simulator of a multi-effect evaporation plant
Ludvig Björklund
Civilingenjör, Hållbar energiteknik 2020
Luleå tekniska universitet
Institutionen för teknikvetenskap och matematik
I would like to thank Optimation AB for giving me the opportunity to do my thesis and a thanks for the great reception by everyone at the company, I had a great time. I would especially like to thank my supervisors, Peter Lingman for answering all my questions and much support during the entire thesis, Lena Modin for helping me out more times then I can count and finally Magnus Aråker for helping me with software and process understandings and Joakim Wallbing for help with Dymola. I would also like to thank Sara Ingves and Södra Cell for providing me with a interesting case study and data.
I would also like to thank Luleå University of Technology for years of education and for allowing me to design my own education. A special thanks goes out to Khalid Atta, my examinator at the University, for challenging and pushing me for the last 3 years.
I would also like to acknowledge the work done by Dr Gerardo Santillán Martinez and Dr Marcus Olsson and for allowing me to use their illustrations in my thesis.
Keywords: Tracking simulator, Digital Twin, control, Multi-effect evaportion
The world is becoming more and more connected and the digitalisation is becoming increasingly cheaper and more accessible. Around the turn of the millennium, the concept of the digital twin was coined by Michael Grieves, professor at the University of Michigan. The idea of a digital twin is to create a virtual replica of a product, where the virtual copy is present throughout the life cycle of the product, from the design process, to providing information about its physical counterpart. The advances in the field of Internet of Things over the last couple of years, with lower prices and better sensors, with increased connectivity, has led to an increased interest in digital twins. In this master thesis, a method for adjusting states in a simulator against measurement data from a multi-effect-evaporation plant is investigated. The objective is to explain and minimize the differences between the measured data and the simulators corresponding measurements.
The approach consists of evaluating state-of-the art research in the field of tracking simulators in test benches of opportune processes, in order to finally apply the concept to a evaporation step in an integrated paper and pulp mill. By using methods from the control theory, a strategy is presented to append tracking capabilities to existing simulators. Controllers are used to adjust the simulator’s model parameters to get the simulator values to track actual measurement data. Relative gain array is used for automatic pairing of desired measurements with suitable model parameters whilst a gray box model is used to initialize values of the model parameters, given a-priori knowledge of the process.
The results of the thesis indicate that a generalized software can be written. This software takes an exported Functional Mockup Unit (FMU) and pairs variables with parameters, initiates parameters and follows measurement values, given an existing model. The method has been evaluated on two test benches before being validated against a real process and historical data. The results from the actual process show potential, but further tuning of parameter controllers and an improved choice of control volume is recommended before taking the simulator online.
Världen blir allt mer uppkopplad och möjligheten till digitalisering blir kontinuerligt billigare och en- klare. Kring millenieskiftet myntades konceptet digital tvilling av Michael Grieves, dåvarande professor vid University of Michigan. Idéen med en digital tvilling är att skapa en virtuell kopia av en produkt, där den virtuella kopia är närvarande under hela produktens livscykel. Från design till att ge informationen om dess fysiska motsvarighet. De senaste årens utveckling inom sakernas internet, där priser pressas och uppkopplingen blir snabbare har ökat intresset för digital tvillingar. I detta examensarbete behandlas en metod för att justera tillstånd i en simulator mot mätdata i en indunstningseffekt, en så kallad tracking simulator. Målet med metoden och examensarbete är att förklara och minimera skillnaderna mellan simulatorvärden och de reella mätvärdena.
Tillvägagångssättet består av att utvärdera den senaste forskning inom området, detta görs i test- bänkar av lämpliga processer. I slutändan appliceras konceptet på ett indunstningssteg i ett integrerat pappers-och massabruk. Genom att nyttja metoder från reglertekniken presenteras en strategi för att addera trackingmöjligheter till befintliga simulatorer. Regulatorer används för att justera simulatorns modellparametrar för att få simulatorvärdena att följa verkliga mätdata. Relative gain array används för att para ihop lämpliga mätningar med modellparametrar, samtidigt som en gråboxmodellering används för att initiera värden på parameterarna, givet kunskap om processen.
Resultaten från examensarbetet indikerar att en generaliserad mjukvara kan skrivas, som tar en exporterad FMU och parar ihop variabler med parametrar, initierar parametrar och följer mätvärden, givet en existerande modell. Metoden har utvärderats på två testbänkar innan den validerats mot en verklig process och historiska data. Resultaten från den verkliga processen visar potential, men ytterligare trimning av regulatorerna som styr parametrarna och ett förbättrat val av kontrollvolym rekommenderas. Optimation AB rekommenderas att utveckla och generalisera metoden för framtida implementationer.
1 Introduction 1
1.1 Background . . . 1
1.2 Objectives . . . 1
1.3 Scope and limitations . . . 2
2 Literature Review 4 2.1 Terminology of the field . . . 4
2.2 Model update . . . 5
2.3 Parameter selection . . . 7
2.4 Model Initialization . . . 9
2.5 Applications . . . 9
3 Theory 10 3.1 Initial Parameters Estimation . . . 10
3.2 Parameter control . . . 10
3.3 Pairing of tracking variables and parameters . . . 11
3.4 Pulping Process . . . 12
4 Method 16 4.1 Software . . . 16
4.2 Development of a tracking simulator . . . 17
4.3 Initialization . . . 18
4.4 Pairing of tracking variables and parameters . . . 18
4.5 State compensation . . . 18
4.6 Test benches . . . 19
5 Results 24 5.1 Heat exchanger . . . 24
5.2 Heat production process . . . 28
5.3 Mörrum Evaporation Step . . . 37
6 Discussion 53 6.1 The methodology . . . 53
6.2 Results of the tracking . . . 54
6.3 Proposed Improvements . . . 55
6.4 Conclusion . . . 55
6.5 Future work . . . 55
6.6 Reflections . . . 56
7 References 57
Glossary
Analysis Model A model which performs future transient state, steady state predictive calculations, optimization schemes.
Digital Shadow A virtual replica of a physical system with automated data flow into the digital replica from the physical object.
Digital Model A virtual replica of a physical system without automated flow of data.
Digital Twin A virtual replica of a physical system fully integrated in both directions with the con- nected physical object.
Dynamic Data Reconciliation To compensate the measurement error of the sensor with a plant model, without the constraint of steady state..
First Principle Model Modeling based on engineering, physics or chemical descriptions to represent the behavior of the plant..
Identification Model A model which is used to estimate performance parameters..
Mirror Model A model which adjusts the operating state in the the model in order to perform online follow up of the state of the real plant..
Parameter controller A controller that updates model parameters..
Prediction error Difference between measured output and the predicted output.
Tracking variable The variable chosen to be tracked to match the actual plant measurements..
