Grey-box Model Research Articles

Rheological Behavior of Air in the Two-Pass Solar Collector

This study pivoted on the flow behavior of air streams across solar air collectors provided with wooden baffles under the absorber plates. The two-pass system was used for both flat and finned surfaces. The von Kármán momentum integral and Blasius equations were solved with the help of PDPE and ODE45 techniques. The solution was assumed to be a part of the initial value problem (IVP). The energy analysis of both solar air collectors was carried out using the Hottel–Whillier–Bliss equation (HWB) equation. The Sankey diagram was used for energy distribution across the solar collectors. The gray box modeling approach was adopted to comprehend the airflow behavior across the channel. The objective of this study is to examine the intrinsic behavior of the proposed design. The displacement of boundary to compensate for the momentum of air stream (θt) decreased by 31.25%–62.50% with an increase in mass flow rate (m)˙of 24.69%–49.38% for the flat plate collector (FPC). Similarly, the shear stress posed by the absorber plate (τw) dropped by 15.89%–37.20% with the augmentation of the mass flow rate. The momentum thickness for the flat plate with triangular fin (FPTF) increased relatively by 31.25%, compared to FPC at 8.10 g·s−1. The estimated value of collector efficiency (ηI) FPTF soared up by 4%–11.51% when it was juxtaposed against the corresponding values derived for FPC. The wall shear stress near the absorber plate followed that of a second-order Gaussian model. It was noticed in this study that the addition of the fin slowed down the shear effect and the momentum defect of airstream at the same mass flow rate.

Design for energy flexibility in smart buildings through solar based and thermal storage systems: Modelling, simulation and control for the system optimization

The present study investigates the use and implementation of energy efficient measures and strategies for building applications, toward the Nearly Zero Energy Buildings target. Specifically, objective of the study is to implement building integrated photovoltaic thermal devices coupled with a phase change materials heat exchanger acting as an active thermal storage building component, with the aim to add flexibility to the building while still maintaining indoor comfort conditions. To show the potentials of the novel configuration proposed in this paper, a multi-zone grey-box model is developed and validated to capture the thermal dynamics of a building, and a control strategy applied to the whole system is developed for energy management purpose. The whole simulation model, including thermophysical properties of the building-system and the control features, is implemented in a MATLAB environment. To assess the model and application potentials toward the optimal design and operation of the proposed system for energy efficiency and flexibility goals, a suitable case study analysis is conducted. Thus, a sensitivity analysis, using an evolutionary algorithm, is performed by considering economic and energy objective functions which focuses on the reduction of the building energy demand, load variability and economic aspects. In this regard, the optimal design configuration is underlined in a way that the operation of the components can be maximized to provide flexibility to the building: in average working conditions one single layer of PCM can provide around 186.3 Wh/K per unit of temperature and width. A rule-based management strategy is proposed to prove the possibility to shift and shave the energy peaks during high energy request periods, demand response events. Finally, by considering an approximate economic calculation, the simple payback, taking into account only the positive effects on the winter management, is around 13.5 years.

Stochastic modelling of flexible load characteristics of split-type air conditioners using grey-box modelling and random forest method

Split-type air conditioners (ACs) are the major contributors to the total electricity use and peak power demand in residential buildings due to their high penetration. Accurate prediction of their energy consumption plays a significant role in demand side management (DSM), because it can help exploit the demand response (DR) potential of these ACs fully. However, the existing studies on the load characteristics modelling of split-type ACs are still not comprehensive, especially in the consideration of occupant behavior and appliance characteristics. To solve this problem, this study has developed a novel flexible load characteristics model by combining the stochastic method, grey-box modelling (i.e., equivalent thermal parameter (ETP) model) and random forest method. The stochastic method can help capture the dynamic occupants’ energy-related behaviors considering various family structures. Random forest can address the difficulties in simulating the power characteristics of variable-speed ACs under various operating conditions. With the prediction error of 2.8%, the proposed model can effectively characterize the energy performance of split-type ACs at both individual and aggregate levels. To better show the load flexibility of ACs, an investigation on DR potential of split-type ACs was also carried out by resetting temperature setpoints. The result showed that the maximum DR potentials at the scope of 1000 aggregated households are 394.54 kWh and 323.82 kWh on weekdays and weekends, respectively. The developed flexible load characteristics model of ACs can be used by utility companies for DR potential assessment and model-based DR control for a single household or building clusters.

