A laplace-based method and system for modeling tractive effort

Abstract

This invention discloses a Laplace-based traction load modeling method and system, which involves acquiring traction load data; constructing a traction load frequency histogram based on the traction load data; analyzing the zero traction load in the traction load frequency histogram to obtain the zero load probability; removing the zero traction load from the traction load frequency histogram and modeling the non-zero traction load using a Laplace mixed distribution to obtain a non-zero load model; integrating the zero load probability and the non-zero load model to obtain a probabilistic model; and using an iterative solution method for the Laplace mixed distribution parameters to analyze and solve the probabilistic model to obtain the optimal probabilistic model. The beneficial effects of this invention are that by using the Laplace modeling method to separate and integrate zero and non-zero load models, the intermittent and impulsive nature of traction loads is introduced into the modeling method, reducing the computation time required for modeling, improving the modeling speed, and increasing the modeling efficiency.

Description

Technical Field

[0001] This invention relates to the field of traction load modeling technology, and more specifically, to a traction load modeling method and system based on Laplace. Background Technology

[0002] Because my country's electrified railways use single-phase power supply, electrical phase separation is installed both within and between traction substations that are not powered by single-phase transformers. When a train passes through an electrical phase separation, the roof circuit breaker must be disconnected, causing the traction load to exhibit significant impact characteristics. Furthermore, trains operate according to train timetables, and to ensure safe following distances, the follow-up time is generally over 5 minutes, and even during peak travel periods like the Spring Festival, it is over 3 minutes. This inevitably leads to the intermittency of the traction load. Accurately characterizing the intermittency and impact of the traction load becomes a key issue in traction load modeling.

[0003] In the existing technology, the dynamic modeling method based on traction calculation is usually as follows: This type of method is based on the basic theory of traction calculation and combined with the actual parameters of the traction power supply system to establish a dynamic load mathematical model of the entire vehicle network system. Although it has high simulation accuracy, the amount of calculation is large and the simulation time is long.

[0004] Therefore, when using existing technologies to model traction loads, a large amount of data is usually required, which leads to excessive computation and long simulation time, resulting in slow modeling speed and low efficiency.

[0005] In view of the above, this application is hereby submitted. Summary of the Invention

[0006] The technical problem to be solved by the present invention is that the existing technology has a large amount of computation and long simulation time when modeling traction load, resulting in slow modeling speed and low efficiency. The purpose is to provide a traction load modeling method and system based on Laplace, which can reduce the amount of computation and improve the modeling speed and efficiency.

[0007] This invention is achieved through the following technical solution:

[0008] A Laplace-based traction load modeling method, comprising the following steps:

[0009] Acquire traction load data, which includes traction load power data and traction load probability density obtained within one cycle;

[0010] Based on the traction load data, a traction load frequency histogram is constructed;

[0011] The zero traction load in the traction load frequency histogram is analyzed to obtain the zero load probability;

[0012] Remove the zero traction loads from the traction load frequency histogram, and use a Laplace mixed distribution to model the non-zero traction loads to obtain a non-zero load model;

[0013] The zero-load probability is integrated with the non-zero-load model to obtain a probability model;

[0014] The probability model is analyzed and solved using the Laplace mixture distribution parameter iterative solution method to obtain the optimal probability model.

[0015] Traditional traction load modeling typically employs methods based on fundamental traction calculation theories and combined with actual parameters of the traction power supply system to establish a dynamic load mathematical model of the entire vehicle-to-grid system. However, this method usually requires a large amount of data, leading to excessive computation and long simulation times, resulting in slow modeling speed and low efficiency. This invention provides a Laplace-based traction load modeling method. By using the Laplace modeling method, zero-load and non-zero-load models are integrated separately, incorporating the intermittency and impulsiveness of traction loads into the modeling method. This reduces the computation time required for modeling, improves modeling speed, and increases modeling efficiency.

[0016] Preferably, the zero-load probability is the proportion of zero traction load to all traction loads.

[0017] Preferably, the specific method for obtaining the probability model is as follows:

[0018] The zero-load probability is integrated with the non-zero-load model using the binomial distribution method.