Tracking parameter Parameter which is chosen to be adjusted to make the tracking variable match the actual plant measurements..
Tracking Simulator A dynamic simulator running in parallel to a physical process and using process measurements to continuously compensate for modelling errors in order to align the simulator to the real process..
CPS Cyber-Physical-System.
DCS Distributed Control System.
DDR Dynamic data reconciliation.
dP Differential pressure.
DT Digital Twin.
FI Flow indicator.
FMI Functional Mockup Interface.
FMU Functional Mockup Unit.
FPM first principle model.
IMC Internal mode control.
IoT Internet of Things.
MEEV Multiple-effect evaporator.
MIMO multiple input multiple output.
PI Pressure indicator.
PT Pysical twin.
RGA Relative Gain Array.
SBDT Simulation-Based Digital Twin.
SISO Single Input Single Output.
SMC Sliding mode control.
TI Temperature indicator.
1 Introduction
1.1 Background
Since the industrial revolution began by replacing repetitive manual labor with automated aids or re- placements, industrial productions and processes have been through subsequent revolutions which have resulted in radical changes in industrial processes (Mohajan, 2019). The first industrial revolution being the mechanical revolution, when machines were introduced into manufacturing, with textile produc- tions as a major driver of technical progress. The second industrial revolution was integrating electrical machines into the production lines and the third being the implementation of information technology (Schmidt et al., 2015). We stand at the start of a new revolution, Industry 4.0 as it has been coined in popular science. Benefiting from the development of the Internet of Things (IoT) and Cyber-Physical- System (CPS), material, machines, products, supply chains etc. can be interconnected(Wollschlaeger et al., 2017) (Grieves, 2019). This allows the objects to exchange information and control actions with each other, independently and autonomously. This technological development has paved the way for the digital twin, which is intended to be a highly connected virtual model of a physical system or process.
1.1.1 Simulation-based applications in the process industry
The need for highly accurate simulators in the process industry is increasing and in recent years, dy- namic simulations have been utilized by the industry. Dynamic simulators are widely used from plant engineering (Paganus et al., 2016), to improved operators training (Ravikanth et al., 2018) as a base for control validation, and for predictions of future plant evolution.
1.1.2 Optimation AB
Optimation AB has provided high fidelity process simulators to the process industry for more than 18 years. The company provides consultation to global and local companies in a variety of branches i.e the pulp and paper-, mineral- and energy sectors. The technical demands have led to an increasing demand of process simulations from the process industry, for operator training, predictions and optimization. The main applications of the simulators developed are in training of process operators and the increasing need of verifying solutions in order to reduce or avoid costly mistakes in the real process and to serve as an aid during the development cycle to save resources and time. Optimation AB developed model libraries called Visa2Base and Visa2Control, libraries used during this thesis.
1.2 Objectives
• Review the current state-of-the-art methods to align online simulators with real process measure- ment data
• Design a dynamic estimation method to align a simulator with real process measurement data in order to minimize residuals of the variables.
1.3 Scope and limitations
• Literature review of current state-of-the-art tracking simulators and model update methods.
Research development and current status of tracking simulators, comparing the different solutions implemented and providing a concise overview of the field, including a clear description of termi- nology used in the field. Defining problems currently being investigated in the field, such as the initialization of the tracking simulators and the different limitations of model update methods.
• Evaluate update methods of tracking simulators. This is intended to be done by constructing a test bench in Dymola. One simulator model to represent the real process plant with first principle modeling and adding process disturbances and measurement noise to this simulator to emulate a real process. Then a process simulator will be modeled using the same principles but without noise and disturbances and with approximations of the physical representation.
• Implementing the tracking simulator, with selected model update method. Optimation AB will provide a simulator of a multi-effect evaporation plant, used in an integrated pulp and paper mill. The simulator is modeled after a evaporation plant in Mörrum, Sweden. The tracking simulator will be implemented on this case study and enable tests of the previously chosen methods on real process measurements.
Digital Twins
Data driven DT FPM DT
Applications ICT Tracking Simulator
State Update Parameter Adjustment
Figure 1: An overview of the scope of the project. The dashed lines in the block diagram indicate areas that are not the priority of the project, but are described in the thesis. The acronyms can be found in the preamble of the thesis.
The scope of the project is visualized in a block diagram in Figure 1. The focus of the thesis is on defining a method of constructing tracking simulator from a existing simulator. The Mörrum Case study is part of a larger scale DT project. The effort will be focused on implementing a methodology to make adjustments of the simulator, to track the measurements of the real process. The thesis will limit the creation of the tracking simulator to one step of the evaporation plant.
The difference between a online simulator and a tracking simulator is illustrated in Figure 2.
DCS Plant
Simulator
u y
ˆ y
(a) Online simulator
DCS Plant
Simulator
Model Update
u y
ˆ y
(b) Tracking simulator
Figure 2: Both simulators run parallel to the real process, but the tracking simulator uses information from the plants sensor measurements to adjust the simulator and minimize the residuals.
The online simulator runs in parallel with the real process, due to a necessity of simplifications, approximations and degradation of components, the outputs from the real process and the simulator are unlikely to align. This is where the tracking simulator comes in, the idea is to adjust the model based on the differences of the measured and simulated output.
2 Literature Review
The section on literature review spans the research performed on the main areas involved in the project. The literature review begins with a look on different simulation based applications in the process industry. Then a overview of the different terminology found in literature is done to sort out different definitions in the field use of the terminology concerning Digital Twins and tracking simulators.
Following this is a literature review on the results and evaluated methods for tracking simulators, to highlight the current state of the field as well as serve as a benchmark for the scope of this project.
2.1 Terminology of the field
This subsection is aimed at providing the reader an overview of the terminology used in this paper, based on definitions of case studies and current research articles.
2.1.1 Digital Twin
In 2003 the concept of the Digital Twin was coined by Michael Grieves, then of the University of Michi- gan(Grieves, 2019). A definition of a Digital Twin (DT) provided by Michael Grieves is cited below:
”The Digital Twin is a set of virtual information constructs that fully describes a potential or actual physical manufactured product from the micro atomic level to the macro geometrical level. At its opti- mum, any information that could be obtained from inspecting a physical manufactured product can be obtained from its Digital Twin” (Grieves and Vickers, 2016).
As interpreted from the quote, the Digital Twin is a digital replica of a real system. Varying degrees of the level of connectivity that define a Digital Twins exists. In a categorical literature review of the Digital Twins in manufacturing, the authors define three levels of complexity used when the term digital twin is used (Kritzinger et al., 2018). The lowest complexity is defined as a Digital Model, which uses no automated data exchange between the physical object and the digital object. The digital model may be a first principle model, a statistical model or any other model which do not use automatic data generation, digital data may be used but its processed into the model manually.
