Linear Dynamic Model Research Articles

Time-varying trends from Arctic ozonesonde time series in the years 1994-2022.

Although evidence of recovery in Antarctic stratospheric ozone has been found, evidence of recovery in Arctic ozone is still elusive, even though 25 years have passed since the peak in ozone depleting substances. Here we have used a Dynamic Linear Model to derive time-varying trends over 20-year periods in the Arctic ozone time series, measured in-situ by ozonesondes from 6 stations, from 1994 to 2022. The model accounts for seasonality, external forcing and 1st-order correlation in the residuals. As proxies for the external forcing, we have used tropopause pressure (replaced with Arctic Oscillation in the troposphere), eddy heat flux, the volume of polar stratospheric clouds multiplied by effective equivalent stratospheric chlorine, and solar radio flux at 10.7 cm for the 11-year solar cycle. Our results indicate that the ozone recovery in the lower Arctic stratosphere is not detectable. Though significant positive trends have been detected prior to 2017 at some stations, there are no statistically significant positive trends after 2017. Moreover, at a number of stations the trends after 2019 are rather negative and significant, varying between -0.30 ± 0.25 and -1.00 ± 0.85% per decade. Furthermore, the Arctic troposphere exhibited only statistically significant negative trends over 20-year periods ending in 2017 or later, varying between -0.31 ± 0.27 and -1.76 ± 0.41% per decade. These results highlight the importance of continued monitoring of the Arctic ozone.

Stability of steady-state solutions of Jeffcott rotor with varying rotational speed

AbstractThe behavior of flexible rotating systems with varying rotational speeds is essential in engineering applications. Analysis methods that consider linear dynamic models and many existing nonlinear analysis approaches assume constant rotational speed. These approaches are unsuited to study the dynamic interaction between driving torque and whirling motion in this class of applications. In this paper, an analysis of the stability and control of a Jeffcott rotor under varying operational conditions is presented. A nonlinear dynamic model of the system is formulated to enable a detailed stability and parametric analysis. A proportional-integral (PI) torque command is employed to achieve a steady-state rotational speed. Assuming constant lateral control effort, system equilibrium points and their stability characteristics as functions of the system’s parameters are analyzed. A control law that minimizes the lateral effort is derived. A feedback proportional lateral control strategy is introduced to enhance the system’s region of stability, particularly in the supercritical speed range. Finally, a simulation study is conducted to validate the analytical findings. Simulation results demonstrate the effectiveness of the proposed approach for defining stable operating conditions and improving system performance.

Revisiting time-varying dynamics in stock market forecasting: A Multi-source sentiment analysis approach with large language model

This paper presents the Heterogeneous Dynamic Seemingly Unrelated Regression with Dynamic Linear Models (HD-SURDLM), an innovative framework for stock return prediction that combines cutting-edge sentiment analysis with dynamic financial modeling. The model integrates sentiment data from 2.5 million Twitter posts and various news sources, utilizing state-of-the-art sentiment analysis tools such as VADER, TextBlob, and RoBERTa. HD-SURDLM refines Gibbs sampling for enhanced numerical stability and efficiency while capturing cross-sectional dependencies across multiple assets such as a portfolio. The model consistently outperforms traditional methods like LSTM, Random Forest, and RNN in forecasting accuracy. Empirical results show a 1.02% improvement in 1-day horizon forecasts, a 0.42% gain for 20-day predictions, and a 0.36% increase for 50-day forecasts. By effectively merging public sentiment with dynamic asset modeling, HD-SURDLM offers substantial improvements in short- and long-term prediction accuracy. Its capacity to capture both cross-sectional insights and temporal dynamics makes it an invaluable tool for investors, traders, and financial institutions navigating sentiment-driven markets. HD-SURDLM not only enhances predictive accuracy but also provides a robust decision-support system for financial stakeholders.

