<p>Stricter emission legislation for heavy trucks in combination with the customers demand on low fuel consumption has resulted in intensive technical development of engines and their control systems. To control all these new solutions it is desirable to have reliable models for important control variables. One of them is the air mass-flow, which is important when controlling the amount of recirculated exhaust gases in the EGR system and to make sure that the air to fuel ratio is correct in the cylinders. The purpose with this thesis was to use system identification theory to develop a model for the air mass-flow through the compressor. First linear black-box models were developed without any knowledge of the physics behind. The collected data was preprocessed to work in the modeling procedure and then models with one or more inputs where built according to the ARX model structure. To further improve the models performance, non-linear regressors was developed from physical relations for the air mass-flow and used to form grey-box models of the air mass-flow.In conclusion, the performance was evaluated through comparing the estimated air mass-flow from the best model with the estimate that an extended Kalman filter together with a physical model produced.</p> / <p>Hårdare utsläppskrav för tunga lastbilar i kombination med kundernas efterfrågan på låg bränsleförbrukning har resulterat i en intensiv utveckling av motorer och deras kontrollsystem. För att kunna styra alla dessa nya lösningar är det nödvändigt att ha tillförlitliga modeller över viktiga kontrollvariabler. En av dessa är luftmassflödet som är viktig när man ska kontrollera den mängd avgaser som återcirkuleras i EGR-systemet och för att se till att kvoten mellan luft och bränsle är korrekt i motorns cylindrar. Syftet med det här examensarbetet var att använda systemidentifiering för att ta fram en modell över luftmassflödet förbi kompressorn. Först togs linjära svartboxmodeller fram utan att ta med någon kunskap om den bakomliggande fysiken. Insamlade data förbehandlades för att passa in i modelleringsproceduren och efter det skapades i enlighet med ARX-modellstrukturen modeller med en eller flera insignaler. För att ytterligare förbättra modellernas prestanda togs icke-linjära regressorer fram med hjälp av fysikaliska relationer för luftmassflödet. Dessa användes sedan för att skapa gråboxmodeller av luftmassflödet. Avslutningsvis utvärderades prestandan genom att det estimerade luftmassflödet från den bästa modellen jämfördes med det estimat som ett utökat kalmanfilter tillsammans med fysikaliska ekvationer genererade.</p>

<p>This thesis presents a grey-box model of the temperature and moisture content for each layer of the multi-ply paperboard inside the drying section of a paper mill. The distribution of the moisture inside the board is an important variable for the board quality, but is unfortunately not measured on-line. The main goal of this work is a model that predicts the moisture evolution during the drying, to be used by operators and process engineers as an estimation of the unmeasurable variables inside the drying section.</p><p>Drying of carton board is a complex and nonlinear process. The physical phenomena are not entirely understood and the drying depends on a number of unknown parameters and unmodelled or unmeasurable features. The grey-box modelling approach, which consists in using the available measurements to estimate the unknown disturbances, is therefore a suitable approach for modelling the drying section.</p><p>A major problem encountered with the modelling of the drying section is the lack of measurements to validate the model. Consequently, the correctness and uniqueness of the estimated variables and parameters are not guaranteed. We therefore carry out observability and identifiability analyses and the results suggest that the selected model structure is observable and identifiable under the assumption that specific measurements are available. Based on this analysis, static measurements in the drying section are carried out to identify the parameters of the model. The parameters are identified using one data set and the results are validated with other data sets.</p><p>We finally simulate the model dynamics to investigate if predicting the final board properties on-line is feasible. Since only the final board temperature and moisture content are measured on-line, the variables and parameters are neither observable nor identifiable. We therefore regard the predictions as an approximation of the estimated variables. The semiphysical model is complemented with a nonlinear Kalman filter to estimate the unmeasured inputs and the unmodelled disturbances. Data simulations show a good prediction of the final board temperature and moisture content at the end of the drying section. The model could therefore possibly be used by operators and process engineers as an indicator of the board temperature and moisture inside the drying section.</p>

