The relationship between compartment models and their stochastic counterparts:A comparative study with examples of the COVID-19 epidemic modeling

Deterministic compartment models(CMs)and stochastic models,including stochastic CMs and agent-based models,are widely utilized in epidemic modeling.However,the relationship between CMs and their corresponding stochastic models is not well understood.The present study aimed to address this gap by conducting a comparative study using the susceptible,exposed,infectious,and recovered(SEIR)model and its extended CMs from the coronavirus disease 2019 modeling literature.We demonstrated the equivalence of the numerical solution of CMs using the Euler scheme and their stochastic counterparts through theoretical analysis and simulations.Based on this equivalence,we proposed an efficient model calibration method that could replicate the exact solution of CMs in the corresponding stochastic models through parameter adjustment.The advancement in calibration techniques enhanced the accuracy of stochastic modeling in capturing the dynamics of epidemics.However,it should be noted that discrete-time stochastic models cannot perfectly reproduce the exact solution of continuous-time CMs.Additionally,we proposed a new stochastic compartment and agent mixed model as an alternative to agent-based models for large-scale population simulations with a limited number of agents.This model offered a balance between computational efficiency and accuracy.The results of this research contributed to the comparison and unification of deterministic CMs and stochastic models in epidemic modeling.Furthermore,the results had implications for the development of hybrid models that integrated the strengths of both frameworks.Overall,the present study has provided valuable epidemic modeling techniques and their practical applications for understanding and controlling the spread of infectious diseases.

Predictive modeling for postoperative delirium in elderly patients with abdominal malignancies using synthetic minority oversampling technique

BACKGROUND Postoperative delirium,particularly prevalent in elderly patients after abdominal cancer surgery,presents significant challenges in clinical management.AIM To develop a synthetic minority oversampling technique(SMOTE)-based model for predicting postoperative delirium in elderly abdominal cancer patients.METHODS In this retrospective cohort study,we analyzed data from 611 elderly patients who underwent abdominal malignant tumor surgery at our hospital between September 2020 and October 2022.The incidence of postoperative delirium was recorded for 7 d post-surgery.Patients were divided into delirium and non-delirium groups based on the occurrence of postoperative delirium or not.A multivariate logistic regression model was used to identify risk factors and develop a predictive model for postoperative delirium.The SMOTE technique was applied to enhance the model by oversampling the delirium cases.The model’s predictive accuracy was then validated.RESULTS In our study involving 611 elderly patients with abdominal malignant tumors,multivariate logistic regression analysis identified significant risk factors for postoperative delirium.These included the Charlson comorbidity index,American Society of Anesthesiologists classification,history of cerebrovascular disease,surgical duration,perioperative blood transfusion,and postoperative pain score.The incidence rate of postoperative delirium in our study was 22.91%.The original predictive model(P1)exhibited an area under the receiver operating characteristic curve of 0.862.In comparison,the SMOTE-based logistic early warning model(P2),which utilized the SMOTE oversampling algorithm,showed a slightly lower but comparable area under the curve of 0.856,suggesting no significant difference in performance between the two predictive approaches.CONCLUSION This study confirms that the SMOTE-enhanced predictive model for postoperative delirium in elderly abdominal tumor patients shows performance equivalent to that of traditional methods,effectively addressing data imbalance.

Scenario analysis of the Indonesia carbon tax impact on carbon emissions using system dynamics modeling and STIRPAT model

This study aims to develop a system dynamic(SD)forecasting model based on the STIRPAT model to forecast the effect of an IDR 30 per kg CO_(2)e carbon tax on carbon emissions,estimate future carbon emissions under ten scenarios,without and with the carbon tax,and estimate the environmental Kuznets curve(EKC)to predict Indonesia’s carbon emission peak.Carbon emission drivers in this study are decomposed into several factors,namely energy structure,energy intensity,industrial structure,GDP per capita,population,and fixed-asset investment.This study included nuclear power utilization starting in 2038.The research gaps addressed by this study compared to previous research are(1)use of the ex-ante approach,(2)inclusion of nuclear power plants,(3)testing the EKC hypothesis,and(4)contribution to government policy.The simulation results show that under the carbon tax,carbon emissions can be reduced by improving renewable energy structures,adjusting industrial structures to green businesses,and emphasizing fixed asset investment more environmentally friendly.Moreover,the result approved the EKC hypothesis.It shows an inverse U-shaped curve between GDP per capita and CO_(2)emissions in Indonesia.Indonesia’s fastest carbon emission peak is under scenario seven and is expected in 2040.Although an IDR 30 per kg CO_(2)e carbon tax and nuclear power will take decades to reduce carbon emissions,the carbon tax can still be a reference and has advantages to implement.This result can be a good beginning step for Indonesia,which has yet to gain experience with a carbon tax that can be implemented immediately and is helpful to decision-makers in putting into practice sensible measures to attain Indonesia’s carbon emission peaking.This research provides actionable insights internationally on carbon tax policies,nuclear energy adoption,EKC dynamics,global policy implications,and fostering international cooperation for carbon emission reductions.

