On Modelling, System Identification and Control of Servo-Systems with a Flexible Load

The present study was done with two different servo-systems. In the first system, a servo-hydraulic system was identified and then controlled by a fuzzy gainscheduling controller. The second servo-system, an electro-magnetic linear motor in suppressing the mechanical vibration and position tracking of a reference model are studied by using a neural network and an adaptive backstepping controller respectively. Followings are some descriptions of research methods. Electro Hydraulic Servo Systems (EHSS) are commonly used in industry. These kinds of systems are nonlinearin nature and their dynamic equations have several unknown parameters.System identification is a prerequisite to analysis of a dynamic system. One of the most promising novel evolutionary algorithms is the Differential Evolution (DE) for solving global optimization problems. In the study, the DE algorithm is proposed for handling nonlinear constraint functionswith boundary limits of variables to find the best parameters of a servo-hydraulic system with flexible load. The DE guarantees fast speed convergence and accurate solutions regardless the initial conditions of parameters. The control of hydraulic servo-systems has been the focus ofintense research over the past decades. These kinds of systems are nonlinear in nature and generally difficult to control. Since changing system parameters using the same gains will cause overshoot or even loss of system stability. The highly non-linear behaviour of these devices makes them ideal subjects for applying different types of sophisticated controllers. The study is concerned with a second order model reference to positioning control of a flexible load servo-hydraulic system using fuzzy gainscheduling. In the present research, to compensate the lack of dampingin a hydraulic system, an acceleration feedback was used. To compare the results, a pcontroller with feed-forward acceleration and different gains in extension and retraction is used. The design procedure for the controller and experimental results are discussed. The results suggest that using the fuzzy gain-scheduling controller decrease the error of position reference tracking. The second part of research was done on a PermanentMagnet Linear Synchronous Motor (PMLSM). In this study, a recurrent neural network compensator for suppressing mechanical vibration in PMLSM with a flexible load is studied. The linear motor is controlled by a conventional PI velocity controller, and the vibration of the flexible mechanism is suppressed by using a hybrid recurrent neural network. The differential evolution strategy and Kalman filter method are used to avoid the local minimum problem, and estimate the states of system respectively. The proposed control method is firstly designed by using non-linear simulation model built in Matlab Simulink and then implemented in practical test rig. The proposed method works satisfactorily and suppresses the vibration successfully. In the last part of research, a nonlinear load control method is developed and implemented for a PMLSM with a flexible load. The purpose of the controller is to track a flexible load to the desired position reference as fast as possible and without awkward oscillation. The control method is based on an adaptive backstepping algorithm whose stability is ensured by the Lyapunov stability theorem. The states of the system needed in the controller are estimated by using the Kalman filter. The proposed controller is implemented and tested in a linear motor test drive and responses are presented.

Life cycle costs in heating, ventilation and air-conditioning systems with drive

Energy consumption and energy efficiency have become an issue. Energy consumption is rising all over the world and because of that, and the climate change, energy is becoming more and more expensive. Buildings are major consumers of energy, and inside the buildings the major consumers are heating, ventilation and air-conditioning systems. They usually run at constant speed without efficient control. In most cases HVAC equipment is also oversized. Traditionally heating, ventilation and air-conditioning systems have been sized to meet conditions that rarely occur. The theory part in this thesis represents the basics of life cycle costs and calculations for the whole life cycle of a system. It also represents HVAC systems, equipment, systems controls and ways to save energy in these systems. The empirical part of this thesis represents life cycle cost calculations for HVAC systems. With these calculations it is possible to compute costs for the whole life cycle for the wanted variables. Life cycle costs make it possible to compare which variable causes most of the costs from the whole life point of view. Life cycle costs were studied through two real life cases which were focused on two different kinds of HVAC systems. In both of these cases the renovations were already made, so that the comparison between the old and the new, now existing system would be easier. The study indicates that energy can be saved in HVAC systems by using variable speed drive as a control method.