Mechanism of airfoil stall flutter: New insights from global linear stability analysis

Stall flutter is a self-excited aeroelastic vibration phenomenon that occurs in lifting systems near the stall angle of attack, characterized by the distinct single-degree-of-freedom behavior. Despite its significance, this phenomenon remains not fully understood and is often vaguely attributed to nonlinear effects. To address this gap, the present study aims to reveal the underlying fluid–structure interaction mechanisms of stall flutter through global linear stability analysis (LSA). For this purpose, a reduced-order model (ROM)-based aeroelastic stability analysis framework is established using the autoregressive with exogenous input method. The ROM-based aeroelastic model provides a low-order representation of the coupled dynamics near the equilibrium steady state and can accurately capture the stability characteristics of the fluid-elastic system. It is found that as the angle of attack approaches the static stall angle, a low-frequency weakly stable fluid mode emerges, whose frequency is sufficiently lower than that of the von Kármán vortex shedding. The interaction between this fluid mode and the structure mode ultimately leads to the instability of the aeroelastic system at high reduced velocities, which is the fundamental cause of stall flutter. Moreover, dynamic mode decomposition is employed to successfully extract the spatial coherent structures and frequency characteristics of this low-frequency fluid mode, thereby confirming the validity of the LSA results. Further analysis indicates that, as the angle of attack decreases, this low-frequency fluid mode gradually weakens and eventually degenerates into more stable non-oscillatory fluid modes, resulting in structural stabilization and the cessation of stall flutter. Overall, the linear dynamic model accurately predicts the onset of instability and the vibration frequency of the airfoil, which challenges the traditional nonlinear perspectives and supports the feasibility of using linear control theory for stall flutter suppression in future research.

Monitoring monthly mortality of maricultured Atlantic salmon (Salmo salar L.) in Scotland II. A hierarchical dynamic linear model

The sustainability of the salmon farming industry is being challenged by increased mortality rates. Scotland’s open-source salmon production data provides the possibility of developing an industry-wide mortality monitoring model, valuable for identifying and addressing unexpected increases in mortality without needing data sharing agreements across different companies. This study aimed to utilize these data to develop a hierarchical dynamic linear model (DLM) for monitoring monthly mortality of maricultured Atlantic salmon in Scotland. We evaluated whether considering the hierarchical structure present in the data (country, region, and site) would improve mortality predictions when compared to the production cycle level DLMs developed in a previous study. Our findings demonstrated that the hierarchical DLM outperformed the production cycle level DLMs, confirming the value of this more complex modelling approach. Nevertheless, the hierarchical model, like the production cycle level DLMs, exhibited some uncertainty in the mortality predictions. When mortality is higher than expected, site level warnings are generated, which can encourage producers and inspectors to further investigate the cause. Between 2015 and 2020, approximately 25% of the production cycles and 50% of the sites encountered at least one warning, with most warnings happening in the summer and autumn months. Additionally, the hierarchical model enabled monitoring mortality at multiple levels. This information is useful for various stakeholders as part of a monitoring system, offering insights into mortality trends at national, regional, and sites levels that may benefit from strategic resource management. Recommendations for model improvements include utilizing shorter data aggregation periods, such as weekly, which are not currently available as open-source data.

Trajectory optimization and stability control for a novel unmanned intelligent wheel-legged vehicles on unstructured terrains

The trend of intelligent vehicles is currently expanding, and a new class of unmanned intelligent vehicles known as wheel-legged vehicles (WLVs) is emerging. WLVs excel in transportation on unstructured terrain by offering a unique combination of the efficiency of wheels on flat ground and the versatility of legs to tackle obstacles. To enhance the locomotion performance of WLVs on unstructured terrains, this paper presents a novel framework for improving their locomotion through nonlinear programming-based (NLP) trajectory optimization and stability control. The framework optimizes the vehicle’s body and wheel positioning while incorporating terrain information and employs a linear rigid body dynamic model for efficient motion planning. The stability control framework combines feedforward control using ground reaction forces with feedback control through joint PD control and utilizes model predictive control (MPC) to adjust the wheel slip ratio to prevent slip on steep slopes. Experimental validation on the real vehicle with torque-controlled wheels demonstrated the capability of driving over a 1 m height with a 30°slope at an average speed of 0.7 m/s and a maximum speed of 1.03 m/s. Our approach also enables the WLV to overcome obstacles, such as inclines, while dynamically negotiating these challenging terrains.

