Grey-box Model Research Articles

Grey-Box Method for Urban Building Energy Modelling: Advancements and Potentials

Urban building energy modelling (UBEM) has consistently been a pivotal tool to evaluate and control a building stock’s energy consumption. There are two main approaches to build up UBEM: top-down and bottom-up. The latter is the most commonly used in engineering. The bottom-up approach includes three methods: the physical-based method, the data-driven method, and the grey-box method. The first two methods have previously received ample attention and research. The grey-box method is a modelling method that has emerged in recent years that combines the traditional physical method with the data-driven method while it aims to avoid their problems and merge their advantages. Nowadays, there are several approaches for modelling the grey-box model. However, the majority of existing reviews on grey-box methods concentrate on a specific technical approach and thus lack a comprehensive overview of modelling method perspectives. Accordingly, by conducting a comprehensive review of the literature on grey-box research in recent years, this paper classifies grey-box models into three categories from the perspective of modelling methods and provides a detailed summary of each, concluding with a synthesis of potential research opportunities in this area. The aim of this paper is to provide a foundational understanding of grey-box modelling methods for similar research, thereby removing potential barriers in the field of research methods.

A combined mechanistic and empirical models for tailored microwave-assisted extraction of rice bran phenolic

ABSTRACT Rice bran is a promising source of functional food due to its high phenolic content. Microwave-assisted extraction (MAE) has become a widely used method for optimizing phenolic extraction from rice bran. However, understanding the phenolic extraction process using the MAE method is challenging due to the system’s complexity. Modeling and simulation are powerful tools to provide a better understanding of how the system behaves and can be optimized. This study proposes a novel approach that combines mechanistic and empirical models (gray box) to predict the phenolic content in rice bran extraction using MAE. It involved phenolic extraction using different ethanol concentrations (40%, 60%, 80%), microwave application time (1 min, 2 min, 3 min), and microwave power (90 W, 180 W, 270 W). The results showed a good agreement between experimental and computed extraction yields, as indicated by the reported statistical parameters and gray box model. The optimum conditions were reached at 60% ethanol concentration, 2-min microwave application time, and 180 W microwave power with the phenolic content at 0.534 mg/mL (model) and 0.561 mg/mL or 25.06 mg/g (experiment). Following the study, this combined approach can potentially reduce the time and cost required for optimization studies of phenolic extraction.

Artificial intelligence assisted prediction of optimum operating conditions of shell and tube heat exchangers: A grey‐box approach

AbstractIn this study, a Grey‐box (GB) model was developed to predict the optimum mass flow rates of inlet streams of a Shell and Tube Heat Exchanger (STHE) under varying process conditions. Aspen Exchanger Design and Rating (Aspen‐EDR) was initially used to construct a first principle model (FP) of the STHE using industrial data. The Genetic Algorithm (GA) was incorporated into the FP model to attain the minimum exit temperature for the hot kerosene process stream under varying process conditions. A dataset comprised of optimum process conditions was generated through FP‐GA integration and was utilised to develop an Artificial Neural Networks (ANN) model. Subsequently, the ANN model was merged with the FP model by substituting the GA, to form a GB model. The developed GB model, that is, ANN and FP integration, achieved higher effectiveness and lower outlet temperature than those derived through the standalone FP model. Performance of the GB framework was also comparable to the FP‐GA approach but it significantly reduced the computation time required for estimating the optimum process conditions. The proposed GB‐based method improved the STHE's ability to extract energy from the process stream and strengthened its resilience to cope with diverse process conditions.

Data-driven discovery of chemotactic migration of bacteria via coordinate-invariant machine learning

