Fatigue Design Load Identification Using Engineering Data Analytics

Ha-Rok Bae

Assistant Professor

Mem.ASME Department of Mechanical

and Materials Engineering, Wright State University,

Dayton,OH45435

Hiroaki Ando

Engineering Specialist

Advanced VPD,PD>,

Caterpillar,Inc.,

1901S.First Street,

Champaign,IL61874 Sangjeong Nam

Staff Analyst Information Analytics,PD>,

Caterpillar,Inc.,

1901S.First Street,

Champaign,IL61874

Sangkyum Kim

Engineering Team Lead Information Analytics,PD>,

Caterpillar,Inc.,

1901S.First Street,

Champaign,IL61874

Christopher Ha

Manager Information Analytics,PD>,

Caterpillar,Inc.,

1901S.First Street,

Champaign,IL61874Fatigue Design Load Identification Using Engineering Data Analytics

Selecting an appropriate concept design in the early stage of the product development process is crucial for successful machine development.As one of the important design requirements,a structural design needs to validate the structural fatigue life against physical tests of actual?eld operations.Traditionally,the fatigue design loads for the concept design evaluations are generated by hand calculations based on past experience to capture envelopes of expected system responses.But such an approach often does not capture actual loading behaviors in the?eld.An alternative approach of leveraging observed data from physical tests is highly desired,and a new method of this approach is introduced in this study.Our goal is to develop a new methodology of identifying fundamental fatigue load(FFL)contents from observed data by using engineering data analytics(EDA)techniques.The proposed methodology is applied to determine a new sensor layout which enables us to capture fundamental structural damage load patterns. Numerical demonstrations and case studies of the proposed method are presented with a common structural component,an I-section cantilever beam,and an industrial large-scale structure,a front linkage of a hydraulic excavator.[DOI:10.1115/1.4027849] Keywords:sensor layout,load identi?cation,engineering data analytics,fundamental fatigue loads,pattern mining,feature selection

1Introduction

In heavy earth moving industries,a typical new machine devel-opment process starts with a survey of a wide range of customers to understand the full spectrum of machine applications and criti-cal needs.Based on the survey,design targets are determined and cascaded through all subsystems of the new machine to be built. For a structural system,one of the most important design objec-tives is to meet a structural fatigue life target.Engineers should have high con?dence in structural durability assessments achieved by running physical dynamic tests with a full scale prototype machine at a test ground.However,it is expensive and time consuming to perform physical tests at every stage of design de-velopment.Therefore,using advanced simulation power,a virtual product development(VPD)process[1,2]is employed to reduce dependency on physical tests.Since a typical sampling rate of a test measurement is around several hundred hertz,measured data is often too big to be used for an iterative simulation based concept design exploration in VPD.In practice,instead of the measured loads,designers use a static design load set usually de?ned by worst cases of machine operations to assess the dura-bility envelope,especially for a concept design evaluation. Obtaining a good concept design is crucial to achieve successful machine development because it can reduce any budgetary or pro-ject schedule risk that can arise from unnecessary physical tests and design alterations.In concept design exploration,the accuracy of the durability evaluation obviously depends on how well the fatigue design loads represent the measured load data.Conven-tionally,the fatigue design loads are determined mainly based on experiences and simple hand calculations,considering potential extreme cases of machine operations.However,these design loads may not be appropriate to account for all critical fatigue load content during actual operation.Therefore,as an alternative, it is desirable to extract representative fatigue design loads directly from the measured loads.For load extraction,the?rst concern is how to place a limited number of sensors on a test machine to obtain quality measured load data that contains all crit-ical fatigue load content.

Optimal sensor placement is a typical problem in structural health monitoring(SHM).The main focus of sensor placement in SHM is how to maximize the chance of detecting system faults or potential damage with a limited number of sensors.In practice, the number of sensors is usually limited by the monitoring equip-ment channel capacity.Accessibility and serviceability will also pose constraints for the sensor layout design.Therefore,optimal sensor placements should be customized for applications and con-?gurations of a target machine https://www.360docs.net/doc/a48111056.html,prehensive surveys of SHM sensor placement can be found in Refs.[3–6].One of the popular approaches to measure the effectiveness of sensor place-ments is to use the Fisher information matrix[7],which shows the sensitivity of measurements of interest with respect to the sensor locations.Additional common approaches include modal assur-ance criterion(MAC)[8],effective independence method[9], kinetic energy method[10],mode shape sensitivity method with a dynamic reduction system[11],and energy index method with empirical mode decomposition[12,13].Most sensor layouts in SHM are determined by focusing on dynamic response changes of a targeted structure to detect structural damage,mostly through a

Contributed by the Design Automation Committee of ASME for publication in the J OURNAL OF M ECHANICAL D ESIGN.Manuscript received September12,2013;?nal manuscript received June3,2014;published online November14,2014.Assoc. Editor:Xiaoping Du.

pattern recognition process.The dynamic responses include struc-tural mode shapes,modal strain energy,nonlinear crack behavior, and dynamic?exibility[5].However,these SHM sensor layouts may not be optimal for identifying fatigue design load patterns and recently a modal stress weighting method was proposed to identify fatigue loads[14].In this study,the research effort is focused on the optimum sensor layout that can capture all critical fatigue load patterns from the sensor data rather than the detection of a change in structural dynamic responses.

