Patent Description:
Industrial use of additive manufacturing (AM) is becoming ever so common for manufacturing complex parts with high repeatability and performance. Use of AM technologies save time and resources, which are one of the advantages of AM over conventional manufacturing techniques. However, parts fabricated by AM generally have poor surface roughness. Moreover, surface roughness varies from region to region within a component based on geometry (e.g. overhang angle).

Surface quality of a part may have a significant impact on the fatigue life of the part. Surface preparation and machining techniques that reduce surface roughness have been successfully employed to extend fatigue lives of parts that are subjected to cyclic stresses. While such methods may be applicable generally to external surfaces of additively manufactured parts, the internal "as-built" surfaces of complex geometry parts may prove more challenging to modify.

Techniques have been developed for assessing the influence of surface roughness on fatigue performance. However, state of the art techniques require expensive and time-consuming experimentation and/or heavy computational resources.

The publication from <NPL> describes a method for surface damage prediction for the case of metal forming, more precisely flow forming where a workpiece coming from a primary process is plastically deformed under the action of a roller, which influences the surface fatigue of the roller.

Patent document <CIT> (<NUM>-<NUM>-<NUM>) pertains to the prediction of fatigue strength of steel alloys comprising deriving data like steel fatigue from material databases.

Briefly, aspects of the present disclosure are directed to techniques for prediction of fatigue response based on surface roughness that address at least some of the technical challenges mentioned above.

According to an aspect of the present disclosure, a computer-implemented method is provided for predicting a fatigue response of a material. The method comprises receiving a user input specifying one or more surface roughness parameters that characterize a surface of a material for which fatigue life is to be predicted. The method further comprises generating at least one realistic virtual surface profile from the specified one or more surface roughness parameters. The method further comprises predicting fatigue life of the material in dependence of a stress field applied to the generated virtual surface profile.

In accordance with specific non-limiting embodiments disclosed herein, the virtual surface profile may be generated utilizing machine learning based generative models, frequency pattern matching, Autoregressive Moving Average (ARMA) models, or combinations thereof. Furthermore, in accordance with specific non-limiting embodiments disclosed herein, the prediction of the fatigue life may be carried out utilizing finite element analysis based simulations, machine learning methods, or combinations thereof.

Other aspects of the present disclosure implement features of the above-described method in computing systems and computer program products.

The foregoing and other aspects of the present disclosure are best understood from the following detailed description when read in connection with the accompanying drawings. To easily identify the discussion of any element or act, the most significant digit or digits in a reference number refer to the figure number in which the element or act is first introduced.

Aspects of the present disclosure relate to prediction of fatigue response based on surface roughness. Surface roughness is generally poor for parts fabricated by additive manufacturing (AM), which may significantly affect the fatigue performance of such parts. To assess surface roughness, one can perform surface height measurements, which may be expensive to perform and/or not accessible to all users. To assess the fatigue life of a part, a known approach is to not only quantify the surface roughness, but also generate a huge database of fatigue data corresponding to the different surface conditions. Generating such database currently is done through experiments, meaning that a large number of test specimens need to be manufactured with different surface conditions and then tested. Such an experimental campaign may be time consuming and expensive. Moreover, one needs to repeat it for different AM machines, process settings and powders. An alternative to the experimental approach is to predict the effect of surface roughness on fatigue life through simulation techniques. However, such techniques may be computationally intensive and time consuming. Furthermore, such techniques also require surface measurements, which may be difficult and expensive to perform.

The techniques disclosed herein address at least the above described problems by automatically generating a realistic virtual surface profile based on user-specified surface roughness parameters and predicting the corresponding fatigue property in dependence of a stress field applied to the virtual surface profile. The proposed techniques rely on finite element analyses (FEA), advanced machine learning (ML) methods, or combinations thereof. Using the proposed techniques, one can obtain in an efficient numerical way the fatigue property corresponding to any user defined surface roughness parameters, thereby avoiding expensive and time-consuming experimental methods. Aspects of present disclosure may be embodied in a computer-aided engineering (CAE) or computer-aided manufacturing (CAM) package.