A slightly more integrated model which uses data flow in one direction, from the physical object or process to the digital replica, is referenced as a Digital Shadow. A change in state of the physical project produces changes in the digital replica, but not vice versa. The most complex system is defined as a Digital Twin includes systems that automatically exchange data from the physical object to the digital replica and vice versa, to produce changes in the other (Kritzinger et al., 2018). In this thesis, digital twins will be used to refer to a digital model with the level of connectivity as the definition of a digital shadow and above.
2.1.2 Simulation-Based Digital Twin
A Digital Twin can be either physics-based or data driven models. This thesis focuses on physics-based DTs referred to as Simulation-Based Digital Twin (SBDT), which utilize physical, chemical or engi- neering descriptions, first principle models (FPM) as a base. The definition used in this thesis of the Simulation-Based Digital Twin (SBDT) is inspired by (Martinez, 2019) and is defined as
”A virtual replica of a physical system based on first principle modeling, run in parallel with the process and continuously adjusted to facilitate convergence to the real process measurements. Applied to derive information and predict dynamics of the modeled system”.
A data driven digital twin on the other hand is based on vast amount of historical data in order to emulate the plant,this is not aligned with the objective of the thesis.
2.1.3 Tracking simulator
A tracking simulator is defined as a real time simulator that adjusts its model by comparing simulator outputs to real process measurements(Friman and Airikka, 2012; Ruusu et al., 2017; Pietilä et al., 2013;
Nakaya et al., 2006). The real process will be noted as the physical twin or the plant in the thesis. The tracking simulator runs in parallel with a plant with the same inputs, then the model is updated by adjusting the selected tracking parameter through a dynamic estimation (Hedengren and Eaton, 2015), see Figure 2a.
This definition is widespread in the field although slight differences occur e.g in early papers on a case study, which investigates applying a tracking simulator on a steam reforming process, the authors include a Mirror Model, Identification Model and an Analysis Model in the structure of a tracking simulator (Seki et al., 2008). The main idea is still the same regarding the tracking simulator, the Mirror Model and the Identification Model are simply a strategy to update the model parameters, the Analysis Model is more focused on the applications of this calibrated simulator. In later works by some of the same authors, this structure is referred to as a Mirror Plant (Kashiwa et al., 2016). The structure called a tracking simulator in (Eaton et al., 2018) is part of a larger scale project, a subgoal of the automatic generation of a Simulation-Based Digital Twin (SBDT) (Martínez et al., 2018).
2.2 Model update
This part of the literature review aims to evaluate the current state of tracking simulators in operation, state-of-the art update methods and obstacles in implemented online tracking simulators.
2.2.1 Model update methods
Progress in tracking simulators include reported studies e.g (Nakaya et al., 2008); (Nakaya and Li, 2013);
(Ishimaru et al., 2010). These studies and articles use a proportional parameter update of the models in the simulator as seen in equation 1
p(k) = p(k − 1) + Ke(k) (1)
where p(k) is the parameter at time instant k that is to be updated using the previous value of the parameter and proportionally to the measurement error term e(k), with tuning of gain parameters throughout. In later studies, this is found to be insufficient, it may cause concentration of model error on a few selected tracking parameters. The authors proposed a dynamic data reconciliation method, abbreviated DDR, to augment the parameter update method. By setting constraints on the evolution of the state variable and adjusting some parameters in the the plant model periodically by formulating the problem as an optimization problem. Defining a target function as in equation 2 and attempting to find the argument which minimizes the objective function.
J =X
i
wi(yi− ˆyi)2 (2)
wi is the weighting factor and the suffix i is for the measured variables in the target function. y is the measured value from the sensors at the plant and ˆy is the output of the simulator. In the case study the DDR is run to adjust the parameter about once a day (Nakaya and Li, 2013).
The method of parameter adjustment with the proportional gain method has been applied to a fuel cell. The simulation voltage decay in a model of a fuel cell to measurement, which was performed by adjusting parameters related to activation and ohmic losses which outperformed the conventional track- ing simulator (Nakaya et al., 2008). A tracking simulator with the DDR have been applied to a three phase separation process to estimate a total of 10 tracking variables, the addition of the DDR method to the tracking simulator improved the alignment (Seki et al., 2008).
A slightly different approach has been evaluated, a PI controller is used as a parameter controller to update the parameters of a simulator (Friman and Airikka, 2012). This is done in the same fashion as the proportional methods as described before, with the integral term added to improve speed. The case study also suggests a method for autotuning the parameter controller using methods described in (Åström and Wittenmark, 2013),e.g with the Internal mode control (IMC) tuning guidelines for PI- control in (Chien and Fruehauf, 1990). The update of the tracking parameter using a PI controller can be seen in equation 3
p(k) = p(k − 1) + Kp(e(k) − e(k − 1)) +Kp Ti
e(k) (3)
The study suggest using one parameter controller per measured output to tune one tracking param- eter. Based on traditional control theory the limit on the numbered of parameters to tune is based on the amount of available measurements. The method is applied on historical real process data of a economizer, the experiments estimates and adjusts the specific heat capacity and the heat transfer coeffi- cients (two PI controllers), with output temperature measurements of flue gas and feed water respectively.
A more recent study has been made that introduces a sliding mode controller (SMC) to improve on the results from more classic controllers (Ruusu et al., 2017). The author proposes a SMC in order to avoid potential instability issues caused by the integral term in previous works, in case of insufficiently tuned controller parameters. An experimental test is evaluated using a laboratory scale heat production process, using a flow estimation from the simulator and corresponding plant measurements, see Figure 3.
The values of the flows in F100 are fed back to the SMC and the control signal adjusts the form loss coefficient, a model parameter representing pressure losses due to geometry changes or added compo- nents. The adjustment of this tracking parameter is used to align the flows measured at F100. In the designed experiment, the SMC outperformed the PI-control.
All the described model update methods rely on Single Input Single Output (SISO) approaches, feed one measured parameter from the simulator and the plant respectively and this is used to update a parameter in the output, based on the prediction error. The approach can be simplified in more classic control terminology, the process measurements is used as a setpoint to the controller and the outputs of the simulator is used as measurement values fed to the parameter controller, with the control output used to update the tracking parameter in the simulator.
2.2.2 Other methods
Kalman filtering was named after Rudolf E. Kalman after his proposal for a recursive solution to the discrete-data linear filtering problem in his now famous paper (Kalman, 1960). The Kalman Filter was originally designed for state estimation and have been applied in numerous industrial estimation appli- cations since first introduced(Auger et al., 2013). A educational introduction to the underlying concepts
Figure 3: The FLC (form loss coeffiecient) is adjusted to align the simulators output with the mea- surement of the flow in F100 before pump M100 (Ruusu et al., 2017)
of the Kalman Filter can be found in (Maybeck and Siouris, 1980). In the field of Digital Twin (DT)s the Kalman Filter, or more specifically according to the author advanced Kalman Filter based algorithms have been used in the tracking of slowly varying model parameters to perform the model update in a DT(General Electric Company, 2015).
