Extended Dynamic Mode Decomposition (EDMD) and its variant, the pqEDMD, which uses a p-q-quasi norm reduction of polynomial basis functions, are attractive tools to derive linear operators approximating the dynamic behavior of nonlinear systems. This study highlights how this methodology can be applied to data-driven modeling and control of bioprocesses by discussing the selection of several ingredients of the method, such as the polynomial basis, order, data sampling, and preparation for training and testing, and ultimately, the exploitation of the model in linear model predictive control.

Precision modeling and forecasting of soil moisture are essential for implementing smart irrigation systems and mitigating agricultural drought. Most agro-hydrological models are based on the standard Richards equation, a highly nonlinear, degenerate elliptic-parabolic partial differential equation (PDE) with first order time derivative. However, research has shown that standard Richards equation is unable to model preferential flow in soil with fractal structure. In such a scenario, the soil exhibits anomalous non-Boltzmann scaling behavior. Incorporating the anomalous non-Boltzmann scaling behavior into the Richards equation leads to a generalized, time-fractional Richards equation based on fractional time derivatives. As expected, solving the time-fractional Richards equation for accurate modeling of water flow dynamics in soil faces extensive computational challenges. To target these challenges, we propose a novel numerical method that integrates finite volume method (FVM), adaptiv... [more]

Deep learning faces significant challenges in efficiently training large-scale models. These issues are closely linked, as efficient training often depends on precise and computationally feasible gradient calculations. This work introduces innovative methodologies to improve deep learning network (DLN) training in complex systems. A novel approach to DLN training is proposed by adapting the block coordinate descent (BCD) method, which optimizes individual layers sequentially. This is combined with traditional batch-based training to create a hybrid method that harnesses the strengths of both techniques. Additionally, the study explores Iterated Control Random Search (ICRS) for initializing parameters and applies quasi-Newton methods like L-BFGS with restricted iterations to enhance optimization. By tackling DLN training efficiency, this contribution offers a comprehensive framework to address key challenges in modern machine learning. The proposed methods improve scalability and effect... [more]

This study presents an integrated approach combining the Analytic Hierarchy Process (AHP) with a Mixed-Integer Multi-Objective Linear Programming (MOMILP) model to evaluate sustainable power generation alternatives for Pamplona, Colombia. The MOMILP model includes solar, wind, biomass, and diesel technologies, aiming to minimize costs (net present value) and CO2 emissions while considering design, operational, and budget constraints. The AHP method evaluates multiple criteria such as social acceptance, job creation, technological maturity, and environmental impact. The results show that solar panels are prioritized, with small diesel plants added due to resource limitations. The most sustainable option is a hybrid system with 49% solar, 29% wind, 14% biomass and 8% diesel, generating a net present value of 121,360 USD and 94,720 kg of CO2 emissions. The proposed methodology can be applied to assess and select the most feasible alternative within a wide range of new projects for the int... [more]

In process systems engineering (PSE), obtaining accurate process models for optimization can be expensive and time-consuming. Black-box Bayesian Optimization (BO) with Gaussian process (GP) surrogates offers a promising approach. However, full black-box optimization neglects valuable prior knowledge, which could otherwise improve the optimization process. This work explores methods of integrating prior knowledge in the form of low-fidelity data into BO by evaluating these methods on synthetic multi-fidelity test functions. Our results highlight possibilities for improved convergence of the BO optimization. However, our work further highlights potential pitfalls of these multi-fidelity models, such as bias, convergence to local optima, and overfitting on low-fidelity data. Hence, leveraging low-fidelity data in multi-fidelity models can improve BO convergence, but there are instances where the algorithms are more susceptible to failure.

The definition of strategies for operation of process networks is a key research focus in process systems engineering. This challenge is commonly formulated as a numerical constraint satisfaction problem, where most practical algorithms are limited to identifying inner approximations to the feasible operational envelope. Sampling-based approaches so far have only been developed for formulations that required coordinated operation of the units within the network. We propose a decomposition approach that enables decentralized operation for acyclic muti-unit processes by sampling. Our methodology leverages problem structure to decompose unit-wise and deploys surrogate models to couple the resultant subproblems. We demonstrate it on a serial, batch chemical reactor network. In future research, we will extend this framework to consider the presence of uncertain unit parameters robustly.

