State Transition Matrix Research Articles

SHM-informed life-cycle intelligent maintenance of fatigue-sensitive detail using Bayesian forecasting and Markov decision process

Civil and maritime engineering systems must be efficiently managed to control the failure risk at an acceptable level as their performance is gradually degraded throughout the operational life, caused by fatigue and corrosion. Structural health monitoring develops a timely capability to assess the structural condition and performance metrics. However, using actual long-term monitoring data to guide the life-cycle management under stochastic environments has not been sufficiently studied. To realize an optimal maintenance strategy within the service life, an integrated monitoring-based optimal management framework is developed on the basis of the partially observable Markov decision processes (POMDPs) and Bayesian forecasting. In the proposed framework, the stochastic fatigue processes are quantified by the state transition matrix. The Bayesian dynamic linear model is embedded in POMDPs as a continuous observation part to forecast the cycling impacts and estimate the deterioration rate using long-term dynamic strain responses. In addition, making use of the special features of the problem considered in this paper, an adaptive discretization strategy is proposed to alleviate the complexity of large discrete observed spaces in the POMDP. The applicability and feasibility of the framework are evaluated by intelligent maintenance of fatigue-sensitive components with real-world monitoring data. After solving the POMDP by an efficient offline solver, the results obtained in this paper demonstrate that structural interventions are uneconomical to extend the life when a welded detail is approaching its end of life due to the normal service. Furthermore, if multiple interventions are available, the framework can find optimal maintenance actions based on the trade-off between long-term utility and the corresponding cost. This framework as the prototype could also be adjusted to aid life-cycle intelligent maintenance of other types of components under different deterioration scenarios.

Dynamics and stability analysis of five-axis ball end milling with low radial immersion considering cutter runout

The inevitable cutter runout has an important influence on the cutter dynamic properties and transient cutting condition, whereas it is usually neglected in analyses of mechanics and dynamics in five-axis ball end milling for lack of efficient mechanism modeling methods. This paper presents a novel mechanical and dynamic model considering runout to develop stability analysis suitable in five-axis ball end milling with low radial immersion. Firstly, the mathematical modeling of the cutting edge trajectory is derived from the cutting process considering runout effect. The impact of runout on the motility pattern of the cutter center and cutting edge is clarified. Then, the optimized tool coordinate system independent on runout parameters is defined to decompose the cutter complex elliptical or quasi elliptical motion caused by runout into two regular circular motion combinations. One is the center of cutter rotates around spindle, and the other is the cutting edge of cutter rotates around cutter center. Taking advantage of this strategy, the mechanics and dynamics of five-axis ball end milling considering runout are determined. A new analytic method is developed to extract the cutter and workpiece engagement (CWE) for five-axis ball end milling considering runout effect based on the transient cutting force signal. The superiority of the proposed dynamic and CWE models are both immune from the runout parameters. Thereafter, generalized precise integration method (GPIM) is presented to deduce dynamic system with multiple time delays into the state transition matrix. The axial angle of cutting edge acts as a bridge between transition matrix and the limit cutting positions defined by the analytic CWE to develop stability analysis for five axis ball end milling. The accuracy and efficiency of the GPIM is validated by the classic benchmarks and experimentally verified examples. Finally, five-axis ball-end milling experiments are performed to confirm the effectiveness of the proposed mechanical and dynamic models.

Robust optimal control of logical control networks with function perturbation

Optimal control is an important branch in modern control theory. In this article, the robustness of optimal control sequence is investigated for logical control networks (LCNs) subject to function perturbation. Firstly, the impact of function perturbation on the Bolza-type optimal control problem of LCNs is analyzed, and several sufficient conditions are presented for the robustness of optimal control sequence. Secondly, combining the characteristics of state transition matrix and stage cost function, a kind of optimal matrix is constructed, which brings a new way for the solvability of Bolza-type optimal control problem. Thirdly, the optimal matrix is used to measure the deviation of cost function with respect to function perturbation, and several necessary and sufficient conditions are proposed to guarantee the robustness of optimal control sequence. Finally, the robustness of optimal control sequence in the Bolza-type optimal control problem is applied to other types of finite-horizon and infinite-horizon optimal control problems of LCNs.

