Method, system for carrying out such a method; computer program and computer-readable medium for generating a test profile for vibration testing of vehicle equipment on the basis of data acquisition during route journeys

Abstract

In a method for generating a test profile (4), comprising a pseudo-damage spectrum calculation process (P1), in the context of which a plurality of pseudo-damage spectra (2.1, 2.2, …, 2.n) are calculated from a plurality of measurement signals (1.1, 1.2, …, 1.n) by means of a spectrum calculation algorithm, such that a pseudo-damage spectrum (2.1, 2.2, …, 2.n) is generated for each measurement signal (1.1, 1.2, …, 1.n), wherein each measurement signal (1.1, 1.2, …, 1.n) was recorded before the beginning of the method in the context of a route journey of a test vehicle, an extrapolation and superposition process (P2), comprising an extrapolation subprocess (P5) and a superposition subprocess (P6), wherein in the context of the extrapolation subprocess (P5) each pseudo-damage spectrum (2.1, 2.2, …, 2.n) is multiplied by a proportionality constant, such that a plurality of extrapolated pseudo-damage spectra (7.1, 7.2, …, 7.n) are generated, wherein in the context of the superposition subprocess (P6) the extrapolated pseudo-damage spectra (7.1, 7.2, …, 7.n) are added up to give rise to a superposed pseudo-damage spectrum (3), a test profile generation process (P3), in the context of which the test profile (4) is generated, a reference signal processing process (P4), in the context of which, from a reference signal (5), firstly by means of the spectrum calculation algorithm, firstly a reference signal pseudo-damage spectrum (17) is calculated and subsequently the reference signal pseudo-damage spectrum (17) is multiplied by the proportionality constant, such that an extrapolated reference signal pseudo-damage spectrum (6) is generated, the test profile (4) is generated in the context of the test profile generation process (P3) on the basis of the superposed pseudo-damage spectrum (3) and the extrapolated reference signal pseudo-damage spectrum (6).

Description

[0001] ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 Method, system for carrying out such a method; computer program and computer-readable medium for generating a test profile for vibration testing of vehicle equipment based on data acquisition during route travel. Technical field The invention relates to a method for generating a test profile according to the preamble of claim 1, a system for carrying out such a method according to claim 12, a computer program according to claim 1, and a computer-readable medium according to claim 13. The invention further relates to a system, a computer program, and a computer-readable medium according to the independent claims. State of the art Within the framework of approval processes for newly developed technical products in the automotive industry, the vibration resistance of such products is typically tested, among other things. The products are typically any type of component,Assemblies or devices that are installed in vehicles and are subjected to vibrations during the operation of these vehicles. These vibrations may be generated by the operation of the vehicle or by the products themselves (e.g., electric motors), or a combination of different types of vibration. In vibration resistance tests on such products, the products are typically subjected to specific vibration patterns on special test benches (e.g., so-called shaker test benches) that simulate the vibrations during the operation of a vehicle in which the products are intended to be used.should be simulated as accurately as possible. Such vibration patterns are defined by test profiles. Ideally, such test profiles should, on the one hand, represent the vibration stresses for the respective products during their service life as realistically as possible. ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18. On the other hand, such test profiles should also enable the duration of the vibration tests on the test benches to be kept as short as possible, e.g., to minimize the costs of the vibration tests. DE10 2020114973 A1 refers to a procedure,to determine a test profile for tests or simulations on a component or motor vehicle under test. Data is measured or calculated and stored as a function of time during different use cases. This data is then analyzed for damage content. The identified damage content of a specific use case is made available to the user. The user can then select and combine specific time periods from various use cases to create a customized test profile. Methods for generating test profiles, which are determined, for example, based on data recorded during test drives, have already been proposed. The disadvantages of the known profile creation methods are briefly described below. For greater clarity, the methods have been classified according to the characteristics "model-based / non-model-based.""damage-based / non-damage-based." Model-based methods are based on describing the dynamic properties of the component under investigation using a physical system model, e.g., in the form of an FE model [10, 11] (references to the bibliography are given in square brackets at the end of the description), or mathematically, using a set of differential equations [5 - 9]. If the profile calculation algorithm is defined in such a way that a profile created with it should satisfy the (calculated) equality of the damage coefficients from operational vibration measurements (e.g., in the vehicle on routes) with those from the shaker test (so-called principle of damage equivalence), it is classified as a damage-based method. The major disadvantages of these methods are: ^ the profile calculated using a non-damage-based method (regardless of whether it is model-based or non-model-based),ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 does not guarantee that the damage experienced by the product during its life cycle in a vehicle (operational damage) is simulated in a vibration test (test damage). Therefore, in the case of a passed test, it cannot be ruled out that the damage applied to the product in the vibration test was too small compared to the actual damage in the vehicle (i.e., the test was too weak). On the other hand, in the case of a failed test, the test damage could exceed the operational damage (test too harsh). In both cases, this would mean that the test was not carried out correctly. All non-damage-based methods have this disadvantage, e.g. [2, 3, 4] ^ In model-based methods, the model of a linear,weakly damped single-mass oscillator (EMS). This is the case with the methods [5-9]. However, the complex, nonlinear mechanical-dynamic behavior of real products (components) can only be represented inaccurately by a relatively simple EMS model. The other methods [10, 11] use a computer model created with the help of a finite element tool. However, setting up an FE model requires a lot of work and consequently leads to high costs for profile calculation. Other disadvantages of the profiling methods known in technology for vibration testing of vehicle equipment: ^ They are not universally applicable, as they either produce o profiles of a specific type (e.g. only sweep profiles [2, 3] or only noise profiles [4, 9, 12, 13]), or o profiles only for the vibration excitation (further - excitation profiles) but not for the vibration response (reaction profiles,which, for example, allow the limitation of the test specimen's reaction amplitudes when creating an excitation profile) [4 – 9], or o profiles which allow damage-equivalent testing can only be calculated for a specific combination of calculation parameters (e.g. only ZF Friedrichshafen AG file 212889 Friedrichshafen 2024-01-18 for the slope coefficient 4 of the Wöhler curve)

[0013] , or ^ they require data to trigger the profile calculation algorithm, recorded on a vibration test bench, possibly in a pre-test

[0013] ; the invention has recognized that such data can also be generated simulatively without the use of hardware (e.g. a test bench), which minimizes effort and costs, or ^ they only function recursively [8, 9, 13]; this is inefficient and results in high computational effort, since the profile amplitude for each individual frequency must be calculated iteratively, in a loop,or ^ they do not take into account the need for extrapolation and superposition of the load spectra or the damage figures calculated from the data recorded in driving tests, so that they apply to the full required service life of the component in the vehicle