An essential problem in precision agriculture is to accurately model and predict root-zone (top 1 m of soil) soil moisture profile given soil properties and precipitation and evapotranspiration information. This is typically achieved by solving agro-hydrological models. Nowadays, most of these models are based on the standard Richards equation (RE), a highly nonlinear, degenerate elliptic-parabolic partial differential equation that describes irrigation, precipitation, evapotranspiration, runoff, and drainage through soils. Recently, the standard RE has been generalized to time-fractional RE with any fractional order between 0 and 2. Such generalization allows the characterization of anomalous soil exhibiting non-Boltzmann behavior due to the presence of preferential flow. In this work, we focus on inverse modeling of time-fractional RE; that is, how to accurately estimate the fractional order and soil property parameters of the fractional RE given soil moisture content measurements. S... [more]

Contains 423 original peer-reviewed research articles presented at the 35th European Symposium on Computer Aided Process Engineering (ESCAPE 35). Subject categories include Modelling and Simulation, Sustainable Product Development and Process Design, Large Scale Design and Planning/Scheduling, Model Based Optimisation and Advanced Control, Concepts, Methods and Tools, Digitalization and AI, CAPEing with Societal Challenges, CAPE Education and Knowledge, PSE4Food and Biochemical, and PSE4BioMedical and (Bio)Pharma.

Contains 134 original peer-reviewed research articles and 10 extended abstracts submitted to FOCAPD 2024. Subject categories include Invited Plenary and Keynote Submissions, Advances in PSE Design, Design and Emerging Fields, Design and Energy Transitions, Design and Sustainability, and Design Education and Future of Design. The scope is process design as it applies to process systems engineering in chemical engineering, energy systems engineering, and related fields.

Some educators place an emphasis on the commonalities between engineering mathematics with process control, among others and this helps students see the bigger picture of what is being taught. Traditionally, some of the concepts such as diffusion and heat transfer are taught with a mathematical point of view. Now-a-days, Machine Learning (ML) has emerged as topic of greater interest to both educators and learners and new and disparate modules are sometimes introduced to teach the same. With the emergence of these new topics, some students (falsely) believe that ML is a new field that is somehow different and not linked to engineering mathematics. In this work, we show the link between the different topics from engineering mathematics, that are traditionally taught in UG education, with ML. We hope that educators and learners will appreciate the treatise and think differently, and we further hope that this will further increase the interest to improve ML models.

The Anaerobic Digestion Model 1 is the quasi-industry standard for modelling anaerobic digestion, and it has seen several new implementations in recent years. It is assumed that these implementations would give the same results; however, a thorough comparison of these implementations has never been reported. This paper considers four different implementations of ADM1: one in Julia, one in Java, and two in Python. The Julia code is a de novo implementation of the ODE formulation of ADM1 that is reported here for the first time. The existing Java and Python codes implement the more common DAE formulation. Therefore, this paper also examines how DAE implementations compare to ODE implementations in terms of computational speed as well as solutions returned. As expected, the ODE and DAE forms both return comparable solutions. However, contrary to popular belief, the Julia ODE implementation is faster than the DAE implementations, namely by one to three orders of magnitude of compute time,... [more]

Advanced control strategies, together with state-estimation methods, are frequently applied to nonlinear and complex systems. It is crucial to understand which of these are the most efficient methods for the best use of these approaches in a chemical process. In the current work, nonlinear model predictive control (NMPC) approaches were developed that considered three numerical methods: single shooting (SS), multiple shooting (MS), and orthogonal collocation (OC). Their performance was compared against the Van de Vusse reactor benchmark while considering set-point changes, unreachable set-point, disturbances, and mismatches. The results showed that the NMPC based on OC presented less computational cost than the other approaches. The extended Kalman filter (EKF), constrained extended Kalman filter (CEKF), and the moving horizon estimator (MHE) were also developed. The estimators’ performance was compared for the same benchmark by considering the computational cost and the mean squared e... [more]

The results of numerical investigations of heat transfer and pressure drops in a channel with 30° helical micro-fins are presented. The main aim of the analysis is to examine the influence of the height of the micro-fins on the heat-flow characteristics of the channel. For the tested pipe with a diameter of 12 mm, the micro-fin height varies within the range of 0.05−0.40 mm (with 0.05 mm steps), which is equal to 0.4−3.3% of its diameter. The analysis was performed for a turbulent flow, within the range of Reynolds numbers 10,000−100,000. The working fluid is water with an average temperature of 298 K. For each tested geometry, the characteristics of the friction factor f(Re) and the Nusselt number Nu(Re) are shown in the graphs. The highest values of Nusselt numbers and friction factors were obtained for pipes with the micro-fins H = 0.30 mm and H = 0.35 mm. A large discrepancy is observed in the friction factors f(Re) calculated from the theoretical relationships (for the irregular r... [more]

