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In this paper, we provide an optimization design for a step‐stress accelerated life test (ALT) with two stress variables when the lifespan of test units is assumed to follow the inverse Weibull (IW) distribution. We first utilize progressive type‐I censoring and accelerated life testing to shorten the time and reduce cost of testing and then adopt a cumulative exposure (CE) model to look at the impact of varying stress levels. A log‐linear relationship between the scale parameter of the IW distribution and stress has been postulated. We obtain the maximum likelihood estimators and Bayes estimators of the unknown model parameters. Under normal operating conditions, we design an optimal test plan via minimizing the asymptotic variance (AV) of the percentile life. We carry out simulation studies to illustrate the performance and optimality of the proposed model. Finally, a real‐life data is analyzed for illustrative purposes. [ABSTRACT FROM AUTHOR]

In this paper, a reduced-order interval observer (R-IO) design technique is developed for continuous-time descriptor linear-parameter-varying systems with unknown-but-bounded uncertainties. First, by introducing an intermediate variable, the R-IO design amounts to estimating the linear functional of the system states. Then, with a parameter-dependent Luenberger-like structure, the R-IO existence condition is eventually formulated into a set of differential-algebraic equations, not involving any linear transformation process. Further, a parametric solution to such an R-IO is derived through solving the equation set, which clearly shows the design degrees of freedom. Finally, the correctness of the proposed results is verified by a numerical system and an electrical circuit system. [ABSTRACT FROM AUTHOR]

Copyright of Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales is the property of Academia Colombiana de Ciencias Exactas, Fisicas y Naturales and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In order to achieve accurate and reliable prediction of the dissolved oxygen in ponds and mitigate aquaculture risks, we propose a predictive model based on Feature Construction (FC) pretreatment and Temporal Convolutional Network (TCN) coupled with Bidirectional Gate Recurrent Unit (BiGRU). By constructing statistical features, environmental factor features and seasonal features from the samples, deep-level correlations between variables are explored. Then, the structural feature sequences are processed using multiple layers of convolution and dimensionality reduction through TCN, while preserving the global temporal characteristics and removing redundant information. By integrating BiGRU to model the reduced features, accurate prediction of dissolved oxygen levels is achieved. Furthermore, the Sand Cat Swarm Optimization (SCSO) algorithm is employed to optimize the non-parametric Kernel Density Estimation (KDE) for estimating the distribution range of dissolved oxygen prediction errors. The experimental results indicate that the proposed model achieves superior performance compared to other comparative models, with respective values of 0.027 5 for Mean Squared Error (MSE), 0.143 2 for Mean Absolute Error (MAE), 0.165 8 for Root Mean Squared Error (RMSE), and 0.94 for the Coefficient of Determination (R²). Meanwhile, the interval estimation effectively covers the fluctuation range of dissolved oxygen, thereby quantifying the uncertainty in the prediction process. In the short-term prediction of dissolved oxygen levels in ponds, this model demonstrates notable accuracy and robustness. It is instructive for water quality monitoring in aquaculture and the enhancement of farming efficiency. [ABSTRACT FROM AUTHOR]

The point-biserial correlation is a commonly used measure of effect size in two-group designs. New estimators of point-biserial correlation are derived from different forms of a standardized mean difference. Point-biserial correlations are defined for designs with either fixed or random group sample sizes and can accommodate unequal variances. Confidence intervals and standard errors for the point-biserial correlation estimators are derived from the sampling distributions for pooled-variance and separate-variance versions of a standardized mean difference. The proposed point-biserial confidence intervals can be used to conduct directional two-sided tests, equivalence tests, directional non-equivalence tests, and non-inferiority tests. A confidence interval for an average point-biserial correlation in meta-analysis applications performs substantially better than the currently used methods. Sample size formulas for estimating a point-biserial correlation with desired precision and testing a point-biserial correlation with desired power are proposed. R functions are provided that can be used to compute the proposed confidence intervals and sample size formulas.