The fly connectome reveals a path to the effectome

A goal of neuroscience is to obtain a causal model of the nervous system. The recently reported whole-brain fly connectome1–3 specifies the synaptic paths by which neurons can affect each other, but not how strongly they do affect each other in vivo. To overcome this limitation, we introduce a combined experimental and statistical strategy for efficiently learning a causal model of the fly brain, which we refer to as the ‘effectome’. Specifically, we propose an estimator for a linear dynamical model of the fly brain that uses stochastic optogenetic perturbation data to estimate causal effects and the connectome as a prior to greatly improve estimation efficiency. We validate our estimator in connectome-based linear simulations and show that it recovers a linear approximation to the nonlinear dynamics of more biophysically realistic simulations. We then analyse the connectome to propose circuits that dominate the dynamics of the fly nervous system. We discover that the dominant circuits involve only relatively small populations of neurons—thus, neuron-level imaging, stimulation and identification are feasible. This approach also re-discovers known circuits and generates testable hypotheses about their dynamics. Overall, we provide evidence that fly whole-brain dynamics are generated by a large collection of small circuits that operate largely independently of each other. This implies that a causal model of a brain can be feasibly obtained in the fly.

Event-Triggered Model-Free Adaptive Control for Nonlinear Multiagent Systems Under Jamming Attacks.

This article addresses the security problem of tracking control for nonlinear multiagent systems against jamming attacks. It is assumed that the communication networks among agents are unreliable due to the existence of jamming attacks, and a Stackelberg game is introduced to depict the interaction process between multiagent systems and malicious jammer. First, the dynamic linearization model of the system is established by applying a pseudo-partial derivative method. Then, a novel model-free security adaptive control strategy is proposed, so that the multiagent systems can achieve bounded tracking control in the mathematical expectation sense in spite of jamming attacks. Furthermore, a fixed threshold event-triggered scheme is utilized to reduce communication cost. It is worth noting that the proposed methods only require the input and output information of the agents. Finally, the validity of the proposed methods is illustrated through two simulation examples.

Pupillary responses to directional uncertainty while intercepting a moving target.

Pupillary responses serve as sensitive indicators of cognitive processes, attentional shifts and decision-making dynamics. Our study investigates how directional uncertainty and target speed (V T) influence pupillary responses in a foveal tracking task involving the interception of a moving dot. Directional uncertainty, reflecting the unpredictability of the target's direction changes, was manipulated by altering the angular range (AR) from which random directions for the moving dot were extracted. Higher AR values were associated with reduced pupillary diameters, indicating that heightened uncertainty led to smaller pupil sizes. Additionally, an inverse U-shaped relationship between V T and pupillary responses suggested maximal diameters at intermediate speeds. Analysis of saccade-triggered responses showed a negative correlation between pupil diameter and directional uncertainty. Dynamic linear modelling revealed the influence of past successful collisions and other behavioural parameters on pupillary responses, emphasizing the intricate interaction between task variables and cognitive processing. Our results highlight the dynamic interplay between the directional uncertainty of a single moving target, V T and pupillary responses, with implications for understanding attentional mechanisms, decision-making processes and potential applications in emerging technologies.

Colonial status and income inequality in developing countries

This paper assesses the effect of the colonial status of ex-colonies, settler’s mortality rate, and duration of colonization on income inequality using a dataset comprising 78 developing countries over the period 1990 to 2019. We run Ordinary Least Square regressions on the cross-sectional data and subsequently test for sensitivity of the baseline model to historical, geographical as well as sociocultural factors. For robustness checks, we re-estimate the baseline model on a panel data setting using the Hausman Taylor estimator and a GMM linear dynamic panel data model that factors-in time-invariant historical and cultural variables. Results suggest that: (a) average increase in Gini income inequality for ex-settler’s colonies was higher when compared to ex-peasant colonies; (b) an extra year of the duration of colonization augmented typical overall income inequality and (c) the middling rise in income inequality of ex-British colonies was less than the other ex-colonies whilst ex-Spanish colonies posted an average increase in inequality that was higher than the other former colonies. Results were unaltered when we undertake sensitivity and robustness tests. Furthermore, colonial status mediates the relationships between Gini income inequality and settler’s mortality rate as well as Gini income inequality and duration of colonization. Thus, institutions established since colonization and perpetuated after independence have been more or less prone to incorporating redistribution (inequality) issues.

