System Dynamics Research Articles

Serial metamorphic manipulator dynamics formulation implementing screw theory tools

Abstract In this work, a framework is proposed for the analytical formulation of dynamic equations for serial metamorphic manipulators using screw theory tools. The integration of structure reconfiguration is achieved in a compact and comprehensive manner. Based on the previously proposed Modular Structure Representation, additional statements are provided to strictly define the metamorphic structure assembly. To validate the precision of the extracted dynamics, two simulations are performed for paths defined in cartesian space. The generated trajectory is evaluated by comparing the dynamic matrices produced by the proposed method with those from an established dynamic modeling algorithm. Additionally, the trajectory is simulated in an open-source simulator, and the torques extracted from system dynamics are compared with the corresponding simulator torques under the same kinematic constraints.

Mean-motion resonances with interfering density waves

ABSTRACT In this work, we study the dynamics of two less massive objects moving around a central massive object, which are all embedded within a thin accretion disc. In addition to the gravitational interaction between these objects, the disc–object interaction is also crucial for describing the long-term dynamics of the multibody system, especially in the regime of mean-motion resonances. We point out that near the resonance the density waves generated by the two moving objects generally coherently interfere with each other, giving rise to extra angular momentum fluxes. The resulting backreaction on the objects is derived within the thin-disc scenario, which explicitly depends on the resonant angle and sensitively depends on the smoothing scheme used in the two-dimensional theory. We have performed hydrodynamical simulations with planets embedded within a thin accretion disc and have found qualitatively agreement on the signatures of interfering density waves by measuring the torques on the embedded objects, for the cases of $2:1$ and $3:2$ resonance. By including in interference torque and the migration torques in the evolution of a pair of planets, we show that the chance of resonance trapping depends on the sign of the interference torque. For negative interference torques the pairs are more likely located at off-resonance regimes. The negative interference torques may also explain the $1~{{\ \rm per\ cent}}-2~{{\ \rm per\ cent}}$ offset (for the period ratios) from the exact resonance values as observed in Kepler multiplanet systems.

Optimal Control of an R2R Dry Transfer Process with Bounded Dynamics Convexification

Abstract For efficient roll-to-roll (R2R) production of flexible electronic components, a precise R2R transfer peeling process is essential, requiring accurate modeling and control. This paper introduces a novel approach to confining the dynamics of a nonlinear R2R mechanical peeling system within a convex set known as a norm-bounded linear differential inclusion (NLDI). This method utilizes constraints on uncertain system variables to create a tighter NLDI representation compared to other convexification techniques. Moreover, it offers drastically reduced computational cost compared to previous methods applied to convexify the R2R peeling system. The NLDI is employed to generate an H_8-optimal controller for the R2R peeling system, and both simulations and experiments demonstrate better dynamic performance compared to other controllers for R2R transfer.

Quantum next generation reservoir computing: an efficient quantum algorithm for forecasting quantum dynamics

Next Generation Reservoir Computing (NG-RC) is a modern class of model-free machine learning that enables an accurate forecasting of time series data generated by dynamical systems. We demonstrate that NG-RC can accurately predict full many-body quantum dynamics in both integrable and chaotic systems. This is in contrast to the conventional application of reservoir computing that concentrates on the prediction of the dynamics of observables. In addition, we apply a technique which we refer to as skipping ahead to predict far future states accurately without the need to extract information about the intermediate states. However, adopting a classical NG-RC for many-body quantum dynamics prediction is computationally prohibitive due to the large Hilbert space of sample input data. In this work, we propose an end-to-end quantum algorithm for many-body quantum dynamics forecasting with a quantum computational speedup via the block-encoding technique. This proposal presents an efficient model-free quantum scheme to forecast quantum dynamics coherently, bypassing inductive biases incurred in a model-based approach.

