Fatigue spectrum optimization

Abstract

A method for optimizing a fatigue spectrum includes a step of performing a load case reduction method that reduces a number of load cases in the source fatigue spectrum. The method further includes th

Description

FATIGUE SPECTRUM OPTIMIZATIONBACKGROUND

[0001] In order to comply with regulatory and certification requirements, aircraft structure is analyzed and / or tested to ensure that the structure has sufficient fatigue service life. In some cases, fatigue analysis is performed using S-N curves, wherein for a given stress range (S), a number of cycles to failure (N) is calculated. In other cases, finite element (FE) utilizes computer simulations to predict the fatigue capabilities of structural components. In still other cases, E-N curves, wherein for a given strain (E), a number of cycles to failure (N) is calculated. Various other analysis methods are also used.

[0002] When analyzing or testing aircraft structure for fatigue capability, a fatigue load / pressure spectrum is required to describe the various loading sequences / maneuvers that are representative of the particular aircraft operations carried out during its service life. For the purpose of the present disclosure, the fatigue analysis is described as FE analysis performed on landing gear structure. It will be appreciated, however, that the disclosed subject matter is not limited to landing gear structure but can be utilized with respect to any suitable aircraft structure and utilizing any suitable type of fatigue analysis. Further, it will be understood that the disclosed subject matter can also be utilized for structure other than aircraft structure for which fatigue analysis may be performed.

[0003] For landing gear structure, the fatigue load / pressure spectrum can be a full ground load spectrum that describes, for example, a retraction / lowering spectrum for a lock-link assembly, a load / pressure spectrum for an actuator, a pressure spectrum for a NLG steering cylinder, or any other landing gear component(s) and associated fatigue loads. The definition of such spectra is not unique despite the multiple constraints such as realistic operations / events ordering, fixed number of occurrences pertaining to each load case or total number of flight cycles.

[0004] FIGURE 1 shows an example of a known mission fatigue spectrum, i.e. a set of flight spectra and the number and order of their repetitions for the service life of a particular aircraft. A given mission spectrum comprises one or more different flight types (also referred to herein as “flight blocks”) that an aircraft may carry out during the aircraft service life. Different flight types may vary according to the length, payload, etc. Each flight type, in turn, comprises one or more flight spectra associated with particular flights that make up one or more flight types.

[0005] Referring now to FIGURES 1 and 2, in an embodiment, a flight spectrum might include loads from a known “ground-air-ground” sequence. Further, one or more maneuver sequences make up each flight spectrum. For example, the illustrated “ground-air-ground” flight spectrum may include maneuvers selected from landing, braking, engine spin-up, engine spin-down, taxiing, turning, etc. As illustrated in FIGURE 2, during each maneuver, a particular aircraft component or assembly is subject to one or more load cases, e.g., tensile loads, axial loads, bending moments, etc.

[0006] Referring back to FIGURE 1, each mission spectrum can be expressed as a collection of individual load cases. The fatigue service life of an aircraft could be determined by analyzing the fatigue performance of the aircraft when subjected to each of the collection of load cases, but the extremely high number of load cases that make up a mission spectrum make such an approach impractical. Accordingly, mission spectra are generated by combining and adjusting load cases sothat each mission spectrum includes a significantly reduced number of load cases that approximates the actual load cases that would otherwise make up the mission spectrum. As a result, fatigue analysis is significantly simplified and, in the case of FE analysis, computational resources and runtime are significantly reduced.

[0007] Known methods for generating fatigue spectra suffer from various challenges and limitations. Current methods lack criteria to assess the validity of the generated fatigue spectra. In addition, there is no traceability throughout the fatigue analysis. The lack of defined, measurable, and, thus, tangible criteria that is traceable by nature, introduces uncertainty into the assessment by analysis of fatigue damages precision. Further, the lack of optimization in known methods results in fatigue spectra that required excessive computational resources to conduct fatigue analyses.SUMMARY

[0008] Embodiments of methods for optimizing a fatigue spectrum are set forth according to technologies and methodologies of the present disclosure. The methods optimize, i.e., simplify in a repeatable and traceable manner, source fatigue spectra. The optimized fatigue spectra include fewer load cases, thereby enabling fatigue analysis that is faster and requires less computer resources than the corresponding source fatigue spectra.