A methodology for damage evaluation of underground tunnels subjected to static loading using numerical modeling

We have proposed a methodology to assess the robustness of underground tunnels against potential failure.This involves developing vulnerability functions for various qualities of rock mass and static loading intensities.To account for these variations,we utilized a Monte Carlo Simulation(MCS)technique coupled with the finite difference code FLAC^(3D),to conduct two thousand seven hundred numerical simulations of a horseshoe tunnel located within a rock mass with different geological strength index system(GSIs)and subjected to different states of static loading.To quantify the severity of damage within the rock mass,we selected one stress-based(brittle shear ratio(BSR))and one strain-based failure criterion(plastic damage index(PDI)).Based on these criteria,we then developed fragility curves.Additionally,we used mathematical approximation techniques to produce vulnerability functions that relate the probabilities of various damage states to loading intensities for different quality classes of blocky rock mass.The results indicated that the fragility curves we obtained could accurately depict the evolution of the inner and outer shell damage around the tunnel.Therefore,we have provided engineers with a tool that can predict levels of damages associated with different failure mechanisms based on variations in rock mass quality and in situ stress state.Our method is a numerically developed,multi-variate approach that can aid engineers in making informed decisions about the robustness of underground tunnels.

Modeling time-dependent mechanical behavior of hard rock considering excavation-induced damage and complex 3D stress states

To investigate the long-term stability of deep rocks,a three-dimensional(3D)time-dependent model that accounts for excavation-induced damage and complex stress state is developed.This model comprises three main components:a 3D viscoplastic isotropic constitutive relation that considers excavation damage and complex stress state,a quantitative relationship between critical irreversible deformation and complex stress state,and evolution characteristics of strength parameters.The proposed model is implemented in a self-developed numerical code,i.e.CASRock.The reliability of the model is validated through experiments.It is indicated that the time-dependent fracturing potential index(xTFPI)at a given time during the attenuation creep stage shows a negative correlation with the extent of excavationinduced damage.The time-dependent fracturing process of rock demonstrates a distinct interval effect of the intermediate principal stress,thereby highlighting the 3D stress-dependent characteristic of the model.Finally,the influence of excavation-induced damage and intermediate principal stress on the time-dependent fracturing characteristics of the surrounding rocks around the tunnel is discussed.

A Hierarchical Modeling Framework for Electrochemical Behaviors in Lithium-Ion Batteries with Detailed Structures

The accurate representation of lithium plating and aging phenomena has posed a persistent challenge within the battery research community.Empirical evidence underscores the pivotal role of cell structure in influencing aging behaviors and lithium plating within lithium-ion batteries(LIBs).Available lithium-ion plating models often falter in detailed description when integrating the structural intricacies.To address this challenge,this study proposes an innovative hierarchical model that intricately incorporates the layered rolling structure in cells.Notably,our model demonstrates a remarkable capacity to predict the non-uniform distribution of current density and overpotential along the rolling direction of LIBs.Subsequently,we delve into an insightful exploration of the structural factors that influence lithium plating behavior,leveraging the foundation laid by our established model.Furthermore,we easily update the hierarchical model by considering aging factors.This aging model effectively anticipates capacity fatigue and lithium plating tendencies across individual layers of LIBs,all while maintaining computational efficiency.In light of our findings,this model yields novel perspectives on capacity fatigue dynamics and local lithium plating behaviors,offering a substantial advancement compared to existing models.This research paves the way for more efficient and tailored LIB design and operation,with broad implications for energy storage technologies.

