CN114881359A - GBDT and XGboost fused road surface IRI prediction method - Google Patents

Abstract

The invention relates to a pavement IRI prediction method fusing GBDT and XGboost, and belongs to the technical field of pavement monitoring. The method comprises the following steps: s1: acquiring pavement characteristic data, and selecting a characteristic data set by adopting a random forest algorithm; s2: constructing a Stacking fusion model: dividing the characteristic data set of the step S1 into a plurality of sub data sets, inputting the sub data sets into each base learner of the first layer prediction model, and outputting a respective prediction result by each base learner; then, taking the model output of the first layer and the characteristic data set of the step S1 as the input of the second layer, training a meta-learner of a prediction model of the second layer, and averaging the model output of the second layer to obtain a final prediction result; the first layer of prediction models comprise a GBDT model and an XGboost model. The invention improves the road IRI prediction precision, greatly improves the maintenance fund planning benefit and realizes the goal of optimal cost benefit.

Description

GBDT and XGboost fused road surface IRI prediction method

Technical Field

The invention belongs to the technical field of pavement monitoring, and relates to a pavement IRI prediction method fusing GBDT and XGboost.

Background

The existing pavement evenness evaluation index (IRI) prediction method mainly comprises two main types, one type is a prediction method based on a time sequence, and the other type is a learning type prediction method based on characteristic parameters.

The prediction method based on the time series mainly predicts the decay of performance indexes in the whole life cycle of a road surface and is used for maintenance planning and fund allocation, and the utilized data mainly comprises structural characteristic data, traffic environment data and historical detection data and often needs enough historical detection data for modeling. The method does not fully utilize bottom layer detection data including disease information, characteristic parameters and the like. The main problem is that the prediction model has poor precision and can only be applied to network level road management decision.

The learning type prediction method based on the characteristic parameters is mainly divided into two types, one type is used for assisting the modeling of a time sequence model, and the other type is used for predicting other performance indexes based on certain detection data. The precision is relatively high, but a large amount of data is needed as a support, and the portability of different project management modes is poor.

Therefore, a new road surface IRI prediction method is needed to improve the prediction accuracy.

Disclosure of Invention

In view of the above, the invention aims to provide a road surface IRI prediction method fusing GBDT and XGboost, which solves the problem of feature selection of the existing learning type prediction model; and the fusion model is adopted, so that the road surface IRI prediction precision is improved, the maintenance fund planning benefit can be greatly improved, and the goal of optimal cost benefit is realized.

In order to achieve the purpose, the invention provides the following technical scheme:

a road surface IRI prediction method fusing GBDT and XGboost specifically comprises the following steps:

s1: acquiring pavement characteristic data, and selecting a characteristic data set by adopting a random forest algorithm;

s2: constructing a Stacking fusion model: dividing the characteristic data set of the step S1 into a plurality of sub data sets, inputting the sub data sets into each base learner of the first layer prediction model, and outputting a respective prediction result by each base learner; then, the model output of the first layer and the feature data set of step S1 are used as the input of the second layer, the meta-learner of the second layer prediction model is trained, and the model outputs at the second layer are averaged to obtain the final prediction result. The first layer of prediction model comprises a GBDT model and an XGboost model; and the meta-learner of the second layer of prediction model adopts a Bagging model.

Further, in step S1, the random forest algorithm specifically includes: and selecting the features by using an average impurity degree reduction index, using classification or regression precision as a criterion function and using a sequence backward selection method and a generalized sequence backward selection method.

Further, in step S1, the average impure reduction index MDI is calculated by the formula:

wherein, IMP _R 、IMP _L The overall purity and the purity of the left and right sides of the bifurcation, N, are indicated ^t 、

Respectively representing the number of samples of the global, left and right nodes, N being the sample size.

