Groundwater pollution mathematical modelling : Improvement or stagnation ?

Buildings, consuming over 70% of the electricity in the U.S., play significant roles in smart grid infrastructure. The automatic operation of buildings and their subsystems in responding to signals from a smart grid is essential to reduce energy consumption and demand, as well as improve the resilience to power disruptions. In order to achieve such automatic operation, high fidelity and computationally efficiency building energy forecasting models under different weather and operation conditions are needed. Currently, data-driven (black box) models and hybrid (grey box) models are commonly used in model based building control operation. However, typical black box models often require long training period and are bounded to weather and operation conditions during the training period. On the other hand, creating a grey box model often requires long calculation time due to parameter optimization process and expert knowledge during the model structure determining and simplification process. An earlier study by the authors proposed a system identification approach to develop computationally efficient and accurate building energy forecasting models. This paper attempts to extend this early study and to quantitatively evaluate how the most important characteristics of a building energy system: its nonlinearity and response time, affect the system identification process and model accuracy. Two commercial building: a small-size and a medium-size commercial building, with varying chiller nonlinearity, are simulated using EnergyPlus in lieu of real buildings for model development and validation. The system identification method proposed in the early study is applied to these two buildings that have varying nonlinearity and response time. Adaption of the proposed system identification method based on systems’ nonlinearity and response time is proposed in this study. The energy forecasting results demonstrate that the adaption is capable of significantly improve the performance of the system identification model.

One promising approach to reduce carbon foot print of internal combustion engines (ICEs) is using alternative fuels like hydrogen, particularly by converting medium and heavy-duty diesel engines to dual-fuel hydrogen-diesel engines. To minimize elevated NOx emissions from hydrogen-fueled engine, fast and accurate emission models are essential for engine model-based control and for engine calibration and optimization using hardware-in-the-loop (HIL) setups. In this study, a fast-response NOx emissions sensor is used to measure the transient NOx emissions from a dual-fuel hydrogen-diesel engine. Subsequently, steady-state models (SSMs), quasi steady-state models (QSSMs), and transient sequential models (TSMs) in the form of black-box (BB) and gray-box (GB) models are developed for transient NOx emissions prediction. GB models utilize both information from a one dimensional (1D) physical engine model and experimental data for training, while BB models only use experimental data. SSMs are optimized artificial neural networks (ANNs) trained using steady-state data, QSSMs are optimized ANNs trained using transient data, and TSMs are time-series networks trained using transient data. Long short-term memory (LSTM) and gated recurrent unit (GRU) networks are used as the time-series deep learning networks. The results showed that the 1D physical model has the poorest performance with successive model performance improvement from SSM to QSSM and from QSSM to TSM. The developed BB TSM model in this study can predict transient NOx emissions with an R2 value greater than 0.96 at 89,000 predictions per second which makes this model suitable for real-time engine model-based control where computational efficiency is crucial. The developed GB TSM model can predict transient NOx emissions with an R2 value greater than 0.97 but it is computationally more expensive. The extra accuracy of the GB TSM models makes them the best choice for HIL setups where more computational power is available, and accuracy is more crucial.

Virtual sensors, or soft sensors, have greatly contributed to the evolution of the sensing systems in industry. The soft sensors are process models having three fundamental categories, namely white-box (WB), black-box (BB) and gray-box (GB) models. WB models are based on process knowledge while the BB models are developed using data collected from the process. The GB models integrate the WB and BB models for addressing the concerns, i.e., accuracy and intuitiveness, of industrial operators. In this work, various design aspects of the GB models are discussed followed by their application in the process industry. In addition, the changes in the data-driven part of the GB models in the context of enormous amount of process data collected in Industry 4.0 are elaborated.

System identification based on the black box models was utilized for understanding of the transfer function of the foot and ankle exposed to vertical excitation. Various linear polynomial structures and state-space model were tested by comparing the measured acceleration at the base, the Medial Malleolus, and the Tibial Tuberosity respectively for input and output. Identified models are well matched with the measured data when the high model order was selected. The Output Error model has generally shown the best fit to the data, while in several cases the state-space model presents better fit. These results can be used as a starting point for the nonlinear black box model and the grey box model.

Thermal models of buildings are helpful to forecast their energy use and to enhance the control of their mechanical systems. However, these models are building-specific and require a tedious, error-prone and time-consuming development effort relying on skilled building energy modelers. Compared to white-box and gray-box models, data-driven (black-box) models require less development time and a minimal amount of information about the building characteristics. In this paper, autoregressive neural network models are compared to gray-box and black-box linear models to simulate indoor temperatures. These models are trained, validated and compared to actual experimental data obtained for an existing commercial building in Montreal (QC, Canada) equipped with roof top units for air conditioning. Results show that neural networks mimic more accurately the thermal behavior of the building when limited information is available, compared to gray-box and black-box linear models. The gray-box model does not perform adequately due to its under-parameterized nature, while the linear models cannot capture non-linear phenomena such as radiative heat transfer and occupancy. Therefore, the neural network models outperform the alternative models in the presented application, reaching a coefficient of determination R2 up to 0.824 and a root mean square error down to 1.11 °C, including the error propagation over time for a 1-week period with a 5-minute time-step. When considering a 50-hour time horizon, the best neural networks reach a much lower root mean square error of around 0.6 °C, which is suitable for applications such as model predictive control.

