Application of arti®cial neural networks to load
identi®cation
X.Cao a,b,*,Y.Sugiyama c ,Y.Mitsui d
chfa
College of Eng.,Shinshu Univ.,500Wakasato,Nagano 380,Japan
b
China Flight Test Establishment,Xi'an 710089,China c
College of Eng.,Univ.of Osaka Prefecture,Osaka 593,Japan
d
Dept.of Civil Eng.,College of Eng.,Shinshu Univ.,500Wakasato,Nagano 380,Japan
ointmentReceived 17December 1996;accepted 5February 1998
Abstract
The intended aim of the study is to develope an approach to the identi®cation of the loads acting on aircraft wings,which us an arti®cial neural network to model the load-strain relationship in structural analysis.
As the ®rst step of the study,this paper describes the application of an arti®cial neural network to identify the loads distributed across a cantilevered beam.The distributed loads are approximated by a t of concentrated loads.The paper demonstrates that using an arti®cial neural network to identify loads is feasible and a well trained arti®cial neural network reveals an extremely fast convergence and a high degree of accuracy in the process of load identi®cation for a cantilevered beam model.#1998Elvier Science Ltd.All rights rerved.
Keywords:Arti®cial neural network;Load identi®cation;Inver problem
1.Introduction
Accurate and reliable data on aircraft wing loads are highly necessary not only to design and develop an air-craft but also to draw up strength and rigidity speci®-cations for aircraft.However,due
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to the complexity of wing structure and loading conditions,it is di cult to determine accurate and reliable aircraft wing loads only by means of wind-tunnel tests or theoretical analysis.Therefore,it is desirable to obtain wing loads through ¯ight tests to supplement and con®rm the results from wind-tunnel tests and theoretical analysis [1].Unlike parameters such as ¯ight height or velocity,¯ight loads can not be directly obrved and measured in ¯ight.Conquently,it rais an inver it is required to identify ¯ight loads act-ing on aircraft wings on the basis of some kind of structural respon of the wing,such as the strain re-
你好吗的英语spon,which is caud by ¯ight loads and can be measured in ¯ight.
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Even though the relation between loads and the structural respon of the wing only depends on the wing structure itlf,due to the complexity of the wing structure,the relation can not easily be formulated.In most cas,while direct problems may be easily formu-lated,their inver problems are usually di cult or even impossible to be formulated.The solution to the problem is focud on ®nding a means of establishing a load-strain relationship that reprents dynamically mechanical characteristics of the wing structure.
Arti®cial neural networks have attracted consider-able attention and shown promi for modeling co
m-plex nonlinear relationships.Arti®cial Neural Networks are derived through a modeling of the human brain and are compod of a number of inter-connected units (arti®cial neurons)[2].
A signi®cant bene®t of using an ANN-bad model is its ability to learn relationships between variables with repeated exposure to tho variables.Therefore,instead of using an analytical relationship derived from
Computers and Structures 69(1998)63±78
0045-7949/98/$±e front matter #1998Elvier Science Ltd.All rights rerved.PII:S 0045-7949(98)00085-
6
PERGAMON
*Corresponding author.
mechanical principles to model a system,the arti®cial neural network learns the relationship through an adaptive training process.
Among various types of architecture of arti®cial neural networks,the multilayer neural networks have some attractive features[3]:(1)One can automatically construct a non-linear mapping function from multiple input data to multiple output data within the network in a distributed manner through a training process;(2) The trained network has a feature of the so-called `generalization',i.e.a kind of interpolation,such that the well-trained network estimates appropriate output data even for untrained patterns;(3)The trained net-work operates quickly in an application process. ANNs have the ability to consider both discrete as well as continuous variables.Massively parallel data processing is one of the main features of arti®cial neural networks.Arti®cial neural networks have the ability to abstract.Such networks can extract the core concept embedded in a quence of input patterns,and can therefore be ud to construct or identify an ideal-ized model[4].
Taking advantage of the ANNs described above,
this paper propos an approach to identify¯ight loads acting on a wing utilizing ANNs as the frame-work for constructing a model of the relationship of load and strain on the wing structure.The approach is shown in Fig.1and contains the following four sub-process.
1.Ground calibration test
grace什么意思An actual aircraft wing is ud as a calibrated object before a¯ight test and distributed loads are applyed as calibration samples that are lected on the basis of theoretical analysis and the design load envelope over a whole region,in which the aerodynamic center of distributed loads varies.Strain respons of the wing are then measured in order to gain data that will be ud in the next pha as learning data along with the applied loads,for the arti®cial neural networks.The ®rst pha is to prepare vast amounts of learning pat-terns for ANNs.Even though the obtained learning data ts are discrete measured data,the mechanical characteristic of the wing structure is contained in the data ts.
2.Training the arti®cial neural network
Using the strains as input signals given to the input units of the network,and loads as teaching signals (desired outputs),training the arti®cial neural network is performed iteratively until the error between actual and desired outputs reaches an acceptable level.Then, the con®guration of the arti®cial neural network for identifying loads acting on the investigated aircraft wing is decided.
In the cond pha,the``learning''and``generaliz-ation''ability of the ANN is invoked.The relation of the load-strain that exists inherently in the wing struc-ture but is di cult to formulate will be constructed automatically and embedded in the well-trained ANN.
3.Flight test
Measure the strain respons caud by aerodynamic loads in the main parts of the wing through¯ight tests.
4.Identi®cation of¯ight loads
Input¯ight-measured strains of the wing to the well-trained arti®cial neural network and identify¯ight loads bad on the outputs of the neural network.
