Automatic driving acceleration test method compatible with variable correlation

By using Cramér's V coefficient, kernel density estimation method and Copula model in autonomous driving acceleration test, combining importance sampling method and Bayesian optimization method, the problem of incompatibility of variable correlation is solved, and the sampling probability and testing efficiency of dangerous scenarios are improved.

CN120086493APending Publication Date: 2025-06-03JIANGSU UNIV

Patent Information

Application Number
CN202510007884.1
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-01-03
Publication Date
2025-06-03

AI Technical Summary

Technical Problem

The existing autonomous driving acceleration testing methods are not compatible with the correlation of variables, resulting in low accuracy of scenario hazard rate estimation, limiting the application scope of probability sampling in accelerated testing.

Method used

The correlation between variables was quantified by Cramér's V-system, and the probability density function of the variable was fitted through the kernel density estimation method, and the Copula model was constructed to capture the correlation structure between variables, and the sample sampling weight was adjusted using the importance sampling method and Bayesian optimization method to improve the sampling probability of dangerous scenarios.

Benefits of technology

It improves the accuracy of scenario hazard rate estimation, expands the application scope of probability sampling method in accelerated testing, and significantly accelerates the process of autonomous driving safety assessment.

✦ Generated by Eureka AI based on patent content.

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Patent Text Reader

Abstract

The invention discloses an automatic driving acceleration test method compatible with variable correlation, which comprises the following steps of: taking vehicle driving data as variables, quantifying the correlation among the variables to select variables needing to be concerned, and fitting a probability density function of the variables by adopting a kernel density estimation method; converting the probability density function into cumulative distribution of the same space; solving Copula parameters by utilizing a Copula model so as to obtain a joint probability density function of the variables; introducing an evaluation index of the scene risk degree, constructing an indicator function, and counting the occurrence probability of the dangerous scene based on the indicator function; adjusting the joint probability density function by using an importance sampling method, establishing a target function based on the number of test times, and solving an optimal sample sampling weight by using a Bayesian optimization method; obtaining the optimal importance joint probability density based on the optimal sample sampling weight, and carrying out random sampling to obtain new observation data of the variable; and constructing a test scene by using the new observation data to perform simulation test on automatic driving.
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Description

Technical Field

[0001] The present invention relates to the technical field of autonomous driving, and involves the safety evaluation and accelerated testing of autonomous driving scenarios. Specifically, it relates to an autonomous driving accelerated testing method that is compatible with variable correlation. Background Art

[0002] Although autonomous driving has great potential in improving road traffic efficiency and reducing the probability of accidents, safety remains a key prerequisite for its widespread application. Autonomous driving will encounter various complex situations in the actual road environment, such as different weather conditions, traffic flows, and road conditions. These factors may all affect the safety of the autonomous driving system. Therefore, before putting autonomous driving into public use, it is necessary to conduct strict and effective test evaluations on its control performance.

[0003] Traditional mileage-based testing methods based on real roads and driving simulations rely on the collection of a large amount of natural driving data, require huge vehicle resources and time costs, and have low testing efficiency. To improve testing efficiency, scenario-based simulation testing methods can simulate dangerous collision scenarios in simulations, evaluate vehicle performance in real time, and can accept multiple scenarios for simultaneous testing, and have become the core means for autonomous driving safety evaluation.

[0004] During the scenario-based testing process, the dangerous scenarios that rarely occur are the ones that truly determine the safety performance of autonomous driving. Quickly searching for dangerous scenarios and increasing the testing probability of dangerous scenarios, thereby shortening the testing time and the number of test cases, and more quickly evaluating the performance of autonomous driving, is the key to accelerated testing.

[0005] In the prior art, CN107421752A selects independent variables (the relative distance between two vehicles) in the scenario, statistically analyzes the probability distribution of this variable, and uses importance sampling to increase the sampling probability of dangerous scenarios (the relative distance is less than a certain threshold); CN118446012B proposes a segmented importance sampling method considering the number of segments and the number of tests through optimization theory to improve the fitting accuracy of the probability distribution of a certain variable and testing efficiency; CN118395662A aims to minimize the estimation variance and optimizes the importance sampling function. Random sampling is performed on the optimized importance distribution to generate test scenarios.

