Approximately Bi-Similar Symbolic Model for Discretetime Interconnected Switched System

Dear Editor,This letter concerns the development of approximately bi-similar symbolic models for a discrete-time interconnected switched system(DT-ISS).The DT-ISS under consideration is formed by connecting multiple switched systems known as component switched systems(CSSs).Although the problem of constructing approximately bi-similar symbolic models for DT-ISS has been addressed in some literature,the previous works have relied on the assumption that all the subsystems of CSSs are incrementally input-state stable.

A novel method for simulating nuclear explosion with chemical explosion to form an approximate plane wave: Field test and numerical simulation

A nuclear explosion in the rock mass medium can produce strong shock waves,seismic shocks,and other destructive effects,which can cause extreme damage to the underground protection infrastructures.With the increase in nuclear explosion power,underground protection engineering enabled by explosion-proof impact theory and technology ushered in a new challenge.This paper proposes to simulate nuclear explosion tests with on-site chemical explosion tests in the form of multi-hole explosions.First,the mechanism of using multi-hole simultaneous blasting to simulate a nuclear explosion to generate approximate plane waves was analyzed.The plane pressure curve at the vault of the underground protective tunnel under the action of the multi-hole simultaneous blasting was then obtained using the impact test in the rock mass at the site.According to the peak pressure at the vault plane,it was divided into three regions:the stress superposition region,the superposition region after surface reflection,and the approximate plane stress wave zone.A numerical simulation approach was developed using PFC and FLAC to study the peak particle velocity in the surrounding rock of the underground protective cave under the action of multi-hole blasting.The time-history curves of pressure and peak pressure partition obtained by the on-site multi-hole simultaneous blasting test and numerical simulation were compared and analyzed,to verify the correctness and rationality of the formation of an approximate plane wave in the simulated nuclear explosion.This comparison and analysis also provided a theoretical foundation and some research ideas for the ensuing study on the impact of a nuclear explosion.

Existence of Approximate Solutions to Nonlinear Lorenz System under Caputo-Fabrizio Derivative

In this article,we developed sufficient conditions for the existence and uniqueness of an approximate solution to a nonlinear system of Lorenz equations under Caputo-Fabrizio fractional order derivative(CFFD).The required results about the existence and uniqueness of a solution are derived via the fixed point approach due to Banach and Krassnoselskii.Also,we enriched our work by establishing a stable result based on the Ulam-Hyers(U-H)concept.Also,the approximate solution is computed by using a hybrid method due to the Laplace transform and the Adomian decomposition method.We computed a few terms of the required solution through the mentioned method and presented some graphical presentation of the considered problem corresponding to various fractional orders.The results of the existence and uniqueness tests for the Lorenz system under CFFD have not been studied earlier.Also,the suggested method results for the proposed system under the mentioned derivative are new.Furthermore,the adopted technique has some useful features,such as the lack of prior discrimination required by wavelet methods.our proposed method does not depend on auxiliary parameters like the homotopy method,which controls the method.Our proposed method is rapidly convergent and,in most cases,it has been used as a powerful technique to compute approximate solutions for various nonlinear problems.

UAMP-Based Delay-Doppler Channel Estimation for OTFS Systems

Orthogonal time frequency space(OTFS)technique, which modulates data symbols in the delayDoppler(DD) domain, presents a potential solution for supporting reliable information transmission in highmobility vehicular networks. In this paper, we study the issues of DD channel estimation for OTFS in the presence of fractional Doppler. We first propose a channel estimation algorithm with both low complexity and high accuracy based on the unitary approximate message passing(UAMP), which exploits the structured sparsity of the effective DD domain channel using hidden Markov model(HMM). The empirical state evolution(SE) analysis is then leveraged to predict the performance of our proposed algorithm. To refine the hyperparameters in the proposed algorithm,we derive the update criterion for the hyperparameters through the expectation-maximization(EM) algorithm. Finally, Our simulation results demonstrate that our proposed algorithm can achieve a significant gain over various baseline schemes.