To solve the problems of complex calculation and weak applicability of the traditional interval estimation methods such as Weibull distribution with the different parameters, a simple interval estimation method suitable to the conditions of multi-parameters was proposed. Through the expression of Weibull distribution, the pivotal-variable obeying chi-square distribution was obtained and the degrees of freedom were modified. Combined with the point estimation results from maximum likelihood estimation and the empirical estimation shape parameter in the Weibull distribution, the interval estimation method of two parameters in Weibull distribution was established. The confidence of proposed interval estimation method was verified by Monte Carlo simulation, and the applicability of the method on different parameters was also analyzed. Furthermore, comparisons with the results computed from traditional least square and maximum likelihood estimation methods were carried out by using simulation. Simulation results indicated that the modified pivotal-variable method has simple calculation process and small deviation from predefined nominal confidence with the different parameters. Therefore, it can be concluded that proposed method executes the more effective estimation than the traditional methods.

High maintenance costs and safety risks due to lithium-ion battery degeneration have significantly and seriously restricted the application potential of batteries. Thus, this paper proposes an efficient calculation approach for state of health (SOH) estimation in lithium-ion batteries that can be implemented in battery management system (BMS) hardware. First, from the variables of the charge profile, only the complete voltage data is taken as the input to represent the complete aging characteristics of the batteries while limiting the computational complexity. Then, this paper combines the light gradient boosting machine (LightGBM) and weighted quantile regression (WQR) methods to learn a nonlinear mapping between the measurable characteristics and the SOH. A confidence interval is applied to quantify the uncertainty of the SOH estimate, and the model is called LightGBM-WQR. Finally, two public datasets are employed to verify the proposed approach. The proposed LightGBM-WQR model achieves high accuracy in its SOH estimation, and the average absolute error (MAE) of all cells is limited to 1.57%. In addition, the average computation time of the model is less than 0.8 ms for ten runs. This work shows that the model is effective and rapid in its SOH estimation. The SOH estimation model has also been tested on the edge computing module as a possible innovation to replace the BMS bearer computing function, which provides tentative solutions for online practical applications such as energy storage systems and electric vehicles. [ABSTRACT FROM AUTHOR]

Using the augmented Dickey-Fuller test to verify the existence of a unit root in an autoregressive process often requires the correctly specified intercept, since the test statistics can be distinctive under different model specifications and lead to contradictory results at times. In this article, we develop a unified inference that not only unifies the specifications of the intercept but also accommodates different degrees of persistence of the underlying process and heteroscedastic errors. A simulation study shows that the resulting unified unit root test exhibits excellent size control and reasonably good power. In an empirical application, we implement the proposed test to re-examine the presence of unit roots within eleven widely used variables in stock return predictability. [ABSTRACT FROM AUTHOR]

This paper is an attempt to study the Xgamma–Weibull distribution using an adaptive progressive type-II censoring plan. This scheme effectively ensures that the experimental time does not exceed a predetermined time limit. Using two classical estimation methods—namely, maximum likelihood and maximum product of spacing—both point and interval estimations for the unknown model parameters, as well as some parameters of life—namely, reliability and hazard rate functions—were obtained. The asymptotic normality of both classical methods was used to determine the approximate confidence intervals for the various parameters. Based on the two conventional methodologies, Bayesian estimations were also investigated using the MCMC technique under the squared error loss function. In addition, the credible intervals of the different parameters were also obtained. To compare the performance of the various approaches, a thorough simulation study was carried out. Furthermore, we propose using several optimality criteria to select the best sampling technique. Finally, two real-world datasets were used to demonstrate how the suggested estimators and optimality criteria operate in real-world circumstances. [ABSTRACT FROM AUTHOR]

Generalized logistic distribution, as the generalized form of the symmetric logistic distribution, plays an important role in reliability analysis. This article focuses on the statistical inference for the stress–strength parameter R = P (Y < X) of the generalized logistic distribution with the same and different scale parameters. Firstly, we use the frequentist method to construct asymptotic confidence intervals, and adopt the generalized inference method for constructing the generalized point estimators as well as the generalized confidence intervals. Then the generalized fiducial method is applied to construct the fiducial point estimators and the fiducial confidence intervals. Simulation results demonstrate that the generalized fiducial method outperforms other methods in terms of the mean square error, average length, and empirical coverage. Finally, three real datasets are used to illustrate the proposed methods. [ABSTRACT FROM AUTHOR]

