Method for determining importance degree of uncertain factors of traffic network-power distribution network based on moment independence method and related equipment

Abstract

The invention relates to a method for determining the importance degree of uncertain factors of a traffic network-power distribution network based on a moment independence method and related equipment. The method comprises the following steps: acquiring uncertain factors meeting a set condition in a to-be-determined traffic network-power distribution network, then acquiring first distribution characteristic information corresponding to any current uncertain factor in a plurality of uncertain factors, and inputting the current uncertain factor and other uncertain factors except the current uncertain factor into a PCK model; the method comprises the steps of obtaining first distribution feature information, obtaining second distribution feature information, further inputting uncertain factors into a PCK model to obtain third distribution feature information, and finally obtaining probability joint flow global sensitivity index information corresponding to the uncertain factors based on the first distribution feature information, the second distribution feature information and the third distribution feature information. And the importance degree of each uncertain factor is determined according to the probability joint flow global sensitivity index information. By adopting the method, the accuracy of determining the importance degree of the uncertain factors in the traffic network-power distribution network can be improved.

Description

Technical Field

[0001] The present application relates to the technical field of transportation network-distribution network coupled operation analysis, and in particular to a method, device, computer equipment, computer-readable storage medium and computer program product for determining the importance of uncertainty factors in a transportation network-distribution network based on a moment independence method. Background Art

[0002] With the large-scale promotion and application of electric vehicles, the coupled operation characteristics of the transportation network and the distribution network are becoming increasingly prominent. In this context, a large number of uncertainties will continue to propagate along with the interaction process of the coupled system and affect the safe operation of the transportation network-distribution network. However, the impact of various uncertainties on traffic flow and power flow is not the same. How to quantify the impact of "road", "vehicle", "source" and "load" on traffic flow and power flow to reflect the interactive impact of the coupled system under the propagation of uncertainty is a problem that needs to be further solved.

[0003] Sensitivity analysis method is an effective means to quantify the influence of input variables. The traditional local sensitivity method based on partial derivatives has the problem of low accuracy in determining the importance of uncertain factors in the transportation network-distribution network. Summary of the invention

[0004] Based on this, it is necessary to provide a method, device, computer equipment, computer-readable storage medium and computer program product for determining the importance of uncertain factors in a transportation network-distribution network based on the moment independence method, which can improve the accuracy of determining the importance of uncertain factors in response to the above-mentioned technical problems.

[0005] In a first aspect, the present application provides a method for determining the importance of uncertain factors of a transportation network-distribution network based on the moment independence method, comprising:

[0006] Obtain multiple uncertain factors that meet the set conditions in the to-be-determined transportation network-distribution network; the multiple uncertain factors include road capacity, road ambient temperature, automobile travel demand, electric vehicle initial SOC, electric vehicle charging end SOC, renewable resources and load;

[0007] Obtaining first distribution feature information corresponding to any current uncertainty factor among the multiple uncertainty factors, and inputting the current uncertainty factor and other uncertainty factors except the current uncertainty factor into a pre-constructed PCK model, and obtaining second distribution feature information through the PCK model;

[0008] Input the uncertain factors into the PCK model, and obtain the third distribution characteristic information through the PCK model;

[0009] Based on the first distribution feature information, the second distribution feature information and the third distribution feature information, the probability joint flow global sensitivity index information corresponding to each uncertain factor is obtained, and the importance of each uncertain factor is determined according to the probability joint flow global sensitivity index information.

[0010] In one embodiment, based on the first distribution feature information, the second distribution feature information, and the third distribution feature information, obtaining the probability joint flow global sensitivity index information corresponding to each uncertain factor includes:

[0011] Acquire multiple global sensitivity index information corresponding to each uncertainty factor according to the first distribution characteristic information, the second distribution characteristic information, and the third distribution characteristic information;

[0012] The multiple global sensitivity index information is normalized to obtain the global sensitivity index information of the probability joint flow corresponding to each uncertain factor.

[0013] In one embodiment, obtaining global sensitivity index information corresponding to each uncertainty factor according to the first distribution feature information, the second distribution feature information, and the third distribution feature information includes:

[0014] Based on the second distribution feature information and the third distribution feature information, obtaining distribution feature distance information;

[0015] According to the first distribution feature information and the distribution feature distance information, global sensitivity index information corresponding to each uncertain factor is obtained.

[0016] In one embodiment, a plurality of uncertain factors satisfying set conditions in the to-be-determined transportation network-distribution network are obtained, including:

[0017] Obtaining the transportation network data and distribution network data that meet the set conditions in the transportation network-distribution network to be determined;

[0018] The traffic network data is input into the pre-built traffic network uncertainty acquisition model to obtain the road capacity, road ambient temperature, automobile travel demand, electric vehicle initial SOC and electric vehicle charging end SOC;

[0019] The distribution network data is input into the pre-built distribution network uncertainty acquisition model to obtain renewable resources and loads.

[0020] In an exemplary embodiment, the PCK model is constructed by the following steps:

[0021] The PCK model to be trained is constructed by using the kriging proxy model and polynomial chaos expansion technology;

[0022] The PCK model to be trained is continuously iterated and trained through the minimum angle regression strategy until the preset conditions are met, and the PCK model to be trained at this time is used as the PCK model.

[0023] The PCK model to be trained is continuously iterated through the minimum angle regression strategy until the preset conditions are met, and the PCK model to be trained at this time is used as the PCK model, including:

[0024] Initialize the coefficients, fitting results, residuals and key basis function set of the candidate basis function in the candidate basis function set in the PCK model to be trained;

[0025] Based on each candidate basis function and the correlation function, correlation information between each candidate basis function and the residual is obtained, and a target basis function is determined from a plurality of candidate basis functions according to the correlation information;

[0026] The target basis function is added to the key basis function set to obtain the current key basis function set, and the LOO error, the candidate PCK model and the forward step length are obtained based on the current key basis function set, and the coefficients, fitting results and residuals of the target basis function are updated based on the forward step length;

[0027] Return to execute the steps of obtaining LOO error, candidate PCK model and forward step length based on each candidate basis function and correlation coefficient, and updating the coefficient of the target basis function, fitting result and residual based on the forward step length, until the residual is less than the preset residual threshold or all candidate basis functions are included in the key basis function set, and multiple candidate PCK models are obtained;

[0028] According to the LOO error, a PCK model is determined from multiple candidate PCK models.

[0029] In a second aspect, the present application also provides a device for determining the importance of uncertain factors of a transportation network-distribution network based on the moment independence method, comprising:

[0030] The uncertainty factor acquisition module is used to obtain multiple uncertain factors that meet the set conditions in the to-be-determined transportation network-distribution network; the multiple uncertain factors include road capacity, road ambient temperature, automobile travel demand, electric vehicle initial SOC, electric vehicle charging end SOC, renewable resources and load;

[0031] A first distribution feature acquisition module is used to acquire first distribution feature information corresponding to any current uncertainty factor among multiple uncertainty factors, and input the current uncertainty factor and other uncertainty factors except the current uncertainty factor into a pre-built PCK model, and obtain second distribution feature information through the PCK model;

[0032] A second distribution feature acquisition module is used to input uncertainty factors into the PCK model and obtain third distribution feature information through the PCK model;

[0033] The importance determination module is used to obtain the probability joint flow global sensitivity index information corresponding to each uncertain factor based on the first distribution feature information, the second distribution feature information and the third distribution feature information, and determine the importance of each uncertain factor according to the probability joint flow global sensitivity index information.

[0034] In a third aspect, the present application further provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the following steps are implemented:

[0035] Obtain multiple uncertain factors that meet the set conditions in the to-be-determined transportation network-distribution network; the multiple uncertain factors include road capacity, road ambient temperature, automobile travel demand, electric vehicle initial SOC, electric vehicle charging end SOC, renewable resources and load;

[0036] Obtaining first distribution feature information corresponding to any current uncertainty factor among the multiple uncertainty factors, and inputting the current uncertainty factor and other uncertainty factors except the current uncertainty factor into a pre-constructed PCK model, and obtaining second distribution feature information through the PCK model;

[0037] Input the uncertain factors into the PCK model, and obtain the third distribution characteristic information through the PCK model;

[0038] Based on the first distribution feature information, the second distribution feature information and the third distribution feature information, the probability joint flow global sensitivity index information corresponding to each uncertain factor is obtained, and the importance of each uncertain factor is determined according to the probability joint flow global sensitivity index information.