Several researchers[15–17]have proposed load extraction methods that can generate static design loads from measured loads for fast design iterations.Kang et al.[15]developed an analytical method based on modal analysis for the transformation of dynamic loads into equivalent static loads.However,the static loads are aimed at reproducing equivalent displacement?elds,not fatigue damage.Based on the fatigue history wavelet transform [18],Abdullah et al.[19]developed the wavelet bump extraction (WBE)algorithm to?nd fatigue design loads.In this method,the signal is converted from the time domain to the frequency domain using the fast Fourier transform method.The frequency domain signal is decomposed into multiple wavelets in which each wave-let covers frequency regions of speci?c failure locations.Then the fatigue damage events or bumps are identi?ed such that they pro-duce equivalent signal statistics and fatigue damage to the original signal.In practical cases,however,WBE is ineffective to interpret the critical features of the fatigue loads method when it deals with many damage locations related with different frequency ranges. In this study,a new sensor layout method is proposed based on data analytics processes,such as pattern mining and feature extraction coupled with fatigue mechanics to amplify and capture fundamental damaging load patterns.By using data analytics,?rst,FFL elements are identi?ed from large amounts of measured load data.Damage-based sensitivity is proposed to amplify hidden patterns of the FFLs.Then,based on the identi?ed FFLs, optimized sensor placements are extracted from a number of can-didate sensor locations.Section2gives a brief description of the cumulative fatigue analysis with quasi-static stress responses, which outlines a typical approach used for the durability evalua-tion of concept designs.The proposed EDA approach for the sen-sor layout is presented in Sec.3.This is followed by numerical demonstrations and case studies with a common structural compo-nent,an I-section cantilever beam,and an industrial large-scale structure,the front linkage of a hydraulic excavator.The paper concludes with a summary of the research?ndings and potential next topics.

2Cumulative Fatigue Analysis

Fatigue life for vehicle machine components is typically esti-mated based on a damage accumulation method,Miner’s rule [20].For particular stress amplitudeeD r=2T,the number of cycles to fatigue failure(2N f)is de?ned by the stress-life curve as shown in Fig.1.When stress amplitudes D r1and D r2are repeated n1 and n2cycles,respectively,in a stress history,the total damage is obtained by the Miner’s rule which is expressed by the following equation:

D?

X n i

N i

i?1;2(1)

The fatigue life is the reciprocal of the total damage whose value one indicates a fatigue failure occurs.In practice,most of the stress(or strain)history data has varying amplitudes.To con-vert the varying stress history into a series of constant amplitude cycles,the rain?ow counting method[21]is generally used to give an accurate number of cycles de?ned as closed stress or strain hysteresis loops.

Two main approaches are used to obtain the stress or strain his-tory data for the damage estimation;transient dynamic analysis methods[22,23]and quasi-static stress analysis[24].Transient dynamic analysis methods can address a structural system under high inertial and vibrational effects.For a structural system with less inertia effect and external loads applied below the system nat-ural frequency,the quasi-static stress method can approximate the stress history which would be accurate enough for a concept design evaluation.Hence in this study,the stress or strain history of a vehicle machine is generated by the quasi-static stress analy-sis method as follows:First,a linear elastic?nite element(FE) analysis is performed by applying static unit loads at the degrees of freedom where individual load histories are applied.The result-ing unit load stress responses are static stress in?uence coef?-cients which will be scaled based on the load histories.A complete stress history for the damage accumulation is obtained by combining all the scaled unit load stresses at each loading time point.When the stress status is not uniaxial but multi-axial,the phase relationship between the stress components is not constant. In this case,it is not intuitive which plane direction will have the most severe fatigue damage.The critical plane method projects the stresses onto several planes and calculates fatigue damage at each plane.The most severe plane for fatigue damage is interpo-lated with the calculated planes.For comprehensive details on the speci?c multi-axial fatigue life analysis method used in this study, the reader is referred to Refs.[25]and[30].

3Optimal Sensor Layout for Fatigue Design

Load Extraction

Data analytics is a general knowledge discovery process to obtain better understanding and new information out of huge amounts of data[26,27].In data analytics,a broad range of techni-ques are used,such as data acquisition and selection,data cleaning and screening,data transformation,interpretation and feature modeling,and prediction.In this study,the proposed approach for the optimal sensor layout is based on data transformation,pattern mining,and data featuring techniques.First,instead of working on the measured loads directly,the engineering fatigue mechanics is incorporated to transform and characterize the data in terms of the fatigue damage.Fatigue-based sensitivity is also utilized to highlight hidden damage patterns within the large amounts of load data.By using data pattern mining,critical load patterns of fatigue damage are identi?ed along with optimal sensor locations.The overall process of the proposed sensor layout method via EDA is presented in Fig.2.Sections3.1–3.4show detailed steps of the proposed method.

3.1Full Life Analysis and Worst Cycle Fatigue Loads. Assuming a FE model is available for the quasi-static stress analysis,the unit load analysis is performed to obtain the stress in?uence data by applying unit loads at the degrees of freedom where individual load histories are applied.Then,the full

stress Fig.1Stress amplitude and life curve

history at a location of interest is recovered by multiplying load history data to the stress in?uence data under the assumption of linearity as in the following equations:

r j ?