In a number of real-world situations, one encounters count data with over-dispersion such that the typical Poisson distribution does not suit the data. In the current situation, it is appropriate to employ a combination of mixed Poisson and Poisson-Sujatha (PS) distributions. The PS distribution has been investigated for count data, which is of primary interest to a number of disciplines, including biology, medicine, demography, and agriculture. However, no research has been conducted regarding generating bootstrap confidence intervals for its parameter. The coverage probabilities and average lengths of bootstrap confidence intervals derived from the percentile, basic, and biasedcorrected and accelerated bootstrap methods were compared using Monte Carlo simulation. The results indicated that it was impossible to achieve the nominal confidence level using bootstrap confidence intervals for tiny sample sizes, regardless of the other settings. Furthermore, when the sample size was large, there was not much of a difference in the performance of the several bootstrap confidence intervals. The biascorrected and accelerated bootstrap confidence interval demonstrated superior performance compared to the other methods in all of the cases examined. Moreover, the effectiveness of the bootstrap confidence intervals was proven through their application to agricultural data sets. The calculations offer significant evidence in favor of the suggested bootstrap confidence intervals. [ABSTRACT FROM AUTHOR]

This paper concerns state and fault simultaneous interval estimations for discrete-time linear systems with unknown but bounded uncertainties. Unlike most existing works on interval estimation, the system considered in this work is subject to actuator and sensor faults, while bounded uncertainties exist in both components. Thus, the method developed in this paper can be used for more general conditions. First, the considered system is reformulated as a descriptor one through the augmented vector method. An important lemma for descriptor systems is given in a more accurate description and proven in a very simple way. Then, by using the reachability analysis technique, a new proportional-integral observer-based interval estimation method is proposed. The H∞ technique reduces the influences of time-varying actuator faults and uncertainties. To build the zonotope of bounded uncertainties in the residual system, an equivalent description is introduced. Finally, a numerical example and an industrial system are simulated to demonstrate the efficacy and applicability of the developed method. [ABSTRACT FROM AUTHOR]

This paper presents a first-order integer-valued autoregressive time series model featuring observation-driven parameters that may adhere to a particular random distribution. We derive the ergodicity of the model as well as the theoretical properties of point estimation, interval estimation, and parameter testing. The properties are verified through numerical simulations. Lastly, we demonstrate the application of this model using real-world datasets. [ABSTRACT FROM AUTHOR]

The uncertain vector autoregressive model is able to model the interrelationships between different variables, which is more advantageous compared to the traditional autoregressive model, when modeling real-life objects and where the observed values are imprecise. In this paper, the parameters of the uncertain vector autoregressive model are estimated by using least absolute deviation estimation (LAD) to obtain a fitted uncertain vector autoregressive model, and residual analysis is performed to obtain estimates of expected values and variances of the residuals. In addition, future values are modeled by using forecasting methods, i.e., point estimation and interval estimation. The order of the uncertain vector autoregressive model is also determined by the indicator summation of test errors (STE) in the cross-validation, and we also analyze that the least absolute deviation estimation outperforms the least squares estimation method in the presence of outliers. [ABSTRACT FROM AUTHOR]

This note is concerned with evaluation of location parameters for polytomous items in multiple-component measuring instruments. A point and interval estimation procedure for these parameters is outlined that is developed within the framework of latent variable modeling. The method permits educational, behavioral, biomedical, and marketing researchers to quantify important aspects of the functioning of items with ordered multiple response options, which follow the popular graded response model. The procedure is routinely and readily applicable in empirical studies using widely circulated software and is illustrated with empirical data. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Mechanical Strength / Jixie Qiangdu is the property of Zhengzhou Research Institute of Mechanical Engineering and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper is concerned with the interval estimation issue for switched systems subject to the bounded noise signal and disturbance signal. By virtue of the positiveness feature of the interval estimation error dynamics, the multiple co‐positive Lyapunov functions strategy is presented to build the interval estimators for the switched linear systems under the dwell‐time dependent switching signal. A new criterion is driven to ensure the boundedness of the interval estimation errors. This criterion can be checked by linear programming technique. In the end, a beneficial application of estimating the speeds of an engine model is offered to verify the estimation performances of the established interval estimation technique. [ABSTRACT FROM AUTHOR]

