Analysis Of Dynamical Systems Research Articles

Electricity Energy Demand in Banjarnegara District for the Year 2021-2030 Using Linear Regression Method and Leap Software

Electricity demand is expected to increase from year to year. Central Java's electricity demand in 2013 reached 18.205 GWh with a total of 8.092.964 customers. This energy demand has increased in 2018 to 22.945 GWh with a total of 10.011.388 customers. Continuous use of electricity, both directly and indirectly, will also affect economic needs and people's welfare. It is estimated that electricity sales will continue to increase in line with the growth of customers who will also continue to increase. In predicting the need for electrical energy, various forecasting methods are commonly used to predict the need for electrical energy, such as the Regression Method, Time Series Method, Causal Method, Neural Network Method, and Dynamic System Analysis Method. In predicting the need for electrical energy there are advantages and disadvantages of the forecasting method. Based on the availability of data, this research analyzes forecasting the demand for electrical energy in Banjarnegara district using the regression and time series method which is applied using LEAP software. The results show that the total demand for electrical energy using the regression method in 2030 will reach 50.616 GWh while the LEAP software in 2030 will be 59.677 GWh.

A semi-analytical multi-harmonic balance method on full-3D contact model for dynamic analysis of dry friction systems

Dry friction damping structures are widely-used in aero-engines to mitigate vibration. The nonlinear nature of friction and the two-dimensional in-plane motion on the contact interface bring challenges to accurately and efficiently predict the forced response of frictionally damped structures. The state-of-the-art Multi-Harmonic Balance Method (MHBM) on quasi-3D contact model in engineering cannot precisely capture the kinematics on the friction interface although the efficiency is high. The full-3D contact model can describe the constitutive relationship of the interface in a more accurate manner; however, the efficiency and convergence are not guaranteed for large-scale models. In this paper, a semi-analytical MHBM on full-3D contact model is proposed. The original Trajectory Tracking Method (TTM) for evaluating the contact force is reformulated to make the calculation more concise and the derivation of the Analytical Jacobian Matrix (AJM) feasible. Based on the chain rule of derivation, the AJM which is the core to upgrade the performance is deduced. Through a shrouded blade finite element model, the accuracy and efficiency of the proposed method are compared with both the MHBM on full-3D contact model with numerical Jacobian matrix and the MHBM on quasi-3D contact model with AJM. The results show that the AJM improves significantly the efficiency of the MHBM on full-3D contact model. The time cost of the proposed method is in the same order of magnitude as that of the MHBM on quasi-3D contact model. We also confirm that the full-3D contact model is necessary for the dynamic analyses of shrouded blades. If one uses the quasi-3D model, the estimation relative error of damping can even reach 31.8% in some cases. In addition, the AJM also brings benefits for stability analysis. It is highly recommended that engineers use the MHBM on full-3D contact model for the dynamic analysis and design of shrouded blades.

Improved explicit quartic B-spline time integration scheme for dynamic response analysis of viscoelastic systems

A quartic B-spline based explicit scheme is extended for dynamic analysis of viscoelastic systems. In the calculation formulation, different integration approximation schemes for exponential damping models and other damping models are presented. The mathematical derivation of the convolution solving strategy is formulated for viscoelastic systems. For the damping models composed of exponential function, this scheme only requires once convolution calculation in each time step, even though the dynamic equations are used twice. This significantly reduces the calculation time for the damping models composed of exponential function. Numerical examples show that the proposed quartic B-spline based explicit scheme achieves higher accuracy and efficiency compared to other competitive explicit schemes, not only for damping models composed of exponential functions, but also for other viscoelastic damping models.

Dynamic Analysis and Adaptive Synchronization of a New Chaotic System

Dynamic Analysis and Adaptive Synchronization of a New Chaotic System

Two-body dynamic simulations of a combined semi-submersible floating offshore wind turbine and torus wave energy converter

Dynamic responses of a combined wind and wave energy system which consist of a 5MW semi-submersible floating offshore wind turbine (FOWT) and a torus-shaped wave energy converter (WEC) are investigated. In the investigated configuration, the torus WEC is constrained to move only in the heave direction with respect to the FOWT. This results in a two-body dynamic system that allows for the extraction of wave energy through the relative heave motion. A Modelica-based multi-body system (MBS) code is used to perform fully coupled dynamic analyses of the combined system. The wind turbine loads are calculated using the state-of-the-art Blade Element Momentum (BEM) method, while the wave power take-off (PTO) system is modelled as a linear spring and a viscous damper. A case study is presented where the mass of the torus is varied to investigate the impact on the two-body dynamics of the combined system. The system performance is assessed in terms of the maximum wave power absorption and the quality of wind power production.

