Method for determining the reliability of modeling the nonlinear dynamics of a traffic intersection

Abstract

Procedure for determining the reliability of the modeling of the dynamics of a traffic intersection, comprising the steps: S1 - Recording sensor data regarding the movement of road users at the traffic junction; S2 - Using a trained deep learning network model with the sensor data, wherein the deep learning network model includes at least one echo-state network unit (ESN), and wherein a result of the deep learning network model is a model of the dynamics of the traffic node; S3 - Determining a learned regularization coefficient of the deep learning network model, where the regularization coefficient indicates the reliability of the modeling of the dynamics of the traffic junction.

Description

[0001] The present invention relates to a method for determining the reliability of a model of the nonlinear dynamics of a traffic intersection. The invention further relates to a control unit, a computer program, and a computer-readable medium for executing the method. The invention also relates to a vehicle system. State of the art

[0002] Due to the increasing safety and reliability requirements in road traffic and the continuous development of autonomous vehicles, methods for modeling traffic dynamics at a traffic junction are increasingly being developed.

[0003] Determining reliability parameters for modeling traffic intersections is known from the prior art. A reliability parameter can relate to various aspects of traffic management; for example, it can relate to connectivity between traffic intersections. A reliability parameter can also relate to the quality of a traffic dynamics model, i.e., indicate the extent to which a modeled traffic dynamic at an intersection corresponds to the actual traffic dynamic at that intersection. Furthermore, a reliability parameter can represent a metric that allows for a comparison of traffic intersections, the traffic dynamics prevailing at those intersections, and abstract models of traffic dynamics.

[0004] Diagnostic procedures used in driver assistance systems for motor vehicles, such as those for dynamic discrete event systems like traffic intersection dynamics, involve methods for handling objects and resources and their changing states. Furthermore, it is necessary to process vague and nonlinear data. Methods based on classical techniques, such as fault tree analysis and neural networks, are not particularly well-suited for determining this reliability, especially with regard to changes and branching.

[0005] It is an object of the invention to provide an alternative or improved method for determining the reliability of the modeling of a nonlinear dynamics of a traffic intersection, as well as a control unit of a technical system, a vehicle system, a computer program product for carrying out the method, and a computer-readable medium. Disclosure of the invention

[0006] The object of the invention is solved by means of a method according to claim 1, by a method according to claim 8, by a control unit according to claim 9, by a traffic infrastructure component according to claim 10, by a computer program product according to claim 11, and by a computer-readable medium according to claim 12. Advantageous further developments, additional features and / or advantages of the invention will become apparent from the dependent claims and the following description.

[0007] According to a first aspect, the present disclosure discloses a method for determining the reliability of the modeling of the dynamics of a traffic junction, comprising the steps: S1 - Recording sensor data regarding the movement of road users at the traffic junction; S2 - Using a trained deep learning network model with the sensor data, wherein the deep learning network model includes at least one echo-state network unit (ESN), and wherein a result of the deep learning network model is a model of the dynamics of the traffic node; S3 - Determining a learned regularization coefficient of the deep learning network model, where the regularization coefficient indicates the reliability of the modeling of the dynamics of the traffic intersection.

[0008] The deep learning network model can include a mapping layer, an extension layer, and an output layer, with at least one echo-state network unit being able to be added to the extension layer.

[0009] The deep learning algorithm can be optimized at least partially in step S3 based on at least one nonlinearity metric determined in step S2.

[0010] The optimization can include an incremental algorithm that determines the number of echo-state network units to add to the deep learning network model.

[0011] The number of echo-state network units to be added to the deep learning network model can be determined, at least partially, in the incremental algorithm by comparing a mean-squared prediction error (RMSE) of the deep learning network model with an error limit.

[0012] In step 1, the sensor data can be tested for nonlinearity using an extended Dickey-Fuller test (ADF), and at least one nonlinearity metric of the sensor data can be determined.

