Device and computer-implemented method for modeling a speed curve

Abstract

The invention relates to a device and a computer-implemented method for modelling a speed curve, wherein: the speed curve is modelled (216) by a speed, in particular mean speed, and a time series; the time series characterizes a speed fluctuation about the speed, in particular mean speed; for modeling of the speed curve, a value of the speed, in particular mean speed, is specified (212); the time series is defined by an unsteady restricted stochastic process; the process is defined by an autocorrelation coefficient of the random variables of the process and by red noise; the red noise is defined by an autocorrelation coefficient and by white noise; the white noise is drawn from a normal distribution; the values of the following parameters: autocorrelation coefficient of the red noise, autocorrelation coefficient of the random variables, and standard deviation, in particular logarithm of standard deviation, of the white noise, are drawn (214) from a specified three-dimensional distribution, in particular normal distribution or uniform distribution; the distribution is clearly determined by the mean values and the covariance matrix of the distribution and is associated with the specified value of the speed, in particular mean speed; and the time series is determined (216) with the restricted stochastic process parameterized by the values of the parameters drawn from the three-dimensional distribution, the value of the autocorrelation coefficient of the red noise and the value of the autocorrelation coefficient of the process being restricted to a value from the interval from 0 to 1.

Description

[0001] R.412370 - 1 -Description Title Device and computer-implemented method for modeling a speed profile Prior art The invention relates to a device and a computer-implemented method for modeling a speed profile. For the reliability design of technical components, e.g., vehicle components, load distributions from the field are required. In the early development phase, when no field data is yet available, these distributions are estimated using a virtual measurement campaign. In this type of simulation, the behavior of a large number of users is simulated, and the load distribution in the field is calculated in this way. Of central importance is the simulation-based prediction of speed profiles, i.e., the modeling of speed profiles.Disclosure of the invention: A computer-implemented method for modeling a velocity profile provides that the velocity profile is modeled by a, in particular, average velocity and a time series, wherein the time series characterizes a velocity fluctuation around the, in particular, average velocity, wherein a value of the, in particular, average velocity is specified for modeling the velocity profile, wherein the time series is defined by an unsteady bounded stochastic process, wherein the process is defined by an autocorrelation coefficient of the random variables of the process and by red R.412370 -. 2 -noise is defined, wherein the red noise is defined by an autocorrelation coefficient and white noise is defined, wherein the white noise is drawn from a normal distribution, wherein the values ​​of the parameters autocorrelation coefficient of the red noise, autocorrelation coefficient of the random variable, and in particular logarithmic standard deviation of the white noise are drawn from a given three-dimensional distribution, in particular a normal distribution or a uniform distribution, wherein the distribution is uniquely determined by the means and the covariance matrix of the distribution and is assigned to the given value of the mean velocity, in particular, and wherein the time series is determined by the bounded stochastic process parameterized by the values ​​of the parameters drawn from the three-dimensional distribution.where the value of the red noise autocorrelation coefficient and the process autocorrelation coefficient are restricted to a value in the interval from zero to one. The computer-implemented method for modeling the velocity profile uses a stochastic process from which a velocity profile is generated along a predefined route. The process is uniquely described by its distribution as well as its correlation structure, i.e., the autocorrelation function. The process includes a noise term. The unsteadiness and the correlation structure of the noise term make it possible to generate a realistic velocity profile. In one example, the process is uniquely described by its second-order, time-dependent statistical moments as well as by its correlation structure, i.e., the autocorrelation function. The process includes a noise term,which describes the dynamics of the system. This noise term has a time-varying distribution and is therefore unsteady. Taking this unsteadiness into account, as well as the correlation structure of the noise term, makes it possible to generate a realistic velocity profile. The velocity profile is modeled, for example, by adding the values ​​of the time series to obtain the average velocity, or by multiplying the average velocity by the values ​​of the time series. R.412370 -, 3 -It may be provided that a measured velocity profile is made available, wherein the measured velocity profile is divided into windows, wherein for each window the autocorrelation coefficient of the red noise and the autocorrelation coefficient of the process and the standard deviation of the