Models Of Physical Systems Research Articles

Demonstration of lossy linear transformations and two-photon interference on a photonic chip

Studying quantum correlations in the presence of loss is of critical importance for the physical modeling of real quantum systems. Here, we demonstrate the control of spatial correlations between entangled photons in a photonic chip, designed and modeled using the singular value decomposition approach. We show that engineered loss, using an auxiliary waveguide, allows one to invert the spatial statistics from bunching to antibunching. Furthermore, we study the photon statistics within the loss-emulating channel and observe photon coincidences, which may provide insights into the design of quantum photonic integrated chips. Published by the American Physical Society 2024

Research on the Possibilities of Expanding the Photovoltaic Installation in the Microgrid Structure of Kielce University of Technology Using Digital Twin Technology

Global challenges related to sustainable development are increasingly focusing on the use of digital twin technology as a universal tool for optimizing and monitoring renewable energy installations. This article discusses digital twin technology as a support for sustainable development based on the analysis of microgrid structures. Digital twins allow the creation of virtual models of physical systems. This capability facilitated the accurate replication of the microgrid model at Kielce University of Technology using ETAP (Electrical Transient Analyzer Program) software (version 22.5). The operational parameters of the microgrid structure were analyzed for the examined power range of the photovoltaic installation to determine the possibilities of expanding the existing installation. The impact of the photovoltaic installation’s power on the operational parameters of the microgrid structure was visualized, and final conclusions were formulated. Moreover, the integration of digital twin technology into renewable energy systems not only enhances operational efficiency but also plays a pivotal role in advancing sustainability objectives. Through real-time monitoring and predictive maintenance, digital twin technology facilitates the optimization of energy production and distribution, thereby reducing waste and contributing to the overall sustainability of energy systems. This technology enables the simulation of various scenarios, such as fluctuations in energy demand or the integration of new renewable sources, which can inform more sustainable decision-making processes. In the context of microgrids, digital twin technology ensures that energy production is closely aligned with consumption patterns, minimizing energy losses and enhancing grid resilience. Furthermore, digital twin technology supports the sustainable expansion of renewable installations by providing detailed insights into potential environmental impacts and the long-term sustainability of various energy configurations. As the demand for clean energy continues to grow, digital twin technology will be indispensable in achieving a balance between energy needs and environmental stewardship, ensuring that the expansion of renewable energy sources contributes positively to global sustainability objectives.

Fourier phase retrieval using physics-enhanced deep learning.

Fourier phase retrieval (FPR) aims to reconstruct an object image from the magnitude of its Fourier transform. Despite its widespread utility in various fields of engineering and science, the inherent ill-posed nature of the FPR problem poses a significant challenge. Here we propose a learning-based approach that incorporates the physical model of the FPR imaging system with a deep neural network. Our method includes two steps: First, we leverage the image formation model of the FPR to guide the generation of data for network training in a self-supervised manner. Second, we exploit the physical model to fine-tune the pre-trained model to impose the physics-consistency constraint on the network prediction. This allows us to integrate both implicit prior from training data and explicit prior from the physics of the imaging system to address the FPR problem. Simulation and experiments demonstrate that the proposed method is accurate and stable, showcasing its potential for wide application in fields utilizing the FPR. We have made our source code available for non-commercial use.

Effects of Aerodynamic Damping and Gyroscopic Moments on Dynamic Responses of a Semi-Submersible Floating Vertical Axis Wind Turbine: An Experimental Study

Abstract Floating vertical-axis wind turbines (VAWTs) offer certain advantages over floating horizontal-axis wind turbines (HAWTs), particularly in terms of the potential to lower the cost of energy. In this study, a 5 MW floating VAWT concept with three straight blades and a semi-submersible hull deployed in a water depth of 42 m was presented. In addition, the experimental setup is introduced, and calibration tests are also performed to validate the physical model system. Subsequently, the aerodynamic damping and gyroscopic moment effects were investigated by wind/wave basin model tests with a scale ratio of 1/50. Results indicate that aerodynamic damping can suppress the fluctuations of the platform's surge and pitch motion at their respective resonance frequencies and tends to increase with wind speed at below-rated wind speed. Additionally, surge-induced and pitch-induced aerodynamic damping hardly affect the wave frequency response. Meanwhile, the surge natural frequency is substantially altered due to the wind loads. The rotating rotor and pitch motion of the platform together excite significant gyroscopic moments, leading to noticeable oscillations in roll motion. Additionally, there is an increasing trend in the gyroscopic moment effect with rotational speed. During normal operation of the floating VAWT, aerodynamic damping and gyroscopic moment together influence hull roll/pitch motions. Overall, this study contributes to providing valuable insights into the motion characteristics of floating VAWTs.