Non-equilibrium Statistical Mechanics in Biological Systems

Unlike equilibrium systems, which are characterized by a time-independent distribution of particles and energy, non-equilibrium systems experience constant fluxes of matter or energy, often due to external driving forces. These systems can exhibit a wide range of dynamic behaviors some of which can appear as self-organizing. Building on the framework of non-equilibrium statistical mechanics, Jeremy England in his paper "Statistical Physics of Adaptation" derives an equation which relates the relative forwards probability of transitioning between two possible macrostates with their respective reverse probability, entropy, and average energy dissipation across all possible micro trajectories. He showed that structures which are better at absorbing and dissipating energy into their surroundings during their formation have a higher likelihood of occurring, which can possibly explain how life-like behaviors emerge in non-equilibrium systems. In this project, we test England's equation on a toy model of self replicating populations, as well as attempt to apply it to a biological dataset. In the toy model under certain constraints we do find that our intuition of the systems dynamics does track with England's equation, that is we observe that the population with the greatest replication rate tends to have the highest energy dissipation when it's population makes up the greater fraction of the total population of particles. In the biological dataset we analyze protein-protein interactions and how the relative bonding energy and binding rates compare for different mutations. We explore the limitations of his equation when trying to make predictions about highly complex biological systems.

Study on Non-Point Source Pollution Prevention and Control System in Nansi Lake Basin Based on System Dynamics Approach

Agriculture, as an important activity on which human beings depend for their livelihood, brings serious environmental problems while meeting the needs of human survival, among which agricultural non-point source (NPS) pollution is one of the most urgent environmental problems. This study quantitatively assessed the loading characteristics spatial and temporal evolution patterns of two agricultural NPS pollutants, chemical oxygen demand (COD) and ammonia nitrogen (NH3-N), from 2010 to 2020 in the Nansi Lake Basin as an example, and constructed a system dynamics (SD) simulation model to simulate and analyze agricultural NPS pollution under different development and treatment scenarios, based on an investigation of the regional prevention and control strategy of agricultural NPS pollution and the technological system. The results show that the current status of agricultural NPS pollution load in the Nansi Lake Basin is poor, and the level of pollution load is high, showing obvious geographical differences. In terms of temporal changes, the pollution loads of the two pollutants showed a decreasing trend from 2010 to 2020, among which the pollution load of NH3-N showed the largest change. Spatially, the spatial distribution of each type of pollutant has some similarities, with smaller pollution loads in Jining and Zaozhuang and relatively larger pollution loads in Heze and Ningyang. The main source of COD pollution in the Nansi Lake Basin is rural life, with an emission proportion of 52.85%, and the main sources of NH3-N pollution from agricultural NPS pollution in the area are rural life and livestock and poultry farming, with emission proportions of 47.55% and 35.36%, respectively. Under the status quo continuum scenario, the pollution load values for COD are consistently higher than those for NH3-N, so the relative impact of COD is greater. In this study, the principles and methods of SD in system science are adopted to deal with the agricultural NPS pollution of Nansi Lake Basin, and the evolution of its behavioral characteristics are simulated, forecasted, and predicted, and policy experiments are conducted, with a view to providing references for the prevention and control of agricultural NPS pollution in Nansi Lake Basin and further research.

Influencing Factors and Mechanisms of Value Co-Creation in Artificial Intelligence-Driven Human Resource Management: A System Dynamics Simulation

In the era of artificial intelligence, human resource management has undergone significant changes compared to traditional approaches regarding value creation methods and influencing factors. This research aims to utilize grounded theory to comprehensively explore the influencing factors of value co-creation in enterprise human resource management within the context of artificial intelligence. Additionally, this research seeks to capture the dynamic relationships, causal links, and evolutionary patterns among the various elements within the system by constructing a system dynamics model. The results indicated that (1) Environmental factors primarily play a regulatory role, organizational factors serve a supportive role, and participant factors act as the driving force in influencing value co-creation in human resource management. (2) In the context of artificial intelligence, both hardware infrastructure and software capabilities can significantly impact value co-creation in human resource management. This research complements current research on the influencing factors of value co-creation in enterprise human resource management. It offers new perspectives and frameworks for the theoretical development and practical application of value co-creation in this area, supporting companies in effectively managing and developing value co-creation in human resource management.