The expanding role of renewable energy sources in the electricity market share implies the increasing role of hydropower and the exploitation of unharnessed hydraulic potential, in the scope of sustainability and net zero emissions. Hydro-turbine design practices are expected to expand beyond achieving high efficiency goals, to multi-objective criteria ranging from efficient reversible operation to fish-friendly concepts. The present review paper outlines fundamental characteristics of hydropower, summarizing its potential impact toward aquatic life. Estimates of lethality for each damage mechanism are discussed, such as barotrauma, blunt impact and shearing, along with relevant advances in experimental techniques. Furthermore, numerical techniques are discussed, ranging from simple particle tracking to fully coupled six-degree-of-freedom tracking, which can be used to investigate candidate designs and their fish-friendly performance, presenting their advantages and disadvantages. Subs... [more]

The article deals with the issue of the influence of selected material and construction solutions for a floor in a historic wooden building on heat exchange with the ground. The scope of the work included continuous measurements of selected parameters of internal and external microclimate, which were later used for numerical analysis of selected calculation variants. The research was carried out in a historic wooden church located in southern Poland. The research period covered 2019, while all measurements were performed every 1 h. For the variant analysis, a building with a wooden and stone floor was adopted. The influence of the heating system on the heat exchange with the ground for wooden and stone floors was also analysed. As a result of a detailed analysis, it was found that the material and construction solutions, as well as the heating system, have a significant impact on the formation of heat exchange with the ground. The building with a wooden floor was characterised by signi... [more]

Advances in the field of material engineering, computerization, automation, and equipment miniaturization enable modernization of the existing technologies and development of new solutions for construction, inspection, and renovation of underground pipelines. Underground pipe installations are used in the energy sector, gas industry, telecommunications, water and sewage transport, heating, chemical industry, and environmental engineering. In order to build new pipeline networks, dig and no-dig techniques are used. Horizontal Directional Drilling (HDD) is one of the most popular trenchless technologies. The effectiveness of HDD technology application is mostly determined by its properly designed trajectory. Drilling failures and complications, which often accompany the application of the HDD technology, result from poor design of the well path in relation to the existing geological and drilling conditions. The article presented two concepts of Horizontal Directional Drilling well path t... [more]

The accuracy of fitting the rheological model to the properties of actual drilling fluid minimises the errors of the calculated technological parameters applied while drilling oil wells. This article presents the methodology of selecting the optimum drilling fluid rheological model. Apart from classical rheological models, i.e., the Newtonian, Bingham Plastic, Casson, Ostwald de Waele and Herschel−Bulkley models, it has been proposed to consider the Vom Berg and Hahn-Eyring models, which have not been applied to describe drilling fluids so far. In the process of determining rheological parameters for the Bingham Plastic, Casson, Ostwald de Waele and Newtonian models, it is proposed to use a linear regression method. In the case of the Herschel−Bulkley, Vom Berg and Hahn-Eyring models, it is suggested to use a non-linear regression method. Based on theoretical considerations and mathematical relations developed in the Department of Drilling and Geoengineering, Drilling, Oil and Gas Facu... [more]

Electromechanical coupling devices have been playing an indispensable role in modern engineering. Particularly, flexoelectricity, an electromechanical coupling effect that involves strain gradients, has shown promising potential for future miniaturized electromechanical coupling devices. Therefore, simulation of flexoelectricity is necessary and inevitable. In this paper, we provide an overview of numerical procedures on modeling flexoelectricity. Specifically, we summarize a generalized formulation including the electrostatic stress tensor, which can be simplified to retrieve other formulations from the literature. We further show the weak and discretization forms of the boundary value problem for different numerical methods, including isogeometric analysis and mixed FEM. Several benchmark problems are presented to demonstrate the numerical implementation. The source code for the implementation can be utilized to analyze and develop more complex flexoelectric nano-devices.