[0019] Preferably, the specific expression of the probability model is:

[0020]

[0021] f(x) represents the traction load probability density, P is the zero load probability, and π k The mixing coefficients are L, where L is the Laplace operator, and L(x|μ) k ,λ k ) is called the k-th component in the hybrid model, where K is the number of hybrid components, μ is the position parameter, and λ is the shape parameter.

[0022] Preferably, the specific expression of the Laplace operator L is:

[0023]

[0024] p(x) represents the probability that x is x.

[0025] Preferably, the mixing coefficient πk The specific expression is:

[0026]

[0027] Preferably, the probability model is analyzed and solved using an iterative solution method for the Laplace mixture distribution parameters, and the specific sub-steps include:

[0028] A: Set the number of components K in the mixture, and set π for each component k. k ,μ k ,λ k Find the initial value and calculate the value of the log-likelihood function;

[0029] B: Based on the current π k ,μ k ,λ k Calculate the posterior probability γ(i,k);

[0030] C: Based on the parameter γ(i,k), recalculate the new parameter value π. k ,μ k ,λ k ;

[0031] D: Based on the new parameter value π k ,μ k ,λ k Recalculate the value of the log-likelihood function until the parameter π is obtained. k ,μ k ,λ k If convergence is achieved, the iteration stops.

[0032] Preferably, the specific expression of the log-likelihood function is:

[0033] λ is the mixing coefficient vector, μ is the position parameter vector, λ is the shape parameter vector, and N is the number of traction load data.

[0034] Preferably, the specific expression for the posterior probability is:

[0035]

[0036]

[0037]

[0038]

[0039] γ(i,k) represents the posterior probability, N k This represents the posterior probability of the k-th sub-component. Indicates the new position parameter. Indicates the new shape parameters. This represents the new scaling parameter. N represents the number of samples.

[0040] The present invention also provides a traction load modeling system based on Laplace, including a data acquisition module, a histogram construction module, an analysis module, a modeling module, an integration module, and a solution module;

[0041] The data acquisition module is used to acquire traction load data, which is traction load power data and traction load probability density obtained within one cycle.

[0042] The histogram construction module is used to construct a traction load frequency histogram based on the traction load data.

[0043] The analysis module is used to analyze the zero traction load in the traction load frequency histogram to obtain the zero load probability.

[0044] The modeling module is used to remove zero traction loads in the traction load frequency histogram and to model non-zero traction loads using a Laplace mixed distribution to obtain a non-zero load model.

[0045] The integration module is used to integrate the zero-load probability with the non-zero-load model to obtain a probability model;

[0046] The solution module is used to analyze and solve the probability model using the Laplace mixture distribution parameter iterative solution method to obtain the optimal probability model.

[0047] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0048] The present invention provides a Laplace-based traction load modeling method and system. The Laplace modeling method separates zero load and non-zero load for model integration, and introduces the intermittency and impact of traction load into the modeling method, thereby reducing the calculation time required for modeling, improving the modeling speed, and increasing the modeling efficiency. Attached Figure Description

[0049] To more clearly illustrate the technical solutions of the exemplary embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly described below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0050] Figure 1 This is a schematic diagram of the modeling method;

[0051] Figure 2 This is a histogram of traction load frequency.

[0052] Figure 3 The traction load frequency histogram after removing zero load;

[0053] Figure 4 This is a modeling effect diagram when the sub-component of the Laplace mixture distribution is 1;

[0054] Figure 5 This is a modeling effect diagram when the Laplace mixture distribution has 2 sub-components;

[0055] Figure 6 This is a modeling effect diagram when the Laplace mixture distribution has 3 sub-components;

[0056] Figure 7 This is a modeling effect diagram when the Laplace mixture distribution has 4 sub-components;

[0057] Figure 8 This is a modeling effect diagram when the Laplace mixture distribution has 5 sub-components;

[0058] Figure 9 This is a modeling effect diagram when the Laplace mixture distribution has 6 sub-components. Detailed Implementation

[0059] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the embodiments and accompanying drawings. The illustrative embodiments and descriptions of the present invention are only used to explain the present invention and are not intended to limit the present invention.