[0009] A representative embodiment of a method for generating an optimized fatigue spectrum includes a step of performing a load case reduction method that reduces a number of load cases in the source fatigue spectrum. The method further includes the steps of performing a flight block merging method that reduces a number of flight blocks included in the source fatigue spectrum and validating the optimized fatigue spectrum.

[0010] In any embodiment, the load case reduction method includes a step of performing a silhouette analysis to obtain an optimal number of load case clusters.

[0011] In any embodiment, the load case reduction method further includes a step of performing a k-means clustering step using the optimal number of load case clusters

[0012] In any embodiment, the flight block merging method includes a step of aligning at least two flight blocks using dynamic time warping.

[0013] In any embodiment, the flight block merging method further includes a step of performing a k-means clustering step using an optimal number of flight blocks.

[0014] In any embodiment, the flight block merging method further includes a step of combining the at least two flight blocks after the k-means clustering step is performed.

[0015] In any embodiment, the combined at least two flight blocks includes load cases are weighted according to a number of occurrences in each of the at least two flight blocks.

[0016] In any embodiment, the step of validating the optimized fatigue spectrum includes the steps of performing a first fatigue analysis based on the optimized fatigue spectrum; performing a second fatigue analysis based on the source fatigue spectrum; and comparing results of the first fatigue analysis to the second fatigue analysis.

[0017] In any embodiment, if a difference between the first fatigue analysis and the second fatigue analysis is within an acceptable range, the optimized fatigue spectrum is considered validated.

[0018] In any embodiment, if a difference between the first fatigue analysis and the second fatigue analysis is within an acceptable range, the optimized fatigue spectrum is considered not validated.

[0019] In any embodiment, the when the optimized fatigue spectrum is considered not validated, the method returns to the load case reduction method.

[0020] In any embodiment, the method defines a closed loop system.

[0021] This summary is provided to introduce a selection of concepts in a simplified form that are further described below in the Detailed Description. This summary is not intended to identify key features of the claimed subject matter, nor is it intended to be used as an aid in determining the scope of the claimed subject matter.DESCRIPTION OF THE DRAWINGS

[0022] The foregoing aspects and many of the attendant advantages of claimed subject matter will become more readily appreciated as the same become better understood by reference to the following detailed description, when taken in conjunction with the accompanying drawings, wherein:

[0023] FIGURE 1 shows an example of a known service life mission spectrum for an aircraft;

[0024] FIGURE 2 shows ground loading for a known example of a “Ground- Air-Ground” flight spectrum sequence;

[0025] FIGURE 3 shows an example method of fatigue spectrum optimization according to aspects of the present disclosure;

[0026] FIGURE 4 shows an example embodiment of a load case reduction method that forms part of the fatigue spectrum optimization method of FIGURE 3;

[0027] FIGURE 5 shows an example of optimized clustering of flight blocks obtained by the method of FIGURE 4;

[0028] FIGURE 6 shows an alignment of two time series for a dynamic time warping calculation; and

[0029] FIGURE 7 shows an example embodiment of hardware configured to carry out the method of FIGURE 3.DETAILED DESCRIPTION

[0030] Embodiments of a disclosed method generate optimized fatigue spectra using defined, traceable criteria. The optimized fatigue spectra provide simplified bases for conducting fatigue analysis. By simplifying the basis for the analysis, the optimized fatigue spectra enable more efficient fatigue analysis that is faster, requires less computer resources, and does so without introducing unacceptable degradation of the fatigue analysis results.

