Component

Figure 5.1:Designproedure basedon theV-Model

Therefore,additional steps have to be inorporated into this model tomake

it possible to derive quantitative requirements of subsystems from overall

re-quirements ofa large-salesystem[78 ℄.

In the rst step, it should be laried, whih design variables of eah

sub-systeminuenewhihobjetivequantities,possiblyinterat withotherdesign

variables of other subsystems, and aet the overall performanes of a

large-sale system. This is done by reating a so-alled dependeny graph. In the

seond step, so-alled bottom-upmappings, heresurrogate models,have to be

established, whih evaluate thequantitative performanes of a large-sale

sys-tem, depending on the design variables of the subsystems. Surrogate models

mustbeassimpleaspossibleandasomplexasneessary. Inthethirdstep,the

so-alled top-downmappings,permissiblerangesofdesignvariablesarederived

from quantitative requirements formulated on the large-sale system. Figure

5.2 showsthe overviewof allthese three steps.

Figure 5.2:Three-enablersforderivingthequantitativerequirementsof

subsys-tems from theoverall requirements ofa large-sale system

Werstlarifywhatadependenygraphisandhowitisonstruted. Seond,

weexplainthebuttom-upmapping proedureandneessarymathematialand

physial surrogate models for ontrol systems, atuators, and vehiles. Third,

we desribe the proedure of top-down mapping and give a brief review of

the optimization method whih delivers permissible ranges of design variables

of atuators and ontrol systems with respet to unertainties and objetive

driving dynamis performanemeasures.

5.1 Dependeny graph

In the proess of designing an atuator and parametrization of a ontrol

sys-tem,a struturedmodelisrequired whih doumentsthe dependeniesamong

thedesign variables ofthesubsystemsand theobjetivedrivingdynamis

per-formane measures. This model is important, as it an manage know-how in

the proess ofthe development. A so-alled dependeny graph is usedfor this

purpose.

As explained in hapter 2, the vehile performane is identied in dierent

dynamis domains, namely longitudinal, lateral and vertial domain. Eah

domain isassessed by dierent assessment indies (AI). These AIsare targets

on thehighestleveloftheV-model,i.e. on thesystemLeveldepited ingure

5.1 . EahAIisharaterized bydierentmaneuversandtherelevant objetive

driving dynamisperformanemeasuresofthese maneuvers. Forexample,"AI

ornering" is one of the assessment indies in the domain of vehile lateral

dynamis. This AI is evaluated by dierent maneuvers suh as aeleration

while ornering (ACWC), brake while ornering (BRWC), quasi steady state

ornering(QSSC),Rampsteer,et. Refereningagaintothehapter2,eahof

thesemaneuvershasdierentobjetivedrivingdynamisperformanemeasures

whih are altered by the hassis' properties, namely subsystem properties in

the V-model. These subsystem properties are also aeted by the properties

ofomponentsomposingthesubsystem. Theexamplesofsuhomponentsin

thehassis areontrolsystems andthe atuators.

So, a dependeny graph is a graph in whih the measurable system

(AIs),objetivedrivingdynamisperformanemeasuresandomponent

prop-erties(ontrol systemparametersandatuatorsdesign variables)aredisplayed

asverties. Their dependenies areexpressedasanarrow.

5.2 Bottom-up mapping

For bottom-up mapping, quantitative evaluation of outputs as a funtion of

inputs, amodelisrequired whihrepresentsthe physial relations between

in-puts and outputs, i.e. design variables of atuators and ontrol systems and

objetive driving dynamis performane measures. The physial model of the

vehile, funtional model of the atuators, and the model of the ontrol

sys-temhavebeenpointedoutintheprevioushapters. Simulationofthesemodels

andlateroptimizationoftheoutputsofthe simulation areusuallyrestritedby

verylargeomputationaltime. Asinglesimulationofouromplex modeltakes

several hours or even a day. Therefore,the optimization problem, nding

per-missible ranges of design variables,is very time-onsuming, beauseit usually

needs morethan thousandsimulation iterations. Therefore,substitutemodels,

based on mathematial funtions, an be applied inorder to approximate and

preditthe realmodelbehaviorwithextremely loweralulation time[31 ℄,but

at a prie of yielding a small error on thenal result. Asmentioned before, a

meta-model an also predit theoutput of the physial modelwith respet to

new sets ofdesign variableswithout a need forfurther simulations.

Meta-models usedinthis work areassoiated withlassiation and

regres-sion methods of the supervised learning tehnique of mahine learning, whih

are trained byalreadyknowninput andoutputdata and arethenable to

pre-dit the output under new ombination of input parameters [62 ℄. The used

regression modelsinthis work areartiial neural networks. Thesupport

ve-tor mahine is then used for the lassiation. These meta-models need an

adequate numberof inputs andoutputs. Asa result, we introdue inthenext

of inputs and outputs. Afterwards, we give a brief reviewof howthe artiial

neural networks(ANN) andthe supportvetor mahine(SVM) workand why

weneed both ofthem.

5.2.1 Design of experiments

InordertotrainANNandSVMproperly,wehavetoonsidertworequirements

on thedesign spaeof alldesign variables (inputsto ANNandSVM):

•

^{The sampleof the designspae mustbewell}distributed.

•

^{Thedesignspaemustbeoveredasmuhaspossiblewithminimal}

num-berof sample pointsin order to aelerate theproess of the simulation

and optimization.

Theonsequeneoftherealizationofthesetworequirementsisthatthe

meta-modelan bewellttedto the realmodelandlater predit theoutputwellfor

a newombinationof inputvariables.

There aredierent kindsof samplingmethods [69℄. Someof them are

•

^Sobolsequene

•

^{SrambleSobolsequene}

•

^{Full fatorial sequene}

•

^{Halton sequene}

•

^{SrambleHalton sequene}

Thequestionarises,whihmethodfulllstheabove-mentioned requirements

most properly. Therefore, we introdue a term, alled disrepany, whih

dif-ferentiates between sampling methods. Imagining that the number of design

variables is

P

^{,the design spae islabeledas}

Ω _ds

^with

N

^samples,and

z

^isan

arbitrarypointfromthedesign spae

Ω _ds

^,

b[0, z]

^{isdened asaboxontaining}

all points loated inthe boxfrom origin to

z

^.

n(b)

^{isthe number of points in}

this boxand

V ol(b)

^{showsthevolumeofthebox. Aordingly,thedisrepany}

of thepoint

z

^{is omputed asfollows:}

Discrepancy(z) =

n(b)

N − V ol(b)

(5.1)

Anotherterm is dened asfollows:

D _∞ = max

z∈Ω ds

(Discrepancy(z))

^(5.2)

The smaller

D ∞

^{is , the better the method is in terms of the dened}

re-quirements. It means, the method with the smallest

D _∞

^{an sample the}

P-dimensional design spae

Ω _ds

^{eiently by overing most of its orners and}

edges. In this way, the data will be more informative by minimum possible

number of samples and aordingly simulations. [72℄ investigates all possible

methods ofsamplingbasedon theintrodued terms. Theresultisthat

Sram-bleSobolsequeneandSrambleHaltonsequenearethebestoptionsinterms

of

D _∞

^{,gure5.3 .}

0 0.2 0.4 0.6 0.8 1

0

0.2

0.4

0.6

0.8

1

Im Dokument On the Design of Actuator and Control Systems in Early Development Stages (Seite 108-112)