BackgroundE. coli chemotactic motion in the presence of a chemonutrient field can be studied using wet laboratory experiments or macroscale-level partial differential equations (PDEs) (among others). Bridging experimental measurements and chemotactic Partial Differential Equations requires knowledge of the evolution of all underlying fields, initial and boundary conditions, and often necessitates strong assumptions. In this work, we propose machine learning approaches, along with ideas from the Whitney and Takens embedding theorems, to circumvent these challenges.ResultsMachine learning approaches for identifying underlying PDEs were (a) validated through the use of simulation data from established continuum models and (b) used to infer chemotactic PDEs from experimental data. Such data-driven models were surrogates either for the entire chemotactic PDE right-hand-side (black box models), or, in a more targeted fashion, just for the chemotactic term (gray box models). Furthermore, it was demonstrated that a short history of bacterial density may compensate for the missing measurements of the field of chemonutrient concentration. In fact, given reasonable conditions, such a short history of bacterial density measurements could even be used to infer chemonutrient concentration.ConclusionData-driven PDEs are an important modeling tool when studying Chemotaxis at the macroscale, as they can learn bacterial motility from various data sources, fidelities (here, computational models, experiments) or coordinate systems. The resulting data-driven PDEs can then be simulated to reproduce/predict computational or experimental bacterial density profile data independent of the coordinate system, approximate meaningful parameters or functional terms, and even possibly estimate the underlying (unmeasured) chemonutrient field evolution.

Grey‐box modelling for estimation of optimum cut point temperature of crude distillation column

AbstractA grey‐box modelling framework was developed for the estimation of cut point temperature of a crude distillation unit (CDU) under uncertainty in crude composition and process conditions. First principle (FP) model of CDU was developed for Pakistani crudes from Zamzama and Kunnar fields. A hybrid methodology based on the integration of Taguchi method and genetic algorithm (GA) was employed to estimate the optimal cut point temperature for various sets of process variables. Optimised datasets were utilised to develop an artificial neural networks (ANN) model for the prediction of optimum values of cut points. The ANN model was then used to replace the hybrid framework of the Taguchi method and the GA. The integration of the ANN and FP model makes it a grey‐box (GB) model. For the case of Zamama crude, the GB model helped in the decrease of up to 38.93% in energy required per kilo barrel of diesel and an 8.2% increase in diesel production compared to the stand‐alone FP model under uncertainty. Similarly, for Kunnar crude, up to 18.87% decrease in energy required per kilo barrel of diesel and a 33.96% increase in diesel production was observed in comparison to the stand‐alone FP model.

Model predictive control with self-learning capability for automated demand response in buildings

This paper presents an optimal management strategy, called Building Optimizer, based on a Model Predictive Control (MPC) approach with self-learning capabilities for buildings. The proposed MPC is a key enabler of cooperative demand response strategies at community level, ensuring the allocation of an optimal demand profile at each participating member of the community according to an optimal consumption reference defined by a complementary agent at community level. In this way, the proposed solution can contribute to provide demand response services exploiting the unlocked residential flexibility. The MPC calculates the optimal setpoints of the HVAC system’s terminal units, considering the expected usage of the buildings and the outdoor conditions, and exploiting the building’s thermal inertia. The models embedded in the MPC are grey-box models representing a thermal zone of the building. An adaptive MPC is proposed to mitigate the high uncertainty present in building management due to the time-variant characteristics of the building and the uncertain internal heat gains due to occupancy and other disturbances. For that, the reduced models incorporate self-learning capabilities implemented as Moving Horizon Estimators that perform a continuous calibration based on real-time measurements. This solution allows full automation for model calibration and management of the terminal units. This paper presents a case study to assess the thermal comfort assurance and power flexibility provision potential of the proposed solution. First, the Building Optimizer is compared to a regular benchmark consisting of an on–off controller, evaluating the performance of each controller for indoor temperature tracking. For the assessment of the flexibility provision, a baseline MPC with fixed model parameters obtained by an offline calibration is used for comparison to the Building Optimizer with self-learning capabilities. Different flexibility scenarios are simulated, considering different restrictions regarding thermal comfort and various flexibility request signals. Notably, the Building Optimizer outperforms the baseline MPC in all scenarios, particularly guaranteeing thermal comfort. Incorporating self-learning capabilities enhances controller performance by mitigating the effect of uncertainty, allowing the Building Optimizer to shift up to 13.08% of peak periods into valley periods, and tracking a flexibility request scenario of 10% with no discomfort.