Orbit design and control for periodically revisiting multiple formation satellites

In the formation flying mission, the periodic revisit of multiple formation satellites can provide periodic surveillance of satellite status, e.g., on-orbit inspection. This paper studies the orbit design problem and the single-impulse control problem for periodically revisiting multiple formation satellites. Two periodic revisit conditions under the J2 perturbation are considered: the J2 invariant orbit and the same mean semi-major axis. By analyzing the numbers of free variables and constraint equations, the maximum numbers of revisiting satellites are obtained for both the coplanar and non-coplanar cases. A hybrid method is proposed by combining the state transition matrix and the second-order state transition tensor, which are used to solve the required velocity vector and to propagate the relative state vector, respectively. The original multi-dimensional nonlinear equation is reduced into a one- or two-dimensional equation, which is solved by numerical methods. Several numerical examples show that the revisit orbit drifts after 30 revolutions by the proposed method for the coplanar and non-coplanar cases are less than 0.3 km and 4.5 km, respectively.

A two-state Markov chain model for slug flow in horizontal ducts

Intermittent flows are common flow patterns in gas–liquid horizontal flow and attract attention and great research effort due to its importance for industrial and engineering applications. The slug flow is typically modelled based on a unit cell varying from an elongated air bubble with a liquid film in segregated flow pattern and an aerated liquid plug, the slug region, with remarkable stochastic characteristics of its alternating regions. In this paper, a two-state Markov chain model is proposed to represent the stochastic dynamics of developed slug flow in horizontal pipes. Each state represents either the liquid slug or the elongated bubble regions and the transition probabilities dictate the change of the given discrete time measurement to stay at a given state or change. This simple but insightful description of the phenomenon allows an analytical treatment of the statistics of Markov chain stochastic process. Measurement stations with two double wire resistive sensors are used to obtain the void fraction time series and a corresponding two-state representation. Each state is classified by a threshold defined by an unsupervised and non-parametric pattern recognition approach. The state transition matrix is then estimated for each corresponding experimental point. Thus random samples can be synthetically regenerated with the same statistical features of the corresponding measurements. It is shown that the Markov chain model can successfully represent second-order statistics of the measurement, such as the autocorrelation and power spectral density, given an appropriate choice of the chain order. Moreover, a cross correlation-based time delay estimation is proposed for the two-sensor measurement station and additional information is obtained from the slug flow. Subsequently, statistics of some slug flow features are estimated using the proposed approach and their interpretation as random variables derived from the void fraction stochastic process is discussed.

Dynamic Target Enclosing Control Scheme for Multi-Agent Systems via a Signed Graph-Based Approach

Dear Editor, This letter investigates the target enclosing control problem of multi-agent systems. A signed graph-based control strategy is presented, where the agents are steered to enclose the dynamic target from both sides as they move. This is inspired by the phenomenon that signed networks exhibit bipartite clustering if the underlying graph is structurally balanced, so that the agents may naturally enclose the zero point from opposite sides (+ and -) if proper controllers are applied. By adopting a distributed observer to estimate the information of dynamic target, a consensus-based enclosing control scheme is designed. Furthermore, a complete Laplacian matrix (CLM)-based Lyapunov analysis method is introduced to prove the control stability, which provides simpler theoretical validation for the stability analysis of average consensus than the conventional method based on state transition matrix. Finally, some numerical simulations are shown to verify the effectiveness of the proposed control scheme.

Indirect Optimization of Fuel-Optimal Many-Revolution Low-Thrust Transfers With Eclipses

An efficient indirect method is presented to determine fuel-optimal many-revolution low-thrust transfers in the presence of Earth-shadow eclipses. Specifically, the events of shadow entrance and exit are modeled as interior-point constraints. Following the observation that an ill-conditioned state transition matrix may occur when the spacecraft flies over the edge of the shadow, a two-level continuation scheme is introduced to generate many-revolution trajectories. The established computational framework integrates analytic derivatives, switching detection, and continuation with an augmented flowchart, which yields discontinuous bang-bang solutions and their gradients. Transfers from a geostationary transfer orbit to a geostationary orbit are simulated to illustrate the effectiveness and efficiency of the method developed.

