State Transition Equation Research Articles

Research on the Propagation Model of Unsafe Behaviors among Construction Workers Based on a Two-Layer NAN-SIRS Network

Unsafe behaviors among construction workers are a leading cause of safety accidents in the construction industry, and studying the mechanism of unsafe behavior propagation among construction workers is essential for reducing the occurrence of safety accidents. Safety attitude plays a pivotal role in predicting workers’ behavioral intentions. We propose a propagation model of unsafe behaviors based on a two-layer complex network, in which the upper layer depicts the change in construction workers’ safety attitudes, and the lower layer represents the propagation of unsafe behaviors. In this model, we consider the impact of individual heterogeneity and herd mentality on the transmission rate, establishing a partial mapping relationship based on behavioral feedback. After that, by building a probability transition tree, we establish the risk state transition equation in detail using the microscopic Markov chain approach (MMCA) and analyze the established equations to deduce the propagation threshold of unsafe behaviors analytically. The results show that enhancing the influence of individual heterogeneity and behavioral feedback increases the threshold for the spread of unsafe behaviors, thereby reducing its scale, while herd mentality amplifies the spread. Furthermore, the coexistence of safety education and behavioral feedback may lead to one of the mechanisms fails. This research enhances understanding of the propagation mechanism of unsafe behaviors and provides a foundation for managers to implement effective measures to suppress the propagation of unsafe behaviors among construction workers.

Distributed Dynamic State Estimation of Power Systems Considering Dynamic State Constraints based on Phasor Measurements Units

Background: Dynamic state estimation can provide detailed information about power systems. However, there is no clear, dynamic equation for the state transition of bus voltages in power systems. Currently, smoothing methods based on historical data are commonly used, but they cannot ensure accurate state prediction in power systems with a large amount of renewable energy. Moreover, the fast sampling rate of phasor measurement units generates a vast amount of real-time data for the dispatch center, making it challenging for centralized state estimation to meet real-time demands. Objective: This paper proposes a distributed power system state estimation considering dynamic state constraints to address the above issues. Methods: By incorporating the constraints between the dynamic states of the system dynamic components and the bus voltage phasors, the state transition equations for bus voltage phasors are constructed based on the predicted dynamic states and the nodal injection power equations. This allows taking the dynamic model constraints into account when predicting bus voltage phasors. Then, based on the principle of hierarchical coordination and distributed state estimation, the method of estimation-coordination-correction is adopted to acquire system state information quickly and accurately. method: By incorporating the constraints between the dynamic states of the system dynamic components and the bus voltage phasors, the state transition equations for bus voltage phasors are constructed based on the predicted dynamic states and the nodal injection power equations. This allows taking the dynamic model constraints into account when predicting bus voltage phasors. Then, based on the principle of hierarchical coordination and distributed state estimation, the method of estimation-coordination-correction is adopted to acquire system state information quickly and accurately. Results: Furthermore, an IEEE 9-bus system and an IEEE 39-bus system are used to validate the proposed method. The proposed method is compared with other algorithms to prove its superiority. result: Furthermore, an IEEE 9-bus system and an IEEE 39-bus system are used to validate the proposed method. And the proposed method is compared with other algorithms to prove its superiority. Conclusion: The simulation results show that the proposed method can effectively improve the accuracy of the state estimation results of power systems under dynamic conditions. conclusion: The simulation results show that the proposed method can effectively improve the accuracy of the state estimation results of power systems under dynamic conditions. other: None

Attractor-Transition Control of Complex Biological Networks: A Constant Control Approach.

This article presents attractor-transition control of complex biological networks represented by Boolean networks (BNs) wherein the BN is steered from a prescribed initial attractor toward a desired one. The proposed approach leverages the similarity between attractors and Boolean algebraic properties embedded in the underlying state transition equations. To enhance the clarity of expression regarding stabilization toward the desired attractor, a simple coordinate transformation is performed on the considered BN. Based on the characteristics of transformed state equations, self-stabilizing state variables requiring no control efforts are derived in the first. Next, by applying the feedback vertex set (FVS) control scheme, control inputs stabilizing the remaining state variables are determined. The proposed control scheme exhibits versatility by accommodating both fixed-point and cyclic attractors. We validate the effectiveness of the proposed strategy through extensive numerical experiments conducted on random BNs as well as complex biological systems. In adherence to the reproducible research initiative, detailed results of numerical experiments and all the implementation codes are provided on the authors' website: https://github.com/choonlog/AttractorTransition.