[0039] In a fourth aspect, the present application further provides a computer-readable storage medium having a computer program stored thereon, and when the computer program is executed by a processor, the following steps are implemented:

[0040] Obtain multiple uncertain factors that meet the set conditions in the to-be-determined transportation network-distribution network; the multiple uncertain factors include road capacity, road ambient temperature, automobile travel demand, electric vehicle initial SOC, electric vehicle charging end SOC, renewable resources and load;

[0041] Obtaining first distribution feature information corresponding to any current uncertainty factor among the multiple uncertainty factors, and inputting the current uncertainty factor and other uncertainty factors except the current uncertainty factor into a pre-constructed PCK model, and obtaining second distribution feature information through the PCK model;

[0042] Input the uncertain factors into the PCK model, and obtain the third distribution characteristic information through the PCK model;

[0043] Based on the first distribution feature information, the second distribution feature information and the third distribution feature information, the probability joint flow global sensitivity index information corresponding to each uncertain factor is obtained, and the importance of each uncertain factor is determined according to the probability joint flow global sensitivity index information.

[0044] In a fifth aspect, the present application further provides a computer program product, including a computer program, which implements the following steps when executed by a processor:

[0045] Obtain multiple uncertain factors that meet the set conditions in the to-be-determined transportation network-distribution network; the multiple uncertain factors include road capacity, road ambient temperature, automobile travel demand, electric vehicle initial SOC, electric vehicle charging end SOC, renewable resources and load;

[0046] Obtaining first distribution feature information corresponding to any current uncertainty factor among the multiple uncertainty factors, and inputting the current uncertainty factor and other uncertainty factors except the current uncertainty factor into a pre-constructed PCK model, and obtaining second distribution feature information through the PCK model;

[0047] Input the uncertain factors into the PCK model, and obtain the third distribution characteristic information through the PCK model;

[0048] Based on the first distribution feature information, the second distribution feature information and the third distribution feature information, the probability joint flow global sensitivity index information corresponding to each uncertain factor is obtained, and the importance of each uncertain factor is determined according to the probability joint flow global sensitivity index information.

[0049] The above-mentioned method, device, computer equipment, computer-readable storage medium and computer program product for determining the importance of uncertain factors in the transportation network-distribution network based on the moment independence method obtains uncertain factors that meet the set conditions in the transportation network-distribution network to be determined, and the uncertain factors include road capacity, road ambient temperature, car driving demand, electric vehicle initial SOC, electric vehicle charging end SOC, renewable resources and load, and then obtains the first distribution feature information corresponding to any current uncertain factor among multiple uncertain factors, inputs the current uncertain factor and other uncertain factors except the current uncertain factor into a pre-constructed PCK model, obtains the second distribution feature information through the PCK model, further inputs the uncertain factor into the PCK model to obtain the third distribution feature information, and finally obtains the probability joint flow global sensitivity index information corresponding to each uncertain factor based on the first distribution feature information, the second distribution feature information and the third distribution feature information, and determines the importance of each uncertain factor according to the probability joint flow global sensitivity index information. By paying comprehensive attention to the global sensitivity index information, and not using a certain time period as the basis for judgment, but a truly global one, paying attention to all time periods and integrating all times to form the global sensitivity index information of the probabilistic joint flow, and determining the importance of multiple uncertain factors in the transportation network-distribution network based on this index information, the global approach improves the accuracy of determining the importance of uncertain factors, thereby helping users to better utilize the corresponding importance of uncertain factors to formulate strategies to ensure the stability of system operation. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] In order to more clearly illustrate the technical solutions in the embodiments of the present application or related technologies, the drawings required for use in the embodiments of the present application or related technical descriptions will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without paying creative work.

[0051] Figure 1 It is an application environment diagram of a method for determining the importance of uncertain factors of a transportation network-distribution network based on the moment independence method in one embodiment;

[0052] Figure 2 It is a flowchart of a method for determining the importance of uncertain factors of a transportation network-distribution network based on the moment independence method in one embodiment;

[0053] Figure 3 It is a flowchart of a method for determining the importance of uncertain factors of a transportation network-distribution network based on the moment independence method in another embodiment;

[0054] Figure 4A topological diagram of a transportation network-distribution network coupling network A in one embodiment;

[0055] Figure 5 A diagram showing calculation results of moment-independent global sensitivity index in one embodiment;

[0056] Figure 6 Schematic diagram of CDF of V8 in three scenarios in one embodiment;

[0057] Figure 7 A topological diagram of a transportation network-distribution network coupling network B in one embodiment;

[0058] Figure 8 It is a structural block diagram of a device for determining the importance of uncertain factors of a transportation network-distribution network based on the moment independence method in one embodiment;

[0059] Fig. 9 FIG. 4 is a diagram showing the internal structure of a computer device in one embodiment. DETAILED DESCRIPTION

[0060] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0061] The method for determining the importance of uncertain factors of the transportation network-distribution network based on the moment independence method provided in the embodiment of the present application can be applied to Figure 1In the application environment shown. Among them, the coupling system of the transportation network-distribution network communicates with the server 102 through the network. The uncertain factors in this coupling system include road capacity, road environment temperature, automobile travel demand, electric vehicle initial SOC, electric vehicle charging end SOC, renewable resources and load, and multiple uncertain factors all change randomly. The data storage system can store the data that the server 102 needs to process. The data storage system can be integrated on the server 102, or it can be placed on the cloud or other network servers. The server 102 obtains multiple uncertain factors that meet the set conditions in the transportation network-distribution network to be determined, obtains the first distribution feature information corresponding to any current uncertain factor among the multiple uncertain factors, and inputs the current uncertain factor into the pre-built PCK model, obtains the second distribution feature information through the PCK model, inputs the current uncertain factor and other uncertain factors except the current uncertain factor into the PCK model, obtains the third distribution feature information through the PCK model, and finally obtains the probability joint flow global sensitivity index information corresponding to each uncertain factor based on the first distribution feature information, the second distribution feature information and the third distribution feature information, and determines the importance of each uncertain factor according to the probability joint flow global sensitivity index information. The power distribution-transportation network can be understood as a cluster of buildings in a certain area, including road information and grid structure information in the cluster, which are coupled with each other to maintain the operation of the system. The server 102 can be an independent physical server, a server cluster or distributed system composed of multiple physical servers, or a cloud server that provides cloud computing services.

[0062] In an exemplary embodiment, Figure 2 As shown in the figure, a method for determining the importance of uncertain factors in the transportation network-distribution network based on the moment independence method is provided. Figure 1 The server 102 in the example is used as an example to illustrate the method, which includes the following steps S201 to S204. Among them:

[0063] Step S201, obtaining multiple uncertain factors that meet set conditions in the transportation network-distribution network to be determined; the multiple uncertain factors include road capacity, road ambient temperature, automobile travel demand, electric vehicle initial SOC, electric vehicle charging end SOC, renewable resources and load.

[0064] Among them, road capacity can be understood as the maximum number of vehicles that can pass through a certain section of road within a certain period of time; automobile travel demand can be understood as the need for automobile travel services by individuals or groups within a certain period of time; the initial SOC (State of Charge) of electric vehicles and the SOC at the end of charging of electric vehicles can be understood as the ratio of the current energy storage capacity of the battery in the corresponding state to the battery capacity; renewable resources can be understood as natural resources that can generate electricity repeatedly, such as wind energy and solar energy;

[0065] The set conditions can be understood as firstly that the uncertain factors all change randomly, and secondly that they have specific values ​​that meet the set threshold at a certain moment. The set threshold means that the system can still operate normally when the current device does not exceed this threshold.

[0066] Optionally, server 102 obtains multiple uncertain factors such as road capacity, road ambient temperature, automobile travel demand, electric vehicle initial SOC, electric vehicle charging completion SOC, renewable resources and load that meet set conditions in the transportation network-distribution network to be determined through the transportation network, collects uncertainties from multiple aspects, and comprehensively considers the variables of the transportation network and distribution network, thereby laying a solid data foundation for the subsequent determination of key uncertainties and improving the credibility of the determined key uncertainties.

[0067] Step S202, obtaining first distribution feature information corresponding to any current uncertainty factor among multiple uncertainty factors, and inputting the current uncertainty factor and other uncertainty factors except the current uncertainty factor into a pre-built PCK model, and obtaining second distribution feature information through the PCK model.

[0068] Step S203: input the uncertainty factor into the PCK model, and obtain the third distribution feature information through the PCK model.

[0069] Among them, any current uncertain factor can be understood as an uncertain factor with clear data at a certain moment, the first distribution characteristic information can be understood as the distribution characteristic information of the current uncertain factor itself, and the PCK (Polynomial-Chaos-Kriging) model can be understood as a mathematical model with small computational complexity and fast data calculation speed obtained by combining the polynomial chaos expansion technology on the basis of the Kriging proxy model.