X

i

L ij U i i ?1;2;…;I j ?1;2;…;J (2)U i ?f U xx i U yy i U xy i g T (3)r j ?f r xx j r yy j r xy j g T

(4)

Here,I is the total number of loading locations,J is the total number of load history time points,L ij is a load component (unit:N)on the i th loading location at the j th time point in the load his-tory data,U i is the stress in?uence coef?cient data (unit:m à2)obtained by applying a unit load at the i th loading location con-sisting of three in?uence coef?cients U xx_i ,U yy_i ,and U xy_i for the plane stress,and r j is the stress status at the j th time point at a location of interest also consisting of three plane stress components r xx_j ,r yy_j and r xy_j .In practice,there are many dif-ferent fatigue life assessment algorithms depending on load types (high or low cycles),materials,temperature,or residual stress and manufacturing methods such as a casting or fabricated structure.In this study,the main purpose of performing the full life analysis is to examine the load data by transforming it into cyclic loads.Therefore,the multi-axial principal stress algorithm with no mean stress correction is selected for a conservative life assessment of a general fabricated structure.

Once the fatigue analysis is performed,damage information can be extracted from the recovered full stress history in terms of the critical damage plane,worst damaging cycles,and their fre-quencies for the following EDA process.For the worst cycle extraction,the strain time history is obtained from the stresses normal to the critical damage plane.With the strain time history,individual fatigue cycles are collected by using a rain?ow cycle algorithm [21].As an example shown in Fig.3,a worst cycle that contributes to the total fatigue damage is identi?ed as a pair of time points,wc 1and wc 2,from the history.The number of worst cycles depends on the coverage ratio of the total fatigue damage to be covered at a location and the complexity of the load history data.For example,the 90%coverage ratio of the total fatigue life would include more worst cycles than the 80%coverage ratio.In practical cases,the number of extracted worst cycles can be con-trolled by segmenting the measured load data based on unique types of dynamic events.With the worst cycle time points,fatigue damaging load vectors are obtained as in the following equations:

L j ?f L ij j 8i g

(5)FL k ?eL wc 2k àL wc 1k Tk ?1;…;K p

(6)

Here,L j is the load vector given at the j th time point in a load

history data,wc 1k and wc 2k are the load history time points for the k th worst cycle,K p is the total number of identi?ed worst cycles at the location of interest p ,and FL k is the k th worst cycle fatigue load vector.As a result,a matrix of worst cycle fatigue load vec-tors is obtained at each candidate sensor location as

FL p ?f FL k j k ?1;2;…;K p g ;

p ?1;2;…;P

(7)

where P is the total number of candidate sensor locations and the FL p matrix has the size of K p ?I .

The next step is to ?nd basic patterns among the fatigue load vectors in each FL p .Based on the basic patterns obtained in this step,our goal is to select essential locations of sensors.In practice,typically the total number of the fatigue loads from all the loca-tions is computationally challenging to deal with altogether within a signal EDA process.In the proposed method,to take advantage of parallel computing power,the pattern mining is divided into two stages,local and global pattern mining.The local pattern min-ing is performed at each observation location to collect locally unique load patterns.And then,all local load patterns obtained from the individual observation locations are processed by a global-level pattern mining to identify FFL patterns.The local pattern identi?cations can be distributed to multiple processors

to

Fig.2Overall process of the proposed sensor layout

method

Fig.3Worst cycle identi?ed with time points,wc 1k and wc 2k ,via Rain?ow cycle counting

reduce the computational time since the interaction effects among the basic patterns are addressed by the global pattern mining. In the pattern mining,it should be considered that the same load patterns can be found in multiple locations.And load patterns which are insigni?cant at one location could be highly damaging at other locations,depending on the sensitivities of loads to fatigue damage.Hence the sensitivity needs to be incorporated along with the pattern mining.

3.2Pattern Amplification by Using Damage Based Sensitivity.Before pattern mining,the fatigue load vectors are weighted with damage based sensitivities to amplify hidden pat-terns in terms of fatigue damage according to the location they belong.The fatigue damage at a location is a function of stress ranges along the critical plane direction obtained from the previ-ous full fatigue analysis.At a given critical plane direction(h c) for the j th load history point,the stress is obtained as

r x1j?r xx jtr yy j

2

t

r xx jàr yy j

2

cos2h ctr xy j sin2h c(8)

where the plane stress components,r xx_j,r yy_j,and r xy_j,are from Eqs.(2)–(4).The damage based sensitivity is approximated by the stress sensitivity which will be unique at each observation location as

@r x1

@L i

?U xx ie1tcos2h cT=2tU yy ie1àcos2h cT=2

tU xy i sin2h c(9)

where U xx_i,U yy_i,and U xy_i are the three stress in?uence coef?-cients from the unit load stress analysis.The sensitivity vector which approximates the damage sensitivity is obtained by Eq.(10)at each candidate sensor location p.Then a matrix of pattern-ampli?ed fatigue load vectors(wFL p)is obtained by Eq.(11),which is essentially scaled by the damage based sensitiv-ity(DS p)for each fatigue loads at each location p

DS p?