Natural Water Sources and Small-Scale Non-Artisanal Andesite Mining: Scenario Analysis of Post-Mining Land Interventions Using System Dynamics

Small-scale open-pit, non-artisanal mining of low-value ores is an understudied practice despite its widespread occurrence and potential impact on freshwater resources due to mining-induced land-use/cover changes (LUCCs). This research investigates the long-term impacts of andesite mining in Pasuruan, Indonesia, on the Umbulan Spring’s water discharge within its watershed. System Dynamics (SD) modeling captures the systemic and systematic impact of mining-induced LUCCs on discharge volumes and groundwater recharge. Agricultural and reservoir-based land reclamation scenarios then reveal post-mining temporal dynamics. The no-mining scenario sees the spring’s discharge consistently decrease until an inflection point in 2032. With mining expansion, reductions accelerate by ~1.44 million tons over two decades, or 65.31 thousand tons annually. LUCCs also decrease groundwater recharge by ~2.48 million tons via increased surface runoff. Proposed post-mining land interventions over reclaimed mining areas influence water volumes differently. Reservoirs on reclaimed land lead to ~822.14 million extra tons of discharge, 2.75 times higher than the agricultural scenario. Moreover, reservoirs can restore original recharge levels by 2039, while agriculture only reduces the mining impact by 28.64% on average. These findings reveal that small-scale non-artisanal andesite mining can disrupt regional hydrology despite modest operating scales. Thus, evidence-based guidelines are needed for permitting such mines based on environmental risk and site water budgets. Policy options include discharge or aquifer recharge caps tailored to small-scale andesite mines. The varied outputs of rehabilitation scenarios also highlight evaluating combined land and water management interventions. With agriculture alone proving insufficient, optimized mixes of revegetation and water harvesting require further exploration.

Investigation of the dynamics of transverse oscillations of a vertical rod under gravity, friction, and thermal expansion

The paper considers the mathematical formulation of the problem of transverse oscillations of a vertical rod under gravity, friction and external pulse effect, leading to thermal expansion of the rod. The dynamics of the system under consideration corresponds to the behavior of a fuel element (FE) in a pulsed reactor and is related to the dynamic stability of the processes occurring in it.The FE dynamics is described by inhomogeneous linear differential equation of the fourth order with non-constant coefficients. Initial boundary conditions are not smooth since they correspond to the instant heating of the part of the FE surface exposed to neutron pulse radiation. The general solution of the homogeneous linear equation can be found using the concept of generalized functions expressed as a series expansion in terms of coordinate eigenfunctions dependent on p parameter. The p parameter is related with the FE mass and at some certain values results in bifurcation points of the boundary value problem for eigenfunctions. The partial solution can be found in several ways: using the Fourier transform, the method of Green's function, and in terms of series expansion by eigenfunctions.Eigenfunction expansion coefficients in an explicit form have been obtained and the numerical solution accuracy has been estimated for some important particular cases. The results of the obtained exact solutions appear to be very close to the results of the ANSYS numerical estimations. In the future the obtained exact solutions will be used as input data to simulate self-consistent system dynamics of more than 400 FE. Therefore, the advantage of the exact solution in practical use is that its calculation is much faster as compared with the finite element method done with ANSYS.

A Switching Observer for State-of-Charge Estimation of Reconfigurable Supercapacitors

While State-of-Charge (SOC) estimation for supercapacitors has been extensively studied, most research focuses on single units. However, the recent introduction of reconfigurable circuits significantly alters system dynamics, rendering existing SOC estimation techniques inadequate. This paper addresses this challenge by employing a switching systems approach to estimate the SOC of supercapacitors with reconfigurable circuits. We first establish an RC model for the supercapacitor integrated with the reconfigurable circuit and thoroughly analyze the state continuity and observability of the resulting switched system. Subsequently, we propose a switching observer and evaluate its convergence properties by comparing its performance against other observer techniques. Experimental validation on a hardware platform demonstrates the superiority of our proposed observer for accurate SOC estimation in this context.

Modelagem da estrutura de gestão dos efeitos dos gases de efeito estufa e seus impactos no ciclo hidrológico nas cidades

The complexity of cities and the challenges of sustainable planning and management require processes to be treated from a systemic perspective, which, in this study, were carried out using the concept of urban metabolism and modeling of system dynamics. Thus, a model was investigated and proposed to evaluate the effects of Greenhouse Gases (GHG) emissions on climate change and their impacts on the hydrological cycle in a hydrographic basin, addressing economic, social and environmental issues. The structured model makes it possible to visualize the cascade effect of the processes, leading to the observation of the necessary responses, in order to understand their effects, in a systemic, flexible and transparent way. The possibility of creating different scenarios through the dynamic model enables simulations of the present and the future that can be tested to facilitate physical interventions and strategic actions, helping in decision-making processes and in the formulation of public policies in cities.