A Survey about Integration of Journal Systems with Repositories in Brazil

Poster at Open Repositories 2014, Helsinki, Finland, June 9-13, 2014

Real-time simulation of multibody systems with applications for working mobile vehicles

This dissertation describes an approach for developing a real-time simulation for working mobile vehicles based on multibody modeling. The use of multibody modeling allows comprehensive description of the constrained motion of the mechanical systems involved and permits real-time solving of the equations of motion. By carefully selecting the multibody formulation method to be used, it is possible to increase the accuracy of the multibody model while at the same time solving equations of motion in real-time. In this study, a multibody procedure based on semi-recursive and augmented Lagrangian methods for real-time dynamic simulation application is studied in detail. In the semirecursive approach, a velocity transformation matrix is introduced to describe the dependent coordinates into relative (joint) coordinates, which reduces the size of the generalized coordinates. The augmented Lagrangian method is based on usage of global coordinates and, in that method, constraints are accounted using an iterative process. A multibody system can be modelled as either rigid or flexible bodies. When using flexible bodies, the system can be described using a floating frame of reference formulation. In this method, the deformation mode needed can be obtained from the finite element model. As the finite element model typically involves large number of degrees of freedom, reduced number of deformation modes can be obtained by employing model order reduction method such as Guyan reduction, Craig-Bampton method and Krylov subspace as shown in this study The constrained motion of the working mobile vehicles is actuated by the force from the hydraulic actuator. In this study, the hydraulic system is modeled using lumped fluid theory, in which the hydraulic circuit is divided into volumes. In this approach, the pressure wave propagation in the hoses and pipes is neglected. The contact modeling is divided into two stages: contact detection and contact response. Contact detection determines when and where the contact occurs, and contact response provides the force acting at the collision point. The friction between tire and ground is modelled using the LuGre friction model, which describes the frictional force between two surfaces. Typically, the equations of motion are solved in the full matrices format, where the sparsity of the matrices is not considered. Increasing the number of bodies and constraint equations leads to the system matrices becoming large and sparse in structure. To increase the computational efficiency, a technique for solution of sparse matrices is proposed in this dissertation and its implementation demonstrated. To assess the computing efficiency, augmented Lagrangian and semi-recursive methods are implemented employing a sparse matrix technique. From the numerical example, the results show that the proposed approach is applicable and produced appropriate results within the real-time period.

Characterization of Microparticle Retention Systems with Retention Process Analyzer

In the literature survey retention mechanisms, factors effecting retention and microparticles were studied. Also commercial microparticle retention systems and means to measure retention were studied. Optical retention measurement with RPA and Lasentec FBRM was studied. The experimental part contains study of different cationic polyacrylamides, anionic silica, bentonite and new generation micropolymer. In these studies the dosage, dosing order and dosing history were changing factors. The experimental work was done with RPA-apparatus with which, the retention process can be followed in real time. In testing was found that silica yielded better retention, when dosed nontraditionally before the polymer. Also silica was very dependant on the polymer dosage. With bentonite good colloidal retention was achieved with relatively low doses. Unlike silica bentonite was not dependant on polymer dosage. The relation of bentonite and polymer dosage is more defining when high retention is wanted. With 3-component systems using bentonite very high retention was achieved. With silica no improvement in retention was found in 3-component systems compared to dual component systems.

Solving large sparse linear systems over the field GF(2)

Nowadays problem of solving sparse linear systems over the field GF(2) remain as a challenge. The popular approach is to improve existing methods such as the block Lanczos method (the Montgomery method) and the Wiedemann-Coppersmith method. Both these methods are considered in the thesis in details: there are their modifications and computational estimation for each process. It demonstrates the most complicated parts of these methods and gives the idea how to improve computations in software point of view. The research provides the implementation of accelerated binary matrix operations computer library which helps to make the progress steps in the Montgomery and in the Wiedemann-Coppersmith methods faster.