[0060] In the following description, numerous specific details are set forth in order to provide a thorough understanding of the invention. However, it will be apparent to those skilled in the art that these specific details are not necessary to practice the invention. In other embodiments, well-known structures, circuits, materials, or methods have not been specifically described in order to avoid obscuring the invention.

[0061] Throughout this specification, references to "an embodiment," "an example," or "an example" mean that a particular feature, structure, or characteristic described in connection with that embodiment or example is included in at least one embodiment of the present invention. Therefore, the phrases "an embodiment," "an example," "an example," or "an example" appearing in various places throughout the specification do not necessarily refer to the same embodiment or example. Furthermore, specific features, structures, or characteristics can be combined in one or more embodiments or examples in any suitable combination and / or sub-combination. Moreover, those skilled in the art will understand that the illustrations provided herein are for illustrative purposes and are not necessarily drawn to scale. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0062] In the description of this invention, the terms "front", "rear", "left", "right", "up", "down", "vertical", "horizontal", "high", "low", "inner", and "outer" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limiting the scope of protection of this invention.

[0063] Example 1

[0064] Traditionally, when modeling traction loads, this type of method is usually based on the basic theory of traction calculation and combined with the actual parameters of the traction power supply system to establish a dynamic load mathematical model of the entire vehicle network system. However, when using this method to model traction loads, a lot of data is usually required, which leads to excessive calculation and long simulation time, resulting in slow modeling speed and low efficiency.

[0065] This embodiment provides a Laplace-based traction load modeling method. By employing the Laplace modeling method, it separates zero-load and non-zero-load models for integration, incorporating the intermittent and impulsive nature of traction loads into the modeling method. This reduces the computation time required for modeling, improves modeling speed, and increases modeling efficiency. Specific steps are as follows: Figure 1 As shown, the method steps include:

[0066] S1: Obtain traction load data, which is the traction load power data and traction load probability density obtained within one cycle;

[0067] S2: Based on the traction load data, construct a traction load frequency histogram;

[0068] S3: Analyze the zero traction load in the traction load frequency histogram to obtain the zero load probability;

[0069] Because traction load exhibits a clear daily periodicity, the probability density distribution of traction load is analyzed using traction load data from a substation on a specific day. First, a traction load frequency histogram is plotted, as shown below. Figure 2 As shown. By Figure 2 It can be seen that the frequency histogram of traction load has a significant spike at zero load, which is due to the intermittency of traction load. Locomotives are not always running on the power supply arm, which is related to the line traffic density. Therefore, the proportion of zero load to all loads is defined as the zero load probability p.

[0070] S4: Remove the zero traction loads in the traction load frequency histogram, and use the Laplace mixed distribution to model the non-zero traction loads to obtain a non-zero load model;

[0071] For ease of observation and analysis, in Figure 2 After removing the zero load, redraw the traction load frequency histogram, as follows: Figure 3 As shown. By Figure 3 It can be seen that traction loads occur more frequently at certain specific power levels, such as around 8MW and 24MW. Due to the special phase-segmented structure of the traction power supply system, the traction load has a large moving impact characteristic, which is precisely reflected in high-frequency loads.

[0072] S5: Integrate the zero-load probability with the non-zero-load model to obtain a probability model;

[0073] The specific method for obtaining the probability model is as follows:

[0074] The zero-load probability is integrated with the non-zero-load model using the binomial distribution method.

[0075] The specific expression for the probability model is:

[0076]

[0077] f(x) represents the traction load probability density, P is the zero load probability, and π k The mixing coefficients are L, where L is the Laplace operator, and L(x|μ) k ,λ k ) is called the k-th component in the hybrid model, where K is the number of hybrid components, μ is the position parameter, and λ is the shape parameter.