Feeding the Needy through Feedback – A Systems Dynamics Analysis of New Jersey’s Supplemental Nutrition Assistance Program

Social welfare initiatives in the United States strive to help as many people as possible with limited resources and within budgetary constraints. One such program is the Supplemental Nutrition Assistance Program (SNAP), colloquially known as food stamps, which provides income to people in need so they can purchase groceries. Although well-intended, critics of SNAP question not only its efficiency but also its efficacy due to its lack of access and inability to provide adequate benefits to its participants (Oliveira et al., 2018). This study models SNAP using systems dynamics, allowing us to examine these concerns and, when warranted, develop potential solutions. Specifically, we leverage the software Vensim to simulate New Jersey’s SNAP. Our findings suggest SNAP should focus its efforts on reaching the eligible population versus the program. These results are not merely academic; they are potentially actionable, as they can be used to reallocate existing funding.

Dynamical analysis, circuit realization, and applications of 4D hyperchaotic systems with bursty oscillations and infinite attractor coexistence

Dynamical analysis, circuit realization, and applications of 4D hyperchaotic systems with bursty oscillations and infinite attractor coexistence

What Is in a Simplicial Complex? A Metaplex-Based Approach to Its Structure and Dynamics.

Geometric realization of simplicial complexes makes them a unique representation of complex systems. The existence of local continuous spaces at the simplices level with global discrete connectivity between simplices makes the analysis of dynamical systems on simplicial complexes a challenging problem. In this work, we provide some examples of complex systems in which this representation would be a more appropriate model of real-world phenomena. Here, we generalize the concept of metaplexes to embrace that of geometric simplicial complexes, which also includes the definition of dynamical systems on them. A metaplex is formed by regions of a continuous space of any dimension interconnected by sinks and sources that works controlled by discrete (graph) operators. The definition of simplicial metaplexes given here allows the description of the diffusion dynamics of this system in a way that solves the existing problems with previous models. We make a detailed analysis of the generalities and possible extensions of this model beyond simplicial complexes, e.g., from polytopal and cell complexes to manifold complexes, and apply it to a real-world simplicial complex representing the visual cortex of a macaque.

Dynamical responses and analysis of rotor-nacelle systems subjected to aerodynamic and base excitations

Dynamical responses and analysis of rotor-nacelle systems subjected to aerodynamic and base excitations

Automated Data–Driven Model Extraction and Validation of Inverter Dynamics with Grid Support Function

This research focuses on the evolving dynamics of the power grid, where traditional synchronous generators are being replaced by non-synchronous power electronic converter (PEC)-interfaced renewable energy sources. The non-linear dynamics must be accurately modeled to ensure the stability of future converter-dominated power systems (CDPS). However, obtaining comprehensive dynamic models becomes more complex and computationally intensive as the system grows. This study proposes a scalable and automated data-driven partitioned modeling framework for CDPS dynamics. The method constructs reduced-ordered dynamic linear transfer function models using input-output measurements from a PEC switching model. Validation experiments were conducted on single-house and multi-house scenarios, demonstrating high accuracy (over 97%) and significant computational speed improvements (6.5 times faster) compared to comprehensive models. This framework and modeling approach offer valuable insights for efficient analysis of power system dynamics, aiding in planning, operation, and dispatch.

Analysis and Optimal Control Measures of a Typhoid Fever Mathematical Model for Two Socio-Economic Populations

Typhoid fever is an infectious disease that affects humanity worldwide; it is particularly dangerous in areas with communities of a lower socio-economic status, where many individuals are exposed to a dirty environment and unclean food. A mathematical model is formulated to analyze the impact of control measures such as vaccination of susceptible humans, treatment of infected humans and sanitation in different socio-economic communities. The model assumed that the population comprises of two socio-economic classes. The essential dynamical system analysis of our model was appropriately carried out. The impact of the control measures was analyzed, and the optimal control theory was applied on the control model to explore the impact of the different control measures. Numerical simulation of the models and the optimal controls were carried out and the obtained results indicate that the overall combination of the control measures eradicates typhoid fever in the population, but the controls are more optimal in higher socio-economic status communities.

Dynamic performance analysis of a gear transmission system due to cavitation in gerotor pump

In this work, a dynamic model considering time-varying mesh stiffness and backlash was proposed and a test rig was built to investigate the vibration behavior of the idle gear set in a gerotor pump. The effects of input shaft speed, torque fluctuation, and gear tooth backlash on the dynamic performance of gerotor pump were analyzed according to the numerical and experimental results. Results demonstrate that when the torque fluctuation is neglected, the dynamic transmission error of drive gear is dominated by the first three mesh harmonic components; however, the RMS values of vibration acceleration have high frequency characteristics. When the torque fluctuation is considered, the dynamic responses of gerotor pump are modulated by the torque fluctuation. The effect of tooth backlash on the dynamic performance of gerotor pump is limited and mostly depended on the torque fluctuation condition. The gerotor pump noise is dominated by the low frequency component around the mesh frequency. The vibration energy can be divided into two parts in the frequency domain. In the low frequency band, the vibration energy is caused by the mechanical vibration. However, in the high frequency band, the cavitation phenomena may cause the concentration of the vibration energy and resonant of pump structure.