Modularized and Parametric Modeling Technology for Finite Element Simulations of Underground Engineering under Complicated Geological Conditions

The surrounding geological conditions and supporting structures of underground engineering are often updated during construction,and these updates require repeated numerical modeling.To improve the numerical modeling efficiency of underground engineering,a modularized and parametric modeling cloud server is developed by using Python codes.The basic framework of the cloud server is as follows:input the modeling parameters into the web platform,implement Rhino software and FLAC3D software to model and run simulations in the cloud server,and return the simulation results to the web platform.The modeling program can automatically generate instructions that can run the modeling process in Rhino based on the input modeling parameters.The main modules of the modeling program include modeling the 3D geological structures,the underground engineering structures,and the supporting structures as well as meshing the geometric models.In particular,various cross-sections of underground caverns are crafted as parametricmodules in themodeling program.Themodularized and parametric modeling program is used for a finite element simulation of the underground powerhouse of the Shuangjiangkou Hydropower Station.This complicatedmodel is rapidly generated for the simulation,and the simulation results are reasonable.Thus,this modularized and parametric modeling program is applicable for three-dimensional finite element simulations and analyses.

Integrated Hydrological Modeling of the Godavari River Basin in Maharashtra Using the SWAT Model: Streamflow Simulation and Analysis

Hydrological modeling plays a crucial role in efficiently managing water resources and understanding the hydrologic behavior of watersheds. This study aims to simulate daily streamflow in the Godavari River Basin in Maharashtra using the Soil and Water Assessment Tool (SWAT). SWAT is a process-based hydrological model used to predict water balance components, sediment levels, and nutrient contamination. In this research, we used integrated remote sensing and GIS data, including Digital Elevation Models (DEM), land use and land cover (LULC) maps, soil maps, and observed precipitation and temperature data, as input for developing the SWAT model to assess surface runoff in this large river basin. The Godavari River Basin under study was divided into 25 sub-basins, comprising 151 hydrological response units categorized by unique land cover, soil, and slope characteristics using the SWAT model. The model was calibrated and validated against observed runoff data for two time periods: 2003-2006 and 2007-2010 respectively. Model performance was assessed using the Nash-Sutcliffe efficiency (NSE) and the coefficient of determination (R2). The results show the effectiveness of the SWAT2012 model, with R2 value of 0.84 during calibration and 0.86 during validation. NSE values also ranged from 0.84 during calibration to 0.85 during validation. These findings enhance our understanding of surface runoff dynamics in the Godavari River Basin under study and highlight the suit-ability of the SWAT model for this region.

Temperature-dependent solubility of Rebaudioside A in methanol/ethanol and ethyl acetate mixtures:Experimental measurements and thermodynamic modeling

The equilibrium solubility of Rebaudioside A(Reb A)FormⅡin binary mixtures of methanol/ethanol and ethyl acetate was quantitatively determined within the temperature range of 283.15—328.15 K at ambient pressure.The experimental findings indicate a positive correlation between the solubility of Reb A(FormⅡ)and both the temperature and the methanol/ethanol content in the solvent system.To describe the solubility data,six distinct models were employed:the modified Apelblat equation,theλh model,the combined nearly ideal binary solvent/Redlich—Kister(CNIBS/R—K)model,the van't HoffJouyban-Acree(VJA)model,the Apelblat-Jouyban-Acree(AJA)model,and the non-random two-liquid(NRTL)model.The combined nearly ideal binary solvent/Redlich—Kister model exhibited the most precise fit for solubility in methanol+ethyl acetate mixtures,reflected by an average relative deviation(ARD)of 0.0011 and a root mean square deviation(RMSD)of 12×10^(-7).Conversely,for ethanol+ethyl acetate mixtures,the modified Apelblat equation provided a superior correlation(ARD=0.0014,RMSD=4×10^(-7)).Furthermore,thermodynamic parameters associated with the dissolution of Reb A(FormⅡ),including enthalpy,entropy,and the Gibbs energy change,were inferred from the data.The findings underscore that the dissolution process is predominantly endothermic across the solvent systems examined.Notably,the entropy changes appear to have a significant influence on the Gibbs free energy associated with the dissolution of Reb A(FormⅡ),suggesting that entropic factors may play a pivotal role in the studied systems.