@r x1

@L i

p

;i?1;2;:::;I

()

p?1;2;…;P(10)

wFL p?f wFL p k?DS P:?FL p k;k?1;…;K p g p?1;2;…;P

(11) Here,the operator(.*)is for the component wise vector by ma-trix multiplications.

3.3Local and Global Basic Pattern Identifications.The proposed method employs two stages—the local and global min-ing processes of the FFL patterns.Again,our goal in this study is to minimize the number of sensors across the target structure while all the FFL patterns are captured by the measured data. Therefore,identifying all the fundamental load patterns is the key task in the proposed method.Once the FFL patterns are identi?ed, they can be used to determine the optimum layout.

First,the local pattern mining is performed at each observation location p.For the simplicity,the superscript p for a sensor loca-tion is omitted in Eqs.(12)and(13).The pattern-ampli?ed fatigue load vectors are cross-compared to each other to obtain a normal vector correlation(NVC)which is de?ned by

NVC mn?

wFL T máwFL n

2

wFL T

m

wFL m wFL T

n

wFL n

m?1;…;K p;n?1;…;K p

(12)

where the superscript T indicates the transposition of the vector. The NVC measurement is essentially the same as the MAC[28]which is a common measure to estimate the correlation among the modal shapes in SHM.In this study,NVC measures the degree of correlation between two fatigue load vectors,instead of mode shapes.And the load patterns are ampli?ed with the damage-based sensitivity calculated at each observation location.In the local pat-tern identi?cation process,if any vector show high NVC,it will be taken as a dependent load pattern and excluded from wFL.However all fatigue load vectors that show the NVC values to all other vectors lower than a correlation threshold(corr_tol)are regarded as unique load patterns and kept in the local fatigue load(LFL)matrix as LFL?f wFL m j8NVC mn

n?mt1;…;l K p;m?1;2;…;l K p g

(13)

where l K p are the number of the identi?ed unique load vectors and the size of LFL is l K p?I.

This local pattern mining will eliminate correlated load patterns sequentially in the order of fatigue damage severity.At the end of the local pattern mining with a given correlation threshold,only uncorrelated patterns are stored in LFL as locally unique fatigue loads for the current observation location.The correlation thresh-old is a user de?ned control parameter for the pattern mining.It is expected the higher the correlation threshold,the larger the num-ber of unique fatigue load vectors.This local process is repeated for all candidate sensor locations and the matrix of locally unique fatigue load vectors at a location p is obtained as LFL p.Each LFL p could have the different size of l K p?I at each location p. Typically,the size of LFL p becomes much smaller than FL (Eq.(7))as only unique pattern fatigue loads are collected from each observation location.

Next,the global mining process is performed to identify FFLs for the entire structure.For the global process,all the LFL p matrices are appended into the one local fatigue load vectors(LFLV)matrix as in Eq.(14)where C is the total number of the identi?ed load pat-terns from all observation locations,and the size of LFLV is C?I

LFLV?f LFL1;LFL2;ááá;LFL P g

?f LFLV c j c?1;2;…;C g(14)

In the global process,the NVC measurements for the LFLV vectors are again compared to each other to?nd fundamentally unique fatigue load patterns through the entire observation loca-tions.However,unlike the local mining,the global process needs to consider a global NVC matrix which consists of multiple sets of the NVC values obtained by applying different damage based sensitivity ampli?cations of individual observation locations as

gNVC p c

1

c2

?

wLFLV p

c1

TáwLFLV p c

2

2

wLFLV p c

1

T wLFLV p c

1

wLFLV p c

2

T wLFLV p c

2

c1?1;…;C;c2?1;…;C;p?1;…;P(15) where

wLFLV p

c

?DS p:?LFLV p

c

The global NVC matrix starts with all LFLV load vectors in the beginning of the global process.However,if a pair of LFLVs shows higher values than the user de?ned correlation threshold at all the observation locations,they are taken as the same load pattern.The process is performed sequentially in the order of structural damage contribution until only FFL vectors are left (Eq.(16))

FFL q?f LFLV c

1

j8emin?gNVC p

c1c2

;p?1;2;…;P T

c2?c1t1;…;l C;c1?1;2;…;l C g(16)

Here,l C starts with the total number of LFLV and updated itself sequentially as any correlated LFLV vector is detected and removed from gNVC.As a result of the global mining process,the patterns of FFLs are obtained by

FFL ?f FFL q j q ?1;2;…;Q g

(17)

where Q is the total number of FFL patterns and the size of the FFL matrix becomes Q ?I .In most practical cases,the size of FFL is signi?cantly smaller than the originally measured load data.The process also keeps the association information (Eq.(18))of LFLV to the individual FFL patterns which are used in the next step to determine the sensor location selection

FFL q ?f LFLV q /LFLV h h ?1;2;…;H q g

(18)

Here,H q is the number of correlated local fatigue load vectors for the q th FFL pattern.

3.4Sensor Location Selection.The patterns in FFLs obtained from the previous step are not actual loads,but they represent fundamental patterns for the fatigue damage from the measured load data.As mentioned before,the FFL patterns are obtained according to the severity of fatigue damage.However,in this step,our goal is to select the minimum number of sensors across the target structure while all the FFLs are captured.