A Jupyter Notebook for teaching mathematical modeling with experiments

AbstractMathematical modeling and numerical simulation have a considerable presence in the vast universe of engineering disciplines, given their usefulness in explaining, comprehending, and simulating phenomena and processes with which engineers are in contact in their daily creative and problem‐solving work. For this reason, engineering study programs have at least one course dedicated to dealing with the mathematical modeling of dynamic systems as an essential complement to subsequent courses such as automatic control, structural dynamics, and mechanical vibrations. Nowadays, many technological tools illustrate the applications of mathematical modeling interactively through experiments that offer an incomparable motivation to the students to corroborate with real‐world examples, the utility and veracity of the theory presented to them in the classroom and that in many occasions seems lacking utility and direct relation with the world in which they develop. Based on those mentioned above, this paper presents an example of applying the Laplace transform in modeling physical systems, using a second‐order circuit attached to an Arduino Due board in conjunction with the Jupyter Notebook environment. The numerical and experimental results can be obtained through three optional kernels: Python, Octave, or MATLAB®. For educational purposes, the resulting computer application was presented to undergraduate students of Mechatronics Engineering as an illustrative complement to two courses entitled Signals and Systems Analysis, part of the second semester, and Mathematical Modeling, part of the fifth semester.

Kalman filter-driven state observer for thermal error compensation in machine tool digital twins

Sustainable reduction of thermal errors during production is the key challenge in modern high-precision manufacturing. Numerical compensation models provide an energy-efficient solution, but in the case of data-driven models, high-quality experimental data must be time-consuming and expensive to produce, negatively impacting overall productivity. Furthermore, robustness concerns arise in the case of new operating conditions, which were not contained in the training data. This paper presents a novel use of a Kalman filter together with model order reduced finite element models to observe the entire thermal state, which allows the subsequent solution of the mechanical model and computation of the thermal errors in real-time without requiring any training data but instead purely based on the physical system model. The effectiveness of this approach is evaluated using experiments on a thermal test bench with 16 out of 40 temperature sensors employed for observation and demonstrated on a 5-axis machine tool (MT) with 13 out of 25 temperature sensors used. Due to the combination of the reduced order model and Kalman filter these 13 temperature sensors are sufficient to represent a MT mesh of more than 350’000 elements. The entire temperature profile of the thermal test bench is reconstructed to achieve a root mean square error (RMSE) of the unobserved temperature sensors of only 2.7 °C, which accounts for more than 83% of all temperature variations and 1.3 °C for the 5-axis MT. For the thermal error of the thermal test bench, the RMSE could be reduced from 67.4μm to 33.3μm, corresponding to a reduction of 52.7 %. This could be achieved without the need for experimental data for model calibration, in a real-time capable physics-based model.

SDYN-GANs: Adversarial learning methods for multistep generative models for general order stochastic dynamics

We introduce adversarial learning methods for data-driven generative modeling of dynamics of nth-order stochastic systems. Our approach builds on Generative Adversarial Networks (GANs) with generative model classes based on stable m-step stochastic numerical integrators. From observations of trajectory samples, we introduce methods for learning long-time predictors and stable representations of the dynamics. Our approaches use discriminators based on Maximum Mean Discrepancy (MMD), training protocols using both conditional and marginal distributions, and methods for learning dynamic responses over different time-scales. We show how our approaches can be used for modeling physical systems to learn force-laws, damping coefficients, and noise-related parameters. Our adversarial learning approaches provide methods for obtaining stable generative models for dynamic tasks including long-time prediction and developing simulations for stochastic systems.

Developing discharge-head equation for radial-gated spillways based on physical modeling

Determination of the discharge through the spillways with radial gates is essential, depending on the application of these spillways in check dams and flood discharge systems in larger dams. On the other hand, physical modeling is often required due to the complexity and impact of various factors. This study investigated the efficiency of various methods in estimating the discharge through the spillways with radial gates using 958 experimental datasets from physical models of flood discharge systems in 17 large reservoir dams in Iran. In addition to dimensional analysis of the parameters, affecting the discharge of spillways with radial gates, new equations were proposed to determine the gate opening and the deviation angle of the gate. The mean absolute relative error in estimating the discharge at every flow condition showed a decreasing trend from about 9.1 % (for the previous methods) to about 3.9 % (the proposed equation in the present study). Later, the effects of different factors on the discharge through the spillways with the radial gate in large dams were evaluated. The results showed the errors of the previous methods in estimating the discharge for transient flow conditions, non-standard spillways, increase in the number of gates, and operation of only one gate with up to 22.2 %, 11.8 %, 21.5 %, and 10.5 %, respectively. However, under the abovementioned conditions, the mean absolute relative error of the proposed method error of discharge estimation, in the present study, decreased to about 4 %, 4.3 %, 3.3 %, and 3.5 %, respectively. Accordingly, using the new proposed equation involving the different factors to determine the discharge through the spillways with the radial gates in larger dams is recommended.

