Search Results (42)

Many dynamic systems experience unwanted actuation caused by an unknown exogenous input. Typically, when these exogenous inputs are stochastically bounded and a basis set cannot be identified, a Kalman-like estimator may suffice for state estimation, provided there is minimal uncertainty regarding the true system dynamics. However, such exogenous inputs can encompass environmental factors that constrain and influence system dynamics and overall performance. These environmental factors can modify the system’s internal interactions and constitutive constants. The proposed control scheme examines the case where the true system’s plant changes due to environmental or health factors while being actuated by stochastic variances. This approach updates the reference model by utilizing the input and output of the true system. Lyapunov stability analysis guarantees that both internal and external error states will converge to a neighborhood around zero asymptotically, provided the assumptions and constraints of the proof are satisfied. Full article

The classical exponential model, despite its flexibility, fails to describe data with non-constant failure or between-event dependency. To overcome this limitation, two new bivariate lifetime distributions are introduced in this paper. The Farlie–Gumbel–Morgenstern (FGM)-based and Ali–Mikhail–Haq (AMH)-based modified Fréchet–exponential (MFE) models, by embedding the flexible MEF margin in the FGM and AMH copulas. The resulting distributions accommodate a wide range of positive or negative dependence while retaining analytical traceability. Closed-form expressions for the joint and marginal density, survival, hazard, and reliability functions are derived, together with product moments and moment-generating functions. Unknown parameters are estimated through the maximum likelihood estimation (MLE) and inference functions for margins (IFM) methods, with asymptotic confidence intervals provided for these parameters. An extensive Monte Carlo simulation quantifies the bias, mean squared error, and interval coverage, indicating that IFM retains efficiency while reducing computational complexity for moderate sample sizes. The models are validated using two real datasets, from the medical sector regarding the infection recurrence times of 30 kidney patients undergoing peritoneal dialysis, and from the economic sector regarding the growth of the gross domestic product (GDP). Overall, the proposed copula-linked MFE distributions provide a powerful and economical framework for survival analysis, reliability, and economic studies. Full article

The main goal of this paper is to study Jarratt-like iterative methods to obtain their order of convergence under weaker conditions. Generally, obtaining the $p^{th}$-order convergence using the Taylor series expansion technique needed at least $p+1$ times differentiability of the involved operator. However, we obtain the fourth- and sixth-order for Jarratt-like methods using up to the third-order derivatives only. An upper bound for the asymptotic error constant (AEC) and a convergence ball are provided. The convergence analysis is developed in the more general setting of Banach spaces and relies on Lipschitz-type conditions, which are required to control the derivative. The results obtained are examined using numerical examples, and some dynamical system concepts are discussed for a better understanding of convergence ideas. Full article

This study advances the theory of power-law fluid infiltration grouting by developing spherical and columnar diffusion models rooted in fractal porous media theory and power-law rheological equations. An analytical solution for determining the slurry diffusion radius is derived and validated through laboratory experiments and numerical simulations. Key findings include the following: (1) The fractal permeability constant demonstrates an exponential dependence on the rheological index (n), with a critical threshold at n = 0.4. Below this threshold, the constant asymptotically approaches zero (slope < 0.1), while beyond it, sensitivity intensifies exponentially, attaining 0.48 at n = 0.9. (2) Non-linear positive correlations exist between the slurry diffusion radius and both the grouting pressure (P) and the water–cement ratio (W/C). Spherical diffusion dominates over columnar diffusion, with their ratio shifting from 1:0.96 at P = 0.1 MPa to 1:0.82 at P = 0.5 MPa. The diffusion distance differential increases from 22 mm to 38 mm as the W/C rises from 0.5 to 0.7, attributable to reduced interfacial shear resistance from decreasing slurry viscosity and yield stress. (3) Experimental validation confirms exponentially decaying model errors: spherical grouting errors decrease from 21.54% (t = 5 s) to 8.43% (t = 15 s) and columnar errors from 25.45% to 10.17%, both within the 50% engineering tolerance. (4) Numerical simulations show that the meander fractal dimension (48 mm) demonstrates a higher sensitivity than the volume fractal dimension (37 mm), with both dimensions reaching maximum values. These findings establish a theoretical framework for optimizing grouting design in heterogeneous porous media. Full article