Stricter emission legislation for heavy trucks in combination with the customers demand on low fuel consumption has resulted in intensive technical development of engines and their control systems. To control all these new solutions it is desirable to have reliable models for important control variables. One of them is the air mass-flow, which is important when controlling the amount of recirculated exhaust gases in the EGR system and to make sure that the air to fuel ratio is correct in the cylinders. The purpose with this thesis was to use system identification theory to develop a model for the air mass-flow through the compressor. First linear black-box models were developed without any knowledge of the physics behind. The collected data was preprocessed to work in the modeling procedure and then models with one or more inputs where built according to the ARX model structure. To further improve the models performance, non-linear regressors was developed from physical relations for the air mass-flow and used to form grey-box models of the air mass-flow.In conclusion, the performance was evaluated through comparing the estimated air mass-flow from the best model with the estimate that an extended Kalman filter together with a physical model produced. / Hårdare utsläppskrav för tunga lastbilar i kombination med kundernas efterfrågan på låg bränsleförbrukning har resulterat i en intensiv utveckling av motorer och deras kontrollsystem. För att kunna styra alla dessa nya lösningar är det nödvändigt att ha tillförlitliga modeller över viktiga kontrollvariabler. En av dessa är luftmassflödet som är viktig när man ska kontrollera den mängd avgaser som återcirkuleras i EGR-systemet och för att se till att kvoten mellan luft och bränsle är korrekt i motorns cylindrar. Syftet med det här examensarbetet var att använda systemidentifiering för att ta fram en modell över luftmassflödet förbi kompressorn. Först togs linjära svartboxmodeller fram utan att ta med någon kunskap om den bakomliggande fysiken. Insamlade data förbehandlades för att passa in i modelleringsproceduren och efter det skapades i enlighet med ARX-modellstrukturen modeller med en eller flera insignaler. För att ytterligare förbättra modellernas prestanda togs icke-linjära regressorer fram med hjälp av fysikaliska relationer för luftmassflödet. Dessa användes sedan för att skapa gråboxmodeller av luftmassflödet. Avslutningsvis utvärderades prestandan genom att det estimerade luftmassflödet från den bästa modellen jämfördes med det estimat som ett utökat kalmanfilter tillsammans med fysikaliska ekvationer genererade.

Over the last decades, the frequency on the Nordic electrical power grid has deteriorated. Therefore, new stricter requirements are developed for the hydropower delivering regulating active power on the Frequency Containment Reserve market (FCR). This thesis aims to investigate the possibility of modeling two double-regulated hydropower plants, referred to as Unit 1 and 2, to evaluate their compliance with the new FCR-requirements.  By modeling the hydropower plants, the first goal was to find a model structure that captures the essential dynamics of the systems. A second goal was to evaluate whether the two units currently fulfill the new FCR-requirements, and investigate how the turbine governors’ settings could be optimized to fulfill the new requirements. Data obtained from FCR-tests was used in MATLAB to evaluate the two stations’ dynamic stability and performance requirements. Through system identification in MATLAB, grey-box modeling was used to create linear and non-linear turbine and waterways models for Unit 1 and Unit 2. The non-linear turbine and waterways models were implemented in Simulink, together with corresponding turbine governors, to find optimal parameter settings to fulfill the FCR-requirements.  The evaluation of the new FCR-requirements shows that none of the two units fulfills the dynamic stability requirement. However, Unit 1 fulfills the performance requirement. The results imply that double-regulated turbines will most likely have difficulties fulfilling the new requirements, which will cause major consequences in improving the frequency regulation quality. The results from the grey-box modeling present that the linear models are not validated with the step response data, due to not capturing the system dynamics when compared with provided data from the units. On the other hand, the non-linear models are validated with step response data as the model captures the system dynamics more accurately. However, the non- linear Simulink models cannot capture the dynamics of the hydropower systems for sinusoidal signals with varying frequencies which are used in the new FCR-requirement test. Consequently, the thesis has no result of the optimal parameter setting of the turbine governors to fulfill the new FCR-requirements. In conclusion, the grey-box models, with the level of detail presented in this thesis, are inadequate in capturing the system’s dynamics to evaluate the new FCR-requirements. Thus, the thesis contributes to filling a knowledge gap within the area of modeling for frequency regulation.