[0013] The regularization coefficient can be determined, at least partially, on the basis of a deviation between the dynamics of the traffic node predicted by the deep learning network model and the actual dynamics of the traffic node.

[0014] The process can be executed on a central computing unit, for example, cloud-based, or on a local control unit installed near the traffic junction, for example, on a traffic infrastructure component. The process can also be executed partly locally and partly in the cloud.

[0015] According to another aspect, the present disclosure discloses a control unit of a technical system that is configured to perform the procedure described above.

[0016] According to another aspect, the present disclosure discloses a traffic infrastructure component for observing and / or monitoring a traffic junction, comprising a control unit as described above.

[0017] According to another aspect, the present disclosure discloses a computer program product for carrying out the above-described method, if the computer program product is executed by a control unit of a driver assistance system or is stored on a computer-readable data carrier.

[0018] According to another aspect, the present disclosure discloses a computer-readable medium on which a computer program product as defined above is stored. Brief description of the characters

[0019] The invention is explained in more detail below with reference to exemplary embodiments and the accompanying schematic drawing, which is not to scale. The figures (Fig.) in the drawing are merely examples and show: Fig. 1. Examples of a linear and a non-linear signal; Fig. 2. Schematic representation of a deep learning flowchart; Fig. 3. Schematic representation of a deep learning flowchart; Fig. 4. Schematically, a flowchart of a process.

[0020] Based on the Fig. Sections 1 to 4 below schematically describe the structure and function of a method for determining the reliability of the modeling of a nonlinear dynamics of a traffic junction.

[0021] The dynamic system at a traffic intersection comprises several simultaneously active objects that share resources such as lanes. The dynamics of the traffic intersection can be captured using suitable sensors, for example, a corner radar sensor mounted on a single vehicle. Such a sensor is designed to detect objects, their position, their relative speed to the ego-vehicle, and their direction of movement with extreme precision. In highly automated or advanced automated vehicles, corner radar sensors can be configured to warn the driver or even trigger emergency braking if necessary.

[0022] Fig. Figure 1a shows an example of a linear signal recorded by radar sensors at a traffic intersection. The abscissa represents the number of detection tests at the intersection, and the ordinate shows a performance indicator reflecting the quality of the detections across the tests. Signals 12 and 14 represent two different calendar years. Fig. Signals 12 and 14 shown in Figure 1a are referred to as linear signals in the context of the application, since the course of the performance indicators over time corresponds very well for both signals 12 and 14, which suggests a good predictive quality of a traffic hub model trained on these signals.

[0023] On the contrary, the inventors found that with chaotic signals, such as those found in Fig. 1b, as shown in signals 16 and 18, the prediction of traffic dynamics using state-of-the-art prediction models does not yield good results.

[0024] Regarding the evaluation of sensor data, the inventors further determined that deep learning-based AI methods ("artificial intelligence") are generally well-suited to mapping the states of the dynamic system at the traffic intersection. Increasing the number of parameters in deep learning reduces the possibilities for their precise determination and makes nonlinear effects more apparent, particularly in the case of embedded real-time applications. Based on deep learning-based AI methods, a new learning algorithm is presented below, which can be used to specify the reliability of determining the status of a traffic intersection. An extended Dickey-Fuller test is applied to account for nonlinear effects.

[0025] In relation to Fig. 1 The deep learning network model used in the procedure comprises a mapping layer 210, an extension layer 220, and an output layer 230, which will be described in more detail below.

[0026] In the deep learning system, the original radar sensor channel data of a traffic intersection dynamics are first mapped as input to a first mapping node. The output of the first mapping node then represents the input of a second mapping node, and so on, creating a network structure.

[0027] The improved structure of the deep learning scheme is suitable for enhancing its feature extraction capabilities from the original radar sensor data to a certain extent. The mapping nodes and the extension nodes of the extension layer are important for a reliable representation of the radar sensor data. To improve the deep learning algorithm's ability to make predictions based on nonlinear radar data, it is proposed to incorporate an echo state network (ESN) into the extension layer of the deep learning scheme to create a broad echo state using a cascade of mappings. This structure is described in Fig. 2 shown.