Studies on integrating kinematic design method with mechanical systems simulation techniques

Theultimate goal of any research in the mechanism/kinematic/design area may be called predictive design, ie the optimisation of mechanism proportions in the design stage without requiring extensive life and wear testing. This is an ambitious goal and can be realised through development and refinement of numerical (computational) technology in order to facilitate the design analysis and optimisation of complex mechanisms, mechanical components and systems. As a part of the systematic design methodology this thesis concentrates on kinematic synthesis (kinematic design and analysis) methods in the mechanism synthesis process. The main task of kinematic design is to find all possible solutions in the form of structural parameters to accomplish the desired requirements of motion. Main formulations of kinematic design can be broadly divided to exact synthesis and approximate synthesis formulations. The exact synthesis formulation is based in solving n linear or nonlinear equations in n variables and the solutions for the problem areget by adopting closed form classical or modern algebraic solution methods or using numerical solution methods based on the polynomial continuation or homotopy. The approximate synthesis formulations is based on minimising the approximation error by direct optimisation The main drawbacks of exact synthesis formulationare: (ia) limitations of number of design specifications and (iia) failure in handling design constraints- especially inequality constraints. The main drawbacks of approximate synthesis formulations are: (ib) it is difficult to choose a proper initial linkage and (iib) it is hard to find more than one solution. Recentformulations in solving the approximate synthesis problem adopts polynomial continuation providing several solutions, but it can not handle inequality const-raints. Based on the practical design needs the mixed exact-approximate position synthesis with two exact and an unlimited number of approximate positions has also been developed. The solutions space is presented as a ground pivot map but thepole between the exact positions cannot be selected as a ground pivot. In this thesis the exact synthesis problem of planar mechanism is solved by generating all possible solutions for the optimisation process ¿ including solutions in positive dimensional solution sets - within inequality constraints of structural parameters. Through the literature research it is first shown that the algebraic and numerical solution methods ¿ used in the research area of computational kinematics ¿ are capable of solving non-parametric algebraic systems of n equations inn variables and cannot handle the singularities associated with positive-dimensional solution sets. In this thesis the problem of positive-dimensional solutionsets is solved adopting the main principles from mathematical research area of algebraic geometry in solving parametric ( in the mathematical sense that all parameter values are considered ¿ including the degenerate cases ¿ for which the system is solvable ) algebraic systems of n equations and at least n+1 variables.Adopting the developed solution method in solving the dyadic equations in direct polynomial form in two- to three-precision-points it has been algebraically proved and numerically demonstrated that the map of the ground pivots is ambiguousand that the singularities associated with positive-dimensional solution sets can be solved. The positive-dimensional solution sets associated with the poles might contain physically meaningful solutions in the form of optimal defectfree mechanisms. Traditionally the mechanism optimisation of hydraulically driven boommechanisms is done at early state of the design process. This will result in optimal component design rather than optimal system level design. Modern mechanismoptimisation at system level demands integration of kinematic design methods with mechanical system simulation techniques. In this thesis a new kinematic design method for hydraulically driven boom mechanism is developed and integrated in mechanical system simulation techniques. The developed kinematic design method is based on the combinations of two-precision-point formulation and on optimisation ( with mathematical programming techniques or adopting optimisation methods based on probability and statistics ) of substructures using calculated criteria from the system level response of multidegree-of-freedom mechanisms. Eg. by adopting the mixed exact-approximate position synthesis in direct optimisation (using mathematical programming techniques) with two exact positions and an unlimitednumber of approximate positions the drawbacks of (ia)-(iib) has been cancelled.The design principles of the developed method are based on the design-tree -approach of the mechanical systems and the design method ¿ in principle ¿ is capable of capturing the interrelationship between kinematic and dynamic synthesis simultaneously when the developed kinematic design method is integrated with the mechanical system simulation techniques.