Buildings are currently controlled in a sub optimal way, using a WC controller that is dependent only on the external temperature. A rich amount of real-time data from installed sensors is available within the buildings and the network and can be used to counteract this. To better control the indoor temperature and the heat supply this degree-project develops a model and optimizer for control of the indoor temperature, where industry standard data streams are used as inputs. The model and optimizer can be implemented in a MPC which takes the future external temperature into consideration and enhances the ability to control the heat supply. There are two main reasons why enhanced control is interesting to look at, the economic aspects and the comfort of the occupancies. This degree project is focused on developing a general building model for the purpose of utilizing the building as an energy storage for peak-shaving.  The finalized model is a dynamic grey-box model developed using data from a multifamily building, Building A, located in Västerås Sweden. The training period is set to 408 hours, and the prediction horizon is set to 48 hours as a result of the verification. To demonstrate the utilization possibilities of using the building as a heat storage, an optimizer is constructed to evaluate a peak shaving control strategy. The control objective (Qsupply) is controlled by manipulating the indoor temperature (Tin) within a set interval. By setting a fixed interval for the indoor temperature within the comfort interval, the comfort is still maintained. For the peak shaving different flexibilities within the indoor temperature have been examined with a range from 22 +/- 0.25 degrees Celcius to 22 +/- 2.00 degrees Celcius.  The model is verified in 4 steps: prediction ability on the historic data, parametric verification on the time constant, simulation of heat supply separately from the historic data and model generality by implementing the model on a second multifamily building, Building B. The model has a RRMSE of 8% for Building A and 9% for Building B which is considered excellent.  Due to the lack of access to the real building, the developed model is not validated. Based on peak shaving and energy consumption, the preferred solution is 22+/- 1.25 degrees Celcius. But based on surveys about occupancies attitude toward flexibility in the indoor temperature and economical aspects, an indoor temperature of 22 +/- 0.50 degrees Celcius is considered the best choice with the maximum peak in the heat supplied decreased by 35% and the energy consumption is decreased by 10% compared to the historical case. We suggest allowing the customers to choose their preferred flexibility to ensure comfort.

This research aims to explore new ways of assessing energy performance within housing units. The mainobjective of this work is to propose a heat dynamics model based on monitoring data, to contribute towardsan energy-efficient transition in the building sector. An extensive study on the available mathematical and statistical tools is described in order to determine aholistic solution, found in grey-box models. This model approach offers the possibility of understandingmultivariate systems, which can be applied to a housing-unit heat flow dynamics. Through the iterative process of testing each possible model, this work determines the one with bestexplanatory power, defining the thermal characteristics of the studied housing unit. This method allows thedetection of underperforming dwellings among constructions with high energy-efficiency standards. This investigation reflects the feasibility of employing grey-box models to predict the dynamics of heatrelated systems. Moreover, it sets the basis for new ways of employing the monitoring data of dwellings. / Denna forskning syftar till att utforska nya sätt att bedöma energiprestanda inom bostäder. Huvudsyftetmed detta arbete är att föreslå en värmedynamikmodell baserad på övervakningsdata för att bidra till enenergieffektiv övergång inom byggsektorn. En omfattande studie av tillgängliga matematiska och statistiska verktyg beskrivs för att bestämma enhelhetslösning, som finns i gråboxmodeller. Denna modellstrategi ger möjlighet att förstå multivariatasystem, som kan tillämpas på en hushålls värmedynamik. Genom den iterativa processen att testa varje möjlig modell bestämmer detta arbete den med bästförklarande kraft, och definierar de studerade husenhetens termiska egenskaper. Denna metod gör detmöjligt att upptäcka underpresterande bostäder bland anläggningar med hög energieffektivitetsstandard. Denna undersökning återspeglar möjligheten att använda gråboxmodeller för att förutsäga dynamiken ivärmerelaterade system. Dessutom lägger den grunden för nya sätt att använda övervakningsdata förbostäder.