[0078] To more accurately describe the traction load impact characteristics analyzed in step 2, a Laplace distribution is proposed to fit the traction probability density distribution. The Laplace distribution, also known as the double exponential distribution, has good impact fitting properties. Furthermore, considering that there are multiple impact points in the probability distribution diagram, a mixed Laplace distribution is used to model the non-zero traction load, as detailed below.

[0079] Let X be a random variable, and let the probability density function of the Laplace distribution be:

[0080] In the formula, x represents a value of the random variable X, and p

[0081] Here, the traction load is considered as a random variable X, where x is a certain value of the traction load.

[0082] Let formula (1) be denoted as

[0083] X~L(x|μ,λ)(2) where L represents the Laplace operator and x represents the random variable X

[0084] Then the Laplace mixed distribution model of non-zero traction load can be expressed as:

[0085] In the formula, L(x|μ k ,λ k ) is called the kth in the mixture model.

[0086] In step 3, the impact of the traction load is determined by the Laplace hybrid...

[0087] In the formula, f(x) represents the traction load.

[0088] S6: The probability model is analyzed and solved using the Laplace mixture distribution parameter iterative solution method to obtain the optimal probability model.

[0089] The probability model is analyzed and solved using an iterative method for solving the parameters of the Laplace mixture distribution. Specific sub-steps include:

[0090] A: Set the number of components K in the mixture, and set π for each component k. k ,μ k ,λ k Find the initial value and calculate the value of the log-likelihood function;

[0091] A: Set the number of components K in the mixture, and set π for each component k. k ,μ k ,λ k The initial value is then calculated, and the value of the log-likelihood function in formula (6) is then calculated.

[0092] In the formula, π, μ, and λ are the mixing coefficients, respectively.

[0093] B: Based on the current π k ,μ k ,λ k Calculate the posterior probability γ(i,k);

[0094] According to the current π k ,μ k ,λ k Calculate γ(i,k)

[0095] γ(i,k) represents the posterior probability.

[0096] C: Based on the parameter γ(i,k), recalculate the new parameter value π. k ,μ k ,λ k ;

[0097] Specifically,

[0098] In the formula, for μ k Taking the derivative and setting it to zero, we can obtain μ. k The estimator is:

[0099] In the formula,

[0100] N k Represents the k-th sub-component

[0101] Similarly, we can conclude that:

[0102] Using the Lagrange operator to find

[0103] D: Based on the new parameter value π k ,μ k ,λ k Recalculate the logarithm

[0104] The value of the log-likelihood function in formula (6) is calculated using the newly obtained parameter values ​​from formulas (8), (10), and (11).

[0105] Test parameter π k ,μ k ,λ k Check if the iteration has converged. If it has converged, end the iteration. If it has not converged, return to S52.

[0106] Specific implementation process:

[0107] Based on the traction load probabilistic modeling method proposed in this invention, the modeling effect of traction load at a certain traction station is analyzed. Considering the model convergence speed, seven sub-components are used to model the traction load of a certain traction station. The model is constructed using the mean absolute error (MEA), root mean square error (RMSE), and cosine angle transform formula (I0). cos Three indicators are used to evaluate the accuracy of the probability density distribution model fitting effect. The smaller the indicator value, the more accurate the model. The specific table is shown in Table 1.

[0108] Table 1

[0109]

[0110]

[0111] It can be seen that the model accuracy gradually improves with the increase of sub-components. The model achieves the highest accuracy when using 7 sub-components, with the modeling effect as shown in the figure. Figures 4-9 As shown.

[0112] This embodiment proposes a Laplace-based traction load modeling method that considers the intermittency of traction load caused by train following intervals and takes into account the impact of traction load due to the existence of phase separation in the traction network. This solves the problem of difficulty in characterizing the intermittency and impact of traction load. Therefore, this method provides a theoretical basis for traction substation load forecasting, power grid probabilistic power flow calculation, and power grid line capacity design.

[0113] Example 2

[0114] This embodiment discloses a traction load modeling system based on Laplace's algorithm. This embodiment is designed to implement the modeling method described in Embodiment 1, and includes a data acquisition module, a histogram construction module, an analysis module, a modeling module, an integration module, and a solution module.