[0070] For example, the server 102 obtains the first distribution feature information corresponding to any current uncertainty factor among multiple uncertainties, and then inputs the current uncertainty factor and other uncertainties except the current uncertainty factor into the pre-built PCK model. It should be noted that the value of the current uncertainty factor is fixed, and the other uncertainties are random variables. Therefore, the PCK model outputs the second distribution feature information with conditional restrictions. In addition, the remaining multiple uncertainties without restrictions are input into the PCK model. Since there are no conditional restrictions, the PCK model outputs the unconditional third distribution feature information. Considering the conditional distribution feature information of fixed size at a fixed time and the unfixed unconditional distribution feature information at the same time, it avoids the situation of focusing on a certain time period and ignoring the global situation, thereby improving the accuracy of the global sensitivity index information of the probability joint flow corresponding to each determined uncertain factor.

[0071] Step S204, based on the first distribution feature information, the second distribution feature information and the third distribution feature information, obtain the probability joint flow global sensitivity index information corresponding to each uncertain factor, and determine the importance of each uncertain factor according to the probability joint flow global sensitivity index information.

[0072] Among them, the global sensitivity index information of the probabilistic joint flow can be understood as focusing on the distribution characteristics of multiple variables and considering the changes of all input variables and their impact on the indicators. The index information can include traffic, delay, efficiency, etc.

[0073] Optionally, the server 102 obtains the probability joint flow global sensitivity index information corresponding to each uncertain factor based on the first distribution feature information, the second distribution feature information and the third distribution feature information, and determines the importance of each uncertain factor according to the probability joint flow global sensitivity index information, wherein the larger the probability joint flow global sensitivity index information, the higher the importance of the corresponding uncertain factor in the transportation network-distribution network. Determining the importance of each uncertain factor and formulating corresponding strategies for each uncertain factor according to the importance plays a vital role in the operation of the system, and selecting by integrating multiple variables and global time eliminates the determination error caused by focusing on the local, and improves the accuracy of determining the importance of each uncertain factor.

[0074] In the above-mentioned method for determining the importance of uncertain factors in the transportation network-distribution network based on the moment independence method, multiple uncertain factors that meet the set conditions in the transportation network-distribution network to be determined are obtained, and the uncertain factors include road capacity, road ambient temperature, car driving demand, electric vehicle initial SOC, electric vehicle charging end SOC, renewable resources and load. Then, the first distribution characteristic information corresponding to any current uncertain factor among the multiple uncertain factors is obtained, and the current uncertain factor and other uncertain factors except the current uncertain factor are input into the pre-constructed PCK model to obtain the second distribution characteristic information, and the uncertain factor is further input into the PCK model to obtain the third distribution characteristic information. The third distribution characteristic information is obtained through the PCK model, and finally, based on the first distribution characteristic information, the second distribution characteristic information and the third distribution characteristic information, the probability joint flow global sensitivity index information corresponding to each uncertain factor is obtained, and the importance of each uncertain factor is determined according to the probability joint flow global sensitivity index information. By comprehensively focusing on the global sensitivity index information, and not using a certain time period as the basis for judgment, but a truly global perspective, focusing on all time periods and integrating all times to form a probabilistic joint flow global sensitivity index information, and based on this index information, determining the target uncertainty factor as the key uncertainty factor from multiple uncertainties. The global approach improves the accuracy of determining the key uncertainties, thereby helping users to better utilize key uncertainties to formulate strategies and ensure the stability of system operation.

[0075] In one embodiment, based on the first distribution feature information, the second distribution feature information, and the third distribution feature information, obtaining the probabilistic joint flow global sensitivity index information corresponding to each uncertain factor includes:

[0076] According to the first distribution characteristic information, the second distribution characteristic information and the third distribution characteristic information, multiple global sensitivity index information corresponding to each uncertain factor is obtained; the multiple global sensitivity index information is normalized to obtain the probabilistic joint flow global sensitivity index information corresponding to each uncertain factor.

[0077] Among them, the global sensitivity index information can be understood as the index information under the current uncertainty factors, but the current uncertainty factors have multiple values, so it is necessary to further obtain a more comprehensive global situation.

[0078] For example, server 102 obtains multiple global sensitivity index information corresponding to each uncertain factor at the current moment based on the first distribution feature information, the second distribution feature information and the third distribution feature information, and further performs index normalization processing on the global sensitivity index information at multiple moments to obtain the probabilistic joint flow global sensitivity index information corresponding to each uncertain factor. Here, the global sensitivity index information at the current moment is first obtained, and then the global sensitivity index information at multiple moments is normalized to enhance the comprehensiveness of the finally obtained probabilistic joint flow global sensitivity index information and improve the comparability between the global sensitivity index information of each probabilistic joint flow through normalization processing, thereby accelerating the determination speed and accuracy of the importance of uncertain factors in the transportation network-distribution network based on the moment independence method.

[0079] In one embodiment, obtaining global sensitivity index information corresponding to each uncertainty factor according to the first distribution feature information, the second distribution feature information, and the third distribution feature information includes:

[0080] Based on the second distribution feature information and the third distribution feature information, distribution feature distance information is obtained; based on the first distribution feature information and the distribution feature distance information, global sensitivity index information corresponding to each uncertain factor is obtained.

[0081] The distribution feature distance information can be understood as the k-Wasserstein distance, which is distance information used to quantify the distance between two distribution feature information.

[0082] Optionally, the server 102 obtains the k-Wasserstein distance between the second distribution feature information of the fixed condition and the third distribution feature information of the unfixed condition, and obtains the global sensitivity index information corresponding to each uncertain factor based on the first distribution feature information and the k-Wasserstein distance. By focusing on the distance information between the conditional probability distribution and the unconditional probability distribution, the variables with greater influence in the system are obtained, and finally, more accurate global sensitivity index information of each uncertain factor is obtained based on the first distribution feature information and the distance information.

[0083] In an exemplary embodiment, multiple uncertainties satisfying set conditions in a transportation network-distribution network to be determined are obtained, including: obtaining transportation network data and distribution network data satisfying set conditions in the transportation network-distribution network to be determined; inputting the transportation network data into a pre-built transportation network uncertainty acquisition model to obtain road capacity, road ambient temperature, automobile travel demand, electric vehicle initial SOC, and electric vehicle charging end SOC; inputting the distribution network data into a pre-built distribution network uncertainty acquisition model to obtain renewable resources and loads.

[0084] Optionally, the server 102 obtains the traffic network data and distribution network data that are randomly changing in the to-be-determined traffic network-distribution network and have specific values ​​that meet the normal operation of the system at any time, and then inputs the traffic network data into the pre-built traffic network uncertainty factor acquisition model to obtain the uncertainties that have the greatest impact on the operation of the traffic network in the traffic network data—road capacity, road ambient temperature, automobile travel demand, electric vehicle initial SOC, and electric vehicle charging end SOC, and inputs the distribution network data into the pre-built distribution network uncertainty factor acquisition model to obtain the uncertainties that have the greatest impact on the operation of the distribution network—renewable resources and load. By preliminarily processing a large amount of variable data, more critical uncertainties are screened out, avoiding processing of all uncertainties, greatly reducing processing costs, and thus accelerating the determination of uncertainties in the traffic network-distribution network.

[0085] In one embodiment, the PCK model is constructed by the following steps: using the kriging proxy model and polynomial chaos expansion technology to construct the PCK model to be trained; continuously iteratively training the PCK model to be trained through the minimum angle regression strategy until the preset conditions are met, and the PCK model to be trained at this time is used as the PCK model.

[0086] Among them, the kriging model can be understood as predicting the value of unobserved points through known data points (samples), and the polynomial chaos expansion technology uses a linear combination of orthogonal polynomials to express the changes in random variables, making the description of system responses more systematic and computable; the least angle regression strategy (LAR) can be understood as setting the initial value of all basis function coefficients to 0, selecting the basis function with the largest correlation with the output variable from the candidate basis function set as the key basis function, and walking along the direction of the basis function until there is a second basis function whose correlation with the current residual is consistent with the first basis function, then the basis function is also listed as the key basis function, and continues to walk along the direction of the angle bisector of the two basis functions until there is a third basis function, so that the correlation between the three basis functions and the current residual is consistent, then continue to walk along the equiangular direction of the three basis functions... and so on, always keep the correlation between the selected key basis function and the current residual consistent on the solution path until the residual is small enough, or there are no remaining basis functions.

[0087] For example, server 102 uses the kriging proxy model as the benchmark model and combines it with the polynomial chaos expansion technology to construct a PCK model to be trained that is adapted to the current multivariable scenario. Then, the minimum angle regression strategy is used to continuously iterate and train the PCK model to be trained until the set conditions are met, and the PCK model to be trained at this time is used as the PCK model.

