Emission estimation model updating method with robustness

Abstract

The invention relates to the technical field of road moving source emission estimation, and discloses an emission estimation model updating method with robustness, which comprises the following steps of: constructing a labeled data set based on a labeled monitoring sample and a corresponding emission label, constructing a plurality of sub-models based on a labeled data set and an original emission estimation model trained on the labeled data set and used for emission estimation; solving an optimal sub-model by adopting a cross optimization method; selecting a key monitoring sample based on the estimated difference of the maximum branch sub-model, and carrying out manual labeling to obtain a plurality of labeled monitoring samples; on the basis of the newly obtained multiple labeled monitoring samples, a maximum correlation entropy criterion is introduced to deal with the problem that part of labels are not reliable, and emission estimation model updating with robustness is achieved. In order to solve the problem of high annotation data acquisition cost, the method realizes establishment of an update emission estimation model based on few sample annotations through selection of key samples.

Description

Technical Field

[0001] The invention relates to the technical field of road mobile source emission estimation, and in particular to a robust emission estimation model updating method. Background Art

[0002] The standard operating condition emission estimation of road mobile sources refers to the estimation of the emission conditions under standard operating conditions (that is, the vehicle under specific conditions, such as specific vehicle speed, specific acceleration, specific load, etc.) based on the real-time on-road emission monitoring data of the mobile sources. Since the real-time on-road emissions are related to the vehicle type, fuel type, emission standards, road conditions and environmental factors, the above factors need to be fully considered in the standard operating condition emission estimation in order to achieve accurate estimation.

[0003] Since there is less data on standard operating condition emissions, there is a problem of insufficient labeled data in the estimation of standard operating condition emissions from road mobile sources. To address this problem, the present invention adopts an active learning method. Active learning uses limited labeled samples and a relatively large number of unlabeled samples to improve the model learning effect. By screening out a small number of samples that require manual labeling from the unlabeled samples, the model performance is maximized with the least possible labeling cost. Therefore, in active learning, how to define the importance of unlabeled samples in model updating to achieve sample screening is a key issue. On the other hand, in the standard operating condition emission estimation scenario for road mobile sources, the labels of labeled monitoring samples may be noisy. In this case, how to reliably update the emission estimation model based on noisy labels also becomes an important issue. Summary of the invention

[0004] In order to solve the above technical problems, the present invention provides a robust emission estimation model updating method. The present invention respectively proposes a key sample selection method based on the maximum divergence sub-model and a model updating method integrating related entropy to achieve the establishment of a robust updated emission estimation model.

[0005] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0006] A robust emission estimation model updating method is used to update an original emission estimation model of a standard working condition of a road mobile source to obtain an updated emission estimation model, which specifically includes the following steps:

[0007] Step 1: construct a labeled data set based on the labeled monitoring samples and the corresponding emission labels, and construct m sub-models based on the labeled data set and the original emission estimation model trained on the labeled data set for emission estimation; construct formula 1 so that the sub-models have the maximum divergence, so as to obtain m optimal sub-models:

[0008] Formula 1:

[0010] Among them, Ω m is the parameter of the mth sub-model, represents the parameters of the mth optimal sub-model, J1 represents the objective function of the optimized sub-model, λ Z ,λ P is the trade-off factor; W0, H0, y0 are the training error weight matrix, feature matrix and corresponding emission label based on the labeled monitoring samples respectively; Ω i ,Ω j are the parameters of the i-th sub-model and the j-th sub-model, respectively, 1≤i,j≤m; Ω0 is the parameter of the original emission estimation model; ‖·‖2 represents the F2 norm;

[0011] The cross optimization method is used to solve the optimization problem corresponding to formula 1, and we get

[0012] Step 2: Use m optimal sub-models to transform u unlabeled monitoring samples x p Divide into c intervals, and select some unlabeled monitoring samples in each interval to add to the monitoring sample set to be labeled, and manually label α samples to be labeled in the monitoring sample set to be labeled, and obtain α labeled monitoring samples x s ;

[0013] Step 3: Initialize the updated emission estimation model through the original emission estimation model, that is, let Ω = Ω0, Ω is the parameter of the updated emission estimation model; construct formula 2 to optimize the parameters of the updated emission estimation model:

[0014] Formula 2:

[0015] Among them, Ω * represents the optimal Ω, J2 represents the objective function of optimizing and updating the emission estimation model, is the complexity measure for updating the emission estimation model, λ Q ,λ x is a weighing factor; To introduce the true emission label and update the emission estimation model, the emission estimation result is related to the entropy to obtain the empirical loss term, H k is the kth labeled monitoring sample The characteristic vector of for The true emission label of σ1 is the Gaussian kernel width; It is a measure of the difference between the updated emission estimation model and the original emission estimation model, which is used to constrain the degree of updating; ‖·‖2 represents the F2 norm; ‖·‖1 represents the F1 norm;

[0016] The proximal descent method is used to optimize the parameters of the updated emission estimation model. When the change of J2 is less than the preset value V T When , the optimization is stopped and the optimal updated emission estimation model parameters are obtained, that is, the final updated emission estimation model is obtained.