Workload-Aware Scheduling of Real-Time Jobs in Cloud Computing to Minimize Energy Consumption

Cloud computing is a powerful paradigm that can provide high-quality computation services to customers. Because its energy consumption has a large effect on its service price, this study investigates how to minimize the energy consumption while achieving adequate response times for requested computations. Such a problem is formulated as a nonlinear integer program. By deriving a state transition equation, this problem is transformed into an unconventional 0-1 knapsack problem, and dynamic programming is then used to solve it. In addition to this solution, we develop an energy-efficient job accommodation scheme that can manage dynamic jobs with varying frequencies throughout a day. Unlike existing studies that abruptly switch off old virtual machines and create new ones for upcoming jobs, this scheme tries to accommodate them with current virtual machines, and new virtual machines are not created unless necessary. Conversely, when the workload declines, jobs on energy-inefficient servers are moved to other servers, such that some energy-inefficient servers can be switched off to save energy. This scheme adjusts the computing power adaptively and smoothly without lowering the system’s quality of service. Experimental results demonstrate that the proposed solution outperforms a particle swarm optimizer and two other heuristics in terms of accommodating jobs and saving energy consumption.

Bellman filtering and smoothing for state–space models

This paper presents a new filter for state–space models based on Bellman’s dynamic-programming principle, allowing for nonlinearity, non-Gaussianity and degeneracy in the observation and/or state-transition equations. The resulting Bellman filter is a direct generalisation of the (iterated and extended) Kalman filter, enabling scalability to higher dimensions while remaining computationally inexpensive. It can also be extended to enable smoothing. Under suitable conditions, the Bellman-filtered states are stable over time and contractive towards a region around the true state at every time step. Static (hyper)parameters are estimated by maximising a filter-implied pseudo log-likelihood decomposition. In univariate simulation studies, the Bellman filter performs on par with state-of-the-art simulation-based techniques at a fraction of the computational cost. In two empirical applications, involving up to 150 spatial dimensions or highly degenerate/nonlinear state dynamics, the Bellman filter outperforms competing methods in both accuracy and speed.

New buckling solutions of truncated conical shells incorporating pre-buckling nonlinearity

The pre-buckling nonlinearity is found to have a remarkable effect on both the buckling loads and modes of shells according to the previous studies. In this study, we present a novel accurate buckling analysis of the truncated conical shells under broad boundary constraints incorporating the pre-buckling nonlinearity by a quasilinearization-precise integral method (Q-PIM). Specifically, the nonlinear buckling equations of the shells are transformed into several linear ones by the perturbation and quasilinearization, and they are then solved by the PIM. The produced state transition equations by the PIM are assembled into a global matrix equation, involving the boundary conditions (BCs), to yield the buckling solutions of the shells with or without incorporating the pre-buckling nonlinearity. The convergence study and benchmark buckling solutions verified by the refined finite element method are presented. The quantitative effects of the size parameters and BCs on the nonlinear critical buckling loads as well as the pre-buckling nonlinearity are investigated.

Study on the influence of the information diffusion and vaccination behavior on disease transmission in multiplex networks

To investigate the influence of information diffusion and vaccination behavior on disease transmission. In this paper, a coupling model is proposed to describe the co-evolution process of information diffusion, vaccination behavior and disease transmission in multiplex network. In the information layer, two types of information are diffused, including the positive information and the negative information, respectively. During the process of information diffusion, the influence of mass media on information diffusion is considered, due to the herd effect, which type of information is believed to depend on the information state of the surrounding neighbors based on the Heaviside step function. In the behavioral layer, the individuals with different types of information will choose different immune behavioral responses, which in turn will influence the disease transmission. The coupling model was analyzed by using the Micro Markov Chain Approach (MMCA) to obtain state transition equations and the prevalence thresholds for disease. By simulating the simulation experiments, it demonstrates that the information diffusion has no direct effect on disease prevalence thresholds, but affects the proportion of infected; vaccination behavior has a significant effect on disease prevalence thresholds and also affects the proportion of infected. The results of the study suggest that when the disease transmission is within the controllable range, the stronger the diffusion of positive information, the higher the vaccination rate, which has a more positive influence on inhibiting disease transmission; once out of control, the official will lose trust, which is not conducive to disease control.