[0006] However, most of the existing technologies perform probability statistics and random sampling based on independent variables and cannot be compatible with variable correlation. In actual autonomous driving test scenarios, variables often affect each other, and it is impossible to perform random sampling on a single variable alone. Ignoring variable correlation may affect the estimation accuracy of the scenario danger rate and limit the application scope of the probability sampling method in accelerated testing. Summary of the Invention

[0007] In view of the deficiencies in the prior art, the present invention proposes an autonomous driving acceleration test method that is compatible with variable correlation. The purpose of the present invention is to fully consider the correlation between variables to improve the accuracy of scene risk rate estimation.

[0008] The technical solution adopted by the present invention is as follows: An autonomous driving acceleration test method that is compatible with variable correlation, comprising the following steps: Step 1, extract the vehicle driving data in a certain test scenario, take each type of vehicle driving data as a variable in the autonomous driving test, and obtain multiple variables for the autonomous driving test; Step 2, use the Cramér's V coefficient to quantify the correlation between variables to obtain a correlation evaluation value; according to the correlation evaluation value, select at least one group of variables that need to be concerned; for the variables that need to be concerned, use the kernel density estimation method to fit the probability density function of each variable; Step 3, convert the probability density function of the variable into a cumulative distribution in the same space, construct a Copula model based on the cumulative distribution, and use the maximum likelihood estimation method to solve the Copula parameters of the Copula model; obtain the joint probability density function of the variable based on the Copula parameters; Step 4, set the evaluation index of the scene risk degree according to the variable and construct an indicator function of the dangerous scene, and statistically calculate the occurrence probability of the dangerous scene based on the indicator function; and introduce the importance sampling method to adjust the joint probability density function; based on the indicator function of the dangerous scene, the occurrence probability, and the adjusted importance joint probability density function, establish an objective function based on the number of tests, and use the Bayesian optimization method to solve the optimal sample sampling weight; Step 5, based on the optimal sample sampling weight, obtain the optimal importance joint probability density function; perform random sampling based on the optimal importance joint probability density function to obtain new observation data of the variable; use the new observation data to construct a test scenario to perform a simulation test on the autonomous driving.

[0009] Furthermore, the method for fitting the probability density function of each variable by using the kernel density estimation method is as follows: Step 2.1, for the variables that need to be concerned X , construct the kernel density estimation of the overall density function , expressed as: ; Among them, is the estimated density point; is the X th observation data in the variable i , n is the sample number of the observation data; h is the bandwidth; is the kernel function, and the Gaussian kernel function is selected and denoted as , is the distance between the estimated density point and the observed data point; Step 2.2: Measure the accuracy of the kernel density estimation using the minimum criterion of the average integrated squared error function ; Step 2.3: According to the properties of the probability density function, obtain the optimal bandwidth by minimizing ; ; Step 2.4: Substitute the Gaussian kernel function and the optimal bandwidth into the kernel density estimation in Step 2.1, and solve for the kernel density estimation function X of , and use it as the probability density function of the variable X ; Step 2.5: Refer to the above Steps 2.1 - 2.4 to obtain the probability density functions of other variables that need to be concerned about.

[0010] Furthermore, the method for obtaining the joint probability density function of the variables in Step 3 is as follows: Step 3.1: Based on the probability density functions of the variables, convert all the variables that need to be concerned about into cumulative distributions in the same space; Step 3.2: Based on the cumulative distributions of the variables, construct a Copula function; Step 3.3: Use the maximum likelihood estimation method to define the likelihood function of the Copula function, and introduce the log-likelihood function to solve for the Copula parameters ; According to the obtained Copula parameters , establish the joint distribution of the variables that need to be concerned about; take the second-order partial derivative of the joint distribution to obtain the joint probability density function of the variables.

[0011] Furthermore, the method for setting the evaluation index of the scenario risk in Step 4 is as follows: For the variables that need to be concerned about, set the corresponding risk thresholds for each variable respectively. If all variables exceed their corresponding risk thresholds, it is considered that the variables are in a risk scenario .