[0017] Furthermore, the original emission estimation model and the updated emission estimation model are multivariate polynomial regression models.

[0018] Furthermore, step 2 specifically includes:

[0019] The unlabeled monitoring sample x p Input into m optimal sub-models respectively, and calculate the mean of the m emission estimation results And variance δ, then for u unlabeled monitoring samples x p The sequence that can get the mean and the sequence of variances δ1,δ2,…,δ u , and δ u is the u-th unlabeled monitoring sample The corresponding mean and variance; the mean sequence Discretized into c intervals, different intervals represent different emission levels. The unlabeled monitoring samples in each interval are arranged from large to small according to the corresponding variance, and the first a unlabeled monitoring samples are selected to be added to the monitoring sample set to be labeled. Then, the α unlabeled monitoring samples in the monitoring sample set to be labeled are manually labeled to obtain α labeled monitoring samples x s , where α = a·c.

[0020] During actual reasoning, the unlabeled monitoring samples are input into the updated emission estimation model to predict the emission estimation results of the unlabeled monitoring samples.

[0021] Compared with the prior art, the beneficial technical effects of the present invention are:

[0022] In order to solve the problem of high cost of obtaining labeled data, this patent adopts active learning to select key samples to establish an updated emission estimation model based on a small number of labeled samples. A maximum divergence sub-model construction method is proposed, so that the sub-model performs well on the initially labeled samples, and produces the largest possible output divergence on the unlabeled samples. The samples to be labeled are selected based on the output difference of the sub-model to the samples. At the same time, considering the problem of skewed data distribution, the emission estimation results of the unlabeled samples are discretized, and the same number of key samples are selected in each interval. Finally, when updating the model based on actively requested offline annotations, the problem of noise in the annotations is considered, and the maximum relevant entropy criterion is introduced to deal with the noise in the data, thereby realizing the establishment of a robust updated emission estimation model. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 It is a schematic diagram of the process of the present invention. DETAILED DESCRIPTION

[0024] A preferred embodiment of the present invention is described in detail below with reference to the accompanying drawings.

[0025] The present invention provides a robust emission estimation model updating method, which specifically comprises the following steps:

[0026] S1, based on the labeled dataset and the original emission estimation model for emission estimation trained on the labeled dataset, construct m sub-models so that the sub-models have the maximum divergence, that is, optimize the following problem:

[0027] Formula 1:

[0029] in, Respectively represent the optimal Ω1,Ω2,…,Ω m , J1 represents the objective function of the optimization sub-model, λ Z ,λ P >0 are the weight factors used to weigh the corresponding items; W0, H0, y0 are the training error weight matrix, feature matrix and label vector based on the labeled monitoring samples respectively.

[0030] Here, making the sub-models have the greatest divergence means making the parameters of each sub-model as different as possible, which is measured by the second term in formula 1.

[0031] S2 is solved by cross optimization method.

[0032] S3, based on the estimated differences of the maximum divergence sub-model, select key monitoring samples and manually label them; specifically, pInput them into the m optimal sub-models respectively to obtain the corresponding emission estimation results And find its mean and variance δ, then for the unlabeled monitoring sample set The u unlabeled monitoring samples in can obtain the mean sequence of emission estimation results of all optimal sub-models. and the variance sequence δ1,δ2,…,δ u ,in represents an unlabeled monitoring sample, k=1,2,...u, and u represents the number of unlabeled monitoring samples in the unlabeled monitoring sample set.

[0033] The mean series Discretized into c intervals, different intervals represent different emission levels, such as high emission, medium emission, low emission, etc. In each interval, the unlabeled monitoring samples are arranged from large to small according to their corresponding variances, and the first a unlabeled monitoring samples are selected to be added to the set of monitoring samples to be labeled, c and a are two preset values, and then the obtained α = a·c samples to be labeled are manually labeled, that is, α labeled monitoring samples x are obtained s .

[0034] S4, based on the newly obtained α labeled monitoring samples, introduce the maximum correlation entropy criterion to deal with the problem of unreliable partial annotations and realize the update of the emission estimation model with robustness. Specifically: introduce the Gaussian kernel function, for the obtained labeled monitoring samples The new empirical loss term is obtained by introducing the real emission label and updating the emission estimation model. Where Ω represents the parameters of the updated emission estimation model, H k For labeled monitoring samples The eigenvector of σ1 is the Gaussian kernel width. At the same time, the difference measure between the updated emission estimation model and the original emission estimation model is introduced To constrain the degree of model update; in summary, model update can be described as the following optimization problem:

[0035] Formula 2:

[0036] Among them, Ω * represents the optimal Ω, J2 represents the objective function of optimizing and updating the emission estimation model, is the complexity measure for updating the emission estimation model, λ Q ,λ x >0 are the weighting factors used to weigh the corresponding items.