The concept of fuzzy instrumental variable and an approach for fuzzy identification of nonlinear discrete time systems were proposed. Convergence conditions for identification in a noisy environment in a fuzzy context were studied. Simulation results for off-line and on-line schemes evidence the good quality of this fuzzy instrumental variable approach for identification and function approximation with observation errors in input and output data.

• Enhanced SSV airflow rate estimation of empirical models via data-driven modeling • Achieved high accuracy by customizing models individually for each room • Compared gray-box (physics-informed) with black-box (purely data-driven) models • Assessed data efficiency and model generalization using learning curve analysis • Revealed model robustness and key factors affecting airflow by sensitivity analysis Empirical models are widely used in building design and simulation to estimate airflow rates for single-sided natural ventilation (SSV). However, these models often suffer from limited accuracy. Data-driven modeling offers a viable solution to improve model accuracies by customizing models for various practical scenarios. This study investigates the feasibility and performance of two data-driven modeling approaches for SSV: gray-box modeling (physics-informed using polynomial regressions) and black-box modeling (purely data-driven using machine learning regressions). Taking SSV through a solitary bottom-hung window as a case study, training data were acquired from a full-scale test bench via tracer gas measurements conducted over 11 days. The results indicate that both modeling approaches significantly improve accuracy compared to existing empirical models from the literature. Notably, individual models tailored for each test room generally outperform generalized models developed for all rooms. This finding highlights the importance of customizing models on-site in real-world applications. When comparing the two modeling approaches, gray-box models require lower training ratios to achieve good generalization, demonstrating higher data efficiency than black-box models. Furthermore, sensitivity analysis reveals that gray-box models are more robust and reliable during interpolation and extrapolation, making them particularly suitable for scenarios with limited data availability. Incorporating opening area corrections and selecting root mean square error (RMSE) as the objective function are crucial for achieving optimal gray-box model performance. Overall, this study highlights the potential of physics-informed gray-box data-driven modeling as an advanced strategy for enhancing SSV airflow rate estimation, providing valuable insights to guide future research.

Classical theory for systems of the first order partial differential equations for a scalar function can be rephrased as the submanifold theory of contact manifolds (geometric first order jet spaces). In the same spirit, we will develop the geometric theory of systems of partial differential equations of second order for a scalar function as the Contact Geometry of Second Order, following E. Cartan.We will formulate the submanifold theory of second order jet spaces as the geometry of PD manifolds (R;D 1 ,D 2 ) of second order. Moreover we will establish the First Reduction Theorem for (R;D 1,D 2) admitting non-trivial Cauchy characteristic systems. By utilizing Parabolic Geometry, we will give, directly or combined with reduction theorems, several classes of systems of partial differential equations of second order, for which the model equation of each class admits the Lie algebra of infinitesimal contact transformations, which is finite dimensional and simple.

Gray box model and artificial neural network (ANN) model of central air-conditioning cold source system have been established with simulation data to predict system operation energy consumption and compare the prediction accuracy difference of models under variable training data. A hybrid model is proposed to combine gray box model and ANN model based on K-means cluster algorithm. The results show that ANN model has higher prediction accuracy than gray box model when the membership of model input variables to trained input data is greater than 0.4. Otherwise, the gray box model has higher energy consumption prediction accuracy. Compared with gray box model and ANN model, prediction accuracy of hybrid model increases 27.7% and 33.85% on average under different training data.

Entropy measures the disorderness or randomness of the systems. It may affect the effectiveness and performance of the thermal systems. That is why entropy analysis is one of the trending research topic in modern era of society. The motive of this article is to present a comprehensive analysis of entropy generation and thermal dispersion effect on mixed convective flow of (Cu-Al2O3)/(H2O) based hybrid nanofluid along a plate submerged in a non-Darcy porous medium. The mathematical model describing the flow problem encompasses a system of partial differential equation, resulting from the single-phase flow model of the nanofluid combined with the Darcy-Forchheimer expression for porous medium flow. The dimensional system of partial differential equation is transformed into a non-dimensional nonlinear ordinary differential system through a similarity transformations and subsequently, the system is solved using the BVP4C module in MATLAB. The study analyzes the flow variables and entropy generation with respect to the parameters inherent in the problem. The findings suggests that, the increasing thermal dispersion effects enhances the Heat transfer rate of the hybrid nanofluid. Further, it is reported that the entropy generation in hybrid nanofluid is lower than the mono nanofluid which makes the hybrid nanofluid a better choice for entropy management in the thermal systems. The outcome of the research has practical implications in various real-life applications, such as crude oil production, oil flow filtration, electronic cooling equipment, etc.