[0013] . General description of the invention The object of the invention is to eliminate or at least reduce the disadvantages of the prior art. This object is achieved by a method for generating a test profile according to claim 1. The inventor has recognized that this object can be achieved by means of a new,damage-based and non-model-based method for generating a test profile according to claim 1. The term "test profile" is to be understood broadly. In particular, a test profile is to be understood as, for example, the following functional dependencies: ^ the course of the amplitude of an acceleration signal (or another physical quantity) over the frequency (especially in the case of sweep profiles), ^ the course of the power density spectrum (LDS) of an acceleration signal (or another physical quantity) over the frequency (especially in the case of noise profiles). ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 The inventors have found,that such a method for generating a test profile can be more versatile and efficient than known methods. This method according to the invention is referred to below as the ASPEN method (abbreviation for "Automated Vibration Profile Development") or the ASPEN-RoMi method. It is used to create test profiles from test drives on routes. These are defined as special routes for various vehicle usage profiles (e.g., on a motorway, cross-country route, mountain road, in the city). During test drives on these routes, realistic conditions regarding the vibration load on the component in question are recreated. The routes can be combined in any ratio, hence the name "RoMi" - RouteMix. A well-known representative of the route mix in the passenger car segment is CARLOS [1,15]. Special tests must be distinguished from route drives. These are relatively short-term tests with a smooth, continuous increase (“run up”) or decrease (“run down”) of one or more driving condition parameters. This parameter is usually a speed in the vehicle's drivetrain, e.g., that of the combustion engine or the electric drive (in electrified vehicles). Since the duration of the driving condition parameters in these tests generally does not correspond to typical operational use, they are not suitable for creating test profiles using the ASPEN-RoMi method. The data required for profile creation are, as described above, preferably recorded in a test vehicle during test drives on one or more routes (route mix). Alternatively, a suitable functional and / or load test bench can be used if it allows the simulation of the vibrations experienced by the product.similar to journeys in a vehicle on routes. In such tests, mechanical-dynamic load and / or stress variables (e.g. vibration acceleration, vibration velocity, dynamic vibration displacement, dynamic forces, mechanical strains, etc.) with oscillating characteristics are measured on the product and / or at its attachment points on the support using suitable sensors (e.g. acceleration, velocity, displacement, force sensors, strain gauges, etc.) and a suitable vibration recording system. ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 After completion of a measurement campaign conducted in this way, the input data required for profiling with the ASPEN method are available as digitized vibration signals. After a standard signal preprocessing procedure known to the person skilled in the art (e.g. elimination of measurement disturbances, cutting out relevant measurement intervals,Filtering) they can be fed directly to the computer unit or other system in which the ASPEN method is programmed for profile calculation. For the calculation of the test profile, the ASPEN method advantageously processes, in addition to the signals recorded on the routes, a special time signal, called the reference signal. In advantageous embodiments, all test profiles calculated with the method mathematically fulfill the principle of damage equivalence with respect to the pseudodamage spectra calculated in the method. In advantageous embodiments, the reference signal processing process runs parallel to the pseudodamage spectrum calculation process and / or the extrapolation and superposition process. One advantage of this isthat both the superimposed pseudodamage spectrum and the extrapolated reference signal pseudodamage spectrum are available for the test profile generation process essentially simultaneously. In typical embodiments, the reference signal pseudodamage spectrum is calculated as part of the pseudodamage spectrum calculation process. In typical embodiments, the extrapolated reference signal pseudodamage spectrum is calculated as part of the extrapolation and superposition process, in particular as part of the extrapolation sub-process. Alternatively, however, it is also possible to calculate the reference signal differently, for example at different times. Each measurement signal preferably describes a temporal progression of one and the same measurement variable, typically recorded on different routes of a route mix. This is to be understood in particular in such a way that a measurement variable, for example an acceleration,at a specific location on a component of a ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 vehicle in a specific measurement direction. This measurement value is then observed over a number of route runs of a test vehicle, and for each route run, a measurement signal of this measurement value is recorded, always in the same direction. At the end of the multiple route runs, a number of measurement signals (in other words – a set of measurement signals) for one and the same measurement value are available – each measurement signal per route. The measurement signals differ more or less in their course because the route runs each cause different vibrations. During your first,In a typical embodiment of the method, a set of measurement signals from only one measurement variable is processed. The method then delivers (as the main result) only one test profile. This profile is used to apply the same stress to the component (at its selected measurement location) during a vibration test of a defined duration, as is expected to occur on the route mix for the full required service life (mileage). "Expected" means that the operational damage is mathematically predicted through an extrapolation and superposition process. In this sense, the method delivers damage-equivalent profiles. The principle of damage equivalence forms the basis of the definition of the method and is its most important characteristic. In a second, typical embodiment, several test profiles are generated within the framework of the method based on a plurality of measurement signal sets.Each measurement signal set is obtained by measuring the signals of a specific measurement variable on the route mix. In other words, the method considers not just one measurement variable, but a plurality of measurement variables. For example, imagine that accelerations at different points on a specific component in a vehicle are to be measured in the same direction. The respective acceleration at each measuring point in a direction is to be considered as a separate measurement variable. This results in a plurality of measurement signal sets for this component, with each measurement signal set corresponding to a specific measurement variable. Instead of a plurality of measurement signals for one and the same measurement variable, there are different measurement signal sets, with each measurement signal set consisting of a number of measurement signals.which corresponds to the number of route trips performed by the test vehicle (since in all embodiments of the method, preferably one signal of the same measured variable is recorded per route). In the embodiment with a plurality of measurement signal sets, different measurement signal sets for the plurality of measured variables are processed within the framework of the aforementioned processes instead of the measurement signals for only a single measured variable, whereby the number of measurement signal sets corresponds to the number of measured variables under consideration. In other words, the simplest case of the method according to the invention (see the first embodiment) thus corresponds to the case where only one measured variable is considered. In the latter, second typical embodiment, however, two, three, four or more measured variables are considered in the method.whose respective measurement signals are incorporated into the calculations of the aforementioned processes. In this case, after running through the extrapolation and superposition process, the method delivers several profiles, each of which is damage-equivalent for the considered location and direction on the component (i.e., for the respective measurand) in the aforementioned sense. Furthermore, the method is typically based on the calculation of so-called pseudo-damage spectra. In typical embodiments, the method (depending on the task, the input data, and the setting parameters) uses test profiles of several different types or profiles with different characteristics, including excitation and response profiles, profiles for single- and multi-point control, as well as profiles that cover the damage on individual routes or on the entire route mix.generated. In advantageous embodiments, the pseudodamage spectrum calculation process comprises the following steps: - a signal filtering step, in which each measurement signal is filtered using a plurality of bandpass filters, resulting in a plurality of filtered measurement signals, ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 - a classification step, in which a load spectrum is formed from each filtered measurement signal by means of classification, typically by dividing an entire amplitude range of each filtered measurement signal into classes, wherein a number of fatigue cycles is determined for the amplitude of each class, preferably using a counting method, - a conversion step,in which a possibly averaged amplitude of each cycle (a cycle may have a mean value not equal to zero) is first converted into a damage-equivalent mean-free amplitude, preferably using a Haigh diagram, and then the mean-free amplitudes are sorted in ascending order, - a partial damage contribution calculation step, in which a partial damage contribution is calculated for the number of cycles for each damage-equivalent mean-free amplitude, preferably using a Wöhler curve, - a total damage calculation step, in which the partial damage contributions are summed up for each filtered measurement signal to form a total damage, each total damage being referred to as the pseudo-damage number of the respective filtered measurement signal, and - a pseudo-damage spectrum generation step,In this process, the pseudodamage spectra are formed from the pseudodamage numbers by representing the pseudodamage numbers as a function of the bandpass center frequencies of the bandpass filters. The filtered measurement signals are preferably narrowband filtered measurement signals. In typical embodiments, the classification step comprises a rainflow counting step, in which a rainflow matrix is ​​created for each filtered measurement signal using rainflow parameters. ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 For the sake of simplicity, the term "pseudodamage spectrum" is abbreviated to "PSS" in some places below. In advantageous embodiments, a noise profile and / or a sweep profile are calculated as part of the test profile generation process. In typical embodiments, the sweep profile is calculated according to the following formula: where S U (f) is the desired amplitude of the amplitude-frequency response (AFV) of the sweep profile, S Ref (f) is the amplitude of the AFV of the monoharmonic reference signal, D U (f) the ordinate of the PSS, which is for monoharmonic oscillation with the desired amplitude S U comes about is, D Ref (f) the ordinate of the PSS of the reference signal with the AFV S Ref (f) is, and k WL is the slope coefficient of the S-N curve. In typical embodiments, the noise profile is calculated according to the following formula: where PSD U (f) is the desired height of the power density spectrum (LDS) of the noise profile, PSD Ref (f) is the height of the LDS of the stochastic reference signal, ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 D U (f) the ordinate of the PSS, which for stochastic oscillation with the desired LDS PSD U comes about is, D Ref(f) the ordinate of the PSS of the reference signal with the LDS PSD Ref (f) is, and k WLis the slope coefficient of the Wöhler curve. In typical embodiments, the method is a computer-implemented method. In typical embodiments, the method is automated, at least in part. The object is further achieved by a system for carrying out one of the aforementioned methods, wherein the system is preferably suitable for at least partially carrying out and / or coordinating and / or controlling a method for generating a test profile according to at least one of the aforementioned embodiments. For this purpose, the system advantageously comprises suitable components,for example, a pseudodamage spectrum calculation component and / or a spectrum calculation component and / or an extrapolation and superposition component and / or an extrapolation subcomponent and / or a superposition subcomponent and / or a test profile generation component and / or a reference signal processing component and / or a signal filter component and / or a classification component and / or a conversion component and / or a partial damage contribution calculation component and / or a total damage calculation component and / or a pseudodamage spectrum formation component and / or a noise profile calculation component and / or a sweep profile calculation component. Advantageously, at least some of the aforementioned components are implemented in the system by means of computer program code. The object is further achieved by a computer program comprising steps which, when executed on a computer, cause the computer toa method for generating a test profile according to at least one of the aforementioned embodiments. ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18. In one embodiment of the invention, a computer-readable medium comprises computer program code for implementing one of the aforementioned methods. The term "computer-readable medium" is understood to mean, in particular but not exclusively, hard drives and / or servers and / or memory sticks and / or flash memories and / or DVDs and / or Blu-rays and / or CDs. In addition, the term "computer-readable medium" is also understood to mean a data stream, such as that which arises, for example, when a computer program product is downloaded from the Internet. Brief Description of the Drawings The invention is briefly explained below with reference to drawings, in which: Figure 1: a schematic representation of a method according to the invention in a first embodiment as a block diagram,Figure 2: a schematic representation of a method according to the invention in a second embodiment as a block diagram, Figure 3: a schematic representation of a pseudo-damage spectrum calculation process, as is typically used in a method according to the invention, as a block diagram, Figure 4: a schematic representation of a method according to the invention in a third embodiment, Figure 5: a schematic representation of a pseudo-damage spectrum calculation process, as is typically used in a method according to the invention, ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 Figure 6: a schematic representation of an extrapolation and superposition process for a plurality of measured variables, Figure 7: a schematic representation of a test profile generation process for a plurality of measured variables, Figure 8: an exemplary representation of load spectra and a Wöhler curve,and Figure 9: a schematic representation of a method according to the invention in a fourth embodiment as a block diagram. Description of Preferred Embodiments Figure 1 shows a schematic representation of a method according to the invention in a first embodiment as a block diagram. In particular, Figure 1 shows a pseudo-damage spectrum calculation process P1, an extrapolation and superposition process P2, a test profile generation process P3, and a reference signal processing process P4. The extrapolation and superposition process P2 comprises an extrapolation sub-process P5 and a superposition sub-process P6. A plurality of measurement signals 1.1, 1.2, ..., 1.n are fed to the pseudo-damage spectrum calculation process. These measurement signals 1.1, 1.2, ...,1.n are typically recorded during route travel of a test vehicle (not shown) and each represents the temporal progression of a specific oscillating measurement variable in the test vehicle. Each of the N measurement signals 1.1, 1.2, ..., 1.n is measured on a specific route of the test vehicle, so that one measurement signal per route is available for profile calculation. In the pseudodamage spectrum calculation process P1, a plurality of pseudodamage spectra 2.1, 2.2, ..., 2.n are calculated from these measurement signals 1.1, 1.2, ..., 1.n using a spectrum calculation algorithm. This results in a pseudodamage spectrum 2.1, 2.2, ..., 2n for each measurement signal 1.1, 1.2, ... 1.n. Details of the pseudodamage spectrum calculation process P1 (ZF Friedrichshafen AG, File 212889 Friedrichshafen, 2024-01-18) are explained in more detail below. Pseudodamage spectra 2.1, 2.2, …2n are then fed into the extrapolation and superposition process P2. Within this process, each pseudodamage spectrum 2.1, 2.2, …, 2n is first multiplied by a proportionality constant, thus generating a plurality of extrapolated pseudodamage spectra. For the sake of clarity, the extrapolated pseudodamage spectra are not explicitly shown in Figure 1. Subsequently, the extrapolated pseudodamage spectra are summed within the superposition subprocess P6, resulting in a superposed pseudodamage spectrum 3. In other words, from the plurality of measurement signals 1.1, 1.2, …, 1.n, which were recorded on different route runs of a test vehicle,a single superimposed pseudodamage spectrum 3 is formed. This superimposed pseudodamage spectrum 3 is then fed to the test profile generation process P3. In parallel to the pseudodamage spectrum calculation process P1 and the extrapolation and superposition process P2, the reference signal processing process P4 also runs in the method shown in Figure 1. Within the scope of this reference signal processing process P4, a reference signal pseudodamage spectrum is first calculated from a reference signal 5 using the spectrum calculation algorithm, which is also applied within the pseudodamage spectrum calculation process P1. This reference signal pseudodamage spectrum is not explicitly shown in Figure 1 for the sake of clarity. The reference signal pseudodamage spectrum is then multiplied by the proportionality constant, which was already applied in the extrapolation sub-process P5.multiplied to produce an extrapolated reference signal pseudodamage spectrum 6. This extrapolated reference signal pseudodamage spectrum 6 is also fed to the test profile generation process P3. Within the test profile generation process P3, test profile 4 is then generated based on the superimposed pseudodamage spectrum 3 and the extrapolated reference signal pseudodamage spectrum. Test profile 4 can then be applied to a test specimen on a test bench, whereby the test specimen experiences stress on the test bench by being subjected to the test profile 4 calculated in this way.which corresponds to the stress from all previous route runs. Although the generation of the extrapolated reference signal pseudo-damage spectrum 6 is shown in Figure 1 as being generated in a separate reference signal processing process P4, other variants of generating the extrapolated reference signal pseudo-damage spectrum 6 are also conceivable. For example, it is possiblethat the reference signal is generated directly within the framework of the pseudodamage spectrum calculation process P1 and the extrapolation and superposition process P2. In other words, for example, the reference signal processing process P4 can be carried out partly by the pseudodamage spectrum calculation process P1 and partly by the extrapolation and superposition process P2. Figure 2 shows a schematic representation of a method according to the invention in a second embodiment as a block diagram. The method in Figure 2 is very similar to the method in Figure 1. In contrast to the method shown in Figure 1, however, in the method shown in Figure 2, in addition to the superimposed pseudodamage spectrum 3, a plurality of extrapolated pseudodamage spectra 7.1, 7.2, ..., 7n are output by the extrapolation and superposition process P2. These extrapolated pseudodamage spectra 7.1, 7.2, ...,7n are then also fed to the test profile generation process P3, which processes them in such a way that, in addition to test profile 4, which, as explained, covers the damage on a complete route mix, a plurality of test profiles 8.1, 8.2, ..., 8.n for individual routes are output at the output of the test profile generation process P3. These test profiles 8.1, 8.2, ..., 8n for individual routes are then available as secondary results of the procedure, in addition to test profile 4 for the route mix (the main result of the procedure), and can also be used when testing the same product on test benches. The special feature of test profiles 8.1, 8.2, ..., 8n is that they cover the damage on each individual route (for the full driving duration on this route within the route mix).However, they do not cover the route mix. ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 Figure 3 shows a schematic representation of a pseudo-damage spectrum calculation process P1, as it is typically used in a method according to the invention, as a block diagram. It can be seen that the pseudo-damage spectrum calculation process in Figure 3 comprises a signal filtering step S1, a classification step S2, a conversion step S3, a partial damage contribution calculation step S4, a total damage calculation step S5, and a pseudo-damage spectrum formation step S6. In the signal filtering step S1, each measurement signal is filtered using a plurality of bandpass filters, resulting in a plurality of filtered measurement signals. In the classification step S2, a load spectrum is formed from each filtered measurement signal by means of a classification. This is typically done bythat an entire amplitude range of each filtered measurement signal is divided into classes, whereby a number of cycles is preferably determined for the amplitude of each class. In the conversion step S3, a possibly averaged amplitude of each cycle (a cycle may have a mean value other than zero) is then first converted into a damage-equivalent, mean-free amplitude. This conversion step is optional in certain embodiments. The conversion in the conversion step S3 is preferably performed using a Haigh diagram. After generating the damage-equivalent, mean-free amplitudes, these mean-free amplitudes are sorted in ascending order. In the partial damage contribution calculation step S4, a partial damage contribution is calculated for each damage-equivalent, mean-free amplitude.preferably using a Wöhler curve. In the total damage calculation step S5, the partial damage contributions for each filtered measurement signal are summed to form a total damage, with each total damage being referred to as a pseudo-damage number of the respective filtered measurement signal. Finally, in the pseudo-damage spectrum generation step S6, the pseudo-damage spectra are formed from the pseudo-damage numbers. This is typically done by representing the pseudo-damage numbers as a function of the bandpass center frequencies of the bandpass filters. ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 Figure 4 shows a schematic representation of a method according to the invention in a third embodiment. In particular, Figure 4 showsHow different computer-implemented components of the inventive method are interconnected and how the profile calculation proceeds in detail. Figure 4 shows a pseudo-damage spectrum calculation process P1, an extrapolation and superposition process P2, and a test profile generation process P3. Figure 4 also shows a pseudo-damage spectrum calculation component 13, an extrapolation subcomponent 14, a superposition subcomponent 15, and a test profile generation component 16. In Figure 4, some of these components 13, 14, and 16 are shown more than once, so a corresponding instance of each component is discussed below. In each instance of the same component 13, 14, and 16, an identical calculation algorithm (FDDC, SPEX, or PRGN algorithm—they are explained below) is implemented. Components 13, 14, and 16 are active at different points in the inventive method.particularly when processing different signals and / or further processing the characteristic values ​​calculated in one of the previous steps. The method in Figure 4 is provided with n measurement files 9.1, 9.2, …, 9.n on the input side. These measurement files 9.1, 9.2, …, 9.n are typically generated by signal recording only on a small, representative section of each of the n routes and each contain a measurement signal of the same measurand (not explicitly shown in Figure 4). The measurement files 9.1, 9.2, …, 9.n are each fed to an instance of the pseudodamage spectrum calculation component 13. The pseudodamage spectrum calculation component 13 outputs pseudodamage spectra on the output side. In Figure 4, only the first pseudodamage spectrum 2.1 is provided with a reference symbol.so as not to overload the figure. The pseudodamage spectra are then fed to the extrapolation and superposition process P2, where they are first processed by the different instances of the extrapolation subcomponent 14 (one instance per pseudodamage spectrum). This results in a total of n instances. On the output side, a plurality of extrapolated pseudodamage spectra 7.1, 7.2, ..., 7.n are then available at the extrapolation subcomponent 14. Here, too, only the first two extrapolated pseudodamage spectra 7.1, 7.2 are provided with reference symbols for the sake of clarity. The extrapolated pseudodamage spectra 7.1, 7.2, ...,7.n are fed to the superposition subcomponent 15 on the one hand and directly to the n instances of the test profile generation component 16 on the other. The superposition subcomponent 15 superposes the extrapolated pseudodamage spectra 7.1, 7.2 (and all other available extrapolated pseudodamage spectra not explicitly provided with reference symbols, thus a total of n spectra) and thus provides a superposed (and extrapolated) pseudodamage spectrum 3 on the output side. This superposed pseudodamage spectrum 3 is also fed to the test profile generation component 16. It thus consists of a total of n+1 instances – n instances of the test profile generation components 16 for the extrapolated pseudodamage spectra 7.1, 7.2, ..., 7.n, as well as one instance of the test profile generation component 16 for the superposed pseudodamage spectrum 3. Parallel to the processes P1,P2 and P3, an extrapolated reference signal pseudodamage spectrum 6 is also generated in Figure 4, which is also fed to all n+1 instances of the test profile generation component 16. This extrapolated reference signal pseudodamage spectrum 6 is generated by first processing a (separately generated) reference signal 5 in an instance of the pseudodamage spectrum calculation component 13, resulting in a reference signal pseudodamage spectrum 17. This reference signal pseudodamage spectrum 17 is then fed to an instance of the extrapolation subcomponent 14, which generates the extrapolated reference signal pseudodamage spectrum 6. Also shown in Figure 4 are pseudodamage calculation parameters 10, extrapolation and superposition calculation parameters 11,Test profile calculation parameters 12 and reference signal extrapolation parameters 18 are shown. The pseudodamage calculation parameters 10 typically include one or more definitions for bandpass filters (e.g., their corner frequencies, filter order, coverage of the individual filters, etc.), one or more parameters for rainflow counts, and / or a Wöhler curve. The pseudodamage calculation parameters 10 are provided to the pseudodamage spectrum calculation component 13. The extrapolation and superposition calculation parameters ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 11 typically include information about the full travel times on each of the routes that make up the route mix.preferably in hours. The extrapolation and superposition calculation parameters 11 are transferred to the extrapolation and superposition process P2. The reference signal extrapolation parameters 18 typically include the intended duration of the vibration testing of the product, preferably in hours. They are transferred to the extrapolation subcomponent 14 of the reference signal. The test profile calculation parameters 12 typically include a slope factor of the S-N curve and / or a safety factor and / or a test factor and / or a safety and test factor. The test profile calculation parameters 12 are transferred to the test profile generation component 16, in particular within the framework of the test profile generation process P3. Figure 5 shows a schematic representation of a pseudodamage spectrum calculation process, as is typically used in a method according to the invention. In particular, Figure 5 showshow a plurality of damage numbers are determined from a measurement signal 1.1, which form a pseudo-damage spectrum. This is shown in Figure 1 by a sequence of steps: signal filtering step S1, classification step S2, conversion step S3,jointly presented partial damage contribution calculation step S4 and total damage calculation step S5 as well as pseudo damage spectrum formation step S6. Further details on Figure 5 are described below. Figure 6 shows a schematic representation of an extrapolation and superposition process P2 for a plurality of measured variables. Details of Figure 6 are described below. Figure 7 shows a schematic representation of a test profile generation process P3 for a plurality of measured variables. Further details of Figure 7 are described below. Figure 8 shows an exemplary representation of load spectra and a Wöhler curve. Details of Figure 8 are described below. ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 Figure 9 shows a schematic representation of a method according to the invention in its fourth, most complex embodiment as a block diagram. In contrast to the processes shown in Figures 1,2 and 4, the method shown in Figure 9 processes multiple measurement signals measured on multiple routes, with the signals belonging to different measurement variables. In this embodiment, it is assumed that measurements were performed on a total of m routes in a test vehicle (not shown), and n signals were recorded on each route. As a result, a total of mxn measurement signals MS are provided to the method according to the invention. 1,1 , MS 1,2 , …, MS 1,n , MS 2,1 , MS 2,2 , …, MS 2,n , …, MS m,1 , MS m,2 , …, MS m,n The signals measured on a route (time-synchronized) were stored in the same measurement file (digitized). For example, measurement file 2, recorded during the journey on route 2, contains n measurement signals MS 2,1 , MS 2,2 , …, MS 2,n. The number of measurement files m is thus equal to the number of routes. Furthermore, this embodiment of the method assumes that signals with the same last index were generated by recording the same measurement value on different routes, e.g., the signals MS 1,1 , MS 2,1 , …, MS m,1 – by recording the measured value 1, the signals MS 1,2 , MS 2,2 , …, MS m,2 – by recording the measured value 2 etc. This leads, in contrast to the embodiment of the method in Figures 1, 2 and 4, to the following special features: ^ in the pseudodamage spectrum calculation process P1, mxn pseudodamage spectra PS are now calculated from measurement signals instead of n 1,1 , PS 1,2 , …, calculated, ^ in the extrapolation subprocess P5 of the extrapolation and superposition process P2, mxn extrapolated pseudodamage spectra ES are now also calculated from these pseudodamage spectra instead of n 1,1 , ES 1,2 , …, IT 1,n , ES 2,1 , ES 2,2 , …, IT 2,n , …, IT m,1 , ES m,2 , …, IT m,n calculated; each of them describes the damage for a measuring point and direction on the component (product) under consideration on each individual route (but not on a complete route mix), ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 ^ In the test profile generation process P3, mxn test profiles PP are extrapolated from these pseudo damage spectra 1,1 , PP 1,2 , …, PP 1,n , PP 2,1 , PP 2,2 , …, PP 2,n , …, PP m,1 , PP m,2 , …, PP m,ncalculated. Each of them covers the damage for a measuring point and direction on the component under consideration on each individual route (but not on a complete route mix), and is suitable for conducting a vibration test of the component with profile control at this point, with vibration introduction in this direction; in such a test, this damage equivalent to the corresponding route is applied at the corresponding point on the component and in the corresponding direction. ^ In the superposition sub-process P6 of the extrapolation and superposition process P2, instead of one, a plurality of superposed (and extrapolated) pseudo-damage spectra SS1, SS2, ..., SS ncalculated. Namely, one pseudodamage spectrum per measurement variable. Each such spectrum describes the damage of the component under consideration on a complete route mix for the corresponding measuring point (ie the location of the sensor) and direction. ^ Consequently, in the next step in the test profile generation process P3, these n pseudodamage spectra SS1, SS2, …, SS n n Test profiles SPP1, SPP2, …, SPP ncalculated. They all cover the damage to the component along the entire route mix—each profile for its measuring point and direction on the component—and are suitable for conducting vibration testing of the component in question with profile control at the corresponding location (the location of the sensor), with vibrations initiated according to the profile in the corresponding direction. In such a test, this damage equivalent to the entire route mix is ​​applied at a specific point on the component and in the corresponding direction. In this embodiment of the method, the reference signal processing process P4 remains the same as the previously explained embodiments in Figures 1 and 2. ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 Some embodiments of the invention are described in particular detail below, using Figures 4 to 9, among others.Numbers in square brackets are still to be understood as references to the bibliography at the end of the description. Numbers or lowercase letters in parentheses are to be understood as references to the corresponding mathematical formulas, which are denoted by these numbers or lowercase letters in parentheses. In a particular embodiment, a method according to the invention (as mentioned above, this specific method according to the invention is referred to as the ASPEN method or ASPEN-RoMi method) is based on the calculation and equivalence of damage numbers; thus, it belongs to the group of damage-based methods.Their calculation is carried out using the following procedure, well-known in fatigue strength: - Formation of a load spectrum from the time variable under consideration (using a classification or counting method) and - its conversion into a damage index using the Wöhler fatigue hypothesis (mathematically described by a Wöhler curve) and the hypothesis of linear damage accumulation (Palmgren-Miner rule). It should be noted at this point that the Wöhler curve used to calculate damage indexes is based on an assumption in most practical cases and is not necessarily applicable to the measured variable and / or the stress state under consideration. It is therefore fictitious.Therefore, the damage numbers calculated in this way are not meaningful for an absolute failure time or the remaining service life of the component under consideration, and for this reason, they are referred to in this document as pseudo-damage numbers (abbreviated to PSN). However, PSNs can be usefully used for comparative damage-based calculations and analyses, such as in the ASPEN method. ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 Based on the PSN, a new, fundamental parameter – the pseudo-damage spectrum (PSS) – is introduced in the ASPEN method. It describes the dependence of the PSN of an oscillating time signal on the vibration frequency. It is explained in detail below in the subsection "Pseudo-Damage Spectra."The basic idea of ​​the ASPEN-RoMi method is as follows: The test profile created for vibration testing of a component should mathematically ensure the equality of the following two PSS at each vibration frequency f: - the PSS resulting from the route mix driven, after extrapolation and, if necessary, superposition to the required component service life, and - the PSS that the component will experience in a vibration test with the created profile for the specified test time in a spatial axis. In this sense, the ASPEN-RoMi method delivers damage-equivalent test profiles. The damage equivalence applies individually to each considered location at which signals were measured for profile creation – e.g., on the component or its supports.The ASPEN-RoMi method comprises three calculation modules, as shown in Figure 4: - an FDDC (Frequency Dependent Damage Calculation) module, also referred to as pseudodamage spectrum calculation component 13, - a SPEX (SuperPosition and EXtrapolation) module, also referred to as extrapolation and superposition component, which comprises an extrapolation subcomponent 14 and a superposition subcomponent 15, and - a PRGN (PRofile GeNeration) module, also referred to as test profile generation component 16. ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 On the one hand, acceleration signals are measured (with the ASPEN method, profiles can be created for any oscillating measured variable; for the sake of simplicity, acceleration is referred to here as the input variable for the profile calculation) during the test drives on the routes, and on the other hand, a specially generated time signal - the reference signal - is evaluated.Therefore, for profile calculation using the method, two of the three modules – FDDC and SPEX – are executed twice, see Figure 4. The evaluation of both the measurement signals from the route runs and the reference signal is carried out in the same way. Typical calculation steps of the method are: - calculation of a PSS for each individual signal (FDDC module), - extrapolation and superposition of the individual PSS to form a PSS (SPEX module), and - generation of a test profile (PRGN module). For the sake of simplicity, the procedure for profile creation using the ASPEN-RoMi method from measurement data of only one measurand will be explained first. This leads to some restrictions, e.g., it excludes profile creation for multi-point control. This will be removed later, in the individual description of the SPEX and PRGN modules.The following metrology terms are used in the description of the method: ^ According to DIN 1319-1, the measured quantity is the time-varying physical quantity to be measured (e.g., acceleration); it always refers to a specific measuring point and (because vibrations are direction-dependent) direction. It is referred to further in the document. ^(t) denotes ^ Measuring point (measurement location) is a spatially limited, local point on the component or on its supports, which is selected to record a measurand. ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 For this purpose, a sensor (e.g. acceleration sensor) is attached at this point. ^ Measurement signal is the result of the measurement of a measurand; it is generated while driving on a section (measurement section) of a route, after a single triggering and stopping of the measurement by the measuring system, and is available in digital form. A measurement signal of the measurand ^(t), recorded on such a measurement section while driving on route i, is ^ i(t) denotes ^ Measurement file is a file containing measurement signals of all measured variables, which are recorded synchronously by the measuring system during travel on a measuring section of a route, digitized, and stored on a data medium. The measurement file has a name, and the measurement signals appear there in digital form, under the name of the respective measured variable. It is assumed that a route mix consisting of n different design-relevant routes has been defined for the vibration approval of a component (intended for operation in a motor vehicle). The travel time T RM on the entire route mix consists of the travel times on the individual routes T Ri (i = 1, …, n). The component in question is to reach its full lifetime T LD by driving the vehicles (possibly cyclically) on this route mix. This means (3.1) Furthermore, for data collection, tests were carried out on each section of each route (e.g. in a test vehicle), with the measurement at one point of the examined component of a size ^ (e.g. acceleration in one direction). Thus, for each measuring interval (measuring section) of duration t ^ i on each route i (i = 1, …, n) an acceleration signal ^ i(t). It is also assumed that it was saved in a separate measurement file, so that there is one measurement file with this signal for each route driven (this assumption applies to the description of the ZF Friedrichshafen AG file 212889 Friedrichshafen 2024-01-18 ASPEN RoMi method at all points in this description, with the exception of the following "additional explanations" at the end of the description, which deals with the extrapolation and superposition of the PSS for the case of multiple measurement files per route driven). From these n signals (as input data), a damage-equivalent test profile is to be derived using the ASPEN RoMi method. The PSS is calculated for an assumed (fictitious) Wöhler curve. Mathematically, it is defined by the parameters N A , a A (Support point A) and k WL (slope coefficient) according to formula (3.8). Since they have the same slope coefficient k for all amplitudes a WL, it runs without a kink, in particular without a fatigue strength range. Further in the document, it is referred to as a simple Wöhler curve. As is well known, the mathematical description of component failure using a Wöhler curve only applies to fatigue [1, 15]; this is therefore required for profiling in the ASPEN method. The test frequency range is from f unt , …, f ob . The profile creation for the considered case is described below, in steps a) to g). In Figure 4, they are illustrated as follows: the calculation steps a) to c) are marked by thick branches with arrows in the left part of the diagram, d) to f) – by thin branches in the right part of the diagram; for the calculation step g), these branches are finally combined in the PRGN module. a) Calculation of the PSS for route travel First, for each acceleration signal ^ i(t), measured on each section of the route i = 1, … , n, in the defined test frequency range f = f unt , …, f ob one PSS D each ^ i (f) is calculated. For this purpose, a set of linear bandpass filters (e.g., Butterworth type), each with a narrow passband, is defined. The passbands of the adjacent bandpass filters are adjacent to each other in such a way that they neither overlap nor have gaps between them, and they cover the entire test frequency range. ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 ^ i(t) is filtered with them. Subsequently, a load spectrum is generated from each bandpass-filtered signal using a counting method. A classification method is preferred which, in addition to the amplitudes, also provides mean values ​​of the fatigue cycles (so-called two-parameter load spectrum). In the ASPEN method, rainflow counting is used for classification, which generates rainflow spectra in the form of rainflow matrices. Each such two-parameter load spectrum is then converted into a damage-equivalent, mean-free one-parameter amplitude spectrum using an amplitude transformation according to Haigh