[0031] Referring to FIGURE 3, an example embodiment of a fatigue spectrum optimization method 100 (“the optimization method 100”) according to aspects of the present disclosure is shown. As will be described in further detail, the optimization method 100 includes a load case reduction method 120, a flight block merging method 150, and a validation method 170 that cooperate to generates an optimized fatigue spectrum. The load case reduction method 120 reduces the number of load cases for a given flight block using a clustering method. The flight block merging method 150 reduces the number of flight blocks in the fatigue spectrum by merging similar flight blocks based on a time series comparison. The validation method 170 verifies the generated fatigue spectrum by comparing a fatigue analysis based on the generated fatigue spectrum to a fatigue analysis based on the original (“source”) fatigue spectrum. The fatigue spectrum generated by the optimization method 100 is a simplified fatigue spectrum that reduces fatigue analysis time and required computational resources while providing fatigue analysis results similar to the results based on the source fatigue spectrum.

[0032] The optimization method 100 begins at block 122 of the load case reduction method 120. Load case scale factors of a fatigue spectrum to be optimized, i.e., a source fatigue spectrum, are provide. In an embodiment, the load case scale factors are included in an LCS file accessed by a computer system that performs the flight spectrum generation. In block 124, the source fatigue spectrum is analyzed. If the source fatigue spectrum is not a structured spectrum, the method 100 proceeds to block 152 of the flight block merging method 150. If the source fatigue spectrum is a structured spectrum, the method 100 proceeds to block 126 of the load case reduction method 120.

[0033] Referring now to FIGURE 4, an embodiment of a load case clustering step 126 will be described. During the load case clustering step 126, the number of load cases is reduced by “clustering” similar load cases. Each cluster of load cases can then be considered a single load case during the fatigue analysis

[0034] In block 128, a number of initial clusters k is determined for the set of load cases. In an embodiment, the initial number of clusters k is chosen based on an empirical probability distribution of each point’s (load case) contribution to the overall “within-cluster sum-of squares.”

[0035] In block 130, a silhouette analysis is conducted for each of the number of initial clusters k to determine an optimal number of clusters. Each cluster has a centroid p. The mean intra-cluster distance a and the mean nearest-cluster distance b are calculated. With a and be calculated, the silhouette score is determined by the equation: b — a max a, b~)

[0036] The optimal number of clusters is the number with the highest silhouette score.

[0037] FIGURE 5 shows a graph of the results of an example silhouette analysis. In the graph, a silhouette analysis was conducted on 424 load cases. As the number of clusters increase, the corresponding silhouette scores initially increases and then decreases. A parabolic fit of the silhouette scores has a maximum silhouette score 0.396 when the number of clusters is 129. Accordingly, the optimal number of clusters is 129 for the illustrated load cases.

[0038] Referring back to FIGURE 4, the load case clustering step 126 continues to block 132, in which a k-means clustering is performed to cluster similar load cases according to the optimal number of clusters determined at block 130. The centroids for the clusters are determined according to an empirical probability distribution of each point’s (load case) contribution to the overall within-cluster sum-of square, which is determined according to the following criterion:

[0039] Each load case is assigned to the nearest centroid, and then new centroids are calculated by averaging the samples in each cluster until each centroid does not significantly move. With the centroids optimized in the manner, each centroid constitutes a new load case. Scale factors for each cluster are calculated by averaging scale factors of each load case j in the cluster, weighted by the estimated damage d using the Basquin equation (averaged across materials) according to the following equations:

[0040] The load case clustering step 126 then moves to block 134 to begin verifying the accuracy of the simplified load spectrum. In block 134, a full field FE analysis is conducted using the simplified load spectrum.

[0041] The load case clustering step 126 continues to block 136, in which the accuracy of the simplified fatigue spectrum generated in block 128 through block 132 is determined by comparing the fatigue results of generated in block 136 to the fatigue results of the source fatigue spectrum. If the differences between fatigue results provided using the simplified fatigue spectrum and those provided using the source fatigue spectrum are within an acceptable range, then process moves to block 140, and the load case reduction is complete. If the differences between fatigue results provided using the simplified fatigue spectrum and those provided using the source fatigue spectrum are not within an acceptable range, then process moves to block 138, and the k-means clustering is conducted using 110% of the previously determined optimal number of clusters. The load case clustering step 126 then returns to block 134 to verily the accuracy of the new fatigue spectrum determined with the increased number of clusters.