[0037] The above optimization problem is solved by the following idea: Initialize Ω = Ω0, use the proximal descent method to solve Ω, and wait until the change of J2 is less than the preset value V T When the optimization is stopped, the optimal updated emission estimation model parameters can be obtained, that is, the establishment of a robust updated emission estimation model for standard operating condition emission estimation of road mobile sources is completed.

[0038] During actual reasoning, the unlabeled monitoring samples are input into the updated emission estimation model to predict the emission estimation results of the unlabeled monitoring samples.

[0039] It is obvious to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the present invention can be implemented in other specific forms without departing from the spirit or essential features of the present invention. Therefore, from any point of view, the embodiments should be regarded as exemplary and non-limiting, and the scope of the present invention is defined by the appended claims rather than the above description, and it is intended that all changes falling within the meaning and scope of the equivalent elements of the claims are included in the present invention, and any reference numerals in the claims should not be regarded as limiting the claims involved.

[0040] In addition, it should be understood that although this specification is described in terms of implementation methods, not every implementation method contains only one independent technical solution. This narrative method of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation methods that can be understood by those skilled in the art.

Claims

1. A robust emission estimation model updating method is used to update the original emission estimation model of the standard working condition of the road mobile source to obtain an updated emission estimation model, specifically The following steps are involved: Step 1: construct a labeled data set based on the labeled monitoring samples and the corresponding emission labels, and construct m sub-models based on the labeled data set and an original emission estimation model trained on the labeled data set for emission estimation; Construct formula 1 to maximize the divergence between sub-models so as to obtain m optimal sub-models: Formula 1: Among them, Ω m is the parameter of the mth sub-model, represents the parameters of the mth optimal sub-model, J 1 represents the objective function of the optimized sub-model, λ Z ,λ P is the trade-off factor; W 0 , H 0 ,y 0 are the training error weight matrix, feature matrix and corresponding emission labels based on the labeled monitoring samples; Ω i ,Ω j are the parameters of the i-th sub-model and the j-th sub-model, 1≤i, j≤m; Ω 0 Estimate the parameters of the model for the original emissions; ||·|| 2 represents the F2 norm; The cross optimization method is used to solve the optimization problem corresponding to formula 1, and we get Step 2: Use m optimal sub-models to divide u unlabeled monitoring samples xp into c intervals, and select some unlabeled monitoring samples in each interval to add to the set of unlabeled monitoring samples, and manually label α unlabeled samples in the set of unlabeled monitoring samples to obtain α labeled monitoring samples xp. s ; Step 3: Initialize the updated emission estimation model through the original emission estimation model, that is, let Ω = Ω 0 , Ω is the parameter of the updated emission estimation model; construct formula 2 to optimize the parameters of the updated emission estimation model: Formula 2: Among them, Ω * represents the optimal Ω, J 2 represents the objective function for optimizing and updating the emission estimation model, is the complexity measure for updating the emission estimation model, λ Q ,λ X is a weighing factor; To introduce the true emission label and update the emission estimation model, the emission estimation result is related to the entropy to obtain the empirical loss term, H k is the kth labeled monitoring sample The characteristic vector of for The true emission label of σ 1 is the Gaussian kernel width; is a measure of the difference between the updated emission estimation model and the original emission estimation model, used to constrain the degree of updating; ||·|| 2 represents the F2 norm; ||·|| 1 represents the F1 norm; The proximal descent method is used to optimize the parameters of the updated emission estimation model. 2 The change is less than the preset value V T When , the optimization is stopped and the optimal updated emission estimation model parameters are obtained, that is, the final updated emission estimation model is obtained.

2. The robust emission estimation model updating method according to claim 1, It is characterized in that The original emission estimation model and the updated emission estimation model are multivariate polynomial regression models.

3. The robust emission estimation model updating method according to claim 1, It is characterized in that Step 2 specifically includes: Input the unlabeled monitoring samples xp into the m optimal sub-models respectively, and calculate the mean of the m emission estimation results and variance 6, then for u unlabeled monitoring samples xp, the sequence of the mean can be obtained and the sequence of variance δ 1 , δ 2 , ..., δ u , and δ u is the u-th unlabeled monitoring sample The corresponding mean and variance; the mean sequence Discretized into c intervals, different intervals represent different emission levels. The unlabeled monitoring samples in each interval are arranged from large to small according to the corresponding variance, and the first a unlabeled monitoring samples are selected to be added to the monitoring sample set to be labeled. Then, the α unlabeled monitoring samples in the monitoring sample set to be labeled are manually labeled to obtain α labeled monitoring samples x s , where α=ac.

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