Pour atteindre les objectifs de réduction de consommation et augmenter la flexibilité de la demande des bâtiments, il est nécessaire de disposer de modèles de prévision de charge de climatisation facilement diffusables sur site et performants qui permettent la mise en place de stratégies d’optimisation énergétique et d’effacement. Cette thèse compare plusieurs architectures de modèles inverses (« boite noire », « boite grise »). Un modèle semi-physique d’ordre 2 (R6C2) a été retenu pour prévoir la puissance de climatisation et la température intérieure moyenne en chauffage et en refroidissement. Il permet aussi d’interpréter des situations inédites (effacement), absentes de la phase d’apprentissage. Trois stratégies d’optimisation énergétique et d’effacement adaptées aux contraintes d’exploitation sont étudiées. La première permet d’optimiser la relance en chauffage afin de réduire la consommation et d’atteindre effectivement la température de confort le matin. La seconde stratégie optimise les températures de consigne sur une journée dans un contexte de prix variable de l’énergie, ceci afin de réduire la facture énergétique. Enfin, la troisième stratégie permet au bâtiment de s’effacer en limitant la charge tout en respectant des critères de confort spécifiés. Le modèle R6C2 et les stratégies ont été confrontés à un bâtiment réel (une école élémentaire). L’étude montre qu’il est possible de prévoir la puissance électrique et la température moyenne d’un bâtiment complexe avec un modèle mono-zone ; elle permet d’évaluer les stratégies développées et d’identifier les limites du modèle. / To reach the objectives of reducing the energy consumption and increasing the flexibility of buildings energy demand, it is necessary to have load forecast models easy to adapt on site and efficient for the implementation of energy optimization and load shedding strategies. This thesis compares several inverse model architectures ("black box", "grey box"). A 2nd order semi-physical model (R6C2) has been selected to forecast load curves and the average indoor temperature for heating and cooling. It is also able to simulate unknown situations (load shedding), absent from the learning phase. Three energy optimization and load shedding strategies adapted to operational constraints are studied. The first one optimizes the night set-back to reduce consumption and to reach the comfort temperature in the morning. The second strategy optimizes the set-point temperatures during a day in the context of variable energy prices, thus reducing the energy bill. The third strategy allows load curtailment in buildings by limiting load while meeting specified comfort criteria. The R6C2 model and strategies have been faced with a real building (elementary school). The study shows that it is possible to forecast the electrical power and the average temperature of a complex building with a single-zone model; the developed strategies are assessed and the limitations of the model are identified.