Rank the spreading influence of nodes using dynamic Markov process

Ranking the spreading influence of nodes is of great importance in practice and research. The key to ranking a node’s spreading ability is to evaluate the fraction of susceptible nodes being infected by the target node during the outbreak, i.e. the outbreak size. In this paper, we present a dynamic Markov process (DMP) method by integrating the Markov chain and the spreading process to evaluate the outbreak size of the initial spreader. Following the idea of the Markov process, this method solves the problem of nonlinear coupling by adjusting the state transition matrix and evaluating the probability of the susceptible node being infected by its infected neighbors. We have employed the susceptible-infected-recovered and susceptible-infected-susceptible models to test this method on real-world static and temporal networks. Our results indicate that the DMP method could evaluate the nodes’ outbreak sizes more accurately than previous methods for both single and multi-spreaders. Besides, it can also be employed to rank the influence of nodes accurately during the spreading process.

Further results for synchronization of two coupled Boolean networks

AbstractThis paper investigates the complete synchronization of drive‐response Boolean networks (BNs) using the semi‐tensor product of matrices. First, a necessary and sufficient condition for complete synchronization is obtained. Next, a pinning control method for achieving complete synchronization of drive‐response BNs is proposed, based on certain transformations of the state transition matrix of drive BN. Then, an algorithm is proposed to obtain the minimum number of pinning nodes, based on the perturbation method. Finally, two numerical examples are given to verify the validity of the study results.

Almost sure stability criterion for continuous-time linear systems with uniformly distributed uncertainty

Assuming the uncertain parameter of a linear polytopic system to be uniformly distributed, we can prove that the system is almost sure exponentially stable if and only if its averaging system is stable. Computing the mathematical expectation of the state-transition matrix and characterizing the martingale structure embedded in its variance is the key for deriving this stability criterion.

Learned Lifted Linearization Applied to Unstable Dynamic Systems Enabled by Koopman Direct Encoding

This paper presents a Koopman lifting linearization method that is applicable to nonlinear dynamical systems having both stable and unstable regions. It is known that DMD and other standard data-driven methods face a fundamental difficulty in constructing a Koopman model when applied to unstable systems. Here we solve the problem by incorporating knowledge about a nonlinear state equation with a learning method for finding an effective set of observables. In a lifted space, stable and unstable regions are separated into independent subspaces. Based on this property, we propose to find effective observables through neural net training where training data are separated into stable and unstable trajectories. The resultant learned observables are used for constructing a linear state transition matrix using method known as Direct Encoding, which transforms the nonlinear state equation to a state transition matrix through inner product computations with the observables. The proposed method shows a dramatic improvement over existing DMD and data-driven methods.

Optimal Multi-impulse Linear Rendezvous via Reinforcement Learning

A reinforcement learning-based approach is proposed to design the multi-impulse rendezvous trajectories in linear relative motions. For the relative motion in elliptical orbits, the relative state propagation is obtained directly from the state transition matrix. This rendezvous problem is constructed as a Markov decision process that reflects the fuel consumption, the transfer time, the relative state, and the dynamical model. An actor–critic algorithm is used to train policy for generating rendezvous maneuvers. The results of the numerical optimization (e.g., differential evolution) are adopted as the expert data set to accelerate the training process. By deploying a policy network, the multi-impulse rendezvous trajectories can be obtained on board. Moreover, the proposed approach is also applied to generate a feasible solution for many impulses (e.g., 20 impulses), which can be used as an initial value for further optimization. The numerical examples with random initial states show that the proposed method is much faster and has slightly worse performance indexes when compared with the evolutionary algorithm.