Increasing the efficiency of the solar energy harvesting system is an urgent need in light of the climate changes we live in nowadays. The most significant data to be processed in the photovoltaic harvesters are the curve of solar radiation intensity to achieve the maximum benefits of the solar incident light. This processing contains complicated procedures, and the used algorithms are also high computational power-consuming which makes using special software and high potential hardware essential requirements. An explanation of the Minimum Energy Effect method is presented in this article. Our proposed algorithm uses this method to provide a simple and high-accuracy mathematical tool for generating a simple alternative curve instead of the complicated original nonlinear curve of solar radiation intensity. The produced curve is suitable for further operations, such as derivatives, integrals, or even simple addition/subtraction. Our algorithm provides a gradual procedure to find an optim... [more]

Mathematical models of induction motor (IM) used in direct field-oriented control (DFOC) strategies are characterized by parametrization resulting from the IM equivalent circuit and model-type selection. The parameter inaccuracy causes DFOC detuning, which deteriorates the drive performance. Therefore, many methods for parameter adaptation were developed in the literature. One class of algorithms, popular due to their simplicity, includes estimators based on the model reference adaptive system (MRAS). Their main disadvantage is the dependence on other machines’ parameters. However, although typically not considered in the respective literature, there are other aspects that impair the performance of the MRAS estimators. These include, but are not limited to, the nonlinear phenomenon of iron losses, the effect of necessary discretization of the algorithms and selection of the sampling time, and the influence of the supply inverter nonlinear behavior. Therefore, this paper aims to study t... [more]

Various technological fluids, such as drilling muds, drill-in fluids, fracturing fluids, spacers, washes and cement slurries are used in the wellbore drilling process. The fundamental issue, which needs to be addressed in order to become acquainted with the phenomena occurring during fluids flow through a circulatory system, is to establish mutual dependencies between a stream of fluid being pumped and flow resistances. The awareness of these dependencies enables the optimisation of hydraulic parameters in order to minimise costs and maximise drilling works safety. This article presents rheological models of drilling fluids and proposes the application of a new rheological model, not used in the drilling industry so far, namely the Vom Berg model. The model has been presented in other publications; however, there is an unsolved and unpublished problem of determining the effect of rheological parameters of the model on the value of resistance to laminar and turbulent flow. In this artic... [more]

This article presents rheological models of fluids used in the drilling practice. It discusses the principles of determining drilling fluid rheological parameters based on data acquired from measurements by means of viscometers used in the drilling practice. The authors propose the application of the three-parameter Vom Berg and Hahn−Eyring models not used in the drilling industry so far. Necessary relationships have been developed for these models, which enable the determination of rheological parameters. In order to account for the influence of different flow conditions on the value of drilling fluid rheological parameters, the approach proposing the determination of rheological parameters of a given three-parameter model separately for low shear rates and high shear rates has been suggested. A practical application of the methodology proposed in this paper for determining the rheological parameters of the three-parameter Vom Berg and Hahn−Eyring models is presented using real drilli... [more]

Long electromagnetic transients occur in electrical systems because of switching and impulse actions As a result, the simulation time of such processes can be long, which is undesirable. Simulation time is significantly increased if the circuit in the study is complex, and also if this circuit is described by a rigid system of state equations. Modern requests of design engineers require an increase in the speed of calculations for realizing a real-time simulation. This work is devoted to the development of a unified spectral method for calculating electromagnetic transients in electrical circuits based on the representation of solution functions by series in algebraic and orthogonal polynomials. The purpose of the work is to offer electrical engineers a method that can significantly reduce the time for modeling transients in electrical circuits. Research methods. Approximation of functions by orthogonal polynomials, numerical methods for integrating differential equations, matrix metho... [more]

The numerical study of solid/liquid phase change problems represents a large and ongoing field of research with many applications. These simulations should run as fast and accurately as possible. Therefore, proceeding from previous work and findings from the literature, this study investigates enthalpy methods for solving solid/liquid phase change problems. The relationship between temperature and enthalpy is strongly non-linear and requires special treatment; iteratively corrected methods, as well as approaches that do not correct the temperature/enthalpy relationship at all or only once per time step, were considered for a one-dimensional test problem. Based on the results of this study, two solvers can be recommended, the so-called optimum approach and a simple explicit method; both provide accurate results. The explicit method is easy to program, but the optimum approach allows larger time steps and is, therefore, faster. The influence of several parameters was investigated. The me... [more]

This paper describes the further development of the virtual flow meter concept based on the author’s simulator of an unsteady gas−liquid flow in wells. The results of comparison with commercial simulators based on real well data are given as practical applications. The results of the comparison of the simulators demonstrated high correspondence (<10% error) for a number of target parameters. The description of the architecture and results of testing the algorithm for automatic settings of the model parameters are given. Operating speed was the key criterion in the architecture development. According to the test results, it became possible to achieve the adaptation accuracy of 5% specified.