Air conditioning load prediction based on hybrid data decomposition and non-parametric fusion model

Accurate prediction of air conditioning load is the pivotal problem of air conditioning optimization control, which is of great significance for reducing building energy consumption. In order to improve the prediction accuracy of air conditioning load, this paper proposes a load prediction method of air conditioning based on hybrid data decomposition (HRD) and non-parametric fusion model (NPFM). First, the historical load data is decomposed into linear term and nonlinear term by using HRD, which are employed to combine the temporal convolutional network (TCN) and long short term memory (LSTM) method to achieve the priori prediction of air conditioning load, and are regarded as the state transition equation. Secondly, the strong correlation index based on correlation screening is used as the observation parameter, and the nonlinear relationship between air conditioning load and real-time operating parameters of air conditioning equipment is mapped by back propagation (BP) neural network, which works as the observation equation, and forming a set of NPFM. Thirdly, the particle filter (PF) algorithm is introduced to correct the prior load prediction, suppress the noise disturbance, and realize the closed-loop control. Finally, the effectiveness of the proposed method is validated by two examples, and the results indicate that the proposed method can provide more accurate and robust air conditioning load prediction compared with existing methods.

Approximate dynamic programming approach to efficient metro train timetabling and passenger flow control strategy with stop-skipping

Urban metro systems continuously face high travel demand during rush hours, which brings excessive energy waste and high risk to passengers. In order to alleviate passenger congestion, improve train service levels and reduce energy consumption, a nonlinear dynamic programming (DP) model of efficient metro train timetabling and passenger flow control strategy with stop-skipping is presented, which consists of state transition equations concerning train traffic and passenger load. To overcome the curse of dimensionality, the formulated nonlinear DP problem is transformed into a discrete Markov decision process, and a novel approximate dynamic programming (ADP) approach is designed based on the lookahead policy and linear parametric value function approximation. Finally, the effectiveness of this method is verified by three groups of numerical experiments. Compared with Particle Swarm Optimization (PSO) and Simulated Annealing (SA), the designed ADP approach could obtain high-quality solutions quickly, which makes it applicable to the practical implementation of metro operations.

Studying the co-evolution of information diffusion, vaccination behavior and disease transmission in multilayer networks with local and global effects

Today, with the rapid development of the internet, a large amount of information often accompanies the rapid transmission of disease outbreaks, and increasing numbers of scholars are studying the relationship between information and the disease transmission process using complex networks. In fact, the disease transmission process is very complex. Besides this information, there will often be individual behavioral measures and other factors to consider. Most of the previous research has aimed to establish a two-layer network model to consider the impact of information on the transmission process of disease, rarely divided into information and behavior, respectively. To carry out a more in-depth analysis of the disease transmission process and the intrinsic influencing mechanism, this paper divides information and behavior into two layers and proposes the establishment of a complex network to study the dynamic co-evolution of information diffusion, vaccination behavior, and disease transmission. This is achieved by considering four influential relationships between adjacent layers in multilayer networks. In the information layer, the diffusion process of negative information is described, and the feedback effects of local and global vaccination are considered. In the behavioral layer, an individual’s vaccination behavior is described, and the probability of an individual receiving a vaccination is influenced by two factors: the influence of negative information, and the influence of local and global disease severity. In the disease layer, individual susceptibility is considered to be influenced by vaccination behavior. The state transition equations are derived using the micro Markov chain approach (MMCA), and disease prevalence thresholds are obtained. It is demonstrated through simulation experiments that the negative information diffusion is less influenced by local vaccination behavior, and is mainly influenced by global vaccination behavior; vaccination behavior is mainly influenced by local disease conditions, and is less influenced by global disease conditions; the disease transmission threshold increases with the increasing vaccination rate; and the scale of disease transmission increases with the increasing negative information diffusion rate and decreases with the increasing vaccination rate. Finally, it is found that when individual vaccination behavior considers both the influence of negative information and disease, it can increase the disease transmission threshold and reduce the scale of disease transmission. Therefore, we should resist the diffusion of negative information, increase vaccination proportions, and take appropriate protective measures in time.