Investigating new solutions for a general form of q$$ \mathfrak{q} $$‐deformed equation: An analytical and numerical study

SummaryThis paper contributes to the study of a new model called the ‐deformed equation or the ‐deformed tanh‐Gordon model. To understand physical systems with violated symmetries. We utilize the ‐expansion approach to solve the ‐deformed equation for specific parameter values. This method generates solutions that provide valuable insights into the system's dynamics and behavior. To verify the accuracy of our solutions, we also apply the finite difference technique to obtain numerical solutions to the ‐deformed equation. This dual approach ensures the reliability of our results. We present our findings using tables and graphics to enhance clarity and facilitate comparison between the analytical and numerical solutions. These visual aids help readers better understand the similarities and differences between the two approaches. The ‐deformation is significant as it models physical systems with nonstandard symmetry features, like extensivity, offering a more accurate representation of real‐world phenomena. The growing significance of this equation across various disciplines highlights its potential in advancing our understanding of complex physical systems. This paper contributes valuable knowledge about the ‐deformed equation, demonstrating its potential for accurately modeling physical systems with violated symmetries. Through both analytical and numerical techniques, we offer comprehensive solutions and validate their accuracy, with graphical representations enhancing the clarity and understanding of our results. This exploration of ‐deformation advances modeling techniques, providing a more precise depiction of real‐world processes with nonstandard symmetry features.

Neural Network-Based Aggregated Equivalent Modeling of Distributed Photovoltaic External Characteristics of Faults

Distributed power networks have a large number of photovoltaic power sources. The bidirection of power flow, different transient control strategies, and installation locations make the transient characteristics highly complex and unpredictable. The vast network of the distribution system makes it almost impossible to predict the electrical quantities of each branch. Reasonable aggregation modeling of the distribution network can greatly simplify the network topology, facilitating transient control and the setting of relay protection settings. An aggregated equivalent modeling method based on the LSTM neural network for distributed PV fault external characteristics is proposed. This method equates the complex distribution network to a highly nonlinear but controllable current source. The method can output the I–V curves of equivalent PV system parallel points under any output power and is able to predict the fault characteristics of the equivalent system after a voltage drop at the parallel point. Compared to traditional mechanistic modeling, this method does not require specific modeling of complex physical systems and is able to accurately map the strong nonlinear inputs and outputs of distribution networks. The established LSTM model first uses a one-dimensional convolutional layer for feature extraction of the PV power coefficients (input), and then two hidden layers are utilized to process the sequence data; the vectors are mapped into a sequence of external characteristic curves (output) in a fully connected layer. A typical distribution network is built based on the traditional PV power model, and a large number of different output combinations are selected for simulation to provide an effective training set and validation set data for LSTM model training. By using the training set data, the weights and offset coefficients of each layer of the LSTM are continuously optimized until the model with the smallest overall error is obtained, which is the optimal model. Finally, the optimal model is utilized to establish an equivalent distribution network system, different degrees of voltage drops are set up at the grid-connected points, the fault characteristics are compared with those of the complete model, and the simulation results can prove the reliability and practicality of the proposed method.

Header Height Detection and Terrain-Adaptive Control Strategy Using Area Array LiDAR

During the operation of combine harvesters, the cutting platform height is typically controlled using manual valve hydraulic systems, which can result in issues such as delays in adjustment and high labor intensity, affecting both the quality and efficiency of the operation. There is an urgent need to enhance the automation level. Conventional methods frequently employ single-point measurements and lack extensive area coverage, which means their results do not fully represent the terrain’s variations in the area and are prone to local anomalies. Given the inherently undulating terrain of farmland during harvesting, a control strategy that does not adjust for minor undulations but only for significant ones proves to be more rational. To this end, a sine wave superposition model was established to simulate three-dimensional ground elevation changes, and an area array LiDAR was used to collect 8 × 8 data for the header height. The effects of mounds and stubble on the measurement results were analyzed, and a dynamic process simulation model for the solenoid valve core was developed to analyze the on/off delay characteristics of a three-position four-way electromagnetic directional valve. Moreover, a physical model of the hydraulic system was constructed based on the Simscape module in Simulink, and the Bang Bang switch predictive control system based on position threshold was introduced to achieve early switching of the electromagnetic directional valve circuit. In addition, an automatic control system for cutting platform height was designed based on an STM32 microcontroller. The control system was tested on the hydraulic automatic control test rig developed by Shanxi Agricultural University. The simulation and experimental results demonstrated that the control system and strategy were robust to output disturbances, effectively enhancing the intelligence and environmental adaptability of agricultural machinery operations.