Magnetic Resonance Experiments with Atomic Hydrogen

In this thesis three experiments with atomic hydrogen (H) at low temperatures T<1 K are presented. Experiments were carried out with two- (2D) and three-dimensional (3D) H gas, and with H atoms trapped in solid H2 matrix. The main focus of this work is on interatomic interactions, which have certain specific features in these three systems considered. A common feature is the very high density of atomic hydrogen, the systems are close to quantum degeneracy. Short range interactions in collisions between atoms are important in gaseous H. The system of H in H₂ differ dramatically because atoms remain fixed in the H₂ lattice and properties are governed by long-range interactions with the solid matrix and with H atoms. The main tools in our studies were the methods of magnetic resonance, with electron spin resonance (ESR) at 128 GHz being used as the principal detection method. For the first time in experiments with H in high magnetic fields and at low temperatures we combined ESR and NMR to perform electron-nuclear double resonance (ENDOR) as well as coherent two-photon spectroscopy. This allowed to distinguish between different types of interactions in the magnetic resonance spectra. Experiments with 2D H gas utilized the thermal compression method in homogeneous magnetic field, developed in our laboratory. In this work methods were developed for direct studies of 3D H at high density, and for creating high density samples of H in H₂. We measured magnetic resonance line shifts due to collisions in the 2D and 3D H gases. First we observed that the cold collision shift in 2D H gas composed of atoms in a single hyperfine state is much smaller than predicted by the mean-field theory. This motivated us to carry out similar experiments with 3D H. In 3D H the cold collision shift was found to be an order of magnitude smaller for atoms in a single hyperfine state than that for a mixture of atoms in two different hyperfine states. The collisional shifts were found to be in fair agreement with the theory, which takes into account symmetrization of the wave functions of the colliding atoms. The origin of the small shift in the 2D H composed of single hyperfine state atoms is not yet understood. The measurement of the shift in 3D H provides experimental determination for the difference of the scattering lengths of ground state atoms. The experiment with H atoms captured in H2 matrix at temperatures below 1 K originated from our work with H gas. We found out that samples of H in H2 were formed during recombination of gas phase H, enabling sample preparation at temperatures below 0.5 K. Alternatively, we created the samples by electron impact dissociation of H₂ molecules in situ in the solid. By the latter method we reached highest densities of H atoms reported so far, 3.5(5)x10¹⁹ cm^-3. The H atoms were found to be stable for weeks at temperatures below 0.5 K. The observation of dipolar interaction effects provides a verification for the density measurement. Our results point to two different sites for H atoms in H2 lattice. The steady-state nuclear polarizations of the atoms were found to be non-thermal. The possibility for further increase of the impurity H density is considered. At higher densities and lower temperatures it might be possible to observe phenomena related to quantum degeneracy in solid.

Non-Markovian Dynamics in Continuous Variable Quantum Systems

The present manuscript represents the completion of a research path carried forward during my doctoral studies in the University of Turku. It contains information regarding my scientific contribution to the field of open quantum systems, accomplished in collaboration with other scientists. The main subject investigated in the thesis is the non-Markovian dynamics of open quantum systems with focus on continuous variable quantum channels, e.g. quantum Brownian motion models. Non-Markovianity is here interpreted as a manifestation of the existence of a flow of information exchanged by the system and environment during the dynamical evolution. While in Markovian systems the flow is unidirectional, i.e. from the system to the environment, in non-Markovian systems there are time windows in which the flow is reversed and the quantum state of the system may regain coherence and correlations previously lost. Signatures of a non-Markovian behavior have been studied in connection with the dynamics of quantum correlations like entanglement or quantum discord. Moreover, in the attempt to recognisee non-Markovianity as a resource for quantum technologies, it is proposed, for the first time, to consider its effects in practical quantum key distribution protocols. It has been proven that security of coherent state protocols can be enhanced using non-Markovian properties of the transmission channels. The thesis is divided in two parts: in the first part I introduce the reader to the world of continuous variable open quantum systems and non-Markovian dynamics. The second part instead consists of a collection of five publications inherent to the topic.