[0012] Furthermore, the indicator function of the risk scenario is expressed as follows: ; where is the j th scenario, is the risk scenario.

[0013] Furthermore, the occurrence probability is expressed as: ; where m is the number of scenarios.

[0014] Further, a new probability density function is constructed using the importance sampling method as follows: ; where is the joint probability density function of the variables to be concerned, is the sampling weight of the sample.

[0015] Further, the steps to solve for the sample sampling weight with the fastest convergence in step 4 using the Bayesian optimization method are as follows: Step 4.1: Based on the indicator function, occurrence probability, and adjusted importance joint probability density function of the hazardous scenario, establish the relative half-width, denoted as: ; where N is the number of tests; is the relative half-width; is the half-width; is the confidence level; is the cumulative distribution function value corresponding to the confidence level; is the variance of the hazard rate, is the expectation of the importance joint probability density function; Step 4.2: Establish an objective function based on the number of tests, denoted as: ; where is the convergence threshold; Use the Gaussian process model to model as follows: ; where is the Gaussian process model, is the mean function of the Gaussian process model, is the variance function of the Gaussian process model; Step 4.3: Initialize , , , and evaluate the corresponding objective function value to obtain the observed data; Step 4.4: Set the current optimal objective function value as , and use the expected improvement function to select a new sample weight function ; For the new sample weight function , calculate its mean function and variance function , recalculate the mean function and variance function according to the new sample weight function, and update the objective function value , and add the new observed data to the observation database; through continuous training and optimization until the objective function value reaches convergence; obtain the optimal sample sampling weight .

[0016] Advantages of the present invention: 1. The proposed autonomous driving acceleration test method in the present invention adopts a non-parametric kernel density estimation method for distribution fitting, without making prior assumptions about the distribution form, and can well adapt to complex real distributions. In addition, the kernel density estimation method can construct density estimates based on local information around variables and is more robust to outliers, and can effectively reflect the overall distribution trend of variables.

[0017] 2. The proposed autonomous driving acceleration test method in the present invention uses a Copula model to construct the correlation structure between variables and generate correlated random variables, effectively dealing with the problem of random sampling of correlated variables and improving the application scope of the probability sampling method in acceleration testing.

[0018] 3. The proposed autonomous driving acceleration test method in the present invention realizes weight allocation for non-parametric probability distributions by designing an importance sampling function, and proposes a weight allocation method based on the number of tests, and uses the Bayesian optimization method to solve the optimal importance distribution, effectively improving the sampling probability and test efficiency of dangerous scenarios. Description of the drawings

[0019] Figure 1 is the flow chart of the autonomous driving vehicle acceleration test method provided by the present invention.

[0020] Figure 2 is the solution process diagram of the importance sampling method based on Copula provided by the present invention. Among them, (a) is the iterative process of Copula parameters, (b) is the iterative process of the objective function , and (c) is the comparison diagram of the leading vehicle speed in the natural driving distribution and the importance distribution.

[0021] Figure 3 is the importance joint distribution diagram of the ego vehicle speed and the leading vehicle speed provided by the present invention.

[0022] Figure 4 is the comparison diagram of the evaluation of the scenario collision rate by different acceleration test methods provided by the present invention.

[0023] Figure 5 is the comparison diagram of the convergence of the collision rate by different acceleration test methods provided by the present invention. Detailed implementation manners

[0024] In order to make the objectives, technical solutions and advantages of the present invention more clear and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0025] As Figure 1 shown, a method for accelerating the test of an autonomous driving compatible with variable correlation according to the present invention includes the following steps: Step 1: Based on natural driving data, extract the vehicle driving data in a certain test scenario. The vehicle driving data has various types, including the vehicle speed, acceleration, position, heading angle, etc.; each type of vehicle driving data is used as a variable in the autonomous driving test; for example, the vehicle speed is denoted as the variable X , and the n observed data of the vehicle speed is denoted as , the acceleration is denoted as the variable Y , and the n observed data of the acceleration is denoted as .