Method for determining the Lyapunov exponent of a continuous model using the monodrome matrix

The Lyapunov exponent is a measure of the sensitivity of a dynamic system to any changes and disturbances. It is therefore applicable in many fields of science, including physics, chemistry, economics, psychology, biology, medicine, and technology. Therefore, there is a need to have effective methods for determining the value of this exponent. In particular, it concerns the definition of its sign. The positive value of the Lyapunov exponent confirms the sensitivity of the system, especially when the system is chaotic. A negative value indicates the stability of the dynamic system being tested. The numerical value of the Lyapunov exponent indicates the degree of sensitivity of the dynamic system under study. Although the mathematical definition of the Lyapunov exponent is clear and simple, in practice determining its value is not a trivial matter, especially for continuous models. This paper presents a method for determining the Lyapunov exponent for continuous models. This method is based on the monodromy matrix. The work, for example, presents research on the following models of physical systems: the Van der Pol model with external forcing, the nonlinear mathematical pendulum model with external forcing and the Lorenz weather model.

Applying the Markov chain in natural language processing and three-pool model

This paper delves into the application of Markov chains in Natural Language Processing (NLP), and the Markov Chain Monte Carlo (MCMC) methodology relevant to the three-pool model. The former outlines the basic principles of Markov chains, highlighting their utility in predicting word sequences in language modelling and text generation, despite certain limitations. Also, the former describes mathematical frameworks like n-gram models that enhance prediction accuracy by considering multiple preceding words. It acknowledges challenges in NLP such as oversimplification and emotional depth, as well as computational issues in higher-order models. It concludes by discussing the integration of Markov chains with other models to mitigate these limitations, and their enduring relevance in computational linguistics. The later investigates the MCMC methodology, a seminal development in the field of statistical inference, which is especially useful when analysing complicated systems when traditional statistical techniques are inadequate. Moreover, this later explores the fundamental concepts of MCMC, clarifies how it is inherently related to Markov chains, presents the three-pool model that is commonly applied to models of physical, chemical, or ecological systems, and discusses how MCMC can be used to analyse these models.

Cyber-Physical Modeling and Vulnerability Assessment of Substations for Transmission System Operator

In bulk power systems, the majority of interaction between cyber and physical components takes place in substations. However, in most of the cyber–physical power system models the physical layer is typically done using the bus-branch (BB) model, where each substation is considered as a single node. This approach will not capture the details of the cyber layer. This paper proposes a framework to model the substations using node-breaker (NB) models for physical system representation so that the detailed station configurations, the current and the voltage transformer positions, arrangements of protective relays, bay control units and associated communication infrastructure within the substations and its dependencies on the physical elements can be captured effectively using a single cyber–physical graph. Keeping a transmission system operator in view, who does not use power flow and security assessment tools for station operations and maintenance, a vulnerability assessment approach is proposed to assess the risk using some representative attack scenarios. The proposed approach is demonstrated using WECC 3-machine system for breaker and half station configuration. The attack scenarios are developed based on the real substation configuration and the adversary’s ability to understand the substation protection and BI/BO operations.

Model‐Based Cybertronics Systems Engineering (MBCSE)

AbstractThe cybertronics challenges evolve around the complexity of systems and increase in detail and data involved. Existing methods and tools can master some of the rising challenges, but a method being able to handle the challenges was not introduced yet. MBSE is a potential approach to solve these problems, but the available methods were developed for modeling physical systems and software, not cybertronics. Because of the diversity of implementation domains participating in cybertronics systems, the modeling methodology must support the holistic management of requirements, properties, and design data. This paper introduces some promising emerging technologies like Arcadia, SysML V2, SysMD and PMM, that have the potential to interact with other methods and tools, closing the gaps in requirements tracing, system modeling, documentation, and verification. One potential methodology is introduced through a design example from requirements to implementation interface.