Predictive building energy management with user feedback in the loop

Retrofitting buildings with predictive control strategies can reduce their energy demand and improve thermal comfort by considering their thermal inertia and future weather conditions. A key challenge is minimizing additional infrastructure, such as sensors and actuators, while ensuring user comfort at all times. This study focuses on retrofitting with intelligent software, incorporating the users’ feedback directly into the control loop. We propose a predictive control strategy using an optimisation-based energy management system (EMS) to control thermal zones in an office building. It uses a physically motivated grey-box model to predict and adjust thermal demand, with individual zones modelled using an RC-approach and parameter estimation handled by an unscented Kalman filter (UKF). This reduces deployment effort as the parameters are learned from historical data. The objective function ensures user comfort, penalises undesirable behaviour and minimises heating and cooling costs. An internal comfort model, automatically calibrated with user feedback by another UKF, further improves system performance. The practical case study is an office building at the ”Innovation District Inffeld”. Operation of the system for one year yielded significant results compared to conventional control. Thermal comfort was improved by 12% and thermal energy consumption for heating and cooling was reduced by about 35%.

Intelligent optimal control model of selection pressure for rapid culture of aerobic granular sludge based on machine learning and simulated annealing algorithm

Aerobic Granular Sludge (AGS) has advantages over Activated sludge (AS) but faces challenges with long granulation periods. In this study, a novel grey-box model is devised to optimize the cultivation of AGS to shorten the formation time. This model is based on an existing white-box model. The modeling process starts with the application of four sensitivity analysis methods to assess the 12 model metrics selected. Subsequently, 12 prediction models were constructed by combining the six Machine learning (ML) algorithms and integrated algorithms, with the best performance selected (R2 = 0.98). Finally, an AGS selection pressure planning model was designed in conjunction with a simulated annealing (SA) algorithm to guide AGS training. The results demonstrate that AGS formation could be achieved within four days under the model’s optimal control. Therefore, the establishment of this model provides a new technique for the cultivation of AGS.

Predictive heating load management and energy flexibility analysis in residential sector using an archetype gray-box modeling approach: Application to an experimental house in Québec.

This paper presents a methodology to develop archetype gray-box models and use them in an economic model-based predictive control algorithm to simulate optimal heating load management in response to a newly-introduced static time-of-use tariff for Québec's residential sector, rate Flex-D. The methodology is evaluated through a case study, wherein in situ measurements from a two-storey unoccupied research house of Hydro-Québec are used to develop an 11R6C network with a heuristic zoning-by-floor approach and compute the sequence of optimal electric heating input for the next control horizon. Properly-tuned economic model-based predictive control under rate Flex-D shows potential for an approximately 30% reduction in daily heating cost compared to the reference operation, with a minimal average deviation of indoor air temperature from the reference setpoint. Also, the analysis of the response's sensitivity to weather forecast uncertainties indicates that the most influential uncontrolled input directing the performance of economic model-based predictive control is the structure price signal, rendering the impact of uncertainty in the weather forecast negligible.

Transient NOx emission modeling of a hydrogen-diesel engine using hybrid machine learning methods

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.

Accuracy and applicability of ship's fuel consumption prediction models: A comprehensive comparative analysis

The available extensive ship activity data enables employing a complex data-driven resistance-based power model to estimate ship's instantaneous power, and thus the ship's fuel consumption. The Ship Traffic Emissions Assessment Model emerges as a prominent example of such models. However, the performance of the Ship Traffic Emissions Assessment Model in ship's fuel consumption estimation is rarely verified by real fuel consumption data. Hence, this study aims to validate the accuracy of the Ship Traffic Emissions Assessment Model using real fuel consumption data and evaluates its applicability in terms of input features. Situations where the Ship Traffic Emissions Assessment Model shows large errors are identified to analyze its applicability. Furthermore, the Ship Traffic Emissions Assessment Model is compared with other popular fuel consumption prediction models, including the propeller law, the gradient-boosted regression tree model, and two grey box models. A systematical analysis is conducted to evaluate the applicability of various fuel consumption prediction models in different sailing scenarios, providing insights in selecting appropriate models for accurate ship's fuel consumption estimation. The findings contribute to optimizing the ship energy efficiency and facilitating the transition to alternative energy options, ultimately leading to a reduction in greenhouse gas emissions of the maritime industry.

