Improving distributed simulation in a workstation environment

Technological development brings more and more complex systems to the consumer markets. The time required for bringing a new product to market is crucial for the competitive edge of a company. Simulation is used as a tool to model these products and their operation before actual live systems are built. The complexity of these systems can easily require large amounts of memory and computing power. Distributed simulation can be used to meet these demands. Distributed simulation has its problems. Diworse, a distributed simulation environment, was used in this study to analyze the different factors that affect the time required for the simulation of a system. Examples of these factors are the simulation algorithm, communication protocols, partitioning of the problem, distributionof the problem, capabilities of the computing and communications equipment and the external load. Offices offer vast amounts of unused capabilities in the formof idle workstations. The use of this computing power for distributed simulation requires the simulation to adapt to a changing load situation. This requires all or part of the simulation work to be removed from a workstation when the owner wishes to use the workstation again. If load balancing is not performed, the simulation suffers from the workstation's reduced performance, which also hampers the owner's work. Operation of load balancing in Diworse is studied and it is shown to perform better than no load balancing, as well as which different approaches for load balancing are discussed.

CloudSimDisk: Energy-Aware Storage Simulation in CloudSim

Cloud Computing paradigm is continually evolving, and with it, the size and the complexity of its infrastructure. Assessing the performance of a Cloud environment is an essential but strenuous task. Modeling and simulation tools have proved their usefulness and powerfulness to deal with this issue. This master thesis work contributes to the development of the widely used cloud simulator CloudSim and proposes CloudSimDisk, a module for modeling and simulation of energy-aware storage in CloudSim. As a starting point, a review of Cloud simulators has been conducted and hard disk drive technology has been studied in detail. Furthermore, CloudSim has been identified as the most popular and sophisticated discrete event Cloud simulator. Thus, CloudSimDisk module has been developed as an extension of CloudSim v3.0.3. The source code has been published for the research community. The simulation results proved to be in accordance with the analytic models, and the scalability of the module has been presented for further development.

Flexible Multibody Simulation Approach in the Dynamic Analysis of Bone Strains Activity

The objective of this study is to show that bone strains due to dynamic mechanical loading during physical activity can be analysed using the flexible multibody simulation approach. Strains within the bone tissue play a major role in bone (re)modeling. Based on previous studies, it has been shown that dynamic loading seems to be more important for bone (re)modeling than static loading. The finite element method has been used previously to assess bone strains. However, the finite element method may be limited to static analysis of bone strains due to the expensive computation required for dynamic analysis, especially for a biomechanical system consisting of several bodies. Further, in vivo implementation of strain gauges on the surfaces of bone has been used previously in order to quantify the mechanical loading environment of the skeleton. However, in vivo strain measurement requires invasive methodology, which is challenging and limited to certain regions of superficial bones only, such as the anterior surface of the tibia. In this study, an alternative numerical approach to analyzing in vivo strains, based on the flexible multibody simulation approach, is proposed. In order to investigate the reliability of the proposed approach, three 3-dimensional musculoskeletal models where the right tibia is assumed to be flexible, are used as demonstration examples. The models are employed in a forward dynamics simulation in order to predict the tibial strains during walking on a level exercise. The flexible tibial model is developed using the actual geometry of the subject’s tibia, which is obtained from 3 dimensional reconstruction of Magnetic Resonance Images. Inverse dynamics simulation based on motion capture data obtained from walking at a constant velocity is used to calculate the desired contraction trajectory for each muscle. In the forward dynamics simulation, a proportional derivative servo controller is used to calculate each muscle force required to reproduce the motion, based on the desired muscle contraction trajectory obtained from the inverse dynamics simulation. Experimental measurements are used to verify the models and check the accuracy of the models in replicating the realistic mechanical loading environment measured from the walking test. The predicted strain results by the models show consistency with literature-based in vivo strain measurements. In conclusion, the non-invasive flexible multibody simulation approach may be used as a surrogate for experimental bone strain measurement, and thus be of use in detailed strain estimation of bones in different applications. Consequently, the information obtained from the present approach might be useful in clinical applications, including optimizing implant design and devising exercises to prevent bone fragility, accelerate fracture healing and reduce osteoporotic bone loss.