By using the association information of FFL,all LFL load vec-tors at the local observation locations are translated in terms of the FFL patterns.Since FFL is typically a smaller set than LFL,there could be many locations having the same FFL patterns.Consider-ing individual observation locations as design variables for the sensor layout,each variable has a different amount of information for the fatigue load patterns.Hence to select minimum observa-tion locations or the sensor placements,most signi?cant design variables are selected ?rst which can yield maximum information on the FFLs.It is a typical feature selection problem in data ana-lytics.This feature selection problem is basically a combinatorial optimization problem for selecting a minimum number of obser-vation locations considering discrete association relationships of FFL.A typical approach for the combinatorial optimization prob-lem is to use genetic algorithm with constraint for the combination rule [29].

In this study,a heuristic search method is adopted to ?nd the minimum sensor locations in terms of both fatigue damage and full coverage of fatigue load patterns.In a practical application,there would be additional considerations such as accessibility to install sensors,signal to noise sensitivity,geometrical layout requirements,and historical or highly expected fatigue failure locations.To address all the considerations in practice along with the FFL patterns,the numerical optimization approach would come into picture.

4Numerical Examples

As demonstrations of the proposed method,numerical exam-ples are presented in this section.First a basic and common struc-tural component,a cantilever beam,is presented to facilitate better understanding of the effectiveness of the proposed method.4.1I-Section Cantilever Beam.The cantilever beam described by Fig.4is used as a numerical demonstration of the proposed method.The cantilever beam has the I-type cross sec-tion.With one end ?xed,the other free side has two loading inputs:bending and axial.Material properties are assumed to be the typical steel properties of E ?205,000N/mm 2and ?0.3.As described in Sec.3,unit load stress analysis is performed to obtain the stress in?uence coef?cient data as shown in Fig.5.It is found that the bending stress (unit:MPa)is higher than the axial stress with the unit loads.Load history data which has a limited number of cyclic fatigue loads for the demonstration is shown in Fig.6.From the load history data,the fatigue damage from the repetitive segment is expected to occur.The fatigue analysis is performed by using the commercial fatigue life analysis code Fe-Safe [30].As discussed in Sec.3,the linear damage fatigue analysis with quasi-static stress history is performed with the maximum princi-pal stress algorithm and the SN curve for the ISO steel 1020from the material database built into Fe-safe.The detailed material fatigue strength properties and SN curve are shown in Table 1and Fig.7,respectively.The fatigue life contour over the cantilever beam is shown in Fig.8in terms of the repetitions of the given load history.

Since the load history is simple repetitions of the load block,only ?ve exact FFL patterns exist as shown in Table 2.Due to

the

Fig.4I-section cantilever

beam

Fig.5Stress plot with bending unit load

high magnitudes of axial forces versus bending,the overall NVC values of the loads are close to unit values as shown in Fig.9.The NVC results indicate all the load vectors are strongly correlated and can be combined into a single load vector.However,by applying the damage based sensitivity at the location close to the ?xed end,the NVC values become more distinctive for ?nding the patterns of the loads as shown in Fig.10.This shows the bene-?t of using the pattern-ampli?ed fatigue load vectors introduced in Sec.3.Based on the damage sensitivity of an observation loca-tion,the signi?cance of an individual FFL to the fatigue damage would be different.For example,at the location close to the ?xed boundary,it is expected the majority of the fatigue damage is from the bending dominant loads,such as FFL_01and FFL_02while the axial force,such as FFL_03,will contribute more dam-age at the locations close to the free end.

To ?nd the best sensor locations,a total of 48locations are con-sidered as candidate sensor locations as shown in Fig.11.Both top and bottom sides of marked locations in the ?gure are consid-ered.In the proposed EDA method,the number of

candidate

Fig.6Axial and bending load history data Table 1

SAE-1020Steel fatigue material property

Material property

Steel Ultimate tensile strength

393Cyclic strain hardening coef?cient (Mpa)1487Cyclic strain hardening exponent 0.3Basquin’s fatigue strength exponent

à0.135Cof?n–Manson fatigue ductility exponent à0.459Fatigue ductility coef?cient

0.2340Fatigue strength coef?cient (Mpa)855.0

Surface ?nish

Smooth

surface

Fig.7SAE-1020Steel SN

plot

Fig.8Cantilever beam fatigue analysis result

Table 2FFLs Axial (N)

