Inter-event Time Research Articles

Event-triggered integral sliding mode control for uncertain networked linear control systems with quantization.

In this paper, the integral sliding mode (ISM, SM) controller is designed to address the problem of implementing non-periodic sampled data for a class of networked linear systems with matched and unmatched uncertainties. Due to the redesigned gain of the nominal controller, the feedback control used by the nominal controller guarantees the asymptotic stability of the uncertain networked linear system. The discontinuous control uses intermittent control based on the reaching law to achieve the finite-time reachability of practical SM band. Based on the defined measurement error, the event-triggered (ET) condition can be derived, and furthermore, it guarantees a sufficient condition for the existence of the actual SM. On this basis, a quantization scheme is added to further decrease the network transmission burden of the linear system. No Zeno behavior occurs in the system owing to the existence of a positive lower bound of inter-event time. Compared with the conventional integral sliding mode control (ISMC, SMC), the proposed control law can not only relieve the network burden, but also decrease the transmission energy loss. Finally, simulation results of a numerical example and a mass-spring damping system demonstrate the effectiveness of the proposed method.

Dynamic Event-Triggered Communication-Based Adaptive Consensus Tracking of Uncertain Nonlinear Multiagent Systems in Pure-Feedback Form

This study is aimed at investigating a dynamic event-triggered communication-based adaptive distributed consensus control problem for a class of uncertain pure-feedback nonlinear multiagent systems with limited communication resources. The nonaffine nonlinear functions of multiagent systems are assumed to be unknown and heterogeneous, and intermittent inter-agent communication is considered to occur within a directed network. A novel adaptive distributed dynamic surface control strategy using neural networks is developed to manage non-differentiable virtual control laws associated with the intermittent communication between agents with uncertain nonaffine nonlinear parts. The key contribution of this research is the derivation of dynamic event-triggering conditions using distributed tracking errors to efficiently adjust inter-event times, while ensuring the consensus tracking performance and robustness against unexpected external disturbances. Compared with the existing static event-triggered communication approach, the proposed controller can alleviate the communication burden among agents. Using technical lemmas, it is shown that all signals of the considered system are semiglobally uniformly ultimately bounded, and Zeno behavior is strictly excluded. Comparative simulation results illustrate the effectiveness of the proposed dynamic event-triggered control approach.

Burst and Memory-aware Transformer: capturing temporal heterogeneity.

Burst patterns, characterized by their temporal heterogeneity, have been observed across a wide range of domains, encompassing event sequences from neuronal firing to various facets of human activities. Recent research on predicting event sequences leveraged a Transformer based on the Hawkes process, incorporating a self-attention mechanism to capture long-term temporal dependencies. To effectively handle bursty temporal patterns, we propose a Burst and Memory-aware Transformer (BMT) model, designed to explicitly address temporal heterogeneity. The BMT model embeds the burstiness and memory coefficient into the self-attention module, enhancing the learning process with insights derived from the bursty patterns. Furthermore, we employed a novel loss function designed to optimize the burstiness and memory coefficient values, as well as their corresponding discretized one-hot vectors, both individually and jointly. Numerical experiments conducted on diverse synthetic and real-world datasets demonstrated the outstanding performance of the BMT model in terms of accurately predicting event times and intensity functions compared to existing models and control groups. In particular, the BMT model exhibits remarkable performance for temporally heterogeneous data, such as those with power-law inter-event time distributions. Our findings suggest that the incorporation of burst-related parameters assists the Transformer in comprehending heterogeneous event sequences, leading to an enhanced predictive performance.

Inter-event time distribution pattern of earthquakes and its spatial, temporal, and magnitude sensitivity: the case of Turkey

Inter-event time distribution pattern of earthquakes and its spatial, temporal, and magnitude sensitivity: the case of Turkey

Burstiness and information spreading in active particle systems.

We construct a temporal network using the two-dimensional Vicsek model. The bursts of the interevent times for a specific pair of particles are investigated numerically. We found that, for different noise strengths, the distribution of the interevent times of a target edge follows a heavy tail, revealing the burstiness of the signals. To further characterize the nature of the burstiness, we calculate the burstiness parameters and the memory coefficients. The results show that, near the phase transition points of the Vicsek model, the burstiness parameters reach the minimum values for each density, indicating a relationship between the phase transition of the Vicsek model and the bursty nature of the signals. Furthermore, we investigate the spreading dynamics on our temporal network using a susceptible-infected model and observe a positive correlation between them.