[0015] (Haigh diagram). From this, a PSZ is then calculated using a simple Wöhler curve and a linear damage accumulation hypothesis (e.g., in the form of "Miner elementary"). Furthermore, each PSZ calculated in this way is assigned to the center frequency of the passband of the corresponding bandpass.The sequence of these PSZs in ascending order of the filter center frequencies ultimately results in the PSS D. ^ i (f) of the signal ^ i (t). All these calculations are carried out in the FDDC module, see n calculation blocks FDDC (also referred to as pseudodamage spectrum calculation component 13) in the left part of the diagram in Figure 4. The FDDC algorithm for calculating a PSS from a time signal is described in more detail below. b) Extrapolation of the PSS for route travel These individual PSS D ^ i (f) (i = 1, …, n) apply to the signal measurement duration t ^ i on the measuring section of the corresponding route. In order to keep the experimental and measurement effort during data collection as low as possible, t ^ i usually significantly smaller than the actual travel time T Ri which the vehicle can use on this route (within the required lifetime T LD ) will complete: t ^ i ^ ^ TRi To obtain the PSS, which represents the total travel time T Ri on route i, the PSS D calculated in the previous step is ^ i (f) with a factor k ^ i multiplied: ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 ^ ^^,^^ = ^ ^^ × ^ ^^ (3.2) The proportionality constant k ^ i is calculated as the ratio of the two travel times explained above: This procedure is called extrapolation of the PSS. It is based on a well-known and established method for extrapolating damage numbers (PSZ) in fatigue strength and is now applied to the PSS. The proportionality constant k ^ iis known as the extrapolation factor [1, 15]. The extrapolation of the PSS is carried out in the SPEX module, see calculation blocks 14 (also referred to as extrapolation subcomponent 14) in the left part of the diagram in Figure 4. c) Superposition of the PSS for route trips The extrapolated PSS D ^ i,EX (f), calculated in the previous step according to (3.2), represent the degree of damage of the component when driving only on each individual route i (of the corresponding duration T Ri ). However, the component is assumed to be designed for operation on the entire route mix. Therefore, the total damage that the component will experience in the complete mix, consisting of n different routes, must be determined. Since the travel time on the route mix is ​​made up of travel times T Rion individual routes, see relation (3.1), the damage measure of the route mix can also be calculated as the sum of the damage measures of the individual routes. Therefore, the individual extrapolated PSS D ^ to a total PSS D ^,SPEX (f) are added together: ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 This procedure is called the superposition of the PSS. It is again based on the well-known method in fatigue strength of superposition of the damage numbers or PSZ of individual operating states (here: routes) to the total damage. The superposed PSS D ^,SPEX (f) applies to the travel time T RM on the entire route mix; the travel times T R1 , T R2 , … , T Rn . on n individual routes this mix to each other according to (3.1). Since according to assumption T LD .= T RM , represents the superposed PSS D ^,SPEX(f) at the same time, the degree of damage of the component for its entire intended lifetime T LD The superposition of the PSS is also performed in the SPEX module, specifically in the superposition subcomponent 16, see Figure 4. d) Generation of the reference signal Now the question arises as to how to determine the damage-equivalent height of the test profile. According to the formulation of the ASPEN-RoMi method, this means: in a vibration test of duration T VT With the profile of this height, the same damage should be applied to the component as the damage it has in the route mix of duration T RM This damage was calculated in steps a) – c) and is represented by the extrapolated and superposed PSS D ^,SPEX(f). The problem of converting a PSS into damage-equivalent profile amplitudes is that the relationship between these two quantities must be known, which depends, among other things, on the specified type of vibration test (sweep or random). To solve this problem, it is proposed to independently generate a time signal r(t), appropriate to the type of vibration test, and to measure its damage for the intended duration of the vibration test T. VTto calculate. r(t) was referred to as the reference signal. It is nothing other than a control signal that a vibration test system at ZF Friedrichshafen AG, file 212889 Friedrichshafen, 2024-01-18, would generate to implement a test profile of a specific type (sweep or noise profile). It can, for example, be generated as a real vibration signal on a vibration test bench equipped with a suitable control system and recorded with a suitable measurement system. An alternative option is offered by many PC-based signal processing tools, e.g., Matlab, Famos, Labview. In their environment, the reference signal can be generated as a fictitious, digital signal (e.g., for creating noise profiles using a random number generation algorithm).This is a time-saving and cost-effective option, as it requires neither a vibration test bench for generating vibrations nor a measurement system for signal recording. The level of the reference signal can be chosen arbitrarily, but (according to the concept of the ASPEN method) it must be constant over the frequency f across the entire test frequency range f = f. unt , …, f ob be constant. The level determines the amplitude-frequency response (AFV) S Ref meant when r(t) is a sweep signal (for a sweep test) or the LDS PSD Ref , if r(t) is a stochastic signal (for a noise test). Therefore, S Ref = const, PSD Ref = const. In the latter case, this condition means that r(t) in the test frequency range f = f unt , …, f ob White noise is generated. The procedure for generating such a signal, together with the next steps e) and f), has been called the concept of the reference signal. It is described in detail below. e) Calculating the PSS of the Reference Signal After the reference signal r(t) has been generated as described above, its PSS is calculated. For this purpose, the FDDC algorithm is executed again, see calculation block 13 in the right-hand part of Figure 4. For the ASPEN method to function correctly, the same calculation parameters must be used as for calculating the PSS of the signals from the route mix runs (in step a)). This particularly applies to the configuration of the bandpass filters, as well as the classification and S-N curve parameters. ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 The calculated PSS is D r (f) is defined, it applies for the duration t rof the generated reference signal r(t) f) Extrapolation of the PSS of the reference signal For the calculation of the damage degree, which is determined in a vibration test of the specified duration the PSS of the reference signal D calculated in the previous step must r (f) are extrapolated to this duration. This is done in the same way as the extrapolation of the PSS for route trips (see step b)), namely, by multiplying D r (f) with the corresponding extrapolation factor ^ ^,^^ ( ^ ) = ^^ × ^^(^)(3.5) It is calculated as follows: ^ ^ = ^ ^^ / ^ ^(3.6) The extrapolation of the PSS of the reference signal is carried out in the SPEX module 14, like the PSS from route measurements; the SPEX module 14 is executed again for this purpose, see calculation block 14 (also referred to as extrapolation subcomponent 14) in the right part of Figure 4. g) Calculation of the height of the test profile Now the two damage measures are available – the superimposed PSS from the route mix D ^,SPEX (f), and the extrapolated PSS of the reference signal D r,EX (f). In addition, it is now also known that the component damage D r,EX (f) in a vibration test with sweep excitation by amplitude S Ref , or with the noise excitation by the LDS PSD Ref (calculatively) comes about when the two tests of the duration each. This allows S Ref or PSD Ref into a different amplitude S U or into another LDS value PSD U which leads to the damage D ^,SPEX(f). This damage equivalent conversion is defined, depending on the profile type, by formula (3.17) (for sweep profile) or formula (3.16) (for noise profile) (where D Ref (f) = D r,EX (f) and D U (f) = D ^,SPEX (f)). The two relationships (3.16) and (3.17) were developed independently and called the ASPEN transformation (AT). For this conversion of the PSS into the profile amplitudes, the PRGN module (also referred to as test profile generation component 16) is executed, see Figure 4. The conversion is performed separately for each frequency f in the defined test frequency range f = f unt , …, f ob. A sweep or noise profile calculated in this way is the result of the procedure. It is suitable for damage-equivalent vibration testing of the component under consideration with profile control at the point where the acceleration value x(t) was measured during the route runs (single-point control). Special features or additions to the procedure described above (a) – (g): ^ it is used separately for the creation of the profiles in each spatial axis. For this purpose, signals ^ i(t), measured in the corresponding spatial direction. Thus, the method is primarily suitable for vibration testing on test benches with the option of generating vibrations in only one spatial axis (e.g., on electrodynamic shaker test benches). If a vibration testing facility allows vibrations to be generated simultaneously in three spatial directions (as is typically the case on servo-hydraulic test benches, for example), profiles can first be created separately for each direction using the procedure described above.Afterwards, during the test, vibrations generated by the vibration control system according to these profiles in mutually perpendicular directions can be introduced into the test object simultaneously. The reference signal can also be a multisweep (for creating a multisweep test profile) or a sine wave with a fixed frequency (for creating a profile with which duration testing can be carried out). Excitation and response profiles are created according to this uniform procedure; it only distinguishes between the use of signals from different measuring points – on the component itself (for creating a reaction profile) or on its supports (for creating an excitation profile). All of these signals must be recorded synchronously in route mix runs; the excitation profiles are usuallyR for the test bench control, the reaction profiles – used to limit the amplitudes of the component reaction ^ for the case when signals are available from several measuring points and are to be evaluated together to create a profile, see subsection "Multiple measuring points" immediately below ^ apart from for the entire route mix, profiles for covering component damage are also created using this procedure only on individual routes; for this purpose, in the AT (3.16), (3.17) are used instead of D. ^,SPEX (f) the corresponding extrapolated PSS D ^ i,EX (f) used (they were calculated as standard for each route in step b); such profiles cover the component stress for the travel time T Rion each route. Multiple measuring points: So far, the method has been described for a simpler case, where test profiles could only be derived from signals of one measured quantity (defined for one measuring point). In a slightly modified form, the procedure can also be used when measurement signals were recorded in the same direction at multiple locations (e.g., on the component and / or its supports) during route runs, and they are to be evaluated together to create a profile. The difference in the method only affects the PRGN algorithm, and only the case of multi-point control. This case is discussed further below. Pseudo-damage spectra (PSS): The term pseudo-damage spectrum was introduced in the ASPEN method for the parameter that expresses the dependence of the PSZ on the center frequency of each narrowband bandpass filter. PSS is a fundamental, central parameter of the ASPEN method.Considering an oscillating time signal, the PSS represents a distribution of the PSZ of its individual harmonic components over the oscillation frequency. Since the dependence of a function on frequency has a physical analogy to the term spectrum (as calculated from a time signal in the classical way using the Fourier transform

