifications in the maintenance history. Generally, the length of the multiple road element units is 1km. Step 1.2: Collect and organize the maintenance plans of each road element over the years in the maintenance history, and compile them into a road element performance change sample in the form of "pre-maintenance test indicators - maintenance plan - post-maintenance test indicators". Specifically, the test information of the year before the implementation of the maintenance plan, the actual maintenance plan, and the test information of the year after the implementation of the maintenance plan for each road element are merged to generate a pavement performance change database.

[0076] Step 2: Construct a Bayesian neural network model f: Construct a fully connected neural network model based on samples from a pavement performance change database. After adding a Dropout layer after each hidden layer of this network, the fully connected neural network is equivalent to a Bayesian neural network whose model parameters follow a certain normal distribution. The inputs to the Bayesian neural network model f are the tensor x of pre-maintenance detection information and the maintenance plan e. i The output of the Bayesian neural network model f is the predicted value of the tensor of pavement inspection information after maintenance. Data uncertainty and model uncertainty σ e Where data uncertainty and model uncertainty are represented by standard deviation;

[0077] The input and output terms of the constructed Bayesian neural network f satisfy the following conditions:

[0078] Input items:

[0079] Output items:

[0080] Where F represents the number of test indicators that meet the maintenance specifications during the maintenance history; for input e i "1" appears at the i-th position, n2 represents the types of maintenance schemes in the pavement performance change database, and K represents the number of types of pavement inspection indicators after maintenance in the pavement performance change database.

[0081] Step 3: Construct the loss function: Establish a Bayesian optimization function for solving the posterior distribution of the model parameters. Construct a loss function that approximates the Bayesian optimization function based on the variational method, which is used for the fast solution of the posterior distribution of the parameters of the Bayesian neural network model f in Step 2; that is, solve for the parameter M' of the posterior distribution of the parameters of the Bayesian neural network model f.

[0082] The loss function is constructed as follows:

[0083] Step 3.1: Construct the Bayesian optimization function: Let Ω represent all random variable parameters of a conventional Bayesian neural network model, i.e., w∈Ω. The posterior distribution of Ω is solved through Bayesian optimization:

[0084]

[0085] In the formula, P(Ω) represents the prior distribution of the model parameters; P(Ω|x,y) represents the posterior distribution of the model parameters; P(y|Ω,x) is the likelihood; P(y|x) is the marginal likelihood; x and y are the input value and the true value, respectively. It is the predicted value of y;

[0086] Step 3.2, Variational Function:

[0087] Let q(Ω) denote a distribution of the posterior distribution of the approximate model parameters, whose form is consistent with the distribution of the model parameters w. Based on the Kullback-Leibler (KL) divergence, a variational function is constructed to quantitatively represent the degree of difference between q(Ω) and P(Ω|x,y), as shown in the following expression:

[0088]

[0089] In the formula, Let represent the divergence between q(Ω) and P(Ω|x,y), and log(·) be the logarithmic function. The constructed variational function is considered as the degree of difference between the distributions q(Ω) and P(Ω|x,y); when When q(Ω) equals 0, it indicates that q(Ω) is equal to the posterior distribution P(Ω|x,y), and the two distributions are identical. In this case, obtaining the posterior distribution is equivalent to finding a distribution such that... The smallest q(Ω), i.e. It is a loss function that needs to be minimized continuously.

[0090] Furthermore, assuming that the predicted values ​​of each detection index after maintenance are independent of each other, the likelihood function in the second term of equation (6) can be written as:

[0091]

[0092] In the formula, N represents the sample size, K represents the number of predicted detection indicators, and y n,kThis represents the detection index of the nth sample after the kth maintenance.

[0093] In equation (7), P(y) n,k |x,Ω) is given by the mean of Standard deviation is Calculation of normal distribution:

[0094]

[0095] Through a first MCMC approximation The second item is:

[0096]

[0097] In the formula, and When the input is x, the Bayesian neural network model f samples its parameter Ω once and then performs a forward pass. This sampling is equivalent to performing Dropout once on the fully connected neural network established in step 2. The second term is essentially part of the loss function of the established fully connected neural network model.

[0098] The value of equation (9) is essentially equivalent to the value obtained by the model established in step 2 after a dropout.