Event-Triggered Finite-Time Synchronization Control for Quaternion-Valued Memristive Neural Networks by an Non-Decomposition Method

Applying the event-triggered control, this paper discusses the finite-time synchronization issue of quaternion-valued memristive neural networks (QVMNNs) with time-varying delays. By employing the improved one norm and sign function of quaternion, the QVMNNs can be analyzed as an entirety without any decomposition. To relieve the communication pressure, a proper event-triggered controller is designed, then the event-triggered conditions and some criteria are also established to guarantee finite-time synchronization. Moreover, the synchronization time is estimated by direct analysis, and the positive lower bound of the inter-event time is obtained to get rid of the Zeno behavior. In addition, according to the acquired event-triggered scheme, a self-triggered scheme is further provided to refrain from continuous detection. Ultimately, the validity of the obtained theoretical results is demonstrated by a numerical simulation.

A More Realistic Earthquake Probability Model Using Long-Term Fault Memory

ABSTRACTForecasts of the probability of a large earthquake occurring on a fault during a specific time interval assume that a probability distribution describes the interevent times between large earthquakes. However, current models have features that we consider unrealistic. In these models, earthquake probabilities remain constant or even decrease after the expected mean recurrence interval, implying that additional accumulated strain does not make an earthquake more likely. Moreover, these models assume that large earthquakes release all accumulated strain, despite evidence for partial strain release in earthquake histories showing clusters and gaps. As an alternative, we derive the necessary equations to calculate earthquake probabilities using the long-term fault memory (LTFM) model. By accounting for partial strain release, LTFM incorporates the specific timing of past earthquakes, which commonly used probability models cannot do, so it can forecast gaps and clusters. We apply LTFM to the southern San Andreas fault as an example and show how LTFM can produce better forecasts when clusters and gaps are present. LTFM better forecasts the exceptionally short interevent time before the 1857 Fort Tejon earthquake. Although LTFM is more complex than existing models, it is more powerful because (unlike current models) it incorporates fundamental aspects of the strain accumulation and release processes causing earthquakes.

Nucleation Process of the 2017 Nuugaatsiaq, Greenland Landslide

Seismic precursors prior to the failure of rocks are essential for probing the nucleation process and mitigating hazards. However, such precursory events before large landslides are rarely reported possibly due to the lack of near-source observations. The 2017 Nuugaatsiaq, Greenland landslide that was preceded by an abundance of small earthquakes and captured by a local seismic station is a notable exception and offers us a valuable opportunity to investigate how a large landslide initiated. Prior work suggests that accelerated creeping plays an important role during the landslide nucleation process. However, by analyzing the temporal evolution of the waveform similarities, waveform amplitudes, and inter-event times of the seismic precursors, we find that the Nuugaatsiaq landslide was very likely triggered by a series of accelerated and migratory small earthquakes approaching the nucleation area of the upcoming landslide, thus providing important insights into the failure initiation of massive landslides.

Production and energy mode control of a production-inventory system

Energy efficiency in manufacturing can be improved by controlling energy modes and production dynamically. We examine a production-inventory system that can operate in Working, Idle, and Off energy modes with mode-dependent energy costs. There can be a warm-up delay to switch between one mode to another. With random inter-arrival, production and warm-up times, we formulate the problem of determining in which mode the production resource should operate at a given time depending on the state of the system as a stochastic control problem under the long-run average profit criterion considering the sales revenue together with energy, inventory holding and backlog costs. The optimal solution of the problem for the exponential inter-arrival, production and warm-up times is determined by solving the Markov Decision Process with a linear programming approach. The structure of the optimal policy for the exponential case uses two thresholds to switch between the Working and Idle or Working and Off modes. We use the two-threshold policy as an approximate policy to control a system with correlated inter-event times with general distributions. This system is modelled as a Quasi Birth and Death Process and analyzed by using a matrix-geometric method. Our numerical experiments show that the joint production and energy control policy performs better compared to the pure production and energy control policies depending on the system parameters. In summary, we propose a joint energy and production control policy that improves energy efficiency by controlling the energy modes depending on the state of the system.