Cubicle: A family of space‐hard ciphers for IoT

As IoT has increasingly evolved in recent years, it has become more important to ensure security on IoT devices. Many of such devices are under the threat of attacks in the beyond black-box model. To protect from the threat, the cryptographic implementation that can offer secure execution in the grey-/white-box model is important. However, such cryptographic implementations require a large number of clock cycles to execute and cannot fully cover resistance against various types of side-channel attacks. In this paper, a new family of table-based cipher dubbed Cubicle is proposed, which can offer efficient execution and sufficient security against side-channel attacks on IoT devices powered by ARM Cortex-M processors, which are widely deployed in IoT applications. To evaluate the security of Cubicle in the grey-box model, the authors derive the bound of table leakage in the grey-box model by applying space hardness, which is the notion to evaluate the security against code lifting attacks in the white-box. The security of Cubicle in the grey-box model is shown by using this bound. In addition, the security of Cubicle is also shown in the black-box and white-box models. Finally, the performance of Cubicle and other ciphers in some devices powered by ARM Cortex-M3, -M4, and -M7 processors is evaluated. The authors show that Cubicle is significantly efficient compared to other grey-/white-box- model-secure ciphers in target experiments for IoT applications.

Hybrid model of a physics-based model and machine learning for real-time estimation of unmeasurable parts: Mapping from measurable to unmeasurable variables

In some dynamic systems, such as offshore drilling, it is important to estimate the behaviour of unmeasurable parts in real-time, using measurable data. This article proposes a novel hybrid model of a physics-based model and machine learning (proposed model), which maps measurable variables to unmeasurable variables. The effectiveness of the proposed model was verified by comparing it with the conventional physics-based model and grey-box model, using an offshore drilling system as a case study application. As a result, it was confirmed that the proposed model could relax the required conditions of the measured data’s sampling period and time length when compared to the conventional model by directly inputting the measurable data. Additionally, we confirmed that the proposed model solves the time cost for parameter adjustment in the grey-box model and is superior in real-time performance. The proposed model was also shown to be robust against measurement errors. Thus, it is demonstrated that the proposed model has a high performance when the real phenomena can be represented within the physics-based model’s uncertainty of the initial states and parameters. The proposed model is expected to be suitable for various dynamic systems in addition to offshore drilling systems.

Reduced order dynamical models for complex dynamics in manufacturing and natural systems using machine learning

Dynamical analysis of manufacturing and natural systems provides critical information about production of manufactured and natural resources, respectively. Current dynamic models for full industrial process plants exist as highly accurate first-principle relationships. However, their integration is computationally intensive and provides no simplified understanding of the underlying mechanisms driving the overall dynamics. Similarly, for natural systems, most dynamical models are first principle based, with high data requirements and low state accuracy. Consequently, lower-order models that may sacrifice accuracy for simplicity and ease of training can prove useful. Yet, there have been few attempts at finding low-order models of chemical manufacturing processes and natural systems, with work focusing on modeling individual mechanisms. We seek to fill this research gap by using a machine learning (ML) approach, SINDy, validated on a soybean-diesel process plant and watershed system. This ML method combines sparse, grey-box modeling with additional nonlinear optimization to identify governing dynamics as ODEs. We find a linear ODE model for the process plant that gives an accurate relation between input and output and selected internal molar flow rates reflective of underlying linear stoichiometric mechanisms and an internal mass balance. For the natural system, we modify the SINDy approach to include the effect of past dynamics on training the model, which gives a nonlinear model for streamflow dynamics. This improves dynamical transitions, but falls short of accurate state estimation. We conclude that the proposed ML approach works well for non-chaotic systems with minimal hysteresis, but is limited when this condition is not met.