[0026] Step 2: Since there is a correlation between variables and they will affect each other, in order to be compatible with variable correlation, the present invention needs to fully consider the correlation between variables. For this reason, the present invention uses the Cramér's V coefficient to quantify the correlation between variables and obtains a correlation evaluation value; according to the correlation evaluation value, one or more groups of variables to be concerned are selected. For the variables to be concerned, the probability density function of the variable is fitted by combining the kernel density estimation method.

[0027] More specifically, according to the Cramér's V coefficient, a correlation evaluation value is obtained, and the group of variables with the largest correlation evaluation value is used as the relevant variables to be concerned. There are at least two variables in this group of variables. For example, in this embodiment, according to the correlation quantified by the Cramér's V coefficient, a group of variables to be concerned includes X and Y , which indicates that X and Y The correlation between them cannot be ignored.

[0028] More specifically, the specific method for fitting the probability density function of each variable by using the kernel density estimation method is as follows: Step 2.1: Assume that the two variables to be concerned in the scenario are respectively X and Y, and X and Y The observed data of are denoted as and , is the variableX the i th observed data, is the variable Y the i th observed data.

[0029] Taking the relevant variable X as an example, at any point i within the observed data, the kernel density estimate of the overall density function is defined as: where,

[0030] where, is the estimated density point; n is the number of samples; h is the bandwidth; K (·) is the kernel function.

[0031] In this embodiment, to ensure the smoothness and mean square consistency of the fitting, the kernel function K (·) selects the Gaussian kernel function for kernel density calculation, and its expression is:

[0032] where, is the distance between the estimated density point and the observed data point.

[0033] Step 2.2: Use the minimum criterion of the mean integrated square error function (MISE) to measure the accuracy of the kernel density estimate:

[0034] where, is the accuracy of the kernel density estimate, is the expectation of the sum of squared deviations between the kernel density estimate function and the overall density function.

[0035] According to the properties of the mean square error, can be expressed as:

[0036] where, is the variance of the kernel density estimate function.

[0037] Substituting equations (1) and (2) into equation (4), we can get:

[0038] where, is the second derivative of the overall density function .

[0039] Step 2.3: According to the following properties of the probability density function:

[0040] Minimize Denoted as , the bandwidth can be obtained h The optimal expression of is:

[0041] Step 2.4: Substitute the selected kernel function and the optimal expression of the bandwidth h into Equation (1), and the kernel density estimation function of can be solved X , and use it as the probability density function of the variable . X

[0042] Step 2.5: Similarly, referring to the above Steps 2.1 - 2.4, the probability density function of the variable Y can be obtained .

[0043] Step 3: Convert the probability density functions of the variables to be concerned into cumulative distributions in the same space, construct a Copula model based on the cumulative distributions, and use the Copula model to capture the correlations between the variables; and use the maximum likelihood estimation method to solve the Copula parameters, so as to obtain the joint probability density function of the related variables.

[0044] In this embodiment, the dependence strength between related variables can be captured by constructing a Copula model. The specific method for constructing the Copula model is as follows: Step 3.1: Convert the probability density functions of the variables to be concerned into cumulative distributions in the same space

[0045] where and are the cumulative distributions of the variables X and Y respectively. Based on the cumulative distributions of X and Y , the observed data of X and Y are respectively converted into , which are respectively expressed as follows:

[0046] where is the cumulative distribution of , is the cumulative distribution of ​​The cumulative distribution, and according to the probability integral transformation theorem, and follow a uniform distribution on [0, 1].

[0047] Step 3.2. For the cumulative distribution of variables, construct a Copula function, expressed as:

[0048] where is the CDF of a two-dimensional normal distribution; is the Copula parameter, characterizing the dependence strength between variables; are the quantile functions of the standard normal distributions of u and v respectively; for simplicity of formula writing, are respectively denoted as , , that is .

[0049] Step 3.3. If we want to measure the dependence strength of related variables, we need to estimate the Copula parameter. Define the likelihood function using the maximum likelihood estimation method as:

[0050] The Copula function is expressed as follows:

[0051] For computational convenience, introduce the log-likelihood function,

[0052] Solve through a numerical optimization algorithm to obtain .