Workload-Aware Scheduling of Multiple- Criticality Real-Time Applications in Vehicular Edge Computing System

In this article, we study the problem of designing an adaptive scheduling scheme for dynamic multiple-criticality real-time applications in vehicular edge computing systems. This scheduling problem is formulated as a mixed-integer nonlinear problem. We propose a workload-aware scheduling approach that not only guarantees the applicaitons' mixed-criticality schedulability but also adaptively manages their execution depending on their released frequencies at runtime. In particular, we first present the response time analysis for multiple-criticality applications in the edge computing system with different computing capability servers. Then, we derive a state-transition equation that makes the dynamic programming applicable to building an excellent schedule for one specific criticality-level mode. Such an approach is extended to the system's different criticality-level modes. For the purpose of increasing the quality-of-service toward low-critical applications, we leave low-critical applications to execute as much as possible at runtime, depending on their predicted frequencies. Extensive experimental results show the superiority of our proposed approaches in terms of improving the schedulability success rate and reducing the number of suspended applications online

Automatic Treatment Planning for Multi-focal Dynamic Conformal Arc GRID Therapy for Late-Stage Lung Cancer: A Feasibility Study

Palliative management of large, symptomatic pulmonary lesions, either as primary lung cancers or metastases, can be challenging due to need to balance effective radiation doses for cytoreduction with safety. Spatially Fractionated Radiation Therapy (SFRT), or GRID Therapy, is an emerging technique, which delivers ablative doses of radiotherapy to small, selected areas of tumor, while sparing organs-at-risk (OARs), and has been shown to debulk large lesions in preliminary studies. Conventionally, an alloy GRID block is manufactured to deliver GRID therapy. However, this delivery technique poses a challenge due to need for block, and dosimetrically when the tumor is deep-seated as excess dose may be delivered to OARs, such as skin and chest wall. This study aims to develop a fast, automatic planning solution using multi-focal dynamic conformal arcs (DCA) on modern Linear Accelerator. One late-stage lung cancer patient with simulated sphere target grid was included in this study. The sphere targets are 1.5cm in diameter and 4.3cm spacing. Four co-planar full arcs were used for optimization. The problem is formalized as finding optimal multi-leaf collimator (MLC) sequencing to cover N targets with K control points (CPs) for each arc. The state of each target's MLC opening at each CP is binary. In order to solve this NP-hard problem, the optimal solution was approximated by eliminating projection collision at each CP. MLC motion continuity and maximum speed were included in the cost function to ensure deliverability. The optimization started with randomized initial CP apertures, followed by solving state-transition equations for following CPs. Two grid arrays (9 and 10 targets respectively) were tested for plan quality. For each grid of target, the arc collimator angle was planned with 0 and 30 degrees for comparison. Prescription was 20 Gy per fraction. Monte Carlo simulation dose engine from matRad toolkit was used for dose calculation. Key dosimetric endpoints including target mean dose, D5%(Gy) and D95%(Gy), were reported. Average calculation time on the AMD Ryzen 5 5600 × 6-Core 3.7GHz CPU and 32GB RAM platform varied from 31 to 44 minutes. One zero-degree collimator and one thirty-degree collimator were generated for each target array. For nine-target array, mean target dose from both plans ranged from 23.41 to 26.55 Gy, while D5%(Gy) and D95%(Gy) ranged from 25.45 to 30.16 Gy, and 20.00 to 22.21 Gy, respectively. For ten-target array, the range of target mean, D5%(Gy) and D95%(Gy) were 23.82 to 28.74 Gy, 26.50 to 33.11 Gy, and 20.00 to 22.49 Gy. A fast, automatic planning solution for multi-focal DCA GRID therapy was developed. It provides clinically feasible plans with high efficiency for small target arrays for the late-stage cancer patient. The implementation provides excellent coverage for deep-seated tumors where alloy grid solution could fail to meet coverage objectives. Additional patients are needed in the future to further refine the technique.

A Bayesian Filtering Approach to Multimode Separation and Retrieval of Ultrasonic Guided Waves

In this paper, a Bayesian filtering approach to adaptively extracting the crossed time-frequency (TF) ridges of ultrasonic guided waves (GWs) and retrieving their overlapped modes is proposed. Based on the generalized non-parametric GW signal model, the phase evolution of each overlapped mode can be described by the state transition equation developed by a polynomial prediction model. When an analyzed GW in the frequency domain is viewed as the measurement equation of the states, a state space model in the frequency domain for describing the GW and its modes is established. As a result, a Bayesian filtering approach can be used to extract the crossed TF ridges and separate the overlapped modes in an analyzed GW when the mode number in the signal is known as a priori. When such a priori is unavailable, an adaptive detection method of the mode number in a GW is acquired by a non-parametric iterative adaptive estimation scheme. In this way, the proposed method can be applied to the cases where an analyzed GW with unknown modes can also be extracted and separated accurately. Simulation results show that the proposed method can correctly extract the crossed TF ridges and separate the overlapped modes when the signal-to-noise ratio (SNR) is higher than -5 dB. In the steel plate experiment, the correlation coefficients of S0, A0, and A1 modes between the original and retrieved signals are 0.900, 0.772, and 0.915 respectively, which are over the reported results in the literature.