Three-Dimensional Dynamic Modeling and Motion Analysis of a Fin-Actuated Robot

Dynamic modeling has beencapturing the attention for its fundamentality in precise locomotion analyses and control of underwater robots. In this article, we focused on the 3-D dynamic modeling and the experimental validation of multiple motion patterns of underwater robots in large-scale parameter space. A 3-D dynamic model of an active-tail-actuated robotic fish with a barycentre regulating mechanism was first built by combining Newton’s second law for linear motion and Euler’s equation for angular motion. Then, the model parameters were determined by 3-D computer-aided design software SolidWorks, HyperFlow-based computational fluid dynamics simulation, and grey-box model estimation method. Finally, both kinematic experiments with a prototype and numerical simulations were applied to validate the dynamic model’s accuracy mutually. Based on the dynamic model, multiple 3-D motions, including rectilinear motion, turning motion, surfacing motion, and spiral motion, were analyzed. The experimental and simulation results demonstrated the effectiveness of the proposed model in evaluating the trajectory, attitude, and motion parameters such as the velocity, turning radius, turning angular velocity of the robotic fish.

Machine-learning-aided improvement of mechanics-based code-conforming shear capacity equation for RC elements with stirrups

The development of shear capacity equations for reinforced concrete (RC) beams and columns has been historically pursued starting from the conceptualization of a resisting mechanism. Recently, machine learning techniques are attracting more and more interest in this field. Mechanics-based and data-driven approaches (i.e., white box and black box modeling, respectively) have been considered independently so far. Conversely, this work aims at exploring a hybrid alternative way (i.e., gray box modeling) for deriving the shear capacity equation for RC beams and columns, in which a mechanics-based code-conforming formulation is improved thanks to a machine-learning-aided approach. Specifically, the capacity equation currently in use within Europe that relies on the variable-angle truss resisting mechanism is enriched by means of Genetic Programming. Easy-to-use novel expressions for the two fundamental coefficients ruling the concrete contribution are defined to better match experimental data. The performance of the newly obtained equation is first discussed within the largest comparative assessment ever presented so far among shear strength formulations reported into existing technical codes around the world. Afterward, it is recast into a code-formatted design capacity equation using a simple, yet reliable, procedure. Overall, the results demonstrate that merging mechanics-based and data-driven methods can be beneficial in the development of capacity equations since it allows preserving the physical meaning of the resisting mechanism while enhancing the accuracy of the final predictions by means of machine learning techniques. Although the methodology is here applied to evaluate the shear strength of RC beams and columns, it is very general and can be readily extended to the development of further capacity equations.

Hybrid Models for Indoor Temperature Prediction Using Long Short Term Memory Networks—Case Study Energy Center

In the European Union States, household energy usage accounts on average for 40% of overall energy consumption and is responsible for a considerable amount of carbon dioxide emissions. The urgent need to take concrete action to identify solutions that can ensure more effective usage of energy in households, both because of environmental and political reasons, has been repeatedly stated by the European Parliament. White box, grey box and black box predictive models were demonstrated to be a feasible approach to predict the indoor temperature to implement an effective energy management strategy. This study has the purpose of illustrating the potentiality of an LSTM Artificial Neural Network in a short and long-term prediction of the indoor temperature in 15 offices distributed on three storeys of an existing building (Energy Center of Turin (Italy)). The indoor temperature was predicted two hours, five hours and one entire day ahead. The performance of these algorithms has been evaluated not only based on two main criteria (i.e., Root Mean Squared Error and Mean Absolute error) but also by considering the adaptability of the model between the three floors and in terms of different years. Moreover, the proposed work explains how parameters affect performances, aiming to properly identify the optimal model structure. Current results indicate that these models can provide accurate predictions for all the proposed time scales and could all potentially be used for predictive control purposes to optimise the energy demand. The novelty of this study is to show that these models can only be trained on data for a limited period and a specific plane, and then be reliable in predicting indoor temperature, both for different planes and for random periods, taking into account temperature and relative humidity. Furthermore, input parameters are limited to indoor HVAC variables, to ensure acceptable predictions regardless of outdoor parameters availability. The only exception is the outdoor temperature, because of its undeniable and proven importance, it was retained as the only exogenous input variable. Based on current literature and temperature perception capabilities, the results were considered acceptable if the RMSE was less than 0.15 or better yet 0.10, which is equivalent to an inaccuracy between the predicted and actual indoor temperature of 0.15 °C/0.10 °C. On average, the models trained on the Energy Center database achieved an error of 0.1 °C in terms of RMSE.

