A System Approach 09

8/12/2019 A System Approach 09

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SISTEM REKAYASA SIPIL

Acuan : A Sistem Approach To Civil Engineering Planning And esign

Planning And Design Process

System Approach System Analysis

e!inition o! pro"lem e!inition o! s#stem componen

$athering o! data ata a%uisition and anal#sis

evelopment o!evaluate criteria

&"'ective !unction

(ormulation o! alternatives

Model "uilding andEsta"lishment o! constraints

Evaluation o! alternatives

Choosing "estalternative

&ptimi)ation and * or economic !easi"ilit#

(inal design*planand implementation

Management techni%uesPERT * CPM



PLA++I+$ * ESI$+Planning :

Is the !ormulation o! goals and o"'ectives that are consistent ,ith political- social-environmental- economic- technological- and aesthetic constrains. and the generalde!inition o! procedures designed to meet those goals and o"'ectives/

Should "e involved in all aspects o! an engineering pro'ect- including preliminar#Investigations- !easi"ilit# studies- detailed anal#sis and speci!ication !or implementationand*or construction- and monitoring and maintenance/

esign

The Accreditation 0oard !or Engineering and Technolog# 1A0ET 23456- de!ines design

The process o! devising a s#stem- component- or process to meet desired needs/ It is adecision7ma8ing process 1o!ten iterative6- in ,hich the "asic sciences- mathematics- andengineering sciences are applied to con!ert resources optimall# to meet a stated o"'ective/Among the !undamental elements o! the design process are the esta"lishment o!o"'ectives and criteria- s#nthesis- anal#sis- construction- testing- and evaluation/

9ill 123426 has stated that students ,ho have mastered the !undamentals o! design ,illha"ittuall#

2/ $et a correct ans,er to the correct pro"lem/ 0e counted on to : a/ Ma8e appropriate assumtions

"/ Select reasona"le values !or missing data ;/ Set up pro"lems in a concise ta"ular !rom ,hen iterative or repetitive calculation are re%uire

</ Esta"lish an e!!icient procedure "e!ore attempting to solve a pro"lem- and thanuse that procedure

=/ Relate mathematical models to their real7,orld counterparts>/ 9ave an understanding o! the limitations o! design !ormulas and pertinent design

Procedures?/ 9ave the a"ilit# to com!orta"l# and con!identl#

a/ Arrive at an appropriate solution "/ See8 the help o! a consultant 1specialist6

4/ etermine the most e!!icient computational tool- mind- calculator or computer

Interaction of planning and design

The planning and design processes complement each other/ Essentiall# the same stepsare re%uired in "oth- and the s#stem approach can "e applied e%uall# as e!!ectivel# toeither process/

The s#stem approach is essentiall# a planning !rame,or8 to improve the design process/



A!ter the designer determines the "est design !or the end product- "e it a high7rise "uilding or a section o! high,a#- the orderl# implementation 1construction6 o! the must "e planed/

SYSTEMSA s#stem is some collection o! components that are connected "# some t#pe o!interaction or interrelationship/ These components collectivel# ,ill respond to a giveninput and produce some !orm o! output/The s#stems approach can also "e thought o! as a s#stem- ,hich the tools o! s#stemsanal#sis comprising its components/

epicts the p#ramidal structure o! a t#pical hierarch# o! s#stems

S#stem

Transportation s#stem

su" s#stem su" s#stem

E@press,a# Air transport

s#stem s#stem

component component component component

Interchanges 9igh,a# Air tra!!ic Airport

segment control

Systems Approach

The s#stems approach is a general pro"lem7 solving techni%ue that "rings moreo"'ectivit# to the planning*design processes/ The s#stems approach esta"lishes the propermood o! in%uir# and helps in the selection o! the "est course o! action that ,illaccomplish a presscri"ed goal "# "roadening the in!ormation "ase o! the decision ma8er/