The isotropic Cauchy distribution is a member of the central $\alpha$-stable family that plays a role in the set of heavy-tailed distributions similar to that of the Gaussian density among finite second-moment laws. Given a sequence of n observations, we are interested in characterizing the performance of Likelihood Ratio Tests, where two hypotheses are plausible for the observed quantities: either isotropic Cauchy or isotropic Gaussian. Under various setups, we show that the probability of error of such detectors is not always exponentially decaying with n, with the leading term in the exponent shown to be logarithmic instead, and we determine the constants in that leading term. Perhaps surprisingly, the optimal Bayesian probabilities of error are found to exhibit different asymptotic behaviors. Full article

This study conducted dynamic triaxial tests on a typical poured asphalt concrete material of core walls in Xinjiang, exploring the dynamic characteristics of poured asphalt concrete under various confining pressures, principal stress ratios, and vibration frequencies. On this basis, the dynamic constitutive relationship of poured asphalt concrete was investigated using the Hardin–Drnevich model. The results indicate that under different confining pressures, principal stress ratios, and vibration frequencies, the variation patterns of the backbone lines of dynamic stress-strain of poured asphalt concrete are basically identical, consistent with a hyperbolic curve. The confining pressure and principal stress ratio significantly affect the backbone line of dynamic stress-strain. By comparison, frequency has a minimal effect. The changing trends of dynamic elasticity modulus and damping ratio of poured asphalt concrete under various factors are almost the same. When the material has high dynamic stress and strain, the hysteresis loop is large. When the curve of the damping ratio becomes flat, the asymptotic constant can be used as the maximum damping ratio. The relationship between the reciprocal of the dynamic elasticity modulus and the dynamic strain of poured asphalt concrete exhibits a linear distribution. Under different ratios of confining pressure to principal stress, there are large discrepancies between the calculated values from the formula and the experimental fitting values of the maximum dynamic elasticity modulus, and the maximum relative errors reach 16.65% and 18.15%, respectively. Therefore, the expression for the maximum dynamic elasticity modulus was modified, and the calculated values using the modified formula were compared with the experimental fitting values. The relative errors are significantly reduced, and the maximum relative errors are 3.02% and 2.04%, respectively, in good agreement with the fitting values of the experimental data. The findings of this article render a theoretical basis and reference for the promotion and application of poured asphalt concrete. Full article

This paper explores the inference for a constant-stress accelerated life test under a ranked set sampling scenario. When the lifetime of products follows the Fréchet distribution, and the failure times are collected under a maximum ranked set sampling with unequal samples, classical and Bayesian approaches are proposed, respectively. Maximum likelihood estimators along with the existence and uniqueness of model parameters are established, and the corresponding asymptotic confidence intervals are constructed based on asymptotic theory. Under squared error loss, Bayesian estimation and highest posterior density confidence intervals are provided, and an associated Monte-Carlo sampling algorithm is proposed for complex posterior computation. Finally, extensive simulation studies are conducted to demonstrate the performance of different methods, and a real-data example is also presented for applications. Full article