Grey-box Model Develop and MPC Simulation of Campus Office Zone Based on Actual Measurement

This study aimed to develop a grey-box building model in a zone of a high-rise building on a university campus and to simulate model-based predictive control. Grey-box modeling was performed using various indoor and external environment data measured within a single-person office space on a high floor. The residence schedule was indirectly calculated using values such as indoor CO2 concentration and plug power. In addition, the catalog rating value was applied as the cooling energy value of the indoor 4-ways air conditioner as this could not be measured. Measurements were performed for approximately 4-weeks, and operating data of the heat pump and non-operating (i.e., free-floating) data were obtained according to the weekday and weekend schedules. The grey-box model was parameterized using the linear time-invariant and linear time-variant models. Both models showed good predictive performance with a root mean square error of less than 1°C in the 2-week estimation and 2-week validation results. Based on these results, an MPC simulation was performed. MPC simulation in a single zone were conducted for various electricity cost structures to derive quantitative electricity cost savings compared to those of feedback control.

A virtual meter-based visualization tool to present energy flows in multiple zone variable air volume air handling unit systems

Energy data estimated by virtual meters provide operational staff with an opportunity to improve building energy performance. Interactive visualization of virtual metered energy serves as a tool that can be used to identify energy consumption patterns and gain insights that can support operational decisions. This paper introduces a novel interactive visualization tool that applies visual analytics principles in developing a standalone application that illustrates equipment-level virtual metered energy trends. Users can interact with these visualizations via a user interaction panel designed to support operational decisions. Interviews with building operation professionals in two facility management companies are conducted to gain insights into visualization requirements that would assist decision-making processes. The use of the visualization tool is demonstrated using operational data collected from a commercial building located in Ottawa, Canada. The data are used to train inverse greybox models representing heat transfer mechanisms in an air handling unit and a variable air volume zone. Optimal values for model parameters are fed into the visualization tool to develop virtual meters that estimate the heat added or extracted by the air handling unit and the heat added by zone-level radiant heaters. The virtual metered energy is presented through a visualization interface that allows user interaction via processes including select, filter, explore, and compare. The potential of the visualization tool for assisting decision-making processes and improving building energy performance is demonstrated through illustrative examples.

A grey-box modelling methodology to express home heat-energy usage as statistical distributions — case studies in urban Ireland

Home energy retrofit has recurred in public policy throughout recent decades. However, the savings in energy usage attributable to home retrofit have remained difficult to accurately predict. Occupants cause prediction inaccuracies by varying different factors, especially heating setpoints temperatures and heating patterns. Acting together, such occupant factors result in distributions — not single values — of heat-energy usage, even among similar homes. Datasets of heat-energy distributions can be found by building performance simulation using modern grey-box models. This study presents a methodology to simulate grey-box models of home heating through ranges of heating setpoints and patterns. An entire process to calibrate, validate and simulate at a large scale is described, and then demonstrated using case studies. Grey-box models, written in Modelica language, can conveniently simulate through large ranges of occupant factors. The case studies exploited this advantage of grey-box models to simulate empirical data on occupant factors. (For instance, empirical data found that home heating setpoints shifted before and after home energy retrofit.) In doing so, the datasets of simulation results enabled the exploration of home heat-energy usage with the normal and Weibull statistical distributions. Additionally, the heat-energy distributions of case-study homes were statistically tested, first for retrofit savings, second for equality to each other and third for equality to an official heat-energy estimate. Results demonstrate that home heat-energy usage, at a large scale, is best expressed as a Weibull distribution not normality. After home energy retrofit, heat-energy usage displays less variation (in general), less skewness, and thus becomes closer to normality. Occupant factors were found to vary home heat-energy usage into distinct distributions, even within similar homes. Therefore, in most case-study homes, heat-energy usage did not equal an official estimate. Finally, shallow retrofit of a modern home in Ireland fails to save heat-energy usage by most occupants.

A nonlinear dynamic approach to cash flow forecasting

We propose a novel grey-box model to capture the nonlinearity and the dynamics of cash flow model parameters. The grey-box model retains a simple white-box model structure, while their parameters are modelled as a black-box with a Padé approximant as a functional form. The growth rate of sales and firm age are used as exogenous variables because they are considered to have explanatory power for the parameter process. Panel data estimation methods are applied to investigate whether they outperform the pooled regression, which is widely used in the extant literature. We use the U.S. dataset to evaluate the performance of various models in predicting cash flow. Two performance measures are selected to compare the out-of-sample predictive power of the models. The results suggest that the proposed grey-box model can offer superior performance, especially in multi-period-ahead predictions.