Investigating Entropic Dynamics of Multiqubit Cavity QED System

AbstractEntropic dynamics of a multiqubit cavity quantum electrodynamics system is simulated and various aspects of entropy are explored. In the modified version of the Tavis–Cummings–Hubbard model, atoms are held in optical cavities through optical tweezers and can jump between different cavities through the tunneling effect. The interaction of atom with the cavity results in different electronic transitions and the creation and annihilation of corresponding types of photon. Electron spin and the Pauli exclusion principle are considered. Formation and break of covalent bond and creation and annihilation of phonon are also introduced into the model. The system is bipartite. The effect of all kinds of interactions on entropy is studied. And the von Neumann entropy of different subsystems is compared. The results show that the entropic dynamics can be controlled by selectively choosing system parameters, and the entropy values of different subsystems satisfy certain inequality relationships.

Variable Structure Controller for Energy Savings in an Underwater Sensor Platform.

This paper introduces a new variable structure controller designed for depth control of an autonomous underwater sensor platform equipped with a variable buoyancy module. To that end, the prototype linear model is presented, and a finite element-based method is used to estimate one of its parameters, the hull deformation due to pressure. To manage potential internal disturbances like hull deformation or external disturbances like weight changes, a disturbance observer is developed. An analysis of the observer steady-state estimation error in relation to input disturbances and system parameter uncertainties is developed. The locations of the observer poles according to its parameters are also identified. The variable structure controller is developed, keeping energy savings in mind. The proposed controller engages when system dynamics are unfavorable, causing the vehicle to deviate from the desired reference, and disengages when dynamics are favorable, guiding the vehicle toward the target reference. A detailed analysis determines the necessary switching control actions to ensure the system reaches the desired reference. Finally, simulations are run to compare the proposed controller's performance with that of PID-based controllers recently developed in the literature, assessing dynamic response and energy consumption under various operating conditions. Both the VBM- and propeller-actuated vehicles were evaluated. The results demonstrate that the proposed controller achieves an average energy consumption reduction of 22% compared to the next most efficient PID-based controller for the VBM-actuated vehicle, though with some impact on control performance.

Dynamics and adaptive backstepping control of rotor-hybrid foil-magnetic bearings system

The hybrid foil-magnetic bearing (HFMB) is a contactless-type bearing composed of a foil bearing (FB) in the inner side and an active magnetic bearing (AMB) in the outer side. It has the advantages of low drag torque, high DN value (bearing inner diameter times rotating speed), and high supporting efficiency. However, significant subsynchronous vibration will degrade the stability of the rotor-HFMBs system, which is an obstacle to the industrial implementation of HFMBs. To control the rotor vibration, this paper presents a dynamic model of the rotor-HFMBs system with unknown parameters and the design of an adaptive backstepping controller (ABC) for it. The stability of the closed-loop system is established. Simulation results of the rotor-HFMBs system controlled by ABC are compared with the proportional-integral-derivative controller (PID), illustrating that the ABC is capable of eliminating rotor vibration, and it is more effective than the PID.

Establishing the robustness of chip trade networks by dynamically considering topology and risk cascading propagation

Risk cascading propagation research mostly focuses on complex theoretical networks. Recently, the vulnerability of international chip supply has increased notably, and it is strategically important to explore how shortage risk affects the emergence dynamics of the real chip trade systems. This study abstracts the global chip trade relationship data for 2009–2021 into multiple asymmetrically weighted networks. Using macro-network and micro-node indicators, we explore the topological traits of international chip trade networks and their evolutionary laws. Accordingly, we propose risk cascading propagation models driven by node failure and edge restraint and further innovate to open up the research paradigm of focused-edge networks. Furthermore, a community infection-driven risk cascading propagation mechanism that incorporates community risk absorption capacity is introduced, considering both the propagation attenuation effects and the trade dependency degree. A multi-dimensional dynamic perspective reveals the hidden systemic risks in international chip trade. The main results are as follows: first, international chip trade networks are highly connected and cohesive, consistent with small-world characteristics. Second, the proportion of economies that collapse because of supply shortage risk shocks increases with the impact coefficient α/β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha /\\beta$$\\end{document}. The dominant power in chip crisis propagation has shifted from Europe and America to Asia, and mainland China’s risk penetration capacity has enhanced significantly. Third, focused-edge networks conform to a multi-hub radiation pattern. Before the COVID-19 pandemic, the degree of control and spillover effects of chip supply shortages in hub economies on the international trade was increasing progressively. Fourth, an increase in absorption capacity λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda$$\\end{document} or attenuation factor γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma$$\\end{document} consistently leads to a decline in avalanche scale, with λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda$$\\end{document} exhibiting critical thresholds. These findings will help policymakers pursue efficient management strategies for chip trade, thereby improving supply stability and security.