white noise are estimated, in particular using least-squares estimation, from the measured velocity profile in the window, wherein for each window, in particular for each window for which the value of the standard deviation is greater than zero, a parameter family is determined, wherein the parameter family includes, in particular, the mean velocity, the autocorrelation coefficient of the red noise, the autocorrelation coefficient of the process, and, in particular, the logarithmic standard deviation of the white noise, wherein the parameter families are each assigned to a velocity zone of several velocity zones.in which the mean speed of the respective parameter family lies, wherein a three-dimensional distribution, in particular a normal distribution or uniform distribution, of the parameters autocorrelation coefficient of the red noise, autocorrelation coefficient of the process, and in particular logarithmic standard deviation of the white noise is determined for each speed zone, wherein the three-dimensional distribution of the respective speed zone is defined by a mean vector, wherein the mean vector comprises the mean of the autocorrelation coefficient of the red noise, the mean of the autocorrelation coefficient of the process, and the mean of the, in particular logarithmic, standard deviation of the white noise of the parameter families assigned to the respective speed zone.and wherein the three-dimensional distribution of the respective velocity zone is defined by the covariance matrix of the autocorrelation coefficients of the red noise, the autocorrelation coefficients of the process, and, in particular, the logarithmic standard deviation of the white noise of the parameter families assigned to the respective velocity zone. It may be provided that the values ​​of the parameters autocorrelation coefficient of the red noise, autocorrelation coefficient of the random variable, and, in particular, logarithmic standard deviation of the R.412370 -, 4 -White noise is extracted from the three-dimensional distribution determined for the velocity zone in which the mean velocity, in particular, used to model the time series lies. This means that previously determined parameters from the parameter family are used.It can be provided that the three-dimensional distribution from which the values ​​of the parameters autocorrelation coefficient of the red noise, autocorrelation coefficient of the random variable, and in particular logarithmic standard deviation of the white noise are drawn, is determined with a function, wherein the function describes a continuous dependence of the mean vector and the covariance matrix that define the distribution of the autocorrelation coefficient of the red noise, the autocorrelation coefficient of the process, and in particular the logarithmic standard deviation of the white noise, and with the function the values ​​of the parameters autocorrelation coefficient of the red noise, autocorrelation coefficient of the random variable, and in particular logarithmic standard deviation of the white noise are determined for the mean velocity by which the time series is modeled.This means that interpolated values ​​are determined and used with the function. For example, the tuples of mean speed, distribution means, and distribution covariance matrix from adjacent speed zones are used as support points for a continuous interpolation of the distribution means and covariance matrices as a function of the mean speed. The parameters of the respective parameter family assigned to each speed zone serve as support points for the continuous interpolation function.It can be provided that the function describes the continuous dependence between the average speed and an upper speed limit, wherein an upper speed limit is determined using the function for the average speed by which the time series is modeled, and / or wherein the function describes the continuous dependence between the average speed and a lower speed limit, wherein the function for the average speed by which the R.412370 -. 5 -When a time series is modeled, a lower speed limit is determined. The support points are given by the average speeds of the respective speed zone and the upper speed limit and / or the lower speed limit of the respective speed zone. It can be provided that the values ​​of the time series or the speeds in the modeled speed profile are limited to values ​​below an upper speed limit, whereby a maximum of the speeds in each window is determined and assigned, depending on the average speed determined for the respective window, to the speed zone in which the average speed lies, whereby the upper speed limit depends on an upper quantile, particularly in the range of 90% to 100%, of the maxima assigned to the speed zone in which the average speed lies.by which the time series is modeled, is determined, and / or that the values ​​of the time series or the speeds in the modeled speed profile are restricted to values ​​above a lower speed limit, wherein for each window a minimum of the speeds in the window is determined and, depending on the speed determined for the respective window, in particular the average speed, is assigned to the speed zone in which the average speed lies, wherein the lower speed limit is determined depending on a lower quantile, in particular in the range of 0% to 10%, of the minima assigned to the speed zone in which the average speed, by which the time series is modeled, lies. It may be provided