Research into a Marine Helicopter Traction System and Its Dynamic Energy Consumption Characteristics

As countries attach great importance to the ocean-going navigation capability of ships, the energy consumption of shipborne equipment has attracted much attention. Although energy consumption analysis is a guiding method to improve energy efficiency, it often ignores the dynamic characteristics of the system. However, the traditional dynamic analysis method hardly considers the energy consumption characteristics of the system. In this paper, a new type of electric-driven helicopter traction system is designed based on the ASIST system. Combined with power bond graph theory, a system dynamic modeling method that considers both dynamic and energy consumption characteristics is proposed, and simulation analysis is carried out. The results indicate that the designed traction system in this study displays high responsiveness, robust, steady-state characteristics, and superior energy efficiency. When it engages with helicopter-borne aircraft, it swiftly transitions to a stable state within 0.2 s while preserving an efficient speed tracking effect under substantial load force, and no significant fluctuations are detected in the motor rotation rate or the helicopter movement velocity. Moreover, it presents a high energy utilization rate, achieving an impressive energy utilization rate of 84% per single working cycle. Simultaneously, the proposed modeling methodology is validated as sound and effective, particularly apt for the dynamic and power consumption analysis of marine complex machinery systems, guiding the high-efficiency design of the transmission system.

Dynamic Characteristic Analysis of a Half-Vehicle Seat System Integrated with Nonlinear Energy Sink Inerters (NESIs)

To enhance the dynamic performance of half-vehicle seat systems and reduce vibrations in both the vertical and pitching directions, a nonlinear energy sink inerter (NESI) can be introduced and aligned with lightweight design principles. A dynamic model of a half-vehicle seat system integrated with NESIs is constructed using Newton’s second law. The dynamic response of the system under pavement harmonic and random excitations is obtained using the pseudo-arc-length and harmonic balance methods and the numerical method, respectively. The dynamic behavior of the system is assessed using eight evaluation indexes. The optimal structural parameters of the NESIs are determined through the genetic algorithm. The results indicate that using NESIs attenuates resonance peaks and reduces root mean square (RMS) values for vehicle seat suspension strokes, front and rear suspension system strokes, and front and rear dynamic tire loads. However, the resonance peaks and RMS values for other performance indexes, which are vehicle seat vertical acceleration, the bodywork vertical, and pitching accelerations, exhibit an increase. When the structural parameters of the NESIs are optimized and contrasted with the original NESIs, the RMS values of the bodywork’s vertical and pitching acceleration, seat vertical acceleration, and seat suspension stroke will decrease by 23.97%, 27.48%, 23.59%, and 14.29%, respectively, and the other evaluation indexes will satisfy the limit conditions.

Dynamic modeling and analysis of planetary gear system for tooth fault diagnosis

This study concentrates on the dynamic modeling and analysis of a planetary gear system with tooth broken faults. Firstly, a systematic calculation method of time-varying mesh stiffness (TVMS) for the planetary gear system is developed. Analytical models are established for both external-external and external-internal gear pairs under both healthy and tooth broken conditions. Then, a translational-torsional nonlinear dynamic model is established for a planetary gear system and coupled with the TVMS calculation method, to achieve dynamic simulations with tooth broken faults on the sun, planet and ring gears. The influences of tooth broken faults at different gears and at different damage degrees on the vibration responses are revealed. In addition, 15 condition indicators are chosen to assess their sensitivity to the tooth broken faults in a wide range of operational speed rather than a specific operational speed, in order to provide comprehensive information for evaluating the vibration characteristics and health conditions. Finally, experimental vibration signals from a gear transmission test rig are applied to verify the proposed dynamic model. The modeling method and analysis results here could provide some suggestions for the vibration analysis and fault diagnosis of planetary gear systems, and further provide data basis for the development of fault diagnosis methods.

The [formula omitted]-compound of a difference–algebraic system

The multiplicative and additive compounds of a matrix have important applications in geometry, linear algebra, and the analysis of dynamical systems. In particular, the k-compounds allow to build a k-compound dynamical system that tracks the evolution of k-dimensional parallelotopes along the original dynamics. This has recently found many applications in the analysis of non-linear systems described by ODEs and difference equations. Here, we introduce the k-compound system corresponding to a difference–algebraic system, and describe several applications to the analysis of discrete-time dynamical systems.