Further, in step S2, constructing a GBDT model specifically includes: input training sample set T { (x) ₁ ,y ₁ ),…,(x _i ,y _i ),…,(x _N ,y _N )}，

Where X is the input sample space, X _i Is an index for evaluation of the properties of the specimen,

y is the performance condition and the loss function is L (Y) _i ,f(x _i ) The output is regressionTree (R)

The specific training process of the GBDT model is as follows:

1) initializing an estimation function to minimize a loss function;

wherein f is ₀ (x) Is a tree with only one root node, L (y) _i C) is a loss function, c is a constant that minimizes the loss function;

2) let M be 1,2, …, M representing the maximum number of iterations;

calculating the negative gradient of the loss function for the ith sample, i is 1,2, …, N, and using the negative gradient as a residual error estimation;

wherein r is _mi Represents the residual estimate of the ith sample;

② fitting residual error pairs rm _j Generating a regression tree to estimate regression leaf node region to obtain mth tree node region R _mj Wherein J is 1,2, …, J and J represents the number of leaf nodes;

(iii) for J ═ 1,2, …, J, the values of the leaf node regions are estimated using a linear search, minimizing the loss function:

fourthly, updating the learner f _m (x _i )：

3) All c's in the same leaf node area _mj And accumulating the values to obtain a final regression tree:

further, in step S2, constructing an XGBoost model specifically includes: input training sample set T { (x) ₁ ,y ₁ ),…,(x _i ,y _i ),…,(x _N ,y _N )}，

Where X is the input sample space, X _i Is an index for evaluation of the properties of the specimen,

y is the performance condition;

objective function

Comprises the following steps:

wherein the content of the first and second substances,

representing a predicted value;

in the XGboost, each tree needs to be added one by one, so that the effect can be improved;

wherein t is the number of trees;

if the leaves have too many nodes, the risk of over-fitting the model increases. So at the targetAdding penalty term omega (f) into function _t ) Limiting the number of leaf nodes;

wherein gamma is punishment, T is the number of leaves, omega is the weight of a leaf node, lambda is an adjustable parameter, and omega is _j A leaf node score set is set for each tree;

complete objective function Obj ^(t) Comprises the following steps:

note the book

To obtain

Solving the optimal solution of the objective function:

the above formula can be used as the cotyledon fraction of the tree, and the structure of the tree is excellent along with the increase of the fraction; and once the post-splitting result is less than the maximum resultant value for the given parameter, the algorithm will stop growing the cotyledon depth.

The invention has the beneficial effects that:

(1) the invention solves the problem of feature selection of the existing learning type prediction, and the selection of the feature index is inspected by using the support degree based on feature learning instead of using a simple correlation analysis technology (such as a Pearson correlation coefficient). The accuracy can be greatly improved, and the model has strong application scene transplanting capability.

(2) The invention adopts the fusion model, improves the road surface IRI prediction precision compared with a single model, and overcomes the problem that the traditional prediction model only solves the average fitting precision.

(3) The invention can be widely applied to different areas through improving the precision and the transplanting performance. By improving the prediction precision, the maintenance fund planning benefit can be greatly improved, and the aim of optimizing the cost benefit is fulfilled.

Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objectives and other advantages of the invention may be realized and attained by the means of the instrumentalities and combinations particularly pointed out hereinafter.

Drawings

For the purposes of promoting a better understanding of the objects, aspects and advantages of the invention, reference will now be made to the following detailed description taken in conjunction with the accompanying drawings in which:

FIG. 1 is a schematic flow chart of a road surface IRI prediction method fusing GBDT and XGboost according to the invention;

FIG. 2 is a schematic diagram of feature importance scoring based on a random forest algorithm;

FIG. 3 is a comparison graph of the prediction effect of the Stacking fusion model of the present invention and the existing multivariate linear regression, SVM, GBDT, XGboost models.

Detailed Description

The embodiments of the present invention are described below with reference to specific embodiments, and other advantages and effects of the present invention will be easily understood by those skilled in the art from the disclosure of the present specification. The invention is capable of other and different embodiments and of being practiced or of being carried out in various ways, and its several details are capable of modification in various respects, all without departing from the spirit and scope of the present invention. It should be noted that the drawings provided in the following embodiments are only for illustrating the basic idea of the present invention in a schematic way, and the features in the following embodiments and examples may be combined with each other without conflict.