Exploration and Design of Power-Efficient Networked Many-Core Systems

Multiprocessing is a promising solution to meet the requirements of near future applications. To get full benefit from parallel processing, a manycore system needs efficient, on-chip communication architecture. Networkon- Chip (NoC) is a general purpose communication concept that offers highthroughput, reduced power consumption, and keeps complexity in check by a regular composition of basic building blocks. This thesis presents power efficient communication approaches for networked many-core systems. We address a range of issues being important for designing power-efficient manycore systems at two different levels: the network-level and the router-level. From the network-level point of view, exploiting state-of-the-art concepts such as Globally Asynchronous Locally Synchronous (GALS), Voltage/ Frequency Island (VFI), and 3D Networks-on-Chip approaches may be a solution to the excessive power consumption demanded by today’s and future many-core systems. To this end, a low-cost 3D NoC architecture, based on high-speed GALS-based vertical channels, is proposed to mitigate high peak temperatures, power densities, and area footprints of vertical interconnects in 3D ICs. To further exploit the beneficial feature of a negligible inter-layer distance of 3D ICs, we propose a novel hybridization scheme for inter-layer communication. In addition, an efficient adaptive routing algorithm is presented which enables congestion-aware and reliable communication for the hybridized NoC architecture. An integrated monitoring and management platform on top of this architecture is also developed in order to implement more scalable power optimization techniques. From the router-level perspective, four design styles for implementing power-efficient reconfigurable interfaces in VFI-based NoC systems are proposed. To enhance the utilization of virtual channel buffers and to manage their power consumption, a partial virtual channel sharing method for NoC routers is devised and implemented. Extensive experiments with synthetic and real benchmarks show significant power savings and mitigated hotspots with similar performance compared to latest NoC architectures. The thesis concludes that careful codesigned elements from different network levels enable considerable power savings for many-core systems.

Structural and operational optimisation : applications in energy systems

In this work mathematical programming models for structural and operational optimisation of energy systems are developed and applied to a selection of energy technology problems. The studied cases are taken from industrial processes and from large regional energy distribution systems. The models are based on Mixed Integer Linear Programming (MILP), Mixed Integer Non-Linear Programming (MINLP) and on a hybrid approach of a combination of Non-Linear Programming (NLP) and Genetic Algorithms (GA). The optimisation of the structure and operation of energy systems in urban regions is treated in the work. Firstly, distributed energy systems (DES) with different energy conversion units and annual variations of consumer heating and electricity demands are considered. Secondly, district cooling systems (DCS) with cooling demands for a large number of consumers are studied, with respect to a long term planning perspective regarding to given predictions of the consumer cooling demand development in a region. The work comprises also the development of applications for heat recovery systems (HRS), where paper machine dryer section HRS is taken as an illustrative example. The heat sources in these systems are moist air streams. Models are developed for different types of equipment price functions. The approach is based on partitioning of the overall temperature range of the system into a number of temperature intervals in order to take into account the strong nonlinearities due to condensation in the heat recovery exchangers. The influence of parameter variations on the solutions of heat recovery systems is analysed firstly by varying cost factors and secondly by varying process parameters. Point-optimal solutions by a fixed parameter approach are compared to robust solutions with given parameter variation ranges. In the work enhanced utilisation of excess heat in heat recovery systems with impingement drying, electricity generation with low grade excess heat and the use of absorption heat transformers to elevate a stream temperature above the excess heat temperature are also studied.

Working fluid selection and design of small-scale waste heat recovery systems based on organic Rankine cycles