Another approach for the alignment of the simulation is to approach the states directly. Instead of adjusting the parameters of the models, the states are adjusted, e.g adding/subtracting states directly to align with the measurement of the state/tracking variable. For example the massflow in a tank based on the difference in level indicators of the simulator and the process.
˙
msim(k + 1) = ˙msim(k) + K(Li,sim− Li) (4) This direct approach can provide more modular solutions compared to the requirement of a high process knowledge for tracking through a parameter adjustment method.
2.3 Parameter selection
In tracking simulator experiments based on the parameter controller method, tracking parameters are often selected manually to perform the parameter adjustment.
2.3.1 Variance decomposition method
In (Martinez et al., 2016) the authors explain their reasoning behind the manual selection of the FLC parameter discussed in section 2.2.1. The tracking parameter is selected based on knowledge of the process, in the system process seen in Figure 3. To avoid violating changes that will impact the levels in the feedwater and preheater tanks of the model, a difference that would affect the temperature of the
simulation system. This provides some physical constraints in the choice of best tracking parameter to explain the water flow in the process, the desired tracking variable.
In complex processes with a vast amount of variables, the method of manually selecting tracking variables can be both tedious and require a in-depth knowledge of the system. This motivates the introduction of a method to automate the tracking parameter selection process (Martinez et al., 2016), based on desired tracking variables. The desired qualities, to determine the most suitable parameter- variable pairings, are listed below:
1. The parameter that affects the desired tracking variable the most
2. Minimized impact on other tracking variables.
In order to fulfill the criterias above a variance-based sensitivity analysis, often called the Sobol method after the russian mathematician of the same surname (Sobol, 2001). This method measures the effect a shift or adjustment of a parameter have on the variance of the examined tracking variables. The method allows for a measure of the effect which the parameter has jointly with all other parameters (total effect index). The study was conducted to evaluate whether or not this method can be used to select opportune tracking parameters based on the effect on the tracking variables in a global sense. The method was evaluated by implementing it in a search for opportune parameters for a combined heat and power plant. The objective of the study was to track the following variables, searching through a database of 22 parameters. The results are presented in Table 1.
Table 1: Results from automated method
Tracking variable Tracking Parameter
Gas turbine (GT) power GT air compression efficiency Steam turbine (ST) power ST nominal mass flow Steam temperature to steam turbine Spray water flow
Steam temperature to condenser Condenser heat transfer efficiency Hot water flow into condenser Control valve position
Hot water pressure before condenser Line pressure loss coeff.
Hot water temperature before condenser Heat usage in hot water line GT air cooling water temperature Heat transfer efficiency
Flue gas (FG) temperature from gas turbine Air-to-gas ratio setpoint in GT FG temperature after superheater 1 Superheater 1 heat transfer efficiency FG temperature after post-combustion Air-to-gas ratio in post-combustion FG temperature after superheater 2 Superheater 2 heat transfer efficiency FG temperature after evaporator Evaporator heat transfer efficiency FG temperature after economizer Economizer heat transfer efficiency
The result of the variance decomposition method showed that some inputs affected many outputs with relatively similar weights, an iterative search was required to obtain the results seen in Table 1. Only a few of the pairings were found by the variance decomposition method, however the initial selection made by process experts found slightly fewer of the pairs. The results deduce that the method therefore can be an aid for providing a set of pairs for the first iteration. It also provides an insight into the inter- dependence’s of the process and the control automation. The addition of tracking improved matching overall, but not all e.g the flue gas temperature from the gas turbine.
2.3.2 Relative Gain Array
An often used method for input-output pairing for multivariable process control systems is the Relative Gain Array (RGA) (Skogestad and Postlethwaite, 2005), (Bristol, 1966). The RGA, have also been shown to work for non-square systems, and dynamics of the system have in dynamic Relative Gain Array been used for better performance of input output pairing in control problems (Chang and Yu, 1990), (Mc Avoy et al., 2003). The necessity of decoupling MIMO-systems is to avoid coupling, an input change can cause unintended changes in coupled outputs (Skogestad and Postlethwaite, 2005). In the area of parameter control and tracking simulators the method has not been used.
2.3.3 Candidate parameters
Using a automated pairing of tracking parameters and tracking variables still requires a reasonable set of potential parameters that can be adjusted and maintain the idea of first principle modeling. This makes the boundaries, variability of the candidate parameters interesting. In (Friman and Airikka, 2012), (Martínez et al., 2015) the authors use heat transfer coefficient and flow model coefficients, which are parameters that depend on empirical studies and that also differs depending on the flow, fouling on the heat transfer surface. The idea for selecting the candidate parameters is to select candidate parameters based on the uncertainty of the parameter or the degree to which the parameter varies for example due to flow changes. This knowledge can be obtained through process understanding and data from empirical studies on degradation of component, such as (Eaton et al., 2018), . Other parameters such as dynamic pressure changes due to the flow or composition of the medium etc. Ideally, the parameter candidates should correspond to process parameters that typically fluctuate, such as the parameters listed in Table 1.
2.4 Model Initialization
To use a FPM and connect it directly to real process measurements, or the plant as it is referred to in this paper is not a straightforward approach since the state of the plant will affect the parameter adjustment in an undesirable way. This problem has been tackled in (Martínez et al., 2015), where the authors propose a hybrid approach to the initialization which is a combination of two methods, a rough initialization and a automatic model validation sequence. The necessity of initializing the simulator is increased in a online simulator. By utilizing said hybrid approach, the authors can start the tracking closer to the real process value. The hybrid approach is done by using the control system of the real pro- cess and drive the simulator towards a state whilst saving child models that aim to optimize the variables.
A parameter estimation can be done by gray box modeling, using a-priori knowledge of the process (Arendt et al., 2019). The cited literature proposes the usage of an evolutionary algorithm on old data to estimate the parameters. This package available for implementation in Python attempts to find the parameters that best explains the data by defining the mean squared error as cost function. Using real process measurements, boundaries of the parameters the objective is to minimize the cost function by finding the best parameter fits, this is done through a evolutionary algorithm, followed by a gradient based optimization solver.
2.5 Applications
The applications of the different approaches, parameter adjustment and state adjustment shares alot of the applications. The main difference however is the fact that in a successful parameter adjustment method, the simulator allows for a more reliable prediction of future states, by continuously updating the model parameters. The parameter adjustment can also, if opportune selections are made, indicate degradation of components, such as fouling in heatexchangers.