Turning now to <FIG>, a computing system <NUM> is generally shown wherein aspects of the present disclosure may be implemented. The computing system <NUM> can be an electronic, computer framework comprising and/or employing any number and combination of computing devices and networks utilizing various communication technologies. The computing system <NUM> may be easily scalable, extensible, and modular, with the ability to change to different services or reconfigure some features independently of others. The computing system <NUM> may be, for example, a server, desktop computer, laptop computer, tablet computer, or smartphone. In some examples, computing system <NUM> may be a cloud computing node.

Computing system <NUM> may be described in the general context of computer executable instructions, such as program modules, being executed by a computing system. Generally, program modules may include routines, programs, objects, components, logic, data structures, and so on that perform particular tasks or implement particular abstract data types. Computing system <NUM> may be practiced in distributed cloud computing environments where tasks are performed by remote processing devices that are linked through a communications network. In a distributed cloud computing environment, program modules may be located in both local and remote computing system storage media including memory storage devices.

As shown in <FIG>, the computing system <NUM> has one or more processors <NUM>, which may include, for example, one or more central processing units (CPU), graphics processing units (GPU), or any other processor known in the art. The processors <NUM> can be a single-core processor, multi-core processor, computing cluster, or any number of other configurations. The processors <NUM>, also referred to as processing circuits, are coupled via a system bus <NUM> to a system memory <NUM> and various other components. The system memory <NUM> can include a read only memory or ROM <NUM> and a random access memory or RAM <NUM>. The ROM <NUM> is coupled to the system bus <NUM> and may include a basic input/output system (BIOS), which controls certain basic functions of the computing system <NUM>. The RAM <NUM> is read-write memory coupled to the system bus <NUM> for use by the processors <NUM>. The system memory <NUM> provides temporary memory space for operations of said instructions during operation. The system memory <NUM> can include random access memory (RAM), read only memory, flash memory, or any other suitable memory systems.

The computing system <NUM> comprises an I/O adapter <NUM> (input/output adapter) and a communications adapter <NUM> coupled to the system bus <NUM>. The I/O adapter <NUM> may be a small computer system interface (SCSI) adapter that communicates with a hard disk <NUM> and/or any other similar component. The I/O adapter <NUM> and the hard disk <NUM> are collectively referred to herein as a mass storage <NUM>.

Software <NUM> for execution on the computing system <NUM> may be stored in the mass storage <NUM>. The mass storage <NUM> is an example of a tangible storage medium readable by the processors <NUM>, where the software <NUM> is stored as instructions for execution by the processors <NUM> to cause the computing system <NUM> to operate, such as is described herein below with respect to the various figures. Examples of computer program product and the execution of such instruction is discussed herein in more detail. The communications adapter <NUM> interconnects the system bus <NUM> with a network <NUM>, which may be an outside network, enabling the computing system <NUM> to communicate with other such systems. In one embodiment, a portion of the system memory <NUM> and the mass storage <NUM> collectively store an operating system, which may be any appropriate operating system, to coordinate the functions of the various components shown in <FIG>.

Additional input/output devices are shown as connected to the system bus <NUM> via a display adapter <NUM> and an interface adapter <NUM>. In one embodiment, the I/O adapter <NUM>, the communications adapter <NUM>, the display adapter <NUM> and the interface adapter <NUM> may be connected to one or more I/O buses that are connected to the system bus <NUM> via an intermediate bus bridge (not shown). A display <NUM> (e.g., a screen or a display monitor) is connected to the system bus <NUM> by the display adapter <NUM>, which may include a graphics controller to improve the performance of graphics intensive applications and a video controller. A keyboard <NUM>, a mouse <NUM>, among other input/output devices, can be interconnected to the system bus <NUM> via the interface adapter <NUM>, which may include, for example, a Super I/O chip integrating multiple device adapters into a single integrated circuit. Suitable I/O buses for connecting peripheral devices such as hard disk controllers, network adapters, and graphics adapters typically include common protocols, such as the Peripheral Component Interconnect (PCI). Thus, as configured in <FIG>, the computing system <NUM> includes processing capability in the form of the processors <NUM>, and, storage capability including the system memory <NUM> and the mass storage <NUM>, input means such as the keyboard <NUM> and the mouse <NUM>, and output capability including the display <NUM>.

In some embodiments, the communications adapter <NUM> can transmit data using any suitable interface or protocol, such as the internet small computing system interface, among others. The network <NUM> may be a cellular network, a radio network, a wide area network (WAN), a local area network (LAN), or the Internet, among others. An external computing device may connect to the computing system <NUM> through the network <NUM>. In some examples, an external computing device may be an external webserver or a cloud computing node.