Modeling and Validation of Diamagnetic Rotor Levitated by Permanent Magnetics

As an innovative,low-power consuming,and low-stiffness suspension approach,the diamagnetic levitation technique has attracted considerable interest because of its potential applicability in miniaturized mechanical systems.The foundation of a diamagnetic levitation system is mathematical modeling,which is essential for operating performance optimization and stability prediction.However,few studies on systematic mathematical modeling have been reported.In this study,a systematic mathematical model for a disc-shaped diamagnetically levitated rotor on a permanent magnet array is proposed.Based on the proposed model,the magnetic field distribution characteristics,diamagnetic levitation force characteristics(i.e.,levitation height and stiffness),and optimized theoretical conditions for realizing stable levitation are determined.Experiments are conducted to verify the feasibility of the proposed mathematical model.Theoretical predictions and experimental results indicate that increasing the levitation height enlarges the stable region.Moreover,with a further increase in the rotor radius,the stable regions of the rotor gradually diminish and even vanish.Thus,when the levitation height is fixed,a moderate rotor radius permits stable levitation.This study proposes a mathematical modeling method for a diamagnetic levitation system that has potential applications in miniaturized mechanical systems.

Two-temperature modeling of lamellar cathode arc

A three-dimensional, two-temperature(2T) model of a lamellar cathode arc is constructed,drawing upon the conservation equations for mass, momentum, electron energy, and heavy particle energy, in addition to Maxwell's equations. The model aims to elucidate how the physical properties of electrons and heavy particles affect heat transfer and fluid flow in a lamellar cathode arc. This is achieved by solving and comparing the fields of electron temperature,heavy particle temperature, fluid flow, current density, and Lorentz force distribution under varying welding currents. The results show that the guiding effect of the lamellar cathode on current density, the inertial drag effect of moving arc, and the attraction effect of Lorentz force at the lamellar cathode tip primarily govern the distribution of the arc's physical fields. The guiding effect localizes the current density to the front end of the lamellar cathode, particularly where the discharge gap is minimal. Both the inertial drag effect and the attraction effect of Lorentz force direct arc flow toward its periphery. Under the influence of the aforementioned factors, the physical fields of the lamellar cathode arc undergo expansion and shift counter to the arc's direction of motion. A reduction in welding current substantially weakens the guiding effect,causing the arc's physical fields to deviate further in the direction opposite to the arc motion. In comparison with a cylindrical cathode arc, the physical fields of the lamellar cathode arc are markedly expanded, leading to a reduction in current density, electron temperature, heavy particle temperature, cathode jet flow velocity, and Lorentz force.

Combining field data and modeling to better understand maize growth response to phosphorus(P) fertilizer application and soil P dynamics in calcareous soils

We used field experimental data to evaluate the ability of the agricultural production system model (APSIM) to simulate soil P availability,maize biomass and grain yield in response to P fertilizer applications on a fluvo-aquic soil in the North China Plain.Crop and soil data from a 2-year experiment with three P fertilizer application rates(0,75 and 300 kg P_(2)O_(5) ha^(–1)) were used to calibrate the model.Sensitivity analysis was carried out to investigate the influence of APSIM SoilP parameters on the simulated P availability in soil and maize growth.Crop and soil P parameters were then derived by matching or relating the simulation results to observed crop biomass,yield,P uptake and Olsen-P in soil.The re-parameterized model was further validated against 2 years of independent data at the same sites.The re-parameterized model enabled good simulation of the maize leaf area index (LAI),biomass,grain yield,P uptake,and grain P content in response to different levels of P additions against both the calibration and validation datasets.Our results showed that APSIM needs to be re-parameterized for simulation of maize LAI dynamics through modification of leaf size curve and a reduction in the rate of leaf senescence for modern staygreen maize cultivars in China.The P concentration limits (maximum and minimum P concentrations in organs)at different stages also need to be adjusted.Our results further showed a curvilinear relationship between the measured Olsen-P concentration and simulated labile P content,which could facilitate the initialization of APSIM P pools in the NCP with Olsen-P measurements in future studies.It remains difficult to parameterize the APSIM SoilP module due to the conceptual nature of the pools and simplified conceptualization of key P transformation processes.A fundamental understanding still needs to be developed for modelling and predicting the fate of applied P fertilizers in soils with contrasting physical and chemical characteristics.