3 Theory
In this section the underlying theory behind the applied model update methods are explained.
3.1 Initial Parameters Estimation
To get an initial estimation of the parameters, a gray box estimation process can be used. The evolution- ary algorithm used in the initialization attempts to minimize the residuals by adjusting the suggested parameters, see equation 5.
θ = argmin
θΘ
X
i
PN
t=1(ˆy − y)2
N (5)
The objective of the evolutionary algorithm is to minimize the mean squared error between the measurements y and the simulators outputs ˆy. The algorithm uses a tournament style evolutionary algorithm where the best parameters advance themselves and their properties to the next generation and spawn a new generation of parameters for the tournament. This allows the convergence of the parameters to increasingly more likely parameters, with some randomized traits to try and keep the parameter set from entering a local minima. After a couple of generations the evolutionary algorithm stops and a gradient based algorithm searches for improvements. A pseudocode for the algorithm is highlighted by the authors of the ModestPy package in (Arendt et al., 2019).
3.2 Parameter control
Almost all of the presented theories of parameter adjustments, in the literature review are based on the same tracking simulator architecture, using a parameter controller to update the model.
3.2.1 PI-controller
The PI controller consists of a proportional and an integral part that outputs a signal to drive a output towards a setpoint, by comparing the error between the setpoint and the process value, see equation 6.
p(k) = p(k − 1) + Kp(e(k) − e(k − 1)) +Kp
Ti e(k) (6)
In this thesis the PI controllers setpoint is the measured value of the real process and the simulators corresponding measurement is used as the process value, the error e(k) between these measurements is used to adjust model parameters p(k).
In order to minimize instability due to sudden process changes, typically approximated in simulators, a state derailing protection scheme is used in accordance with equation 7. This is done to allow the process to balance out a bit.
˙
msim(k + 1) = ˙msim(k) + K(Li,sim− Li) (7)
3.3 Pairing of tracking variables and parameters
The idea of tracking the variables in a physical twin by adjusting model parameters requires pairing between the variable and a opportune parameter. For larger MIMO systems, decoupling allows for decentralized single loop controllers (Skogestad and Postlethwaite, 2005). In a large system, there may be coupled outputs that are to be tracked and in order to optimize the pairing of variable and parameter, decoupling the parameter controllers is suitable.
3.3.1 Variance-based sensitivity analysis
The Sobol method considers an expansion of a square integrable function f over Ωk, the k-dimensional unit hypercube (Saltelli et al., 2008),
Ωk = (X | 0 ≤ xi ≤ 1; i = 1, ..., k) , (8) with the expansion of f in terms of increasing dimensions as in equation 9,
f = f0+X
i
fi+X
i
X
j>i
fij+ ... + f12...k (9)
in which each individual term is square integrable over the domain of existence and is a function only of the factors in its index, i.e fi = fi(Xi), fij(Xi, Xj) etc. This expansion is not unique, such that the model f can have an infinite choices for it’s terms. Sobol proved that with the assumption that each term has zero mean, then all the terms of the decomposition are orthogonal in pairs. A consequence of this is that the terms can be calculated using the conditional expectations of the model output Y ,
f0= E(Y ), (10a)
fi= E (Y | Xi) − E (Y ) , (10b)
fij= E (Y | Xi, Xj) − fi− fj− E (Y ) , (10c) The variance of the conditional expectation V (fi(Xi)) = V (E(Y | Xi)) can then be used as a measure of sensitivity. The first-order sensitivity index Sidivides the variance of the conditional expectation with the unconditional variance V (Y ),
Si =V (E(Y | Xi))
V (Y ) (11)
The first-order index thus measures the main effect contribution of each input to the variance of the output,in this thesis the first-order index will be interchangeably called the main effect index. The total effect index computes the total contribution to the output variation due to the factor Xi, the summation of the main effect index and the subsequent higher order effects,providing information on the overall effect adjusting the parameter would bring.
3.3.2 Relative Gain Array
The relative gain array is a common method for decoupling by pairing inputs and outputs. G(0) is calculated using the steady state change in outputs when a step change in input is applied. Each element in the matrix gij is the change in output yi with a change in input uj, see equation 12 for an example of a matrix with m outputs and n inputs.
G(0) =
dy1 du1
dy1
du2 · · · dudy1
n
dy2
du1
...
... . .. . .. ...
dym
du1 · · · dydum
n
(12)
The rows in the matrix is each output response to each parameter change. The relative gain matrix array is computed, from the plant at steady state, G(0) see equation 13
Λ = G(0) ◦ (G(0)†)T (13)
Λ is the relative gain array, ◦ denotes the Hadamard product, also known as the elementwise product,
† marks the pseudoinverse in case the matrix G(0) is non-square. Each element in Λ, λi,j is a unit- invariant measurement of the how the output yi depends on the input ui. The ideal value for a pairing is 1, the closer to 1 the more direct dependency between parameter and output.
3.4 Pulping Process
To produce paper, wood is first converted into pulp. The composition of dry wood is primarily cellu- lose,hemicellulose and lignin. The cellulose fibers are converted to pulp, and in order to separate the fibers, white liquor and steam is added with the wood chips to wash the product of the digester. The overall process is shown in Figure 4.
Figure 4: A simplification of the integrated paper making process (Olsson, 2009). Wood chips are treated and washed in the digester, in real life, this occurs in separate processes, to create pulp. In this process white liquor is used, the integrated paper making process allows for reusing the weak black liquor exiting the washing process.
Logs are debarked and then fed into the wood chipper. The wood chips are then fed into the digester and de-lignified then the product is washed and screened, black liquor is then extracted from the process in the recovery process in order to reproduce white liquor. Part of this recovery process is the evaporation plant to produce more potent black liquor, by evaporating water content. The black liquor at the exit of the washing plant has 14-15 %DM and needs to be concentrated to 70-80 %DM, to increase its calorific heating value prior to its combustion in the recovery boiler (Ek et al., 2009). This is typically done using a Multiple-Effect-Evaporator (Olsson, 2009).
3.4.1 Multi Effect Evaporator System
In Figure 5 a counter-current Multiple-effect evaporator (MEEV) is shown. Different variations of the flow directions exist but the main idea is that using heat from the steam evaporates the water content in the liquor. The effects operate at different pressure points, allowing the reuse of steam for the next effect and a lower boiling point for the water in the black liquor. In the counter-flow MEEV high pressure steam is fed into the first step and is used to evaporate the last water content in the black liquor that have had water content evaporated in the previous stage. The condensate is extracted and the steam goes to the next stage, evaporating water content at a lower pressure.