A common method of testing the reasonableness of estimates of unknown parameters in uncertain differential equations is to judge them by the α -path of the differential equation. If all observations fall between the α -paths, the estimates are considered reasonable. This paper introduces uncertain hypothesis testing into uncertain differential equations to test the reasonableness of the estimates, which is another new approach. Further, the concept of interval estimation of unknown parameters for uncertain differential equations is introduced. Some numerical examples are given to verify the feasibility of the method. The uncertain differential equations are also used to model global average temperature data, and the results are satisfactory. [ABSTRACT FROM AUTHOR]

This article investigates the reduced‐order interval observer (R‐IO) design technique for continuous‐time linear systems with unknown external disturbances and measurement noises. First, we propose a coupled R‐IO structure with more design degrees of freedom, and it can be directly applied not only to solve the difficulty of the error system cooperativity construction but to relax the constraint on the sensor measurement noises. Second, the R‐IO existence condition is derived as a set of matrix equations (MEs), and a complete solution, explicitly showing the available design parameters, to such an R‐IO is further obtained by solving the MEs. Third, using the solution, an integrated optimization indicator of the R‐IO performance is built as the valid selection mechanism of these parameters. Finally, the efficiency of the obtained results is illustrated through a numerical example and a practical example. [ABSTRACT FROM AUTHOR]

The Weibull distribution has been widely used to model strength properties of brittle materials. Estimation of confidence intervals for Weibull shape parameter has been an important concern, since small sample sizes in materials science experiments bring about large intervals. Many methods have been proposed in the literature for constructing shorter intervals; the methods of maximum likelihood, least square, and Menon are among the most extensively studied methods. However, they all use an equal-tails approach. The pivotal quantities used for constructing confidence intervals have right-skewed and unimodal distributions, thus, they clearly do not produce the shortest intervals for a given confidence level in equal tail form. This study constructs the shortest confidence intervals for the three aforementioned methods and compares their performances by their equal-tails counterparts. To this end, a comprehensive simulation study has been conducted for the shape parameter values between 1 to 80 and the sample sizes between 3 to 20. The comparison criterion is chosen as the expected interval length. The results show that the shortest confidence intervals in each of three methods have yielded considerably narrower intervals. Further, the unknown parameter values are more centered in these intervals. [ABSTRACT FROM AUTHOR]

The uniformly most accurate (UMA) is an important optimal approach in interval estimation, but the current literature often introduces it in a confusing way, rendering the learning, teaching and researching of UMA problematic. Two major aspects cause this confusion. First, UMA is often interpreted to maximize the accuracy of coverage, but in fact, it minimizes the falseness of coverage. Second, even though it is a major concept in interval estimation, the most common proof of UMA requires the result of the uniformly most powerful (UMP) test, which has nothing to do with the rest of the interval estimation concept. To resolve these issues, in this article we propose a new method of introducing UMA that aligns its terminology with its definition and proves it entirely within the concept of confidence interval, independent to the knowledge of hypothesis testing. The new method eliminates the aforementioned confusion and allows for a smoother learning, teaching and research experience in UMA. [ABSTRACT FROM AUTHOR]

In this paper, we provide a framework to achieve interval estimation for nabla Caputo fractional order linear time-invariant (LTI) systems in the presence of bounded model uncertainties. Interval observers based on fractional order positive systems theory are designed by possessing desired stable and positive error dynamics. Specifically, the basic concepts and conditions for guaranteeing stability and positivity of the considered systems are derived systematically by finding the system responses. Using the developed criteria and the structure of Luenberger-type observers, a classic interval observer is designed directly which further extends the system classes of interval estimation. Besides, due to the possible absence of a gain matrix which ensures positivity requirement, a more general interval observer design scheme is given by exploiting the coordinate transformation technique. Finally, some simulated cases including fault detection and fractional order circuits related scenarios are developed to validate the usefulness and practicality of the framework. [ABSTRACT FROM AUTHOR]