Sparse Bayesian Estimation of Parameters in Linear-Gaussian State-Space Models

State-space models (SSMs) are a powerful statistical tool for modelling time-varying systems via a latent state. In these models, the latent state is never directly observed. Instead, a sequence of data points related to the state are obtained. The linear-Gaussian state-space model is widely used, since it allows for exact inference when all model parameters are known, however this is rarely the case. The estimation of these parameters is a very challenging but essential task to perform inference and prediction. In the linear-Gaussian model, the state dynamics are described via a state transition matrix. This model parameter is known to behard to estimate, since it encodes the relationships between the state elements, which are never observed. In many applications, this transition matrix is sparse since not all state components directly affect all other state components. However, most parameter estimation methods do not exploit this feature. In this work we propose SpaRJ, a fully probabilistic Bayesian approach that obtains sparse samples from the posterior distribution of the transition matrix. Our method explores sparsity by traversing a set of models that exhibit differing sparsity patterns in the transition matrix. Moreover, we also design new effective rules to explore transition matrices within the same level of sparsity. This novel methodology has strong theoretical guarantees, and unveils the latent structure of the data generating process, thereby enhancing interpretability. The performance of SpaRJ is showcased in example with dimension 144 in the parameter space, and in a numerical example with real data.

E2DTF: An End-to-End Detection and Tracking Framework for Multiple Micro-UAVs With FMCW-MIMO Radar

Due to the weak radar echoes and strong background clutters in low-altitude airspace, the detection and tracking for multiple micro-unmanned aerial vehicles (UAVs) have posed formidable challenges in radar surveillance field. Consequently, this paper proposes an end-to-end detection and tracking framework (E <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> DTF) for multiple micro-UAVs by utilizing the frequency modulated continuous wave-multiple input multiple output (FMCW-MIMO) radar. To address the low signal-to-noise ratio (SNR) problem, E <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> DTF presents a frame-range-Doppler-azimuth information fusion filter to integrate the target energy by exploiting the spatio-temporal dependence of positions within a sequence of unthresholded frames. Additionally, considering that a target may enter/leave the radar field-of-view (FOV), E <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> DTF introduces a target model state, updated by an extended Markov state transition matrix sequentially, to realize an unknown, time-varying number of micro-UAVs tracking. Another nice feature of E <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> DTF is that it avoids the complex data association procedure thanks to removing the threshold-decision operation. Finally, both numerical simulations and experiments with five different scenarios, i.e., horizontal line, cross-trajectory, circular loop, rainy condition and 3D trajectory tracking are presented to verify the effectiveness of the proposed method. The results show that E <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> DTF can obtain superior detection and tracking performance for multiple micro-UAVs in contrast to the state-of-the-art methods considering detection and tracking processes independently, especially under low SNR conditions.

Vibration analysis using a state transition matrix calculated by a hybrid of experiment and finite element analysis

Vibration analysis using a state transition matrix calculated by a hybrid of experiment and finite element analysis

Nonsingularity of Trivium-like cascade FSRs over finite fields via semi-tensor product

In stream cipher designing, nonsingularity is a crucial requirement to ensure that the feedback shift registers (FSRs) do not produce keys that are equivalent to one another. This study uses a semi-tensor product to examine the nonsingularity of Trivium-like cascade FSRs over a finite field. The Trivium-like cascade FSRs are expressed algebraically using the semi-tensor product, allowing them to be viewed as logical networks and introducing a novel state transition matrix. Several necessary and sufficient conditions for the nonsingularity of FSRs and Trivium-like cascade FSRs over a finite field are established by dividing the structural matrices of feedback functions into different parts. These findings are also applicable to binary FSRs and binary Trivium-like cascade FSRs.

Set stabilizability of switched Boolean control networks via Ledley antecedence solution

This paper studies two kinds of set stabilizability issues of switched Boolean control networks (SBCNs) by Ledley antecedence solution, that is, pointwise set stabilizability and set stabilizability under arbitrary switching signals. Firstly, based on the state transition matrix of SBCNs, the mode-dependent truth matrix is defined. Secondly, using the mode-dependent truth matrix in every step, a switching signal and the corresponding Ledley antecedence solutions are determined. Furthermore, a state feedback switching signal and a state feedback control are obtained for the pointwise set stabilizability. Thirdly, with the help of all mode-dependent truth matrices, the Ledley antecedence solutions are derived for a set of Boolean inclusions, which admits a state feedback control for the set stabilizability under arbitrary switching signals. Finally, an example is given to show the effectiveness of the proposed results.