Figure 5: A counter-current flow example of a Multi effect evaporator system. C marks the flow condensate and S marks the flow of the steam. The effects are operated at different pressures allowing for the reuse of the steam in the follwing effect. The figure is a example from a generic evaporation plant.
In Figure 6 one step of a Multi-Effect Evaporator system is shown, medium pressure steam is fed into a tank to serve as a heating fluid to evaporate parts of the water content in the weak black liquor and produce stronger black liquor. Heat is exchanged through the separating wall, causing the water in the black liquor to evaporate and the produced vapor leaves the black liquor cycle. The black liquor is either recirculated into the cycle to go through the evaporator again and a controlled amount of black liquor is forwarded into a flash tank for a final separation process of water from the black liquor. The steam condensate is fed into a condensate tank and vapor is separated from the condensate and the flash-steam at the exit of the tank is fed into subsequent tanks.
Figure 6: The last stage effect, from the black liquors point of view. Steam and black liquor enters the effect and the phase change and the higher temperature of the steam transfers heat to the liquor tank, causing evaporation of water in the liquor.
In the flash tank the high pressure black liquor condensate is exposed to a low pressure steam source and a certain percentage of the water content in the black liquor will flash to steam at the lower pressure.
Figure 7: A conceptual illustration of a flashtank. The black liquor enters the tank and the sudden pressure change cause the water content in the liquor to flash-evaporate, vapor exits at the top of the pressure controlled tank and more potent and cooled black liqour continues to the next section of the plant.
3.4.2 Varying model parameters
As described in the literature review the necessity for realistic candidate parameters is important to keep the first principles modeling reliable. This is done for this process by a brief theory surrounding the components that makes up the model. The model mainly consists of pumps,tanks,valves, heat exchange,
mediums. For the pumps, the reduction in pump head is something that occurs over time. This can be illustrated using a plot from a case study done in (Eaton et al., 2018)
Figure 8: Pump Head reduction over time,
The degradation of the heat transfer coefficient in a heatexchanger in evaporation plants is common due to the phenomenon called fouling, which is caused by build-up of insoluble materials on the heat exchange surface (Müller-Steinhagen and Branch, 1997). The fouling means increased heat resistance and less heat transfer between the mediums and the resitance increases exponentially after a certain amount of fouling has occured (Miiller-Steinhagen, 2003).
Pressure drops and flow coefficient are other parameters to investigate, since they can be uncertain when modeling and vary over time and flow.
4 Method
In order to answer the key questions and reach the objective a structured approach was followed.
First the literature review provided knowledge of the methods currently in use and a basis of what could be applied on the problem, i.e PI control of the parameters and sensitivity analysis for the parameter and variable pairing. The first part of this section consists of a brief introduction to the software. Secondly a description of the intended work structure and the necessary steps to develop a tracking simulator. In the following text a description of the test benches and the real process case study will be given.
4.1 Software
The work is highly dependent on quality software, the available simulator of the plant was built in Dymola, making it a fitting software to use for the modeling. In order to enable a simpler analysis on the simulators i.e the pairing of the tracking variables and the tracking parameters, Python was used as a basis with oppurtune packages downloaded for the environment. This transition was enabled through exporting the constructed models from Dymola using the built-in tool for FMU.
4.1.1 Modelica Language
A basic level of understanding of the Modelica language was gained, and necessary, through practice and literature review (Fritzson, 2015). Dymola is built on the foundations of the Modelica language and in order to vary the parameters as desired required a understanding of the language. Modelica is based on classes, known in Modelica as models. A great analogy of the Modelica language is found in (Fritzson, 2015). The models of Modelica can be compared to a blueprint of an object used in a factory and the factory itself is the Modelica language, compiling the objects.
4.1.2 Dymola
Developed by the European company Dassault Systèmes, Dymola is an flow-sheet based modeling and simulation environment. Optimation AB provided a library of previously designed components or models used in both the test benches as well as in the final simulator.
Dymola also provides options for exporting the models as an FMU. This was used to export the simulators, to enable parametric sweep and parametric analyses in a more fitting environment.
4.1.3 Python language
The python environment was used in this project for the visualizing results and handling of large sets of data. The input-output pairing methods is done in Python, the language provides a simple environment to run simulations over a number of different parameter values in order to obtain the data needed to perform the RGA analysis as well as the variance decomposition analysis. To read and run the exported FMU models in Python the PyFMI package is used (Andersson et al., 2016), the Functional Mockup Interface (FMI) is a standardized interface to enable co-simulation and run models in different envi- ronments. To perform the variance decomposition analysis the package SALib is imported and used
(Herman and Usher, 2017).
The package Pandas was used during the project, mainly for handling the historical data, to resample measurement data and to interpolate data for use with the ModestPy package (Arendt et al., 2019).
This was achieved by finding and sorting the overlapping dates of the provided data, then re-sampling all the data to the same sampling time.
To make the input-output pairing method as efficient and reusable as possible, a package was de- veloped by the author to enable the method to be used on FMU models. The package, referred to as
"Tracking Package" consists of visualization tools, functions for analyzing the model, running parameter sweeps and functions that returns the estimated optimal input-output pairing based on the methods described in the theory section.
4.2 Development of a tracking simulator
Before attempting to track the measurements in the Mörrum evaporation plant the methods are tested first on two different test benches of varying complexity. Then the selected methods are evaluated using historical data from the plant. A work breakdown structure of the tracking simulator is illustrated in Figure 9.
Developing a tracking simulator
Heat exchanger Heating pro- duction process
Mörrum Case study Modeling
Manual pairing One tracking variable
Modeling Automatic pairing
Parameter esti- mation
Mulitple tracked vari- ables
State compen- sation
Data handling Model Initial- ization Automatic Pairing
Parameter esti- mation
Tracking State compen- sation
Figure 9: The work breakdown structure of constructing a tracking simulator. The project is based on applying different methods on two different test benches before attempting to track the real evaporation plant. From left to right the tests evaluated on the different models can be seen.
This section of the thesis describes the method of developing a tracking simulator. In order to get familiar with the concept and to evaluate the approaches two test benches are first developed, before attempting to build a tracking simulator of the Mörrum evaporation plant.
As can be seen in Figure 9, the first test bench is used to get familiarized with building models and tracking a variable by a manually selected parameter. The second test bench introduces the automatic pairing, use of the ModestPy package for parameter initialization, tracking of multiple variables and
a state compensation to avoid initial issues with tank level instabilities. The last part of the tracking simulators is to handle the issues that arise when attempting to implement a tracking simulator to a real case study. This involves processing the historical data, re-sampling it and preparing it for interaction with the simulator. In the literature review, the importance of initializing a online simulator was mentioned and this will be adressed in the case study.