Bending (N)FFL_011,800,00045,000FFL_021,800,000à45,000

FFL_031,800,0000FFL_041,800,00030,000FFL_05

1,800,000

à

15,000

Fig.9Five FFLs and their NVC

values

Fig.10Pattern-ampli?ed FFLs and their NVC values

locations considered is limited only by the available computa-tional power.The ?nal sensor placements are obtained by a se-quential process of local and global extractions for unique load vector patterns according to the process in Fig.2.For the pattern mining with the NVC measurements,damage based sensitivity vectors are calculated and utilized at each observation location.In this example,the desired damage coverage is set to 98%,which means the worst cycles will be extracted to cover 98%of fatigue damage at each location.The correlation threshold for the local and global pattern identi?cation is 98%.This means if any NVC value of two load vectors is less than 0.98,the vectors are kept as unique load patterns.Having a higher value of correlation thresh-old will result more FFL patterns since more LFLVs will be selected as unique load patterns.The purpose of this numerical example is to con?rm the accuracy and effectiveness of the pro-posed EDA method in extracting all the damaging FFL patterns from the given input load history and proposing a least number of sensor locations to capture all identi?ed FFLs.As a result,in the current cantilever beam example,the proposed method success-fully ?nds exact ?ve FFLs.And also it suggests that only two sen-sor locations indicated in Fig.12would be enough to capturing all FFLs out of 28candidate locations.It is noted that the sensor loca-tions are not on the ?xed boundary area where the fatigue damage

is most high as a potential fatigue failure location.Instead the pro-posed method selects the locations where both the bending and axial forces are distinctively contributing to the fatigue damage.Case study 1:With low fatigue life coverage,it can be expected less signi?cant worst cycles would be ignored in the EDA process.Figure 13shows the case study result with 90%fatigue life cover-age.The result of the sensor locations for this case study are still away from the ?xed boundary condition,but FFL_05,which is less damaging than other FFLs,is not selected as a unique load pattern.Therefore,by varying the fatigue life coverage and per-forming the EDA process,sensitivity of sensor locations to the FFL coverage can be estimated.

Case study 2:When the set of candidates are limited only on the area close to the ?xed boundary,even though the fatigue life coverage is back up to 98%as before,it is expected to ?nd only FFLs with high bending loads.Figure 14shows the

expected

Fig.11Candidate sensor locations (marked with black

squares)

Fig.12Sensor placement result w/fatigue life coverage

98%

Fig.13Case study 1—sensor placement result w/fatigue life coverage

90%

Fig.14Case study 2—sensor placement result w/fatigue life coverage 98%

result which lists only FFL_01and FFL_02as fundamental loads.It shows if sensors are installed on only the locations of high fa-tigue damage,it could potentially miss some other FFL contents.Therefore,to extract fatigue design loads,the sensor placements should be considered from the perspective of capturing fatigue load patterns rather than high fatigue damages.

4.2Industrial Example:Hydraulic Excavator Front Linkage Structure.To demonstrate the practicality of the pro-posed EDA framework for an industrial scale problem,the front linkage structure of a hydraulic excavator as shown in Fig.15is presented in this section.A general Excavator has three parts of front linkage bodies,usually referred to as a boom,stick,and bucket that are actuated by three main hydraulic cylinders.The boom structure which is the ?rst linkage body from the rotating platform will be investigated for the optimal sensor layout for the FFL pattern detection.The linkage point tagged as PT1in the boom ?gure is the hinge joint to the main platform,PT2is for a boom cylinder,PT3for a stick cylinder,and PT4is the linkage connection to the stick structure.The boom cylinder makes up and down motions,while the stick cylinder is usually for digging in and out positions.With many different con?gurations of the front linkage,excavators can perform many different applications.One of the common applications is truck loading in which an excavator loads materials on a truck as shown in Fig.15above.The truck loading consists of several operations,such as digging,lifting,rotating,dumping,and returning.During the course of operations,the boom structure will be under different loadings that come from the main platform vibrations with a counter weight mass,as well as from soil to bucket interactions.For the boom structure,there are total 14load channels as shown in Table 3where,for example,PT1FX and PT1MX stand for force and moment components in the x direction,respectively.Figure 16shows typical load histories at a few selected channels for the truck loading application data.In a typical design process,yielding loads de?ned from extreme operations are used for con-cept design exploration.However,fatigue damage failures which are different from yield failures would not be addressed correctly unless the yield loads are the same as the fatigue loads embedded in the load history data.Therefore by using the proposed EDA method,the fundamental damage loads from the load history are extracted and applied in the concept design development of the boom

structure.

Fig.15General hydraulic excavator and its front linkage boom structure

Table 3Load channel names for the boom structure

PT1PT2PT3PT4PT1FX PT2FX PT3FX PT1FX PT1FY PT2FY

PT3FY

PT1FY PT1FZ PT1FZ PT1MX PT1MX PT1MY

PT1MY

Fig.16Load history for truck loading application

As in the previous example,the structural fatigue life contour is assessed by using the multi-axial principal stress algorithm with the ISO steel 1020material property as shown in Fig.17.To ?nd FFLs and the best sensor layout for comprehensive damage assessment,50total locations shown in Fig.18are selected as ini-tial candidates.Again,in this proposed method,to cover the entire fatigue life range of the boom structure,we can select as many locations as our computational power allows.To extract FFLs,

the

Fig.17Fatigue life contour with the given load

history

Fig.18Initial candidate sensor locations (marked with black

squares)