[0088] The Kriging model is an application of the Gaussian process regression model. It originated in geostatistics and has been widely used in other fields. The Kriging model performs spatial modeling and prediction of random processes or random fields based on the covariance function. It can provide an estimated value and error estimate for unknown functions. It is one of the most representative and potential proxy models. Based on the Kriging proxy model, this paper combines the polynomial chaos expansion technology to construct the PCK proxy model, which has the advantages of high fitting accuracy and fast calculation speed.

[0089] The traditional Kriging surrogate model consists of two parts: trend function and error term:

[0090] Y=F(X)+σ 2 Z(X)

[0091] Where: Y is the output of the proxy model; X is the input random variable; F(X) is the trend function used to calculate the regression fitting value; σ 2 Z(X) is the error term, where σ 2 is the variance of the Gaussian process, and Z(X) is the standard static Gaussian process function (mean 0, variance 1).

[0092] In order to improve the generalization ability of the Kriging proxy model and effectively deal with the "curse of dimensionality" problem caused by high-dimensional input random variables (i.e., multiple uncertain factors of "road-vehicle-source-load") in the calculation of the probabilistic joint flow of the transportation network-distribution network, this paper introduces the polynomial chaos expansion to construct the trend function F(X), and uses the minimum angle regression strategy to select the key multivariate orthogonal polynomial basis functions, thereby sparsely expanding the polynomial chaos expansion, reducing the number of basis function coefficients required to be calculated, and overcoming the overfitting and "curse of dimensionality" problems that may occur in the construction of the proxy model. The PCK proxy model is shown below:

[0093]

[0094] Where: Ψh(X) is the multivariate orthogonal polynomial basis function; a h are the coefficients corresponding to the multivariate orthogonal polynomials; H is the total number of terms of the key multivariate orthogonal polynomial basis functions.

[0095] When using the PCK proxy model for calculation, the variance σ in PCK can be represented by selecting the autoregressive function R(θ) 2, the autoregressive function contains a hyperparameter θ, which can be determined by the input-output samples used to construct the model when a specific form is given (such as linear, exponential, Matern autocorrelation function, etc.). Suppose the sample set containing W input random variables and output variables is XS = [X(1), X(2), ..., X(W)]T and YS = [Y(1), Y(2), ..., Y(W)]T. After obtaining the polynomial basis function using the LAR strategy, the coefficients A of the multivariate orthogonal polynomial basis function and the variance σ of the Gaussian process can be calculated by the following formulas: 2 , thereby determining the PCK agent model for transportation network-distribution network joint flow calculation.

[0096] A=(Ψ T R -1 Ψ) -1 Ψ T R -1 Y s

[0097]

[0098] Where: A = [a1, a2, ..., aH]T; Ψ and R are the polynomial function matrix and autocorrelation function matrix obtained after substituting the input random variable sample XS, and the elements of the i-th row and j-th column can be expressed as:

[0099] ψ ij =Ψ j (X (i) ), i=1, 2,..., W; j=1, 2,..., H

[0100]

[0101] Where: The hyperparameters obtained by the maximum likelihood estimation method are solved by the following optimization problem:

[0102]

[0103] According to the properties of the Gaussian process, when a new input random variable sample X(w) is given, the predicted value Y(w) of the output variable can be expressed using the mean of the PCK proxy model:

[0104]

[0105] Where: Ψw, Rw are the polynomial function vector and autocorrelation function vector obtained after substituting the input random variable sample X(w).

[0106] In order to further improve the generalization ability of the PCK proxy model and avoid the "overfitting" phenomenon of the model, the cross-validation method can be used to test the fitting accuracy of the proxy model. The essence of the cross-validation method is to divide the data samples into training samples and validation samples, fit the proxy model through the training samples, and test the fitting accuracy of the model through the validation samples. This paper introduces the Leave-One-Out (LOO) error in the process of applying the LAR method, and obtains the PCK proxy model with the best generalization ability based on the LOO error results. As a means of cross-validation, the calculation formula of LOO error is as follows:

[0107]

[0108] Where: M~i(·) is a proxy model constructed with X(~i) = [X(1), X(2), …, X(i-1), X(i+1), …, X(W)]T as training samples. It can be seen that the calculation formula of the above LOO error requires the reconstruction of W proxy models, and the calculation process is relatively complicated. In order to simplify the calculation in actual application, the following formula is used to calculate the LOO error of the PCK proxy model:

[0109]

[0110] Where: Bij is the element in the i-th row and j-th column of matrix B. Matrix B is expressed as follows:

[0111]

[0112] The optimal PCK model is constructed and trained according to the current application scenario, which ensures the reliability and effectiveness of the output results of the PCK model, thereby improving the accuracy of determining the target uncertainties.

[0113] In one embodiment, the PCK model to be trained is continuously iterated by the minimum angle regression strategy until a preset condition is satisfied, and the PCK model to be trained at this time is used as the PCK model, including:

[0114] Initialize the coefficients, fitting results, residuals and key basis function set of the candidate basis functions in the candidate basis function set in the PCK model to be trained; obtain the correlation information between each candidate basis function and the residual based on each candidate basis function and the correlation function, and determine the target basis function from multiple candidate basis functions according to the correlation information;

[0115] The target basis function is added to the key basis function set to obtain the current key basis function set, and based on the current key basis function set, the LOO error, candidate PCK model and advance step length are obtained, and the coefficient, fitting result and residual of the target basis function are updated based on the advance step length; return to execute the steps of obtaining the LOO error, candidate PCK model and advance step length based on each candidate basis function and the correlation coefficient, and updating the coefficient, fitting result and residual of the target basis function based on the advance step length, until the residual is less than the preset residual threshold or all the candidate basis functions are included in the key basis function set, and multiple candidate PCK models are obtained; according to the LOO error, a PCK model is determined from multiple candidate PCK models.

[0116] Among them, LOO (Leave-One-Out) error can be understood as the error measured when evaluating model performance through the leave-one-out cross-validation method.

[0117] In an exemplary embodiment, a specific example of implementing the above method is as follows:

[0118] (1) Initialize the coefficients of all candidate basis functions: a0=a1...=a P-1 =0, and set the initial fitting result μ0=0, the initial residual r0=Y-μ0=Y, and the key basis function set AH of the PCK proxy model is an empty set;

[0119] (2) Select the basis function Ψj(·) with the greatest correlation with the current residual r=Y-μ from the candidate basis function set as the key basis function, specifically: calculate the correlation function C(Ψ)=ΨTr, and obtain a vector of length P, whose component Ci represents the correlation coefficient between the i-th basis function and the current residual r. Select the key basis function Ψj(·) based on the calculation result of the correlation function, where for any i≠j, Cj≥Ci is satisfied. Include the basis function Ψj(·) in the key basis function set AH, fit the PCK proxy model based on the current key basis function and the input-output samples of the model, and calculate the LOO error corresponding to the current key basis function set AH;

[0120] (3) Calculate the direction of the angle bisector of the current key basis function and the forward step length of the LAR method in this direction. Based on the above calculation results, update the coefficients of the key basis function and obtain a new fitting result μ.

[0121] (4) Repeat steps 2 to 3 until the residual is small enough or all candidate basis functions are included in the key basis function set. Select the key basis function set A corresponding to the minimum LOO error of the PCK proxy model. H , and use it as the basis function set used in constructing the actual proxy model to ensure that the generalization ability and fitting accuracy of the constructed PCK proxy model are optimal.

[0122] Through the above method, the basis functions related to the residual are gradually selected and the coefficients are updated using the LAR method, which ensures the high fitting accuracy of the PCK model while also improving the generalization ability and computational efficiency.

[0123] In an exemplary embodiment, Figure 3 As shown, a specific implementation method of a method for determining the importance of uncertain factors of a transportation network-distribution network based on the moment independence method is provided, wherein (the following numbers are all data in a certain example, and it is not limited to only in this case that the solution of this application can be implemented):

[0124] The moment independence method is used to calculate the global sensitivity index and identify the key uncertainty factors of the transportation network-distribution network coupling system, including the following steps:

[0125] Step S1: Input the distribution network and transportation network data, and build a PCK agent model for transportation network-distribution network joint flow calculation based on the distribution network source-load and line information and transportation network road and vehicle flow information. The modeling method specifically includes:

[0126] Step S11: Establish the uncertainty factor model of the traffic network "road-vehicle". Use the probability distribution function to characterize the random characteristics of the uncertainty factors of the traffic network "road" and "vehicle". For the "road", the random variables include road capacity and road ambient temperature; for the "vehicle", the random variables include vehicle travel demand and battery SOC at different travel stages.