It is to be understood that the block diagram of <FIG> is not intended to indicate that the computing system <NUM> is to include all of the components shown in <FIG>. Rather, the computing system <NUM> can include any appropriate fewer or additional components not illustrated in <FIG> (e.g., additional memory components, embedded controllers, modules, additional network interfaces, etc.). Further, the embodiments described herein with respect to computing system <NUM> may be implemented with any appropriate logic, wherein the logic, as referred to herein, can include any suitable hardware (e.g., a processor, an embedded controller, or an application specific integrated circuit, among others), software (e.g., an application, among others), firmware, or any suitable combination of hardware, software, and firmware, in various embodiments.

<FIG> illustrates a method <NUM> for predicting a fatigue response of a material according to an aspect of the present disclosure. The method <NUM> may be implemented, for example, in conjunction with the computing system <NUM> illustrated in <FIG>. Block <NUM> of the method <NUM> involves receiving a user input specifying values of one or more surface roughness parameters. Herein, the user may provide input on one or more roughness parameters that are typically used to characterize the surface of the material for which fatigue life is to be predicted. The one or more parameters may be selected, for example, from the non-limiting examples of surface roughness parameters provided below. It is to be appreciated that the disclosed techniques may be used to account for additional or different parameters.

<FIG> shows an illustrative one-dimensional (1D) surface curve <NUM> defining a surface having microscopic asperities, where the axis <NUM> represents a distance across the surface (x) and the axis y represents asperity height (y). Assuming the profile is represented as a set of (xi, yi) points, the surface roughness parameters can be defined as:.

Referring back to <FIG>, block <NUM> of the method <NUM> involves generating at least one realistic virtual surface profile from the specified one or more surface roughness parameters. In the context of the present specification, a "virtual surface profile" refers to a machine generated surface profile obtained from user-specified surface roughness parameter values using a data-driven generative method. In this regard, a virtual surface profile is an artificial surface profile, and is not to be construed as being generated from surface measurements of a real surface. However, a virtual surface may be generated to closely resemble real surface profiles in an available data set. Accordingly, such a virtual surface profile is also described as being "realistic", while not being real. Example embodiments data-driven approaches for generating virtual surface profiles are illustrated below referring to <FIG>. Continuing with reference to <FIG>, block <NUM> of the method <NUM> involves predicting fatigue life of the material based on a stress field applied to the generated virtual surface profile. This may comprise generating a stress-life (S-N curve) plotting cyclic stress amplitude S against fatigue life Nf defined by number of cycles to failure. The generated S-N curve may be graphically displayed on a display screen. Exemplary non-limiting implementations within the scope of the above-described method <NUM> are illustrated below referring to <FIG>.

<FIG> illustrates a first example method <NUM> for generating one or more virtual surface profiles based on the user-specified surface roughness parameters. The method <NUM> utilizes a machine learning based generative model. Examples of such models include Generative Adversarial Networks (GAN), Variational Auto-Encoders, or their variations (e.g. WGAN-GP), among others. The generative model may be trained on the available data and utilized to generate novel virtual surface profiles that resemble the surface profiles in the available data. In the shown example, the method <NUM> utilizes a GAN.

Block <NUM> of the method <NUM> involves obtaining, as training data, 1D surface profiles s from surface measurements and calculated roughness parameters r of a plurality of real surfaces. The data from real surfaces may be pre-processed, which may, for example, involve the steps of resampling the data to obtain same sampling rate throughout all the samples, splitting the data to obtain the same sample length, detrending, etc. Block <NUM> of the method <NUM> involves training the generative model using the training data obtained at block <NUM>. At block <NUM>, the generative model is modified to request to the generator to match one or more of the surface roughness parameters specified by the user. In the case of GAN, this can be achieved, for example, by modifying the objective function that the process optimizes by adding the following term:
<MAT>.

In the above term, s̃ = G(z, r) are the generated 1D surface profiles, as function of the generator G, z is latent vector and Ri(*) is the function that represents the roughness parameters i. The objective function E is summed over the number of surface roughness parameters specified, which in this case is <NUM>.