[0053] According to the obtained , establish the X and Y joint distribution:

[0054] Take the second-order partial derivative of the joint distribution to obtain the joint probability density function of the two related variables X and Y:

[0055] Step 4: Set the evaluation index of the scenario risk degree according to relevant variables, and statistically calculate the occurrence probability of the dangerous scenario based on the indicator function; and introduce the importance sampling method to adjust the joint probability density function, and adjust the sampling weights of each sample in the joint probability density function. Based on the indicator function, occurrence probability, and adjusted importance joint probability density function of the dangerous scenario, establish an objective function based on the number of tests, and use the Bayesian optimization method to solve the optimal sampling weight of the sample. In this embodiment, for a certain test scenario, set the dangerous scenario according to relevant variables The evaluation index is expressed as:

[0056] Where is the risk threshold of variable X in the test scenario, is the risk threshold of variable Y in the test scenario.

[0057] Based on the evaluation index of the dangerous scenario The state of the scenario can be judged. If the relevant variables in the j-th scenario meet the evaluation index of formula (16), it means that the state of this scenario belongs to the dangerous scenario, which is expressed as ; otherwise, it means that the state of the scenario does not belong to the dangerous scenario, which is expressed as Therefore, the indicator function of the dangerous scenario is expressed as follows:

[0058] Based on the indicator function, statistically calculate the occurrence probability of the dangerous scenario. The occurrence probability can evaluate the risk rate of the test scenario; the occurrence probability is expressed as follows:

[0059] In this embodiment, to increase the sampling probability of the dangerous scenario, use the importance sampling method to construct a new probability density function. Without changing the overall estimation variance, the importance sampling method adjusts the sampling weights of the samples in the joint probability density function.

[0060] Where is the adjusted importance joint probability density function; is the sampling weight of the sample.

[0061] Establish an objective function based on the number of tests, and use the Bayesian optimization method to solve the sampling weight of the sample with the fastest convergence in the test. The specific steps are as follows: Step 4.1: Based on the indicator function, occurrence probability, and adjusted importance joint probability density function of the dangerous scenario, establish the relative half-width; at a given confidence level, the relative half-width can be used to evaluate the convergence of the test.

[0062] The relative half-width is expressed as follows:

[0063] Wherein, N is the number of test times; is the relative half-width; is the half-width; is the confidence level; is the cumulative distribution function value corresponding to the confidence level; is the variance of the hazard rate, is the importance joint probability density function expectation.

[0064] Step 4.2, based on the above expression of the relative half-width, an objective function based on the number of test times can be established, expressed as:

[0065] Wherein, is the objective function, is the convergence threshold.

[0066] Use the Gaussian process model to perform modeling:

[0067] Wherein, is the Gaussian process model, is the mean function of the Gaussian process model, is the variance function of the Gaussian process model; their expressions are respectively:

[0068] Wherein, represents the expectation of the objective function w under the given , represents any two sample weight functions and , and evaluate the corresponding objective function value , to obtain the observed data:

[0069] Wherein, represents the j initial value of the for the th scenario, represents the objective value corresponding to

[0070] Step 4.4, set the current optimal objective function value to , and use the expected improvement function Select a new sample weight function :

[0071] For the new sample weight function , calculate its mean function and variance function ; and let:

[0072] Then the expected improvement function is:

[0073] where denotes Z the cumulative distribution function of the standard normal distribution, denotes Z the probability density function of the standard normal distribution.

[0074] Recalculate the mean function and variance function according to the new sample weight function, update the objective function value , and add the new observed data to the observation database.

[0075] Through continuous training and optimization until the objective function value reaches convergence. Finally, the optimal sample sampling weight is obtained as:

[0076] Step 5. Based on the optimal sample sampling weight , obtain the optimal importance joint probability density function based on Equation (19), and perform random sampling based on to obtain the new observed data X , Y of variables ; use the new observed data to construct a test scenario to simulate and test the autonomous driving.