Bifurcation Analysis of a Nonlinear Vibro-Impact System with an Uncertain Parameter via OPA Method

In this paper,the bifurcation properties of the vibro-impact systems with an uncertain parameter under the impulse and harmonic excitations are investigated.Firstly,by means of the orthogonal polynomial approximation(OPA)method,the nonlinear damping and stiffness are expanded into the linear combination of the state variable.The condition for the appearance of the vibro-impact phenomenon is to be transformed based on the calculation of themean value.Afterwards,the stochastic vibro-impact systemcan be turned into an equivalent high-dimensional deterministic non-smooth system.Two different Poincarésections are chosen to analyze the bifurcation properties and the impact numbers are identified for the periodic response.Consequently,the numerical results verify the effectiveness of the approximation method for analyzing the considered nonlinear system.Furthermore,the bifurcation properties of the system with an uncertain parameter are explored through the high-dimensional deterministic system.It can be found that the excitation frequency can induce period-doubling bifurcation and grazing bifurcation.Increasing the randomintensitymay result in a diffusion-based trajectory and the impact with the constraint plane,which induces the topological behavior of the non-smooth system to change drastically.It is also found that grazing bifurcation appears in advance with increasing of the random intensity.The stronger impulse force can result in the appearance of the diffusion phenomenon.

Relaxed Stability Criteria for Time-Delay Systems:A Novel Quadratic Function Convex Approximation Approach

This paper develops a quadratic function convex approximation approach to deal with the negative definite problem of the quadratic function induced by stability analysis of linear systems with time-varying delays.By introducing two adjustable parameters and two free variables,a novel convex function greater than or equal to the quadratic function is constructed,regardless of the sign of the coefficient in the quadratic term.The developed lemma can also be degenerated into the existing quadratic function negative-determination(QFND)lemma and relaxed QFND lemma respectively,by setting two adjustable parameters and two free variables as some particular values.Moreover,for a linear system with time-varying delays,a relaxed stability criterion is established via our developed lemma,together with the quivalent reciprocal combination technique and the Bessel-Legendre inequality.As a result,the conservatism can be reduced via the proposed approach in the context of constructing Lyapunov-Krasovskii functionals for the stability analysis of linear time-varying delay systems.Finally,the superiority of our results is illustrated through three numerical examples.

Primary frequency control considering communication delay for grid-connected offshore wind power systems

Offshore wind farms are becoming increasingly distant from onshore centralized control centers,and the communication delays between them inevitably introduce time delays in the measurement signal of the primary frequency control.This causes a deterioration in the performance of the primary frequency control and,in some cases,may even result in frequency instability within the power system.Therefore,a frequency response model that incorporates communication delays was established for power systems that integrate offshore wind power.The Padéapproximation was used to model the time delays,and a linearized frequency response model of the power system was derived to investigate the frequency stability under different time delays.The influences of the wind power proportion and frequency control parameters on the system frequency stability were explored.In addition,a Smith delay compensation control strategy was devised to mitigate the effects of communication delays on the system frequency dynamics.Finally,a power system incorporating offshore wind power was constructed using the MATLAB/Simulink platform.The simulation results demonstrate the effectiveness and robustness of the proposed delay compensation control strategy.

Seismic safety assessment with non-Gaussian random processes for train-bridge coupled systems

Extensive high-speed railway(HSR)network resembled the intricate vascular system of the human body,crisscrossing mainlands.Seismic events,known for their unpredictability,pose a significant threat to both trains and bridges,given the HSR’s extended operational duration.Therefore,ensuring the running safety of train-bridge coupled(TBC)system,primarily composed of simply supported beam bridges,is paramount.Traditional methods like the Monte Carlo method fall short in analyzing this intricate system efficiently.Instead,efficient algorithm like the new point estimate method combined with moment expansion approximation(NPEM-MEA)is applied to study random responses of numerical simulation TBC systems.Validation of the NPEM-MEA’s feasibility is conducted using the Monte Carlo method.Comparative analysis confirms the accuracy and efficiency of the method,with a recommended truncation order of four to six for the NPEM-MEA.Additionally,the influences of seismic magnitude and epicentral distance are discussed based on the random dynamic responses in the TBC system.This methodology not only facilitates seismic safety assessments for TBC systems but also contributes to standard-setting for these systems under earthquake conditions.