Refrigerant charge estimation method based on data-physic hybrid-driven model for the fault diagnosis of transcritical CO2 heat pump system

The transcritical CO2 heat pump system is a promising and excellent heating scheme. However, the operating pressure of the transcritical CO2 heat pump system is high, and refrigerant leakage is a frequent problem. It is worth noting that the operating principle of CO2 heat pump systems is unique. Thus, conventional refrigerant charge estimation methods for subcritical systems cannot be directly applied to transcritical systems. In this study, a novel refrigerant charge estimation method for the transcritical CO2 heat pump system is proposed. Based on the heat and mass transfer characteristics of the transcritical system, the grey box model constrained by physical laws is constructed. Based on the machine learning algorithm, the correction model of the grey box model is built. The hybrid model combines the advantages of the high generalization ability of the physic-driven model and the nonlinear fitting ability of the data-driven model. The results show that the novel estimation method can accurately predict the refrigerant charge, enabling fault diagnosis of refrigerant leakage. The data-driven correction model can improve the prediction accuracy of the grey box model. The Mean Relative Error of the hybrid-driven model can be controlled within 5 %.

Occupant-Detection-Based Individual Control of Four-Way Air Conditioner for Sustainable Building Energy Management

In this study, individual control of a four-way air conditioner was developed based on the distribution of occupants to prevent unnecessary energy consumption during room-wide control. An occupancy detection algorithm was created in Python using YOLOv5 object recognition technology to identify the occupants’ distribution in space. Recorded video data were used to test the algorithm. A simulation case study for a building energy model was conducted, assuming that this algorithm was applied using surveillance cameras in commercial buildings, such as cafés and restaurants. A grey-box model was established based on measurements in a thermal zone, dividing one space into two zones. The temperature data for the two zones were collected by individually turning on the air conditioner for each zone in turns for a specific period. Manual closure was applied to each supply blade using a tape to provide cooling to the target zone. Finally, through energy simulations, the decreased rates in energy consumption between the proposed individual control and existing room-wide controls were compared. Different scenarios for the occupants’ schedules were considered, and average rates in energy savings of 21–22% were observed, demonstrating the significance of individual control in terms of energy consumption. However, marginal comfort violations were observed, which is inevitable. The developed control method is expected to contribute to sustainable energy management in buildings.

Automated model order reduction for building thermal load prediction using smart thermostats data

This paper presents a methodology to automatically determine the structure of sufficiently accurate grey-box models for model predictive control, energy efficiency and flexibility applications in buildings. The methodology is based on model reduction and system identification techniques, with a path that enhances data pre-processing, a multistage order reduction, and parameter estimation. The model structure is determined with a cascade approach that either neglects, keeps, or aggregates thermal zones by using discrete and continuous frequency domain techniques. Once the optimal structure is identified, the parameters are calibrated with the measured data from smart thermostats, using the model predictive control relevant identification method. The methodology is applied to a monitored house located in Québec, Canada. The developed algorithm identifies adjacent zones, even when the building layout is unknown, by studying indoor temperature fluctuations. The results concerning the model creation suggest that, for this specific building, the aggregation by floor is the most efficient way for creating reduced order thermal models, limiting uncertainty due to thermal zone interaction. This methodology provides control-oriented models that accurately predict response up to 24-h ahead with Root Mean Square Error less than 0.5 °C and acceptable Fitness Function values for the minimum number of selected parameters. Finally, several scenarios demonstrate the insights gained from using grey-box building thermal models for design, control, and retrofitting applications.

Greybox-Modelle in der Zerspanung

Abstract Compared to uncoated tools, coated tools offer a longer tool life. However, it is difficult to predict the wear of coated tools using only empirical methods. The combination of deterministic whitebox models and data-driven blackbox models to greybox models can enable a prediction of the wear condition. Therefore, this article presents a concept for the application of greybox models for wear prediction.