[0077] In this embodiment, random sampling is performed on the optimal importance distribution to generate a test scenario and perform simulation testing. According to the probability distribution of each sample, the confidence interval of

[0078] is (L, U). Then its convergence threshold should satisfy:

[0079] wherein, is the speedup ratio; is the number of tests when the natural driving data simulation converges; is the number of tests when the acceleration method reaches convergence.

[0080] In this embodiment, the driving data of vehicles in highway scenarios is collected, and the vehicle speed of the vehicle in front before it cuts in V p , the vehicle speed of the test vehicle V c , the relative distance between the two vehicles R and the average time to collision ETTC of the test vehicle are extracted.

[0081] The Cramér's V coefficient is used to select two correlated variables V p and V c , and the dangerous scenario is set as V p > 30 m / s and the importance distribution of the two correlated variables is solved by the method described in the above embodiment.

[0082] Figure 2 The specific solution process is shown. As shown in (a) of Figure 2 , the Copula parameter iteratively solved by the maximum likelihood estimation method finally converges to 0.33, that is, V p and V c have a correlation strength of 0.33. As shown in (b) of Figure 2 , the objective function iteratively solved by the Bayesian optimization method finally converges to 1283. According to the converged objective function value, the optimal sample sampling weight is determined, and the importance distribution of the two correlated variables is obtained. Figure 2 In (c), the importance distribution of the vehicle speed in front and the natural driving distribution are compared. It can be seen from Figure 2 in (c) that after importance sampling, the sampling probability of the dangerous scenario is significantly improved.

[0083] Figure 3 shows the optimal importance joint distribution of V p and V c obtained by optimization.

[0084] Random sampling is performed on this joint distribution to generate new test scenarios Build a test platform for the scenario where the leading vehicle cuts in, and use the newly generated test scenario as the initial state of the simulation test. By observing the driving data of the test vehicle, record the incidence rate of the collision scenario and the number of tests.

[0085] Figure 4 and Figure 5 shows a comparison chart of the test effects of using the acceleration method in the technical solution of the present invention and the existing natural driving method. From Figure 4 it can be seen that the evaluation of the scenario collision rate by the method of the present invention and the existing method is almost the same, indicating that the method of the present invention does not change the structure of the natural driving data and ensures the unbiasedness of the test. From Figure 5 it can be seen that at a confidence level of 80%, the convergence threshold of the method of the present invention is 0.18, and the convergence threshold of the natural driving method is 0.1. The method of the present invention reaches convergence after approximately 4.26×10 4 tests, while the natural driving method reaches convergence after approximately 1.12×10 7 tests, which can improve the test efficiency by 262.91 times and significantly accelerate the evaluation process of the safety of autonomous driving.

[0086]

[0087] The above embodiments are only used to illustrate the design idea and characteristics of the present invention, and their purpose is to enable those skilled in the art to understand the content of the present invention and implement it accordingly. The protection scope of the present invention is not limited to the above embodiments. Therefore, all equivalent changes or modifications made according to the principles and design ideas disclosed by the present invention are within the protection scope of the present invention.

Claims

1. An automatic driving acceleration test method compatible with variable correlation, characterized in that: The steps include: Step 1: extract vehicle driving data in a certain test scenario, use each type of vehicle driving data as a variable in the autonomous driving test, and obtain multiple variables for the autonomous driving test; Step 2: Use Cramér's V coefficient to quantify the correlation between variables and obtain the correlation evaluation value; select at least one group of variables that need attention according to the correlation evaluation value; and use the kernel density estimation method to fit the probability density function of each variable for the variables that need attention; Step 3: Convert the probability density function of the variables into cumulative distribution in the same space, construct a Copula model based on the cumulative distribution, and use the maximum likelihood estimation method to solve the Copula parameters of the Copula model; obtain the joint probability density function of the variables based on the Copula parameters; Step 4: Set the evaluation index of the scene danger degree according to the variables and construct the indicator function of the dangerous scene, and calculate the probability of the dangerous scene based on the indicator function; Importance sampling method is introduced to adjust the joint probability density function. Based on the indicator function of the dangerous scenario, the probability of occurrence, and the adjusted importance joint probability density function, an objective function based on the number of tests is established, and the Bayesian optimization method is used to solve the optimal sample sampling weight. Step 5: Based on the optimal sample sampling weight, obtain the optimal importance joint probability density function; perform random sampling based on the optimal importance joint probability density function to obtain new observation data of the variables; use the new observation data to construct a test scenario to perform simulation testing on autonomous driving.