Control and Simulation of Batch Crystallization

Concerning process control of batch cooling crystallization the present work focused on the cooling profile and seeding technique. Secondly, the influence of additives on batch-wise precipitation process was investigated. Moreover, a Computational Fluid Dynamics (CFD) model for simulation of controlled batch cooling crystallization was developed. A novel cooling model to control supersaturation level during batch-wise cooling crystallization was introduced. The crystallization kinetics together with operating conditions, i.e. seed loading, cooling rate and batch time, were taken into account in the model. Especially, the supersaturation- and suspension density- dependent secondary nucleation was included in the model. The interaction between the operating conditions and their influence on the control target, i.e. the constant level of supersaturation, were studied with the aid of a numerical solution for the cooling model. Further, the batch cooling crystallization was simulated with the ideal mixing model and CFD model. The moment transformation of the population balance, together with the mass and heat balances, were solved numerically in the simulation. In order to clarify a relationship betweenthe operating conditions and product sizes, a system chart was developed for anideal mixing condition. The utilization of the system chart to determine the appropriate operating condition to meet a required product size was introduced. With CFD simulation, batch crystallization, operated following a specified coolingmode, was studied in the crystallizers having different geometries and scales. The introduced cooling model and simulation results were verified experimentallyfor potassium dihydrogen phosphate (KDP) and the novelties of the proposed control policies were demonstrated using potassium sulfate by comparing with the published results in the literature. The study on the batch-wise precipitation showed that immiscible additives could promote the agglomeration of a derivative of benzoic acid, which facilitated the filterability of the crystal product.

Methods and Models for Accelerating Dynamic Simulation of Fluid Power Circuits

The objective of this dissertation is to improve the dynamic simulation of fluid power circuits. A fluid power circuit is a typical way to implement power transmission in mobile working machines, e.g. cranes, excavators etc. Dynamic simulation is an essential tool in developing controllability and energy-efficient solutions for mobile machines. Efficient dynamic simulation is the basic requirement for the real-time simulation. In the real-time simulation of fluid power circuits there exist numerical problems due to the software and methods used for modelling and integration. A simulation model of a fluid power circuit is typically created using differential and algebraic equations. Efficient numerical methods are required since differential equations must be solved in real time. Unfortunately, simulation software packages offer only a limited selection of numerical solvers. Numerical problems cause noise to the results, which in many cases leads the simulation run to fail. Mathematically the fluid power circuit models are stiff systems of ordinary differential equations. Numerical solution of the stiff systems can be improved by two alternative approaches. The first is to develop numerical solvers suitable for solving stiff systems. The second is to decrease the model stiffness itself by introducing models and algorithms that either decrease the highest eigenvalues or neglect them by introducing steady-state solutions of the stiff parts of the models. The thesis proposes novel methods using the latter approach. The study aims to develop practical methods usable in dynamic simulation of fluid power circuits using explicit fixed-step integration algorithms. In this thesis, twomechanisms whichmake the systemstiff are studied. These are the pressure drop approaching zero in the turbulent orifice model and the volume approaching zero in the equation of pressure build-up. These are the critical areas to which alternative methods for modelling and numerical simulation are proposed. Generally, in hydraulic power transmission systems the orifice flow is clearly in the turbulent area. The flow becomes laminar as the pressure drop over the orifice approaches zero only in rare situations. These are e.g. when a valve is closed, or an actuator is driven against an end stopper, or external force makes actuator to switch its direction during operation. This means that in terms of accuracy, the description of laminar flow is not necessary. But, unfortunately, when a purely turbulent description of the orifice is used, numerical problems occur when the pressure drop comes close to zero since the first derivative of flow with respect to the pressure drop approaches infinity when the pressure drop approaches zero. Furthermore, the second derivative becomes discontinuous, which causes numerical noise and an infinitely small integration step when a variable step integrator is used. A numerically efficient model for the orifice flow is proposed using a cubic spline function to describe the flow in the laminar and transition areas. Parameters for the cubic spline function are selected such that its first derivative is equal to the first derivative of the pure turbulent orifice flow model in the boundary condition. In the dynamic simulation of fluid power circuits, a tradeoff exists between accuracy and calculation speed. This investigation is made for the two-regime flow orifice model. Especially inside of many types of valves, as well as between them, there exist very small volumes. The integration of pressures in small fluid volumes causes numerical problems in fluid power circuit simulation. Particularly in realtime simulation, these numerical problems are a great weakness. The system stiffness approaches infinity as the fluid volume approaches zero. If fixed step explicit algorithms for solving ordinary differential equations (ODE) are used, the system stability would easily be lost when integrating pressures in small volumes. To solve the problem caused by small fluid volumes, a pseudo-dynamic solver is proposed. Instead of integration of the pressure in a small volume, the pressure is solved as a steady-state pressure created in a separate cascade loop by numerical integration. The hydraulic capacitance V/Be of the parts of the circuit whose pressures are solved by the pseudo-dynamic method should be orders of magnitude smaller than that of those partswhose pressures are integrated. The key advantage of this novel method is that the numerical problems caused by the small volumes are completely avoided. Also, the method is freely applicable regardless of the integration routine applied. The superiority of both above-mentioned methods is that they are suited for use together with the semi-empirical modelling method which necessarily does not require any geometrical data of the valves and actuators to be modelled. In this modelling method, most of the needed component information can be taken from the manufacturer’s nominal graphs. This thesis introduces the methods and shows several numerical examples to demonstrate how the proposed methods improve the dynamic simulation of various hydraulic circuits.