that the measured speed profile is subdivided into windows of a predetermined length. For example, at least two of the speed zones [0 km / h, 30 km / h), [30 km / h, 50 km / h),[50 km / h, 80 km / h), [80 km / h, 100 km / h), [100 km / h, 120 km / h), [120 km / h, 999 km / h] are specified. The speed zones [0 km / h, 30 km / h), [30 km / h, 50 km / h) are suitable for modeling speed profiles in urban areas. The speed zones [50 km / h, 80 km / h), [80 km / h, 100 km / h) are suitable for R.412370 -, 6 -Modeling of speed profiles on rural roads. The speed zones [100 km / h, 120 km / h), [120 km / h, 999 km / h] are suitable for modeling speed profiles on highways. It can be provided that a distance for which the speed profile is modeled is specified depending on the speed zone for which the speed profile is modeled, in particular wherein a longer distance is specified for a speed zone that includes higher speeds than another speed zone, preferably a distance of 2 km for the speed zone [0 km / h, 30 km / h) and / or [30 km / h, 50 km / h), a distance of 4 km for the speed zone [50 km / h, 80 km / h) and / or [80 km / h, 100 km / h), a distance of 5 km for the speed zone [100 km / h, 120km / h) and / or [120km / h, 999km / h].This means that at higher speeds, a longer distance is modeled than at lower speeds. It can be stipulated that an upper and a lower speed limit are defined, and the speeds in the modeled speed profile are restricted to speeds between the upper and lower speed limits. This prevents unrealistic speeds. For example, if it is determined that a speed in the modeled speed profile exceeds the upper or lower speed limit, the time series that models the speed profile over the distance is recalculated using the constrained stochastic process. This prevents an unrealistic speed profile.For example, for a number of repetitions, the logarithmic standard deviation of the white noise in a single repetition is reduced depending on the number of repetitions. This ensures that a realistic velocity profile is modeled. R.412370 -. 7 -It may be provided that the normal distribution from which the white noise is extracted is a truncated normal distribution, wherein the truncated normal distribution is truncated depending on a parameter, wherein the parameter is determined depending on an upper limit for the red noise, wherein the upper limit for the red noise is determined depending on the upper speed limit, and / or wherein the truncated normal distribution is truncated depending on a parameter, wherein the parameter is determined depending on a lower limit for the red noise, wherein the lower limit for the red noise is determined depending on the lower speed limit.To realistically model the velocity profile along a route, when a predetermined distance for which the velocity profile is modeled is exceeded, values ​​of the parameters autocorrelation coefficient of the red noise, autocorrelation coefficient of the process, and in particular logarithmic standard deviation of the white noise are again drawn from the three-dimensional distribution that is assigned to the velocity zone in which the predetermined value of the, in particular, mean velocity lies, and wherein the time series that models the velocity profile over the distance is determined with the bounded stochastic process parameterized by the values ​​of the parameters drawn again from the three-dimensional distribution.It may be provided that the speed profile is modeled for a reliability design of a technical component, in particular a vehicle component, wherein the reliability of the technical component is tested during operation of the technical component, in particular on a test bench, depending on the modeled speed profile. A device for modeling a speed profile comprises at least one processor and at least one memory, wherein the at least one memory is executable by the at least one processor. R.412370 -. 8 -A computer program for modeling a velocity profile comprises computer-readable instructions, the execution of which by the at least one processor causes the device to execute the method. Further advantageous embodiments can be found in the following description and the drawing. In the drawing: Fig. 1 shows a schematic representation of a device for modeling a velocity profile, Fig. 2 shows a flowchart with steps of a computer-implemented method for modeling the velocity profile. In Figure 1, a device for modeling a velocity profile is shown schematically. The device 100 comprises at least one processor 102 and at least one memory 104. The at least one memory 104 comprises, in this example, volatile memory and non-volatile memory.The at least one memory 104 comprises instructions executable by the at least one processor 102, the execution of which by the at least one processor 102 causes the device 100 to execute a computer-implemented method for modeling the speed profile described below. In the example, a speed profile of a vehicle is modeled. The modeling is used, for example, for stress simulation of vehicle components whose damage depends significantly on the stress caused by different driving behavior of the drivers in the field as well as different external traffic influences. The modeling is used, for example, for the design of components in the vehicle's powertrain whose mechanical stress is strongly influenced by the acceleration behavior of the drivers. R.412370 -. 