A Comparative Evaluation of Lumped and Semi-Distributed Conceptual Hydrological Models: Does Model Complexity Enhance Hydrograph Prediction?

The prediction of hydrological phenomena using simpler hydrological models requires less computing power and input data compared to the more complex models. Ordinarily, a more complex, white-box model would be expected to have better predictive capabilities than a simple grey box or black-box model. But complexity may not necessarily translate to better prediction accuracy or might be unfeasible in data scarce areas or when computer power is limited. Therefore, the shift of hydrological science towards the more process-based models needs to be justified. To answer this, the paper compares 2 hydrological models: (a) the simpler tank model; and (b) the more complex TOPMODEL. More precisely, the difference in performance between tank model as a lumped model and the TOPMODEL concept as a semi-distributed model in Atari River catchment, in Eastern Uganda was conducted. The objectives were: (1) To calibrate tank model and TOPMODEL; (2) To validate tank model and TOPMODEL; and (3) To compare the performance of tank model and TOPMODEL. During calibration, both models exhibited equifinality, with many parameter sets equally likely to make acceptable hydrological simulations. In calibration, the tank model and TOPMODEL performances were close in terms of ‘Nash-Sutcliffe efficiency’ and ‘RMSE-observations standard deviation ratio’ indices. However, during the validation period, TOPMODEL performed much better than tank model. Owing to TOPMODEL’s better performance during model validation, it was judged to be better suited for making runoff forecasts in Atari River catchment.

Reduced-order modeling method for phase-change thermal energy storage heat exchangers

Thermal energy storage can facilitate the effective utilization of renewable energy. To speed up the design process of thermal energy storage devices, it is critical to develop fast and accurate modeling methods for phase change material embedded heat exchangers (PCM HXs). This study developed and compared two approximation-assisted reduced-order PCM HX models for the simulation of thermal storage components and systems, which were verified against a validated finite-volume model. They are a pure black-box model, and a grey-box model based on the Number of Transfer Units (or effectiveness-NTU) approach. We used the reduced-order models to predict the performance of standalone PCM HX for 1000 cases with different fluid inlet conditions and HX designs. We also integrated the models with a vapor compression system to predict the compressor energy consumption and total charging time under various conditions. The results show that overall, the black-box model gave more accurate results than the grey-box model. On average, the mean absolute deviation in the PCM HX fluid outlet temperature was 0.05 K and 0.1 K for the black-box model and grey-box model, respectively. The grey-box model gave larger temperature deviation toward the end of the phase change process, due to the simplified two-node PCM representation. On the system level, the mean absolute deviation in compressor energy consumption was 0.2% and 0.3% for the black-box model and grey-box model, respectively. Their mean absolute deviation in total charging time was 1.1% and 2.6%, respectively. In terms of computation efficiency, the system simulation speedup ratio gained by using the reduced-order models was 11 to 57. System simulation time was decreased from an average of 1465 s to an average of 59 s. This shows that the proposed reduced-order modeling methods can be used to predict system performance of PCM HXs with less than 3% accuracy penalty, and 25 times less computational time than finite-volume models, enabling faster design and evaluation of PCM thermal storage devices.

Influences and Effects on Scaling the Pressure Stiffness of Additively Manufactured Meso Structures

AbstractAM-meso structures offer a high potential for adapted properties combined with lightweight design. To utilize the potential a purposeful design of the meso structures is required. Therefore, this contribution presents an approach for modelling their properties depending on design parameters by scaling relationships. The relationships are investigated based on grey box and axiomatic models of elementary cells. Exemplary the pressure stiffness is determined using FEM in comparison to an analytical approximation. The comparison reveals effects and influences occurring within the elementary cell.