Activity overlap and feedback within systems approach

Time

Problem definition: ma# re%uire iteration and care!ul investigation- "ecause pro"lems#mtoms ma# mas8 the true cause the pro"lem/athering data: to asisst in planning and design decision ma8ing through the s#stemsapproach ,ill generall# "e done in con'uction ,ith several steps/ 1set varia"les and parameters through statistical o"servation- suggest ,hat mathematical models- and chec8the validit# o! an# estimated s#stem outputs6Development of eval!ative criteria: to measure the degree o! attainment o! s#stemo"'ectives/ 1some evaluative criteria ,ill provide an a"solute value o! ho, good thesolution is6

e!initiono! pro"lem

$atherin o! data

evelopmenteval/ crit/

(ormulation o! altr/

Evaluation o! altr/

Choosing "est altr/

(inal plan*design andimplementation



"orm!lation of alternative: is essentiall# the development o! s#stem models that iscon'unction ,ith evaluative criteria ,ill "e used in later anal#sis an decision ma8ing 1 itshould not "e assumed that mathematical model "uilding and optimi)ation techni%ues areeither re%uired or su!!icient !or application o! the s#stems approach/6

An optimi)ation model is a conceptual model consisting o! some o"'ective !unction1evaluative criterion6 that is to "e ma@imi)ed or minimi)ed su"'ect to some set o!constrains/ La,- patents- standards- or regulation Economics Resourse limitations Political and social presures Moralit# and ethical and pro!essional resposi"ilities Phisical principlesEval!ation of alternatives# numerous mathematical techni%ues are availa"le- includingthe simple@ method !or linear programming models- anal#tical and search techni%ues !orsolving nonlinear programming models- partial de!!erential e%uations- matri@ alge"ra-

various economic anal#sis- and deterministic or stochastic computer simulation/$hoosing the best alternatives: must "e made in the conte@t o! the o"'ective andevaluative criteria previousl# esta"lished- "ut also must ta8e into account non7%uanti!ia"le aspects o! the pro"lem such as aesthetic and political considerations/"inal planning%design and impementation: is the culmination o! the s#stems approach/

System analysis

S#stem anal#sis provides tools that- i! used e!!ectivel#- can greatl# assist inimplementation o! the s#stems approach/ S#stem anal#sis cannot replace the s#stemsapproach- "ut it is o!ten an integral part o! it- especiall# i! mathematical optimi)ation is to "e underta8en/Some o! the techni%ues that can "e used in s#stem anal#sis are as !ollo,s:

Linear programming Economic anal#sis#namic programming ecision anal#sisMultio"'ective anal#sis Management techni%ues

+et,or8 and linear graph anal#sis

Applications e&ercises

escri"e ,hat might "e involved in appl#ing each step o! the s#stem approach to each o!the pro'ects listed "ello,/ Approach the pro"lem !rom the perspective o! an engineer,or8ing !or the primar# group responsi"le !or sponsoring the pro'ect

A ne, interchange lin8ing an interstate high,a# ,ith a ne, sport comple@A ,aste,ater treatment plant !or a cit#A high7rise apartment "uildingA rail rapid transit s#stem !or a metropolitan area



DE"I'ITI(' (" P)(*+EM

Pro"lem de!inition is pro"a"l# the most di!!icult step in the application o! the s#stemsapproach/ It is also one o! the most di!!icult steps to descri"e/

Pro"lem de!inition is an investigative stage in ,hich the engineer has to decide i! a pro"lem does indeed e@ist/

Time- !inancial- la"or- and material constraints ma# have considera"le in!luence on allaspects o! pro"lem de!inition/

e!inition o! the pro"lem should also include the development o! preliminar# criteria,hich ,ill "e used to 'udge the validit# o! a possi"le solution/

Pro"lem de!inition is a compromise "et,een including all !actors in!luencing the pro"lem and 8eeping the pro"lem small enough to "e solved ,ith availa"le time "udget

and manpo,er resources/

,ierarchy of systems

S#stems can "e su"divided in to t,o t#pes : physical and organi-ational/ 1thetransportation s#stem !or a metropolitan area is an e@ample o! a ph#sical s#stem- ph#sicalsu"s#stems ,ithin this s#stem could include the e@press,a# s#stem- the rapid transits#stem- and the air transport s#stem6/The airport authorit# 1management structure6 ,ould "e classi!ied as an organi)ationalsu"s#stem ,ithin the air transport s#stem/

Structure s#stem ma#"e devided into deterministic and stochastic. eterministic s#stems- ever# particular input ,ill produce a predicta"le response/Stochastic s#stems one can not e@pect identical output ,hen the s#stem is su"'ected toidentical input/

S!bsystem and component interactions

To assist in de!ining the interaction among various levels o! the s#stem hierarch#-s#stems anal#sts generall# thin8 in terms o! goals/ ob0ective- and criteria/A goal is the speci!ic purpose or !unction o! a particular s#stem or su"s#stem/(b0ectives re!lect the ,a#s in ,hich the goal or goals o! the s#stem can "e met/$riteria indicate ho, the degree o! o"'ective attainment can "e measured/