[0127] Step S12: Establishing a distribution network "source-load" uncertainty factor model. For a distribution network containing distributed renewable energy, intermittent renewable energy generation (wind power, photovoltaic power generation) and fluctuating loads are the main uncertainty factors affecting its operation.

[0128] Step S13: Construct the PCK proxy model based on the least angle regression (LAR). The probabilistic joint flow calculation model of the transportation network-distribution network is a nonlinear system model. Based on the Kriging proxy model, the PCK proxy model is constructed by combining the polynomial chaos expansion technology, which has the advantages of high fitting accuracy and fast calculation speed.

[0129] Step S2: Set the required sample size J s .

[0130] Step S3: Generate input variable samples by considering the randomness of all input variables.

[0131] Step S31: Select the multiple uncertain factors of "road-vehicle-source-load" in the transportation network-distribution network to form the system M-dimensional independent input random variables (ξ, P D ).

[0132] Step S32: Use probability distribution function to describe the multiple uncertainties of “road-vehicle-source-load” in the transportation network-distribution network, and establish input variables (ξ, P D ) is a random model.

[0133] Step S33: Based on the established probability distribution model of the input random variable, a low-discrepancy sequence sampling method such as Sobol sequence sampling or Latin hypercube sampling is applied to obtain J s Group input random variable sample (ξ j , P D，j )(j=1,2,…,J s ).

[0134] Step S4: Calculate the system output through the PCK proxy model to obtain the PDF (CDF) of the output variable.

[0135] Step S41: Establish input variable samples (ξ j , P D，j )(j=1,2,…,J s ) and the standard normal distribution variable sample z j (j=1, 2, ..., J s ) between them.

[0136] Step S42: Select the basis function type of the PCK proxy model as Hermite orthogonal polynomial, and transform the standard normal distribution variable sample z j (j=1, 2, ..., J s ) is used as the input variable sample of the proxy model, and the output variable sample is Y j (j=1, 2, ..., J s ).

[0137] Step S43: Calculate the probabilistic joint flow of the transportation network-distribution network based on the PCK agent model, and quickly obtain the statistical characteristic quantity PDF (CDF) of the coupled system state variables.

[0138] Step S5: Fix the value of the input variable of the global sensitivity to be calculated, and calculate the conditional PDF (CDF) of the output variable.

[0139] Step S6: Traverse the value range of the input variable and solve the moment-independent global sensitivity index.

[0140] Step S7: Compare the global sensitivity index and identify the key uncertainty factors in the transportation network-distribution network coupling system.

[0141] The uncertainty factor modeling of the traffic network "road-vehicle" in step S11 is as follows:

[0142] 1) Road capacity:

[0143] Road capacity refers to the maximum traffic volume under normal traffic conditions. In the operation of the traffic network, for road a = (i, j) ∈ A (i, j ∈ N, and i and j are the starting point and end point of road a respectively), the random fluctuation of its capacity ξ C，a It can be described by normal distribution, denoted as ζ C，s ~N(μ C，a , σ C，a ), where μ C，a With σ C，a They are respectively C，a Therefore, the random fluctuation of road capacity ζ C，a The probability density function of can be expressed as follows:

[0144]

[0145] 2) Road environment temperature:

[0146] The ambient temperature in the traffic network itself has a large uncertainty. The random characteristics of the ambient temperature can be described by the normal distribution, denoted as ξ T ~N(μ T , σ T ). Since the road environment temperature will directly affect the various properties of electric vehicle batteries (charging and discharging efficiency, etc.), and is also related to the user's decision-making behavior such as whether to use air conditioning, this application further constructs an electric vehicle energy consumption rate based on a user's travel record data. and ambient temperature T The functional relationship between them is:

[0147]

[0148] In the formula: bn is a given coefficient, and its value is shown in Table 3-1.

[0149] Table 3-1 Temperature-energy consumption rate model coefficients

[0150] Tab.3-1 Temperature-energy consumption rate model coefficients

[0151]

[0152] 3) Car travel demand:

[0153] Automobile travel demand refers to the mobility demand between OD pairs. The random fluctuation of travel demand between fuel vehicles and electric vehicles between OD pairs w and It can be described by normal distribution, denoted as

[0154] 4) Electric vehicle battery initial SOC:

[0155] Since the initial SOC of electric vehicle batteries is different when starting from the starting point, if a probability distribution function is uniformly used to describe the random characteristics of the initial SOC of different electric vehicles, it will lead to large errors. In order to improve the accuracy of modeling, this paper divides the electric vehicles at the starting point between OD pairs w into Tw categories, and the initial SOC of the batteries of all electric vehicles in each category is approximated by a fixed value, and the proportion of electric vehicles in each category follows a normal distribution, which is recorded as t=1,2,…,Tw. The sum of all categories is 1:

[0156]

[0157] 5) SOC at the end of electric vehicle charging:

[0158] The time that electric vehicle users stay at charging stations is somewhat random, and the electric vehicle may not accurately complete the expected charging target at the end of charging. This paper assumes that the SOC of the electric vehicle at the end of charging approximately follows a normal distribution, denoted by ξ F ~N(μ F , σ F ), and the mean of this distribution is related to the expected charging target.

[0159] In step S12, the probability distribution function is used to model the uncertainty factors of the distribution network "source" and "load" as follows:

[0160] 1) Renewable energy uncertainty modeling:

[0161] The output power of wind turbines and photovoltaic cells is closely related to wind speed and light intensity, respectively. In the long term, wind speed approximately follows the Weibull distribution:

[0162]

[0163] Where: v is wind speed; ξ k and c are the shape parameter and scale parameter of the Weibull distribution respectively.

[0164] The light intensity approximately follows the Beta distribution:

[0165]

[0166] Where: r and r max are light intensity and maximum light intensity respectively; ξ a , b is the shape parameter of Beta distribution; Γ is the gamma function.

[0167] 2) Load uncertainty modeling:

[0168] Active power P of other loads in the distribution network except the charging load of the charging station B，i (i∈EN) can be considered to be approximately subject to normal distribution, denoted by P B，i ~N(μ B，i , σ B，i ), where μ B，i With σ B，i P B，i The mean and standard deviation of P B，i The probability density function of can be expressed as follows:

[0169]

[0170] The power factor and active power P of other loads except the charging load of the charging station at node i B，i , we can get its reactive power Q B，i .

[0171] The Kriging model in step S13 is an application of the Gaussian process regression model, which originated in geostatistics and has been widely used in other fields. The Kriging model performs spatial modeling and prediction of random processes or random fields based on the covariance function, and can provide an estimated value and error estimate for unknown functions. It is one of the most representative and potential proxy models. Based on the Kriging proxy model, this paper combines the polynomial chaos expansion technology to construct the PCK proxy model, which has the advantages of high fitting accuracy and fast calculation speed.

[0172] The traditional Kriging surrogate model consists of two parts: trend function and error term:

[0173] Y=F(X)+σ 2 Z(X)

[0174] Where: Y is the output of the proxy model; X is the input random variable; F(X) is the trend function used to calculate the regression fitting value; σ 2 Z(X) is the error term, where σ 2 is the variance of the Gaussian process, and Z(X) is the standard static Gaussian process function (mean 0, variance 1).

[0175] In order to improve the generalization ability of the Kriging proxy model and effectively deal with the "curse of dimensionality" problem caused by high-dimensional input random variables (i.e., multiple uncertain factors of "road-vehicle-source-load") in the calculation of the probabilistic joint flow of the transportation network-distribution network, this paper introduces the polynomial chaos expansion to construct the trend function F(X), and uses the minimum angle regression strategy to select the key multivariate orthogonal polynomial basis functions, thereby sparsely expanding the polynomial chaos expansion, reducing the number of basis function coefficients required to be calculated, and overcoming the overfitting and "curse of dimensionality" problems that may occur in the construction of the proxy model. The PCK proxy model is shown below:

[0176]

[0177] Where: Ψh(X) is the multivariate orthogonal polynomial basis function; a h are the coefficients corresponding to the multivariate orthogonal polynomials; H is the total number of terms of the key multivariate orthogonal polynomial basis functions.

[0178] When using the PCK proxy model for calculation, the variance σ in PCK can be represented by selecting the autoregressive function R(θ) 2 , the autoregressive function contains a hyperparameter θ, which can be determined by the input-output samples used to construct the model when a specific form is given (such as linear, exponential, Matern autocorrelation function, etc.). Suppose the sample set containing W input random variables and output variables is XS = [X(1), X(2), ..., X(W)]T and YS = [Y(1), Y(2), ..., Y(W)]T. After obtaining the polynomial basis function using the LAR strategy, the coefficients A of the multivariate orthogonal polynomial basis function and the variance σ of the Gaussian process can be calculated by the following formulas: 2 , thereby determining the PCK agent model for transportation network-distribution network joint flow calculation.