Bayesian dynamic models to estimate the impact of halting vehicle fleets on the air quality: a case study from Medellín, Colombia

According to the World Health Organization (WHO, Ambient (outdoor) air pollution (who), 2020), outdoor air pollution is estimated to have caused 4.2 million premature deaths worldwide in 2019. Under this scenario, the development of statistical tools for assessing the impact of a possible reduction of fossil fuels-based transportation systems on air quality is more relevant than ever. This type of instruments can help policy makers to take the right path to tackle the problem of air pollution in urban environments. Thus, this work proposes a method to evaluate the impact of the reduction of vehicle fleets on air quality. The method is based on the construction of counterfactual time series, which represent observed air pollutants under a treatment of interest. In this case, the treatment of interest are the vehicle fleets on the streets. The construction of the counterfactual time series is based on Bayesian dynamic linear models. Several impact assessment measures are implemented, taking advantage of the counterfactual and observed time series (the observed pollutant without the treatment). The flexibility of the Bayesian approach allows easy inference of the impact quantities via high posterior density intervals. Some simulation analyses show that the method works well under different impact scenarios, and one application regarding Medellin’s case in Colombia is presented. For the application, it is shown that the drastic reduction in vehicle fleets during the COVID-19 mobility restrictions led to a significant reduction in the presence of different pollutants (PM10\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {PM}_{{10}}$$\\end{document}, PM2.5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {PM}_{2.5}$$\\end{document}, NO2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {NO}_{{2}}$$\\end{document}, NOx\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {NO}_{{x}}$$\\end{document})

Monitoring monthly mortality of maricultured Atlantic salmon (Salmo salar L.) in Scotland I. Dynamic linear models at production cycle level

The mortality of Atlantic salmon is one of the main challenges to achieving its sustainable production. This sector benefits from generating many data, some of which are collated in a standardized way, on a monthly basis at site level, and are accessible to the public. This continuously updated resource might provide opportunities to monitor mortality and prompt producers and inspectors to further investigate when mortality is higher than expected. This study aimed to use the available open-source data to develop production cycle level dynamic linear models (DLMs) for monitoring monthly mortality of maricultured Atlantic salmon in Scotland. To achieve this, several production cycle level DLMs were created: one univariate DLM that includes just mortality; and various multivariate DLMs that include mortality and different combinations of environmental variables. While environmental information is not collated in a standardized way across all sites, open-source remote-sensed satellite resources provide continuous, standardized estimates. By combining environmental and mortality data, we seek to investigate whether adding environmental variables enhanced the estimates of mortality, and if so, which variables were most informative in this respect. The multivariate model performed better than the univariate DLM (P = .004), with salinity as the only significant contributor out of 12 environmental variables. Both models exhibited uncertainty related to the mortality estimates. Warnings were generated when any observation fell above the 95% credible interval. Approximately 30% of production cycles and more than 50% of sites experienced at least one warning between 2015 and 2020. Occurrences of these warnings were non-uniformly distributed across space and time, with the majority happening in the summer and autumn months. Recommendations for model improvement include employing shorter time periods for data aggregation, such as weekly instead of on a monthly basis. Furthermore, developing a model that takes hierarchical relationships into account could offer a promising approach.

Together in sickness and in health: Spillover of physical, mental, and cognitive health among older English couples.

Using data from eight waves of the English Longitudinal Study of Aging, we study the cross-domain and cross-spouse spillover of health among married adults aged 50 and above in England. We apply the system generalized method of moments to linear dynamic panel models for physical, mental, and cognitive health, controlling for individual heterogeneity and the influence of marriage market matching and shared environments. Our findings reveal bidirectional spillovers between memory abilities and mobility difficulty among men, as well as between depressive symptoms and mobility difficulty among women. Worsening mobility increases the risk of depression in men, but not vice versa. Additionally, gender-specific cross-spouse effects are observed. Women's mental health is significantly influenced by their spouse's mental health, while this effect is weaker for men. Conversely, men's mental health is notably affected by their spouse's physical health. These results highlight the importance of considering spillovers within families and across health domains when developing policies to promote health and reduce health disparities among the elderly population.