Demand for the use of energy systems, entailing high efficiency as well as availability to harness renewable energy sources, is a key issue in order to tackling the threat of global warming and saving natural resources. Organic Rankine cycle (ORC) technology has been identified as one of the most promising technologies in recovering low-grade heat sources and in harnessing renewable energy sources that cannot be efficiently utilized by means of more conventional power systems. The ORC is based on the working principle of Rankine process, but an organic working fluid is adopted in the cycle instead of steam. This thesis presents numerical and experimental results of the study on the design of small-scale ORCs. Two main applications were selected for the thesis: waste heat re- covery from small-scale diesel engines concentrating on the utilization of the exhaust gas heat and waste heat recovery in large industrial-scale engine power plants considering the utilization of both the high and low temperature heat sources. The main objective of this work was to identify suitable working fluid candidates and to study the process and turbine design methods that can be applied when power plants based on the use of non-conventional working fluids are considered. The computational work included the use of thermodynamic analysis methods and turbine design methods that were based on the use of highly accurate fluid properties. In addition, the design and loss mechanisms in supersonic ORC turbines were studied by means of computational fluid dynamics. The results indicated that the design of ORC is highly influenced by the selection of the working fluid and cycle operational conditions. The results for the turbine designs in- dicated that the working fluid selection should not be based only on the thermodynamic analysis, but requires also considerations on the turbine design. The turbines tend to be fast rotating, entailing small blade heights at the turbine rotor inlet and highly supersonic flow in the turbine flow passages, especially when power systems with low power outputs are designed. The results indicated that the ORC is a potential solution in utilizing waste heat streams both at high and low temperatures and both in micro and larger scale appli- cations.

Aircraft tracking and classification with vhf passive bistatic radar

Since the times preceding the Second World War the subject of aircraft tracking has been a core interest to both military and non-military aviation. During subsequent years both technology and configuration of the radars allowed the users to deploy it in numerous fields, such as over-the-horizon radar, ballistic missile early warning systems or forward scatter fences. The latter one was arranged in a bistatic configuration. The bistatic radar has continuously re-emerged over the last eighty years for its intriguing capabilities and challenging configuration and formulation. The bistatic radar arrangement is used as the basis of all the analyzes presented in this work. The aircraft tracking method of VHF Doppler-only information, developed in the first part of this study, is solely based on Doppler frequency readings in relation to time instances of their appearance. The corresponding inverse problem is solved by utilising a multistatic radar scenario with two receivers and one transmitter and using their frequency readings as a base for aircraft trajectory estimation. The quality of the resulting trajectory is then compared with ground-truth information based on ADS-B data. The second part of the study deals with the developement of a method for instantaneous Doppler curve extraction from within a VHF time-frequency representation of the transmitted signal, with a three receivers and one transmitter configuration, based on a priori knowledge of the probability density function of the first order derivative of the Doppler shift, and on a system of blocks for identifying, classifying and predicting the Doppler signal. The extraction capabilities of this set-up are tested with a recorded TV signal and simulated synthetic spectrograms. Further analyzes are devoted to more comprehensive testing of the capabilities of the extraction method. Besides testing the method, the classification of aircraft is performed on the extracted Bistatic Radar Cross Section profiles and the correlation between them for different types of aircraft. In order to properly estimate the profiles, the ADS-B aircraft location information is adjusted based on extracted Doppler frequency and then used for Bistatic Radar Cross Section estimation. The classification is based on seven types of aircraft grouped by their size into three classes.