Wherein the showings are for the purpose of illustrating the invention only and not for the purpose of limiting the same, and in which there is shown by way of illustration only and not in the drawings in which there is no intention to limit the invention thereto; to better illustrate the embodiments of the present invention, some parts of the drawings may be omitted, enlarged or reduced, and do not represent the size of an actual product; it will be understood by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted.

The same or similar reference numerals in the drawings of the embodiments of the present invention correspond to the same or similar components; in the description of the present invention, it should be understood that if there is an orientation or positional relationship indicated by terms such as "upper", "lower", "left", "right", "front", "rear", etc., based on the orientation or positional relationship shown in the drawings, it is only for convenience of description and simplification of description, but it is not an indication or suggestion that the referred device or element must have a specific orientation, be constructed in a specific orientation, and be operated, and therefore, the terms describing the positional relationship in the drawings are only used for illustrative purposes, and are not to be construed as limiting the present invention, and the specific meaning of the terms may be understood by those skilled in the art according to specific situations.

Referring to fig. 1 to 3, a road surface IRI prediction method fusing GBDT and XGBoost mainly includes the following steps:

1) all the characteristic data (according to actual conditions) are obtained, and specific characteristic variables are shown in table 1.

TABLE 1 characterization of characteristic variables

2) Feature selection

And (4) performing feature selection by adopting a machine learning mode, wherein the used model is a random forest. The random forest feature selection is to use a random forest algorithm to automatically select features with high correlation. The method is a random forest based packaging type feature selection algorithm, takes a random forest algorithm as a basic tool, takes classification or regression precision as a criterion function, and adopts a sequence backward selection method and a generalized sequence backward selection method to select features.

The average impurity reduction index is used for feature selection,

wherein, IMP _R 、IMP _L Respective purity, N ^t 、

Respectively, the number of samples of the node, and N is the sample size.

The input port is used for receiving the data set transmitted by the front node, the output port is used for outputting the data set added with the discrete fields, the characteristic index results with the characteristic quantity not more than 20 and the purity reduction gradient result more than 0.02 are selected and shown in fig. 2.

3) GBDT model

The GBDT algorithm is essentially a combination of a large number of simple models, and the core of the GBDT algorithm is that, starting from the second decision tree, the input of each decision tree is the sum of the outputs of all the previous decision trees, and based on the promotion idea, the conclusions of a plurality of decision trees are accumulated to obtain the final output.

GBDT is a decision tree algorithm trained based on the Gradient Boosting strategy, and mainly comprises three parts of Gradient Boosting, decision tree algorithm and reduction. The core idea of GBDT is to reduce the residual error, each iteration of which is to reduce the residual error generated by the previous iteration. And when the model prediction result is inconsistent with the actual observed value, generating a new decision tree in the gradient direction of residual error reduction so as to reduce the residual error of the last time, and continuously and repeatedly iterating until the output result is basically consistent with the actual observed value. One sign of continuous optimization and improvement of the model is iterative descent of the loss function of the model, and the GBDT algorithm is to construct a new model in the gradient descent direction of the loss function.

Input training sample set T { (x) ₁ ,y ₁ ),…,(x _i ,y _i ),…,(x _N ,y _N )}，

Where X is the input sample space, X _i Is an index of evaluation of the amount of the substance,

y is the performance condition and the loss function is L (Y) _i ,f(x _i ) The output is a regression tree

The specific training process of the GBDT model is as follows:

1) initializing an estimation function to minimize a loss function;

wherein f is ₀ (x) Is a tree with only one root node, L (y) _i C) is a loss function, c is a constant that minimizes the loss function;

2) let M be 1,2, …, M representing the maximum number of iterations;

calculating the negative gradient of the loss function for the ith sample, i is 1,2, …, N, and using the negative gradient as a residual error estimation;

wherein r is _mi Represents the residual estimate of the ith sample;

② fitting residual error pairs rm _j Generating a regression tree to estimate regression leaf node region to obtain mth tree node region R _mj Wherein J is 1,2, …, J and J represents the number of leaf nodes;

(iii) for J ═ 1,2, …, J, the values of the leaf node regions are estimated using a linear search, minimizing the loss function:

fourthly, updating the learner f _m (x _i )：

3) All c's in the same leaf node area _mj And accumulating the values to obtain a final regression tree:

4) XGboost model

The XGboost is an iterative tree algorithm, combines a plurality of weak classifiers into a strong classifier together, and is an implementation of a Gradient Boosting Decision Tree (GBDT). XGboost is a powerful sequential integration technique with a modular structure for parallel learning to achieve fast computations, which prevents overfitting by regularization and can generate a weighted quantile sketch that processes weighted data.