[0014] ), the term PSS is used. In terms of its physical content, PSS is similar to the Fatigue Damage Spectrum (FDS). FDS is widely used for the analysis of the fatigue behavior of components and for the synthesis of damage-equivalent profiles using damage- and model-based methods based on the model of a linear weakly damped EMS [6-9].FDS therefore absolutely requires a model of such an EMS (with the acceleration of the base point as the input variable, and the relative deflection amplitude of the EMS as the vibration response). In contrast, the calculation of a PSS in the ASPEN method is not tied to a mathematical model of the component for which the test profile is to be created. This is the difference between FDS and PSS. Since a PSS consists of individual PSZs, a PSS does not represent real, but rather fictitious damage. Therefore, a PSS is not suitable for an absolute lifetime prediction of the component. Only by comparing two PSSs with each other, calculated, for example, for two different time signals, can the PSSs be meaningfully interpreted. Namely, in the following sense: "at a certain vibration frequency, the loading of a component due to one time sequence is more damaging (severe) than the other."However, the calculation of both PSS must always be carried out under the same conditions. This applies to all calculation parameters of the PSS, especially the parameters of the Wöhler curve and the width of the bandpass filter passband. If (in rare cases) a suitable Wöhler curve is actually known for the component, material, measurand, and load case in question, it can be set and used in the ASPEN method. This means that the calculated damage numbers are no longer fictitious and they can (if necessary after extrapolation and superposition) provide information about the actual service life of the component. In this case, these are not the PSZ and the PSS, but real damage numbers or damage spectra. ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 Each PSS D(f) is derived from a time signal x(t) of a specific duration t. Xcalculated and is valid only for this duration. It must be specified together with the PSS. Without this information, it is not known for what time the (pseudo-)damage has accumulated at each frequency. A PSS can be used not only for the synthesis of damage-equivalent test profiles, but also, for example, for comparing the hardness of two profiles of different types (e.g., a sweep profile with a noise profile).

[0002] ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 Calculation of the PSS (FDDC algorithm): The FDDC module calculates the PSS from time signals measured during route travel and from the reference signal. For each signal x(t) of duration t X , regardless of its origin, a PSS D(f) is calculated using the same algorithm described below. In the notations above, x(t) = t X = t ^ i(i = 1, …, n). The FDDC algorithm includes the following, see Figure 5: a) Filtering of the signal x(t) with a set of several narrow bandpass filters in the signal filtering step S1: First, in the selected test frequency range, f = f unt , …, f ob The bandpass filters are configured. They can be of any type, e.g., Butterworth, Bessel, Chebyshev, etc. In order to achieve a sufficiently high resolution of the profile curve to be calculated over the frequency, bandpass filters are used in a frequency range typically found for vibration testing of vehicle equipment from f unt = 10Hz to f ob= 2 kHz, at least 500 to 1000 bandpass filters are configured. As a result, the passband of the bandpass filters is only a few Hertz, so they can be described as narrowband. Depending on the choice of filter synthesis parameters (corner frequencies and the step of changing the center frequencies), the bandpass filters can have an equally wide or a variable passband. Regardless of this, these parameters must be selected so that the passbands of neighboring filters neither overlap nor have gaps between them. Given these considerations, the filter order and type (conventional or zero-phase filtering) can be freely selected. Filtering an input signal x(t) with the set of m such bandpass filters yields m output signals. The output signal of the jth bandpass filter is x BP,j(t) denotes (j = 1, …, m) ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 b) Classification of the bandpass filtered signals in the classification step S2: Subsequently, the output signal x BP,j (t) of each filter is used to create a load spectrum. For this purpose, the entire amplitude range of x BP,j divided into l classes, and for the amplitude a i each class i (i = 1, …, using a counting or classification method, the number of games N OP,i For this purpose, various classification methods known from fatigue strength can be used; however, preferably those which are used for each play except the amplitude a i another mean value m i The rainflow counting method can be used to determine the load spectrum N. OP = N(a, m) the frequency of occurrence of games with certain amplitudes a and mean values ​​m in the considered time signal xBP,j (t). For the above-mentioned reason, the ASPEN method uses rainflow classification to generate load spectra; it provides rainflow spectra in the form of rainflow matrices. They are represented in the coordinates "mean / amplitude," i.e., each counted cycle is characterized by its amplitude (half a span) and the mean (thus, for example, for an acceleration signal with the ordinate unit m / s², the two abscissas of the rainflow matrix are also scaled in m / s², the ordinate containing the number of closed cycles). Any residue that may be present is counted into the matrix after the rainflow count has been completed. In this way, for each filtered signal x BP,j a Rainflow matrix is ​​calculated c) Conversion into damage-equivalent mean-free amplitudes in the conversion step S3: In the Rainflow matrix, as explained above, each cycle has a corresponding amplitude ai and mean m i .. However, to determine the damage degree of a clearance using the Wöhler approach, which is well known in fatigue strength (see the next step d)), only the amplitude is used – as is well known, this approach does not take the mean value of a fatigue cycle into account. Since this can potentially influence the damage degree of a ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 fatigue cycle, the possibly mean-valued amplitude a i each cycle of the Rainflow matrix is ​​first converted into a damage-equivalent mean-free amplitude (SMA) a SM,iThis is done using the Haigh method