[0042] When the accuracy of the new fatigue spectrum has been verified, the load case clustering step 126 moves to block 140, and the load case clustering step is complete. The load case reduction method 120 then proceeds to block 142.

[0043] During the load case reduction method 120, the load case clustering step 126 is performed for each flight block (flight type) in the fatigue spectrum. In block 142, the production of the new load cases and associated cluster centroids for all flight blocks are complete, and the optimization method 100 proceeds from the load case reduction method 120 to the flight block merging method 150.

[0044] Still referring to FIGURE 3, the optimization method 100 proceeds to block 152 of the flight block merging method 150. In block 152, the load cases from different flight blocks are “clustered.” That is, information from the spectrum (SPE file) in block 154 is utilized to plot the load cases from different flight blocks along a common timeline defined by a series of time blocks.

[0045] FIGURE 6 shows an example of two different flight blocks (A and B) plotted along a common timeline. While clustering using two flight blocks is illustrated for the sake of simplicity, it will be appreciated that the described clustering method can be used with any number of flight blocks.

[0046] Still referring to FIGURE 6, each the point at each time block of flight block A is compared to the point at each time block of flight block B. The point for each time block of each flight block corresponds to a load case scale factor, dynamic time warping is used to calculate the distance between (1) each point of one flight block to (2) each point of the other flight block. As shown in FIGURE 6, the dynamic time warping finds the best alignment between the points of the sequences and calculates the Euclidean distances between aligned points. As indicated in FIGURE 6 a point of one flight block may be aligned with one or more points of the other flight block.

[0047] The total distance between flight blocks is defined as the sum of the minimum distances for each flight block sequence. The distances between all flight blocks are used to represent points in a coordinate system, wherein the ithaxis representsthe distance to flight block i. As a result, the ithcoordinate of flight block j is the distance between flight block i and flight block j. The points of the coordinate system are passed through a clustering algorithm, which determines an optimum grouping based on the silhouette score. That is the points of the coordinate system and, therefore, the distances between flight blocks are clustered so that similar flight blocks are a part of the same cluster.

[0048] With the flight blocks clustered in block 152, the flight block merging method 150 proceeds to block 156. In block 156, the clustered flight blocks from block 152 are merged. In this regard, corresponding sequences from the flight blocks are combined and weighted according to the number of flight blocks in which the sequences occur and the corresponding load case scale factor for each sequence. The new scale factors f are computed from a weighted average of the original scale actors f^ in each sequence according to the following equation:

[0049] The new sequence occurrences n are computed from a weighted average of the original sequence occurrences n in each flight block ns, wherein the weights are flight block repeats n^ according to the following equation:

[0050] The optimization method 100 then proceeds from the flight block merging method 150 to block 172 of the validation method 170.

[0051] In block 172, a fatigue analysis is completed using the load cases generated in the flight block merging method 150. In fatigue analysis of block 172generate predicted damages, shown in block 174. The validation method 170 then proceeds to block 176, wherein the fatigue analysis results are compared to the fatigue analysis results for a known set of load cases to assess the accuracy of the simplified fatigue spectrum generated in the flight block merging method 170. The validation method 170 proceeds to block 178, in which the accuracy of the fatigue analysis based on the optimized fatigue spectrum is considered. If the differences between fatigue results provided using the simplified fatigue spectrum and those provided using the corresponding known fatigue spectrum are not within an acceptable range, then optimization method 100 returns to block 124 of the load case reduction, and the optimization method continues in a closed loop until the differences are within an acceptable range. When the differences between fatigue results provided using the simplified fatigue spectrum and those provided using the corresponding known fatigue spectrum are within an acceptable range, then process moves to block 180, and the simplified fatigue spectrum generated in the flight block merging method 170 is considered to be the optimized fatigue spectrum for the aircraft.