The fiducial inference idea was firstly proposed by Fisher as a powerful method in statistical inference. Many authors such as Weeranhandi and Hannig et. al. improved this method from different points of view. Since the Bayesian method has some deficiencies such as assuming a prior distribution when there was little or no information about the parameters, the fiducial inference is used to overcome these adversities. This study deals with the generalized fiducial inference for the shape parameters of the Chen’s two-parameter lifetime distribution with bathtub shape or increasing failure rate . The method based on the inverse of the structural equation which is proposed by Hannig et. al. is used. We propose the generalized fiducial inferences of the parameters with their confidence intervals. Then, these estimations are compared with their maximum likelihood and Bayesian estimations. Simulation results show that the generalized fiducial inference is more applicable than the other methods in terms of the performances of estimators for the shape parameters of the Chen distribution. Finally, a real data example is used to illustrate the theoretical outcomes of these estimation procedures. [ABSTRACT FROM AUTHOR]

Difficulties in both duration and beat-based time perception are common in individuals with dyslexia (DD). It is also known that internalised beat cues may aid in duration processing. This study investigated whether the difficulties in duration processing among DD stem from their inability to utilise internal beat cues. Participants with and without dyslexia estimated intervals ranging from 500 ms to 10 s. In the beat cue condition, participants listened to a sequence of 500 ms beats before the interval, and in the no beat cue condition, they were exposed to silence while EEG was recorded. Interestingly, the two groups did not differ in duration estimation performance, but they did differ in their utilisation of beat cues, with DD showing less sensitivity to these, whether the impact was negative (cues before shorter intervals) or positive (before longer intervals). Brainwave entrainment to the target frequency was significantly higher compared with entrainment to a non-target frequency, and cross-group differences were null. Our findings suggest that DD may have difficulties either in retaining the beat when it is no longer audible, or in using the internalised beat for duration estimation. Nevertheless, they can achieve comparable accuracy to neurotypical adults, possibly through compensatory strategies., (© 2025 The Author(s). Dyslexia published by John Wiley & Sons Ltd.)

A new method integrating techniques of copula and interval estimation to estimate multi-source water supply was proposed. Using the copula theory, joint probability distributions of multiple water sources were constructed for the estimation of water supply. In addition, the interval estimation was used to obtain the interval of water supply under uncertainty for the formulation of water-diversion strategies and the efficient allocation of water resources. This method can give an in-depth investigation on correlations and synchronous–asynchronous characteristics of runoff variations for multiple water sources, thus solving the uncertainty problem of water supply. To demonstrate its applicability, the method was applied to a case study in the Xiong’an New Area, a future metropolis in North China. The results showed that log-normal distributions for the marginal distributions of source 2 (i.e., the Water Diversion Project from the Yellow River to Baiyangdian Lake) and source 3 (i.e., the South-to-North Water Diversion Project) were feasible. The combined channel source, composed of source 2 and source 3, provided [5.20, 12.10] × 108 m3, and reservoir source provided [0.76, 3.60] × 108 m³ of water resources to the Xiong’an New Area per year. Furthermore, without the implementation of multi-source combined water supply pattern in the Xiong’an New Area, there would be a large water supply deficit. This research can provide effective practical suggestions and guidance on water-resource planning and management.

We focus on the construction of confidence intervals for the ratios of medians of two independent, log-normal distributions based on the normal approximation (NA) approach, the method of variance estimate recovery (MOVER), and the generalized confidence interval (GCI) approach. We also compare the performance of the three confidence intervals in terms of the coverage probabilities, and average lengths, using Monte Carlo simulations. The results show that the GCI confidence interval is generally preferred in terms of coverage probabilities; however, the average length for the GCI is always wider than for other approaches. The NA and MOVER approaches could be recommended on the basis of the specific values of μ i , σ i 2 and/or sample sizes. The confidence intervals are illustrated using real data examples. [ABSTRACT FROM AUTHOR]