[0179] A=(Ψ T R -1 Ψ) -1 Ψ T R -1 Y s

[0180]

[0181] Where: A = [a1, a2, ..., aH]T; Ψ and R are the polynomial function matrix and autocorrelation function matrix obtained after substituting the input random variable sample XS, and the elements of the i-th row and j-th column can be expressed as:

[0182] ψ ij =ψ j (X (i) ), i=1, 2,..., W; j=1, 2,..., H

[0183]

[0184] Where: The hyperparameters obtained by the maximum likelihood estimation method are solved by the following optimization problem:

[0185]

[0186] According to the properties of the Gaussian process, when a new input random variable sample X(w) is given, the predicted value Y(w) of the output variable can be expressed using the mean of the PCK proxy model:

[0187]

[0188] Where: Ψw, Rw are the polynomial function vector and autocorrelation function vector obtained after substituting the input random variable sample X(w).

[0189] In order to further improve the generalization ability of the PCK proxy model and avoid the "overfitting" phenomenon of the model, the cross-validation method can be used to test the fitting accuracy of the proxy model. The essence of the cross-validation method is to divide the data samples into training samples and validation samples, fit the proxy model through the training samples, and test the fitting accuracy of the model through the validation samples. This paper introduces the Leave-One-Out (LOO) error in the process of applying the LAR method, and obtains the PCK proxy model with the best generalization ability based on the LOO error results. As a means of cross-validation, the calculation formula of LOO error is as follows:

[0190]

[0191] Where: M~i(·) is a proxy model constructed with X(~i) = [X(1), X(2), …, X(i-1), X(i+1), …, X(W)]T as training samples. It can be seen that the calculation formula of the above LOO error requires the reconstruction of W proxy models, and the calculation process is relatively complicated. In order to simplify the calculation in actual application, the following formula is used to calculate the LOO error of the PCK proxy model:

[0192]

[0193] Where: Bij is the element in the i-th row and j-th column of matrix B. Matrix B is expressed as follows:

[0194]

[0195] The specific steps of building a PCK proxy model based on LAR are as follows:

[0196] (1) Initialize the coefficients of all candidate basis functions: a0 = a1 . ..=aP-1 =0, and set the initial fitting result μ0=0, the initial residual r0=Y-μ0=Y, and the key basis function set AH of the PCK proxy model is an empty set;

[0197] (2) Select the basis function Ψj(·) with the greatest correlation with the current residual r=Y-μ from the candidate basis function set as the key basis function, specifically: calculate the correlation function C(Ψ)=Ψ Tr, and obtain a vector of length P, whose component Ci represents the correlation coefficient between the i-th basis function and the current residual r. Select the key basis function Ψj(·) based on the calculation result of the correlation function, where for any i≠j, Ci≥Ci. Include the basis function Ψj(·) in the key basis function set AH, fit the PCK proxy model based on the current key basis function and the input-output samples of the model, and calculate the LO0 error corresponding to the current key basis function set AH;

[0198] (3) Calculate the direction of the angle bisector of the current key basis function and the forward step length of the LAR method in this direction. Based on the above calculation results, update the coefficients of the key basis function and obtain a new fitting result μ.

[0199] (4) Repeat steps 2 to 3 until the residual is small enough or all candidate basis functions are included in the key basis function set. Select the key basis function set corresponding to the minimum LOO error of the PCK proxy model. Using it as the basis function set used in constructing the actual proxy model can ensure that the generalization ability and fitting accuracy of the constructed PCK proxy model are optimal.

[0200] The global sensitivity analysis of the probability joint flow based on the moment independence method in step S6 is as follows:

[0201] Considering that the statistical moment information such as the mean and variance of the output variables cannot fully characterize the probability distribution characteristics of the output variables of the transportation network-distribution network probabilistic joint flow, the moment independent global sensitivity analysis method uses the PDF or CDF of the output samples to calculate the global sensitivity index.

[0202] The Borgonovo index method is a commonly used moment-independent global sensitivity analysis method. Its essence is to quantitatively evaluate the importance of each input random variable by quantifying the impact of the uncertainty of the system input random variable on the PDF of the system output variable. The calculation formula of the Borgonovo global sensitivity index is as follows:

[0203]

[0204] in,

[0205]

[0206] Where: fY is the PDF of the output response Y when considering the influence of all input random variables; is the i-th input random variable X i is a fixed value x i , the conditional PDF of the output response Y when other input variables change randomly; s(xi) is the difference area between the PDF of the output response Y and its conditional PDF.

[0207] The solution of Borgonovo index needs to be based on MCS method and double loop process, which has huge calculation scale and low calculation efficiency. At the same time, the PDF estimation problem itself is an ill-posed calculation problem, and it is also difficult to accurately estimate PDF.

[0208] In order to solve the above problems, a global sensitivity analysis method based on Wasserstein distance can be used. This method quantifies the average difference between the conditional probability distribution and the unconditional probability distribution of the system output variable, thereby identifying the key system input random variables that have a significant impact on the system output variable. This method calculates the global sensitivity index based on the CDF of the output sample, which can fully consider the probability characteristics of the output sample. At the same time, when calculating the CDF of the output variable based on the sample data, the function value of the empirical CDF at Y* is the number of samples less than or equal to Y* in the sample divided by the total sample size W. Therefore, the empirical CDF can be directly derived by simply sorting the data samples. Compared with PDF, it is simpler to estimate CDF quickly and accurately.

[0209] First, the Wasserstein distance is used to quantify the differences between different probability distributions. Let the variables Y1 and Y2 obey the probability distributions F and G respectively. Then the k-Wasserstein distance between the probability distributions F and G is:

[0210]

[0211] Where: Π(F,G) is the set of all possible joint probability distributions of variables Y1 and Y2, whose marginal distributions are F and G; y1 and y2 are samples obtained using the joint probability distribution γ; D(y1,y2) is the distance function, usually let D(y1,y2) = ‖y1-y2‖; k is the order, which is generally 1 or 2 in practical applications.

[0212] When Y1 and Y2 are one-dimensional variables, the k-Wasserstein distance between probability distributions F and G can be easily calculated as shown in the following formula:

[0213]

[0214] Where: F-1, G-1 are the inverse functions of probability distribution F and G (CDF) respectively.

[0215] Assume that the M-dimensional input random variable of the traffic network-distribution network probability joint flow calculation is X = [X1, X2, …, X M ], the probability joint flow output variable is Y, in order to quantitatively evaluate the i-th input random variable X i The impact on the output variables of the probabilistic joint flow is defined as follows:

[0216]

[0217] Where: For the input random variable X i The global sensitivity index of fX i (x i ) is the input random variable X i PDF; FY is the unconditional probability distribution of the output variable Y, that is, the probability distribution of Y when the n-dimensional input random variable X changes randomly; is the conditional probability distribution of the output variable Y, that is, the input random variable X i Take a fixed value x i , other input random variables [X1,…,X i-1 ,X i+1 …,X M ] are all randomly changing; represents the k-Wasserstein distance between the unconditional probability distribution and the conditional probability distribution of Y. To simplify the calculation of the global sensitivity index, the formula The integral form is converted into the following formula:

[0218]

[0219] Where: x i,max 、x i,min The input random variables X are i The maximum and minimum values ​​that can be taken; N is the value of X i The larger the value of N, the more accurate the calculation result. After normalization, the final calculation result of the global sensitivity index of the probability joint flow is obtained:

[0220]

[0221] After specific actual experiments, this application uses the traffic network-distribution network coupling system A for simulation testing. The coupling system A consists of a 16-node ring traffic network and an improved IEEE 33-node distribution network. The topology diagram is as follows: Figure 4As shown. Considering the 20 system input random variables of the coupled system A, the voltage amplitude of node 8 (V8) and the traffic flow of road 8→9 (x8→9) are taken as output variables, and the global sensitivity index of each system input random variable is calculated respectively.

[0222] When the moment independence method is used to calculate the global sensitivity index, the value interval of each input random variable is set to 20, and the sampling scale of MCS is 10000. When calculating the global sensitivity index based on Wasserstein distance, the order k is selected as the most commonly used 1 and 2, and the three moment-independent global sensitivity indices (Borgonovo index, 1-Wasserstein index and 2-Wasserstein index) of 20 system input random variables for the output variables V8 and x8→9 are calculated respectively. The calculation results are shown in the figure below: Figure 5 shown.