Assessing the Environmental Value of Water Treatment Solutions in the Mining Industry

Environmental accountability has become a major source of competitive advantage for industrial companies, because customers consider it as relevant buying criterion. However, in order to leverage their environmental responsibility, industrial suppliers have to be able to demonstrate the environmental value of their products and services, which is also the aim of Kemira, a global water chemistry company considered in this study. The aim of this thesis is to develop a tool which Kemira can use to assess the environmental value of their solutions for the customer companies in mining industry. This study answers to questions on what kinds of methods to assess environmental impacts exist, and what kind of tool could be used to assess the environmental value of Kemira’s water treatment solutions. The environmental impacts of mining activities vary greatly between different mines. Generally the major impacts include the water related issues and wastes. Energy consumption is also a significant environmental aspect. Water related issues include water consumption and impacts in water quality. There are several methods to assess environmental impacts, for example life cycle assessment, eco-efficiency tools, footprint calculations and process simulation. In addition the corresponding financial value may be estimated utilizing monetary assessment methods. Some of the industrial companies considered in the analysis of industry best practices use environmental and sustainability assessments. Based on the theoretical research and conducted interviews, an Excel based tool utilizing reference data on previous customer cases and customer specific test results was considered to be most suitable to assess the environmental value of Kemira’s solutions. The tool can be used to demonstrate the functionality of Kemira’s solutions in customers’ processes, their impacts in other process parameters and their environmental and financial aspects. In the future, the tool may be applied to fit also Kemira’s other segments, not only mining industry.

Simulation of structural stress history based on dynamic analysis

Modern machine structures are often fabricated by welding. From a fatigue point of view, the structural details and especially, the welded details are the most prone to fatigue damage and failure. Design against fatigue requires information on the fatigue resistance of a structure’s critical details and the stress loads that act on each detail. Even though, dynamic simulation of flexible bodies is already current method for analyzing structures, obtaining the stress history of a structural detail during dynamic simulation is a challenging task; especially when the detail has a complex geometry. In particular, analyzing the stress history of every structural detail within a single finite element model can be overwhelming since the amount of nodal degrees of freedom needed in the model may require an impractical amount of computational effort. The purpose of computer simulation is to reduce amount of prototypes and speed up the product development process. Also, to take operator influence into account, real time models, i.e. simplified and computationally efficient models are required. This in turn, requires stress computation to be efficient if it will be performed during dynamic simulation. The research looks back at the theoretical background of multibody dynamic simulation and finite element method to find suitable parts to form a new approach for efficient stress calculation. This study proposes that, the problem of stress calculation during dynamic simulation can be greatly simplified by using a combination of floating frame of reference formulation with modal superposition and a sub-modeling approach. In practice, the proposed approach can be used to efficiently generate the relevant fatigue assessment stress history for a structural detail during or after dynamic simulation. In this work numerical examples are presented to demonstrate the proposed approach in practice. The results show that approach is applicable and can be used as proposed.