Assessing risk indicators of intimate partner femicide considering victim's coping strategies to violence: A dynamic multilevel linear mixed model based on genetic algorithms

Intimate partner femicide (IPF) is a grave social and health concern affecting women worldwide, with approximately 30,000 deaths annually at the hands of their current or former intimate partners. Previous studies have focused on identifying risk factors for IPF and developing risk assessment tools to identify high-risk cases. However, an important aspect that has been overlooked in these studies is victims' coping strategies in response to intimate partner violence. Understanding victims' coping strategies can provide valuable insights into how they deal with the abuse and can inform the development of effective interventions and prevention strategies. This study aims to address this gap by developing a multilevel linear mixed model (LMM) to analyze the impact of engagement and disengagement coping on the likelihood of IPF and identify common and specific IPF risk indicators for these coping strategies. A total of 491 Spanish cases of violence against women by current or former intimate partners were analyzed from penal sentences issued by Spanish provincial and supreme courts from 2019 to 2022. The LMM model obtained from the study has competitive performance in identifying IPF and non-IPF cases, including risk indicators of prior history of injuries, history of sexual aggression, frequency and escalation of violence, physical violence, place of crime, lonely place of crime, and community presence. Victims with engagement coping and disengagement coping share some risk indicators, while others belong to just one category. Overall, the results suggest that victims with disengagement coping are more predisposed to suffer IPF than victims with engagement coping. This evidenced-based knowledge emphasizes the significance of considering coping strategies in predicting and preventing IPF, with further implications discussed at the end of this paper.

A Joint Temporal Model for Hospitalizations and ICU Admissions Due to COVID‐19 in Quebec

ABSTRACTInfectious respiratory diseases have been of interest in recent years for the great burden they place on health systems, for instance, the severe acute respiratory syndrome coronavirus 2 (SARS‐CoV‐2) that caused the global COVID‐19 pandemic. As many of these diseases might require hospitalization and even intensive care unit (ICU) admission, understanding the joint dynamics of hospitalizations and ICU admissions across time and different groups of the population remains of great importance. We aim to understand the joint evolution of hospital and ICU admissions given COVID‐19 test‐positive cases in the province of Quebec, Canada. We obtain the daily counts, by age group, on the number of confirmed COVID‐19 cases, the number of hospitalizations and the number of ICU admissions due to COVID‐19, from March 2020 through October 2021 in Quebec. We propose a joint Bayesian generalized dynamic linear model for the number of hospitalizations and ICU admissions to study their temporal trends and possible associations with sex and age group. Additionally, we use transfer functions to investigate if there is a memory effect of the number of cases on hospitalizations across the different age groups. The results suggest that there is a clear distinction in the patterns of hospitalizations and ICU admissions across age groups and that the number of cases has a persistent effect on the rate of hospitalization.

Adaptive distributed tracking control for Markov jump multiagent systems with a non-strict leader

This paper investigates the leader-following mean square distributed tracking control problem (DTCP) for a Markov jump multiagent systems (MJMASs) with the general linear dynamical model over an undirected graph. The non-strict control input of the leader is non-zero, unknown, and unavailable to any followers. First, the jump characteristics of the system for the single agent is modeled by a continuous Markov chain. Second, in order to address the leader–follower mean square DTCP, the distributed mode-dependent static controller and the fully distributed mode-dependent adaptive controller are designed for all followers based on the information from the agents’ neighbors and itself, respectively. Then, to further analyze the stability of the MJMASs, two categories of decomposed related Lyapunov functions are constructed using Lyapunov stability theory. The sufficient conditions for the existence of the distributed controller are obtained by derivation. Finally, two simulation cases are presented to verify the validity and feasibility of the proposed strategies.