Migratable Power System Transient Stability AssessmentMethod Based on Improved XGBoost

The data-driven transient stability assessment(TSA)of power systems can predict online real-time prediction by learning the temporal features before and after faults.However,the accuracy of the assessment is limited by the quality of the data and has weak transferability.Based on this,this paper proposes a method for TSA of power systems based on an improved extreme gradient boosting(XGBoost)model.Firstly,the gradient detection method is employed to remove noise interference while maintaining the original time series trend.On this basis,a focal loss function is introduced to guide the training of theXGBoostmodel,enhancing the deep exploration of minority class samples to improve the accuracy of the model evaluation.Furthermore,to improve the generalization ability of the evaluation model,a transfer learning method based on model parameters and sample augmentation is proposed.The simulation analysis on the IEEE 39-bus system demonstrates that the proposed method,compared to the traditional machine learning-based transient stability assessment approach,achieves an average improvement of 2.16%in evaluation accuracy.Specifically,under scenarios involving changes in topology structure and operating conditions,the accuracy is enhanced by 3.65%and 3.11%,respectively.Moreover,the model updating efficiency is enhanced by 14–15 times,indicating the model’s transferable and adaptive capabilities across multiple scenarios.

Actuator and sensor fault isolation in a class of nonlinear dynamical systems

Fault isolation in dynamical systems is a challenging task due to modeling uncertainty and measurement noise,interactive effects of multiple faults and fault propagation.This paper proposes a unified approach for isolation of multiple actuator or sensor faults in a class of nonlinear uncertain dynamical systems.Actuator and sensor fault isolation are accomplished in two independent modules,that monitor the system and are able to isolate the potential faulty actuator(s)or sensor(s).For the sensor fault isolation(SFI)case,a module is designed which monitors the system and utilizes an adaptive isolation threshold on the output residuals computed via a nonlinear estimation scheme that allows the isolation of single/multiple faulty sensor(s).For the actuator fault isolation(AFI)case,a second module is designed,which utilizes a learning-based scheme for adaptive approximation of faulty actuator(s)and,based on a reasoning decision logic and suitably designed AFI thresholds,the faulty actuator(s)set can be determined.The effectiveness of the proposed fault isolation approach developed in this paper is demonstrated through a simulation example.

Approximate Analytic Solution of Solitary Wave for a Class of Nonlinear Disturbed Long-Wave System

In this paper, the approximate expressions of the solitary wave solutions for a class of nonlinear disturbed long-wave system are constructed using the homotopie mapping method.

Approximate trace and singleton failures equivalences for transition systems

Established system equivalences for transition systems, such as trace equivalence and failures equivalence, require the ob- servations to be exactly identical. However, an accurate measure- ment is impossible when interacting with the physical world, hence exact equivalence is restrictive and not robust. Using Baire met- ric, a generalized framework of transition system approximation is proposed by developing the notions of approximate language equivalence and approximate singleton failures （SF） equivalence. The framework takes the traditional exact equivalence as a special case. The approximate language equivalence is coarser than the approximate Slc equivalence, just like the hierarchy of the exact ones. The main conclusion is that the two approximate equiva- lences satisfy the transitive property, consequently, they can be successively used in transition system approximation.

Sampled-data Observer Design for a Class of Stochastic Nonlinear Systems Based on the Approximate Discrete-time Models

In this paper,we studied the approximate sampleddata observer design for a class of stochastic nonlinear systems.Euler-Maruyama approximation was investigated in this paper because it is the basis of other higher precision numerical methods,and it preserves important structures of the nonlinear systems.Also,the form of Euler-Maruyama model is simple and easy to be calculated.The results provide a reference for sampled-data observer design method for such stochastic nonlinear systems,and may be useful to many practical control applications,such as tracking control in mechanical systems.And the effectiveness of the approach is demonstrated by a simulation example.

Approximate Reachability and Bisimulation Equivalences for Transition Systems

Using Baire metric, this paper proposes a generalized framework of transition system approximation by developing the notions of approximate reachability and approximate bisimulation equivalences. The proposed framework captures the traditional exact equivalence as a special case. Approximate reachability equivalence is coarser than approximate bisimulation equivalence, just like the hierarchy of the exact ones. Both approximate equivalences satisfy the transitive property, consequently, they can be used in transition system approximation.

Form invariance and approximate conserved quantity of Appell equations for a weakly nonholonomic system

A weakly nonholonomic system is a nonholonomic system whose constraint equations contain a small parameter. The form invariance and the approximate conserved quantity of the Appell equations for a weakly nonholonomic system are studied. The Appell equations for the weakly nonholonomic system are established, and the definition and the criterion of form invariance of the system are given. The structural equation of form invariance for the weakly nonholonomic system and the approximate conserved quantity deduced from the form invariance of the system are obtained. Finally, an example is given to illustrate the application of the results.