Modeling Energy Futures Returns With Markov Regime Switching Model

Financial time series have a tendency of abruptly changing their behavior and maintain this behavior for several consecutive periods, and commodity futures returns are not an exception. This quality proposes that nonlinear models, as opposed to linear models, can more accurately describe returns and volatility. Markov regime switching models are able to match this behavior and have become a popular way to model financial time series. This study uses Markov regime switching model to describe the behavior of energy futures returns on a commodity level, because studies show that commodity futures are a heterogeneous asset class. The purpose of this thesis is twofold. First, determine how many regimes characterize individual energy commodities’ returns in different return frequencies. Second, study the characteristics of these regimes. We extent the previous studies on the subject in two ways: We allow for the possibility that the number of regimes may exceed two, as well as conduct the research on individual commodities rather than on commodity indices or subgroups of these indices. We use daily, weekly and monthly time series of Brent crude oil, WTI crude oil, natural gas, heating oil and gasoil futures returns over 1994–2014, where available, to carry out the study. We apply the likelihood ratio test to determine the sufficient number of regimes for each commodity and data frequency. Then the time series are modeled with Markov regime switching model to obtain the return distribution characteristics of each regime, as well as the transition probabilities of moving between regimes. The results for the number of regimes suggest that daily energy futures return series consist of three to six regimes, whereas weekly and monthly returns for all energy commodities display only two regimes. When the number of regimes exceeds two, there is a tendency for the time series of energy commodities to form groups of regimes. These groups are usually quite persistent as a whole because probability of a regime switch inside the group is high. However, individual regimes in these groups are not persistent and the process oscillates between these regimes frequently. Regimes that are not part of any group are generally persistent, but show low ergodic probability, i.e. rarely prevail in the market. This study also suggests that energy futures return series characterized with two regimes do not necessarily display persistent bull and bear regimes. In fact, for the majority of time series, bearish regime is considerably less persistent. Rahoituksen aikasarjoilla on taipumus arvaamattomasti muuttaa käyttäytymistään ja jatkaa tätä uutta käyttäytymistä useiden periodien ajan, eivätkä hyödykefutuurien tuotot tee tähän poikkeusta. Tämän ominaisuuden johdosta lineaaristen mallien sijasta epälineaariset mallit pystyvät tarkemmin kuvailemaan esimerkiksi tuottojen jakauman parametreja. Markov regiiminvaihtomallit pystyvät vangitsemaan tämän ominaisuuden ja siksi niistä on tullut suosittuja rahoituksen aikasarjojen mallintamisessa. Tämä tutkimus käyttää Markov regiiminvaihtomallia kuvaamaan yksittäisten energiafutuurien tuottojen käyttäytymistä, sillä tutkimukset osoittavat hyödykefutuurien olevan hyvin heterogeeninen omaisuusluokka. Tutkimuksen tarkoitus on selvittää, kuinka monta regiimiä tarvitaan kuvaamaan energiafutuurien tuottoja eri tuottofrekvensseillä ja mitkä ovat näiden regiimien ominaisuudet. Aiempaa tutkimusta aiheesta laajennetaan määrittämällä regiimien lukumäärä tilastotieteellisen testauksen menetelmin sekä tutkimalla energiafutuureja yksittäin; ei indeksi- tai alaindeksitasolla. Tutkimuksessa käytetään päivä-, viikko- ja kuukausiaikasarjoja Brent-raakaöljyn, WTI-raakaöljyn, maakaasun, lämmitysöljyn ja polttoöljyn tuotoista aikaväliltä 1994–2014, siltä osin kuin aineistoa on saatavilla. Likelihood ratio -testin avulla estimoidaan kaikille aikasarjoille regiimien määrä,jonka jälkeen Markov regiiminvaihtomallia hyödyntäen määritetään yksittäisten regiimientuottojakaumien ominaisuudet sekä regiimien välinen transitiomatriisi. Tulokset regiimien lukumäärän osalta osoittavat, että energiafutuurien päiväkohtaisten tuottojen aikasarjoissa regiimien lukumäärä vaihtelee kolmen ja kuuden välillä. Viikko- ja kuukausituottojen kohdalla kaikkien energiafutuurien prosesseissa regiimien lukumäärä on kaksi. Kun regiimejä on enemmän kuin kaksi, on prosessilla taipumus muodostaa regiimeistä koostuvia ryhmiä. Prosessi pysyy ryhmän sisällä yleensä pitkään, koska todennäköisyys siirtyä ryhmään kuuluvien regiimien välillä on suuri. Yksittäiset regiimit ryhmän sisällä eivät kuitenkaan ole kovin pysyviä. Näin ollen prosessi vaihtelee ryhmän sisäisten regiimien välillä tiuhaan. Regiimit, jotka eivät kuulu ryhmään, ovat yleensä pysyviä, mutta prosessi ajautuu niihin vain harvoin, sillä todennäköisyys siirtyä muista regiimeistä niihin on pieni. Tutkimuksen tulokset osoittavat myös, että prosesseissa, joita ohjaa kaksi regiimiä, nämä regiimit eivät välttämättä ole pysyvät bull- ja bear-markkinatilanteet. Tulokset osoittavat sen sijaan, että bear-markkinatilanne on energiafutuureissa selvästi vähemmän pysyvä.