An online reinforcement learning approach to charging and order-dispatching optimization for an e-hailing electric vehicle fleet

Given the uncertainty of orders and the dynamically changing workload of charging stations, how to dispatch and charge electric vehicle (EV) fleets becomes a significant challenge facing e-hailing platforms. The common practice is to dispatch EVs to serve orders by heuristic matching methods but enable EV drivers to independently make charging decisions based on their experiences, which may compromise the platform’s performance. This study proposes a Markov decision process to jointly optimize the charging and order-dispatching schemes for an e-hailing EV fleet, which provides pick-up services for passengers only from a designated transportation hub (i.e., no pick-up from different locations). The objective is to maximize the total revenue of the fleet throughout a finite horizon. The complete state transition equations of the EV fleet are formulated to track the state-of-charge of their batteries. To learn the charging and order-dispatching policy in a dynamic stochastic environment, an online approximation algorithm is developed, which integrates the model-based reinforcement learning (RL) framework with a novel SARSA(Δ)-sample average approximation (SAA) architecture. Compared with the model-free RL algorithm and approximation dynamic programming (ADP), our algorithm explores high-quality decisions by an SAA model with empirical state transitions and exploits the best decisions so far by an SARSA(Δ) sample-trajectory updating. Computational results based on a real case show that, compared with the existing heuristic method and the ADP in the literature, the proposed approach increases the daily revenue by an average of 31.76% and 14.22%, respectively.

A model of the enterprise supply chain risk propagation based on partially mapping two-layer complex networks

With the trend of economic globalization and the rise of the Internet industry, the business environment has become increasingly complex. The impact of an unexpected event on any member of the supply chain network will quickly affect the upstream and downstream enterprises connected to it, which will then cause risk to the whole supply chain network. Therefore, this paper proposes a new supply chain risk diffusion model based on a partial mapping relationship between two-layer complex networks, which aims to study the impact of risk awareness and risk information disclosure awareness. In this model, one layer represents the propagation of resources in the supply chain network, while the other layer represents the diffusion of the supply chain-related information in the social network. In addition, it divides enterprises into two types, namely with risk-aware enterprises or non-risk-aware enterprises. The model introduces the concept of partial mapping, meaning there are just mapping relationships between only partial pairs of nodes in the two-layered network. If a pair of nodes have the correspondence, the enterprises obtaining the information will take effective measures to avoid infection. This partial mapping relationship reflects the differences in enterprises’ awareness of risk information disclosure. After that, by building a probability transition tree, we establish the risk state transition equation in detail using the microscopic Markov chain approach (MMC) and analyze the established equations to deduce the propagation threshold of their supply chain risks analytically. The results show that the propagation threshold is related to network topology, the risk information disclosure awareness of enterprises, and the risk awareness of enterprises. Specifically, the stronger the risk information disclosure awareness and the greater the risk awareness of enterprises, the smaller the scale of supply chain risks eventually formed and the lower the threshold of risk outbreak. In addition, the influence of information disclosure awareness on the final developed risk scale is more significant than that of risk awareness. Finally, the simulation results further verify the model’s feasibility.

Labeled Multi-Bernoulli Filter Based Multiple Resolvable Group Targets Tracking With Leader-Follower Model

This paper addresses the multiple resolvable group targets tracking (MRGTT) problem wherein the leader-follower (LF) model is adopted to evolve the group structure. Since there is an interaction between the destination and each leader, such that an attraction force of the destination information on the leader needs to be considered. To cope with the time-varying number of targets/groups and target-measurement association uncertainty, the so-called labeled multi-Bernoulli (LMB) filter is regarded as the filtering tool and combined with the LF model, named LF-LMB. Totally speaking, the implementation of the proposed LF-LMB filter consists of three steps. Firstly, the stochastic differential equation (SDE) of the state is used to, respectively, characterize the motion models of the leader and the follower. Then, the state transition equations (STEs) for the leader and the follower are derived. Lastly, the derived STEs are used to modify the prediction process of the standard LMB filter. Simulation experiments are carried out to demonstrate the superiority (e.g., optimal sub-pattern assignment (OSPA) and OSPA <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{(2)}$</tex-math></inline-formula> errors are reduced by at least 15 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> comparing to the standard LMB filter) and robustness of the proposed approach.