Kaivoslastauskoneen hybridisointianalyysi virtuaali- ja in-loop -simuloinnin avulla

Työssä tutkitaan raskaiden työkoneiden hybridisointimitoitusta simuloimalla. Työssä esitetään simulation-in-the-loop-simulointiin perustuva järjestelmä, jolla esimerkkitapauksena oleva kaivoslastauskone työympäristöineen voidaan mallintaa mekaaniselta osaltaan monikappaledynamiikkaan perustuvalla ohjelmistolla ja hybridijärjestelmän osalta Simulinkissa. Yhdistetty simulointi mahdollistaa hybridityökoneen virtuaalimallin ohjaamisen käyttäjän toimesta reaaliajassa. Simuloinnista saadaan tuloksena mm. työsykli, jota voidaan käyttää hybridisointimitoitukseen. Hybridisointi toteutetaan kahdella erilaisella kokoonpanolla, joista analysoidaan suorituskykyä sekä polttoaineen kulutusta. Tuloksia verrataan pelkästään dieselmoottoria voimanlähteenä käyttävään lastauskoneeseen. Työssä tehty tutkimus osoittaa, että (sarja-) hybridisoinnilla voidaan saavuttaa merkittäviä etuja raskaiden työkoneiden polttoainetehokkuudessa. Dieselmoottoria voidaan ajaa sellaisessa staattisessa toimintapisteessä, jonka hyötysuhde on korkea riippumatta työkoneen kuormituksesta. Saavutettu hyöty on toteutetussa tutkimuksessa parhaimmillaan jopa 56 % vähennys polttoaineenkulutuksessa. Lisäksi tarvittava dieselin nimellisteho pienenee huomattavasti. Tutkimuksen osana esitellään myös Hardware-in-the-Loop -laitteisto, jonka avulla voidaan liittää oikea sähkömoottori ja taajuudenmuuttaja osaksi virtuaalisesti simuloitua työkonetta.

Simulation model of wind turbine gearbox and lubrication system

As increasing efficiency of a wind turbine gearbox, more power can be transferred from rotor blades to generator and less power is used to cause wear and heating in the gearbox. By using a simulation model, behavior of the gearbox can be studied before creating expensive prototypes. The objective of the thesis is to model a wind turbine gearbox and its lubrication system to study power losses and heat transfer inside the gearbox and to study the simulation methods of the used software. Software used to create the simulation model is Siemens LMS Imagine.Lab AMESim, which can be used to create one-dimensional mechatronic system simulation models from different fields of engineering. When combining components from different libraries it is possible to create a simulation model, which includes mechanical, thermal and hydraulic models of the gearbox. Results for mechanical, thermal, and hydraulic simulations are presented in the thesis. Due to the large scale of the wind turbine gearbox and the amount of power transmitted, power loss calculations from AMESim software are inaccurate and power losses are modelled as constant efficiency for each gear mesh. Starting values for simulation in thermal and hydraulic simulations were chosen from test measurements and from empirical study as compact and complex design of gearbox prevents accurate test measurements. In further studies to increase the accuracy of the simulation model, components used for power loss calculations needs to be modified and values for unknown variables are needed to be solved through accurate test measurements.

Mechanical design and optics simulation of the illuminated Volvo Iron mark

Utilization of light and illumination systems in automotive industry for different purposes has been increased significantly in recent years. Volvo as one of the leading companies in manufacturing of luxury cars has found the great capacity in this area. The performance of such an illumination systems is one of the challenges that engineers in this industry are facing with. In this study an effort has been made to design a system to make the iron mark of Volvo being illuminated and the system is being evaluated by optics simulation in software using Ray optics method. At the end, results are assessed and some optimizations are carried out. Different kind of light guides, front side of the iron mark and some possible arrangement for LED also evaluated and different materials tested. The best combination from uniformity, color and amount of luminance aspect selected as a possible solution for this special project which can be used as a base for further studies in Volvo.

Dynamic modeling and simulation of the airflow cleaning device

The objective of the work is to study the flow behavior and to support the design of air cleaner by dynamic simulation.In a paper printing industry, it is necessary to monitor the quality of paper when the paper is being produced. During the production, the quality of the paper can be monitored by camera. Therefore, it is necessary to keep the camera lens clean as wood particles may fall from the paper and lie on the camera lens. In this work, the behavior of the air flow and effect of the airflow on the particles at different inlet angles are simulated. Geometries of a different inlet angles of single-channel and double-channel case were constructed using ANSYS CFD Software. All the simulations were performed in ANSYS Fluent. The simulation results of single-channel and double-channel case revealed significant differences in the behavior of the flow and the particle velocity. The main conclusion from this work are in following. 1) For the single channel case the best angle was 0 degree because in that case, the air flow can keep 60% of the particles away from the lens which would otherwise stay on lens. 2) For the double channel case, the best solution was found when the angle of the first inlet was 0 degree and the angle of second inlet was 45 degree . In that case, the airflow can keep 91% of particles away from the lens which would otherwise stay on lens.