Definition of hierarchy of systems

9#droelectric po,er pro'ect

Environmentals#stem

am Reservoir Po,er plant 9#drolog#

ater%ualit#

Landuse

Tur"inesRecreation $eneratorsSpill,a# amsection

Transmissions#stem

$eotechnic

Reservoirelevationcontrols#stem

Thermalstrati!ication

andtemperature

controls#stem

Se,agetreatment

ControlsSupportstructures

(oundation allsCranes#stem

(oundation (loorsInter!ace 9#draulic

iversiontunnels

Penstoc8s Controlstructures

Btilities rainage Structure



evinition o! goals and criteria

9#droelectric po,er pro'ect

$oal : Ma@imi)e return on investment

Reservoir am Po,er plant 9#drolog#

$oal : minimi)e constructioncosts

Criteria : unit and totalcosts

Spill,a# am section $eotechnic

$oal : minimi)ecomple@it# and

si)e

$oal : minimi)evolume o! dam

$oal : choose "est site !or dam

Criterion : minimum cost

(oundation Inter!ace 9#draulics

$oal : minimi)e necessit#!or grouting

$oal : minimi)e necessit#to remove over"urden

$oal : minimi)e tunnelinglength and di!!icult#

Criterion : volume o! groutre%uired

Criterion : #d; o! cut Criterion : tunneling cost



E&ample

A high,a# "ridge is to "e designed to cross a river/ This is a pro"lem that is generall#,ell de!ined ,ith %uanti!ia"le varia"les and parameters/ Pro"lem de!inition ,ould proceed as !ollo,s/The goals !or this "ridge s#stem ,ould "e the save and e!!icient movement o! the

re%uired volume o! tra!!ic/ &"'ectives !or the "ridge s#stem can "e identi!ied !rom thegoals o! the ne@t level o! su"s#stem/ These ,ould include: Pedestrian/ Sa!e passage o! pedestrians across the river Roadway/ Su!!icient carr#ing capacit# at minimum cost Approach/ Smooth transition !rom approach high,a#s to "ridge proper Support Structure/ Support "ridge live and dead load at minimum costControl System/ Maintain sa!e conditions ,hile ma@imi)ing throughput

The environment surrounding the pro"lem ,ould include the approach high,a#s- theriver- topograph# surrounding the site- and an# aesthetic considerations/ Approachhigh,a#s ,ould dictate appro@imatel# ,here the endpoints o! the "ridge ,ould have to "e and ,ould provide the tra!!ic input to the "ride/ The river conditions ,ould control

ho, long the "ridge must "e- and ,hat t#pe o! support might "e re%uired/ Surroundingtopograph# ,ould have to"e considered ,hen deciding alignment o! approachinterchanges and ramp and placement o! end a"utments o! the "ridge/Definition of system hierarchy for bridge pro0ect

Aesthetic considerations ma# dictate the !orm o! the "ridge structure i! it is to "e placedat a site that ,ill "e under pu"lic scrutin#/In de!ining the pro"lem environment- some insight must "e gained into ho, theremainder o! the steps o! the s#stems approach might "e underta8en/ ata that should "egathered and anal#sed can usuall# "e ascertained "# as8ing a series o! %uestions a"out the pro"lem/

Is the river naviga"le9o, man# tra!!ic lanes ,ill "e re%uired Should pedestrian tra!!ic "e accomodatedill intermediate support "e re%uired !or the "ride structure

0ridge

Pedestrian Road,a# Approach Controls#stem

Ramps

Supportstructure

AccessControl Sur!ace Su"grade Interchanges Road,a#supprort

0ridgesupport

Loadtrans!er s#stem

Sign Mar8ing Sign



hat aesthetic conditions should "e consideredhat are the !uture development plans !or the area

Some o! the data that could "e gathered and anal#)ed to ans,er these %uestions ,ould "e2/ Tra!!ic count : a6 volume 1vehicle6 "6 t#pe 1vehicle6 c6 Pedestrian/ Structural material strength and cost data