Interval estimation is one of the most frequently used methods in statistical science, employed to provide a range of credible values a parameter is located in after taking into account the uncertainty in the data. However, while this interpretation only holds for Bayesian interval estimates, these suffer from two problems. First, Bayesian interval estimates can include values which have not been corroborated by observing the data. Second, Bayesian interval estimates and hypothesis tests can yield contradictory conclusions. In this paper a new theory for Bayesian hypothesis testing and interval estimation is presented. A new interval estimate is proposed, the Bayesian evidence interval, which is inspired by the Pereira–Stern theory of the full Bayesian significance test (FBST). It is shown that the evidence interval is a generalization of existing Bayesian interval estimates, that it solves the problems of standard Bayesian interval estimates and that it unifies Bayesian hypothesis testing and parameter estimation. The Bayesian evidence value is introduced, which quantifies the evidence for the (interval) null and alternative hypothesis. Based on the evidence interval and the evidence value, the (full) Bayesian evidence test (FBET) is proposed as a new, model‐independent Bayesian hypothesis test. Additionally, a decision rule for hypothesis testing is derived which shows the relationship to a widely used decision rule based on the region of practical equivalence and Bayesian highest posterior density intervals and to the e‐value in the FBST. In summary, the proposed method is universally applicable, computationally efficient, and while the evidence interval can be seen as an extension of existing Bayesian interval estimates, the FBET is a generalization of the FBST and contains it as a special case. Together, the theory developed provides a unification of Bayesian hypothesis testing and interval estimation and is made available in the R package fbst. [ABSTRACT FROM AUTHOR]

A guaranteed fault-estimation algorithm based on interval set inversion observer filtering is proposed for linear discrete-time systems with unknown but bounded disturbance and noise. The minimal conservative interval observer is designed by minimizing the F-norm of the state error. Vector Boolean operations and dimensional operations are used to develop a new interval set inversion algorithm to further contract the guaranteed interval estimation results of the observer. The computational complexity, memory requirements, and accuracy of the proposed algorithm are also analyzed. Finally, simulation examples are provided to verify the efficiency and practicability of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This study aims to investigate the estimation problems when the parent distribution of the population under consideration is the Nadarajah–Haghighi distribution in the presence of an adaptive progressive Type-II hybrid censoring scheme. Two approaches are considered in this regard, namely, the maximum likelihood and Bayesian estimation methods. From the classical point of view, the maximum likelihood estimates of the unknown parameters, reliability, and hazard rate functions are obtained as well as the associated approximate confidence intervals. On the other hand, the Bayes estimates are obtained based on symmetric and asymmetric loss functions. The Bayes point estimates and the highest posterior density Bayes credible intervals are computed using the Monte Carlo Markov Chain technique. A comprehensive simulation study is implemented by proposing different scenarios for sample sizes and progressive censoring schemes. Moreover, two applications are considered by analyzing two real data sets. The outcomes of the numerical investigations show that the Bayes estimates using the general entropy loss function are preferred over the other methods. [ABSTRACT FROM AUTHOR]

This paper deals with the fault detection (FD) problem for uncertain time-delayed systems with nonlinearities satisfying incremental quadratic constraints. To begin with, an observer is designed to construct the residual system for FD purpose. Because the output disturbance is involved in the residual dynamics, this residual cannot be used for FD directly. To solve this problem, the interval estimation of the residual is introduced by using the zonotope method. Based on the interval estimation of the residual, a residual-based FD scheme is proposed. Finally, a numerical simulation example is given to verify the effectiveness. Besides, some comparisons are also made and to show the advantages of proposed method. [ABSTRACT FROM AUTHOR]

A latent variable modeling-based procedure is discussed that permits to readily point and interval estimate the design effect index in multilevel settings using widely circulated software. The method provides useful information about the relationship of important parameter standard errors when accounting for clustering effects relative to conducting single-level analyses. The approach can also be employed as an addendum to point and interval estimation of the intraclass correlation coefficient in empirical research. The discussed procedure makes it easily possible to evaluate the design effect in two-level studies by utilizing the popular latent variable modeling methodology and is illustrated with an example. [ABSTRACT FROM AUTHOR]

An interval estimation method based on the reduced-order observer and peak-to-peak analysis is proposed for continuous-time linear time-invariant systems with disturbance and measurement noise. The proposed method consists of two steps. First, a reduced-order observer with L ∞ performance is designed to obtain point estimation. Second, interval estimation is achieved by integrating the obtained point estimation and the error interval estimation by peak-to-peak analysis. Steady-state gain optimisation in terms of linear matrix inequalities is used in both steps to improve the estimation accuracy of the proposed method. The superiority of the method over the reduced-order interval observer is illustrated through numerical simulations. [ABSTRACT FROM AUTHOR]