Digital twins-boosted intelligent maintenance of ageing bridge hangers exposed to coupled corrosion–fatigue deterioration

The corrosion–fatigue coupled deterioration of ageing steel bridge hangers presents significant structural challenges, demanding rigorous condition assessments and timely maintenance interventions. This paper introduces a framework of digital twins-boosted intelligent maintenance (DTIM) tailored for ageing hangers, integrating the prediction model, monitoring data and inspection results. The DTIM features a suite of algorithms adaptation and innovations, including dynamic Partially Observable Markov Decision Processes (POMDP), Asynchronous Advantage Actor Critic (A3C), and Bayesian Dynamic Linear Models (BDLM). The DTIM emphasises regular early-life repairs, strategic inspections, and timely replacements towards life-end, tailored to the condition of specific bridge hangers in the case study presented. By coordinating actions across hangers, the DTIM enables opportunistic maintenance to further optimise resource allocation. The output highlights digital twins in exploring the add-on value of monitoring and inspection for the proactive and sustainable maintenance of ageing infrastructure, promising enhanced structural integrity and serviceability in a cost-effective and well-informed manner.

Data driven latent variable adaptive control for nonlinear multivariable processes

This article aims at a new partial least squares (PLS) control design and analysis in a data-driven framework for nonlinear multivariable processes whose mechanistic models are completely unknown. First, a general nonlinear autoregressive moving average with the exogenous input (NARMAX) model is used as the dynamic nonlinear PLS model. Then, by introducing a dynamic linearisation approach in each latent variable (LV) space, the unknown NARMAX-based PLS model is transformed to a linear dynamic PLS data model (dPLSDM), which can be improved in real time by estimating its unknown parameter using the latent input and output (I/O) data. Next, a data-driven latent variable adaptive control (DDLVAC) is proposed in each LV loop. By virtue of the dPLSDM, the multivariable nonlinear process is decoupled into multiple single-loop systems and the high dimensions of the process data are reduced such that the corresponding DDLVAC is simplified. Further, the DDLVAC only depends on the I/O data without requiring any model information of the original process. Theoretical analysis confirms the validity of the DDLVAC. The simulation study demonstrates the advantages of the DDLVAC such as less storage space, smaller computation burden, less control cost, as well as more robustness against uncertainties.

An analytical approach for power system frequency stability evaluation

AbstractRecent years have seen high penetration of renewable energies, which have significantly reduced the inertia of bulk power systems. As a result, the frequency behaviour of power systems is becoming more complex. To resolve this technical challenge, there is a particularly strong interest in developing analytical solutions for frequency dynamics studies. This study first describes a second‐order frequency dynamics model for power systems with renewable energies. A non‐linear perturbation approach is suggested to drive the analytical solution of the model. It is shown that, under many circumstances, frequency dynamics can be effectively approximated using a linear model. Subsequently, the article describes a fourth‐order linear frequency dynamics model that takes into account governor‐turbines. A polynomial eigenvalue method is proposed to identify the dominant and non‐dominant modes of the solution of the four‐order model. It is demonstrated that the dominant mode has a decisive impact on frequency behaviour, while the non‐dominant modes influence the relative frequency oscillations only. Finally, the study derives the analytical expressions of the standard frequency performance metrics and examines the impact of damping and inertia parameters. The introduced results are verified using two test systems, demonstrating the accuracy and effectiveness of the suggested method.

Hybrid-timescale optimal dispatch strategy for electricity and heat integrated energy system considering integrated demand response

An integrated energy system realizes multi-energy management and multi-load integrated supplement. However, because of the uncertainties of the renewable energy and loads and different dynamic characteristics of multi-energy, the efficiency of the system is constrained. To ascend the flexibility, a hybrid-timescale dispatch strategy considering integrated demand response is proposed. Firstly, a deep integrated demand response strategy is proposed using price demand response and ground source heat pump. Secondly, a linear dynamic model of the heat network is adopted to calculate the real-time energy transfer status in the heat pipeline, reflecting the thermal delay. Thirdly, to embed the linear dynamic model into the optimal scheduling process, a hybrid-timescale optimal dispatch framework for electricity and heat integrated energy system is proposed. Simulation results on MATLAB show that compare to the system that does not consider integrated demand response, the wind desertion, user cost and operation cost are reduced by 16.4 %, 0.85 %, and 2.72 %, respectively. And compared with the system only using energy storage, the planning cost is reduced by 47.0 %. By introducing the IDR strategy, and adopting the dynamic model of heat system, the flexibility of the system is released and the balance between economic cost and energy efficiency are achieved.