;/ idth- dept- and other river data</ (oundation conditions in river and at "oth ends o! "ride site=/ Legislated re%uirement>/ Land availa"ilit# and cost?/ Seismic data4/ +avigation data : a6 t#pe and si)e o! "oat "6 volume o! tra!!ic

c6 clearance re%uirement 3/ Aesthetic data : a6 site lines "6 surrounding land use 25/ (uture development plans or pro'ectionsEvaluative criteria !or the pro'ect ,ould "e the li!e c#cle costs o! the "ridge ,hich ,ouldta8e into account the initial cost o! the "ridge- estimated annual maintenance costs- and

the e@pected li!e o! the "ridge/ Cost ,ould "e determine su"'ect to speci!ied levels o! per!ormance !or the various su"s#stems- ,hich ,ould each incorporate their individualo"'ectives/ Aesthetic considerations ma# place a supplementar# evaluative criterion o!the pro"lem/ Adaptiveness o! the "ridge to !uture development and change ,ould alsohave to "e considered/The !ormulation o! alternatives ,ould include the di!!erent t#pes o! structure to "econsidered- length o! span re%uired- and num"er and t#pe o! supports/ Alternate tra!!ic pro'ections might "e use to estimate the num"er o! lanes re%uired/ Constrains on thealternatives ,ould "e include shipping restrictions and an# high,a# regulation re%uirements/ Even in a pro'ect o! this si)e- it ,ould "e impractical to tr# to develop aconstrained optimi)ation model o! the ,hole pro'ect/ Mathematical models could "e usede!!ectivel#- ho,ever- to anal#)e- and in some cases optimi)e- su"s#stem o! the "ridge/&verall optimi)ation could "e le!t up to the 'udgement o! the planners and designers/ +otall alternatives could "e considered- "ut e@perience ,ill dictate ,hich alternatives ,ould pro"a"l# have a changce o! "eing !easi"le/ Economic anal#sis o! the overall pro'ect anddesign anal#sis o! the various components ,ill assist in the evaluation o! the alternativesand the choice o! the "est alternatives/A!ter a decision has "een made as to the pre!ered alternative- !inal design ,ouldcommence/ This ,ould include detailed speci!ication o! all structural and phisicalcomponents o! the s#stem and development o! !a"rication and construction plans /Implementation ,ould include management o! the construction phase o! the pro'ect usingmanagement aids such as PE)T 1Program Eval!ation and )efiew Techni1!e6 and$PM 1$ritical Path Method6- and identi!ication and interpretation o! needs !or changesin the design as the pro'ect proceeds to,ard completion/Consideration o! these su"se%uent steps ,ill help in identi!#ing other s#stems andcomponents that should "e included in the de!inition o! the pro"lem environment/ This,ill reduce the need !or !eed"ac8 during su"se%uent steps- "ut not completel# eliminateit/ Engineer*planners must remain continuall# alert !or ne, in!ormation that ma# "ecomeavaila"le and ma# indicate the need !or !eed"ac8 to a previous step in the process/



Applications e&ercises

Per!orm each o! the activities listed at the end o! this pro"lem !or each o! the !ollo,ingsituations:

a/ You are an engineer overseeing the stud# o! the entire high,a# s#stem !or a largemetropolitas area

"/ You are responsi"le !or developing a plan !or a ne, commercial airport that ma# "e "uild in #our region

c/ Your client ,ants to "uild a high rise "uilding 1,ith "oth o!!ice and apartmentspace6 on the site o! an e@isting theater

d/ You are conducting a stud# o! ,ater diversion !rom one ,atershed to another !orthe purpose o! ,ater suppl#

The activities !or this pro"lem are:

2/ evelop a s#stems hierarch# !or each o! the given situations/ Include severallevels o! su"s#stems and components/ Put #oursel! in the place o! the engineer,ho ,ill "e responsi"le !or the anal#sis and decision ma8ing

/ escri"e ,hat ,hould "e re%uired to de!ine the pro"lem !or each situation given/Include ,hat ,ould "e necessar# to de!ine the pro"lem environment and possi"legoals- o"'ectives- and criteria !or the s#stems #ou have de!ine/ Indicate ,hatinteraction ,ill pro"a"l# occur among su"s#stems and components/

;/ escri"e ,hat t#pe o! data ,ould have to "e gathered throughout application o!the s#stem approach to each situation/ Indicate ho, di!!icult it ma# "e to ac%uirethe necessar# data in each case- and ,h# it is necessar# to gather the particulardata

</ evelop possi"le evaluative criteria !or the situation descri"ed/ escri"e ho,#our evaluative criteria might change depending on #our relationship to the pro"lem/ 9o, might #our relationship to the pro"lem a!!ect #our ,hole approachto the pro"lem