Substitution of a Microstructure-Simulation with a Data-Driven Approach for Modelling Mechanical Degradation of Electrodes

One significant aspect of battery aging involves the mechanical degradation of battery electrodes. The intercalation of ions into the active material particles of a lithium-ion battery creates a concentration profile along the radial direction of the active material particle, influenced by transport properties and kinetics. Mechanical stresses arise due to the spatial constraints of intercalated ions, leading to the mechanical degradation of the electrode.Common cathode materials used in practical applications, such as Lithium Nickel Manganese Cobalt Oxide (NMC) or Lithium Iron Phosphate (LFP), undergo a transition from a lithium-poor phase to a lithium-rich phase during the intercalation process. Along this phase boundary, high mechanical stresses occur due to the inconsistency of the concentration profile, resulting in particle fractures. This can lead to electrical isolation and, consequently, the electrochemical inertization of the active particle material, manifested as a reduced battery capacity on a macroscopic scale.Simulating these processes poses computational challenges. Given current computational power, accurately simulating a sufficient number of cycles for a microstructure simulation, which describes transport processes within a battery, is computationally prohibitive. Therefore, this study employs data-driven models. To predict radial concentration profiles within the particle, a physics-informed neural network (PINN) proves useful by extending the cost function with the transport equation. Classical neural networks (ANN) are utilized to calculate the electrical voltage of active material particles. These models are trained with results from microstructure simulations to develop a grey-box model, enabling the inclusion of mechanical degradation in the electrode simulation.Mechanical stresses and degradations are thus investigated under various galvanostatic discharge rates to define an aging-resistant operational window for the battery.

Explainable and generalizable AI-driven multiscale informatics for dynamic system modelling

Ultra-precision machining requires system modelling that both satisfies explainability and conforms to data fidelity. Existing modelling approaches, whether based on data-driven methods in present artificial intelligence (AI) or on first-principle knowledge, fall short of these qualities in high-demanding industrial applications. Therefore, this paper develops an explainable and generalizable ‘grey-box’ AI informatics method for real-world dynamic system modelling. Such a grey-box model serves as a multiscale ‘world model’ by integrating the first principles of the system in a white-box architecture with data-fitting black boxes for varying hyperparameters of the white box. The physical principles serve as an explainable global meta-structure of the real-world system driven by physical knowledge, while the black boxes enhance local fitting accuracy driven by training data. The grey-box model thus encapsulates implicit variables and relationships that a standalone white-box model or black-box model fails to capture. Case study on an industrial cleanroom high-precision temperature regulation system verifies that the grey-box method outperforms existing modelling methods and is suitable for varying operating conditions.

Modelling a chemical plant using grey‐box models employing the support vector regression and artificial neural network

AbstractIn this work, the performances of a nonlinear dynamic industrial process are examined using grey‐box (GB) models. To understand the dynamics of the system, the transient state is targeted. A white‐box (WB) model holds the prevailing knowledge using some assumptions. The performance of this model is limited. Artificial neural network (ANN) and support vector regression (SVR), which are techniques employed in numerous chemical engineering applications, are employed to construct the associated black‐box (BB) models. GA is used to optimize the SVR parameters. Dimensional and range extrapolations of different manipulated inputs, feed concentrations, feed temperatures, and cooling temperatures of the GB model and BB model are discussed. The different inputs extrapolation has different results because each input's effectiveness in the system is different. The results are compared, and the best model is suggested among the models, ANN, SVR, first principle (FP)‐ANN serial structure, FP‐ANN parallel structure, FP‐SVR serial structure, and FP‐SVR parallel structure.

A Generalized Load Model Considering the Fault Ride-Through Capability of Distributed PV Generation System

Considering the voltage stability problem brought by large-scale distributed PV access to the distribution network, this paper proposes a generalized load model that considers the fault ride-through capability of distributed PV. Firstly, the detailed model of the distribution network is established, and the detailed model is calibrated based on the measured data, the simulation errors are below 1%. And then establish a generalized load model considering distributed PV high and low voltage traversal ability. The sensitivity analysis results are used to rank the parameters to be identified, and the parameters with higher sensitivity are identified. The parameters are obtained from the detailed model and measured data, and four sets of parameters are identified and simulated under different PV penetration rates and fault conditions. The calculated fitting errors are less than 1%. The results show that the generalized load gray box model of the distribution network with distributed PV high and low voltage ride-through capability can reflect the dynamic characteristics of the distribution network well.

Modeling and Aggregation of Electric Water Heaters for the Development of Demand Response Using Grey Box Models

Modeling and Aggregation of Electric Water Heaters for the Development of Demand Response Using Grey Box Models