Universal Non-Extensive Statistical Physics Temporal Pattern of Major Subduction Zone Aftershock Sequences.

Large subduction-zone earthquakes generate long-lasting and wide-spread aftershock sequences. The physical and statistical patterns of these aftershock sequences are of considerable importance for better understanding earthquake dynamics and for seismic hazard assessments and earthquake risk mitigation. In this work, we analyzed the statistical properties of 42 aftershock sequences in terms of their temporal evolution. These aftershock sequences followed recent large subduction-zone earthquakes of M ≥ 7.0 with focal depths less than 70 km that have occurred worldwide since 1976. Their temporal properties were analyzed by investigating the probability distribution of the interevent times between successive aftershocks in terms of non-extensive statistical physics (NESP). We demonstrate the presence of a crossover behavior from power-law (q ≠ 1) to exponential (q = 1) scaling for greater interevent times. The estimated entropic q-values characterizing the observed distributions range from 1.67 to 1.83. The q-exponential behavior, along with the crossover behavior observed for greater interevent times, are further discussed in terms of superstatistics and in view of a stochastic mechanism with memory effects, which could generate the observed scaling patterns of the interevent time evolution in earthquake aftershock sequences.

Forecasting tectonic tremor activity using a renewal process model

In many tectonically active regions of the world, a variety of slow deformation phenomena have been discovered and collectively termed slow earthquakes. Tectonic tremor is the high-frequency component of slow earthquakes and can be analyzed to monitor the overall slow deformation process, both spatially and temporally. Although tectonic tremor activity is complex, it does possess some characteristic patterns, such as spatial segmentation, a quasi-periodic recurrence, migration, and tidal modulation. These features are helpful for forecasting future activity if they are properly modeled in a quantitative manner. Here, we propose a stochastic renewal process to standardize and forecast tectonic tremor activity in the Nankai subduction zone, southwest Japan, using a 12.5-year tremor catalog that is divided into a 10-year estimation period and 2.5-year forecasting period. We group the tremor events into small rectangular 10-km regions and observe that the distribution of inter-event times is nearly bimodal, with the short and long inter-event times representing the characteristic times of nearby tremor interactions and long-term stress accumulation processes, respectively. Therefore, as the probabilistic distribution for the renewal process, we adopt a mixture distribution of log-normal and Brownian passage time distributions for the short and long inter-event times, respectively. The model parameters are successfully estimated for 72% of the entire tremor zone using a maximum likelihood method. This standard model can be used to extract anomalous tremor activity, such as that associated with long-term slow-slip events. We derive a scaling relationship between two characteristic times, the relative plate motion, episodicity of tremor activity, and tremor duration by characterizing the spatial differences in tremor activity. We confirm that the model can forecast the occurrence of the next tremor event at a given reference time for a certain prediction interval. This study can serve as a first step for implementing more complex models to improve the space–time forecasting of slow earthquakes.

Copula-based analysis of the autocorrelation function for simple temporal networks

To characterize temporal correlations in temporal networks, we define an autocorrelation function (ACF) for temporal networks in terms of the similarity between two snapshot networks separated by a certain time interval. By employing a copula-based method recently developed for a single time series, we analyze the ACF for the temporal network in which activity patterns of links are independent of each other but their activity levels are heterogeneous. By assuming that exponential distributed interevent times are weakly correlated with each other in each link, we obtain an analytical solution of the ACF. The validity of the analytical solution is tested against the numerical simulations to find that the numerical results are comparable to the analytical solution.

Dynamically Triggering Resilient Control for Networked Nonlinear Systems under Malicious Aperiodic DoS Attacks

Networked nonlinear systems (NNSs) have great potential security threats because of malicious attacks. These attacks will destabilize the networked systems and disrupt the communication to the networked systems, which will affect the stability and performance of the networked control systems. Therefore, this paper aims to deal with the resilient control problem for NNSs with dynamically triggering mechanisms (DTMs) and malicious aperiodic denial-of-service (DoS) attacks. To mitigate the impact from DoS attacks and economize communication resources, a resilient dynamically triggering controller (RDTC) is designed with DTMs evolving an adaptive adjustment auxiliary variable. Thus, the resulting closed-loop system is exponentially stable by employing the piecewise Lyapunov function technique. In addition, according to the minimum inter-event time, the Zeno behavior can be excluded. Finally, the merits of the proposed controllers and theory are corroborated using the well-known nonlinear Chua circuit.

