Method and system for accelerated fatigue damage testing of an object

In many engineering applications (e.g. in automotive or aero ^¬ space & defense) , hardware equipment (including both mechani ^¬ cal and electronic subsystems and components) is exposed to dynamic loads that may induce failures due to fatigue phenom ^¬ ena. The hardware equipment will also be referred as "ob ^¬ ject". To validate whether the object (also called "test ob ^¬ ject" or "device-under-test" - DUT) will remain operational during the service life (i.e. verify it will not break due to fatigue failures) , extensive vibration tests are conducted, i.e. so-called qualification tests. The purpose of these tests is to reproduce in a laboratory the loading conditions imposed by the real operating environments which are encoun ^¬ tered by the DUT (e.g. driving on road, spaceflight launch, ...) , such that a complete lifetime loading is applied in a fraction of the time.

To achieve this, in a first step measurements are performed in the real operating environments and, based on these meas- urements, in a second step forced vibration signals are cal ^¬ culated such that a shaker test using these signals will cause the same accumulated fatigue damage effect on the DUT as in the real-life operational conditions. The calculated forced vibration signals should hereby be optimized such that an equivalent fatigue behavior is achieved in a shorter amount of time (so-called "accelerated lifetime testing") . Finally, in a third step the forced vibration signals have to be applied in a controlled manner to a shaker installation. The invention addresses the second and third parts of this procedure, i.e. how to calculate the forced vibration signals and apply them in a controlled manner to a shaker installa- tion, so that a damage-equivalent "accelerated" qualification test is achieved.

Different procedures currently exist, e.g. applying standard- ized test profiles (in the form of Power Spectral Density

(PSD) functions, shock profiles, sine sweeps, sine-on-random spectra, ...). These standardized test profiles typically have to cover a wide range of applications. As a consequence, the standard specifications are chosen to be conservative in order to prevent "undertesting" , so that in many specific ap ^¬ plications the test specifications are much more severe than the actual environmental loads.

Another example is replicating the time waveforms which were measured in operation. This method is typically restricted to a limited range of time intervals, continuously repeated. This is suitable for loads with repeating patterns, but less so for environmental loads which are of "stochastic random" nature as in the envisioned applications. The control method - commonly denoted as "Time Waveform Replication" or "Single- Axis Waveform Replication" - is provided by most shaker control applications.

Generating a PSD test specification based on the enveloped PSD spectra of the measured real life loading signals, fol ^¬ lowed by a (Gaussian) random vibration control test is a standard feature in nearly any commercial available shaker control software. This approach allows for a more statisti ^¬ cally representative testing of complex load environments. However, by reducing the data to a PSD, the method implicitly assumes that the environmental loads have a Gaussian ampli ^¬ tude probability density function (PDF) and that they are stationary. In case the real world load environment has an amplitude distribution that is non-Gaussian, e.g. because there are specific events that occur (like potholes or bumps in the road that cause peaks in the loading and in the re ^¬ sponses) , some of the fatigue-related content of the loads can be underestimated, even when the PSD is well approximat ^¬ ed .

An advanced method employs generating of non-Gaussian excita- tion signals by so-called "kurtosis control" methods. In ad ^¬ dition to the PSD, also statistical signal parameters such as the "kurtosis" can be specified and controlled. Kurtosis rep ^¬ resents the "peaked-ness" of the data, mathematically ex ^¬ pressed as the 4-th statistical moment (where K=3 is the Gaussian case and K>3 is non-Gaussian with heavier tails in the amplitude PDF compared to the Gaussian case) .

The goal of these methods is to match the PSD and kurtosis of the originally measured excitation (i.e. the INPUT to the system) . However, the fatigue loading effect on the object (DUT) which is depending on how much of the kurtosis transfers into the system response, i.e. into the OUTPUT of the system, is not considered explicitly by the methods. It is well-known that without precautions, kurtosis may get "lost" in a system response due to adherence to the central limit theorem. As a result, the methods fail in many cases to cor ^¬ rectly represent the fatigue behavior during the laboratory tests. This leads to longer testing times to reach the same fatigue phenomena and it prevents to design accelerated tests.

An example for a solution for kurtosis control is the "Time- Frequency Domain Swapping" method, described in Carella et al . "Using Kurtosis control with random-control vibration tests: theory and practice" - Proceedings of ISMA2014 includ ^¬ ing USD2014.