9 -It may also be possible to model the velocity profile of another technical system, e.g., an aircraft. The velocity profile can be a rotational speed profile, e.g., of an electric motor or a washing machine drum. Figure 2 shows a flowchart with steps of the computer-implemented procedure for modeling the velocity profile. The procedure comprises a first part for determining a database for modeling the velocity profile and a second part for modeling the velocity profile itself. The procedure is described for an example in which the velocity profile is defined by an average velocity and a time series . is modeled, where ^ represents a mean correction. The time series ^ ^This characterizes a velocity fluctuation around the mean velocity ^̅. This means that the time series ^^ varies the mean velocity ^̅. It may be intended that the velocity profile is modeled by a velocity different from the mean velocity and the time series ^^, i.e., that a different given velocity value than the mean velocity ^̅ is represented by the time series^ ^ The time series ^^ is varied by a non-stationary bounded stochastic process with ^ = defined where ^ is the autocorrelation coefficient of the stochastic process, and the stochastic process is red noise. is characterized by an autocorrelation coefficient ^ and white noise The white noise is drawn from a normal distribution ^(0, ^):^^~^(0, ^). R.412370 - 10 -The constrained stochastic process becomes unsteady by redrawing the parameters ^, ^, ^ after a distance ^^^^^. Here, the logarithm of the standard deviation, i.e., a logarithmic standard deviation log (^), is taken into account. The first part comprises step 200. In step 200, a measured velocity profile is provided. In this example, the velocity profile is a measured progression of the speed of a vehicle being driven by a driver along a route. The first part comprises step 202. In step 202, the measured velocity profile is divided into windows. In this example, the measured velocity profile is divided into windows of a predefined length. The first part comprises step 204.In step 204, the autocorrelation coefficient ^ of the red noise ^^ and the autocorrelation coefficient ^ and standard deviation ^ of the white noise ^^ are estimated for each window, in particular using least-squares estimation, from the measured velocity profile in the respective window. The first part comprises step 206. In step 206, a parameter family is calculated for each window: mean velocity ^̅, autocorrelation coefficient ^ of the red noise ^^, autocorrelation coefficient^, and logarithmic standard deviation log (^) of the white noise. determined. In the example, the average speed ^̅ is determined from the speed values ​​in the respective window. In the example, the autocorrelation coefficient ^ of the red noise, determined for each window, is used. ^ , autocorrelation coefficient ^, and logarithmic R.412370 - 11 - Standard deviation log (^) of white noise The average velocity ^̅ determined for the respective window is assigned. It may be provided that, instead of the logarithmic standard deviation log (^), the standard deviation ^ of the white noise is used. to determine and assign to the average speed ^̅ determined for the respective window. It may be provided that a minimum ^^^^ of the speeds in the window and a maximum ^^^^ of the speeds in the window are determined for each window. The first part comprises a step 208. In step 208, the parameter families are each assigned to the value of the average speed ^̅. For example, the values ​​of the average speed ^̅ each lie in one speed zone of several speed zones. It may be provided that for the speed zones a lower quantile^(^^^^) of the minima ^^^^ assigned to the respective speed zone and / or an upper quantile ^(^^^^) of the maxima assigned to the respective speed zone ^ are determined. ^^^The speed limits are determined and assigned to the respective speed zones. Speed ​​zones can be defined for urban areas, rural roads, and motorways, with or without limits. In the example, at least two of the following speed zones are specified: [0 km / h, 30 km / h), [30 km / h, 50 km / h), [50 km / h, 80 km / h), [80 km / h, 100 km / h), [100 km / h, 120 km / h), R.412370 - 12 - [120 km / h, 999 km / h]. The choice of interval boundaries for the different speed zones is flexible. The choice of the different speed zones used for modeling is flexible. It may be provided that the choice is made by the respective user via a user interface. The first part comprises step 212. In step 212, a three-dimensional normal distribution is calculated for each speed zone. The parameters autocorrelation coefficient ^ of the red noise ^^, autocorrelation coefficient ^, and logarithmic standard deviation log (^) of the white noise ^^ are determined as a function of the mean speed ^̅. The respective three-dimensional normal distribution ^ is assigned to the respective speed zone. The respective three-dimensional normal distribution ^ is assigned to the respective speed zone and stored in the database. The three-dimensional normal distribution ^ is an example of a three-dimensional distribution. Instead of the three-dimensional normal distribution ^, another three-dimensional distribution, e.g., a uniform distribution, can be used. The three-dimensional normal distribution ^ of the respective speed zone is defined by a mean vector ^. The mean vector ^ includes the mean ^^ of the autocorrelation coefficient ^ of the red noise. the mean ^^ of the autocorrelation coefficient ^ and the mean