Ac1!isition and Analysis of Data

Attention to detail and good engineering 'udgement are essential ingredients in an#success!ul data ac%uisition program/

Care!ull# ac%uired data ma# "e anal#)ed to accomplish:2/ Model cali"ration and veri!ication/ Esta"lishment o! trends;/ Calculating "asic statistics !or camparison 1mean- mode- standard deviation-

etc6</ Estimation o! model constants 1regression6=/ Statistical correlation 1regression and anal#sis o! variance6>/ (re%uenc# anal#sis

Methods of Data athering

The e@ample sho,s that ,hat t#pes o! methods might "e used to gather data !or a storm7,ater characteri)ation stud#/

As part o! a se,er upgrading and redesign o! pro'ect- it is necessar# to characteri)e the%uantit# and %ualit# o! storm,ater to assist in determining i! storm,ater treatment might "e re%uired/ The !ollo,ing outline indicates ,hat methods o! data gathering might "eutili)ed to characteri)e the %uantit# and %ualit# o! storm,ater/

+iterat!re )eview

Previous studies o! same s#stemPrevious studies o! similar s#stemsPlans o! se,er s#stemTopographic and other maps

Personal Interviews

Municipal engineer Pu"lic ,or8s supervisor Residents along se,er right7o!7,a#- especiall# ,here pro"lems are suspectedEmplo#ees ,ho have ,or8ed on the se,er

Site reconnaisance

Condition and securit# o! access pointsInterior condition o! se,ersConditions o! out!all

Data ac1!isition program

(lo,rateT#pe o! primar# device

Method o! secondar# data ac%uisitionDualit# sampling



Method o! samplingT#pe o! sample to "e ta8en iscrete Simple compositeMethods o! sample anal#sis

2!ality $ontrol in Data Ac1!isition

Although errors ,ill e@ist in an# measurement program- %ualit# control ,ill ensure thatthese errors are minimi)ed and are largel# o! the t#pe that can "e compensated !or/Error is the di!!erence "et,een the measured value o! some %uantit# and the true or e@actvalue/ The amount o! error introduced depends on "oth the sensitivit# and accurac# o! themeasuring device and the a"ilit# and s8ill o! the o"server/Accurac# re!ers to the agreement "et,een the measurement and the true value o! the%uantit# "eing measured/ Accurac# is related to the statistical measures o! centraltendenc# or location 1mean- median and mode6/

Analysis

Measures o! Central Tendenc#

Mean: the mean is the arithmetic average o! data/Several rain gages are located in a large basin, but each covers a different proportion ofthe overall basin. It is desirable to calculate the weighted estimate of the mean rainfall

for this basin, using the area of coverage as the weighting factor for each rain gage

Median: the median is the middle value o! a set data values arranged in order o!magnitude

Mode: the mode is the value in a set o! data ,hich is repeated the most timesCalculate the: a! mean, b! median, and c! mode of the following set of traffic counts.

All data values are in terms of hundreds of vehicles per hour

Measures o! aria"ilit#

ariance and Standard eviation/ The most commonl# used measures o! varia"ilit#- thevariance and standard deviation- provide ,a#s o! %uanti!#ing the scatter o! data set ,ithrespect to its mean value

Coe!!icient o! variation/ The coe!!icient o! variation is a measure o! the relativedispersion o! data- ,hereas- the standard deviation is a measure o! the a"solute dispersion

egrees o! !reedom/ The degrees o! !reedom 1S6 is the num"er o! independent data thatare availa"le !or estimating a particular statistical parameter



9#pothesis Testing/ 9#pothesis testing involves setting up some h#pothesis and thenusing statistical procedures either to re'ect or accept that h#pothesis ,ith some level o!certainl#/

9#pothesis is !ormulated: 9o : F2 G F

The s#m"ol 9o is re!ered to as the null h#pothesis "ecause it is assume that there is nodi!!erence "et,een the parameters "eing elavuated/

"wo batches of steel have mean values of modulus of elasticity of #$ % &$' psi and #& %

&$' psi for sample si(e of ) and ', respectively. If the calculated t is *.)+, can the

hypothesis o: -& -* be re/ected, and if so, with what level of confidence0

t calculated *.)+ 12 n& 3 n* 4 * &*

Chec5 t 6,12 from the tablet $.&,&* &.7)*

t $.$+,&* *.&78

t $.$*,&* *.')&t $.$&,&* #.$++

t $.$$&,&* 9.#&)

t calculated lies between t $.$*,&* and t $.$&,&*

there for, the hypothesis, o: -& -* , can be re/ected at the $.$* significance level but

not at $.$& significance level.