[0099] The first term of equation (6) is equivalent to:

[0100]

[0101] In the formula, p' is the probability of the Dropout layer neuron dropping, and M... l With b l These are the weight parameters and bias parameters of the l-th layer of the fully connected neural network model f, which is equivalent to the Bayesian neural network model f established in step 2. L indicates that the model structure established in step 2 has L hidden layers, and C is a constant.

[0102] In summary, we obtain the final form of equation (6):

[0103]

[0104] Step 4: Train the model: During the training process, Dropout remains active.

[0105] Based on steps 1-3, the gradient descent algorithm is used to solve for the parameter M' of the posterior distribution of the parameters of the Bayesian neural network model f. The parameter that minimizes the loss function is taken as the final parameter of the posterior distribution of the parameters of the Bayesian neural network model f in step 2, thus obtaining the trained Bayesian neural network model f.

[0106] Specifically, the parameters of the posterior distribution of the parameters f of the Bayesian neural network model are obtained by reducing the loss function through the gradient descent algorithm until it is zero or converges.

[0107] Step 5: Perform model prediction: Dropout remains active throughout the prediction process.

[0108] Given the pavement tensor information and maintenance plan of one of the road elements before maintenance as input to the model in step 4, a Monte Carlo simulation with 1000 sampling times is used on the model of the input parameters to estimate the expected predicted value of the pavement inspection index after maintenance and to represent the standard deviation of data uncertainty and model uncertainty.

[0109] When the given input parameter is the pavement inspection index x before road element maintenance n Maintenance plan At that time, model f is based on x n and A prediction is a sampling process, and let j represent the j-th sampling.

[0110] The expected predicted values ​​of the road element maintenance post-inspection indicators, which are used as input parameters, and the standard deviations used to represent the uncertainty of the data and model are estimated through a Monte Carlo simulation with 1000 sampling times. The calculation method is as follows:

[0111]

[0112] In the formula, This indicates that the pre-maintenance detection index x is based on the nth sample. n Maintenance plan The expected prediction results obtained from Monte Carlo simulation, This indicates the uncertainty of the predicted value at this time. This indicates the model uncertainty of the predicted value at this time, f j () represents the j-th prediction of the model. and This represents the uncertainty of the predicted value obtained from the j-th prediction by the model compared to the data.

[0113] Step 6: Based on the estimation results predicted by the model, determine the timing of maintenance and output a decision. The specific processing procedure for this step is as follows:

[0114] Preparation phase:

[0115] Using the data uncertainty in step 5, we obtain the lower limit of the prediction result under a certain confidence level, which serves as the basis for judging the timing of maintenance under the worst possible road conditions in the future.

[0116] Based on the method in step 5, the mean value of the model uncertainty of the expected predicted values ​​of all road element post-maintenance detection indicators in the pavement performance change database of the road segment to be predicted is used as the threshold.

[0117] Decision-making stage:

[0118] Following the method in step 5, the expected predicted values ​​of the road element's detection indicators and maintenance plan are obtained after maintenance. The model uncertainty and prediction uncertainty are then compared with the threshold obtained in the preparation stage. If the model uncertainty of the predicted value of the corresponding road element to be detected exceeds the threshold, the predicted value is considered unreliable, and the corresponding output prediction value is not used for determining the maintenance timing. Conversely, the expected predicted values ​​of the detection indicators and data uncertainty are used to calibrate the lower limit of pavement performance, which is then used for judging and deciding on the maintenance plan and timing.

[0119] Taking a certain expressway in Anhui Province as an example:

[0120] S1. Divide a highway in Anhui Province into multiple road elements with 1km units. Compile historical pavement inspection indicators and maintenance plans (including those requiring no maintenance) for each road element to construct a pavement performance change database in the form of "pre-maintenance inspection indicators - maintenance plan - post-maintenance inspection indicators". This database is used to construct the input and output of a Bayesian neural network model and for model training. In this database, the pavement inspection indicators are the same before and after maintenance, including the Pavement Condition Index (PCI), Road Rutting Index (RDI), and Road Ride Quality Index (RQI). There are seven maintenance plans in total.