Influence of blades’ shape and cutters’ arrangement of PDC drill bit on nonlinear vibration of deep drilling system

In this paper, the surface morphology method is improved and the bit-rock interaction model between the rock and the PDC bit is studied, considering the influence of blades’ shape and the cutters’ arrangement. Based on this model, the dynamic model of the deep drilling system equipped with arbitrary shape PDC bit is established, and the stability prediction method is proposed. Based on the improved surface morphology method, the dynamic characteristics of the drilling system equipped with four different types of bit (an actual bit, a Tian bit, a Tian bit with blades, and a traditional bit) are studied, comparing with the Tian model based on polygon clipping. The results indicate that the influence of blades’ shape and cutters’ arrangement of PDC bit on the nonlinear vibration of the drilling system cannot be ignored. By applying the proposed method, the dynamic model of the drilling system equipped with an actual PDC bit presents excellent computational efficiency, accuracy, and avoids unreasonable behavior, which provides a reliable theory for the dynamic analysis of the drilling system. In addition, the proposed uncut volume error and repeated cutting volume error can be used to evaluate the shape design of the drill bit and the accuracy of the bit-rock interaction model.

Closed-Form Dynamic Modeling and Performance Evaluation of a 4-Degrees-of-Freedom Parallel Driving Mechanism

Abstract Kinematic estimations and dynamic performance assessments are fundamental theoretical issues to realize the mechanism from conceptual design to engineering application. In this article, the closed-form dynamic formulations of a 4-degrees-of-freedom (DoFs) parallel driving mechanism are derived by combining the Lagrange method and the virtual work principle. The selection principle of generalized coordinates and the steps for inverse dynamics modeling of the manipulator are proposed. Simulation results verify the correctness of the dynamic model, and a physical prototype has been built. Based on the dynamic modeling, the concise algebraic expression of the operational space inertia matrix of the parallel driving mechanism is deduced. Because the translation and rotation degrees-of-freedom are inconsistent in the operational space, the Jacobian matrix is adopted to map the inertia matrix from the operational space to the joint space. Based on the inertia matrix in joint space, the average energy transfer efficiency (AETE) index is proposed. Finally, two control techniques for the manipulator implementable in joint space are compared. The AETE index and dynamic modeling method suggested in this article can be further used in other manipulators for dynamic analysis and motion system design.

Dynamic performance analysis of a solar adsorption system: the effect of operating conditions and collectors’ area

A continuous adsorption refrigerator, aiming for cold production to a fruit storage room installed in arid regions, is proposed. After cooling load estimation, a technical-economic study of different types of solar collectors was performed. Then, the dynamic performances of a solar-driven two-bed adsorption chiller are studied. Furthermore, this study shows that an optimal choice of the collector-type area and the operating conditions can reduce the global system cost and ensure better energy management. With 43.47 m 2 collectors’ area, a solar fraction of 55% is reached at cycle time (tcycle) 1600s; however, 49% is obtained at tcycle of 900s. With a total collectors’ area of 43.47 m2, a tcycle of 1600s and a cooling water inlet temperature (TCW,in) of 22°C, 60% of the cooling demand is solar produced. However, 57% is achieved at a tcycle of 900s, 50.61 m2 collectors’ area and TCW,in of 25°C. Highlights The cooling load of a storage room used for indigenous fruit preservation was estimated. A technical-economic study of different types of solar collectors is carried out to choose the most suitable one. A detailed dynamic approach to the thermodynamics of a solar adsorption refrigerator according to the time-varying solar radiation intensity and climatic data were presented. The effect of solar collectors’ area and different operating conditions has been studied to optimise the global system performance and cost.

Optimization on the symplectic Stiefel manifold: SR decomposition-based retraction and applications

Numerous problems in optics, quantum physics, stability analysis, and control of dynamical systems can be brought to an optimization problem with matrix variable subjected to the symplecticity constraint. As this constraint nicely forms a so-called symplectic Stiefel manifold, Riemannian optimization is preferred, because one can borrow ideas from unconstrained optimization methods after preparing necessary geometric tools. Retraction is arguably the most important one which decides the way iterates are updated given a search direction. Two retractions have been constructed so far: one relies on the Cayley transform and the other is designed using quasi-geodesic curves. In this paper, we propose a new retraction which is based on an SR matrix decomposition. We prove that its domain contains the open unit ball which is essential in proving the global convergence of the associated gradient-based optimization algorithm. Moreover, we consider three applications—symplectic target matrix problem, symplectic eigenvalue computation, and symplectic model reduction of Hamiltonian systems—with various examples. The extensive numerical comparisons reveal the strengths of the proposed optimization algorithm.