the logarithmic standard deviation log (^) of the white noise of the respective speed zone. R.412370 - 13 - The three-dimensional normal distribution ^ of the respective velocity zone is given by the covariance matrix Σ of the autocorrelation coefficients ^ of the red noise ^. ^ , the autocorrelation coefficient ^, and the logarithmic standard deviation log (^) of the white noise The respective speed zone is defined. In the example, steps 200 to 208 are executed for a large number of measured speed profiles, and the three-dimensional normal distribution ^ is determined depending on the parameter families defined for the large number of measured speed profiles. It can be provided that steps 200 to 208 are executed for a large number of measured speed profiles assigned to different drivers, and three-dimensional normal distributions ^ specific to the respective drivers are determined. The respective three-dimensional normal distribution ^ is, for example, assigned to the respective speed zone and stored in the database for the respective driver. For example, for each speed zone, the upper quantile Q(^^^^), especially in the range of 90% to 100%, is determined for the maxima ^^^^ that lie in the respective speed zone.For example, for each speed zone, the lower quantile Q(^^^^) is determined for the minima ^^^^ that lie within the respective speed zone, particularly in the range from 0% to 10%. The upper quantiles Q(^^^^) and the lower quantiles Q(^^^^) are determined, for example, for each driver from the measured speed profiles assigned to that driver. The second part comprises step 212. R.412370 -. 14 - In step 212, a mean speed value ^̅ and the distance ^^^^^ for which the speed profile is modeled are specified to model the speed profile. It may be intended that the mean speed value ^̅ is specified for a journey with a vehicle on a given route. The given route, for example, specifies a sequence of mean speed values ​​^̅. The distance ^ ^^^^The distance is specified, for example, depending on the speed zone for which the speed profile is modeled. It may be stipulated that a longer distance ^^^^^ is specified for a speed zone encompassing higher speeds than for another speed zone. For example, the distance ^ ^^^^specified according to one or more of the following assignments: 2 km for the speed zone [0 km / h, 30 km / h], 2 km for the speed zone [30 km / h, 50 km / h], 4 km for the speed zone [50 km / h, 80 km / h], 4 km for the speed zone [80 km / h, 100 km / h], 5 km for the speed zone [100 km / h, 120 km / h], 5 km for the speed zone [120 km / h, 999 km / h]. The second part comprises a step 214. In step 214, values ​​of the parameters autocorrelation coefficient ^ of the red noise ^^, autocorrelation coefficient ^ of the process, and logarithmic standard deviation log (^) of the white noise are aus der three-dimensional normal distribution ^ drawn, which is assigned to the speed zone in which the value of the given average speed ^̅ lies. R.412370 - 15 -The three-dimensional normal distribution ^ assigned to the velocity zone is read from the database. The value of the autocorrelation coefficient ^ of the red noise ^^ is restricted to a value from the interval of zero to one. The value of the autocorrelation coefficient ^ of the process is restricted to a value from the interval of zero to one. The second part comprises step 216. In step 216, the velocity profile over the distance ^^^^^ is determined. In the example, the velocity profile = ^̅^^ depending on a mean value correction ^ and on the given value of the mean speed^̅ and depending on the time series the velocity fluctuation in the velocity profile over the distance ^ ^^^^ modeled, determined. In the example, the constrained stochastic process ^ ^The time series is parameterized with parameters drawn from the three-dimensional normal distribution ^, which is assigned to the velocity zone in which the specified mean velocity ^̅ lies. The time series ^^ is determined using the bounded stochastic process parameterized by the parameters. To limit the stochastic process, it can be stipulated that the normal distribution from which the white noise is drawn is a truncated normal distribution ^(^, ^, 0, ^). The truncated normal distribution depends on a parameter ^ and a parameter ^. The parameter ^ and the parameter ^ are determined, for example, in one iteration ^ by: R.412370 - 16 - ^= ^^ − ^ ∗ ^^^^where ^ ^ a lower limit for red noise ^ ^ and ^ ^ This represents an upper limit for the red noise ^^, which can be determined, for example, in the iteration ^ by: ^^ = ^ − ^ ∗ ^^^^ where ^ represents a lower speed limit, e.g., a given lower speed limit ^ = ^^^^ and ^ represents a given upper speed limit, e.g., a given upper speed limit ^ = ^^^^. The dependency between ^^^^ and ^(^^^^) is given, for example, by so The dependency between ^^^^ and ^(^^^^) is given, for example, by ^(^^^^) = ^ exp so To limit the stochastic process, it can be stipulated that a maximum velocity in the measured velocity profile is defined as ^^^^ and a minimum velocity in the measured velocity profile as ^^^^. R.412370 - 17 -The random variable ^^ is restricted to values ​​between ^^^^ and ^^^^ to limit the stochastic process. This means that the velocities in the modeled velocity profile are restricted, specifically to velocities between ^(^^^^) and ^(^^^^). It can be provided that the velocities in the modeled velocity profile are restricted depending on the upper quantile ^(^^^^) and / or depending on the lower quantile ^(^^^^). It can be provided that the velocities in the modeled velocity profile are restricted to velocities between a predefined upper velocity bound and a lower velocity bound. For example, it is checked whether the velocities in the modeled velocity profile exceed the upper quantile Q(^^^^) and / or the lower quantile ^(^^^^). The upper quantile Q(^^^^) is an example of the upper velocity bound.The lower quantile ^(^^^^ ) is an example of the lower velocity limit. If it is found that the velocities in the modeled velocity profile exceed the upper quantile ^(^^^^) or the lower quantile, it may be necessary to repeat step 214. This means the time series. is determined again using the constrained stochastic process. It can be provided that a number ^^ of repetitions of step 214, i.e., a number ^^ of repetitions in which the time series ^^ is determined again, is counted. It can be provided that in each of the repetitions, the logarithmic standard deviation log (^) of the white noise ^^ is determined, depending on the number^ ^ The number of repetitions is reduced. For example, the logarithmic R.412370 - 18 - Standard deviation log (^) of white noise depending on the number^ ^ certainly: where ^ ^^^A maximum number of iterations is represented, e.g., 100. In the example, the velocity profile for the given value of the mean velocity ^̅ is modeled until the distance ^^^^^ is reached. If it is determined that the distance ^^^^^ is exceeded, step 212 is executed. This means that in step 214, values ​​of the parameters autocorrelation coefficient ^ of the red noise ^^, autocorrelation coefficient^, and logarithmic standard deviation ^ of the white noise are again used. aus der A three-dimensional normal distribution is drawn in which the given value of the mean velocity lies. This means the time series is determined using the bounded stochastic process, which is parameterized by the values ​​of the parameters drawn again from the three-dimensional normal distribution ^. An example of the procedure described above is, for example, described by the following algorithm: 1. Choose a fixed segment of length ^ ^^^ 2. Fix mean velocity ^̅ and three-dimensional normal distribution ^3. Fix upper quantile ^(^^^^), lower quantile ^(^^^^ ) and distance^^^^^ as a function of mean velocity ^̅4. Initialize total distance ^^^^ = 05. Initialize time step in seconds ^ = 06. Initialize red noise ^^ = 0, random variable ^^ = 0, random variable ^^ = 1, and distance ^^ = 07. Initialize number of repetitions ^^ = 0 R.412370 - 19 - 8. Initialize 9. Set mean correction ^= ^^ ^^ + 1(1 − ^^)(1 − ^^)(1 − ^^)while ^^^^ < ^^^^ Draw random parameter family (^, ^, ^) from the three-dimensional distribution ^while ^^^(^) > ^(^^^^) or ^^^(^) < ^(^^^^) Empty velocity vector: ^ = ({}) Reduce variance: while ^^ < ^^^^^ do Calculate correlated noise: ^^ = ^^^^^ + ^^, ^^~^(0, ^^^^) Calculate: ^^ = ^^^^^ + ^^ Calculate velocity fluctuation: Obtain velocity at time Increase distance traveled ^^ ← Increase time step ^ ← ^ + 1 end while Obtain total time ^ in seconds Obtain velocity vector ^ = (^^, … , ^^) Increase required number of repetitions ^^ ← ^^ + 1 end while Increase distance traveled ^^^^ ← ^^^^ + ^^ end while It may be provided that the three-dimensional distribution from which the values ​​of the parameters autocorrelation coefficient of the red noise, autocorrelation coefficient of the random variable, and in particular logarithmic standard deviation of the white noise are drawn, is determined by a function. The function describes, for example, a continuous dependence of the mean vector and the covariance matrix, which determines the distribution of the autocorrelation coefficient of the red noise, the autocorrelation coefficient of the process, and the R.412370 - 20 -In particular, the logarithmic standard deviation of the white noise is defined. For example, the tuples mean speed ^, means of the distribution, and covariance matrix of the distribution from adjacent speed zones are used as support points for the function to continuously interpolate the means of the distribution and the covariance matrices of the distribution as a function of the mean speed ^. The function uses an interpolation method, for example, linear interpolation. The method can provide that the values ​​of the parameters autocorrelation coefficient of the red noise, autocorrelation coefficient of the random variable, and in particular the logarithmic standard deviation of the white noise are determined by the function for the mean speed by which the time series is modeled.The function may describe the continuous relationship between, in particular, the average speed and an upper speed limit. The method may provide that the upper speed limit for, in particular, the average speed used to model the time series is determined using the function. The function may also describe the continuous relationship between, in particular, the average speed and a lower speed limit. The method may provide that the lower speed limit for, in particular, the average speed used to model the time series is determined using the function.It may be provided that the speed profile is modeled for a reliability design of a technical component, in particular a vehicle component, whereby the reliability of the technical component is tested during operation of the technical component, in particular on a test bench, depending on the modeled speed profile.