Etna Output Rate during the Last Decade (2011–2022): Insights for Hazard Assessment

During the last two decades, the Etna volcano has undergone several sequences of lava fountaining (LF) events that have had a major impact on road conditions, infrastructure and the local population. In this paper, we consider the LF episodes occurring between 2011 and 2022, calculating their erupted volumes using the images recorded by the monitoring thermal cameras and applying a manual procedure and a dedicated software to determine the lava fountain height over time, which is necessary to obtain the erupted volume. The comparison between the results indicates the two procedures match quite well, the main differences occurring when the visibility is poor and data are interpolated. With the aim of providing insights for hazard assessment, we have fitted some probabilistic models of both the LF inter-event times and the erupted volumes of pyroclastic material. In more detail, we have tested power-law distributions against log-normal, Weibull, generalised Pareto and log-logistic. Results show that the power-law distribution is the most likely among the alternatives. This implies the lack of characteristic scales for both the inter-event time and the pyroclastic volume, which means that we have no indication as to when a new episode of LF will occur and/or how much material will be erupted. What we can reasonably say is only that short inter-event times are more frequent than long inter-event times, and that LF characterised by small volumes are more frequent than LF with high volumes. However, if the hypothesis that magma accumulates on Etna at a rate of about 0.8 m3s−1 holds, the material accumulated in the source region from the beginning of the observation period (2011) to the present (2022) has already been ejected. In simple terms, there is no accumulated magma in the shallow storage that is prone to be erupted in the near future.

Semiglobal Finite-Time Stabilization of Saturated Spacecraft Rendezvous System by Dynamic Event-Triggered and Self-Triggered Control

This article proposes the dynamic event-triggered control (ETC) and self-triggered control (STC) to achieve the semiglobal finite-time stabilization (SGFTS) of spacecraft rendezvous system with input constraints. Based on the Clohessy–Wiltshire equation, a bounded dynamic ETC algorithm is first designed, where the time-varying control gain will approach to infinity at finite-time and only be scheduled on a specified time determined by an dynamic event-triggered mechanism. This algorithm can achieve the SGFTS of the closed-loop system and save the communication resources. Moreover, the corresponding dynamic STC that only uses the data information at the previously triggered time to precompute the next triggered time is designed. By exploring the properties of the parametric Lyapunov equation, a positive minimal interevent time (MIET) of the designed dynamic ETC and STC can be obtained, such that the Zeno phenomenon is avoided. In some cases, the MIET can totally avoid the relationship with the system itself and be designed as an arbitrarily large bounded constant. Finally, simulation results verify the effectiveness of the designed algorithms.

Investigation of long memory in concrete fracture through acoustic emission time series analysis under monotonic and fatigue loading

The significant dependence of current events on past events is known as a long memory phenomenon in stochastic processes. The fracture process in concrete is interesting due to its complexity arising from long-range interactions of multi-scale cracks which may manifest in the long memory. We quantify the long memory effect in the concrete fracture process using the Hurst exponent for acoustic emission measurements. The magnitude and inter-event time series are studied for three different beam sizes under monotonic and fatigue loading. The long memory is strongly observed under fatigue loading. Local variations in the Hurst exponent reveal the fundamental difference between monotonic and fatigue loading, which can be used for damage detection in concrete.

Dynamically Triggered Control for System Connected to Network With Permissible Imperfections

This article designs a novel dynamic triggering-based control methodology for nonlinear system connected to network. The network suffers from imperfections such as packet losses and delays which are deterrents to the stability of the system. The dynamic triggering mechanism ensures stability and allows computation of permissible values of packet losses and delay from: 1) sensor to the controller and 2) controller to the plant. A lower limit on dynamic inter-event time and boundedness of closed-loop error are analytically discussed for system stability. A comprehensive implementation of the proposed methodology for trajectory tracking by a robot manipulator prone to network imperfections presents its effectiveness.