In other word, we can infer that the two means are different with less than a * chancebeing in error. ;e are 8) sure that the two means are different, but not 88 sure.

T,o other samples are dra,n !rom the same t,o "atches o! steel/ The various values o!modulus o! elasticit# 1E6 are given in the ta"le "elo,

Measurement num"er 0atch 2 E125> psi6 0atch E125> psi62 ;5 3

;2 ;; ; 3 ;; < 4 ;5 = ;2 ;5

> ;2 ;2hat in!erence can "e dra,n a"out the e%ualit# o! strength "et,een these t,o "atches o!steel



)egression and correlation

(or linear regression ,ith one independent varia"le- the regression model "ecomesY G a H "

!or a- ,e get a G

∑ ∑∑ ∑

= =

= =

−

−

n

i

n

i

n

i

n

i

<i < <i

<i= <i=i

2 2

:

2 2 " G Y J aH

>%ample:

"he following dissolved o%ygen 1?!, temperature, and flow rate data are given for a station on the Connecticut River. Since dissolved o%ygen is a function of temperature in

pure waters, it is believed that a model of the form 1? a"! 3 b might be useful in

predicting what the dissolved o%ygen level in the river would be for various watertempetarures. "he flow rate data will not be used at this time, but they will be used in a

later section + G ; 1? G >/=5*; G 3/4<4 ∑ = ;-;;="i " G 2</=4

∑ 1?i"i G 3?=/=? ∑ =:

"i >>5?-23

Then a G 7 5/235 " G 1? 7 a " G 3/4<4 5/2312</=46 G 2/> & G 2/> J 5/231Ti6

Meas!res of oodness of "it for )egression E1!ations

At this point- it is important to "e a"le to estimate ho, ,ell the regression line !its themeasure data point/ In!erences can then "e made as to ho, accurate predicted values ma#

"e/ These ,ill !orm con!idence "ounds on the results/To "egin- de!ine the sum o! s%uares o! deviation o! the measure Y values- Yi- !rom theaverage value o! Y- Y- as

∑:

= G ∑=

−n

i

= =i

2

:61 and ∑∑ −= :: 61 < <i <

∑ ∑= −−=

n

i= =i < <i <=

26611

Coe!!icient o! determination G r G∑∑=

<= a

: G∑∑

:

::

=

< a

Correlation co!!icient G r G∑∑

:

::

=

< aG a

∑∑

:

:

=

<

hen calculating either r or r - it is help !ull to remem"er that



= =i < <i <=

n

i

−−=∑ ∑ 611 6 G ∑ −n

i

<= n <i=i

∑ ∑ −=n

i

< n <i < :: and ∑ ∑ −=

n

i= n=i=

::

>%ample:Calculate the correlation coefficient and coefficient of determination for the regression

developed

∑:

" G 2?23/2 ∑ :

1? G 34/2< and ∑n

i

"i1?i G 3?=/=?

R G 7 5/45 and R G 5/>;

The con!idence interval is given "# the estimated value *7 tshere t G value setected !rom students t distri"ution !or proper degrees o! !reedom

1n76 and desired pro"a"ilit# level s G estimated standard deviation !or the parameter o! varia"le

(or the slope o! the regression e%uation- the "est estimate o! the variance is given "#

s1a6 G∑

:

: 61

<

= s since s1Y6 G

:

:

−

∑n

= G

:

:::

−

−∑ ∑n

< a=

then s1a6 G∑

∑ −:

: 6:*1

<

n= G

6:16:1

:

:

:

−−

− ∑∑

n

a

< n

=

The estimated variance !or an# predicted value- Yi- is given "# the e%uation

S1Yi6 G s1Y6

−++

∑ :

:612

2 <

<i <

n

2or the water @uality problem described aboved, what is the 8+ convidence interval for

the slope a!0

t5/5=-2 G /545

s1a6 G∑

∑ −:

:6:*1

"

n 1?G

6:16:1

:

:

:

−−

− ∑∑

n

a

" n

1?G ;/2>2 @ 257

con!idence interval G 75/235 *7 /541;/2>2@2576 G 75/235 *75/5>>it can "e said that a lies "et,een 7/2< and 75/=>