This paper deals with the possibilities of ground-penetrating radar (GPR)-based quality control testing, which was demonstrated on an experimental road section of a ~220–240 m long Hungarian residential street. The measurements and their assessment aimed to control the prescribed compactness and air void content of newly built asphalt layers. Research has discussed the relationship between the air void content and the dielectric constant of asphalt layers, and provided empirical results for this relationship. We suggest a new logistic model with lower and upper asymptotes instead of the exponential formula often used in the literature. Contrary to this newly developed robust model, existing models are sensitive to extreme dielectric constant values due to the mathematical nature of their exponential function. The results of the new logistic model are compared to those of the Hoegh–Dai (HD) and Minnesota Department of Transportation (MnDOT) models on the basis of a few calibration data points. Through systematic data collection and analysis, the developed robust empirical model demonstrates a significant correlation between the relative permittivity and air void content in asphalt mixes, enabling accurate estimation of the air void content within a ±0.5% margin of error. The air void content can be applied to estimate the asphalt layer modulus. The developed model can be further exploited by utilizing a combination of GPR and drone technology. The “symbiosis” of these technologies can lead to a totally non-destructive imaging system, which can then be applied to environmental monitoring of roads and their surroundings in terms of quality control of asphalt compaction work and the hot asphalt mix behind the compaction roller during pavement construction. Full article

Monitoring life-testing trials for a product or substance often demands significant time and effort. To expedite this process, sometimes units are subjected to more severe conditions in what is known as accelerated life tests. This paper is dedicated to addressing the challenge of estimating the power hazard distribution, both in terms of point and interval estimations, during constant- stress partially accelerated life tests using progressive first failure censored samples. Three techniques are employed for this purpose: maximum likelihood, two parametric bootstraps, and Bayesian methods. These techniques yield point estimates for unknown parameters and the acceleration factor. Additionally, we construct approximate confidence intervals and highest posterior density credible intervals for both the parameters and acceleration factor. The former relies on the asymptotic distribution of maximum likelihood estimators, while the latter employs the Markov chain Monte Carlo technique and focuses on the squared error loss function. To assess the effectiveness of these estimation methods and compare the performance of their respective confidence intervals, a simulation study is conducted. Finally, we validate these inference techniques using real-life engineering data. Full article

In recent years, queuing systems with batch service are emerging as powerful and flexible mathematical models in different frameworks. In this paper, we consider a single server queuing system with Poissonian arrivals, infinite buffers, and a constant batch size b. This paper addresses a little-studied optimization problem, namely the existence of an optimal arrival rate that minimizes the average sojourn time. Unlike the classical $M/M/1$ queue, for any batch size b, the problem admits a non-trivial solution that can be found by solving a polynomial equation of degree $b+1$. Since, in general, only numerical solutions are available, a simple first-order approximation is also derived and the corresponding deviations (in terms of input rate and sojourn time) are calculated. In more detail, it is shown that the approximation improves as the batch size increases and, in any case, the relative error for the average sojourn time is less than 0.34%. Finally, the paper provides new theoretical results about the asymptotic service rate in the equivalent birth–death process, highlighting how it depends on all queue parameters. Full article

The closed-loop constant pressure drop control valve is widely used in aero-engine fuel servo metering systems. However, the available constant pressure drop control valve cannot realize servo tracking without static error and, often, a high proportional gain is used to reduce the static error and improve the servo tracking performance, which reduces the stability margin. In this paper, an integral constant pressure drop control valve is designed, which consists of an integral controller and a stabilizing controller. Moreover, a robust LQR design method is proposed to complete the design task. Firstly, the controlled plant’s state–space model is derived, and the augmented model with tracking error is established based on the robust servo system design theory. Secondly, a servo controller with dual functions of integral control and stabilization control is constructed and decoupled, in which the stabilizing controller guarantees the asymptotic stability as well as the anti-disturbance performance, and the integral controller realizes the servo tracking without static error. Finally, based on the robust LQR design method, two key design parameters, including the integral control gain and the stabilization control gain, are designed to complete the design task. The simulation results indicate that, even when suffering 50 mm² metered flow area step disturbance and 1 MPa inlet pressure step change, the designed integral constant pressure drop control valve can realize the function of servo tracking without static error. The static error is almost 0, the settling time is within 0.01 s, the overshoot is within 10%, and the phase margin is more than 55°. Full article