Adaptive neural network control of a centrifugal chiller system

In this paper, a neuro-adaptive PI control strategy for a water-cooled centrifugal chiller system is developed, and its control performance is examined. The system model consists of a flooded evaporator, a flooded condenser, a centrifugal compressor, and an electronic expansion valve. The overall system consists of three control loops: a compressor speed control loop, an inlet guide vane (IGV) control loop, and a condenser liquid level control loop. A neuro-adaptive control strategy for compressor speed control was designed. The control performance of the chiller was tested by carrying out simulation runs using an integrated building and HVAC (IB-HVAC) system model. The major details of the IB-HVAC model are described in this paper. Results show that the neuro-adaptive controller can adapt to new system dynamics of the IB-HVAC system and give good setpoint tracking responses under a wide range of operating conditions. The results show that the neuro-adaptive controller performs better than the constant gain PI controller in terms of speed of response and setpoint tracking properties.

Internal clock errors in synchrophasor ambient data: Effects, detection, and a posteriori estimation-based correction

Synchrophasor data from real world power systems are exposed to numerous adverse cyber-and-physical operating conditions that can negatively impact their fitness for use in PMU applications. Although the most significant impairments such as GPS loss, instrument transformer failure, data drop-off, etc., have been studied in the literature, there exist other more complex nuisances that impact PMU data quality. This is the case of differences in how clock synchronization, time disciplining, and phasor estimation is performed by different PMU vendors, which have important implications on the PMUs’ data fitness for use in PMU applications. In particular, ambient data applications, which have increasingly become a focus for tracking grid performance indicators, are extremely sensitive to periodic clock errors. Using synchrophasor and waveform data from Dominion Energy’s power system, this article provides an in-depth analysis of the effect of seemingly minor device clock errors on the measurement signals’ content. Finally, a method to distinguish clock errors from normal system dynamics and to correct them is proposed.

Analysis of the influencing factors of the cost of village prefabricated housing in rural revitalization: a southern Shaanxi case study

PurposeUnder the rural revitalization, the effect of China's implementation of rural prefabricated housing is not obvious. Cost has become the biggest obstacle to its development. Therefore, it is necessary to study the factors influencing the cost of prefabricated buildings in villages and clarify the focus of cost control.Design/methodology/approachThis paper focuses on the whole process of prefabricated housing construction in villages in China and uses grounded theory to identify and screen out 27 related factors that affect the construction cost of prefabricated buildings. A system dynamics model is used to dynamically analyze the influencing factors. The engineering examples in rural areas of southern Shaanxi are simulated. Finally, five key factors that influence cost are obtained. Based on this, cost control countermeasures are proposed for rural prefabricated housing in southern Shaanxi.FindingsThe results show that: the key factors affecting the cost of prefabricated buildings in villages include the selection of production methods, the degree of design standardization, the quality of construction personnel, the level of construction technology and the circulation cycle of molds. The cost of prefabricated housing in villages can be controlled through five aspects: mass production of components, design exchange and feasibility analysis, improvement of employee professionalism, strict selection of construction schemes and technologies and improvement of mold turnover rate.Research limitations/implicationsThe system dynamics model applied in this paper is based on the idealized state. The system boundary is narrow and has a certain subjectivity. It needs further detailed research to make it closer to the engineering practice. In addition, this paper applies the rural engineering example in southern Shaanxi to carry out a single case study, and the universality of the research results needs to be further tested. There are many village construction projects and building types, so the research results can be further enriched through large sample research.Practical implicationsRural construction is an important step in the implementation of rural revitalization. Exploring the factors that affect the key costs of prefabricated buildings in villages and towns in view of the particularity of rural areas will help provide a reference for their cost control and help the rural development of prefabricated houses.Social implicationsThe research results of this paper can provide a reference for the development of prefabricated buildings in other rural revitalization areas.Originality/valueDifferent from the traditional research on urban prefabricated buildings, this paper focuses on rural areas and explores the core factors affecting the cost of prefabricated buildings from the micro level. This study establishes a system dynamics model suitable for the cost control of prefabricated housing at the village level and provides methods for its cost control. Based on the identified key factors affecting costs, cost control measures were proposed for prefabricated housing tailored to the unique characteristics of villages.