Standard error o! estimate



S #-@ G

:

61

:

−

−∑

n

=i=i

n

i

APP+I$ATI('S

$alibration%3erification of Model

The acc!racy o! an# model is dependent on the correctness o! the model !ormulation- onthe %ualit# o! the input data used to drive the model- and on the a"ilit# to determinevalues !or the parameters o! the model accuratel#/

9igh7%ualit# !ield and*or la"orator# data can "e used in cali"ration and veri!ication toad'ust model parameters to achieve as accurate as possi"le results and to evaluate the precision 1reproduci"ilit# o! results6 o! the model/

$alibration is the process o! minimi)ing the error "et,een model output and actualmeasured s#stem output !or the same measured s#stem input/ This ma# involveregression anal#sis to estimate empirical parameters !or a deterministic or empiricalmodel or successive ad'ustment o! parameters o! a deterministic or stocastic model tota8e the model output agree ,ith the measured s#stem output ,ithin some errortolerance/

Sensitivity analysis o! the model ,ill help to identi!# parameters that- ,hen changed-,ill have little e!!ect on the model output/

3erification is the process o! testing ho, ,ell the model output compares ,ith realit#

The !ollo,ing discussion o! a metodolog# !or cali"rating storm,ater models ,ill serve toillustrade the process o! cali"ration and veri!ication as applied to an actual situation/Concepts and procedures that are developed in this application are e%uall# applica"le toother modelling situations/



(lo,chart SMM cali"ration program

Input !rom SMM

%uantit# portion

Calculate !lo,de!!erences

Calculate s%uaredde!!erence

Is %ualit#compared

Print %uantit#data

Measure data

input

Calculate !lo, rate

Is %uantit#compared

Calculate measuredmass emission rates Calculate predicted massemission rates !rom SMM

Calculate pollutan

Calculate s%uare di!!erences

Print %uantit# and %ualit# datastop

stop



(PTIMI4ATI(' M(DE+S

&ptimi)ation models are prescriptive models- in that the# suggest the "est methods o!s#stem operation- ,hich is a measure o! the degree o! attainment o! s#stem o"'ectives/

Design constraints- are speci!ied upper or lo,er "ounds on a design varia"le orrelationship ,hich includes several interdependent design varia"les/E@amples are minimum ,idth o! road,a#- ma@imum height o! a "uilding- or minimumlevel o! ,aste removal !rom se,age/

*ehavioral constraints- are derived !rom the "ehavioral re%uirements o! the s#stem/E@amples are limits on ma@imum stresses in !le@ural mem"ers- ma@imum displacemento! truss 'oints- and ma@imum a@ial compressive load to prevent "uc8ling in columns/

Consider the optimum placement o! supports !or a simpl# supported !le@ural mem"er/(or !le@ural mem"er-

Nma@ G I

Ac

,here M G "ending moment in the "eam

c G ma@imum distance !rom neutral a@is I G moment o! inertia o! the cross section a"out its

centroidal a@is Nma@ G ma@imum "ending stress !or an# particural cross section

(or a given cross section- the ma@imum "ending stress ,ill occure ,hen the "endingmoment is a ma@imum- either positive or negative/ In design- Nma@ is replace "# Nallo,

Nallo, O

I

Ac or

c

I A

allow

≤σ

the %uantit# I *c is a propert# o! the cross section o! the mem"er- and is usuall# called S-the section modulus/The usual procedure !or choosing a "eam is as !ollo,s:

2/ Compute and graph moment !unction/ (ind the ma@imum moment- either positive or negative;/ Bsing the allo,a"le stress 15-555 psi !or A ;> steel6- calculate the re%uired

section modulus

Sreg Gallow

A

σ

</ Choose the most economical 1least ,eight per !oot6 "eam !rom the steel ta"lesthat has S O Sreg a"out the appropriate centroidal a@is- and meet an# otherdimentional restrictions/

Since the Nallo, is a material propert# and is constant in this anal#sis- the sectionmodulus 1,hich governs the si)e o! "eam re%uired6 is directl# proportional to thema@imum "ending moment applied to the "eam/

E$('(MI$ "EASI*I+ITY (" P)(5E$T



hen investigating the economic !easi"ilit# o! pro'ect- it is necessar# to determine i! thetotal "ene!it and return on invesment are greater than the cost/ In economic term- adetermination has to "e made as to ,hether or not an alternative investment ,ould produce a greater return/ The methods !or anal#sis o! economic !easi"ilit# include:

2/ +et Present orth/ Bni!orm Annual +et Return;/ Rate &! Return</ 0ene!it*Cost Ratio

A !ree,a# is presentl# "eing "uilt/ Along this !ree,a#- there is an interchange that ,illconnect ,ith a rapid transit station that is to "e "uilt = #r in the !uture/ Three alternativeshave "een developed/

Alternative 6 0uild the interchange and station approach roads along ,ith the !ree,a#-!or a capital cost o! ;-555-555- and a #earl# maintenance cost o! 5-555

Alternative 7 0uild the interchange ,ith the !ree,a#- "ut ,ait = #r to "uild the approachroads/ 0uilding the interchange no, ,ill cost -555-555- and ,ill have an annualmaintenance cost o! 2=-555/ 0uilding the approach roads in = #r is estimated to cost -555-555 at that time/

Alternative 8 ait = #r to "uild "oth the interchange and the approach roads/ Theestimated cost o! "oth in = #r is =-555-555

I! it is assumed that cost in #ears su"se%uent to pro'ect completion 1 = #r in the !uture6 areappro@imatel# e%ual !or each o! the three alternatives- and that all alternatives haveappro@imatel# the same use!ul li!e- !ind the least costl# o! these alternatives !or prevailing interest rates o! 4 and 2Q/hile present ,orth anal#sis ,ill "e used in these calculations- the student should veri!#that e%uivalent uni!orm annual costs ,ill lead to the same conclutions/At a minimum attractive rate o! return o! 4Q- the !ollo,ing calculations can "e made:

Alternative 6

Capital cost ;-555-555Annual maintenance cost o! 5-555 !or = #r

5-5551BSP(- 5/54- =6 G 5-555 1;-33;6 ?3-4>5 Total ;-5?3-4>5

Alternative 7

Capital cost -555-555Annual maintenance cost o! 2=-555 !or = #r G 2=-555 1;-33;6 =3-43=Additional capital e@penditure in = #r

-555-555 1P(- 5-54- =6 G -555-555 15->45>6 2-;>2-55 Total ;-<2-53=

Alternative 8



Capital cost 5Annual maintenance cost 5Capital e@penditure in = #r G =-555-555 15->45>6 ;-<5;-555 Total ;-<5;-555

There!ore- at an 4Q attractive rate o! return- alternative 2 is the most economical/9o,ever- at an attractive rate o! return o! 2Q- alternative ; "ecomes the mostadvantageous- as is sho,n "# the !ollo,ing computations

Alternative 6

Capital cost ;-555-555Annual maintenance cost

5-555 1BSP(- 5/2- =6 G 5-555 1;/>5=6 ?-255 Total ;-5?-255

Alternative 7

Capital cost -555-555Annual maintenance cost G 2=-555 1;->5=6 =<-5?=Additional capital e@penditure in = #r

-555-5551P(- 5/2- =6 G -555-555 15/=>?<6 2-2;<-455 Total ;-244-4?=

Alternative 8

Capital e@penditure in = #r G =-555-555 15/=>?<6 -4;?-555 Total -4;?-555

(PTIMI4ATI(' TE$,'I29ES



&ptimi)ation is the process o! !inding the "est solution to a pro"lem ,ithin an esta"lishedset o! constraint/ It ,ill generall# involve minimi)ation o! cost or material- orma@imi)ation o! gain/ 9o,ever- optimi)ation is onl# possi"le i! there is a range o!choices availa"le/

The success o! optimi)ation depends primaril# on the a"ilit# o! the engineer toe!!ectivel# and realisticall# de!ine the pro"lem- and to develop a reasona"le model o! the pro"lem s#stem/ 1these processes have "een descri"e "e!ore6

(ptimi-ation by methods of calc!l!s

Some pro"lems that can "e modeled "# continuous !unctions can "e optimi)ed throughthe methods o! calculus

E@ampleMinimi)ed the cost o! a rectangular "o@ to hold ; #d; o! sand- ,ith the constraint that the

,idth o! the "ottom o! the "o@ must "e e%ual to 4 !t

Addtional In!ormation2/ There is no top o! the "o@/ Bnit cost o! sides and !ront end G R*!t

;/ Bnit cost o! second end G 2/= R*!t

</ Bnit cost o! "ottom G R*!t

H2 G length o! "o@H G height o! "o@

H

4

H2

A System Approach 09

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