[0028] ESNs are a special type of recurrent or feedback neural network (RNN) designed for the efficient processing of sequential data. They employ a reservoir computing framework containing a fixed, randomly initialized recurring layer called the "reservoir." A key feature of ESNs is their ability to optimally utilize the echo-like dynamics of the reservoir, enabling the effective capture and replication of temporal patterns in sequential inputs.

[0029] ESNs function by linearly combining input and reservoir states to generate the network's output. They are characterized by the fact that only the output layer is trained, while the reservoir weights remain fixed. This approach makes ESNs particularly useful for tasks where capturing temporal dependencies is crucial, such as time series prediction and signal processing.

[0030] In addition to the ESN units added by the applied incremental algorithm, the [data] includes Fig. Figure 2 schematically represents a deep learning network model with a mapping layer 210, an extension layer 220, and an output layer 230. The introduction of the ESN units at 222 ensures the consideration of nonlinearities.

[0031] As in Fig. As shown in Figure 2, the node of mapping layer 210 is represented as Z = [Z1,Z2, ...,Z N ] defined the node of the extension layer 220 as H = [H1,H2, ..., H N ].

[0032] For example, Z1 is the first node of mapping layer 220.

[0033] The output of the nodes of extension layer 220 of the status propagation is defined as: Hj(t+1)=(1−δ)Hj(t)+δ⋅f(WhjZ+WjHj(t))

[0034] The following terms are used: H j the output of the j-th ESN unit in the extension layer; W hj the connection weight of the j-th ESN unit to the output of the mapping layer; and W j the connection weight of the reservoir pool of the j-th ESN unit; and δ the Kronecker symbol.

[0035] The development of H jis thus divided into a linear propagation (first term of the right-hand side of equation 1) and a non-linear part (second term).

[0036] Based on convergence considerations, the output Y and the output weighting matrix W are calculated as follows: Y=[Z1,Z2,…,ZN|H1,H2,…,HN]Wnm=AnmWnm Wnm=(λI+Anm(Anm)T)−1(Anm)TY

[0037] When the incremental algorithm is used to improve performance, which will be discussed in more detail later in connection with Table 2, both a combination matrix A and the output weighting matrix W are changed, and the updated formula is: Note+1=[Note|Hm+1]

[0038] The pseudo-inverse of the combination matrix A is defined as follows: (Note+1)+=[(Note)+−DBTBT]

[0039] The updated output weighting matrix is ​​defined as follows: Wnm+1=[Wnm−DBTYBTY]

[0040] The following applies: D=(Note)+Hm+1 BT={(C)+,C≠0(1+DTD)−1BT(Note)+,C=0 C=Hm+1−NoteD

[0041] As can be seen from the relationships shown in equations 2 to 9, when the network structure is updated by the linear or nonlinear part of the incremental algorithm, it is not necessary to retrain or recalculate the training data. Instead, the update can advantageously be performed using simple matrix operations. The update is therefore fast and accurate.

[0042] A corresponding algorithm for training the Deep Neural Network is given in the following Table 1:

[0043] As described above, an ESN is introduced in extension layer 220 for deep learning to accommodate the nonlinear trend of the data. The ESN's reservoir is its essential component, but its size is difficult to determine. Instead of conventional empirical approaches, an algorithm is proposed here that automatically determines the size of the reserve pool.

[0044] To address the nonlinearity, an incremental algorithm is required, which improves the network's nonlinear adaptability by adjusting the number of ESN units in the extension layer. The execution of the incremental algorithm is shown in Table 2 below.