Age of information analysis for internet of things information status update system with cellular backhaul and dedicated energy harvesting beacons

SummaryThe Internet of Things (IoT) that is usually deployed with the assistance of cellular backhaul and energy harvesting (EH) is characterized by the status update freshness. However, the traditional nature EH results in the loss of information freshness due to the randomness of nature energy process. Although using wireless energy transferring (WET) to charge sensors can overcome this problem, this method has low‐energy efficiency. With these considerations, this paper proposes a novel IoT system under cellular communication scenario by simultaneously exploiting the nature EH and WET. The proposed IoT system is consisted of a cellular backhaul subsystem, a wireless EH and transferring (WEHT) subsystem, and a wireless sensor status update subsystem. The WEHT subsystem employs the dedicated power beacons harvesting energy from natural energy source and transferring the harvested energy to sensor. For the proposed IoT system, this paper first investigates the WEHT subsystem and constructs the Markov Chain (MC) of discrete energy states as well as the MC state transition matrix. Second, the average AoI and peak AoI (PAoI) are formulated by separately considering cellular backhaul and EHTBs. The AoI (PAoI) comparison shows that the proposed EHTB‐based IoT system can outperform the conventional non‐EHTB one where the sensor directly harvests energy from natural source. At the same time, the numerical results exploit the impact of system parameters on AoI and PAoI, respectively. It is found that there exists a trade‐off between the nature energy arrival and EHTB energy transfer so that the average minimum AoI and PAoI are achieved.

Buffer-Aided Max-Link Relaying for Free Space Optical Communication With Delay Constraints

In this paper, we introduce the concept of buffer-aided cooperative relaying for a free-space optical (FSO) communication system. The proposed FSO system consists of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$K$</tex-math></inline-formula> decode-and-forward(DF) relays, each equipped with a buffer of size <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L$</tex-math></inline-formula> . The proposed system undergoes both path loss and atmospheric turbulence (AT) induced fading, and to evaluate the system performance a weak, as well as strong AT region is considered. The Markov chain (MC) approach is used to derive the state transition matrix of the system, which is then further used to model the evolution of buffer states. Analytical expressions of the outage probability and average bit error rate (ABER) are obtained with the help of state transition matrix. The average packet delay of the system is also evaluated with the help of obtained outage probability. The performance of the considered system is analyzed for different values of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$K$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L$</tex-math></inline-formula> . The performance is then further compared with the non-buffer-aided (NBA) cooperative relaying for FSO communication systems and it has been observed that the proposed buffer-aided FSO system significantly outperforms the NBA FSO systems for entire range of turbulence. Finally, the impact of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$K$</tex-math></inline-formula> on the average packet delay of the system is examined.

Stabilizing Large-Scale Probabilistic Boolean Networks by Pinning Control.

This article aims to stabilize probabilistic Boolean networks (PBNs) via a novel pinning control strategy. In a PBN, the state evolution of each gene switches among a collection of candidate Boolean functions with preassigned probability distributions, which govern the activation frequency of each Boolean function. Due to the existence of stochasticity, the mode-independent pinning controller might be disabled. Thus, both mode-independent and mode-dependent pinning controller are required here. Moreover, a criterion is derived to determine whether mode-independent controllers are applicable while the pinned nodes are given. It is worth pointing out that this pinning control is based on the n×n network structure rather than 2n ×2n state transition matrix. Therefore, compared with the existing results, this pinning control strategy is more practicable and has the ability to handle large-scale networks, especially sparsely connected networks. To demonstrate the effectiveness of the designed control scheme, a PBN that describes the mammalian cell-cycle encountering a mutated phenotype is discussed as a simulation.