4.3 Initialization
To initialize the parameter values the ModestPy package in Python is used, the package takes the FMU, inputs used, real measured values, the boundaries and the estimated initial parameter values, known values and the desired solution. This method is used on both test bench 2, ( with measurements and inputs generated by a run with the Physical representation) and the Evaporation Model. The ModestPy package is a package intended for gray box parameter estimation, in this thesis the package is intended to be used as an initial approximation of the interesting parameters. The package includes a evolutionary algorithm for fitting the model simulation to the provided data. The setup of the algorithm is done by setting a-priori (considering parameter uncertainties,degradation,physical limitations) estimations of initial values, upper- and lower boundaries of the parameters. Training data consist of the values of the sensors for a real run, which the algorithm attempts to explain by varying the parameters within the bounds with the objective to minimize the difference between the simulation outputs and the provided measurements.
4.4 Pairing of tracking variables and parameters
The choice of the parameters is based on the theory regarding the degradation of components and the uncertainty in the components specifications, i.e., black liquor flowing into the evaporators cause clog- ging and build-up on the heat exchange surface, causing a degradation of the heat exchange transfer coefficient making it a suitable choice as a tracking parameter. In order to handle larger systems with many potential candidates for tracking parameters and a finite number of measurements, a sensitivity analysis method for pairing is utilized.
To collect the needed data to do the sensitivity analysis, Python and previously described packages are used. Problems because of nonlinearities in the results may occur if the parameter is set at the beginning of the simulation, the outputs may end up in completely different stats due to unforeseen transient behavior. To avoid this, a scheme is implemented to break the closed loop at steady state.
The implementation of the Sobol analysis as well as the relative gain array method used in this thesis is based on the steady state gain of a parameter change and in order to overcome this uncertainty a scheme is developed. The system is driven to the desired states using controllers. After stabilizing around equilibrium’s for all the measured output states the controllers are switched off and replaced with a constant output. after an opportune amount of time (to allow the system to stabilize) the desired parameter step change is applied.
4.5 State compensation
To protect the digital twin from becoming unstable (mainly to avoid the tanks from running empty or overflowing before the simulator has settled) , direct state updates are done for integrating state of components, mainly vessels, if the measuring system of the physical twin provides suitable measurements.
If the states in the digital twin becomes unstable, for example tanks overflowing, the error caused by the difference between the PT and DT will be concentrated on the parameters, when in fact it is due to an unstable DT. This is achieved by adding or extracting external states based on a difference between the measurement and the simulated state. For the project this was conducted on the levels of the tank to keep them from disturbing the process.
4.6 Test benches
In order to evaluate the methods and compare the results, two simple test-benches are first built and evaluated. First a simple heat exchanger system is built and the heat transfer coefficient is selected as the parameter to adjust,based on process knowledge. Using the measurements at the outlets of the hot water side from both the digital twin and the digital model representing a physical plant,henceforth called physical twin PT, with added disturbance and measurement errors to emulate real life. The measurement from the PT is used as the setpoint in the parameter controller and the measurement is used as the process-value, the controller is tuned manually.
4.6.1 Heat Exchanger
The first model built is a simple model to try out the performance of controlling the parameters using a PI controller.
Figure 10: The first model used is a heat exchanger. The process consist of two flows entering a counter-flow heat exchanger. The cold flow is being heated by the warm flow and the amount of heat transferred between the two flows is highly dependent on the heat transfer coefficient. In the figure the physical representation and the digital representation can be seen. The test bench includes disturbances to add to the physical representation to further emulate a real life scenario. The outlet temperature of the hot water flow is used as a tracking variable, with alignment achieved by adjusting the heat transfer coefficient. The tracking measurements are used as setpoint and process value into a parameter controller that has been integrated in the digital heat exchanger model.
The test bench is a simple process, built in order to serve as a first validation of the tracking controller methodology. The tracking controller is integrated in the right heat-exchanger and the measurement from the physical and the digital representation are fed in as set point values and process values respectively.
The controller then outputs a new value for the heat transfer coefficient. The results from the simulations on the test bench can be seen in Section 5.1.
4.6.2 Heat production process
Figure 11: A simplified view of the heat production process.
The second test bench is a more advanced process, loosely based on the system described in (Martínez et al., 2018), with some differences. This was chosen as a test-bench for evaluating problems arising with more complex systems, as well as the pairing of tracking variables and tracking parameters. The model is developed in the Dymola environment using the base library and the library provided by Optimation.
The system uses water as a heating medium to exchange heat to an external flow. The water is preheated in tank T100. Then, controlled by a level controller the water is pumped into a storage tank T200. Based on the external heat demand, water is pumped out of the tank into a pressurized heating tank where the temperature is increased. Then heat is exchanged with the incoming cold stream of the emulated district heating. The flow into the heating unit is controlled by having a required temperature on the outgoing flow of the external flow. Tank T400 exists to provide makeup water and store excess water depending on the external heat demand.
Components such as pipes and pumps use pressure loss diagrams, pump design diagrams, for static and dynamic pressure changes. To closer emulate the difference between the real life process and the simulator of said real process, quadratic curves are used for the physical process and linear curves are used for the digital twin.
The evolutionary algorithm of the ModestPy package is used on data generated by a training run, to estimate the parameters. The measurements and the inputs from the training run is used in the algorithm along with settings for the parameters. The initial guess of, lower and upper bounds of the parameter can be seen in Table 2.
Table 2: Initial guess, lower bound and upper bounds for parameters in the evaporation step.
Parameter Initial Guess Low. Bound Up. Bound
HU300kht 1050.0 945.0 1155.0
HEX300kht 1000.0 850 1150
Pipe100k 0.005 0.0001 0.01
Pipe101k 0.005 0.0001 0.01
Pipe200k 0.005 0.0001 0.01
Pipe201k 0.005 0.0001 0.01
V100KvM ax 1.0 0.9 1.1
V200KvM ax 1.0 0.9 1.1
V300KvM ax 1.0 0.9 1.1
V400KvM ax 1.0 0.9 1.1
PU100V F lowDesign 6.6e-05 6.0e-05 7.3e-05
PU100uRise 40000 36000.0 44000.0
PU200V F lowDesign 8.3e-05 7.5e-05 9.16e-05
PU200uRise 40000 36000 44000
In the table, the parameters indexed with kht marks heat transfer coefficients. The k index on the pipes marks a dynamic pressure drop coefficient, the proportional constant between the flow of the water and the pipe. The remaining parameters are all component parameters, KvM ax marks the design spec- ification for the maximal flow capacity of the valve. V F lowDesign is the index for the volume-flow the pump was designed for, and uRise is the pressure increase of the pump. The design specifications are chosen to emulate potential degradation in components. The results from the global sensitivity analysis was deemed to be too time consuming for more complex models and the analysis was dropped during the second test bench. The method yielded similar pairing recommendations, but required many more iterations compared to the RGA analysis.