Block <NUM> of the method <NUM> involves the generation of a specified number of new (virtual) 1D surface profiles s̃, that closely resemble the surface profiles s in the training data, based on the modified objective function of the generative model. As an additional step, at block <NUM>, the generated virtual 1D surface profile may be smoothed to reduce sharp peaks, for example, using spectral or spline interpolation.

<FIG> illustrates a second example method <NUM> for generating one or more virtual surface profiles based on the user-specified surface roughness parameters. The method <NUM> uses an Autoregressive Moving Average (ARMA) model to generate new surface profiles. The basic principle of this approach is to identify a suitable mathematical model describing the surface height profile from the available data and using the same model to generate new surface profiles.

Block <NUM> of the method <NUM> involves obtaining surface profiles from available data. The available data comprises surface profiles obtained from surface measurements and calculated roughness parameters of a plurality of real surfaces. The data from real surfaces may be pre-processed, which may, for example, involve the steps of resampling the data to obtain same sampling rate throughout all the samples, splitting the data to obtain the same sample length, detrending, etc. Block <NUM> of the method <NUM> involves choosing datasets having surface roughness parameters R that are already close to the user-specified surface roughness parameters R*.

Block <NUM> of the method of the method <NUM> involves determining a mathematical model of the following form from the chosen dataset.

In the above model, yt denotes the surface height at spatial position xt and the coefficients ai and bj determine the autoregressive (AR) and moving average (MA) part of the model, respectively. Furthermore, the quantity εt denotes white noise, i.e. a random input with mean zero and fixed variance σ<NUM>, at position xt.

The following model parameters are determined from the chosen dataset, namely order of the AR and MA contribution p, q, coefficients of the AR and MA contribution a<NUM>,. , ap, b<NUM>,. , bq and variation of the input noise σ<NUM>. For each dataset, these quantities may be identified using, for example, a Box-Jenkins approach in combination with a minimization of Akaike's Information Criterion (AIC). The Box-Jenkins approach is discussed in the publication: <NPL>. The Akaike's Information Criterion (AIC) is discussed in the publication: <NPL>.

Under the assumption that there is a single model describing all surface profiles, the aforementioned model parameters may be obtained by averaging the corresponding results from all datasets. The result is an ARMA model describing the spatial evolution of the surface height profile.

Block <NUM> of the method <NUM> involves obtaining one or more new surface profiles z using the ARMA model developed in block <NUM>. The new surface profile z may be obtained by specifying an initial height at x<NUM> = <NUM> (for simplicity this can be assumed to be zero) and creating a series of random white noise input εt with variance σ<NUM>. As would be expected, the new surface profile z would have surface roughness parameter parameters Rz, where Rz≈R*. Finally, at block <NUM> of the method <NUM>, a virtual surface z* is generated which would have the user-specified surface roughness parameter R*. The surface profile z* is determined as z* = (R*/Rz) · z.

<FIG> illustrates a third example method <NUM> for generating one or more virtual surface profiles based on the user-specified surface roughness parameters. While the method <NUM> shown in <FIG> works directly on the height data of the surface profiles, the method <NUM> shown in <FIG> identifies typical surface height frequency patterns from available data and creating new (virtual) surface profiles based on those patterns.

Block <NUM> of the example method <NUM> involves obtaining surface profiles from available data. The available data comprises surface profiles obtained from surface measurements and calculated roughness parameters of a plurality of real surfaces. The data from real surfaces may be pre-processed, which may, for example, involve the steps of resampling the data to obtain same sampling rate throughout all the samples, splitting the data to obtain the same sample length, detrending, etc. Block <NUM> of the method <NUM> involves choosing a surface profile g from the available data. A particular strategy for the choice is presented at block <NUM>. Block <NUM> of the method <NUM> involves computing a Power Spectrum (PS) of g, namely, PS(g), and an underlying model ĝ for it via the nonlinear least squares (NLS) method. It has been observed that the following parameterized model presents a good candidate.

In the above model, the parameters a, b, c, β may be identified by NLS.

Block <NUM> of the method <NUM> involves identifying a surrogate model for the residual or noise term r̂ = PS(g) - ĝ, again via NLS. Typically, r̂ is normally distributed with variance decaying exponentially for increasing frequencies. This is due to the fact that such frequencies larger than a certain threshold value are essentially non-existent. This decay motivates a model of the form
<MAT>.

In the above model σr̂(f) = γ · exp (-δ · f). It can be seen that the variance decreases if the frequency f increases.