In this article, a novel systematic approach is proposed for a partial sliding mode controller (SMC) design and tuning in non-minimum phase switch-mode power supplies (SMPS). To achieve a more simplified controller in comparison with the conventional SMCs, the partial SMC (PSMC) is introduced in this article, which just requires a part of the sliding surface for controller formulation. The accuracy of the developed PSMC is proved mathematically within the entire range of operation. Since the control parameters of the PSMC are not selected by trial and error, it can maintain the stability and robustness of the closed-loop system in a broad operational range. In this regard, and to develop a systematic approach for robust control of SMPS, a constant frequency equivalent SMC is designed using the converter nominal parameters. Then, the extracted controller is combined with an adaptive component to ensure asymptotical stability against load and line changes. Considering the Lyapunov stability criteria for nonlinear systems, it is proved that the presented SPMC can be used for output voltage regulation in both discontinuous and continuous operating modes with zero steady state error. To avoid the trial and error method during the controller tuning and parameters selection, the system characteristic equation is extracted using the Jacobian approach. Considering the roots of the characteristic equation and the stable range of the closed-loop system, the controller parameters are tuned. Furthermore, in addition to simulation, the developed approach is evaluated practically using the TMS3220F2810 digital signal processor. It is shown that the dynamic response of the proposed approach is faster than the standard double-loop SMC during load and line changes. Additionally, it is seen that the developed controller is robust against model changes in both continuous and discontinuous operations. Full article

Approximating quantiles and distributions over streaming data has been studied for roughly two decades now. Recently, Karnin, Lang, and Liberty proposed the first asymptotically optimal algorithm for doing so. This manuscript complements their theoretical result by providing a practical variants of their algorithm with improved constants. For a given sketch size, our techniques provably reduce the upper bound on the sketch error by a factor of two. These improvements are verified experimentally. Our modified quantile sketch improves the latency as well by reducing the worst-case update time from $O\left(\frac{1}{\epsilon }\right)$ down to $O(log\frac{1}{\epsilon })$. Full article

The constant pressure difference regulating mechanism is widely used in aeroengine fuel servo metering systems, and it almost decides the metering precision. However, the design theory and design method of the available constant pressure difference regulating mechanism are unclear, and it is difficult to follow the high stability, high accuracy, and high robustness requirements of the modern aeroengine fuel servo metering system. In this paper, the design theory of the constant pressure difference regulating mechanism is revealed, and it indicates that it consists of two basic control units: a state feedback stabilization controller to ensure the asymptotic stability and disturbance rejection performance; and a servo and feed-forward compensator to ensure the asymptotic tracking ability. In addition, based on the frequency domain analysis method, the decisive influences about the control gains of the two control units on the dynamic performance and stability are analyzed. On this basis, a frequency domain design method of the two core control gains is proposed to complete the design task of the closed-loop system. The simulation results show that, under the adverse conditions of 1 MPa strong step disturbance of the inlet pressure and 50 mm² strong step disturbance of the variable inlet flow area, the steady-state working range of the controlled pressure difference meets 0.92 ± 0.01 MPa, the steady-state error is not more than 1%, the regulation time is not more than 0.01 s, the dynamic overshoot is not more than 10%, and the designed phase margin is more than 70°. Full article

Uniform error estimates with power-type asymptotic constants of the finite element method for the unsteady Navier–Stokes equations are deduced in this paper. By introducing an iterative scheme and studying its convergence, we firstly derive that the solution of the Navier–Stokes equations is bounded by power-type constants, where we avoid applying the Gronwall lemma, which generates exponential-type factors. Then, the technique is extended to the error estimate of the long-time finite element approximation. The analyses show that, under some assumptions on the given data, the asymptotic constants in the finite element error estimates for the unsteady Navier–Stokes equations are uniformly power functions with respect to the initial data, the viscosity, and the body force for all time $t>0$. Finally, some numerical examples are shown to verify the theoretical predictions. Full article