[0121] S2. Construct a standard fully connected neural network model. Each layer of this model needs to be followed by a Dropout layer, ensuring that all Dropout layers in model f are active. In this case, the model is a Bayesian neural network. The inputs to the constructed neural network model are tensors. With e i ∈{0,1} 7 The 1 appears at the i-th position; the model output is a tensor. These represent the predicted values ​​of pavement inspection indicators after maintenance and the data uncertainty and model uncertainty of those values, respectively.

[0122] S3. Establish the following loss function:

[0123]

[0124] In the formula, and All are the output values ​​of the Bayesian neural network model f after one sampling, M l With b lThese are the weight parameters and bias parameters of the l-th layer of the model, respectively. L indicates that the model structure established in step 2 has L hidden layers, N represents the number of training samples, and K represents the number of detection metrics, which is 3 in this example.

[0125] S4. Divide the road performance change database into a training set and a test set in a 3:1 ratio. Use the training set to reduce the loss function in S3 through the gradient descent algorithm until it is 0 or converges to obtain the parameters of the posterior distribution of the parameters f of the Bayesian neural network model, that is, the parameters of the neurons of the fully connected neural network model.

[0126] S5. Construct and model the pavement performance change database from abnormal datasets derived from different datasets. Based on the method in step 5, calculate the model's predicted values, data uncertainty, and model uncertainty on the training set, test set, and abnormal dataset. Figure 2 This paper presents the expected predicted values ​​of all pavement maintenance indicators on the test set at a confidence level of one standard deviation, along with the results of data uncertainty and model uncertainty. Scatter points represent the actual post-maintenance pavement indicators in the test set, and line segments represent the predicted maintenance effects. The lines in (Equation 12) represent data uncertainty in the inner region. (Equation 13), the outer region represents the model uncertainty. (Equation 14) The lower boundary of the inner layer can be used to determine the maintenance timing for the worst road surface conditions, thereby avoiding delays in maintenance. Figure 3 The results show the predicted values, data uncertainty, and model uncertainty on the training set. The results indicate that the two types of uncertainty in the validation set and the training set have the same trend, both being larger on PCI and smaller on RDI and RQI. Figure 3 The legend in the lower left corner shows that the statistical mean of the model uncertainty for all path elements on the training set across the three detection metrics is 0.72, 0.45, and 0.36, respectively. Let these three values ​​be used as the threshold for anomaly detection. Figure 4 This represents the percentage of road elements whose model uncertainty exceeds a threshold on both the test set and the abnormal dataset. This result indicates that the threshold is relatively conservative. In the test set, some road elements have model uncertainties exceeding this threshold, and the method considers these road elements as unreliable road elements with anomaly detection information. However, on the abnormal dataset, all road elements have model uncertainties exceeding this threshold. In this case, the method provides early warnings for all road elements with anomaly detection information, thereby avoiding incorrect maintenance timing and planning decisions and protecting valuable maintenance resources.

[0127] Through the above steps, the model uncertainty of road elements can be predicted, providing possible and poor road surface conditions with a certain confidence level, thus avoiding delays in maintenance. The model uncertainty output can quantify the degree of abnormality of the predicted values, thereby providing an early warning for road elements that may have abnormal road surface detection indicators before maintenance, avoiding incorrect judgments on maintenance timing, and protecting maintenance resources from waste.

[0128] The preferred embodiments of the present invention have been described in detail above. However, the present invention is not limited to the specific details in the above embodiments. Within the scope of the technical concept of the present invention, various equivalent transformations can be made to the technical solutions of the present invention, and these equivalent transformations all fall within the protection scope of the present invention.