Todennäköisyyspohjaisen paloanalyysimenetelmän kehittäminen ydinvoimalaitoksella

Diplomityössä on tutustuttu ydinvoimalaitosten paloriskejä käsittelevään todennäköisyyspohjaiseen turvallisuusanalyysiin. Tavoitteena on ollut Olkiluoto 1 ja 2 laitosyksiköiden paloanalyysimenetelmän kehittäminen. Työssä esitetään paloanalyysin pääpiirteet, kaksi erilaista palotaajuuksien estimointimenetelmää sekä palojen leviämisen arviointimenetelmiä. Palotaajuuksien estimointimenetelmistä keskitytään Berryn menetelmän sekä NUREG/CR-6850-palotaajuuslaskentamenetelmän tarkasteluun. Palon leviämisen arvioinnissa on esitetty kolmen erilaisen virtausteknisen laskentatyökalun perusteet sekä palon leviämistodennäköisyyksiä arvioivan Probabilistic Fire Simulator (PFS) -ohjelman käyttöä. Työn aikana on laskettu molemmilla palotaajuuden estimointimenetelmillä palotaajuuksia eri tyyppisille huonetiloille. Berryn menetelmän palotaajuudet olivat pääosin alhaisempia kuin NUREG/CR-6850-menetelmällä lasketut palotaajuudet. Palon leviämistarkastelussa on tutkittu ydinvoimalaitoksen relehuoneen tulipaloa. PFS:n avulla laskettujen leviämistodennäköisyyksien arvoja on vertailtu TVO:n paloanalyysissa käytettyihin kvalitatiivisiin peittokertoimiin. Palon leviämistodennäköisyys eri osajärjestelmien välillä todettiin suuresti riippuvan analyysissaoletetuista vaurioitumislämpötiloista. Tutkittuja menetelmiä hyödyntäen diplomityössä kehitettiin paloanalyysimenetelmäkuvaus. Menetelmäkuvauksessa huonetilojen paloriskit kartoitetaan aluksi Berryn menetelmällä. Näin kaikille laitoksen huonetiloille saadaan arvioitua palotaajuus sekä paloalkutapahtumaluokkien sydänvauriotaajuus. Seuraavaksi suoritetaan valintamenettely, jossa valitut kriteerit täyttäville huonetiloille tehdään tarkentava palotaajuuslaskenta. Tarkentava palotaajuuslaskenta perustuu NUREG/CR-6850-menetelmän mukaisesti huonetilojen realistisiin syttymislähteisiin. Kriittisimpien huonetilojen osalta palon leviämisen arviointiin on tarkoitus hyödyntää numeerista simulointia.

Kaupallisen reaaliaikasimulointiohjelmiston mahdollisuudet mekatronisen konejärjestelmän tuotekehityksessä

Työn tavoitteena oli hankkia ja rakentaa kaupallisilla ohjelmistoilla ja laitteistoilla toteutettu reaaliaikasimulaattori. Työssä keskityttiin erityisesti valmiin Patu 655 puutavarakuormaimen simulointimallin visualisointiin reaaliaikasimulaattoriin hankitulla 3D-animointiohjelmalla. Lisäksi työssä selvitettiin reaaliaikasimuloinnin mahdollisuuksia konejärjestelmän tuotekehityksessä. Reaaliaikasimulaattorina käytettiin dSPACE:n reaaliaikasimulointiin valmistamia kaupallisia laitteita ja ohjelmia. Puutavarakuormaimen simulointimalli käännettiin simulaattorissa suoritettavaksi, jonka jälkeen mallin liikkeet visualisoitiin käyttämällä RealMotion 3D-animointiohjelmaa. Animoitu grafiikka tuotiin sekä AutoCAD- että ADAMS -ohjelmasta. Työn tuloksena saatiin hankittua reaaliaikasimulaattori, jonka havaittiin olevan toimiva kokonaisuus. Puutavarakuormaimen ja muiden simulointimallien automatisoitu kääntö simulaattoriin onnistui hyvin. Simulointimallien visualisointi toimi sujuvasti käytetyn 3D-animointiohjelman avulla. Konejärjestelmien tuotekehitysprosessia havaittiin voitavan nopeuttaa reaaliaikasimulaattorin avulla.