[0045] For incoming radar data, the nonlinearity test according to the invention can be performed in three ways: the Dickey-Fuller test (Dickey, DA; Fuller, WA (1979). “Distribution of the Estimators for Autoregressive Time Series with a Unit Root”. Journal of the American Statistical Association. 74 (366): 427-431), the extended Dickey-Fuller test (ADF), and the correlation test.

[0046] In the technical field of radar technology, the ADF test is used as a method for verifying the nonlinearity of radar measurement time series and is based on classical econometric theory. The ADF test mitigates the influence of the random perturbation term on the overall validation result. Unlike the correlation test, the stability of the time series is not assessed based on the presence of lag and cancellation functions. Rather, the ADF criterion is whether the mean and variance of the time series change nonlinearly over time. In this disclosure, the degree of nonlinearity is determined according to the Akaike Information Criterion (AIC) by evaluating the probability values, test statistics, the 1% critical value, the 5% critical value, and the 10% critical value.

[0047] Within the scope of this disclosure, the parameters of deep learning are optimized based on nonlinearity metrics. During the optimization, the probability value of the radar signal is determined by the ADF test, and the nonlinearity indicators are combined into a new indicator that relates to the criterion for optimizing the deep learning regularization coefficient λ.

[0048] The proposed nonlinearity error indicators are as follows: Si=f(p)⋅1n∑k=1n(y^(k)−y(k))2 with: f(p)=|p^−p| sisi+1>M

[0049] Here, p' denotes the ADF probability value of the predicted radar data, and p denotes the ADF probability value of the actual radar data, y'(k) denotes the k-th predicted value, y(k) denotes the k-th actual value, n is the number of radar samples, M is the set limit coefficient, and Si denotes the nonlinearity error indicator for the i-th experiment.

[0050] By summarizing the indicators identified above, a regularization coefficient λ of the nonlinear deep learning model can be fitted using the following formula: λi+1={α⋅λi,L≥0β⋅λi,L<0 with: L=∑k=1ny^(k)−y(k)

[0051] The size λ i where denotes the regularization coefficient in the i-th prediction, and L denotes the error between the predicted and the actual data of the radar series.

[0052] As can be seen from equations 10 to 12, the metrics include the stability difference between the predicted and the actual data, as well as a local error magnitude. According to equation 11, f(p) = |p̂ - p| is a function of the stability difference between the predicted and the actual series. The smaller the value of S, the smaller the prediction error.

[0053] Equations 13 and 14 show that if the value for L results in different intervals, the regulated scaling coefficients are adjusted to different degrees.

[0054] With reference to Fig. Section 3 summarizes how nonlinear effects are taken into account in deep learning. The algorithm starts at S3-0. At S3-1, W ei β ei initialized for i = 1, ..., n, and the output of node Z of mapping layer 210 was recorded.

[0055] At S3-2, the ESN cells of the extension layer are initialized.

[0056] In S3-3, the incremental algorithm shown in Table 2 is performed to obtain the appropriate number of ESN cells.

[0057] Furthermore, in S3-4 the nonlinearity error indicator for the i-th experiment S i determined according to equation 10 and the limit coefficient M set.

[0058] In step S3-5, equation 12 determines whether for two consecutive S i , S i+1 applies: sisi+1>M. If this is the case, in step S3-6, the error between the predicted and the actual data of the radar series is determined and stored according to equation 14. In S3-7, the regularization coefficient λ is determined according to equation 13. In S3-8, the nonlinearity error indicator for the i+1th experiment can then be updated and stored, after which a loop is performed over query S3-5. As soon as it is determined in S3-5 that for two consecutive S i , S i+ , applies: SiSi+1>M, In S3-9, the current values ​​for the nonlinearity error indicator for the present experiment S are given. i The regularization coefficient λ and other potentially relevant metrics are stored. The algorithm then terminates at S3-10.

[0059] The proposed nonlinear deep learning approach is optimized in the ESN extension layer 220. It can be referred to as "nonlinear OE," where OE stands for the optimization of extension layer 220. The optimization includes the incremental algorithm for adjusting the size of the ESN as well as parameter optimization based on the presented nonlinearity metrics.