Block <NUM> of the method <NUM> involves creating a random Power Spectrum ĥ following the trend ĝ(f) and a noise term r̂(f) from above-mentioned distribution. The generated surface profile will eventually have a PS close to ĥ.

Block <NUM> of the method <NUM> involves scaling the profile g by a factor ω such that g' = ω · g attains a desired surface roughness value as specified by the user. In order to minimize the distortion in the data, in block <NUM>, the surface g should be chosen as the one having a roughness value that is closest to the desired surface roughness among all datasets.

Block <NUM> of the method <NUM> involves generating one or more new (virtual) surface profiles such that the new surface profile has (a) the same height distribution and hence the same surface roughness as g', and (b) a Power Spectrum that is very close to ĥ and is therefore assumed to be realistic as ĥ was identified from the data. The new surface profile(s) may be generated using an iterative version of the amplitude adjusted Fourier transform (AAFT). A discussion on AAFT is available in the publication: <NPL>.

One or more of the methods illustrated in <FIG> may be used, individually, or in combination, to generate new (virtual) surface profiles. For example, the methods of <FIG> and <FIG> may be combined to achieve machine learning generated models that resemble the training data and also achieve the frequency patterns extracted from the available data. A first way to accomplish the above is to proceed with the method <NUM> shown in <FIG>, and then (after block <NUM>) add additional blocks as described for the method <NUM> of <FIG>. A second way to accomplish the above is to add a term in the objective function of the generative model (see block <NUM> of <FIG>) to penalize in the generative process surface profiles whose frequency content differ from the desired one.

Referring now to <FIG>, a first example implementation is described of a method <NUM> for predicting fatigue response of a material based on surface roughness. At block <NUM> of the method <NUM>, a user input is received specifying values of one or more surface roughness parameters characterizing a surface of the material for which fatigue life is to be predicted. The specified surface roughness parameters may include one or more of the surface roughness parameters described above, or may include additional or different surface roughness parameters. Block <NUM> of the method <NUM> involves generating at least one virtual surface profile based on the surface roughness parameters specified in block <NUM>. The virtual surface profile may be generated using one or more of the techniques illustrated above referring to <FIG>.

At block <NUM>, the method <NUM> involves creating a simulation model using finite element analysis (FEA), based on the generated virtual surface profile. The method includes applying appropriate loads and constraints to the FEA model to simulate a stress field on the virtual surface. In some embodiments, the simulated stress field may be graphically displayed on a display screen. While at a global level, the material may be assumed to exhibit a linear elastic behavior, at a local level, the material may exhibit plastic behavior due to stress concentration effects caused by surface roughness, porosity, etc. Accordingly, at block <NUM>, the method <NUM> computes a Smith-Watson-Topper (SWT) parameter to account for the localized plastic behavior, in order to predict fatigue life of the material. The SWT parameter, is known in the art (see <NPL>. ), and is defined by the following equation:
<MAT>.

In the above equation, the term on the left is the SWT parameter, which is a product of the maximum stress σmax and the strain value Δε/<NUM> for that said maximum stress. In the expression on the right, Nf denotes fatigue life defined by number of cycles to failure, b is the Basquin exponent, c is the Coffin-Mansion exponent, and σ'f , E and ε'f are constants. The values σmax and Δε/<NUM> may be computed from the FEA model, to thereby determine a value of the SWT parameter for a region of the virtual surface profile, which may be then used to determine fatigue life Nf based on the above equation.

Finally, at block <NUM> of the method <NUM>, a fatigue life of the material is predicted based on the computed SWT parameter. This may comprise generating an S-N curve plotting cyclic stress amplitude S against fatigue life Nf defined by number of cycles to failure. The generated S-N curve may be graphically displayed on a display screen. The computed SWT parameters may be related to the S-N curve through the well-known Basquin-Coffin-Mansion equation.

<FIG> illustrates a second example implementation of a method <NUM> for predicting fatigue response of a material based on surface roughness. The proposed method <NUM> uses a combination of machine learning (ML) and FEA based simulation to speed up the computation of the SWT parameter in order to predict fatigue life.