Identifying of Unsteady Performance of Oil to Water Heat Exchanger Integrated with Process

There are many approaches by which the heat exchanger can be modeled depending on how much information is available to start with. Grey-box model represents one of these approaches which is considered in the present study to modeling the unsteady operation heat exchanger. The available measurements of an unidentified heat exchanger integrated with a process involving oil circulation were statistically analyzed to extract the information that could aid in its identification. The proposed heat exchanger system included a hot oil stream coming from the thermal unit process and cooled by a cold-water circuit. The objective of this study is to develop a grey box model for the unspecified heat exchanger with a suitable nonlinear state-space structure and solved numerically using MATLAB-19 software and engineering equation solver (EES). Suitable parameters included oil and water inventories, heat addition, and conductance divisor factor are chosen to fully identify the heat exchanger from measured temperatures and flow rates. The parameters used to identify the oil process included the oil mass inventory within the process and the quantity of heat added. While for the heat exchanger; oil, water, and solid thermal masses were determined along with a conductance divisor to close its model. The results revealed that, comparing the model output with the measured data was satisfactory. The effect of 10% increment in the oil process heat as external excitation on a heat exchanger can only be controlled by water and oil flow rates and any fluctuation in inlet water temperature is insignificant and considered as a noise disturbance. An increment of 19% in the oil flowrate with unchanged water flowrate resulted in an increase in oil outlet temperature by about 4%. applying a noise of about ±10% on inlet water temperature to the system resulted in insignificant effects on the oil temperatures, and therefore it could be considered as uniform temperature. An effective control system to manage the heat exchanger and therefore the process can be designed according to the predictions of changing the water and oil flow rate responses.

Case-study of a flowsheet simulation using deep-learning process models for multi-objective optimization of petrochemical production plants

This work demonstrates a case-study to create machine-learning based process models from process data, which are connected into an overall process flowsheet and provide a high level of numerical stability for further multi-objective optimization. The used models are black-box and gray-box models, which are further compared to the proven LP approach. The proposed methodology is demonstrated using real-world measurement data from a refinery, involving a distillation unit, a hydrotreater, a reformer and an ethylene plant. The developed unit models are connected into an overall process flowsheet, which is solved by a sequential-modular approach and optimized in view of maximizing production margin and minimizing CO2-emissions. This work points out that the combination of engineering knowledge with data-driven techniques enables the incorporation of indirect information for process units, e.g., the crude oil composition vector for downstream units, leveraging the prediction performance of the unit models, compared to models not involving this information.

Comparative study of supervised algorithms for topology detection of sensor networks in building energy systems

Optimizing the operation of building energy systems holds great potential to reduce energy consumption in buildings. However, this requires detailed system information, such as the relationship of sensor data. Automatic detection of this information requires monitoring data from buildings, which is rarely available in the needed quality for automatic assignment. This study bases on 200 weeks of data collected from eight temperature sensors of a heat pump and a heat exchanger in 5-min samples. We use this data to auto-generate grey-box models to extend the data set with 500 weeks of simulated data. We train six supervised deep learning algorithms with all the data to test whether detecting connections is possible. The maximum F1 score of 94.9% compared to real-based results with a maximum of 34.2%, which is over 60% better. The advantage of the proposed approach is its independence from the low availability of real data.

Demonstration of an MPC framework for all-air systems in non-residential buildings

In educational buildings, the HVAC system is a major contributor to the total energy use. It is well-known that energy reductions could be achieved by more advanced control strategies for HVAC systems. A model predictive control (MPC) strategy could be a viable solution. Contrary to the standard rule based control (RBC), the predictive control can adjust in the supply air temperature, airflow rate prior to the start of a lecture. This study aims to develop and demonstrate an MPC framework for an all-air system that controls both the room temperature and the CO2-concentrations. To predict these variables two model identification techniques were compared: auto-regressive with exogenous input (ARX-MPC) linear model and a grey-box resistor–capacitor nonlinear model (RC-NMPC). In addition, a cost function that minimized the energy use while guaranteeing thermal comfort and indoor air quality (IAQ) was formulated. This study showed that the ARX-MPC was preferred over the RC-NMPC given its simplicity. As for the model identification, the ARX model was less computationally time-consuming than the grey-box model. Furthermore, the RC-NMPC required more computational time than the ARX-MPC, since the RC-NMPC required a non-linear solver while the ARX-MPC used a linear one. The developed MPC framework was than implemented through BACnet in a real-use educational building to test its actual performance. The energy savings calculated for the implemented MPC strategies with an occupancy based heating set-point were respectively 10%–40% for electric energy use and 21%–55% for thermal energy use.