[0060] Fig. Section 4 provides an overview of the process of an embodiment of a method for determining the reliability of the modeling of a nonlinear dynamics of a traffic junction.

[0061] In step S1, radar data are collected at the schematically depicted traffic intersection. In step S1a, the sensor data are tested for nonlinearity using the extended Dickey-Fuller test (ADF). In step S1a, the regularization coefficients S iand λ is determined. In step S2, the deep learning network model is trained with the sensor data, whereby a specific number of echo-state network units (ESNs) are added to the extension layer 220 as described above and using the incremental algorithm. During the execution of the deep learning algorithm, the learned regularization coefficients S and λ are determined as described by equations 10 to 14. The regularization coefficient λ indicates the reliability of the modeling of the traffic intersection dynamics.

[0062] The invention is not limited to the described and illustrated embodiments. Rather, it also encompasses all further developments by skilled craftsmen within the scope of the invention defined by the claims. In addition to the described and illustrated embodiments, further embodiments are conceivable, which may include further modifications and combinations of features. QUOTES INCLUDED IN THE DESCRIPTION

[0000] This list of documents cited by the applicant was automatically generated and is included solely for the reader's convenience. The list is not part of the German patent or utility model application. The DPMA accepts no liability for any errors or omissions. Cited non-patent literature

[0000] Dickey, D. A.; Fuller, W. A. (1979). „Distribution of the Estimators for Autoregressive Time Series with a Unit Root“. Journal of the American Statistical Association. 74 (366): 427-431

[0045]

Claims

[1] Method for determining the reliability of the modeling of the dynamics of a traffic intersection, comprising the steps: S1 - Recording sensor data regarding the movement of road users at the traffic junction; S2 - Using a trained deep learning network model with the sensor data, wherein the deep learning network model includes at least one echo-state network unit (ESN), and wherein a result of the deep learning network model is a model of the dynamics of the traffic node; S3 - Determining a learned regularization coefficient of the deep learning network model, where the regularization coefficient indicates the reliability of the modeling of the dynamics of the traffic junction. [2] Method according to claim 1, characterized by, that the deep learning network model includes a mapping layer 210, an extension layer 220, and an output layer 230, and that at least one echo state network unit is added in the extension layer 220. [3] Method according to any one of the preceding claims, characterized by , that in step S3 the deep learning algorithm is optimized at least partially on the basis of at least one nonlinearity metric determined in step S2. [4] Method according to claim 3, characterized by that the optimization includes an incremental algorithm that determines the number of echo-state network units to be added to the deep learning network model. [5] Method according to claim 4, characterized by, that the number of echo-state network units to be added to the deep learning network model in the incremental algorithm is determined at least partially by comparing a mean-squared prediction error (RMSE) of the deep learning network model with an error limit. [6] Method according to any one of claims 1 to 5, characterized by , that the sensor data in step 1 S1 are tested for nonlinearity in a step S1a using an extended Dickey-Fuller test (ADF) and at least one nonlinearity metric of the sensor data is determined. [7] Method according to any one of claims 1 to 6, characterized by , that the regularization coefficient is determined at least partially on the basis of a deviation between a traffic node dynamics predicted by the deep learning network model and an actual traffic node dynamics. [8] Method for training a deep learning network model with sensor data, wherein the deep learning network model includes at least one echo-state network unit (ESN), and wherein a result of the deep learning network model is a model of the dynamics of a traffic node. [9] Control unit of a technical system configured to perform the method according to any one of claims 1 to 8. [10] Traffic infrastructure component for observing and / or monitoring a traffic junction, comprising a control unit according to claim 9. [11] Computer program product for carrying out the method according to any one of claims 1 to 8, when the computer program product is executed by a control unit. [12] Computer-readable medium on which a computer program product according to claim 11 is stored.

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