2. The automatic driving acceleration test method compatible with variable correlation according to claim 1, characterized in that: The method of fitting the probability density function of each variable using the kernel density estimation method is as follows: Step 2.1: Target variables that require attention X , construct a kernel density estimate of the overall density function , expressed as: ; in, is the estimated density point; For variables X Middle i Observation data, n is the sample size of the observed data; h is bandwidth; As the kernel function, we choose Gaussian kernel function, which is recorded as , is the distance between the estimated density point and the observed data point; Step 2.2: Use the minimum criterion of the mean integrated square error function to measure the accuracy of the kernel density estimation ; Step 2.3: According to the properties of the probability density function, by minimizing Finding the optimal bandwidth ; Step 2.4: Gaussian kernel function and optimal bandwidth Substitute the kernel density estimate from step 2.1 and solve X Kernel density estimation function , as a variable X The probability density function of Step 2.5: Refer to the above steps 2.1-2.4 to obtain the probability density functions of other variables that need attention.

3. The automatic driving acceleration test method compatible with variable correlation according to claim 1, characterized in that: The method to obtain the joint probability density function of the variables in step 3 is as follows: Step 3.1: Based on the probability density function of the variable, convert all variables of interest into cumulative distributions in the same space; Step 3.2: Construct the Copula function based on the cumulative distribution of the variable; Step 3.3: Define the likelihood function of the Copula function using the maximum likelihood estimation method, and introduce the log-likelihood function to solve for the Copula parameters. ; According to the obtained Copula parameters , establish the joint distribution of the variables that need attention; take the second-order partial derivative of the joint distribution to obtain the joint probability density function of the variables.

4. The automatic driving acceleration test method compatible with variable correlation according to claim 1, characterized in that: The method for setting the evaluation index of the scene danger degree in step 4 is: for the variables that need attention, set the corresponding danger threshold of each variable respectively. If all variables exceed their corresponding danger threshold, the variables are considered to be in a dangerous scene. middle.

5. The automatic driving acceleration test method compatible with variable correlation according to claim 4, characterized in that: The indicator function of the dangerous scene is expressed as follows: ; in, For the j A scene, For dangerous scenes.

6. The automatic driving acceleration test method compatible with variable correlation according to claim 5, characterized in that: The probability of occurrence is expressed as: ; Where m is the number of scenes.

7. The automatic driving acceleration test method compatible with variable correlation according to claim 1, characterized in that: The importance sampling method is used to construct a new probability density function as follows: ; in, is the joint probability density function of the variables of interest, is the sampling weight of the sample.

8. The automatic driving acceleration test method compatible with variable correlation according to claim 7, characterized in that: In step 4, the steps for solving the sample sampling weights for the fastest convergence test using the Bayesian optimization method are as follows: Step 4.1: Based on the indicator function, occurrence probability, and adjusted importance joint probability density function of the dangerous scenario, establish the relative half-width, expressed as: ; in, N is the number of tests; is the relative half-width; is half width; is the confidence level; is the cumulative distribution function value corresponding to the confidence level; is the variance of the hazard rate, is the expectation of the joint probability density function of importance; Step 4.2: Establish an objective function based on the number of tests, expressed as: ; in, is the convergence threshold; The Gaussian process model is used to To model: ; in, is a Gaussian process model, is the mean function of the Gaussian process model, is the variance function of the Gaussian process model; Step 4.3: Initialization , , , and evaluate the corresponding objective function value , obtain observation data; Step 4.4: Set the current optimal objective function value to , and adopt the expected improvement function Selecting a new sample weight function ; For the new sample weight function , calculate its mean function and variance function , recalculate the mean function and variance function based on the new sample weight function, and update the objective function value , and the new observation data Add to the observation database; through continuous training optimization, until the objective function value Reach convergence; obtain the optimal sample sampling weight .

Citation Information

Patent Citations

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