Fixed-point Implementation of Approximate Message Passing （AMP） algorithm in massive MIMO systems

In massive multiple input and multiple output （MIMO） systems the challenge is the detection of the individual signals from the composite signal with a large system limit. The optimal detector becomes prohibitively complex. The approximate message passing （AMP） algorithm, designed for compressed sensing, has attracted researchers to counter this problem due to its reduced complexity with a large system limit. For this reason the AMP algorithm has been used for detection in massive MIMO systems. In this paper, we focus on implementing this algorithm in a fixed-point format. To obtain an implementation friendly architecture, we propose approximations for the mean and variance estimation functions within the algorithm. These estimation functions are obtained using the log-sum approximation, then taking the exponent of the result. The log-sum approximation is obtained by the Jacobian logarithm with a correction function. We also provide a modification of the correction function for the approximations that best suits our case. We then transform the algorithm with the approximated functions to fixed-point and provide a BER performance for the algorithm with the variables set to 16-bit word lengths using the hybrid ＂ScaledDouble＂ data types.

Approximate analysis method for displacement responses of structures with active variable stiffness systems

The performance of structures with active variable stiffness (AVS) systems exhibits strong nonlinearity due to the variety with time of the stiffness of each storey unit,in which the AVS system is installed.Hence,the classical dynamic analysis method for linear structures,such as the mode-superposition method,is not applicable to structures with AVS systems.In this paper,an approximate analysis method is proposed for displacement responses of structures with AVS systems.Firstly,an equivalent relationship between single-degree-of-freedom (SDOF) structures equipped with AVS systems and so-called fictitious linear structures is established.Then,an approximate mode-superposition (AMS) method is presented for multi-degree-of-freedom (MDOF) structures equipped with AVS systems.The accuracy of this method is investigated through extensive parametrical study using different types of earthquake excitations,and some modification is made to the method. Numerical calculation results indicate that the modified AMS method is effective for estimating the maximum displacements relative to the ground and the maximum interstorey drifts of MDOF structures equipped with AVS systems.

Approximate Failures Semantics for Polynomial Labelled Transition Systems

Labelled transition systems(LTSs) are widely used to formally describe system behaviour.The labels of LTS are extended to offer a more satisfactory description of behaviour by refining the abstract labels into multivariate polynomials.These labels can be simplified by numerous numerical approximation methods.Those LTSs that can not apply failures semantics equivalence in description and verification may have a chance after using approximation on labels.The technique that combines approximation and failures semantics equivalence effectively alleviates the computational complexity and minimizes LTS.

Approximate Private Quantum Channels on Fermionic Gaussian Systems

The private quantum channel (PQC) maps any quantum state to the maximally mixed state for the discrete as well as the bosonic Gaussian quantum systems, and it has fundamental meaning on the quantum cryptographic tasks and the quantum channel capacity problems. In this paper, we primally introduce a notion of approximate private quantum channel (ε-PQC) on fermionic Gaussian systems (i.e., ε-FPQC), and construct its explicit form of the fermionic (Gaussian) private quantum channel. First of all, we suggest a general structure for ε-FPQC on the fermionic Gaussian systems with respect to the Schatten p-norm class, and then we give an explicit proof of the statement in the trace norm case. In addition, we study that the cardinality of a set of fermionic unitary operators agrees on the ε-FPQC condition in the trace norm case. This result may give birth to intuition on the construction of emerging fermionic Gaussian quantum communication or computing systems.

Vector Approximate Message Passing with Sparse Bayesian Learning for Gaussian Mixture Prior

Compressed sensing(CS)aims for seeking appropriate algorithms to recover a sparse vector from noisy linear observations.Currently,various Bayesian-based algorithms such as sparse Bayesian learning(SBL)and approximate message passing(AMP)based algorithms have been proposed.For SBL,it has accurate performance with robustness while its computational complexity is high due to matrix inversion.For AMP,its performance is guaranteed by the severe restriction of the measurement matrix,which limits its application in solving CS problem.To overcome the drawbacks of the above algorithms,in this paper,we present a low complexity algorithm for the single linear model that incorporates the vector AMP(VAMP)into the SBL structure with expectation maximization(EM).Specifically,we apply the variance auto-tuning into the VAMP to implement the E step in SBL,which decrease the iterations that require to converge compared with VAMP-EM algorithm when using a Gaussian mixture(GM)prior.Simulation results show that the proposed algorithm has better performance with high robustness under various cases of difficult measurement matrices.