[0015] (called the Haigh diagram), which is also well known in fatigue strength. These converted amplitudes are then sorted in ascending order; this results in a dependence of the number of cycles (which remains unchanged during the Haigh transformation) in the rainflow matrix on the SMA N OP = N(a SM ) d) Calculation of the partial damage amounts in the partial damage contribution calculation step S4: Now for each SMA a SM,i of the load collective with l classes (i = 1, …, formed from each filtered signal x BP,j , the degree of damage is calculated: where N i – the number of cycles at the load amplitude a SM,i leads to failure of the component. The parameter N i is determined using a simple Wöhler curve, which is described by the following equation: where NA , a A – the number of cycles that can be performed at a given load amplitude a A leads to component failure, and this amplitude (such a point A with the coordinates (N A , a A ) is known as a so-called base point of the Wöhler line), k WL – the slope coefficient (slope factor) of the Wöhler curve. ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 To perform the calculation according to (3.8), the parameters k WL , N A , a A the Wöhler curve. In the ASPEN method, a Wöhler curve in the form (3.8) must be used. e) Calculation of the total damage for the output signal of each bandpass Total damage calculation step S5: After the partial damage contributions D i for each amplitude a SM,i of each load spectrum according to (3.7), the resulting damage D GS, which are caused by the action on the component l loads with different amplitudes a SM,i (i = 1, …, l) is calculated using the linear damage accumulation hypothesis (Palmgren-Miner rule) as follows: This results in the total damage of the output signal x BP,j (t) of a j-bandpass filter. Since the Wöhler curve used for its calculation is in most cases fictitious (see above), D GS the PSZ of the time sequence f) Formation of the PSS in the pseudo-damage spectrum formation step S6: The PSZ, calculated for output signals of all m bandpass filters, which in the current test frequency range f = f unt , …, f ob were defined, are now assigned to the center frequency f BP of the passband of the respective bandpass; the representation of the PSZ as a function of the respective filter center frequency results in a PSS D(f) (f = f BP). It should be mentioned again here that each measurement signal in the FDDC module (also referred to as pseudo-damage spectrum calculation component 13) is evaluated according to this same algorithm, independently of the signal from another measuring point or from the same point measured on a different route. ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 Therefore, if, for example, several variables (signals from several measuring points) were recorded during the route runs, this does not change the FDDC algorithm. Extrapolation and superposition of the PSS (SPEX algorithm): A PSS D ^ i (f), calculated using the FDDC algorithm from a time signal recorded during a trip on route i ^ i (t), refers only to its measurement duration t ^ i . It is usually significantly shorter than the full travel time T Ri on the corresponding route: t ^ i ≪ T RiHowever, in vibration testing with a test profile, the full service life of the component must be ensured. According to (3.1), the travel times T Rion n individual routes together (i = 1, ..., n). Therefore, all PSS calculated with the FDDC algorithm must be extrapolated and, if necessary, superposed in the next step. The SPEX algorithm was developed for this purpose. The extrapolation and superposition of the PSS in the ASPEN-RoMi method is based on a procedure well known in fatigue strength, with which (real or fictitious) damage numbers are extrapolated and superposed. Extrapolation consists in multiplying the damage numbers, determined from tests on individual routes, with accordingly calculated extrapolation factors, and superposition consists in adding the extrapolated damage numbers to one another. Since each ordinate of a PSS is a PSZ, this procedure can be applied unchanged to the extrapolation and superposition of the PSS. In the explanations of the SPEX algorithm below, as before, it is assumed that there is one measurement file for each route driven.The extrapolation and superposition of the PSS for the case of multiple measurement files per route is described below. To execute the extrapolation and superposition algorithms in the ASPEN RoMi procedure, only the travel times T are required. Ri on n individual routes (i = 1, ..., n). ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 The block diagram of the ASPEN-RoMi procedure in Figure 4 illustrates the extrapolation of the PSS by the n calculation blocks 14 (in the left part of the diagram), the superposition by block 15. Extrapolation of the PSS for route trips: The extrapolation of the PSS is described by formula (3.2). It is a pure multiplication procedure of a PSS D ^ i (f) with a constant k ^ i , called the extrapolation factor. It is expressed as the ratio T Ri the full travel time on a route i to the (individual) measurement time t ^ i of the signal ^ i(t) on the measurement section of this route according to (3.3). Since k ^ i is the same for all frequencies f of a PSS, the extrapolated PSS is D ^ i,EX (f) always a scaled copy of D ^ i (f). Physically, this extrapolation procedure corresponds to the following – idealized – interpretation: the test vehicle k repeats the journey on the measured section of a route i ^ i times. For each repeat run, the exact same PSS D is obtained for the measured signal under consideration. ^ i (f). Then, at the end of all these repeated trips, the specified travel time T Ri and the corresponding damage, expressed by the PSS D ^ i,EX (f), for the considered measurement signal ^ i(t).The extrapolation algorithm of the ASPEN-RoMi method calculates an extrapolated PSS D ^ i,EX (f) per measurement signal ^ i (t) and measurement file. If a measurement file is available for each route driven, and TRi when the total travel time on route i was specified, the extrapolated PSS shows D ^ i,EX (f) frequency-dependent pseudo-damage occurring at the considered location (of the component or its supports, and only at this location) for the entire driving time T Ri on the route considered. Since the driving time on a route exceeds the full required component life T LD does not cover (it is still assumed or required that the component is to be designed for a complete route mix), and T Ri < T LD , form the extrapolated PSS D ^ i,EX (f) a side result of the SPEX algorithm. ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 Nevertheless, the extrapolated PSS D ^ i,EX (f) important practical significance. They allow the comparison of the difficulty of different routes in a route mix. If D ^ i,EX(f), calculated for the same measuring point from journeys on different routes, are superimposed (e.g., graphically), one can draw conclusions about which route in which frequency range is more damaging than another route for the location in question. However, it should be noted that the journey times on different routes may be different: T R1 ^T R2 ^T R3 etc. Superposition of the PSS for route travel: The superposition of the PSS in the ASPEN-RoMi procedure is described by formula (3.4). It follows the extrapolation and is a pure addition procedure of several previously extrapolated PSS D ^ i,EX (f) the signals ^ i (t) of the same measured quantity ^ to a total PSS D ^,SPEX (f). The PSS are added individually for each frequency f. One conclusion is that the superposed PSS D ^,SPEX(f), which applies to the entire route mix, is always more damaging at all frequencies than any of the extrapolated PSS D ^ i,EX (f), which represent the pseudo-damage only on individual routes. This is understandable, because the total travel time on the route mix T RM is greater than the travel time on each individual route T Ri , see formula (3.1). As mentioned above, the superposition algorithm of the ASPEN-RoMi method calculates a superposed PSS D ^,SPEX (f) per measured quantity ^ . This PSS D ^,SPEX (f) determines the pseudo damage that the component will suffer at the respective measuring point for the full specified lifetime T LD at each oscillation frequency f. Thus, all superposed PSS D ^,SPEX(f) the main result of the calculations in the SPEX module. However, as a consequence, the superimposed PSS are not generated if only one measurement file was supplied to the method for profiling. This could be the case, for example, if measurements were only performed on one route (no route mix). ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 Extrapolation of the PSS of the reference signal: The PSS of the reference signal D r (f) (previously calculated in the FDDC algorithm) is extrapolated according to (3.5). The required extrapolation factor k r is determined according to (3.6). Since this formula determines the duration of the vibration test , one must decide on this at the latest during this stage of profile creation using the ASPEN-RoMi method. Because the reference signal is a single signal, superposition is not required for its extrapolated PSS. Typical implementation example: This is an example of the execution of the SPEX algorithm (also called extrapolation and superposition process P2) for two measured variables x, y ( ^ = x, y), whose signals were recorded in tests on n different routes of a route mix. For example, x, y can again be the acceleration quantities measured at two different locations on the component under investigation, or on its supports. Signals of these quantities x and y, measured on a section of the i-th route (i = 1, ..., n), are called x i (t), y i (t), their measurement durations t xi , t yi referred to (generally ^ t yi ). The PSS D xi , D yi were previously calculated in the FDDC algorithm, they are now used together with txi , t yi fed to the SPEX module. The process of extrapolation and superposition is illustrated in Figure 6. First, the PSS D xi , D yi extrapolated. For this purpose, the total travel time T Ri on each route i (the ratio T Ri to the required service life of the component T LD . is still determined by (3.1)), and according to (3.3) the extrapolation factors k xi or k yi , calculated. Extrapolating the PSS D xi , D yi is done by multiplying it with the corresponding extrapolation factor k xi or k yi according to formula (3.2). The extrapolated PSS thus formed are shown in Figure 6 as D xi,EX (f), D yi,EX (f) (i = 1, …, n). They are now superposed. This is done by adding all PSS D xi,EX (f) of channel x and all PSS D yi,EX(f) of channel y from the individual ZF Friedrichshafen AG Akte 212889 Friedrichshafen 2024-01-18 routes according to (3.4). This results in ^ One superposed PSS is formed, so in the example considered a total of two PSS D x,SPEX (f), D x,SPEX (f). The results of the execution of the SPEX algorithm in the example considered (see Figure 6) are: ^ several extrapolated PSS D xi,EX (f), D yi,EX (f) (two PSS per route i, the secondary result), as well as ^ the extrapolated and superposed PSS D x,SPEX (f), D y,SPEX(f) (a total of 2 PSS, the main result). They can all be fed into the PRGN algorithm to calculate various profiles. Calculation of the test profile (PRGN algorithm): The PRGN algorithm is used to determine the profile amplitudes from the PSS. The ASPEN transformation (AT) is used for this purpose. The PRGN algorithm is first described in detail in "Description". In "Types of Result Profiles", the types of resulting profiles calculated by the PRGN algorithm (and thus the entire ASPEN-RoMi procedure) are explained. Then, in "ASPEN transformation", the AT is given for two separate cases – the creation of a noise and a sweep profile. Description: Input data: The input data of the PRGN algorithm are: i) the extrapolated PSS D ^ i,EX (f), or extrapolated and superposed PSS D ^,SPEX (f) for route trips (calculated in the SPEX algorithm) ii) the extrapolated PSS D r,EX(f) of the reference signal r(t) (also calculated in the SPEX algorithm) iii) Parameters of the reference signal r(t): o the amplitude S Ref , if the reference signal r(t) is used as a sweep (for the creation of a sweep profile), or ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 o the height of the LDS PSD Ref , if the reference signal r(t) was generated as white noise (for creating a noise profile). Designations: Regardless of whether the PSS is extrapolated or extrapolated and superposed, the profile calculation in the PRGN module is performed according to the same algorithm. The only important thing for performing the PRGN calculations is the differentiation of the measurement signals. ^ i (t), if profiles from the extrapolated, non-superposed PSS D ^ i,EX (f), or the measured quantities ^ (see definition of the term measured quantity above) if profiles are calculated from extrapolated and superposed PSS D^,SPEX (f) are to be created; and this is only the case if a multi-point control is defined. For a clear explanation of the function of the PRGN module, the following case will be discussed in which the PSS of a total of p measurement signals (or measured variables) from an arbitrary SPEX result file are to be evaluated with the PRGN algorithm, and q of these are intended for a multi-point control (q ^ p). In this case, the input PSS of the PRGN algorithm, which were calculated with the SPEX algorithm (see them above, in the subsection "Input data"), are renamed as follows compared to the above definition: ^ D ^ i,EX = D U,k – the extrapolated PSS of the measurement signal ^ i(t) of a measured quantity ^, measured on a route (the index i, which determines the number i of the route, is irrelevant for the explanation of the PRGN algorithm and is therefore omitted; instead, the measured signals measured on this route are simply numbered, whereby the extrapolated PSS of a measured signal receives a consecutive number k: k = 1, …, p), ^ D ^,SPEX = D U,k – the superimposed PSS for the measured variable ^ , calculated for journeys on all routes of a route mix; these superimposed PSS of each measured variable are also simply numbered with the index k (k = 1, …, p). In other words – since the extrapolated but not superimposed PSS do not need to be distinguished from the extrapolated and superimposed PSS for the explanation of the PRGN algorithm, their PSS are now uniformly referred to as D U,kZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18, where k is the consecutive number of the measurement signal or measured variable in an input file supplied to the PRGN module. Description of the PRGN algorithm: From the PSS D U,k of the total p measurement signals (or measured variables) of an input file (k = 1, …, p) in the PRGN module p individual profiles or profiles for single-point control PR V,k , as well as a profile PR MP for a multi-point control. This is done in the following steps: a) ASPEN transformation (AT) First, from each extrapolated or extrapolated and superposed PSS D U,k , and specifying the extrapolated PSS D r,EX (f) of the reference signal, its amplitude S Ref or his LDS PSD Ref and the slope coefficient k WL the simple Wöhler curve (which is described by equation (3.8)), the height of a single profile PR U,kDepending on the type of test profile to be created, this is done using AT (3.16) or (3.17). Specifically, ^ In the case of creating a sweep profile, AT is used in the form (3.17); in (3.17), the amplitude S Ref of the previously generated sweep reference signal, ^ in the case of creating a noise profile, the AT is used in the form (3.16); in (3.16) the height of the LDS PSD Ref of the previously generated white noise reference signal. In the AT, an equal value of the slope coefficient k WL the S-N curve can be used, as previously in the FDDC algorithm when calculating the PSS from the signals recorded during the route runs and from the reference signal. b) Profile calculation for multi-point control In the case considered, q of the total p available measuring points are intended for the multi-point control. The individual profiles PR U,kthese q measuring points are now combined into a profile PR U,MP offset against each other. A distinction can be made between the mean-value and maximum-value control strategies. To obtain a profile suitable for mean-value control, the individual profiles of all corresponding points are arithmetically averaged at each frequency: ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 is provided, is formed from the highest amplitude of all individual profiles at each frequency (“peak-hold” method): ^^ ^,^^ = ^^^ ^^^ ^,^ , … , ^^ ^,^ ^ (3.11) c) Weighting with safety and test factor The calculated profiles PR U,k and PR U,MPcan already be used in this form for vibration testing (with profile control at the appropriate points). However, the result of component testing with such profiles may often not provide sufficient confidence, as is necessary for series release. The reasons for this are: these profiles do not take into account the scatter of the stress and load capacity of the test specimens, nor the uncertainty of the test result due to a limited sample size (i.e., the uncertainty due to testing a limited number of test specimens). Therefore, to increase the confidence in the test result, and in line with a corresponding procedure in fatigue strength, the ASPEN RoMi procedure provides an option to increase the calculated profile amplitudes. For this purpose, a safety and test factor j is used. STF introduced, and the previously calculated profile amplitudes are applied to it as follows (j STF> 1): ^ When creating a sweep profile, each ordinate of PR U,k and PR U,MP with j STF multiplied ^^ ^,^ = ^^ ^,^ × ^ ^^^ (3.12) ^^ ^^ = ^^ ^,^^ × ^ ^^^ (3.13) ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 ^ When creating a noise profile, each ordinate of PR U,k and PR U,MP with the squared value j STF multiplied (k = 1, …, p): ^^ ^^ = ^^ ^,^^ × (^ ^^^ ) ^ (3.15) The difference between formulas (3.12) and (3.14) and (3.13) and (3.15) has the following reason: In the case of a sweep profile, PR U,k and PR U,MPThe amplitude curves of a harmonic oscillation versus frequency are known from a common definition of a sweep profile (e.g., for an acceleration, they are scaled in m / s²), while in the case of a noise profile, they are the LDS (for acceleration, their unit is then (m / s²)² / Hz). An LDS has a physical similarity to the squared signal amplitudes. For a practical application, the safety and test factor j must be STF determined based on engineering considerations and / or taken from known literature on fatigue strength, e.g.