Claims

R.412370 - 21 -Claims 1. Computer-implemented method for modeling a velocity profile, characterized in that the velocity profile is modeled by a, in particular, average velocity and a time series (216), wherein the time series characterizes a velocity fluctuation around the, in particular, average velocity, wherein a value of the, in particular, average velocity is specified for modeling the velocity profile (212), wherein the time series is defined by an unsteady bounded stochastic process, wherein the process is defined by an autocorrelation coefficient of the random variable of the process and by red noise, wherein the red noise is defined by an autocorrelation coefficient and by white noise, wherein the white noise is drawn from a normal distribution, wherein the values ​​of the parameters autocorrelation coefficient of the red noise,The autocorrelation coefficient of the random variable, and in particular the logarithmic standard deviation of the white noise, are drawn from a given three-dimensional distribution, in particular a normal distribution or a uniform distribution (214), wherein the distribution is uniquely determined by the means and the covariance matrix of the distribution and is assigned to the given value of the, in particular, mean velocity, and wherein the time series is determined with the restricted stochastic process parameterized by the values ​​of the parameters drawn from the three-dimensional distribution (216), wherein the value of the autocorrelation coefficient of the red noise and the value of the autocorrelation coefficient of the process are restricted to a value from the interval from zero to one.

2. The method according to claim 1, characterized in that a measured velocity profile is provided (200), wherein the, R.412370 - 22 -The measured velocity profile is divided into windows (202), wherein for each window the autocorrelation coefficient of the red noise and the autocorrelation coefficient of the process and the standard deviation of the white noise are estimated, in particular using least-squares estimation, from the measured velocity profile in the window (204), wherein for each window, in particular for each window for which the value of the standard deviation is greater than zero, a parameter family is determined (206), wherein the parameter family comprises, in particular, the mean velocity, the autocorrelation coefficient of the red noise, the autocorrelation coefficient of the process, and, in particular, the logarithmic standard deviation of the white noise, wherein the parameter families are each assigned to a velocity zone of several velocity zones (208), in which, in particular, the mean velocity of the respective parameter family lies,wherein a three-dimensional distribution, in particular a normal distribution or uniform distribution, of the parameters autocorrelation coefficient of the red noise, autocorrelation coefficient of the process, and in particular logarithmic standard deviation of the white noise is determined for each velocity zone (210), wherein the three-dimensional distribution of the respective velocity zone is defined by a mean vector, wherein the mean vector comprises the mean of the autocorrelation coefficient of the red noise, the mean of the autocorrelation coefficient of the process, and the mean of the, in particular logarithmic, standard deviation of the white noise of the parameter families assigned to the respective velocity zone, and wherein the three-dimensional distribution of the respective velocity zone is defined by the covariance matrix of the autocorrelation coefficients of the red noise, the autocorrelation coefficients of the process,and is defined, in particular, by the logarithmic standard deviation of the white noise of the parameter families assigned to the respective speed zone.

3. Method according to claim 2, characterized in that the values ​​of the parameters autocorrelation coefficient of the red noise, autocorrelation coefficient of the random variables, and in particular, R.412370 - 23 -logarithmic standard deviation of the white noise is extracted from the three-dimensional distribution (214), which is determined for the velocity zone in which the mean velocity, in particular, by which the time series is modeled lies.4.The method according to claim 2, characterized in that the three-dimensional distribution from which the values ​​of the parameters autocorrelation coefficient of the red noise, autocorrelation coefficient of the random variable, and in particular logarithmic standard deviation of the white noise are extracted, is determined by a function, wherein the function describes a continuous dependence of the mean vector and the covariance matrix, which define the distribution of the autocorrelation coefficient of the red noise, the autocorrelation coefficient of the process, and in particular logarithmic standard deviation of the white noise, and with the function the values ​​of the parameters autocorrelation coefficient of the red noise, autocorrelation coefficient of the random variable, and in particular logarithmic standard deviation of the white noise are determined for the, in particular, mean velocity at which the time series is modeled.The method according to claim 4, characterized in that the function describes the continuous dependence between the, in particular, average speed and an upper speed limit, wherein an upper speed limit is determined using the function for the, in particular, average speed by which the time series is modeled, and / or wherein the function describes the continuous dependence between the, in particular, average speed and a lower speed limit, wherein a lower speed limit is determined using the function for the, in particular, average speed by which the time series is modeled.The method according to one of claims 2 to 5, characterized in that the values ​​of the time series or the velocities in the modeled velocity profile are limited to values ​​below an upper velocity limit (216), wherein a maximum of the velocities in the window is determined for each window and depending on the. R.412370 - 24 -for the respective window, a specific, in particular mean, speed is assigned to the speed zone in which the specific mean speed lies (206), wherein the upper speed limit is determined depending on an upper quantile, in particular in the range of 90% to 100%, of the maxima assigned to the speed zone in which the specific mean speed, by which the time series is modeled, lies, and / or that the values ​​of the time series or of the speeds in the modeled speed profile are restricted to values ​​above a lower speed limit (216), wherein for each window a minimum of the speeds in the window is determined and assigned depending on the specific, in particular mean, speed determined for the respective window to the speed zone in which the specific mean speed lies (206), wherein the lower speed limit is determined depending on a lower quantile,7. The method according to any one of claims 2 to 6, characterized in that the measured speed profile is divided into windows of predetermined length (202).