[0223] Depend on Figure 5 The comparison of the calculation results of the moment-independent global sensitivity index shows that the importance ranking results of the three moment-independent global sensitivity indexes are exactly the same, and the key system input random variables determined by the three methods are also the same. It can also be seen from the calculation results of the two Wasserstein indicators that the calculation results of the global sensitivity index based on the k-Wasserstein distance are basically the same when k is 1 and 2 respectively, and the choice of k value will not affect the identification of the key system input random variables.

[0224] Table 1 shows the identification results of the key input variables of the system.

[0225] Table 1 Global sensitivity analysis results of system input random variables to V8 and x8→9

[0226]

[0227] As shown in Table 2, when the moment independence method is applied, the calculation time of the three global sensitivity indices is close. Among them, the calculation speed of the 1-Wasserstein index and the 2-Wasserstein index is slightly faster than the Borgonovo index. This is because the calculation of the Wasserstein index and the Borgonovo index is based on the CDF and PDF of the output samples, respectively, and the calculation of the CDF is simpler than that of the PDF. In addition, the moment independence method can consider more sample information and comprehensively evaluate the criticality of the system input variables. However, the double-loop process of the moment independence method requires the acquisition of large-scale system input-output samples. Therefore, this method is more suitable for applications where the accuracy of the global sensitivity analysis results is high and the timeliness requirements are not obvious.

[0228] Table 2 Computation time of global sensitivity analysis of system input random variables to V8 and x8→9

[0229]

[0230] In order to verify the effectiveness of the proposed probabilistic joint flow global sensitivity analysis method in identifying key input random variables, this application takes V8 of coupled system A as the output variable and sets the following three scenarios: case 1: consider the randomness of all 20 system input variables; case 2: only consider the randomness of 3 system key input variables, and the remaining non-key input variables take fixed values; case 3: only consider the randomness of the remaining non-key input variables, and the 3 system key input variables take fixed values. Based on the transportation network-distribution network probabilistic joint flow calculation, the CDF of V8 in the three scenarios can be obtained respectively as follows: Figure 6 shown.

[0231] Depend on Figure 6 It can be seen that when only the randomness of the three key input variables of the system is considered (case 2), the CDF of the output variable V8 is basically the same as when the randomness of all 20 system input variables is considered (case 1); on the contrary, when the three key input variables of the system take fixed values ​​and only the randomness of the remaining system input variables is considered (case 3), the CDF of the output variable V8 is very different from case 1. The example results show that the key input variables of the system identified by the global sensitivity index have a significant impact on the output variables, and the randomness of the key input variables of the system is the main source of the randomness of the output variables. Further, the effectiveness of the global sensitivity analysis method of the probabilistic joint flow of the power grid-distribution network proposed in this paper in identifying key uncertainty factors is verified.

[0232] Furthermore, in order to verify the applicability of the proposed probabilistic joint flow global sensitivity analysis method, the proposed method is applied to a larger-scale transportation network-distribution network coupling system B. Taking another coupling system B, Sioux Falls 20-node transportation network and improved IEEE 69-node distribution network, as an example, the topology of the coupling system B is shown in Figure 7 As shown. Select the voltage amplitude (V 56 ) is used as the output variable, and the global sensitivity index of the system input random variables is calculated by the proposed moment independent probability joint flow global sensitivity analysis method. The top 5 system input random variables with the highest global sensitivity index are taken as the key random variables, and the calculation results are shown in Table 3.

[0233] Table 3 System input random variables V 56 The calculation results of the global sensitivity index

[0234]

[0235] It can be seen from Table 3 that the proposed moment-independent probability joint flow global sensitivity index can identify the system input random variables that are most critical to the system output, that is, for the output variable V 56 The most significant key input variables are the renewable energy output power (PR,12, PR,51, PR,52, PR,58, PR,59) located at nodes 12, 51, 52, 58, and 59. The above example results show that the proposed moment-independent probability joint flow global sensitivity analysis method is still applicable in large-scale transportation network-distribution network coupling systems and is extensible.

[0236] Compared with the prior art, this application has the following advantages:

[0237] 1. It makes up for the disadvantage that the traditional partial derivative-based local sensitivity method cannot be applied to the transportation network-distribution network coupling system where the uncertainty propagation process is not instantaneous.

[0238] 2. It can more accurately characterize the impact of uncertainty factors in the transportation network-distribution network coupling system under long-term operation, so as to quantify the impact of multiple uncertainty factors of "road-vehicle-source-load" in the transportation network-distribution network and identify the key uncertainty factors of the coupling system.

[0239] 3. Improved the accuracy of identifying key uncertainty factors of the coupled system.

[0240] It should be understood that, although the steps in the flowcharts involved in the above embodiments are displayed in sequence according to the indication of the arrows, these steps are not necessarily executed in sequence according to the order indicated by the arrows. Unless there is a clear explanation in this article, the execution of these steps is not strictly limited in order, and these steps can be executed in other orders. Moreover, at least a part of the steps in the flowcharts involved in the above embodiments may include multiple steps or multiple stages, and these steps or stages are not necessarily executed at the same time, but can be executed at different times, and the execution order of these steps or stages is not necessarily carried out in sequence, but can be executed in turn or alternately with other steps or at least a part of the steps or stages in other steps.

[0241] Based on the same inventive concept, the embodiment of the present application also provides a device for determining the importance of uncertainties in a transportation network-distribution network based on the moment independence method, which is used to implement the method for determining the importance of uncertainties in a transportation network-distribution network based on the moment independence method mentioned above. The implementation scheme for solving the problem provided by the device is similar to the implementation scheme recorded in the above method, so the specific limitations in the device embodiment for removing one or more target uncertainties provided below can be found in the above limitations on the method for determining the importance of uncertainties in a transportation network-distribution network based on the moment independence method, and will not be repeated here.

[0242] In an exemplary embodiment, Figure 8 As shown, a device for determining the importance of uncertain factors of a transportation network-distribution network based on the moment independence method is provided, comprising: an uncertain factor acquisition module 801, a first distribution feature acquisition module 802, a second distribution feature acquisition module 803 and an importance determination module 804, wherein:

[0243] The uncertainty factor acquisition module is used to obtain multiple uncertain factors that meet the set conditions in the to-be-determined transportation network-distribution network; the multiple uncertain factors include road capacity, road ambient temperature, automobile travel demand, electric vehicle initial SOC, electric vehicle charging end SOC, renewable resources and load;

[0244] A first distribution feature acquisition module is used to acquire first distribution feature information corresponding to any current uncertainty factor among multiple uncertainty factors, and input the current uncertainty factor and other uncertainty factors except the current uncertainty factor into a pre-built PCK model, and obtain second distribution feature information through the PCK model;

[0245] A second distribution feature acquisition module is used to input uncertainty factors into the PCK model and obtain third distribution feature information through the PCK model;

[0246] The importance determination module is used to obtain the probability joint flow global sensitivity index information corresponding to each uncertain factor based on the first distribution feature information, the second distribution feature information and the third distribution feature information, and determine the importance of each uncertain factor according to the probability joint flow global sensitivity index information.

[0247] In one embodiment, the target uncertainty factor acquisition module 804 further includes:

[0248] Obtaining a first submodule, used to obtain a plurality of global sensitivity index information corresponding to each uncertain factor according to the first distribution characteristic information, the second distribution characteristic information and the third distribution characteristic information;

[0249] A second submodule is obtained, which is used to perform index normalization processing on multiple global sensitivity index information to obtain the global sensitivity index information of the probability joint flow corresponding to each uncertain factor.

[0250] In one embodiment, the first submodule is further used to obtain distribution feature distance information based on the second distribution feature information and the third distribution feature information; and to obtain global sensitivity index information corresponding to each uncertain factor based on the first distribution feature information and the distribution feature distance information.

[0251] In an exemplary embodiment, the uncertainty factor acquisition module 801 is also used to obtain traffic network data and distribution network data that meet set conditions in the to-be-determined traffic network-distribution network; input the traffic network data into a pre-built traffic network uncertainty factor acquisition model to obtain road capacity, road ambient temperature, automobile travel demand, electric vehicle initial SOC and electric vehicle charging end SOC; input the distribution network data into a pre-built distribution network uncertainty factor acquisition model to obtain renewable resources and loads.

[0252] In one embodiment, the device for determining the importance of uncertain factors in the transportation network-distribution network based on the moment independence method also includes a model pre-training module, which is used to construct a PCK model to be trained using a kriging proxy model and polynomial chaos expansion technology; the PCK model to be trained is continuously iterated and trained through a minimum angle regression strategy until a preset condition is met, and the PCK model to be trained at this time is used as the PCK model.