A Novel Framework to Construct S-Box Quantum Circuits Using System Modeling: Application to 4-Bit S-Boxes

Quantum computers accelerate many algorithms based on the superposition principle of quantum mechanics.The Grover algorithm provides significant performance to malicious users attacking symmetric key systems.Since the performance of attacks using quantum computers depends on the efficiency of the quantum circuit of the encryption algorithms,research research on the implementation of quantum circuits is essential.This paper presents a new framework to construct quantum circuits of substitution boxes(S-boxes)using system modeling.We model the quantum circuits of S-boxes using two layers:Toffoli and linear layers.We generate vector spaces based on the values of qubits used in the linear layers and apply them to find quantum circuits.The framework finds the circuit bymatching elements of vector spaces generated fromthe input and output of a given S-box,using the forward search or themeet-in-the-middle strategy.We developed a tool to apply this framework to 4-bit S-boxes.While the 4-bit S-box quantum circuit construction tool LIGHTER-R only finds circuits that can be implemented with four qubits,the proposed tool achieves the circuits with five qubits.The proposed tool can find quantum circuits of 4-bit odd permutations based on the controlled NOT,NOT,and Toffoli gates,whereas LIGHTER-R is unable to perform this task in the same environment.We expect this technique to become a critical step toward optimizing S-box quantum circuits.

Dynamics Modeling and Parameter Identification for a Coupled-Drive Dual-Arm Nursing Robot

A dual-arm nursing robot can gently lift patients and transfer them between a bed and a wheelchair.With its lightweight design,high load-bearing capacity,and smooth surface,the coupled-drive joint is particularly well suited for these robots.However,the coupled nature of the joint disrupts the direct linear relationship between the input and output torques,posing challenges for dynamic modeling and practical applications.This study investigated the transmission mechanism of this joint and employed the Lagrangian method to construct a dynamic model of its internal dynamics.Building on this foundation,the Newton-Euler method was used to develop a dynamic model for the entire robotic arm.A continuously differentiable friction model was incorporated to reduce the vibrations caused by speed transitions to zero.An experimental method was designed to compensate for gravity,inertia,and modeling errors to identify the parameters of the friction model.This method establishes a mapping relationship between the friction force and motor current.In addition,a Fourier series-based excitation trajectory was developed to facilitate the identification of the dynamic model parameters of the robotic arm.Trajectory tracking experiments were conducted during the experimental validation phase,demonstrating the high accuracy of the dynamic model and the parameter identification method for the robotic arm.This study presents a dynamic modeling and parameter identification method for coupled-drive joint robotic arms,thereby establishing a foundation for motion control in humanoid nursing robots.

Modeling and analysis of air combustion and steam regeneration in methanol to olefins processes

Light olefins is the incredibly important materials in chemical industry.Methanol to olefins(MTO),which provides a non-oil route for light olefins production,received considerable attention in the past decades.However,the catalyst deactivation is an inevitable feature in MTO processes,and regeneration,therefore,is one of the key steps in industrial MTO processes.Traditionally the MTO catalyst is regenerated by removing the deposited coke via air combustion,which unavoidably transforms coke into carbon dioxide and reduces the carbon utilization efficiency.Recent study shows that the coke species over MTO catalyst can be regenerated via steam,which can promote the light olefins yield as the deactivated coke species can be essentially transferred to industrially useful synthesis gas,is a promising pathway for further MTO processes development.In this work,we modelled and analyzed these two MTO regeneration methods in terms of carbon utilization efficiency and technology economics.As shown,the steam regeneration could achieve a carbon utilization efficiency of 84.31%,compared to 74.74%for air combustion regeneration.The MTO processes using steam regeneration can essentially achieve the near-zero carbon emission.In addition,light olefins production of the MTO processes using steam regeneration is 12.81%higher than that using air combustion regeneration.In this regard,steam regeneration could be considered as a potential yet promising regeneration method for further MTO processes,showing not only great environmental benefits but also competitive economic performance.

A Dynamical Study of Modeling the Transmission of Typhoid Fever throughDelayed Strategies

This study analyzes the transmission of typhoid fever caused by Salmonella typhi using a mathematical model thathighlights the significance of delay in its effectiveness.Time delays can affect the nature of patterns and slow downthe emergence of patterns in infected population density.The analyzed model is expanded with the equilibriumanalysis,reproduction number,and stability analysis.This study aims to establish and explore the non-standardfinite difference(NSFD)scheme for the typhoid fever virus transmission model with a time delay.In addition,the forward Euler method and Runge-Kutta method of order 4(RK-4)are also applied in the present research.Some significant properties,such as convergence,positivity,boundedness,and consistency,are explored,and theproposed scheme preserves all the mentioned properties.The theoretical validation is conducted on how NSFDoutperforms other methods in emulating key aspects of the continuous model,such as positive solution,stability,and equilibrium about delay.Hence,the above analysis also shows some of the limitations of the conventional finitedifference methods,such as forward Euler and RK-4 in simulating such critical behaviors.This becomes moreapparent when using larger steps.This indicated that NSFD is beneficial in identifying the essential characteristicsof the continuous model with higher accuracy than the traditional approaches.