Finding the rhythm: Humans exploit nonlinear intrinsic dynamics of compliant systems in periodic interaction tasks.

Activities like ball bouncing and trampoline jumping showcase the human ability to intuitively tune to system dynamics and excite motions that the system prefers intrinsically. This human sensitivity to resonance has been experimentally supported for interactions with simple linear systems but remains a challenge to validate in more complex scenarios where nonlinear dynamics cannot be predicted analytically. However, it has been found that many nonlinear systems exhibit periodic orbits similar to the eigenmodes of linear systems. These nonlinear normal modes (NNM) are computable with a recently developed numerical mode tool. Using this tool, the present resarch compared the motions that humans excite in nonlinear systems with the predicted NNM of the energy-conservative systems. In a user study consisting of three experiment parts, participants commanded differently configured virtual double pendula with joint compliance through a haptic joystick. The task was to alternately hit two targets, which were either aligned with the NNM (Experiments 1 and 2) or purposefully arranged offset (Experiment 3). In all tested experiment variations, participants intuitively applied a control strategy that excited the resonance and stabilized an orbit close to the ideal NNM of the conservative systems. Even for increased task accuracy (Experiment 2) and targets located away from the NNM (Experiment 3), participants could successfully accomplish the task, likely by adjusting their arm stiffness to alter the system dynamics to better align the resonant motions to the task. Consequently, our experiments extend the existing research on human resonance sensitivity with data-based evidence to nonlinear systems. Our findings emphasize the human capabilities to apply control strategies to excite and exploit resonant motions in dynamic object interactions, including possibly shaping the dynamics through changes in muscle stiffness.

Ecological footprint in Beijing-Tianjin-Hebei urban agglomeration: Evolution characteristics, driving mechanism, and compensation standard

Unbalancing ecological supply-demand is an obstacle to sustainable development in the Beijing-Tianjin-Hebei urban agglomeration (BTHUA), which can be efficiently addressed through regional ecological compensation. However, the driving mechanism of this unbalance is unclear, and the determination of ecological compensation standard (ECS) is not unified. This study uses the ecological footprint (EF) model and integrated inversion model to complete the intelligent evaluation and prediction of ecological supply-demand performance in the BTHUA. The extended nonlinear STIRPAT model and geographic detector are integrated to identify the driving mechanism of EF and its spatial differentiation. ECS at different spatiotemporal scales are then given with consideration of ecological service value and Monte Carlo simulation. Results reveal that EF of the BTHUA exhibits a downward trend, especially under the sustainable scenario (SSP1), falling by 16.85 %. But all cities would be still in unsafety states by 2035, with an average EF value of 6.210 hm2/cap, which is over 27 times greater than its EC. The spatial distribution of EF differs significantly, and high-value areas gradually migrate to the north. The variation of EF is primarily influenced by industrial structure, with population factors and environmental factors following. Per capita GDP is a key factor causing spatial differentiation of EF. The key driving factors and their explanatory powers on EF vary across cities, and the interaction of multiple factors affects EF more than a single in the BTHUA. Past-to-future ECS of the BTHUA shows a decreasing trend, with high-value areas distributed in the pivotal cities for economic development. A total of 19.13 × 1010 CNY needs to be paid to compensate for ecological damage of the BTHUA. Uncertainty analysis shows that ECS is extremely sensitive to grassland footprint in most cities. Furthermore, environmental footprints as well as system dynamics considering multiple factors are still required for comprehensively evaluating the ecological environment quality and further exploring ecological compensation evaluation framework with incorporating various ecological service functions such as carbon sinks in the BTHUA. Findings can facilitate improving regional sustainability and provide a valid approach to determine ECS for the BTHUA and similar regions worldwide.