Kapsel Geofisika_Sistem Dinamik

8/10/2019 Kapsel Geofisika_Sistem Dinamik

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PENGANTARSISTEM DINAMIK

Dr. Eng. AmiruddinGeofisika UNHAS

Email: [email protected]

Sumber: Dr. Asep Sofyan (Teknik Lingkungan ITB); Email: [email protected]


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Sistem dinamik: Pemodelan dan simulasi komputer untukmempelajari dan mengelola sistem umpan balik yangrumit (complex feedback systems), seperti bisnis, sistemlingkungan, sistem sosial, dsb.Sistem: Kumpulan elemen yang saling berinteraksi, berfungsi bersama

untuk tujuan tertentu.

Umpan balik menjadi sangat pentingMasalah dinamik Mengandung jumlah (kuantitas) yang selalu bervariasi Variasi dapat dijelaskan dalam hubungan sebab akibat Hubungan sebab akibat dapat terjadi dalam sistem tertutup yang

mengandung lingkaran umpan balik (feedback loops)

Apakah Sistem Dinamik itu?


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Cybernetics (Wiener, 1948): studi yang mempelajari

bagaimana sistem biologi, rekayasa, sosial, danekonomi dikendalikan dan diaturIndustrial Dynamics (Forrester, 1961): mengaplikasikanprinsip cybernetics ke dalam sistem industri System Dynamics : karya Forrester semakin meluas

meliputi sistem sosial dan ekonomiDengan perkembangan komputer yang sangat cepat,Sistem Dinamik menyediakan kerangka kerja dalammenyelesaikan permasalahan sistem sosial danekonomi

Sejarah


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1. Identifikasi masalah2. Membangun hipotesis dinamik yang menjelaskan

hubungan sebab akibat dari masalah termaksud3. Membuat struktur dasar grafik sebab akibat4. Melengkapi grafik sebab akibat dengan informasi5. Mengubah grafik sebab akibat yang telah dilengkapi

menjadi grafik alir Sistem Dinamik6. Menyalin grafik alir Sistem Dinamik kedalam program

DYNAMO, Stella, Vensim, Powersim, atau persamaanmatematika

Tahap Pemodelan Sistem Dinamik


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Berfikir dalam terminologi hubungan sebab

akibatFokus pada keterkaitan umpan balik (feedbacklinkages) diantara komponen-komponen sistem

Membuat batasan sistem untuk menentukankomponen yang masuk dan tidak di dalam sistem

Aspek Penting


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Berfikir sebab akibat adalah kunci dalam mengorganisir

ide-ide dalam studi Sistem DinamikGunakan kata `menyebabkan` atau `mempengaruhi`untuk menjelaskan hubungan antar komponen didalam sistemContoh yang logis (misalnya hukum fisika) makan berat bertambah api asapContoh yang tidak logis (sosiologi, ekonomi) Pakai sabuk pengaman mengurangi korban fatal

dalam kecelakaan lalu lintas

Hubungan Sebab Akibat


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Berfikir sebab akibat saja tidak cukup

Umpan balik: untuk mengatur/ mengendalikansistem, yaitu berupa suatu sebab yang terlibatdalam sistem namun dapat mempengaruhidirinya sendiri

Umpan balik sangat penting dalam studi SistemDinamik

Umpan balik (Feedback)


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Causal Loop Diagram (CLD)

Gaji VS Kinerja Gaji Kinerja Kinerja Gaji

Gaji Kinerja

Lelah VS TidurLelah tidurTidur lelah ?

Lelah Tidur

CLD menunjukkan struktur umpan balik dari sistem


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Lelah Tidur

Penanda CLD

Gaji Kinerja

+

+

+

-

+ : jika penyebab naik, akibat akan naik (pertumbuhan, penguatan), jika penyebab turun, akibat akan turun

- : jika penyebab naik, akibat akan turun, jika penyebab turun, akibatakan naik


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CLD dengan Positive Feedback Loop

Gaji Kinerja, Kinerja Gaji

Gaji Kinerja Semakin baik kinerja

Gaji akan semakin naik

Semakin gaji naik

Semakin baik kinerja

+

+

+

Semakin gaji naik

Semakin baik kinerja


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Lelah Tidur

The more tired I am

The more I sleep

The more I sleep The less tired I am

The less tired I am

The less I sleep

The less I sleep The more tired I am

+

-

-

Lelah Tidur, Tidur Lelah


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Pemahaman Sebab Akibat

Sales are poor

Sales force is weak

Overworked

Number is limited


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Augmenting CLD 2 - (Determining Loop