Claims

1. A pavement performance prediction algorithm that quantifies data and model uncertainties, characterized in that, Includes the following steps: Step 1: Construct a pavement performance change database, which includes the following steps: Step 1.1: Collect all maintenance history data for the road segment whose pavement performance needs to be predicted. Divide the road segment into R road elements according to the standard length. Filter the pavement inspection indicators from the maintenance history and construct the inspection information tensor for each road element over the years. Where F represents the number of test indicators that meet the maintenance standards during the maintenance history; Step 1.2: Collect and organize the maintenance plans of each road element over the years in the maintenance history, and compile road element performance change samples in the form of "pre-maintenance test indicators - maintenance plan - post-maintenance test indicators" to generate a pavement performance change database. Step 2: Construct a Bayesian neural network model f: Construct a fully connected neural network model based on samples from a pavement performance change database; after adding a Dropout layer after each hidden layer of the fully connected neural network, this fully connected neural network is equivalent to a Bayesian neural network whose model parameters follow a certain normal distribution; the inputs to the Bayesian neural network model f are the pre-maintenance detection information tensor x and the maintenance plan e. i The output of the Bayesian neural network model f is the predicted value of the tensor of pavement inspection information after maintenance. Data uncertainty and model uncertainty σ e Among them, data uncertainty With model uncertainty σ e Expressed in terms of standard deviation; Step 3: Construct the loss function: Construct a loss function that approximates the Bayesian optimization function based on the variational method, and solve for the parameter M' of the posterior distribution of the parameters of the Bayesian neural network model f. Step 4: Train the model. Based on steps 1-3, the gradient descent algorithm is used to solve for the parameter M' of the posterior distribution of the parameters of the Bayesian neural network model f. The parameter that minimizes the loss function is taken as the final parameter of the posterior distribution of the parameters of the Bayesian neural network model f in step 2, thus obtaining the trained Bayesian neural network model f. Step 5: Perform model predictions: Given a tensor x containing pavement information before maintenance for one of the road elements. n Maintenance plan As input to the trained Bayesian neural network model f, a Monte Carlo simulation with 1000 sampling iterations is performed on the model with input parameters, and the expected prediction result is output. Data uncertainty of predicted values Model uncertainty of predicted values Step 6: Based on the model's prediction results, determine the timing and decision-making for maintenance.

2. The road performance prediction algorithm for quantifying data and model uncertainty according to claim 1, characterized in that, The Bayesian neural network model f includes multiple hidden layers, and a Dropout layer is added after each hidden layer; During the training and prediction process of the Bayesian neural network f, each Dropout layer remains active.

3. The road performance prediction algorithm for quantifying data and model uncertainty according to claim 2, characterized in that, The principle that a fully connected neural network with a Dropout layer is equivalent to a Bayesian neural network is as follows: Let M denote the model parameters of a neuron in a hidden layer of a fully connected neural network, p denote the probability of the neuron being retained in the Dropout layer following the neuron, and the random variable z follow this Bernoulli distribution, as expressed below: P(z=x)=p x (1-p) 1-x ,x∈{0,1},(1) Let the random variable ∈ follow a standard normal distribution N(0,1), and let σ>0 represent a positive number. Construct the following random variable: w=z(M+σ∈)+(1-z)σ∈,(2) In summary, w is a function that follows N(M,σ) 2 ) and N(0,σ 2 Weighted mixture normal distribution: P(w)=pN(M,σ 2 )+(1-p)N(0,σ 2 ),(3) Let w be a random variable parameter of a Bayesian neural network model f with the same structure as a fully connected neural network model; let σ approach 0, the parameter w is approximately as follows: w≈zM,(4) M represents the parameters of the fully connected neural network model, and z represents the random variable of whether or not the Dropout layer of the fully connected neural network model is retained. The approximate result of the parameter w means that adding the Dropout layer to the fully connected neural network is equivalent to a Bayesian neural network. Solving for the parameters M of the fully connected neural network model is equivalent to solving for the posterior distribution of the parameters w of a Bayesian neural network model f.

4. The road performance prediction algorithm for quantifying data and model uncertainty according to claim 1, characterized in that, The input and output terms of the Bayesian neural network f satisfy the following conditions: Input items: Output items: Where F represents the number of test indicators that meet the maintenance specifications during the maintenance history; for input e i "1" appears at the i-th position, n2 represents the types of maintenance schemes in the pavement performance change database, and K represents the number of types of pavement inspection indicators after maintenance in the pavement performance change database.