[0052] FIGURE 7 shows a schematic view of a representative embodiment of a computer system 200 configured and programmed to perform methods and algorithms described herein. The computer system 200 includes a CPU 202 and a storage unit 204. The computer system 200 further includes an input device 206 and a display 208 to enable user input and information display, respectively. It will be understood, as previously noted, that any suitable combination of hardware, software, etc., can be utilized to carry out the methods and processes disclosed herein.

[0053] It will be appreciated that certain embodiments disclosed herein utilize circuitry (e.g., one or more circuits) in order to implement standards, protocols, methodologies or technologies disclosed herein, operably couple two or more components, generate information, process information, analyze information, filter signals, generate signals, encode / decode signals, convert signals, transmit and / or receive signals, control other devices, etc. Circuitry of any type can be used. It will beappreciated that the term “information” can be use synonymously with the term “signals” in this paragraph.

[0054] In an embodiment, circuitry includes, among other things, one or more computing devices such as a processor (e.g., a microprocessor), a central processing unit (CPU), a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), a system on a chip (SoC), or the like, or any combinations thereof, and can include discrete digital or analog circuit elements or electronics, or combinations thereof. In an embodiment, circuitry includes hardware circuit implementations (e.g., implementations in analog circuitry, implementations in digital circuitry, and the like, and combinations thereof).

[0055] In an embodiment, circuitry includes combinations of circuits and computer program products having software or firmware instructions stored on one or more computer readable memories that work together to cause a device to perform one or more protocols, methodologies or technologies described herein. In an embodiment, circuitry includes circuits, such as, for example, microprocessors or portions of microprocessor that require software, firmware, and the like for operation. In an embodiment, circuitry includes one or more processors or portions thereof and accompanying software, firmware, hardware, and the like.

[0056] The detailed description set forth above in connection with the appended drawings, where like numerals reference like elements, are intended as a description of various embodiments of the present disclosure and are not intended to represent the only embodiments. Each embodiment described in this disclosure is provided merely as an example or illustration and should not be construed as preferred or advantageous over other embodiments. The illustrative examples provided herein are not intended to be exhaustive or to limit the disclosure to the precise forms disclosed. Similarly, any steps described herein may be interchangeable with other steps, or combinations of steps, in order to achieve the same or substantially similar result. Moreover, some of the methodsteps can be carried serially or in parallel, or in any order unless specifically expressed or understood in the context of other method steps.

[0057] In the foregoing description, specific details are set forth to provide a thorough understanding of example embodiments of the present disclosure. It will be apparent to one skilled in the art, however, that the embodiments disclosed herein may be practiced without embodying all of the specific details. In some instances, well-known method / process steps have not been described in detail in order not to unnecessarily obscure various aspects of the present disclosure. Further, it will be appreciated that embodiments of the present disclosure may employ any combination of features described herein.

[0058] The present application may reference quantities and numbers. Unless specifically stated, such quantities and numbers are not to be considered restrictive, but example of the possible quantities or numbers associated with the present application. Also, in this regard, the present application may use the term “plurality” to reference a quantity or number. In this regard, the term “plurality” is meant to be any number that is more than one, for example, two, three, four, five, etc. The term “about,” “approximately,” etc., means plus or minus 5% of the stated value. For the purposes of the present disclosure, the phrase “at least one of A and B” is equivalent to “A and / or B” or vice versa, namely “A” alone, “B” alone or “A and B.” Similarly, the phrase “at least one of A, B, and C,” for example, means (A), (B), (C), (A and B), (A and C), (B and C), or (A, B, and C), including all further possible permutations when greater than three elements are listed.