[0015] . The result of the execution of steps a) – c) is p individual profiles or profiles for a single-point control PR V,k (k = 1, …, p), as well as a profile PR MPfor a multi-point control. As with the extrapolation and superposition of the PSS (SPEX algorithm), the calculation of the height of the test profiles in the PRGN algorithm is carried out individually for each frequency f, independent of the other frequency. Therefore, the symbol f was used for all PSS D U,k and profile functions PR in the above description, steps a) – c) have been omitted. Typical implementation example: ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 The PRGN algorithm described above will now be illustrated using a concrete example. Assume that after completing the route runs and the FDDC and SPEX calculations, extrapolated or extrapolated and superposed PSS for three measurement signals or quantities x(t), y(t), z(t) are available (in a file). These three PSS are D U,k(k = 1, ..., 3). The first two variables x(t), y(t) are intended for multi-point control. The profiles to be created must cover these PSS. The profile calculation process using the PRGN algorithm, steps a) – c), for this case is shown in Figure 7. In addition to the three PSS D U,k further input variables are necessary for the algorithm: the extrapolated PSS D r,EX and the height A r of the reference signal r(t). It is the constant amplitude S Ref of the harmonic signal r(t), if sweep profiles are to be created, or the LDS of the constant amplitude PSD Ref of the stochastic signal r(t) (white noise), if noise profiles are to be created: A r = {S Ref , PSD Ref}. From these input variables, first, specifying the slope coefficient k WL the Wöhler curve, with AT (3.16) or (3.17) the three individual profiles PR U,k calculated (k = 1, …, 3). The profiles PR U,1, PR U,2 The first two quantities x(t), y(t) are then combined with one of the formulas (3.10) or (3.11) to form a profile PR U,MP for a multi-point control. In Figure 7, these formulas are expressed by the operator ^. Depending on the type of profile to be created (sweep or noise), the ordinates of all four profiles are multiplied by the safety and test factor j or by its square 2 S TF (y STF ) multiplied. In the example considered, the result of the PRGN calculations are the four profile functions PR V,k (k = 1, …, 3) and PR MP Depending on the handling of the reference signal and the use of the AT formula (3.16) or (3.17), they can all be either sweep or noise profiles. The first three PR V,kThese are individual profiles intended for vibration testing with profile control at individual locations where signals of the quantities x(t), y(t), and z(t) were recorded during the route runs. The profile PR MP is to be implemented by means of ZF Friedrichshafen AG file 212889 Friedrichshafen 2024-01-18 multi-point control of the signals of the two sensors, placed as precisely as possible at the points of recording of the variables x(t) and y(t) in the route runs. The profile control strategy at these two points (average or maximum value control) depends on whether the amplitudes of the profile PR are calculated. MPFormula (3.10) or (3.11) was used. Types of result profiles: Depending on the input data and parameterization, the PRGN algorithm (and thus the entire ASPEN RoMi procedure, possibly in a single run) calculates test profiles of several different types or profiles with different characteristics. Their description follows, where appropriate with information on the implementation of the different types of profiles: a) Sweep and noise profiles, profiles for a dwell time test. This involves distinguishing the test profiles according to the type of vibration generated - with harmonic or stochastic vibration excitation. The first category includes testing with sliding frequency excitation (sweep), consisting of one tone (single sweep) or several tones (multisweep), as well as dwell time testing with a fixed frequency. All of these test types are standardized by DIN EN 60068-2-6.A limitation of the ASPEN method is that the frequency bands of the individual sweep tones must not overlap in the case of a multi-sweep profile. The second category includes broadband noise testing according to DIN EN 60068-2-64. The ASPEN method can also be used to create profiles for combined excitation, in which one or more sweep tones are superimposed with noise. This test type is standardized by DIN EN 60068-2-80. The prerequisite is that only one profile amplitude (e.g., only the amplitude of the sweep profile or the LDS value of the noise profile) must be determined at a given frequency. b) Excitation and reaction profiles ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 It makes sense to measure the vibration, load or stress quantities for the profile creation using the ASPEN method both on the affected component and on its fastening or connection points on the beam (the beam can be, for example,A combustion engine, electric, or other motor vehicle drive system, a vehicle transmission, a body, or a vehicle axle. Excitation profiles are derived from data measured at the mounting or fastening points of the affected component using the ASPEN method. These profiles are used to generate vibrations that are introduced into this component (the test object) during vibration testing. In most cases, the excitation profile is also controlled. If vibrations are also recorded directly on the component in question (during route driving), response profiles can be calculated from this data using the ASPEN method. These profiles describe the desired or required vibration amplitudes that the test object should experience during vibration testing in response to the introduced excitation profile.In contrast to an excitation profile, the reaction profile of resonant components is rarely used for shaker control for various reasons. The only difference between excitation and reaction profiles is the choice of measuring points for which a profile is derived and their handling during vibration testing - control of an excitation profile or monitoring (with possible limitations) based on the reaction profile. In the ASPEN method, the excitation and reaction profiles are created using the same algorithm. c) Profiles for single- and multi-point control The difference between these profile types lies in whether a profile is controlled at one or more points (locations) during vibration testing. With single-point control, a vibration sensor is placed at a location in the test setup, and the vibrations are introduced into the structure at this location according to a predefined profile.With multi-point control, the specified profile is controlled according to signals from several vibration sensors placed at various points on the test setup. ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 Profiles for single-point control are created as standard in the ASPEN-RoMi method, PRGN module, from all signals measured on a route or on the complete route mix, using the procedure described above. If signals were recorded at multiple points on the component or its supports in different directions (during driving tests), the difference between these profiles only depends on the point and measurement direction for which they apply. Therefore, if a test profile PR. V,kwas created using the PRGN algorithm from the signal of a sensor with the serial number k, the profile can only be meaningfully used in the test with profile control at the corresponding location where this sensor was placed during the route runs, and in the corresponding direction (measuring direction of the sensor). Profiles for multi-point control can be created from all signals measured on a route or on the complete route mix, in any combination. These signals only need to be specified. If the extrapolated or the extrapolated and superimposed PSS D are present in a SPEX results file, U,k for p measurement signals, any q of them can be used in the PRGN module to calculate a profile PR MP for a multi-point control (2 ^ q ^ p). Such a test profile PR MP, created by jointly processing the q individual profiles according to formulas (3.10), (3.11), should also be controlled in the vibration test according to the signals of all of these q sensors, placed at the corresponding locations. This means that this profile can only be correctly implemented by multi-point control of the signals from the corresponding sensor locations. The control strategy should also correspond to the algorithm for calculating the individual profiles: if formula (3.10) was used for this purpose, a mean value control should be used; if formula (3.11) was used, a maximum value control should be used. These control strategies must be implemented by appropriate settings in the vibration control system of the test bench. ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 A test profile for a multi-point control will not be calculated if only one measurement file (see above) was supplied to the ASPEN RoMi process for profile creation. This could, for example,This may be the case if measurements were only carried out on one route (no route mix). d) Profiles covering the damage on individual routes or on the entire route mix. If measurements are carried out on several different design-relevant routes of a route mix, the ASPEN RoMi procedure creates profiles that cover the damage on each individual route as well as on the entire route mix. This is done in a single pass of the procedure. ^ Individual routes The profiles PR. V,k , PR MP , created from the extrapolated but not superposed PSS, cover the travel time T Ri only on one considered route i. They neither consider journeys on other routes of the route mix, nor do they cover the full required component lifetime T LD (it is still assumed or required that the component is to be designed for a complete route mix). In addition, since T Ri < T LD, such a profile is weaker than the profile that covers the entire route mix and thus the required component life. Therefore, profiles that cover the travel time T Ri only cover individual routes of a route mix, are of secondary importance for practical vibration testing. From this perspective, these profiles are only a by-product of the profiling of the ASPEN RoMi procedure. Nevertheless, the profiles PR V,k , PR MP, created from the extrapolated, non-superimposed PSS, has important practical significance. Above (see the last paragraph in the subsection "Extrapolation of the PSS for route runs"), the possibility (and usefulness) of using this PSS to compare the difficulty of different routes in a route mix was already mentioned. Using the profiles created from this PSS, this task can now be solved in a different way. If PR V,k or PR MP, calculated for the same measuring point or for the same measuring points from journeys on different routes, are superimposed (e.g. graphically), one can draw conclusions as to which route in which frequency range leads to a harder profile in a vibration test for the location(s) under consideration than another route. A harder profile means greater (pseudo-)damage. However, it should be noted that the journey times on different routes may be different: T R1 ^T R2 ^T R3 etc. ^ Route mix Only the profiles PR V,k , PR MP , created from the extrapolated and superposed PSS, cover the travel time on the entire route mix and thus the full specified lifetime T LDof the component. They thus represent the main result of the profile creation of the ASPEN RoMi process. However, for each profile, this result is only available in the case of profile control at a specific, specific location (for an individual profile PR V,k ), or at the several corresponding locations (for the profile PR MP ) are applicable. These are different locations (on the component or on its supports) whose signals are used to create the profiles PR V,k , PR MPwere used. The assignment of the profiles to groups a) – d) results from the input data and the definition of the calculation parameters. The characteristics from groups a) – d) are not contradictory. Each created profile contains one characteristic from each group. For example, a test profile can be a sweep profile with regard to the type of vibrations generated, an excitation profile with regard to the selection of the points for its control / application, and a multi-point control profile with regard to the number of control points, and at the same time cover the driving time on just one route or on the entire route mix. ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18. All of these profiles are usable; the choice of one from them for practical implementation of the vibration test is made by the person responsible. ASPEN transformation: Formulas are used here for converting the PSS calculated using the ASPEN method from the route runs (i.e.Pseudo-damage experienced by the component during driving operation) into the damage-equivalent profile amplitudes. For this purpose, simple, non-iterative, analytical formulas (3.16) and (3.17) were developed in the ASPEN method. They were called the ASPEN transformation (AT) and are implemented in the PRGN algorithm (see above). In both variants, the AT applies only to a simple Wöhler curve. This is described by equation (3.8). As can be seen from formulas (3.16) and (3.17), the desired profile height in this case depends only on the slope coefficient k. WL, but not dependent on the abscissa or ordinate of the reference point of the Wöhler curve. The formula used depends solely on the type of profile to be created. Two profile types are distinguished: a) Noise profiles. Such a profile requires stochastic vibration excitation and is described by an LDS. The AT for calculating the height of the LDS of a noise profile at a frequency f is: where PSD U (f) – the desired height of the LDS of the noise profile, PSD Ref (f) – the height of the LDS of the stochastic reference signal, D U (f) – the ordinate of the PSS, which for stochastic oscillation with the desired LDS PSD U comes into being, ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 D Ref (f) – the ordinate of the PSS of the reference signal with the LDS PSD Ref (f), k WL – Slope coefficient of the Wöhler curve. The AT (3.16) determines the height of the LDS PSD Ua stochastic oscillation at a frequency f to achieve the defined (required) damage value D U at this frequency. To calculate the LDS PSD U from D U a known relationship is used that another stochastic oscillation (called the reference signal) is connected to the LDS PSD Ref at the same frequency the damage value D Ref This relationship is obtained by a procedure that involves generating a reference signal (here: a stochastic vibration signal) suitable for the profile type using the well-known LDS PSD Ref and the calculation of its damage value D Ref at each frequency, see the right part of the diagram in Figure 4. This procedure is described in detail above. The calculation PSD U(f) in (3.16) is performed individually for each oscillation frequency f, independent of any other frequency. In the formula notations of the section describing the PRGN algorithm (see the section entitled “Description” above), D U (f) = D U,k (f), PSD U (f) = PR U,k (f) (the index k is omitted because (3.16) is an arbitrary signal), D Ref (f) = D r,EX(f). Formula (3.16) is mathematically proven below. This is based on considering the relationship between the LDS and the PSS of an ergodic, normally distributed noise signal and its scaled copy. b) Sweep Profiles. Such a profile assumes a harmonic oscillation excitation; it is described by the dependence of the amplitude S of such a harmonic oscillation signal on its instantaneous frequency f, i.e., as an AFV S(f). ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18. The AT for calculating the AFV of a sweep profile (consisting of a single sweep) at a frequency f is: where S U (f) – the desired amplitude of the AFV of the sweep profile, S Ref (f) – the amplitude of the AFV of the monoharmonic reference signal, D U (f) – the ordinate of the PSS, which is for monoharmonic oscillation with the desired amplitude S U comes about, D Ref(f) – the ordinate of the PSS of the reference signal with the AFV S Ref (f), k WL – Slope coefficient of the Wöhler curve. The AT (3.17) determines the amplitude S U a monoharmonic oscillation at a frequency f to achieve the defined (required) damage value D U at this frequency. To calculate the AFV S U from D U a well-known relationship is used that another monoharmonic oscillation (called the reference signal) with the amplitude S Ref at the same frequency the damage value D Ref This relationship is obtained by a procedure that involves generating a reference signal (here: a single sweep signal) suitable for the profile type with the known amplitude S Ref and the calculation of its damage value D Refat each frequency, see the right part of the diagrams in Figure 1 and Figure 4. This is described in detail below. The calculation S U (f) in (3.17) is performed individually for each oscillation frequency f, independent of any other frequency. In the formula notations of the section describing the PRGN algorithm (see the section entitled “Description” above), D U (f) = S U (f) = PR U,k (f) (the index k is omitted because (3.17) is an arbitrary signal), D Ref (f) = D r,EX(f). ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 In addition to single sweep profiles, AT (3.17) is also applicable to the creation of the following profiles: i) profiles for dwell time testing with monoharmonic excitation at a fixed frequency (fixed frequency sine); these can be considered a special case of single sweep profiles if the sweep frequency remains constant, and ii) profiles with multisweep excitation. In case ii), the limitation of the ASPEN method is that the frequency bands of the individual sweep tones of a multisweep profile must not overlap. This limitation means that, even in the case of a multisweep profile, only one single sweep profile is defined at each frequency. Therefore, formula (3.17) remains valid for this case as well. Formula (3.17) is mathematically proven below.This is based on the consideration of the relationship between the amplitudes and the PSS of a monoharmonic time signal with a fixed frequency and its scaled copy. Concept of the reference signal: As already mentioned above, all damage-based profiling methods face the problem of converting the damage numbers experienced by the component during driving into the damage-equivalent amplitudes of the test profile. The difficulty here lies in the fact that for such a conversion to be performed non-recursively, the relationship between these two quantities must be known. In the ASPEN method, this problem is solved based on the concept of the reference signal and the AT. The AT, described by formulas (3.16) and (3.17), was considered in the section "ASPEN Transformation." Here, the concept of the reference signal is discussed.Basically, it is based on the fact that, depending on the profile type, a specially defined time signal is independently generated, its PSS is calculated, and extrapolated to the specified duration of the vibration test – see the right part of the diagram in Figure 4 (this signal can be generated internally or externally to the process). Since the amplitude (or LDS) of this signal is predetermined and its PSS is calculated, this procedure solves the problem described above – the ratio between these two parameters required to convert a PSS into the damage-equivalent profile amplitudes is thus known at every frequency. A signal generated in this way is called the reference signal in the ASPEN process. Its type must correspond to the type of test profile to be created. For example,It must be generated as a sweep when calculating a sweep profile, or as a stochastic signal when calculating a noise profile. Specifically, the concept of the reference signal for creating a test profile in the ASPEN-RoMi method requires the execution of the following steps: a) Determination of the profile type and parameters. At the latest at this point in the profile creation process, the type of test profile to be created and the duration of the vibration test T must be determined. VT (Note: the test frequency range f unt , …, f obhad already been selected earlier for the FDDC evaluation of the signals measured during the route runs – see above. The types of profiles that can be created using the ASPEN method are: ^ Sweep profiles (single or multi-sweep) ^ Profiles for a dwell time test (sinusoidal excitation with a fixed frequency), and ^ Noise profiles (testing with stochastic oscillation excitation). b) Generating the reference signal Depending on the profile type and parameters selected above, a reference signal is now generated, namely: ^ Sweep profiles ^ For single sweep profiles – the reference signal is generated over the entire test frequency range f unt , …, f ob as a single sweep of the selected type (linear, logarithmic), with the amplitude S Ref , tuning rate R and duration t r generated. The duration t rmust contain an integer number of half sweep cycles (this is the transit time from the lower to the upper frequency of a sine wave). The amplitude S Ref may be chosen arbitrarily, but it must be used in the entire frequency range f unt , …, f ob be constant. ^ For multisweep profiles – the reference signal consists of n Swp individual sweep tones (n Swp = 2; 3; 4; …); each of them is defined in its own frequency band, with the following division [f Swp,1 ; f Swp,2 ], …, f unt , f Swp,l = f ob ); together they cover the entire test frequency range f unt , …, f ob The individual frequency bands must not overlap. The type (linear, logarithmic), the amplitude S Refand the tuning rate R must be chosen to be the same for each sweep tone (with respect to the tuning rate R, this condition ensures that all individual sweeps have the same sweep time of their own frequency band, ie they run synchronously). Here, too, the duration t r be an integer number of half sweep cycles, and the amplitude S Ref in the entire frequency range f unt , …, f ob be constant. ^ Profiles for dwell time testing This is the simplest case – the reference signal is defined as a monoharmonic oscillation of the selected duration t r (preferably at least 1000 periods of the sine wave) with a fixed frequency f Ref. generated; this is the test frequency. The amplitude S Ref The oscillation frequency can be freely selected, as for the sweep profiles. ^ Noise profiles The reference signal is defined here as a stationary stochastic signal with a constant power density PSD over the entire test frequency range.Ref , ie generated as a white noise; the value of the LDS PSD Ref may be chosen arbitrarily. ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 Regarding the duration t r As far as this oscillation is concerned, it should be as large as possible to minimize the deviation between the actual LDS of the reference signal and the specified value PSD Ref In practice, the signal duration t r = 400 s has proven to be sufficiently long. If such a noise signal is generated using PC-based signal processing software (e.g., Matlab, Famos, Labview, etc.), the random number generation functions available there can be used (e.g., this function is called "Random" in Famos; it delivers a digital white noise signal in the frequency band up to the Nyquist frequency). c) Calculating the PSS After the reference signal r(t) has been generated as described above, its PSS D r(f) is calculated. For this, the FDDC algorithm is executed again, see calculation block 13 in the right-hand part of the diagram in Figure 4. The same calculation parameters must be used as for calculating the PSS of the signals from the route mix runs (see above). This particularly applies to the configuration of the bandpass filters, as well as the classification and S-N curve parameters. d) Extrapolating the PSS The PSS D calculated in the previous point r (f) applies for the duration t r of the generated reference signal. However, in order to calculate a damage-equivalent profile using the ASPEN method, the damage numbers are required, which are determined over the entire vibration test of duration T VT (calculated). For this purpose, the PSS D r (f) for this period T VTThis is done by re-executing the SPEX algorithm, see calculation block 14 in the right part of the diagram in Figure 4. The extrapolation algorithm is described by formula (3.5), the required extrapolation factor k r is determined according to (3.6). ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 The extrapolated PSS D r,EX (f), which for the specified period of the vibration test (computationally), forms the result of all calculations for the reference signal. This PSS is then used in the PRGN algorithm to determine the profile amplitudes (see section "Description", subsection "Description of the PRGN algorithm", point a)). Practical information: The following options are generally available for generating the reference signal: ^ Generation as a real vibration signal on a vibration test bench equipped with a suitable control system. Since the reference signal is only required to calculate a relationship between its amplitudes (or the LDS) and the degree of damage for the test profile of a specific type, setting up the test specimen is not necessary. The required vibration signal can be recorded on an empty shaker plate, i.e. without a test specimen.This applies regardless of whether the current test profile calculation is an excitation or a response profile. ^ Generation as a fictitious, digital signal in a PC-supported signal processing tool (e.g. in Matlab, Famos, Labview, etc.). This is an alternative, time-saving and cost-effective option, as it does not require a vibration test bench to generate the vibrations, nor a measuring system to record the signals. Formally speaking, the amplitudes of a reference signal generated in this way can have any unit, or even no unit at all, as the signal is fictitious. For ASPEN methods to work correctly, however, the ordinates of the generated reference signal must be assigned the same unit as the unit of the ordinates of the signals from the route runs for which test profiles are to be created. Accordingly, the unit for the amplitude S must also be set. Ref or for the LDS PSD Refof the digital reference signal to be generated, namely: o the unit of amplitude S Ref for the generation of the reference signal of the sweep type (in the case of creating a single or multi-sweep profile) or of the harmonic oscillation type with a fixed frequency (in the case of creating a profile for a dwell time test), the unit must be the same as the signals from the route runs for which test profiles are to be created (e.g. the unit S Ref for the quantity acceleration – m / s²) o the unit of the LDS PSD Ref for generating the white noise reference signal must be the same as the unit of the noise profiles to be created (e.g. the unit PSD Reffor the acceleration quantity, which was measured in m / s² - (m / s²)² / Hz). Further information: ^ Care must be taken to ensure that the signal parameters used to generate the reference signal (e.g. the sweep tuning rate, the number of individual sweep tones and their frequency bands) are identical to those which are actually used in the subsequent implementation of the created test profile on a vibration test rig for vibration testing of the test specimen. ^ The same reference signal that has been generated once can be used to create an excitation and response profile which relate to a test specimen and are used together in its vibration testing.