Real-time hybrid test method for floating wind turbines: Focusing on the aerodynamic load identification

Since the development of floating wind turbine (FWT) shows a rapid trend towards larger capacity and larger rotor size, the traditional full-model basin test method has encountered limits. Especially the balance between the wind generation system (WGS) size and scale ratio of the model FWT system. Under such circumstances, the hybrid model test method provides the possibility to improve the FWT model test. In the hybrid model test method, the original physical model system is divided into physical subsystem and numerical subsystem, and the data acquisition and process module between the 2 subsystems plays an important role. In this paper, a framework of real-time hybrid test (RTHT) system is setup firstly, which combines physical model wind turbine and motion platform. The damping modification to the corresponding numerical code is applied to improve the motion calculation accuracy. Delay implementation is employed to avoid motion divergence. Then a simulation loop is setup in numerical environment to study the identification of aerodynamic load. The influence of identification accuracy to the RTHT result is analyzed. Lastly, the dual-accelerometer method of aerodynamic load identification is employed in the proposed RTHT system. Decay tests and irregular wave only tests are carried out to validate the aerodynamic load identification method. The capability and potential of the RTHT method of floating wind turbine model test is preliminary proved in the work of this paper.

Data-driven identification of stable sparse differential operators using constrained regression

Identifying differential operators from data is essential for the mathematical modeling of complex physical and biological systems where massive datasets are available. These operators must be stable for accurate predictions for dynamics forecasting problems. In this article, we propose a novel methodology for learning differential operators that are theoretically linearly stable and have sparsity patterns of common discretization schemes. These differential operators are obtained by solving a constrained regression problem, involving local constraints to ensure the linear stability of the global dynamical system. We further extend this approach for learning nonlinear differential operators by determining linear stability constraints for linearized equations around an equilibrium point. The applicability of the proposed method is demonstrated for both linear and nonlinear partial differential equations such as 1-D scalar advection-diffusion equation, 1-D Burgers equation and 2-D advection equation. The results indicated that solutions to constrained regression problems with linear stability constraints provide accurate and linearly stable sparse differential operators.

Smart Healthcare Based Cyber Physical System Modeling by Block Chain with Cloud 6G Network and Machine Learning Techniques

Smart Healthcare Based Cyber Physical System Modeling by Block Chain with Cloud 6G Network and Machine Learning Techniques

Casimir–Onsager matrix for weakly driven processes

Modeling of physical systems must be based on their suitability to unavoidable physical laws. In this work, in the context of classical, isothermal, finite-time, and weak drivings, I demonstrate that physical systems, driven simultaneously at the same rate in two or more external parameters, must have the Fourier transform of their relaxation functions composing a positive-definite matrix to satisfy the Second Law of Thermodynamics. By evaluating them in the limit of near-to-equilibrium processes, I identify that such coefficients are the Casimir–Onsager ones. The result is verified in paradigmatic models of the overdamped and underdamped white noise Brownian motions. Finally, an extension to thermally isolated systems is made by using the time-averaged Casimir–Onsager matrix, in which the example of the harmonic oscillator is presented.

Cascade failure modeling and resilience analysis of mine cyber physical systems under deliberate attacks

Guided by the intelligent construction of coal mines and integrating the concept of the Cyber-Physical System (CPS), a novel approach to a coal mine information-physical fusion system is proposed. This concept emerges from the advancement of intelligent mines and the growing need for enhanced safety in coal mine operations. From a system safety perspective, this approach aims to effectively evaluate security issues by better integrating the informational and physical layers of intelligent mines. Currently, research in areas such as power grids and water networks has widely adopted concepts of cascade failures and robustness. It is suggested that the CPS framework be adapted to the mining sector. Considering the critical role of coal mines in China's energy security and their vulnerability to cyber attacks, a mine-specific CPS system is designed. This system incorporates a model of mine information-physical fusion, including networks for mine operations, management, and control, tailored to the unique conditions of mine shafts and underground settings. Utilizing Markov process theory, the paper delves into the theoretical study of the cascade failure process under deliberate attack strategies. This analysis is essential to effectively assess the safety issues within the information-physical system, providing vital support for fault prediction and safety analysis. The model of cascading failures in the mine information-physical system is developed, and based on an analysis of resilience and robustness, the study identifies key factors influencing the security of mine information-physical systems. Critical factors affecting the reliability of these systems include the number of system nodes, node coupling, edge count, and the interconnection methods of the dual-layer dependency network. The paper concludes by discussing the challenges in analyzing the security of information-physical systems and suggesting directions for future research.