5. The road performance prediction algorithm for quantifying data and model uncertainty according to claim 1, characterized in that, The specific steps for constructing the loss function in step 3 are as follows: Step 3.1: Construct the Bayesian optimization function: Let Ω represent all random variable parameters of a conventional Bayesian neural network model, i.e., w∈Ω. The posterior distribution of Ω is solved through Bayesian optimization: In the formula, P(Ω) represents the prior distribution of the model parameters; P(Ω|x,y) represents the posterior distribution of the model parameters; P(y|Ω,x) is the likelihood; P(y|x) is the marginal likelihood; x and y are the input value and the true value, respectively. It is the predicted value of y; Step 3.2, Variational Function: Let q(Ω) denote a distribution of the posterior distribution of the approximate model parameters, whose form is consistent with the distribution of the model parameters w. Based on the Kullback-Leibler divergence, a variational function is constructed to quantitatively represent the degree of difference between q(Ω) and P(Ω|x,y), as shown in the following expression: In the formula, Let represent the divergence between q(Ω) and P(Ω|x,y), and log(·) be the logarithmic function. The constructed variational function is considered as the degree of difference between the distributions q(Ω) and P(Ω|x,y); when When q(Ω) equals 0, it indicates that q(Ω) is equal to the posterior distribution P(Ω|x,y), and the two distributions are identical. In this case, obtaining the posterior distribution is equivalent to finding a distribution such that... The smallest q(Ω), i.e. It is a loss function that needs to be minimized continuously.

6. The pavement performance prediction algorithm for quantifying data and model uncertainty according to claim 5, characterized in that, Equation (6) is simplified through the following steps: Assuming that the predicted values ​​of each test index after maintenance are independent of each other, the likelihood function in the second term of equation (6) can be written as: In the formula, N represents the sample size, y n,k This represents the detection index of the nth sample after the kth maintenance. In equation (7), P(y) n,k |x,Ω) is given by the mean of Standard deviation is Calculation of normal distribution: Through a first MCMC approximation The second item is: In the formula, and When the input is x, the Bayesian neural network model f samples its parameter Ω once and then performs a forward pass. This sampling is equivalent to performing a Dropout operation on the fully connected neural network established in step 2. The second term is essentially a part of the loss function of the established fully connected neural network model. The first term of equation (6) is equivalent to: In the formula, p' is the probability of the Dropout layer neuron dropping, and M... l With b l These are the weight parameters and bias parameters of the l-th layer of the fully connected neural network model that is equivalent to the Bayesian neural network model f, respectively. L indicates that the model structure established in step 2 has L hidden layers, and C is a constant. In summary, we obtain the final simplified form of equation (6):

7. The road performance prediction algorithm for quantifying data and model uncertainty according to claim 1, characterized in that, In step 4, the parameters of the posterior distribution of the parameters f of the Bayesian neural network model are obtained by reducing the loss function through the gradient descent algorithm until it is 0 or converges.

8. The road performance prediction algorithm for quantifying data and model uncertainty according to claim 1, characterized in that, In step 5, when the given input parameter is the pavement inspection index x before road element maintenance... n Maintenance plan At that time, model f is based on x n and Each prediction is a sampling process, let j represent the j-th sampling; The expected predicted values ​​of the road element maintenance post-inspection indicators, which are used as input parameters, and the standard deviations used to represent the uncertainty of the data and model are estimated through a Monte Carlo simulation with 1000 sampling times. The calculation method is as follows: In the formula, This indicates that the pre-maintenance detection index x is based on the nth sample. n Maintenance plan The expected prediction results obtained from Monte Carlo simulation, This indicates the uncertainty of the predicted value at this time. This indicates the model uncertainty of the predicted value at this time, f j () represents the j-th prediction of the model. and This represents the uncertainty of the predicted value obtained from the j-th prediction by the model compared to the data.

9. The road performance prediction algorithm for quantifying data and model uncertainty according to claim 1, characterized in that, The processing procedure in step 6 is as follows: Preparation phase: The lower bound of the prediction result with a certain confidence level is obtained by using the data uncertainty in step 5, which serves as the basis for judging the timing of maintenance under the worst possible road conditions in the future. Based on step 5, the mean of the model uncertainty of the expected predicted values ​​of all road element post-maintenance detection indicators in the pavement performance change database of the road segment to be predicted is used as the threshold. Decision-making stage: Following the method in step 5, the expected predicted value, model uncertainty, and prediction uncertainty of the detection index of the road element to be judged are obtained. The model uncertainty is compared with the threshold obtained in the preparation stage. When the model uncertainty of the predicted value of the corresponding road element to be judged is greater than the threshold, the predicted value is considered unreliable and the corresponding output predicted value is not used for the decision on the timing of maintenance. Otherwise, the expected predicted value of the detection index and the data uncertainty are used to calibrate the lower limit of pavement performance and are used for the judgment and decision on the maintenance plan and the timing of maintenance.

Images