[0003] ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 Further explanations / attachments: Extrapolation and superposition of the PSS with multiple measurement files per route: This describes a special case for the extrapolation and superposition of the PSS in the ASPEN RoMi method when there are multiple measurement files per route driven. This can be the case, for example, if saving the entire section to be measured on this route in one file would result in too large a volume of data. The measurement engineer can therefore decide to trigger and stop the measurement several times during the route drive. For further explanations in this subsection, it is assumed that the data for each measurement interval is saved in a separate measurement file. The division of the measurement data into multiple measurement files can also be done subsequently, for example to reduce the size of a measurement file.Since the travel time to which the PSS of the time signals of this file are extrapolated is specified individually for each measurement file in the SPEX module, it must of course not be considered as the total travel time T for such a file. Ri on the measured route. Rather, the total travel time T Ri be divided between several sections of the route, whereby, as mentioned in the previous paragraph, it is assumed that there is one measurement file per route section. The sum of the travel times on all sections should, accordingly, be the total travel time on route T Ri This explanation will be illustrated by the following numerical example. Suppose that on two sections of a route i of duration 1000s and 1500s an acceleration value ^ (t) and saved in two separate measurement files. The signals of the two sections are and ^ i,2 (t), the corresponding measurement durations – t ^ i,1and t ^ i,2 Accordingly, they are t ^ i,1 = 1000s, t ^ i,2 = 1500s, the full travel time on the considered route i within the framework of a route mix to cover the entire lifetime is, for example, T Ri = 5000h. The operation with the FDDC and SPEX modules of the ASPEN RoMi procedure is carried out as follows. First, the two measurement files are fed to the FDDC module ZF Friedrichshafen AG file 212889 Friedrichshafen 2024-01-18 and from the two signals and the 2 PSS D ^ i,1 (f) and D ^ i,2 (f). These PSS are also saved in individual files. They are then fed into the SPEX module for extrapolation. Since the two PSS D ^ i,1 (f) and D ^ i,2 (f) are again in two separate files, they are extrapolated separately, and the extrapolation algorithm requires the specification of the 2 different travel times T Ri,1 , T Ri,2These are the durations of the journeys on the section of route i on which each measurement signal and ^ i,2 (t) was recorded. Their relationship to each other can be chosen arbitrarily, but it should be ensured that their sum equals the total travel time on the route: T Ri = T Ri,1 + T Ri,2 . A sensible choice would probably be T Ri,1 , T Ri,2 in that they are in the same ratio as the measurement times: T Ri,1 / T Ri,2 = t ^ i,1 / t ^ i,2 . In such a choice, T Ri,1 = 2000h, T Ri,2 = 3000h, and T Ri = T Ri,1 + T Ri,2 = 5000h. In this respect, the PSS D ^ i,1 to D ^ i,1,EX and D ^ i,2 to D ^ i,2,EX extrapolated. The extrapolated PSS D ^ i,1,EX applies to the travel time T Ri,1 (on the first section of route i), the extrapolated PSS D ^ i,2,EX– for the travel time T Ri,2 . The PSS D ^ i,EX , which is valid for the full travel time T Ri = 5000h on the entire route i, is calculated in the SPEX module only by superposition: D ^ i,EX . = D ^ i,1,EX + D ^ i,2,EX . It represents the main result of the SPEX calculations for the case study under consideration.

[0004] ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 Proof of the ASPEN transformation: The mathematical proof of the AT, see formulas (3.16) and (3.17), is based on the derivation of the relationship between the amplitudes (or LDS) and the PSS, calculated for two scaled copies of an arbitrary time signal using a simple S-N curve described by equation (3.8). This relationship is established first. This is followed by the proof of formulas (3.16) and (3.17). Relationship between the PSS of the two scaled signals: An arbitrary time signal a(t) is considered. The PSS of this signal, determined using the FDDC algorithm of the ASPEN method for a simple S-N curve (see above), is given by D a (f). Multiplying the signal amplitudes by a fixed factor (the constant) p results in a new signal b(t) = a(t) · p. If D is used to calculate the PSS b(f) of the signal b(t) with the FDDC algorithm has the same S-N curve, the PSS of the two signals a(t) and b(t) are in the following relation to each other (4.1) where k WL – the slope coefficient of the S-N curve. Proof of equation (4.1): Suppose the signal a(t) was classified using a counting method. Consequently, for each load horizon (i.e., for an amplitude) a i an associated number of cycles N OP (a i ) before. a i can also be the SMA if the counting method used determines the mean value of each game in addition to the amplitude (e.g. the Rainflow counting method). The values ​​[a i ; N OP (a i )] form a load spectrum. In Figure 8 it is schematically shown as a dark brown continuous curve. The damage amount of each amplitude a i is calculated according to (3.7) where N(a i) – number of failure cycles for the amplitude a i (so that [a i ; N / a i )] is a point on the Wöhler curve (see Figure 8). The total damage factor for all amplitudes of the load spectrum, which, for example, has n amplitude levels (i = 1, ..., n), is then obtained according to (3.9) as: For the total damage factor of the signal b(t), the following relationship can be established in the same way: The load spectrum for the signal b(t) is shown schematically in Figure 8 as a light brown dashed curve. Considering an arbitrary number of cycles N OP (a i ) of the load spectrum for a i , it is also the number of games N OP (b i ) of the collective for b i with the ratio b i = a i · p, which is due to the signal scaling b(t) = a(t) · p: N OP (b i ) = N OP (a i ) for b i = a i· p. In addition, the points [b i ; N(b i )] and [a i ; N / a i )] on a Wöhler curve, see Figure 8. Therefore, equation (3.8) applies to them: There b i / a i = p, this equation can be transformed as follows ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 ^(^ ) ^(^ ^ ) = ^ ^ ^^^ After substituting in (ii) instead of N(b i ) of expression (iii) and taking into account N OP (b i ) = N OP (a i ) results for D GS (b) or, subject to (i) Finally, a(t) can be considered as the output signal of a narrow bandpass filter, as defined in the FDDC algorithm of the ASPEN method. Then D GS (b), D GS(a) in (iv) are the ordinates of the PSS of the signals a(t) and b(t) at a given frequency, respectively, and relation (iv) also holds for the PSS. Thus, equation (4.1) is proven. Derivation of the AT for the case of a noise profile: The mathematical derivation of formula (3.16) is based on the following consideration. Assume that the reference signal a(t) is an ergodic normally distributed noise with the LDS PSD a (f) and the PSS D a (f). This PSS was determined using the FDDC algorithm described above. From a(t), a new (reference) signal b(t) is now generated by multiplying the amplitudes a(t) by a constant p: b(t) = a(t) · p. The LDS PSD is sought. b (f) of the noise signal b(t), for which its PSS D b (f) (default value). ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 The LDS of the ergodic signal a(t) of duration T can be expressed by the squared magnitude of its Fourier transform FT a(f) be calculated as follows