Fig.19Optimum sensor layout for capturing all 16FFLs

fatigue damage coverage and the correlation threshold are set to 98%.For the result of local and global pattern mining,a total of 16FFLs (FFL01–FFL16)are identi?ed as unique fatigue load pat-terns that account for up to 98%of the fatigue damage from the given load history.It is also found only the six sensors shown in Fig.19are needed to capture the 16FFLs for the 98%damage and FFL correlation coverage.It is noted the scales and frequen-cies of FFLs need to be determined further in order to fully recover the same fatigue damage as the given load history,which is out of scope of the current research.Hence at this stage we will focus on the FFL patterns.In the Appendix,all 16FFLs are normalized by PT1FX and PT1MX for forces and moments,respectively,to visualize the patterns.For a few selected FFLs,Fig.20shows their distinctive structural deformations.FFL01shows primarily a boom bending deformation while FFL08makes twisting.The combination of bending and twisting is shown

by

Fig.20Stress contours and deformed shapes with FFL01,FFL04,and

FFL08

Fig.21High correlations among the FFL groups

FFL04.To obtain more insight on the obtained FFLs,two more studies were performed by changing(1)the damage coverage to 90%from98%,and(2)the correlation threshold to90%from 98%.

For the?rst case study,where we reduced damage coverage, some FFLs whose damages are not as signi?cant as others among the16FFLs are dropped down.The dropped ones are FFL03, FFL05,FFL09,FFL10,and FFL14.From this study,we can say the remaining FFLs are more important load vectors in terms of the damage contribution to the structure.However,some of the dropped ones,such as FFL09and FFL10,have unique patterns that are irreplaceable by any other remainders.On the other hand, in the second case study with the reduced correlation threshold, but with the previous98%damage coverage,only FFLs which show higher uniqueness or small values in NVC would survive. The dropped FFLs among the16FFLs are FFL03,FFL11,FFL12, FFL13,FFL14,and FFL15.Close observations reveal that FFL03 and FFL13have the similar patterns as FFL02,and the pattern of FFL04can cover FFL11and FFL12.Figure21shows the normal-ized FFL vectors and clearly indicates high correlations among the FFLs,which means the surviving one can potentially make up the damage characteristics of the other dropped ones.Therefore we can say the results from the second case study would better preserve potential damage characteristics by focusing on the unique load patterns instead of the damage coverage.

5Conclusion

Due to recent advancements on power electronics,many heavy machines are equipped with a variety of advanced sensors and control systems to maximize machine performance and availabil-ity.One of the next imminent challenges in advanced VPD would be how to process the huge amount of data generated by on-board sensors directly from job-sites and pull out useful and meaningful information for engineering designs and intelligent maintenance. The proposed EDA could play an important role in addressing this next engineering challenge.In this paper,a new sensor layout method with the EDA approach is proposed to effectively capture all critical fatigue load contents with a minimum number of sensors.The proposed method employs two level pattern iden-ti?cations—local and global fatigue load pattern mining.To dis-tinguish load patterns more effectively,damage-based sensitivity weights are applied before the NVC-based pattern mining.The proposed method is successfully demonstrated with numerical examples highlighting the basic logics of the proposed EDA method and the case studies of several sensor layouts.

As a next step of the study,to increase the effectiveness of the process to the large-size and complex problem,an optimization method can be investigated to address all the practical considera-tions,such as accessibility to install sensors,signal to noise sensi-tivity,geometrical layout requirements,historical or highly expected fatigue failure locations,and so forth.This methodology can be extended to develop fundamental fatigue design loads that can replace the full measured load in estimating structural durabil-ity in an effective and ef?cient manner,especially targeting the application in the concept design development.Also,as more measured data sets are collected for the similar group of machine operations,statistical inference of fatigue design loads can be obtained to address robustness based concept design against uncontrollable variability in real operational conditions. Acknowledgment

This research was supported by Caterpillar,Inc.and Wright State University Research Initiation Grant.This support is grate-fully acknowledged.

Appendix

The normalized vectors of forces and moments of16FFLs are listed here.The bars in the graphs are in the order of PT1FX, PT1FY,PT1FZ,PT2FX,PT2FY,PT3FX,PT3FY,PT4FX, PT4FY,PT4FZ,PT1MX,PT1MY,PT4MX,and PT4MY from the left in Fig.22.

References

[1]Dieter,G.E.,and Schmidt,L.C.,2013,Engineering Design,5th ed.,McGraw-

Hill,New York.

[2]Wang,L.,Shen,W.,Xie,H.,Neelamkavil,J.,and Pardasani, A.,2002,

“Collaborative Conceptual Design—State of the Art and Future Trends,”Com-put.-Aided Des.,34,pp.981–996.

[3]Worden,K.,and Burrows,A.,2001,“Optimal Sensor Placement for Fault

Detection,”Eng.Struct.,23(8),pp.885–901.

[4]Padula,S.L.,Palumbo,D.L.,Kincaid,R.K.,Asme,T.A.,and Ahs,A.,1998

“Optimal Sensor/Actuator Locations for Active Structural Acoustic Control,”

Proceedings of the39th AIAA/ASME/ASCE/AHS/ASC Structures,Structural Dynamics,and Materials Conference,AIAA-98-1865,Long Beach,CA.

[5]Sohn,H.,Farrar, C.R.,Hemez, F.M.,Czarnecki,J.J.,Shunk, D. D.,

Stinemates,D.W.,and Nadler,B.R.,2003,“A Review of Structural

Health Fig.22Normalized forces and moments of16FFLs

Monitoring Literature:1996–2001,”Los Alamos National Laboratory Report, Report https://www.360docs.net/doc/a48111056.html,-13976-MS.