Investigation of nanofluid flows under various conditions is becoming fascinating research due to its numerous applications in many science and engineering fields such as solar energy, geothermal energy, water purification, glass blowing, enhanced oil recovery, petroleum production and food processing. For the present requirements in thermal energy applications, this mathematical model is considered to explore the diffusion and heat source effects on the flow of conductive Casson and Maxwell nanofluids in a porous medium on an elongating sheet with a chemical reaction. Further, the effects of viscous dissipation and thermal radiation are also examined. Moreover, the entropy generation is analyzed since this approach is employed in solar energy exchangers. The governing equations and the corresponding boundary conditions are constructed. This system of partial differential equations (PDEs) is changed into a system of nonlinear ordinary differential equations (ODEs) with the help of a suitable transformation and then solved numerically by the bvp5c MATLAB package. The influences of the physical parameters on the flow phenomena are discussed and presented through figures and tables. This analysis explains that the Casson fluid flow has a higher velocity field than the Maxwell fluid flow. The Nusselt number becomes higher as the Dufour numbers increase. It has also been noticed that increasing the Brinkmann number improves the entropy and, an increase in radiation enriches the temperature profile. The concentration of the fluid is decreased for the increasing values of the higher-order chemical reaction parameter. Furthermore, comparisons of the current results were conducted for limiting examples of the problem and found to be in good agreement with existing results in the literature.

The analysis of dynamic deformation processes is an important task in civil and in mechanical engineering. One main emphasis is set on the derivation of the objects transmission function, represented by systems of ordinary or partial differential equations (“white box”-models). The parametric identification of the initial and boundary conditions and relevant material parameters is one of the new challenges in the application of least-square algorithms. Embedding the investigation of the deformation process in a combination of a theoretical and an experimental system analysis suitable methods are provided with adaptive KALMAN-filtering as central identification tool. In this paper the approach of a full system analysis is shown quantifying a dynamic “white-box”-model for the calculation of thermal deformations of bar-shaped machine elements. The task was motivied from mechanical engineering searching new methods for the precise prediction and computational compensation of thermal influences in the heating and cooling phases of machine tools (i.e. robot arms, etc.). The quantification of thermal deformations under variable dynamic loads requires the modelling of the non-stationary spatial temperature distribution inside the object. Based upon FOURIERS law of heat flow the high-grade non-linear temperature gradient is represented by a system of partial differential equations within the framework of a dynamic Finite Element topology. It is shown that adaptive KALMAN-filtering is suitable to quantify relevant disturbance influences and to identify thermal parameters (i.e. thermal diffusivity) with a deviation of only 0,2%. As result an identified (and verified) parametric model for the realistic prediction respectively simu-lation of dynamic temperature processes is presented. Classifying the thermal bend as the main deformation quantity of bar-shaped machine tools, the temperature model is extended to a temperature deformation model. In lab tests with an aluminium column control measurements show that the identified model can be used to predict the columns bend with a mean deviation smaller than 10 mgon. Consequently the deformation model is a precise predictor and suitable for realistic simulations of thermal deformations under variable dynamic loads. In future our activities will be primarily focussed on applications in industrial manufacturing. 1. Parametric identification of dynamic deformation processes The creation of a realistic parametric dynamic deformation model is directly associated with the task to combine systems of differential equations (theoretical physical model) with empirical measurements. Consequently basic principles of system theory can be adapted to the geodetic deformation analysis. The parametric identification of a dynamic “white box”-model 3rd IAG / 12th FIG Symposium, Baden, May 22-24, 2006

A method for reducing systems of partial differential equations to corresponding systems of ordinary differential equations is proposed. A system of equations describing two-dimensional, cylindrical, and spherical flows of a polytropic gas; a system of dimensionless Stokes equations for the dynamics of a viscous incompressible fluid; a system of Maxwell’s equations for vacuum; and a system of gas dynamics equations in cylindrical coordinates are studied. It is shown how this approach can be used for solving certain problems (shockless compression, turbulence, etc.).

A mathematical model for fluid transport in peritoneal dialysis is constructed. The model is based on a nonlinear system of two-dimensional partial differential equations with corresponding boundary and initial conditions. Using the classical Lie scheme, we establish that the base system of partial differential equations (under some restrictions on coefficients) is invariant under the infinite-dimensional Lie algebra, which enables us to construct families of exact solutions. Moreover, exact solutions with a more general structure are found using another (non-Lie) technique. Finally, it is shown that some of the solutions obtained describe the hydrostatic pressure and the glucose concentration in peritoneal dialysis.

Exact solutions of some nonlinear systems of partial differential equations by using the first integral method