The specific algorithm steps are as follows:

objective function

Comprises the following steps:

wherein the content of the first and second substances,

representing a predicted value;

in the XGboost, each tree needs to be added one by one, so that the effect can be improved;

wherein t is the number of trees;

if the leaves have too many nodes, the risk of over-fitting the model increases. So a penalty term omega (f) is added to the objective function _t ) Limiting the number of leaf nodes;

wherein gamma is punishment, T is the number of leaves, omega is the weight of a leaf node, lambda is an adjustable parameter, and omega is _j A leaf node score set is set for each tree;

complete objective function Obj ^(t) Comprises the following steps:

note book

To obtain

Solving the optimal solution of the objective function:

the above formula can be used as the cotyledon fraction of the tree, and the structure of the tree is excellent along with the increase of the fraction; and once the post-splitting result is less than the maximum resultant value for the given parameter, the algorithm will stop growing the cotyledon depth.

5) Stacking fusion model

The Stacking model fusion method includes the steps that firstly, an original characteristic data set is divided into a plurality of sub data sets, the sub data sets are input into each base learner of a first-layer prediction model, and each base learner outputs a prediction result. Then, the output of the first layer is used as the input of the second layer, the meta-learner of the prediction model of the second layer is trained, and the model positioned at the second layer outputs the final prediction result. The Stacking model fusion method can improve the overall prediction precision by generalizing the output results of a plurality of models.

In the first stage, an original data set is firstly segmented and divided into a training set and a test set according to a certain proportion, then a proper base learner is selected to train the training set in a cross validation mode, each trained base learner predicts the validation set and the test set, and a machine learning model with excellent prediction performance is selected in the first stage, and meanwhile diversification among the models is guaranteed; in the second stage, the prediction result of the base learner is respectively used as feature data for training and predicting the meta learner, the meta learner performs model construction by combining the features obtained in the last stage and the labels of the original training set as sample data, and outputs the final Stacking model prediction result, and the meta learner in the stage generally selects a simple model with better stability to play a role in integrally improving the model performance.

As shown in fig. 1, the Stacking fusion model: and using two different integrated model algorithms of GBDT and XGboost as a base learner to obtain two groups of prediction results, then applying the three groups of prediction results to a second layer of a using element learner, and selecting a Bagging model for training so as to obtain a final prediction result.

6) Stacking fusion model prediction result and evaluation

In order to verify the superiority of the Stacking fusion model in road surface IRI prediction, the same training set and test set are selected, and the Stacking fusion model is compared and analyzed with the existing 4 prediction models (multivariate linear regression, SVM, GBDT and XGboost), as shown in FIG. 3.

Taking the LTPP data in the united states as an example, spanning 62 states, cities, including: traffic volume size (76989 pieces of data), crack length (12964 pieces of data), traffic open date (1817 pieces of data), rut depth (18128 pieces of data), IRI size (97535 pieces of data), texture information (18735 pieces of data), total 6 tables, and total 226128 pieces of data.

As shown in Table 1 and FIG. 3, on the basis of road surface IRI prediction results, the accuracy of the Stacking fusion model is further improved on GBDT and XGboost models which are good in performance, the final RMSE is 0.040, the final MAE is 0.013, and the R is ² 0.996, and meets the high-precision requirement in road surface prediction.

TABLE 1 evaluation index of each prediction model

Finally, the above embodiments are only intended to illustrate the technical solutions of the present invention and not to limit the present invention, and although the present invention has been described in detail with reference to the preferred embodiments, it will be understood by those skilled in the art that modifications or equivalent substitutions may be made on the technical solutions of the present invention without departing from the spirit and scope of the technical solutions, and all of them should be covered by the claims of the present invention.