This report covers the work and results of the thesis project in Mechanical Engineering from Luleå university of technology performed by Niklas Ydebäck. The objective of the thesis project is to research if it is possible, with general principles of fluid flow between components and the corresponding geometric constraints between them and just a few channels of data, to model the leakage of a radial piston hydraulic motor. The model is of the grey box kind which makes use of both numerical and statistical methods together with known physical properties of a system in order to model the system. The unknown parameters of this system that are estimated using the least squares method are the three different gap heights of the system as well as the two different eccentricities in the system. The model contains the physical properties of the system, stated in equations for the leakage in the relevant lubrication interfaces, but no relational properties for the dynamics and affects between the individual lubricating interfaces. The model developed is due to the model generality together with the data quality accessible not able to model the system with reliable quality. The model is however able to capture the general trend of the leakage in the system over the applied time series datasets. / Den här rapporten presenterar arbetsgången och resultatet av examensarbetet för en civilingenjörsexamen i Maskinteknik från Luleå tekniska universitet utförd av Niklas Ydebäck. Målet med examensarbetet är att utvärdera och undersöka om det är möjligt, med generella och vedertagna principer av fluidflöde mellan smorda komponenter tillsammans med de geometriska begränsningarna som hör dem till och några få kanaler av data, att modellera läckaget för en radialkolvsmotor. Modellen är en grålådemodell som med hjälp av numeriska och statistiska metoder och kända fysikaliska principer av ett system bildar en modell av systemet. De okända parametrarna av systemet som estimeras med hjälp av minsta kvadrat metoden är de tre olika typerna av spalthöjderna och de två olika eccentricitetstyperna som finns i systemets smorda kontakter. Modellen består av de fysikaliska egenskaperna i systemet, formerade i ekvationer för läckaget i de relevanta smorda kontakterna, men inga relationella egenskaper för dynamiken och effekterna mellan de olika smorda kontakterna. Den utvecklade modellen är på grund av den generella karaktären av modellen tillsammans med kvaliteten på den data som finns tillgänglig inte möjlig att modellera läckaget i systemet med tillräcklig noggrannhet. Modellen är trots detta kapabel att fånga de generella trender som återfinns i den uppmätta datan på läckaget för de applicerade dataseten.

This study models the energy used for heating in buildings by applying system identification methodology. The model development is grounded in physics to provide guidance and interpretability when evaluated. Time-series of heating demand, outdoor temperature, indoor temperature and solar irradiation are considered for the modelling purpose. Evaluation is done through simulation and relies on quantitative measures, residual analysis and visual inspection of model output. Through model development, the study seeks to extrapolate information of physical properties that drives heating demand in buildings. Seven buildings located in the same geographic area are studied. It is found that linear ARX-models can simulate heating demand with high precision but at times low accuracy. A common system model structure can be identified between buildings, indicating that physical properties shared between buildings can be identified through this methodology. A sensitivity analysis is conducted to derive the contributions from model constituents to simulation results. Two buildings were also modelled as OE-models. These models performed better than the respective ARX-models but were deemed more difficult to use for the purpose of this study. The study finds difficulties in implementing aggregated time-series of indoor temperature, which could be explored further in future studies for more detailed interpretations.

Grey-box models are constructed by combining model components that are derived from first principles with components that are identified empirically from data. In this thesis a grey-box modelling method for describing distributed parameter systems is presented. The method combines partial differential equations with a multi-layer perceptron network in order to incorporate prior knowledge about the system while identifying unknown dynamics from data. A gradient-based optimization scheme which relies on the reverse mode of automatic differentiation is used to train the network. The method is presented in the context of modelling the dynamics of a chemical reaction in a fluid. Lastly, the grey-box modelling method is evaluated on a one-dimensional and two-dimensional instance of the reaction system. The results indicate that the grey-box model was able to accurately capture the dynamics of the reaction system and identify the underlying reaction. / Hybridmodeller konstrueras genom att kombinera modellkomponenter som härleds från grundläggande principer med modelkomponenter som bestäms empiriskt från data. I den här uppsatsen presenteras en metod för att beskriva distribuerade parametersystem genom hybridmodellering. Metoden kombinerar partiella differentialekvationer med ett neuronnätverk för att inkorporera tidigare känd kunskap om systemet samt identifiera okänd dynamik från data. Neuronnätverket tränas genom en gradientbaserad optimeringsmetod som använder sig av bakåt-läget av automatisk differentiering. För att demonstrera metoden används den för att modellera kemiska reaktioner i en fluid. Metoden appliceras slutligen på ett en-dimensionellt och ett två-dimensionellt exempel av reaktions-systemet. Resultaten indikerar att hybridmodellen lyckades återskapa beteendet hos systemet med god precision samt identifiera den underliggande reaktionen.