[0059] It should be noted that for purposes of this disclosure, terminology such as "upper," "lower," "vertical," "horizontal," "fore," "aft," "inner," "outer," "front," "rear," etc., should be construed as descriptive and not limiting the scope of the claimed subject matter. Further, the use of "including," "comprising," or "having" and variations thereof herein is meant to encompass the items listed thereafter and equivalents thereof as well as additional items. Unless limited otherwise, the terms "connected," "coupled," and"mounted" and variations thereof herein are used broadly and encompass direct and indirect connections, couplings, and mountings.

[0060] In the foregoing description, specific details are set forth to provide a thorough understanding of representative embodiments of the present disclosure. It will be apparent to one skilled in the art, however, that the embodiments disclosed herein may be practiced without embodying all of the specific details. In some instances, well-known process steps have not been described in detail in order not to unnecessarily obscure various aspects of the present disclosure. Further, it will be appreciated that embodiments of the present disclosure may employ any combination of features described herein.

[0061] Throughout this specification, terms of art may be used. These terms are to take on their ordinary meaning in the art from which they come, unless specifically defined herein or the context of their use would clearly suggest otherwise.

[0062] The principles, representative embodiments, and modes of operation of the present disclosure have been described in the foregoing description. However, aspects of the present disclosure, which are intended to be protected, are not to be construed as limited to the particular embodiments disclosed. Further, the embodiments described herein are to be regarded as illustrative rather than restrictive. It will be appreciated that variations and changes may be made by others, and equivalents employed, without departing from the spirit of the present disclosure. Accordingly, it is expressly intended that all such variations, changes, and equivalents fall within the spirit and scope of the present disclosure as claimed.

Claims

CLAIMSThe embodiments of the invention in which an exclusive property or privilege is claimed are defined as follows:

1. A method for generating an optimized fatigue spectrum for an aircraft from a source fatigue spectrum, the method comprising the steps of: performing a load case reduction method that reduces a number of load cases in the source fatigue spectrum; performing a flight block merging method that reduces a number of flight blocks included in the source fatigue spectrum; and validating the optimized fatigue spectrum.

2. The method of Claim 1, wherein the load case reduction method includes a step of performing a silhouette analysis to obtain an optimal number of load case clusters.

3. The method of Claim 2, wherein the load case reduction method further includes a step of performing a k-means clustering step using the optimal number of load case clusters4. The method of Claim 3, wherein the flight block merging method includes a step of aligning at least two flight blocks using dynamic time warping.

5. The method of Claim 4, wherein the flight block merging method further includes a step of performing a k-means clustering step using an optimal number of flight blocks.

6. The method of Claim 5, wherein the flight block merging method further includes a step of combining the at least two flight blocks after the k-means clustering step is performed.

7. The method of Claim 6, wherein the combined at least two flight blocks includes load cases are weighted according to a number of occurrences in each of the at least two flight blocks.

8. The method of Claim 7, wherein the step of validating the optimized fatigue spectrum includes the steps of: performing a first fatigue analysis based on the optimized fatigue spectrum; performing a second fatigue analysis based on the source fatigue spectrum; and comparing results of the first fatigue analysis to the second fatigue analysis.

9. The method of Claim 7, wherein if a difference between the first fatigue analysis and the second fatigue analysis is within an acceptable range, the optimized fatigue spectrum is considered validated.

10. The method of Claim 8, wherein if a difference between the first fatigue analysis and the second fatigue analysis is within an acceptable range, the optimized fatigue spectrum is considered not validated.

11. The method of Claim 10, wherein the when the optimized fatigue spectrum is considered not validated, the method returns to the load case reduction method.

12. The method of Claim 11, wherein the method defines a closed loop system.

13. The method of Claim 1, wherein the flight block merging method includes a step of aligning at least two flight blocks using dynamic time warping.

14. The method of Claim 13, wherein the flight block merging method further includes a step of performing a k-means clustering step using an optimal number of flight blocks.

15. The method of Claim 14, wherein the flight block merging method further includes a step of combining the at least two flight blocks after the k-means clustering step is performed.

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