Polarity)

Positive feedback (reinforcing) loops Have an even number of signs Some quantity increase, a snowball effect takes over and that

quantity continues to increase The snowball effect can also work in reverse Generate behaviors of growth, amplify, deviation, and reinforce Notation: place symbol in the center of the loop

Negative feedback (balancing) loops Have an odd number of signs Tend to produce stable, balance, equilibrium and goal -

seeking behavior over time Notation: place symbol in the center of the loop

+

-


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Positive/Reinforcing Loops

Accelerating growth or acceleratingdecline


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Salary Performance, Performance Salary

Salary Performance+

+

+

Positive/Reinforcing Loops

The better I perform

The more salary I get






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Negative /Balancing Loop

Tired Sleep

The less tired I am

The less I sleep

+

-

-

Tired Sleep, Sleep Tired

The more tired I am

The more I sleep

The more I sleep The less tired I am

The less I sleep The more tired I am


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Balancing Loops

Body Temperature

Desired BodyTemperature

Temperature Gap

Adjust Clothing


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Balancing Loops

System reverts to status quoThe goals are implicit


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Loop Dominance

There are systems which have more than onefeedback loop within themThe dominating loop might shift over timeWhen a feedback loop is within another, one loop

must dominateStable conditions will exist when negative loopsdominate positive loops


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Combined Feedback Loops

(Case of Population Growth)

Birth rate Polulation Death rate-+

+ +

+ -


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Exogenous ItemsItems that affect other items in the system but are notthemselves affected by anything in the systemArrows are drawn from these items but there are noarrows drawn to these items

Sunlight reachingeach plant

Density of plants

Sunlight +

+

-

-


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Delays: The Sluggish Shower

Current WaterTemperature

TemperatureGap

Shower TapSetting

Desired WaterTemperature


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Delays

When you tell the story add the wordeventuallyCause the system to overshoot the target


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Delays

Systems often respond sluggishly

From the example below, once the trees are planted,the harvest rate can be 0 until the trees grow enoughto harvest

# of growing trees Harvest rate

Planting rate +

+

-

-

delay


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System Thinking

System Structure

Pattern of Behaviour

Events


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Basic System Behaviors

Exponential Growth

Goal Seeking

Oscillation

S-shaped Growth

S-shaped Growth with Overshoot

Overshoot and Collapse


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Exponential Growth

System Level

Inflow

Net increase rate

Positive feedback loops generate growth, amplify deviations,and reinforce change. An initial quantity of somethingstarts to grow, and the rate of growth increases.


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Goal SeekingNegative feedback loops seek balance, equilibrium, and

static. The quantity of interest starts either above orbelow a goal level and over time moves toward the goal.

System LevelCorrective Action

Discrepancy

GoalRate o f change


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OscillationTime delays cause the state of system to constantly

overshoots its goal or equilibrium state, reverses, thenundershoots, and so on. the quantity of interest fluctuatesaround some level.

System Lev elCorrective Action

Discrepancy

Perception

GoalRate of change

Perception Delay


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S-shaped GrowthNo real quantity can grow or decline forever, eventually one or

more constraints halt the growth. Initial exponential growth isfollowed by goal-seeking behavior which results in thevariable leveling o .

System LevelNet Increase Rate

Resource Adequacy

Carrying CapacityNormal Growth Rate


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S-Shaped Growth with Overshoot

Time delays in lead to the possibility that the stateof the system will overshoot and oscillate aroundthe carrying capacity.

System LevelNet Increa se Rate

Resource Adequa cy

Carrying CapacityNormal Growth Rate

Delayed Resource Ef fect


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Overshoot and CollapseThe ability of the environment to support a growing

population is eroded or consumed by the populationitself.