A PDR/WiFi Indoor Navigation Algorithm Using the Federated Particle Filter

This paper offers a solution to challenge navigation in the indoor environment by making use of the existing infrastructure. Estimating pedestrian trajectory using pedestrian dead reckoning (PDR) and WiFi is a very popular technique. However, cumulative errors and mismatching are major problems in PDR and WiFi fingerprint matching, respectively. PDR and pedestrian heading are used as the state transition equation, and the step length and WiFi matching results are used as observation equations. A federated particle filter (FPF) based on the principle of information sharing is proposed to fusion PDR and WiFi, which improves pedestrian navigation accuracy. The experimental results show that the average positioning accuracy is 0.94 m and 1.5 m, respectively.

IGBT modules fault prediction based on particle filter with an improved nonlinear characteristics representation of state-space model

Insulated Gate Bipolar Transistor (IGBT) modules, being widely applied in many fields, are prone to aging and even fail under high voltage or temperature operation, so it is necessary to conduct IGBT modules fault prediction to avoid critical failures. Particle filter (PF) has strong applicability in IGBT modules fault prediction due to the fact that hidden state of IGBT modules can be evaluated from observed measurements containing noises. Nevertheless, the analytic form of state transition equation for PF is insufficient to represent nonlinear characteristics of complex systems, and the degradation process of IGBT modules in practical engineering does not conform to Markov property. Hence, a novel fault prediction method for IGBT modules based on improved particle filter is proposed in this paper, which has an improved nonlinear characteristics representation of state-space model. Specifically, long short-term memory (LSTM) model and curve fitting function are utilized to construct the state transition equation and the measurement equation, respectively. The IGBT accelerated aging test data published by NASA PCoE research center are used to verify the proposed fault prediction method, and the comparison studies show effectiveness and superiority of the proposed method in the IGBT modules fault prediction.

Simulation of Film and Television Transmission Path Based on Ant Colony Optimization Algorithm

Aiming at the stagnation and precocity of the basic ant colony algorithm in solving the film and television transmission path problem, an ant colony optimization algorithm with forgetting factor is proposed. By adding forgetting factor to artificial ants, a new state transition formula is established, and pheromone update strategy is modified. Combined with the optimal error rate of the current solution, the state transition equation is adjusted. Due to the introduction of the forgetting factor, the new formula can be adjusted in time when the original ant colony algorithm calculation falls into the local optimal solution, and the selection and updation of the next node are carried out according to the new state transition scheme. Pheromone, which can be used to reduce the optimal value error, improves the tracking ability of the optimal value, modifies the path evaluation model, and calculates the probability of each path to the current optimal solution. The simulation results of the film transmission path problem (FTPP) example show that the improved algorithm takes less time and the result of path optimization is better.

Control‐oriented estimation of the exchange current density in PEM fuel cells via stochastic filtering

Increasing efficiency and durability of fuel cells can be achieved through advanced model-based optimal control of its operating conditions, and the efficient online estimation of fuel cell parameters and internal states is fundamental for the implementation of such advanced controllers. The exchange current density is a driving parameter of performance for the catalyst layer of proton exchange membrane fuel cells (PEMFC). This study presents a control-oriented, stochastic filtering approach for online, continuous estimation of the exchange current density in low-temperature PEMFCs. The fuel cell is framed as a Markov model where the exchange current density is posed as the stochastic hidden state. The physics-based static equation of the exchange current density is converted into a state transition equation. This transition equation and the equation for cell voltage are used in the stochastic state estimator to approximate the posterior probability distribution of the exchange current density. In order to highlight the usefulness of the approach, the estimated value of the exchange current density is used to approximate the trend of the electrochemical active surface area (ECSA) in the catalyst layer and train a nonlinear auto-regressive model. This data-driven model is used to forecast the evolution in the ECSA associated with long-term degradation. The estimation algorithm is successfully implemented and tested in two different experimental datasets.