[0115] The data acquisition module is used to acquire traction load data, which is traction load power data and traction load probability density obtained within one cycle.

[0116] The histogram construction module is used to construct a traction load frequency histogram based on the traction load data.

[0117] The analysis module is used to analyze the zero traction load in the traction load frequency histogram to obtain the zero load probability.

[0118] The modeling module is used to remove zero traction loads in the traction load frequency histogram and to model non-zero traction loads using a Laplace mixed distribution to obtain a non-zero load model.

[0119] The integration module is used to integrate the zero-load probability with the non-zero-load model to obtain a probability model;

[0120] The solution module is used to analyze and solve the probability model using the Laplace mixture distribution parameter iterative solution method to obtain the optimal probability model.

[0121] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A traction load modeling method based on Laplace, characterized in that, The method steps include: Acquire traction load data, which includes traction load power data and traction load probability density obtained within one cycle; Based on the traction load data, a traction load frequency histogram is constructed; The zero traction load in the traction load frequency histogram is analyzed to obtain the zero load probability; Remove the zero traction loads from the traction load frequency histogram, and use a Laplace mixed distribution to model the non-zero traction loads to obtain a non-zero load model; The zero-load probability is integrated with the non-zero-load model to obtain a probability model; The probability model is analyzed and solved using the Laplace mixture distribution parameter iterative solution method to obtain the optimal probability model; The zero-load probability is the proportion of zero traction load to all traction loads; The specific method for obtaining the probability model is as follows: The zero-load probability is integrated with the non-zero-load model using the binomial distribution method; The specific expression for the probability model is: ； f(x) This represents the probability density of traction load. P For zero load probability, π k It is the mixing coefficient. L For the Laplace operator, L ( x | μ k , λ k ) is called the first in the hybrid model k One portion, K For each mixed component, μ For position parameters, λ For shape parameters; The Laplace operator L The specific expression is: ； p(x) for x The probability of; The mixing coefficient π k The specific expression is: ； The probability model is analyzed and solved using an iterative method for solving the parameters of the Laplace mixture distribution. Specific sub-steps include: A: Set the number of components to mix K For each component k Set π k , μ k , λ k Find the initial value and calculate the value of the log-likelihood function; B: Based on the current π k , μ k , λ k Calculate the posterior probability γ ( i , k ); C: Based on parameters γ ( i , k ), recalculate the new parameter value π k , μ k , λ k ; D: Based on the new parameter value π k , μ k , λ k Recalculate the value of the log-likelihood function until the parameter π is obtained. k , μ k , λ k If convergence is achieved, the iteration stops.

2. The traction load modeling method based on Laplace as described in claim 1, characterized in that, The specific expression for the log-likelihood function is: ； π is the mixing coefficient vector. μ For position parameter vectors, λ A vector of shape parameters. N This represents the number of traction load data.

3. The traction load modeling method based on Laplace as described in claim 2, characterized in that, The specific expression for the posterior probability is: ； ； ； ； γ ( i , k ) represents the posterior probability. N k This represents the posterior probability of the k-th sub-component. Indicates the new position parameter. Indicates the new shape parameters. This indicates the new scaling parameter. N Indicates the number of samples.

4. A traction load modeling system based on Laplace, characterized in that, The method for implementing the Laplace-based traction load modeling method as described in any one of claims 1-3 includes a data acquisition module, a histogram construction module, an analysis module, a modeling module, an integration module, and a solution module. The data acquisition module is used to acquire traction load data, which is traction load power data and traction load probability density obtained within one cycle. The histogram construction module is used to construct a traction load frequency histogram based on the traction load data. The analysis module is used to analyze the zero traction load in the traction load frequency histogram to obtain the zero load probability. The modeling module is used to remove zero traction loads in the traction load frequency histogram and to model non-zero traction loads using a Laplace mixed distribution to obtain a non-zero load model. The integration module is used to integrate the zero-load probability with the non-zero-load model to obtain a probability model; The solution module is used to analyze and solve the probability model using the Laplace mixture distribution parameter iterative solution method to obtain the optimal probability model.

Images