Another example is the "Analytical phase selection" method described in Steinwolf et al . "Two methods of generating ran- dom excitations with increased Kurtosis for in-house testing of vehicle components" - ICSV22, Florence (Italy) 12-16 July 2015, also described in Cornells et al . "Shaker testing simu ^¬ lation of non-gaussian random excitations with the fatigue damage spectrum as a criterion of mission signal synthesis" - International conference on Engineering Vibration, Ljubljana, Slovenia, 7-10 September 2015. . The most advanced qualification testing methodology is re ^¬ ferred to as "Test Tailoring" or "Mission Synthesis". The methodology first quantifies the "damaging potential" of measured operational loads by calculating the so-called "Fa ^¬ tigue Damage Spectrum" (FDS) function

(https://en.wikipedia.org/wiki/Fatigue_damage_Spectrum). The FDS can be calculated on any type of signal, e.g. shocks, de ^¬ terministic sine waves, Gaussian or non-Gaussian random signals, etc. Therefore, it allows comparing different signals and signal types in terms of fatigue damaging potential. In the subsequent test synthesis stage, a test duration is se ^¬ lected and a PSD test specification is derived such that the generated (Gaussian) excitation signals, which are applied to the shaker installation using a default Gaussian random vibration control method, match the FDS of the operational loads (hence the laboratory test should cause equivalent fa ^¬ tigue damage as the operational environment) .

A problem with the Mission Synthesis method particularly occurs when "accelerated" tests are required, i.e. where the test duration has to be reduced. The only way to achieve this currently is through upscaling the PSD levels - i.e., it is the only way to still match the same FDS in a smaller amount of testing time, given Gaussian excitation signals. There are multiple risks when upscaling the PSD levels, but most im- portant is the fact that the failure mode may change when the levels are too high - i.e., causing the object or DUT to fail by a different mechanism than the intended high-cycle fatigue phenomenon which occurred in real-life. For this and various other reasons, all standards suggest that the "test exaggera- tion factor" (i.e. the ratio of test PSD level over opera ^¬ tional PSD level) should be kept to a minimum if possible. In a recent presentation by Vibration Research (Achatz et al . "Using fatigue damage spectrum for accelerated testing with correlation to end-use environment" - 2014 Workshop on Accel ^¬ erated Stress Testing and Reliability, Sep 10-12, St. Paul, MN, U.S.A.), it is demonstrated that mission synthesis based on FDS can be combined with a method for controlling kurto- sis, hence generating non-Gaussian signals with peaks. The method matches the kurtosis of the measured operational loads (as in regular kurtosis control methods) , and at the same time tries to match the FDS (in contrast to regular kurtosis control methods) . The method first calculates a "shaped" PSD specification from the FDS (in an offline manner) , also taking into account that activation of a method for controlling kurtosis will add some additional damage. When an accelerated test is demanded, the method increases the PSD levels, simi ^¬ lar as in other approaches. Thus, the resulting PSD still has higher levels compared to the operational signals, so that the problems discussed above are still unresolved. Therefore it is an object of the present invention to provide an improved method for accelerated vibration testing.

The solution for this problem is specified in the independent patent claims.

The solution is provided by a method for accelerated fatigue damage testing of an object as defined in claim 1, wherein the object is excited via an actor, wherein a drive signal, i.e. an electric voltage, is generated by a control system and transmitted to the actor, whereby the acceleration of the object or of a mounting base of the actor is measured and fed back to the control system for a cycled closed loop control of the drive signal in the frequency domain, wherein in the control system, a Power Spectral Density PSD and a Fatigue Damage Spectrum FDS are calculated from the measured acceler ^¬ ation, whereby the calculated Power Spectral Density PSD is compared with a target Power Spectral Density PSD based on an operational load, whereby the calculated Fatigue Damage Spec- trum FDS is compared with a target Fatigue Damage Spectrum FDS, whereby, based on the comparisons, a new drive frequency spectrum is calculated, and, from the new drive frequency spectrum, one or multiple time-domain blocks for the drive signal for a next cycle are generated and transmitted to the actor. This method accelerates vibration testing without af ^¬ fecting the failure mode, thus coming to more realistic re ^¬ sults . The solution for the problem is also given by a system for accelerated fatigue damage testing of an object as defined in claim 11, with an actor to excite the object, with a control system, wherein a drive signal is generated and transmitted to the actor, with a sensor, wherein the acceleration of the object or of a mounting base of the actor is measured, the measured acceleration being fed back to the control system for a cycled closed loop control of the drive signal in the frequency domain, wherein, in the control system, a Power Spectral Density PSD and a Fatigue Damage Spectrum FDS are calculated from the measured acceleration, the calculated Power Spectral Density PSD is compared with a target Power Spectral Density PSD based on an operational load, the calcu ^¬ lated Fatigue Damage Spectrum FDS is compared with a target Fatigue Damage Spectrum FDS, whereby, based on the compari- sons, a new drive frequency spectrum is calculated, and, from the new drive frequency spectrum, one or multiple time-domain blocks for the drive signal for a next cycle are generated and transmitted to the actor. With such system the advantages as described for the method can be achieved.