[0014] : Since b(t) was itself obtained by a linear transformation from the ergodic, normally distributed signal a(t), it is also ergodic and normally distributed

[0014] . Therefore, b(t) also From b(t) = a(t) · p follows due to the linearity of the Fourier transformation: FT b (f) = p · FT a (f). Therefore or In addition, the relationship (4.1) applies to the PSS of the two signals a(t) and b(t) (see above): From (ii) we get for the constant p Substituting the expression for p 2 from (iii) in (i) finally leads to the following result Taking other notations into account, this expression is identical to formula (3.16). ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 Derivation of the AT for the case of a sweep profile: Due to the condition of the ASPEN method mentioned above, it is sufficient to derive formula (3.17) only for the case of a single sweep profile. Such a profile determines a sliding frequency sinusoidal oscillation consisting of one tone. Furthermore, for any sufficiently small time interval, it can be assumed to be a monoharmonic oscillation with a fixed frequency. This results in a further simplification: the AT (3.17) only needs to be proven for a monoharmonic oscillation with a fixed frequency. Such a monoharmonic (reference) signal a(t) with a fixed frequency f is now considered (the frequency f can be arbitrary). The AFV of a(t) is S a (f), the PSS – as D a(f). This PSS was determined using the FDDC algorithm described above. From a(t), a new (reference) signal b(t) is now generated by multiplying the amplitudes a(t) by a constant p: b(t) = a(t) · p. The AFV S is sought. b (f) of the signal b(t) for which its PSS D b (f) (default value). Since S b (f) and S a (f) the amplitudes of the two signals are b(t) and a(t), it follows from b(t) = a(t) · p obviously ^ ^ (^) = ^ × ^ ^ (^) (i) In addition, the relationship (4.1) (see above) applies to the PSS of the two signals a(t) and b(t): ^ ^ ( ^ ) = ^^ ( ^ ) × ^ ^^^ (ii) From (ii) we get for the constant p Substituting the expression for p from (iii) into (i) leads to the following result ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 If a(t) in (iv) is a reference signal for a sweep test, and other notations are taken into account, (iv) is identical to formula (3.17). The invention is not limited to the described embodiments. The scope of protection is defined by the claims.

[0005] ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 Literature: 1. Köhler, M.; Jenne, S.; Pötter, K.; Zenner, H.: Counting methods and load assumptions in fatigue strength. Springer, 2012, 205 pages. 2. MBN 10438-2 "Fatigue strength of vibrating engine components - Validation for series production. Requirements and procedure." Mercedes-Benz works standard, January 2014 edition, 22 pages. 3. VW80200-1 "Engine components." Volkswagen AG Group standard, March 2009 edition, 29 pages. 4. DIN 30787-5 "Measurement and evaluation of mechanical-dynamic loads. Part 5: Derivation of test specifications." September 2002, 20 pages. 5. Cornelis, B.; Dendas, B.; Carrella, A.: “Qualification testing of racecar equipment subject to engine-induced vibrations: how to derive a test profile using a mission synthesis procedure”, Siemens Industry Leuven. In: IMAC XXXV, Garden Grove, USA, January 30th - February 2nd, 2017 (URL: https: / / www.researchgate.net / publication / 313368832_A_Mission_Synthesis_pr ocedure_for_Sine-on-Random_excitations_in_a_helicopter_application) 6. Halfpenny, A.: “Accelerated Vibration Testing Based on Fatigue Damage Spectra”. nCode International, 2009 (nCode publication, URL: https: / / www.ncode.com / images / GlyphWorks / Downloads / Whitepaper_nCode_ AHP_AcceleratedVibrationTestingBasedonFatigueDamageSpectra_v2- Halfpenny.pdf) 7. Halfpenny, A.; Kihm, F.: “Mission Profiling and Test Synthesis Based on Fatigue Damage Spectra”.9th Int. Fatigue Congress, Atlanta, USA, 2006 8. Decker, M.; Kinscherf, S.; Hesse, R.; Dillinger, S.: “FatiResponse – Damage Equivalence in Vibration Testing.” DVM Workshop “Testing Methodology for Fatigue Tests in the Automotive Industry,” Ottobrunn, January 25–26, 2017. 9. Decker, M.: “Derivation of Damage-Equivalent Power Density Spectra for Vibration Testing Using Damage-Response Spectra.”ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 Dissertation, Issue 119, TU Darmstadt, Institute for Steel Construction and Material Mechanics, 133S, 2018 10. Patent WO 98 / 14765 A “Method to Specify Random Vibration Tests for Product Durability Validation”. Ford Motor Company, 1998 11. Patent US 005565618A “Method to Specify Sinusoidal Vibration Tests for Product Durability Validation”. Ford Motor Company, 1996 12. Patent EP 3433593 B1 “Method and System for Accelerated Fatigue Damage Testing of an Object”. Siemens Industry Leuven, 2016 13. Patent DE 10236735 A1 "Method for generating noise profiles equivalent to driving damage for vibration testing of vehicle components." BMW AG Munich, 2002 14. Bendat, J.; Piersol, A.: Random Data. Analysis and Measurement Procedures. John Wiley, 566 pp., 1986 15. Haibach, E.: Structural Strength. Methods and Data for Component Calculation. Springer, 2nd edition, 2002, 753 pp.

[0006] ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 Reference symbols 1.1, 1.2, …, 1.n Measurement signals 2.1, 2.2, …, 2.n Pseudodamage spectra 3 Superposed pseudodamage spectrum 4 Test profile (route mix) 5 Reference signal 6 Extrapolated reference signal pseudodamage spectrum 7.1, 7.2, …, 7.n Extrapolated pseudodamage spectra 8.1, 8.2, …, 8.n Test profiles (individual routes) 9.1, 9.2, …, 9.n Measurement files 10 Pseudodamage calculation parameters 11 Extrapolation and superposition calculation parameters 12 Test profile calculation parameters 13 Pseudodamage spectrum calculation component 14 Extrapolation subcomponent 15 Superposition subcomponent 16 Test profile generation component 17 Reference signal pseudo-damage spectrum 18 Reference signal extrapolation parameters For the specific embodiment of the method in Figure 9: m – number of driving routes n – number of measured variables recorded on each route MS i,j , i = 1, …, m, j = 1, …, n – measurement signals PSi,j , i = 1, …, m, j = 1, …, n – Pseudodamage spectra ES i,j , i = 1, …, m, j = 1, …, n – extrapolated pseudodamage spectra SS j , j = 1, …, n – extrapolated and superposed pseudodamage spectra PP i,j , i = 1, …, m, j = 1, …, n – Test profiles (individual routes) SPP j , j = 1, …, n – Test profiles (route mix) ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 P1 Pseudo-damage spectrum calculation process P2 Extrapolation and superposition process P3 Test profile generation process P4 Reference signal processing process P5 Extrapolation sub-process P6 Superposition sub-process S1 Signal filtering step S2 Classification step S3 Conversion step S4 Partial damage contribution calculation step S5 Total damage calculation step S6 Pseudo-damage spectrum formation step

Claims

ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 Patent claims 1. Method for generating a test profile (4), comprising - a pseudo-damage spectrum calculation process (P1), in the context of which a plurality of pseudo-damage spectra (2.1, 2.2, ..., 2.n) are calculated from a plurality of measurement signals (1.1, 1.2, ..., 1.n) by means of a spectrum calculation algorithm, so that a pseudo-damage spectrum (2.1, 2.2, ..., 2.n) is generated for each measurement signal (1.1, 1.2, ..., 1.n), wherein each measurement signal (1.1, 1.2, ..., 1.n) was recorded before the start of the method as part of a route drive of a test vehicle, - an extrapolation and superposition process (P2), comprising an extrapolation sub-process (P5) and a superposition sub-process (P6), whereby in the extrapolation sub-process (P5) each pseudo-damage spectrum (2.1, 2.2, …, 2.n) is multiplied by a proportionality constant so that a plurality of extrapolated pseudodamage spectra (7.1, 7.2, ..., 7.n) is generated, wherein the extrapolated pseudodamage spectra (7.1, 7.2, ..., 7.n) are added together within the framework of the superposition sub-process (P6) so that a superposed pseudodamage spectrum (3) is created, - a test profile generation process (P3), within the framework of which the test profile (4) is generated, - a reference signal processing process (P4), within the framework of which a reference signal pseudodamage spectrum (17) is first calculated from a reference signal (5) by means of the spectrum calculation algorithm and then the reference signal pseudodamage spectrum (17) is multiplied by the proportionality constant so that an extrapolated reference signal pseudodamage spectrum (6) is generated, characterized in that. ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 the test profile (4) is generated within the scope of the test profile generation process (P3) based on the superimposed pseudodamage spectrum (3) and the extrapolated reference signal pseudodamage spectrum (6).

2. Method according to claim 1, characterized in that all test profiles calculated using the method mathematically fulfill the principle of damage equivalence with respect to the pseudodamage spectra (2.1, 2.2, ..., 2.n) calculated in the method.

3. Method according to claim 1, characterized in that the reference signal processing process (P4) runs parallel to the pseudodamage spectrum calculation process (P1) and / or to the extrapolation and superposition process (P2).

4. Method according to one of the preceding claims, characterized in that each measurement signal (1.1, 1.2, ..., 1.n) represents a time course of one and the same measurement variable, typically recorded on different routes (8.1, 8.2, ..., 8.n) of a route mix (4).

5. Method according to one of the preceding claims, characterized in that within the scope of the method, a plurality of test profiles (8.1, 8.2, ..., 8.n) are generated based on a plurality of measurement signal sets, wherein each measurement signal set describes a temporal profile of a specific measurement variable and / or is obtained by measuring the signals of a specific measurement variable on the route mix (4).

6. Method according to one of the preceding claims, characterized in that within the scope of the method (depending on the task, the input data and the setting parameters) test profiles (8.1, 8.2, ..., 8.n) of a plurality of different ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 Types or profiles with different features, including excitation and reaction profiles, profiles for single- and multi-point control, as well as profiles that cover the damage on individual routes or on the entire route mix (4), are generated.

7. Method according to one of the preceding claims, characterized in that the pseudo-damage spectrum calculation process (P1) comprises the following steps: - a signal filtering step (S1), in which each measurement signal (1.1, 1.2, ..., 1.n) is filtered using a plurality of bandpass filters, so that a plurality of filtered measurement signals are generated, - a classification step (S2), in which a load spectrum is formed from each filtered measurement signal by means of classification, typically by dividing an entire amplitude range of each filtered measurement signal into classes,wherein a number of cycles is determined for the amplitude of each class, preferably using a counting method, - a conversion step (S3), in which an amplitude of each cycle, possibly with a mean value, is first converted into a damage-equivalent mean-free amplitude, preferably using a Haigh diagram, and then the mean-free amplitudes are sorted in ascending order, - a partial damage contribution calculation step (S4), in which a partial damage contribution is calculated for the number of cycles for each damage-equivalent mean-free amplitude, preferably using a Wöhler curve, - a total damage calculation step (S5), in which the partial damage contributions to a total damage for each filtered measurement signal, ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 - are summed, each total damage being referred to as a pseudo-damage number of the respective filtered measurement signal, and - a pseudo-damage spectrum generation step (S6), in which the pseudo-damage spectra (2.1, 2.2, ..., 2.n) are formed from the pseudo-damage numbers by representing the pseudo-damage numbers as a function of the bandpass center frequencies of the bandpasses.

8. Method according to one of the preceding claims, characterized in that a noise profile and / or a sweep profile are calculated within the scope of the test profile generation process (P3). 9.Method according to one of the preceding claims, characterized in that, within the test profile generation process (P3), the conversion of the damage into a damage-equivalent test amplitude for creating a sweep profile is carried out using the special transformation in form (3.17), and the conversion of the damage into a damage-equivalent LDS for creating a noise profile is carried out using the special transformation in form (3.16).

10. Method according to one of the preceding claims, characterized in that, for creating a sweep or a noise profile, the entire structure and the entire calculation sequence of the method remain unchanged, with the exception of the supply of the reference signal of a different type to one input of the method and the use of the different conversion formulas (3.17) or (3.16) in the test profile generation process (P3). 11.Method according to one of the preceding claims, characterized in that the method is a computer-implemented method. ZF Friedrichshafen AG File 212889 Friedrichshafen 2024-01-18 12. A system for carrying out a method according to one of the preceding claims, wherein the system is preferably suitable for at least partially carrying out and / or coordinating and / or controlling a method for generating a test profile (4) according to one of the preceding claims.

13. A computer program comprising steps which, when executed on a computer, cause the computer to carry out a method according to one of claims 1 to 11.

14. A computer-readable medium, characterized in that the computer-readable medium comprises computer program code for carrying out a method according to one of claims 1 to 11.

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