8. The method according to any one of claims 2 to 7, characterized in that at least two of the speed zones [0 km / h, 30 km / h), [30 km / h, 50 km / h), [50 km / h, 80 km / h), [80 km / h, 100 km / h), [100 km / h, 120 km / h), [120 km / h, 999 km / h] are predetermined (208).

9. The method according to one of claims 2 to 8, characterized in that a distance for which the speed profile is modeled is specified depending on the speed zone for which the speed profile is modeled (212), in particular wherein for a speed zone which includes higher speeds,a longer distance is specified for a different speed zone than for the other speed zone, preferably a distance of 2km for the speed zone [0km / h,30km / h) and / or, R.412370 - 25 -[30 km / h, 50 km / h), a distance of 4 km for the speed zone [50 km / h, 80 km / h) and / or [80 km / h, 100 km / h), a distance of 5 km for the speed zone [100 km / h, 120 km / h) and / or [120 km / h, 999 km / h].

10. The method according to one of the preceding claims, characterized in that an upper speed limit and a lower speed limit are specified, and the speeds in the modeled speed profile are limited to speeds between the upper speed limit and the lower speed limit (216).

11. The method according to claim 10, characterized in that if it is determined that a speed in the modeled speed profile exceeds the upper speed limit or the lower speed limit, the time series that models the speed profile over the distance is recalculated using the constrained stochastic process (216).12.The method according to claim 11, characterized in that, for a number of repetitions, the standard deviation of the white noise, in particular the logarithm, is reduced depending on the number of repetitions.

13. The method according to any one of claims 10 to 12, characterized in that the normal distribution from which the white noise is extracted is a truncated normal distribution, wherein the truncated normal distribution is truncated depending on a parameter, wherein the parameter is determined depending on an upper limit for the red noise, wherein the upper limit for the red noise is determined depending on the upper speed limit, and / or wherein the truncated normal distribution is truncated depending on a parameter, wherein the parameter is determined depending on a lower limit for the red noise, wherein the lower limit for the red noise is determined depending on the lower speed limit. R.412370 - 26 -14. The method according to one of the preceding claims, characterized in that when a predetermined distance for which the velocity profile is modeled is exceeded, values ​​of the parameters autocorrelation coefficient of the red noise, autocorrelation coefficient of the process, and in particular logarithmic standard deviation of the white noise are again drawn from the three-dimensional distribution (214) which is assigned to the velocity zone in which the predetermined value of the mean velocity lies, and wherein the time series which models the velocity profile over the distance is determined with the restricted stochastic process parameterized by the values ​​of the parameters drawn again from the three-dimensional distribution (216). 15.Method according to one of the preceding claims, characterized in that the speed profile is modeled for a reliability design of a technical component, in particular a vehicle component, wherein the reliability of the technical component is tested during operation of the technical component, in particular on a test bench, depending on the modeled speed profile.

16. Device (100) for modeling a speed profile, characterized in that the device (100) comprises at least one processor (102) and at least one memory (104), wherein the at least one memory (104) comprises instructions executable by the at least one processor (102), the execution of which by the at least one processor (102) causes the device (100) to execute the method according to one of claims 1 to 15. 17.Computer program for modeling a velocity profile, characterized in that the computer program comprises computer-readable instructions, the execution of which by a computer results in the method according to one of claims 1 to 15 being carried out on the computer.

Images