System LevelNet Increase Rate

Resource Adeq uacy

Erosion of Carrying C apacity

Normal Growth Rate

Carrying Capac ity

Consumption rate


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Stock & Flow Diagram


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Three different types of elements are (i)stock/level/accumulation, (ii) flow/rate, and (iii)informationThe stock and flow diagram shows relationshipsamong variables which have the potential to

change over time ( time based variables )Unlike a causal loop diagram, a stock and flowdiagram distinguishes between different typesof variables



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A stock is an accumulation of something (as

representing physical entities/elements/units),state variable rectangular boxA flow is the movement of the something" from onestock to another double line arrow

Rate of flow is controlled by valve Information is symbolized by an arrow Example : the money is a stock, and the transferoperation for the money is a flow



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Materials : this includes all stocks and flows ofphysical goods which are part of a production anddistribution process, whether raw materials, in-process inventories, or finished products.

Personnel : this generally refers to actual people,for example; hours of labour.

Capital equipment : this includes such things asfactory space, tools, and other equipmentnecessary for the production of goods andprovision of services.

Types of Stock & Flow


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Orders : this includes such things as orders for

goods, requisitions for new employees, andcontracts for new space or capital equipment.Orders are typically the result of somemanagement decision which has been made,

but not yet converted into the desired result.Money : this is used in the cash sense. That is, aflow of money is the actual transmittal ofpayments between different stocks of money.

Types of Stock & Flow


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MENU UTAMA STELLA


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Level

Rate

Auxiliary

Source/Sink

Constant

Flow arc

Cause-and-effect arc


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Level:Stock, accumulation, or state variable

A quantity that accumulates over timeChange its value by accumulating orintegrating ratesChange continuously over time even when

the rates are changing discontinuously


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Rate/Flow:

Flow, activity, movement

Change the values of levelsThe value of a rate is Not dependent on previous values of that rate But dependent on the levels in a system along

with exogenous influences


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Auxiliary: Arise when the formulation of a levels influence

on a rate involves one or more intermediatecalculationsOften useful in formulating complex rateequations

Used for ease of communication and clarityValue changes immediately in response tochanges in levels or exogenous influences


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Source and Sink:

Source represents systems of levels andrates outside the boundary of the modelSink is where flows terminate outside thesystem


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Example 2(Children and adults)

Births Children Children maturing Adults

+ + +

+- +

-

Births

children

Childrenmaturing

Adults


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average lifetime = 8Units: Year

birth rate = 0.125Units: fraction/Year

births = Population * birth rateUnits: rabbit/Year

deaths = Population / average lifetimeUnits: rabbit/Year

Population = INTEG(births - deaths,1000)Units: rabbit

RabbitPopulation

births deaths

birth rate average lifetime


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From Causal Loop Diagram

To Simulation Models 2R1

L

EquationsdL/dt = R 1 R 2

R2 = k 2*L

R1 = k 1

dL/dt = k 1 - k 2*L

Flow Graph

Block Model

R2

L1 L

1k 2

- k 1


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From Causal Loop DiagramTo Simulation Models 3

EquationsdL1/dt = R 1 R 2

dL2/dt = R 2 R 3

R1 = k 1

R2 = K 2 * L1

R3 = K 3 * L2 dL 1/dt = k 1 k2*L1 dL 2/dt = k 2*L1 K3*L2

R1

L1

Flow Graph

R2

L2

R3

L1 L1

k 2

-

-

k 1

L2 L2

Block Model

k 3


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Building constructionProblem statement

Fixed area of available land for constructionNew buildings are constructed while old buildings are demolishedPrimary state variable will be the total number of buildings over time

Causal Graph

Industrialbuildings

DemolitionConstruction

Fraction ofland occupied

Constructionfraction

Averagelifetime

for buildings

Average areaper building

Land available for Industrial buildings

+

+

+

+

++ -

-

-

-


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Simulation models

Industrial

Buildings (B)

Construction (C) Demolition (D)

Construction

fraction

(CF) Fraction ofland occupied

(FLO)Land available forindustrial buildings(LA)

Average areaper building(AA)

Average lifetimefor buildings(AL)

Equations

dB l/dt = C r D r

C r = f1(CF, B l)

Dr = f2(AL,B l)

CF = f3(FLO)

FLO = f4(LA,AA,B l)

Flow Graph


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Simulation Model Design and Execution,Fishwick, Prentice-Hall, 1995 (Textbook)Introduction to Computer Simulation: A systemdynamics modeling approach, Nancy Roberts etal, Addison-wesley, 1983

Business Dynamics: Systems thinking andmodeling for a complex world, John D. Sterman,McGraw-Hill,2000

References

Documents

Kapsel Geofisika_Sistem Dinamik