Response of fiber reinforced concrete while entering into the critical stage: An attempt to detect pre-failure indicators in terms of non-extensive statistical mechanics

The main goal of the present study is to explore the potentialities of Non-Extensive Statistical Mechanics (NESM) to provide signals that could be considered as pre-failure indicators. In this direction concrete beams, either unreinforced or reinforced with short fibers, were submitted to three-point bending. The acoustic signals detected during loading were analyzed in terms of their interevent time intervals and the respective cumulative probability. The experimental data were then properly fitted by means of the q-exponential function providing the temporal evolution of the entropic index q throughout the duration of each experiment. The evolution of q was studied in juxtaposition to that of the load applied as well as to that of some additional parameters used to describe the acoustic activity, namely the b-values and the F-, P- and d-functions. The analysis indicated that at load levels approaching the load-carrying capacity of the specimens, the response of both the unreinforced and the fiber reinforced beams corresponds to q-values approaching 2. It is thus highlighted that, according to NESM principles, the damage processes at the specific load levels are characterized by the existence of a number of non-independent subsystems with long-range mutual interactions and memory effects, which cannot be properly described by the concepts of the traditional Boltzmann-Gibbs Statistical Mechanics. On the contrary, description in terms of NESM provided useful information about the damage evolution during the very last loading stages before macroscopic fracture. In addition, the analysis provided indications that the onset of decrease of the q-values, towards the critical limit of 1, could be considered as a potential pre-failure index, warning about upcoming entrance of the system into its critical stage, namely that of impending fracture.

Distributed dynamic event-triggered communication and control for multi-agent consensus: A hybrid system approach

This paper investigates the output-based event-triggered communication and control for linear multi-agent consensus under a directed graph based on a co-design method. The communication among the agents, as well as the controller updates, are determined by some new event-triggering mechanisms, in order to reduce the use of the network resources. To simultaneously guarantee the significant properties including the asymptotic consensus, and strong Zeno-freeness (strictly positive inter-event times), a novel distributed dynamic event-triggered protocol is proposed. Unlike the most-existing emulation-based approaches in which the control gain is previously decided, a systematic co-design procedure is proposed to design the controller gain, the observer gain, and the event-triggering mechanisms altogether in terms of solving a linear matrix inequality optimization problem. Based on the resulting hybrid system framework, a hybrid model is established for the distributed closed-loop system and the asymptotic consensus is achieved. Finally, a numerical example is presented to verify our systematic design methodology.

Spatio-temporal forecasting of future volcanism at Harrat Khaybar, Saudi Arabia

The 180,000 km2 of Arabian lava fields (“harrats” in Arabic) form one of the largest distributed basaltic provinces in the world. The most recent eruption in 1256 AD, on the outskirts of Medina, as well as shallow dike emplacement in 2009, ~ 200 km northeast of the city, suggest future volcanic threat to this area. Harrat Khaybar (~ 1.7 Ma to present) is one of the largest and most compositionally diverse Arabian lava fields; it is located ~ 137 km northeast of Medina and covers ~ 14,000 km2. Here, we present a new eruption event record and the first estimation of future potential locations and timing of volcanism in Harrat Khaybar. Volcanic vents and eruptive fissures were mapped using remote sensing and field studies, and categorized into a geospatial database, complemented by 16 new 40Ar/39Ar ages. Our analysis reveals that Harrat Khaybar developed over five eruptive phases, where vent locations over time focus towards the central axis forming a broad N-S trend, with a central group concentrated along an axis of the regional Makkah-Madinah-Nafud (MMN) line and wider spatial dispersion between vents outwards from there. For the whole field, we estimate a long-term average recurrence rate of ~ 2.3 eruptions per 10 kyr assuming a Poisson distribution for inter-event times, which indicates that Harrat Khaybar would belong to a global group of highly active distributed volcanic fields. Our analysis also reveals that the field likely had a “flare-up” period between 450 and 300 ka where the vast majority of eruptions occurred, with ~ 18 eruptions per 10 kyr. After this intense period, eruption rates fell to < 2 eruptions per 10 kyr. Based on our findings, we estimate cumulative probabilities of 1.09 and 16.3% as lower and upper bounds of at least one eruption occurring over the next 100 years somewhere in Harrat Khaybar, with the highest probabilities within the central axis region, in particular around Jabal Qidr, Bayda and Abyad.