By synthesizing the above description,it can be noted that a complicated structural analysis module
may be replaced by an arti®cial neural network model with this approach.Moreover,for the discusd pro-blem,this proposition has the advantage that it is possible to perform ground calibration tests using the objective aircraft to obtain learning data for ANNs, and ANNs can learn from the learning patterns e -ciently as well as accurately even though the patterns are the discrete actually-measured data[3].
As structures,in some cas,are extremely compli-cated and the mechanical properties or relations between external excitement and structural
respons Fig.1.An approach for the identi®cation of¯ight loads utiliz-ing arti®cial neural networks.
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X.Cao et al./Computers and Structures69(1998)63±78 64
are di cult to formulate,the arti®cial neural network model becomes a more adequate one avoiding compli-cated or even impossible theoretical analysis.In this n,ANNs are quite uful and prent a non-negli-gible advantage.
As the ®rst step of the study,the feasibility of using an arti®cial neural network to identify loads is investi-gated in the paper.An aircraft wing is simpli®ed into a cantilevered beam.Distributed loads are approximated by a t of concentrated loads.The paper demonstrates the applicability of an arti®cial neural network to the load identi®cation for a cantilevered beam model.2.Establishment of a Mechanical Model for Load Identi®cation
2.1.Mechanical model for load identi®cation
Becau identifying ¯ight loads acting on an aircraft wing utilizing arti®cial neural networks is a relatively new study and there are many factors that need to be studied before conducting ¯ight load identi®cation according to the propod approach,the applicability of arti®cial neural networks to loa
d identi®cation is ®rst studied in the work.Since the study is a simu-lation conducted at a laboratory,instead of utilizing an actual wing as an object,a cantilevered beam is investigated.In other words,an aircraft wing is simpli-®ed to a cantilevered beam (Fig.2).Nonuniform dis-tributed loads acting on the wing are approximated by a t of concentrated loads that are applied in a verti-cal direction to the beam axis as shown in Fig.3.Some ts of concentrated loads acting on the beam will be identi®ed bad on its strain respons after accomplishing the training of arti®cial neural net-works.
In order to verify the applicability of ANNs to load identi®cation,the identi®ed results need to be exam-ined by comparing them to the clod form results from some kind of theoretical calculation.The clod form results for this model can be obtained from the theoretical calculations bad on static mechanics.
The material of the beam is assumed to be a kind of alloy,which is linearly elastic E and its mod-ules of longitudinal elasticity is assumed to be
1Â105MPa(108kN/m 2
)and the bending rigidity EI is 5625kN m 2
.
Fig.2.Mechanical model for wing loads.
X.Cao et al./Computers and Structures 69(1998)63±7865
2.2.Preparation of learning data for ANNs
Since the study is conducted at a laboratory instead of a ground calibration test,the learning data to be adopted to train ANNs are prepared by theoretical analysis.Meanwhile,in order to examine the accuracy of the identi®ed results by a trained ANN,a number of data ts that will be ud as check patterns are also prepared.
Thirteen ts of simulation patterns are established.In each pattern,11concentrated loads and 11strain respons caud by the loads are contained.The pos-itions of acting points of the concentrated loads and measuring points of strains are located on the cantilev-ered beam which has been equally divided into 10por-tions (Fig.3).
Since there is no mechanical means of applying a concentrated load at beam-root,for the continuity and smoothness of the curve shaped by connecting the beginning ends of the load vectors,load P 11
is applied at the point where the coordinate in x -axis is near zero but not zero.Here,it is given that x P 11=H =0.002m as shown in Fig.3.The load P 11doesn't in¯uence the results much.In addition concerning E 1,if any measured point between points 1and 2is added,the strain at the measured point will in¯uence the results and is not zero.The intermediate values between the strain measured points are obtainable by interpolation.A ries of curves,which contain straight-lines,obli-que±lines with di erent gradient slopes,cone curved-lines,half circular-lines and ellip-lines with di erent radius lengths,parabola-lines and so on,can be obtained if the beginning ends of the concentrated load vectors are smoothly connected.
Seven patterns shown in Fig.4are ud as learning data for arti®cial neural networks,in which strains are ud as input signals and loads as teaching signals that reprent desired outputs.The remaining six patterns (Fig.13)are ud to check the accuracy of the ident-i®ed results by a trained ANN.3.Computational Principle of ANNs
The following ctions give a brief overview of the computational principle and learning algorithm.3.1.Computational principle of multilayer neural networks
To build an arti®cial neural network to perform some task,one must ®rst decide what kind of ANN is t
o be chon,how many units are to be ud and what kinds of units are appropriate.Both the structure of the network and the connectivity of its processor have a signi®cant in¯uence on its overall behavior.
Due to the attractive features mentioned previously,a multilayer neural network with input,output and inrted hidden layers of neurons,which is shown in Fig.5,is adopted in the study.
Multilayer neural networks can reprent any func-tion,when given enough units [5].This type of arti®-cial neural network is considered a fully-connected network,of which each input will in¯uence all output elements.The multilayer neural network can a ord a broad foundation on which the number of layers and neurons in each layer can be optionally altered accord-ing to a given problem.The neuron numbers in
input
dimensionalFig.3.Model for load identi®cation.
X.Cao et al./Computers and Structures 69(1998)63±78
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tryand output layers are usually decided according to an investigated aim.The numbers of hidden layers and neurons in each hidden layer are determined after con-sidering the type of problem and the computational speed and accuracy,which will be studied during the training of the ANN and discusd later.
Each neuron is a fundamental computational el-ement.Fig.6shows two typical neurons lected
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Fig.4.Patterns ud to train arti®cial neural networks.(Vertical corrdinates-left axis:concentrated load,N ;right axis:strain,Â10À5.Horizontal coordinate-coordinates of acting points of loads and measuring points of strains,M ).
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