This paper proposes a new uncertainty quantification framework for power flow (PF) and optimal power flow (OPF) considering the nonlinear correlations of uncertain power injections with limited information. The D-Vine copula is leveraged to capture the nonlinear correlations among uncertain power injections from historical data. This is further integrated with the evidence theory and the reformulated quadratic affine form to obtain PF and OPF results. The D-Vine copula and evidence theory allow one to effectively eliminate the explosive-growth joint focal elements of large-scale power system with large numbers of partial known uncertain power injections, leading to significant reduction of computing time. The reformulated quadratic affine form aims at characterizing the PF and OPF outputs with partially known uncertain power injections in a simple form based on Dempster-Shafer structure, yielding further computational efficiency improvement without the loss of accuracy. Comparison results with other alternatives show that the proposed framework leads to more accurate PF and OPF outcomes while achieving high computational efficiency for large-scale power systems with large numbers of nonlinear correlated power injections in presence of limited information. [ABSTRACT FROM AUTHOR]

In this study, the estimation of the unknown parameters of an alpha power Weibull (APW) distribution using the concept of an optimal strategy for the step-stress accelerated life testing (SSALT) is investigated from both classical and Bayesian viewpoints. We used progressive type-II censoring and accelerated life testing to reduce testing time and costs, and we used a cumulative exposure model to examine the impact of various stress levels. A log-linear relation between the scale parameter of the APW distribution and the stress model has been proposed. Maximum likelihood estimators for model parameters, as well as approximation and bootstrap confidence intervals (CIs), were calculated. Bayesian estimation of the parameter model was obtained under symmetric and asymmetric loss functions. An optimal test plan was created under typical operating conditions by minimizing the asymptotic variance (AV) of the percentile life. The simulation study is discussed to demonstrate the model's optimality. In addition, real-world data are evaluated to demonstrate the model's versatility. [ABSTRACT FROM AUTHOR]

This paper is concerned with the interval estimation problem of the dynamic liquid level for sucker-rod pumping systems via dynamometer cards. Firstly, a surface dynamometer card-based dynamic liquid level model is established in terms of the operational mechanism of the pump and the dynamics of the rod strings. Then, an underdamped oscillation method and a boxplot-based denoising method are developed respectively to determine the damping coefficient in the dynamics of the rod strings and deal with the uncertainties in the dynamometer card. Based on these, a finite difference-based interval estimation strategy is proposed to determine dynamic liquid level via the surface dynamometer card. Finally, simulation results with the field measurements demonstrate the validity of the proposed method. • A surface dynamometer card-based interval estimation of dynamic liquid level model is established. • An underdamped oscillation method is applied to identify the parameter in the model. • A boxplot-based denoising method is proposed to deal with the uncertainties in the model. [ABSTRACT FROM AUTHOR]

The rotary steerable drilling tools (RSDTs) are invented for high-precision wellpath control. Fault diagnosis is essential for the RSDT as it can improve the reliability of the drilling processes. To estimate the sensor fault of the RSDT, this paper investigates the interval estimation problem for Lipschitz nonlinear systems with sensor fault via the set-membership approach. Firstly, the RSDT is modeled by a discrete-time Lipschitz nonlinear system with unknown inputs, noises, and parameter uncertainties. Next, based on the ellipsoid bundles, a set-membership fault estimator is presented, where the unknown inputs are decoupled. Additionally, a sufficient condition, which is derived based on the P -radius of the ellipsoid bundles, is put forward to design the parameters of the estimator with Lipschitz nonlinear terms. Then, the interval estimations of the states and fault are obtained via ellipsoid bundles. Finally, the efficiency of the proposed approach is evaluated through numerical simulations and experiments. • Interval fault estimation problem is studied for RSDT with Lipschitz nonlinearity. • A new design condition is presented by considering the size of ellipsoid bundles. • Considering Lipschitz nonlinearity, the interval estimations are derived. [ABSTRACT FROM AUTHOR]