Advantageous embodiments of the invention are described in the depending patent claims. The described features can be used individual, or in combination. In an embodiment, for calculating the new drive frequency spectrum the recent drive frequency spectrum is adapted, wherein the amplitudes of the frequency lines in the drive frequency spectrum are adapted according to the comparison of the Power Spectral Density PSD, and the phases of the drive frequency spectrum are adapted according to the comparison of the Fatigue Damage Spectrum FDS. The phases of the drive fre ^¬ quency spectrum have an influence on the amplitude PDF of the generated time signal (hence the link between phases and kur- tosis) . Accordingly, a two channel closed loop control is es ^¬ tablished so that impacts from one channel to the other - and vice versa - can be eliminated. The kurtosis of the generated time signal can be adapted by manipulating the phase at one or several particular frequency lines of the drive frequency spectrum. In an advantageous embodiment, the phases are ma ^¬ nipulated such that the method becomes independent from sin ^¬ gle unknown resonance frequencies of the object. In the control system, it is helpful if the Power Spectral

Density PSD and the Fatigue Damage Spectrum FDS of the vibra ^¬ tion signal are controlled completely independent from each other. This makes it - inter alia - possible to adapt the control cycles to the specific needs of every "channel" and to available computing power.

The target Power Spectral Density PSD and the target Fatigue Damage Spectrum FDS should be regarded as pre-defined "a pri ^¬ ori" constants. Accordingly, a re-calculation during runtime is not necessary. The target Power Spectral Density PSD can be chosen according to vibration load of operational condi ^¬ tion for the object, and the target Fatigue Damage Spectrum FDS can be chosen according to the total damage to the object for a lifetime mission of the object (as determined by opera- tional measurements in the first step of the standard "Test Tailoring" or "Mission Synthesis" methodology) . For example, for an aircraft landing gear the FDS can sum up the permissi ^¬ ble damaging loads for some thousand start-landing-cycles which are expected for the lifetime of a plane; accordingly the FDS is a constant which is pre-defined by the assumed start-landing-cycles and by the forces etc. occurring at the landings. An accelerated testing procedure should apply the same "damage", but in a shorter amount of time or less cycles than in real life.

After the calculations, one or multiple time-domain blocks for the drive signal for a next cycle are generated with an Inverse Fast Fourier Transformation. These time blocks shall be used until the next control cycle is completed.

A schematic overview of the invention is illustrated in the Figure.

The left side of the figure, which entails an actor SH (here: the shaker hardware) and sensors, is the same as in common vibration control systems. The system features as sensor ACCS, a so-called "control accelerometer", e.g. instrumented on a mounting base (in the figure: the shaker table SH) or the object DUT itself. The signal AD (acceleration data) of this control accelerometer ACCS will be checked by the closed-loop FDS + PSD control system CLC, in order to ensure that the forced vibration signals (representing the vibration environment) are correctly simulated by the actor SH. Based on the control acceleration feedback AD (acceleration data) of a previous iteration or previous or last control cycle, the closed-loop control system CLC will calculate a new so- called "drive signal" DS (an electric voltage, also called drive time signal) - e.g by. tuning amplitudes and phases of one or more spectrum lines - which is sent to the actor SH (shaker table, shaker system) amplifier input. Optionally, also other sensors can be instrumented on the object DUT (de- vice under test) . These additional sensors are merely used for monitoring purposes (e.g. to assess whether the vibration levels on critical points on the DUT are not too high) , but are not necessarily further utilized by the control system. The right side of the figure illustrates the two-channel closed-loop control system CLC, which is the core of the sys ^¬ tem. Basically, this controller CLC can be a conventional computer hardware with I/O interfaces and multiple software modules. Some or all calculations might be done by a DSP (DSP - digital signal processor) for reducing calculation time and thus achieving shorter control cycles. In contrast to common control systems, the objective of the method is to control both a specified FDS and PSD at the same time ("FDS+PSD control") . By targeting the FDS as direct con ^¬ trol criterion, the method can achieve damage equivalence compared to the operational load environments (assuming a lifetime FDS specification has been determined from opera ^¬ tional data e.g. through the standard "Mission Synthesis" methodology) .