Figure 12: The automatically generated tracking box connected to the digital twin and the physical twin. Both the DT and the PT gets the same signals from the control system, that uses the measurements of the physical twin to keep desired operating points.
The pairing of the parameters was done by turning off the controllers, applying a step change of each parameter and measuring the effect on all the sensors in the model. Then a sensitivity analysis can be performed to pair the parameter that has an effect on each measurement and aim to pair a tracking variable with a suitable tracking parameter. The number of pairings is fed into a automatic code generator that returns a tracking-box to implement in Dymola. The internal coding and parameter boundaries are set in the code, but the actual connections to the measurements in the PT and the DT need to be connected in Dymola. The inputs of the tracking-box gives the name of the measurement to connect and to where. The implementation of the tracking-box can be seen in Figure 12.
An alternate route from the tracking box is to do the connections in the Python environment. By connecting all available sensors to real expression blocks in Dymola, and connecting these into a scaled PID control block, the output from the controller can be used directly in Python. Scaling the 0-100%
output of the controller in accordance to the selected parameter allows the user to skip the step of integrating the tracking box into Dymola after the initial analysis. The pairing and the function can still be automatically generated.
The tracking of the measurements was also conducted in Python, since the PyFMI package allowed for an easier access to adjusting parameters, both for emulating degradation but also for updating the selected tracking parameter. The work process of tracking the selected parameter is achieved by installing the tracking-box in Dymola and downloading the new FMU. PyFMI allows the user input functions and assign them to a parameter. A function used to adjust the desired parameter is simplified below.
i m p o r t n u m p y as np def P a r C h a n g e ( t ):
if t >1:
p1 = m o d e l . get ( " P a r a m e t e r C o n t r o l l e r _ o u t " ) p2 = m o d e l . get ( " P a r a m e t e r C o n t r o l l e r _ o u t " ) e l s e :
p1 = i n i t i a l v a l u e of p1 p2 = i n i t i a l v a l u e of p2 r e t u r n np . a r r a y ([ p1 , p2 ]) p a r l i s t =[ p a r n a m e 1 , p a r n a m e 2 ]
m o d e l . s i m u l a t e ( i n p u t =( parlist , P a r C h a n g e ))
This creates a dependency, where the parameter is set to the output signal of the corresponding parameter controller. This allows for parameter adjustment without the need to alter components as was done in the first test bench, see Figure 10.
4.6.3 The Mörrum Digital Twin Project
The last part of this thesis aimed to implement the framework developed in the previous test benches on a real process. The process used for evaluating the framework was the last evaporator step, from the perspective of the black liqour, at Södra Cells paper mill in Mörrum.
A simplified description of the last evaporation model: The step is the last step of the evaporators, so the incoming steam have the highest pressure and temperature, able to lower the remaining water content in the liquor. Black liquor is added to the step, with the incoming flow, from the previous evap- orator step, controlled by a valve. This flow is added to the black liquor already in the re-circulation flow and enter into the evaporator. In the evaporator, heat is transferred to the black liquor from steam in a separate tank, a tank of high pressured steam. The heat exchange makes a fraction of the water in the black liquor evaporate, providing a more concentrated liquor.
The outgoing black liquor is either re-circulated into the tank or fed forward in the processes, keeping the evaporation tank at a set level. The level in the tank is estimated by measuring the pressure differ-
ence in the inflow and the outflow of the tank. This measurement is then used in a feedback controller, sending a signal to adjust the opening of a control valve, effectively keeping the level of the black liquor in the evaporator at the setpoint. The liquor that passes through the valve then enters a flash-tank causing additional water content in the black liquor, further refining the liquor quality. The vapor produced in the flash tank is transported away to be used in other steps of the evaporation. The refined black liquor is pumped on-wards by a pump.
The steam that is used for evaporating the water content either condenses or remains steam, with a lower pressure. The condensate goes into the condensate tank, the remaining steam is used at the next evaporation step. The model of the process was constructed by Optimation in an earlier project, there- fore the new tracking simulator is built upon the model. The choice for candidate tracking parameters is based on the available measurements, process knowledge and availability. The model contains a number of components with potential candidates for tracking.
To increase the robustness, the framework is first applied to historical data. Södra Cell provided measurements along with the necessary DCS data. The sampling on the provided data differs from measurement to measurement, in order to be used in the implementation algorithm, linear interpolation was carried out on the data to get matching time instances. The data was separated into training and validation data and applied to the evolutionary algorithm, to provide starting values for the parameters.
The tracking is done in Python, one difficult issue that arised during the tracking of the simulator is the initiation of the mediums. Since the focus is only on one step, the simulator is a sliced part of the complete process. The flow of the mediums are controlled by pressure sources, the pressure source of the steam is controlled by the real measurement before the evaporator. The black liquor is initiated by using a controller that adjusts the pressure source by comparing the real incoming black liquor flow measurements of the process to the simulated to try and align the flows. This was difficult to implement over time periods that had flow stoppages due to the level of the tanks in the simulator presenting undesired characteristics, the quick shift resulted in the temperature after the tank. To deal with this issue of slicing a process with a lot of varying pressures, two runs was conducted. The first tracking simulator, keeps the known pressures closer to the real process measurements. The second run focuses on trying to keep a balanced flow, both methods are simplifications and information will be lost. This will be discussed in the analysis of the results.
5 Results
In this section the results from the Master thesis is presented, the first section starts with the first test bench and the result of the parameter controller implemented on the heat exchanger.
5.1 Heat exchanger
The results from adjusting the heat transfer coefficient on the first test bench can be seen in Figures 13-19. In Figure 13 there is nothing adjusting the heat transfer coefficient and the modeling error results in a a difference between the Pysical twin and the Digital Twin.
Figure 13: The outlet temperatures of the hot water flow for the PT and the DT with no control of the heat transfer coefficient. The two models differ in the modeling of the heat transfer coefficient. The used heat transfer coefficients are kht= 1000 for the DT and kht= 910 for the PT.
In Figure 14, a parameter controller adjusts the heat transfer coefficient in order to align the second outlet temperature.
Figure 14: The outlet temperatures of the streams for the PT and the DT with control of the heat transfer coefficient from the initialization of the system. The two models differ in the modeling of the initial heat transfer coefficient. The used heat transfer coefficients kht= 910 for the physical twin and kht= 910 for the digital twin.
The tracking of the outlet temperature the hot water outlet, can be seen to converge. The adjustment of the heat transfer coefficient in the digital twin and the actual value of the heat transfer coefficient for this scenario is seen in Figure 15.
Figure 15: The only differentiating factor between the digital representation and the physical model is the heat transfer coefficient, the heat transfer coefficient eventually is corrected in the tracking simulator.