At block <NUM> of the method <NUM>, a user input is received specifying values of one or more surface roughness parameters characterizing a surface of the material for which fatigue life is to be predicted. The specified surface roughness parameters may include one or more of the surface roughness parameters described above, or may include additional or different surface roughness parameters. Block <NUM> of the method <NUM> involves generating at least one virtual surface profile based on the surface roughness parameters specified in block <NUM>. The virtual surface profile may be generated using one or more of the techniques illustrated above referring to <FIG>.

At block <NUM> of the method <NUM>, a value of the SWT parameter for a region of the virtual surface profile is determined using an ML based model. The ML based model is trained on previously generated data points pertaining to a large number of sample virtual surface profiles. Each training data point is generated by simulating a stress field on a respective sample virtual surface profile using FEA, and computing therefrom an SWT parameter for a region of the sample virtual surface profile, similar to that described in connection with blocks <NUM> and <NUM> of <FIG>. The ML based model of <FIG> may be thus trained to map the input surface profile to the result of the finite element simulation (i.e., the computed value of the SWT parameter). To this end, the method <NUM> of <FIG> may be utilized for generating the training data points for implementing the method <NUM> of <FIG>. Once a sufficiently large number of data points are generated using the method <NUM>, the method <NUM> may be implemented, to accelerate the computation of the SWT parameter.

At block <NUM> of the method <NUM>, a fatigue life of the material is predicted based on the computed SWT parameter. This may comprise generating an S-N curve plotting cyclic stress amplitude S against fatigue life Nf defined by number of cycles to failure. The generated S-N curve may be graphically displayed on a display screen. The computed SWT parameters may be related to the S-N curve through the well-known Basquin-Coffin-Mansion equation. In case of the method <NUM>, the determination of the predicted fatigue life is greatly simplified by computing the SWT parameter directly based on ML, bypassing the more time-consuming FEA based approach.

<FIG> illustrates a third example implementation of a method <NUM> for predicting fatigue response of a material based on surface roughness. The proposed method <NUM> utilizes ML to predict fatigue life directly from the generated virtual surface profile.

At block <NUM> of the method <NUM>, the fatigue life of the material is predicted (and may also be graphically displayed on a display screen), for example, in the form of an S-N curve, directly from the generated virtual surface profile, using the ML based model. The ML based model is trained on previously generated data points pertaining to a large number of sample virtual surface profiles. Each training data point is generated by simulating a stress field on a respective sample virtual surface profile using FEA, and computing therefrom an SWT parameter for a region of the sample virtual surface profile, and determining fatigue life (S-N curve) corresponding to the sample virtual surface profile from the computed SWT parameter. The ML based model of <FIG> may be thus trained to map the input surface profile to the predicted S-N curve.

To generate the training data points for implementing the method <NUM>, the method <NUM> (<FIG>) and the method <NUM> (<FIG>) may be utilized. The implementation of the method <NUM> is based on the understanding that the simulated stress fields contain enough information to be able to predict when a component would fail. However, this might involve a large amount of data for the ML based model to process and learn patterns from. Accordingly, the method <NUM> may be implemented only after a sufficiently large number of data points are generated linking the stress fields to the eventual S-N curves. The methods <NUM> and <NUM> may be utilized to allow the ML based model to reach to the required level of learning.

Aspects of the present disclosure may include a system, a method, and/or a computer program product at any possible technical detail level of integration. A computer readable storage medium, as used herein, is understood to be a non-transitory storage medium, which is not to be construed as being transitory signals per se, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through a waveguide or other transmission media (e.g., light pulses passing through a fiber-optic cable), or electrical signals transmitted through a wire.

The functions and process steps herein may be performed automatically, wholly or partially in response to user command. An activity (including a step) performed automatically is performed in response to one or more executable instructions or device operation without user direct initiation of the activity.

Claim 1:
A computer-implemented method (<NUM>) for predicting a fatigue response of a material, comprising:
Receiving a user input specifying one or more surface roughness parameters that characterize a surface of a material for which fatigue life is to be predicted (<NUM>),
generating at least one realistic artificial virtual surface profile from the specified one or more surface roughness parameters using a data-driven generative method to closely resemble real surface profiles (<NUM>) by a machine learning based generative model (<NUM>), the machine learning based generative model being developed using training data (<NUM>) comprising surface profiles obtained from surface measurements and calculated roughness parameters of a plurality of real surfaces (<NUM>), and
predicting fatigue life of the material in dependence of a stress field applied to the generated virtual surface profile (<NUM>).