Having determined an FDS for lifetime damage for the object and having information for the original (not accelerated) load duration, a PSD can be calculated which causes in a nonaccelerated test situation an equivalent damage as the origi ^¬ nal load over the original time. As will be further explained below, an accelerated damage- equivalent qualification test (where the same damage has to be applied in a reduced time) can furthermore be achieved by manipulating the kurtosis of the generated forced vibration signals (i.e. making the signals more non-Gaussian, introduc- ing more "peaked-ness") , while the PSD of the signal is kept at the same level as the operational loads and the total FDS over the complete test procedure is maintained.

In more detail, the closed-loop "FDS+PSD" control system CLC in each iteration first analyses the control accelerometer signal AD; the FDS and PSD are calculated e.g. by software or DSP-modules CFDS, CPSD (calculate FDS, calculate PSD) . Next, the calculated FDS and PSD functions are compared to the "Target FDS" and "Target PSD" functions e.g. by software mod- ules COMP-FDS, COMP_PSD (compare FDS, compare PSD) . When the PSD target is either not reached or exceeded at a particular frequency line, an update rule can be applied which deter ^¬ mines the amplitude that should be used for this frequency line when generating the next iteration drive signal DS . When the FDS target is either not reached or exceeded (at a par ^¬ ticular frequency line) , the damaging potential of the exci ^¬ tation has to be increased or decreased, respectively. The procedure should change the damage potential without affect ^¬ ing the PSD level, as this is controlled independently.

Therefore, the procedure will instead alter the kurtosis of the excitation (i.e. increasing the kurtosis if more damage is required, or else decreasing the kurtosis if the damage is too high) .

Based on the comparison of PSD and FDS, a new drive frequency spectrum is created, e.g. in a module SYN for signal synthe ^¬ sis. Therein, the FDS and the PSD of the measured vibration signal should be approached to the a priori defined target values. Various control strategies can be used, including conventional PID control. As previously discussed, the ampli ^¬ tudes are determined by an update rule (based on the PSD com ^¬ parison) . In regular random control, the amplitudes are com- plemented by independent and uniformly-distributed random phases, resulting in a Gaussian signal. In this case, a higher kurtosis (K>3) is however likely required (as dictated by the FDS comparison) . This is achieved by a special phase ma ^¬ nipulation strategy, i.e. where dependencies between the phases are created.

Finally, once the drive frequency spectrum has been tuned, one or multiple time-domain blocks are generated e.g. by ap ^¬ plying an Inverse Fast Fourier Transform (IFFT), and adding windowing and overlapping (as in standard IFFT-based random controllers) . This can be done in the module SYN, as de ^¬ scribed before.

Accordingly, the FDS calculation is an integral part of the control loop, i.e. computed in each iteration or in each control cycle. The method synthesizes time domain signals based on IFFT. However, as the phases are not all chosen as inde ^¬ pendent uniform-distributed random variables, the resulting signal is non-Gaussian with kurtosis > 3. This manner of kur- tosis generation for the purpose of FDS control is distinct from other approaches where an a-priori determined target kurtosis has to be achieved.

The method should manipulate the kurtosis only in order to match the specified target FDS (including "test accelera ^¬ tion") , while the PSD should be controlled separately in or ^¬ der to match a specified target PSD shape. The method thus utilizes a particular "kurtosis generation" method as im ^¬ portant subroutine. Therein, it is possible to control the kurtosis and PSD separately, whereby a change in one property does not affect the other property. This is e.g. a problem with common methods such as the polynomial transform method.

It is known that the response of a lightly-damped linear sys ^¬ tem is closer to Gaussian than the applied excitation. Therefore, in order to increase the response kurtosis in an accel ^¬ erated test, the kurtosis control method must be able to ef- fectively generate kurtosis which passes into the resonances.

The FDS introduces the concept of damage at particular fre ^¬ quency lines. Therefore, the kurtosis generation method is able to directly target a particular frequency line. This is not possible with time-domain kurtosis methods such as the time-frequency domain swapping method.

The main advantages are the fact that the FDS is used as con ^¬ trol criterion which is very important for qualification testing where damage-equivalence to operational environments is the main objective, and moreover that "accelerated test ^¬ ing" (i.e., reducing the testing time by inducing more damage in a shorter amount of time) is achieved without affecting the PSD level, but rather by generating higher kurtosis exci- tation signals. The latter advantage greatly reduces the risk that the object or DUT fails due to a different failure mode than the targeted fatigue phenomena. This solves the main problem with the current Mission Synthesis approaches, which increase the PSD levels in an accelerated test.

To achieve this, FDS calculations, which are an integral part of the control loop, and a specialized kurtosis generation methodology based on a "Analytical Phase Selection" method are combined synergistically in a closed-loop controller, i.e. the "FDS+PSD control" system illustrated in the Figure.