[0253] In one of the embodiments, the model pre-training module is also used to obtain correlation information between each candidate basis function and the residual based on each candidate basis function and the correlation function, and determine a target basis function from multiple candidate basis functions based on the correlation information; add the target basis function to the key basis function set to obtain the current key basis function set, and obtain the LOO error, candidate PCK model and advance step length based on the current key basis function set, and update the coefficient, fitting result and residual of the target basis function based on the advance step length; return to execute the steps of obtaining the LOO error, candidate PCK model and advance step length based on each candidate basis function and the correlation coefficient, and updating the coefficient, fitting result and residual of the target basis function based on the advance step length, until the residual is less than a preset residual threshold or all candidate basis functions are included in the key basis function set, and multiple candidate PCK models are obtained; determine the PCK model from multiple candidate PCK models based on the LOO error.

[0254] Each module in the above-mentioned device for determining the importance of uncertain factors of the transportation network-distribution network based on the moment independence method can be implemented in whole or in part by software, hardware and a combination thereof. Each of the above-mentioned modules can be embedded in or independent of a processor in a computer device in the form of hardware, or can be stored in a memory in a computer device in the form of software, so that the processor can call and execute the operations corresponding to each of the above modules.

[0255] In an exemplary embodiment, a computer device is provided. The computer device may be a server, and its internal structure diagram may be as shown in FIG. Fig. 9As shown. The computer device includes a processor, a memory, an input / output interface (Input / Output, referred to as I / O) and a communication interface. Among them, the processor, the memory and the input / output interface are connected through a system bus, and the communication interface is connected to the system bus through the input / output interface. Among them, the processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The database of the computer device is used to store road capacity, road ambient temperature, automobile travel demand, electric vehicle initial SOC, electric vehicle charging end SOC, renewable resources and loads, first distribution feature information, second distribution feature information, third distribution feature information and probability joint flow global sensitivity index information data. The input / output interface of the computer device is used to exchange information between the processor and an external device. The communication interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, a method for determining the importance of uncertain factors in a transportation network-distribution network based on the moment independence method is implemented.

[0256] Those skilled in the art will understand that Fig. 9 The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than those shown in the figure, or combine certain components, or have a different arrangement of components.

[0257] In an exemplary embodiment, a computer device is provided, including a memory and a processor, wherein a computer program is stored in the memory, and when the processor executes the computer program, the method for determining the importance of uncertainty factors of a transportation network-distribution network based on the moment independence method of the above embodiment is implemented.

[0258] In one embodiment, a computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the method for determining the importance of uncertainty factors of a transportation network-distribution network based on the moment independence method of the above embodiment is implemented.

[0259] In one embodiment, a computer program product is provided, including a computer program, which, when executed by a processor, implements the method for determining the importance of uncertain factors of a transportation network-distribution network based on the moment independence method of the above embodiment.

[0260] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, stored data, displayed data, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of relevant data must comply with relevant regulations.

[0261] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to the memory, database or other medium used in the embodiments provided in the present application can include at least one of non-volatile memory and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. As an illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM). The database involved in each embodiment provided in this application may include at least one of a relational database and a non-relational database. Non-relational databases may include distributed databases based on blockchains, etc., but are not limited to this. The processor involved in each embodiment provided in this application may be a general-purpose processor, a central processing unit, a graphics processor, a digital signal processor, a programmable logic device, a data processing logic device based on quantum computing, an artificial intelligence (AI) processor, etc., but are not limited to this.

[0262] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this application.

[0263] The above embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the present application. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the present application shall be subject to the attached claims.

Claims

1. A method for determining the importance of uncertain factors in a transportation network-distribution network based on the moment independence method, characterized in that: The method comprises: Acquire multiple uncertain factors that meet set conditions in the to-be-determined transportation network-distribution network; the multiple uncertain factors include road capacity, road ambient temperature, automobile travel demand, electric vehicle initial SOC, electric vehicle charging end SOC, renewable resources and load; Obtaining first distribution feature information corresponding to any current uncertainty factor among the multiple uncertainty factors, and inputting the current uncertainty factor and other uncertainty factors except the current uncertainty factor into a pre-constructed PCK model, and obtaining second distribution feature information through the PCK model; Inputting the uncertainty factor into the PCK model, and obtaining third distribution feature information through the PCK model; Based on the first distribution feature information, the second distribution feature information and the third distribution feature information, the probability joint flow global sensitivity index information corresponding to each of the uncertain factors is obtained, and the importance of each of the uncertain factors is determined according to the probability joint flow global sensitivity index information.

2. The method according to claim 1, characterized in that The acquiring, based on the first distribution feature information, the second distribution feature information and the third distribution feature information, the probabilistic joint flow global sensitivity index information corresponding to each of the uncertain factors includes: Acquire a plurality of global sensitivity index information corresponding to each of the uncertain factors according to the first distribution characteristic information, the second distribution characteristic information and the third distribution characteristic information; The multiple global sensitivity index information are normalized to obtain the probabilistic joint flow global sensitivity index information corresponding to each of the uncertain factors.

3. The method according to claim 2, characterized in that The acquiring, according to the first distribution characteristic information, the second distribution characteristic information and the third distribution characteristic information, global sensitivity index information corresponding to each of the uncertain factors comprises: Based on the second distribution feature information and the third distribution feature information, acquiring distribution feature distance information; According to the first distribution feature information and the distribution feature distance information, global sensitivity index information corresponding to each of the uncertain factors is obtained.

4. The method according to claim 1, characterized in that: The obtaining of multiple uncertain factors satisfying set conditions in the to-be-determined transportation network-distribution network includes: Acquire the transportation network data and distribution network data that meet the set conditions in the transportation network-distribution network to be determined; Inputting the traffic network data into a pre-built traffic network uncertainty factor acquisition model to obtain the road capacity, road environment temperature, automobile travel demand, electric vehicle initial SOC and electric vehicle charging end SOC; The distribution network data is input into a pre-built distribution network uncertainty factor acquisition model to obtain the renewable resources and the load.

5. The method according to claim 1, characterized in that The PCK model is constructed by the following steps: The PCK model to be trained is constructed by using the kriging proxy model and polynomial chaos expansion technology; The PCK model to be trained is continuously iterated and trained through the minimum angle regression strategy until a preset condition is satisfied, and the PCK model to be trained at this time is used as the PCK model.

6. The method according to claim 5, characterized in that The method of continuously iteratively training the PCK model to be trained by the minimum angle regression strategy until a preset condition is satisfied, and using the PCK model to be trained at this time as the PCK model, includes: Initialize coefficients, fitting results, residuals, and a key basis function set of candidate basis functions in the candidate basis function set in the PCK model to be trained; Based on each of the candidate basis functions and the correlation function, correlation information between each of the candidate basis functions and the residual is obtained, and a target basis function is determined from the plurality of candidate basis functions according to the correlation information; Adding the target basis function to the key basis function set to obtain a current key basis function set, obtaining an LOO error, a candidate PCK model and a forward step length based on the current key basis function set, and updating coefficients, fitting results and residuals of the target basis function based on the forward step length; Return to the steps of obtaining LOO error, candidate PCK model and forward step length based on each of the candidate basis functions and the correlation coefficient, and updating the coefficient of the target basis function, the fitting result and the residual based on the forward step length, until the residual is less than a preset residual threshold or all the candidate basis functions are included in the key basis function set, thereby obtaining a plurality of candidate PCK models; The PCK model is determined from a plurality of the candidate PCK models according to the LOO error.

7. A device for determining the importance of uncertain factors in a transportation network-distribution network based on the moment independence method, characterized in that: The device comprises: An uncertain factor acquisition module is used to acquire multiple uncertain factors that meet set conditions in the to-be-determined transportation network-distribution network; the multiple uncertain factors include road capacity, road ambient temperature, automobile travel demand, electric vehicle initial SOC, electric vehicle charging end SOC, renewable resources and load; A first distribution feature acquisition module is used to acquire first distribution feature information corresponding to any current uncertainty factor among the multiple uncertainty factors, and input the current uncertainty factor and other uncertainty factors except the current uncertainty factor into a pre-built PCK model, and obtain second distribution feature information through the PCK model; A second distribution feature acquisition module, used for inputting the uncertainty factor into the PCK model, and obtaining third distribution feature information through the PCK model; An importance determination module is used to obtain the probabilistic joint flow global sensitivity index information corresponding to each of the uncertain factors based on the first distribution feature information, the second distribution feature information and the third distribution feature information, and determine the importance of each of the uncertain factors according to the probabilistic joint flow global sensitivity index information.

8. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 6 are implemented.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

10. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

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