[6]Meo,M.,and Zumpano,G.,2005,“On the Optimal Sensor Placement Techni-

ques for a Bridge Structure,”Eng.Struct.,27(10),pp.1488–1497.

[7]Kirkegaard,P.H.,and Brincker,R.,1994,“On the Optimal Location of Sensors

for Parametric Identi?cation of Linear Structural Systems,”Mech.Syst.Signal Process.,8,pp.639–647.

[8]Breitfeld,T.A.,1995,“Method for Identi?cation of a Set of Optimal Points

for Experimental Modal Analysis,”J.Anal.Exp.Modal Anal.,11(1), pp.1–9.

[9]Kammer,D.C.,and Brillhart,R.D.,1996,“Optimal Sensor Placement for

Modal Identi?cation Using System-Realization Methods,”J.Guid.,Control Dyn.,19,pp.729–31.

[10]Heo,G.,Wang,M.L.,and Satpathi,D.,1997,“Optimal Transducer Placement

for Health Monitoring of Long Span Bridge,”Soil Dyn.Earthquake Eng.,16, pp.495–502.

[11]Lam,H.-F.,and Yin,T.,2011,“Dynamic Reduction-Based Structural

Damage Detection of Transmission Towers:Practical Issues and Experimental Veri?cation,”Eng.Struct.,33(5),pp.1459–1478.

[12]Rezaei, D.,and Taheri, F.,2010,“Damage Identi?cation in Beams

Using Empirical Mode Decomposition,”Struct.Health Monit.,10(3),pp.

261–274.

[13]Cheraghi,N.,and Taheri,F.,2007,“A Damage Index for Structural Health

Monitoring Based on the Empirical Mode Decomposition,”J.Mech.Mater.

Struct.,2(1),pp.43–62.

[14]Wentzel,H.,2013,“Fatigue Test Load Identi?cation Using Weighted Model

Filtering Based on Stress,”Mech.Syst.Signal Process.,40,pp.618–627. [15]Kang,B.S.,Park,G.J.,and Arora,J.S.,2005,“Optimization of Flexible Multi-

body Dynamic Systems Using Equivalent Static Load Method,”AIAA J., 43(4),pp.846–852.

[16]Park,K.J.,Lee,J.N.,and Park,G.J.,2005,“Structural Shape Optimization

Using Equivalent Static Loads Transformed From Dynamic Loads,”Int.J.

Numer.Methods Eng.,63,pp.589–602.[17]Wickham,M.J.,Riley, D.R.,and Nachtsheim, C.J.,1995,“Integrating

Optimal Experimental Design Into the Design of a Multi-Axis Load Trans-ducer,”J.Eng.Ind.,117,pp.400–405.

[18]Oh, C.S.,2001,“Application of Wavelet Transform in Fatigue History

Editing,”Int.J.Fatigue,23,pp.241–250.

[19]Abdullah,S.,Choi,J.C.,Giacomin,J.A.,and Yates,J.R.,2006,“Bump

Extraction Algorithm for Variable Amplitude Fatigue Loading,”Int.J.Fatigue, 28,pp.675–691.

[20]Miner,M.A.,1945,“Cumulative Damage in Fatigue,”ASME J.Appl.Mech,

12(3),pp.A159–A164.

[21]Downing,S.D.,and Socie,D.F.,1982,“Simple Rain?ow Counting Algo-

rithms,”Int.J.Fatigue,4(1),pp.31–40.

[22]Haiba,M.,Barton,D.C.,Brooks,P.C.,and Levesley,M.C.,2002,“Review of

Life Assessment Techniques Applied to Dynamically Loaded Automotive Components,”Comput.Struct.,80,pp.481–494.

[23]Huang,L.,Agrawal,H.,and Kurudiyara,P.,1998,“Dynamic Durability Analy-

sis of Automotive Structures,”Society of Automotive Engineering,SAE Paper No.980695.

[24]Conle,F.A.,and Mousseau,C.W.,1991,“Using Vehicle Dynamics Simula-

tions and Finite-Element Results to Generate Fatigue Life Contours for Chassis Components,”Int.J.Fatigue,13(3),pp.195–205.

[25]Socie,D.F.,and Marquis,G.B.,“Multiaxial Fatigue,”SAE International,ed,

Warrendale,PA.

[26]Fayyad,U.,Piatetsky-shapiro,G.,and Smyth,P.,1996,“From Data Mining to

Knowledge Discovery in Databases,”Artif.Intell.(AI)Mag.,17(3),pp.37–54.

[27]Lan,H.,2011,Data Mining:Practical Machine Learning Tools and Techni-

ques,3rd ed.,Morgan Kaufman,Boston.

[28]Allemang,R.J.,2002,“The Modal Assurance Criterion(MAC):Twenty Years

of Use and Abuse,”Proceedings of the International Modal Analysis Confer-ence IMAC20,Los Angeles,CA,pp.397–405.

[29]Gen,M.,and Cheng,R.,2000,Genetic Algorithms and Engineering Optimiza-

tion,Wiley,New York.

[30]“Fe-Safe User’s Manual,”Safe Technology Limited,Shef?eld,UK,2011.