Tapahtumapohjainen simulointi kuljetusketjun automatisoinnin kehittämisessä

Työn tavoitteena oli tutkia kuljetusketjun automatisoinnin kehittämistä tapahtumapohjaisen simuloinnin avulla. Työn teoria osassa käsitellään yleisellä tasolla simuloinnin teoriaa, siihen liittyviä käsitteitä ja erityisesti simulointiprojektin läpiviennin vaiheita. Tässä osassa saadaan vastaukset seuraaviin kysymyksiin: - Mitä tapahtumapohjaisella simuloinnilla tarkoitetaan? - Mitkä ovat simuloinnin hyödyt ja rajoitteet? - Mitä käyttökohteita simuloinnilla on? - Minkälaisia ohjelmia simulointiin käytetään? - Mitä vaiheita simulointiprojekti sisältää? Soveltavassa osassa tutkitaan kuinka tapahtumapohjaista simulointia hyödynnettiin Veto-Ketju -projektissa ja millaisia tuloksia rakennetulla simulointimallilla saavutettiin. Veto-Ketju -projekti käsittelee kuljetusketjun sekä varasto- ja satamakäsittelyn tehostamista automatisoinnin avulla. Projektin vetäjänä ja automaattisen tavarankäsittelyjärjestelmän toimittajana on Pesmel Oy ja satamatoimintojen ja logistiikan asiantuntijana SysOpen-konserniin kuuluva suunnittelu- ja konsulttitoimisto EP-Logistics Oy. Paperiteollisuudesta mukana ovat UPM-Kymmene ja M-real, satamaoperaattorina toimii Rauma Stevedoring ja kuljetusoperaattorina VR Cargo. Veto-Ketju –projektin simulointitutkimuksessa varmistettiin suunnitellun automaattisen junavaunujen purkausjärjestelmän toiminta ennen sen käyttöönottoa ja tutkittiin erilaisten toimintatapojen vaikutuksia satamatoimintoihin, satamassa tarvittavien resurssien määrään ja määritettiin tarvittavien varastojen koko. Simulointimallin avulla pystyttiin osoittamaan selkeästi erilaisten toimintavaihtoehtojen erot. Tällä tavoin saatiin tuotetuksi lisää tietoa päätöksenteon tueksi muun muassa järjestelmän sijoituspaikan ja mahdollisen uuden varaston rakentamisen suhteen.

Strategisten reaalioptioiden mallintaminen Monte Carlo -simulointimenetelmällä, case Voest Alpine Stahl Ag

Tutkielman päätavoitteena oli selvittää, miten Monte Carlo –simulointi soveltuu strategisten reaalioptioiden arvonmääritykseen. Tutkielman teoriaosuudessa käytiin läpi reaalioptioteoriaa ja Monte Carlo –simulointimenetelmää toiminta-analyyttisella tutkimusotteella. Tuloksena todettiin, että simulointimenetelmää on reaalioptioiden yhteydessä yleensä käytetty, kun muu menetelmä ei ole ollut mahdollinen. Tutkielman pääpaino on tapaustutkimukseen pohjautuvassa empiriaosuudessa, jossa rakennettiin päätöksentekometodologista tutkimusotetta seuraten simulointimalli, jolla tutkittiin Voest Alpine Stahl Ag:n vaihtoehtoisten hinnoittelustrategioiden taloudellista vaikutusta. Mallin rakentaminen perustui yrityksen tilinpäätösaineistoon. Havaittiin, ettei yritys ole valitsemansa strategian vuoksi juurikaan menettänyt tuottoja, mutta toisaalta pelkkä tilinpäätösaineisto ei riitä kovin luotettavaan tarkasteluun. Vuosikertomusten antaman tiedon pohjalta analysoitiin lisäksi yrityksen toiminnassa havaittuja reaalioptioita. Monte Carlo –simulointimenetelmä sopii reaalioptioiden arvonmääritykseen, mutta kriittisiä tekijöitä ovat mallin rakentaminen ja lähtötietojen oikeellisuus. Numeerisen mallin rinnalla on siksi aiheellista suorittaa myös laadullista reaalioptioanalyysia.