Characterization and identification towards dynamic-based electrical modeling of lithium-ion batteries

Lithium-ion batteries are widely recognized as a crucial enabling technology for the advancement of electric vehicles and energy storage systems in the grid.The design of battery state estimation and control algorithms in battery management systems is usually based on battery models,which interpret crucial battery dynamics through the utilization of mathematical functions.Therefore,the investigation of battery dynamics with the purpose of battery system identification has garnered considerable attention in the realm of battery research.Characterization methods in terms of linear and nonlinear response of lithium-ion batteries have emerged as a prominent area of study in this field.This review has undertaken an analysis and discussion of characterization methods,with a particular focus on the motivation of battery system identification.Specifically,this work encompasses the incorporation of frequency domain nonlinear characterization methods and dynamics-based battery electrical models.The aim of this study is to establish a connection between the characterization and identification of battery systems for researchers and engineers specialized in the field of batteries,with the intention of promoting the advancement of efficient battery technology for real-world applications.

Modeling the Spatio-Temporal Dynamics of Local Context for a Contextualized Diffusion of Agroecological Intensification Options in Niger

Spatio-temporal variability and dynamics in Sahelian agro-pastoral zones make each local situation a special case. These specificities must be considered to guide the dissemination of agricultural options with a view to sustainable development. The territorial scale of municipalities is not sufficient for this necessary contextualization;the scale of the “village terroir” seems to be a better option. This is the hypothesis we put forward in the framework of the Global Collaboration for Resilient Food Systems program (CRFS), i.e. local context is spatially defined by village terroir. The study is based on data collected through participatory mapping and surveys in “village terroirs” in three regions of Niger (Maradi, Dosso and Tillabéri). Then the links between farm managers and their cultivated land, as well as the spatio-temporal dynamics of local context are analyzed. This study provides evidence of the existence and functional usefulness of the village terroir for farmers, their land management and their activities. It demonstrates the usefulness of contextualizing agricultural options at this scale. Their analysis elucidates the links between “terroirs village” and the specific functioning of the agrosocio-ecosystems acting on each of them, thus laying the systemic and geographical foundations for a model of the spatio- temporal dynamics of “village terroirs”. This initial work has opened up new perspectives in modeling and sustainable development.

From Digital Human Modeling to Human Digital Twin: Framework and Perspectives in Human Factors

The human digital twin(HDT)emerges as a promising human-centric technology in Industry 5.0,but challenges remain in human modeling and simulation.Digital human modeling(DHM)provides solutions for modeling and simulating human physical and cognitive aspects to support ergonomic analysis.However,it has limitations in real-time data usage,personalized services,and timely interaction.The emerging HDT concept offers new possibilities by integrating multi-source data and artificial intelligence for continuous monitoring and assessment.Hence,this paper reviews the evolution from DHM to HDT and proposes a unified HDT framework from a human factors perspective.The framework comprises the physical twin,the virtual twin,and the linkage between these two.The virtual twin integrates human modeling and AI engines to enable model-data-hybrid-enabled simulation.HDT can potentially upgrade traditional ergonomic methods to intelligent services through real-time analysis,timely feedback,and bidirectional interactions.Finally,the future perspectives of HDT for industrial applications as well as technical and social challenges are discussed.In general,this study outlines a human factors perspective on HDT for the first time,which is useful for cross-disciplinary research and human factors innovation to enhance the development of HDT in industry.

Dynamic Modeling and Experimental Verification of an RPR Type Compliant Paralle Mechanism with Low Orders

Efficiency of calculating a dynamic response is an important point of the compliant mechanism for posture adjustment.Dynamic modeling with low orders of a 2R1T compliant parallel mechanism is studied in the paper.The mechanism with two out-of-plane rotational and one lifting degrees of freedom(DoFs)plays an important role in posture adjustment.Based on elastic beam theory,the stiffness matrix and mass matrix of the beam element are established where the moment of inertia is considered.To improve solving efficiency,a dynamic model with low orders of the mechanism is established based on a modified modal synthesis method.Firstly,each branch of the RPR type mechanism is divided into a substructure.Subsequently,a set of hypothetical modes of each substructure is obtained based on the C-B method.Finally,dynamic equation of the whole mechanism is established by the substructure assembly.A dynamic experiment is conducted to verify the dynamic characteristics of the compliant mechanism.