Claims (6)

1. A road surface IRI prediction method fusing GBDT and XGboost is characterized by comprising the following steps:

s1: acquiring pavement characteristic data, and selecting a characteristic data set by adopting a random forest algorithm;

s2: constructing a Stacking fusion model: dividing the characteristic data set of the step S1 into a plurality of sub data sets, inputting the sub data sets into each base learner of the first layer prediction model, and outputting a respective prediction result by each base learner; then, taking the model output of the first layer and the characteristic data set of the step S1 as the input of the second layer, training a meta-learner of a prediction model of the second layer, and averaging the model output of the second layer to obtain a final prediction result; the first layer of prediction models comprise a GBDT model and an XGboost model.

2. The road surface IRI prediction method according to claim 1, wherein in step S1, the random forest algorithm specifically comprises: and selecting the features by using an average impurity degree reduction index, using classification or regression precision as a criterion function and using a sequence backward selection method and a generalized sequence backward selection method.

3. The road surface IRI prediction method according to claim 2, wherein in step S1, the average impure degree reduction index MDI is calculated by the following formula:

wherein, IMP _R 、IMP _L The overall purity and the purity of the left and right sides of the bifurcation, N, are indicated ^t 、

Respectively representing the number of samples of the global, left and right nodes, N being the sample size.

4. The road surface IRI prediction method according to claim 1, wherein in step S2, constructing the GBDT model specifically includes: input training sample set T { (x) ₁ ,y ₁ ),…,(x _i ,y _i ),…,(x _N ,y _N )}，

Where X is the input sample space, X _i Is an index for evaluation of the properties of the specimen,

y is the performance condition and the loss function is L (Y) _i ,f(x _i ) The output is a regression tree

The specific training process of the GBDT model is as follows:

1) initializing an estimation function to minimize a loss function;

wherein f is ₀ (x) Is a tree with only one root node, L (y) _i C) is a loss function, c is a constant that minimizes the loss function;

2) let M be 1,2, …, M representing the maximum number of iterations;

calculating the negative gradient of the loss function for the ith sample, i is 1,2, …, N, and using the negative gradient as a residual error estimation;

wherein r is _mi Represents the residual estimate of the ith sample;

② fitting residual error pairs rm _i Generating a regression tree to estimate regression leaf node region to obtain mth tree node region R _mj Wherein J is 1,2, …, J and J represents the number of leaf nodes;

(iii) for J ═ 1,2, …, J, the values of the leaf node regions are estimated using a linear search, minimizing the loss function:

fourthly, updating the learner f _m (x _i )：

3) In the same leafNode region will all c _mj And accumulating the values to obtain a final regression tree:

5. the road surface IRI prediction method according to claim 1, wherein in step S2, an XGboost model is constructed, specifically comprising: input training sample set T { (x) ₁ ,y ₁ ),…,(x _i ,y _i ),…,(x _N ,y _N )}，

Where X is the input sample space, X _i Is an index for evaluation of the properties of the specimen,

y is the performance condition;

objective function

Comprises the following steps:

wherein the content of the first and second substances,

representing a predicted value;

in XGboost, each tree is added one by one;

wherein t is the number of trees;

adding penalty term omega (f) into the objective function _t ) Limiting the number of leaf nodes;

wherein gamma is punishment, T is the number of leaves, omega is the weight of a leaf node, lambda is an adjustable parameter, and omega is _j A leaf node score set is set for each tree;

complete objective function Obj ^(t) Comprises the following steps:

note the book

To obtain

Solving the optimal solution of the objective function:

the above formula can be used as the cotyledon fraction of the tree, and the structure of the tree is excellent along with the increase of the fraction; and once the post-splitting result is less than the maximum resultant value for the given parameter, the algorithm will stop growing the cotyledon depth.

6. The road surface IRI prediction method according to claim 1, wherein in step S2, the meta-learner of the second layer prediction model employs a Bagging model.

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