Proton exchange membrane fuel cells (PEMFCs) are pivotal components within green energy systems; However, commercialization and large-scale application of these techniques are constrained by the performance degradation prediction problem. Existing prediction methods mainly focus on the performance degradation under static and quasi-dynamic conditions, yet point estimation uncertainty quantification and interval estimation under dynamic conditions would contribute to safe and efficient operation. In this research, a fusion method named Informer-GPR is proposed, which accurately quantifies the uncertainty of performance degradation prediction and demonstrates good adaptability under various dynamic conditions and prediction step sizes. This method utilizes Informer as a point estimation method to circumvent the deficiency of global information extraction in recurrent neural networks and employs sparse self-attention mechanisms to allocate weights, enhancing the extraction of crucial information in the aging process. Furthermore, gaussian process regression (GPR) is employed to quantify the uncertainty of point estimation process, providing safer confidence interval estimation. Experimental findings demonstrate that the Informer-GPR method reduces the RMSE of point estimation by 20.8 %–64.4 % on dynamic cycle condition datasets, offering precise confidence interval estimations. Moreover, its robust performance across diverse dynamic conditions and multiple prediction steps underscores its versatility, thereby enhancing prediction efficacy in dynamic scenarios. • A novel PEMFC performance degradation prediction method. • A prediction framework with Attention mechanism and Uncertainty quantification. • Consider point estimation and interval estimation for PEMFCs. • Comparison under three dynamic conditions with multiple prediction step sizes. [ABSTRACT FROM AUTHOR]

In this paper, an actuator fault and state interval estimation method for a class of nonlinear systems is proposed by integrating observer design and zonotope analysis. For the considered systems, we present a novel unknown input observer structure with broad applications. The design procedure is based on H ∞ method to decrease the influence of unknown but bounded process disturbances and measurement noise. Moreover, a novel interval estimation method is presented based on zonotope analysis to obtain tighter intervals. Numerical simulations of a quadruple-tank system are conducted to assess the performance of the proposed approach. • A novel robust observer is designed to decouple the unknown input and to attenuate the effect of disturbances and noise. • Zonotope analysis is used to achieve tight interval estimation. • The proposed method is applied to a quadruple-tank system. [ABSTRACT FROM AUTHOR]

Bayesian inference is a technique of statistical inference which uses the Bayes' theorem to update the probability distribution as new observed data are available. Uncertain variables are a tool of modeling imprecisely observed quantities associated with experiential information. By integrating Bayesian inference and uncertain variables, this paper proposes an approach of uncertain Bayesian inference to deal with Bayesian inference problems involving imprecise observations. The posterior distribution is derived which gives the probability distribution of an unknown parameter conditional on uncertain observations. And based on the posterior distribution, some inference problems including the point estimation, the interval estimation and the Bayesian prediction, are investigated. [ABSTRACT FROM AUTHOR]

This paper studies the distributed interval state estimation problem for cyber–physical systems with bounded disturbance and random stealthy attacks. Since conventional interval observers cannot complete the task of real-time monitoring system under random attacks, an attack-resistant distributed interval observer is designed by using attack frequency and interval attack estimation. Using the designed observer, upper- and lower-bounding estimation error systems are modeled by positive interconnected systems with hybrid deterministic and random bounded inputs. To explicitly attenuate the effect of disturbance and attacks, the resulting deterministic positive error system between upper- and lower-bounding estimates is formulated. By linear programming, the results of interval observer design and l ∞ -gain optimization are proposed. The remote monitoring of vehicle lateral dynamic is given for numerical verification of the results. • A new distributed interval observation method for general linear system is proposed. • The disturbance attenuation problem of stochastic interval error systems is solved. • The method can provide real-time changing ranges of CPS dynamics against attacks. [ABSTRACT FROM AUTHOR]

Networked control system (NCS) is a multidisciplinary area that attracts increasing attention today. In this paper, we deal with remote supervision of a nonlinear networked control systems class subject to network imperfections. Different from many existing researches that consider only the problem of small and/or constant communication delays, we focus on large and time-varying network delays problem in both measurement and control channels. The proposed method is a set-membership estimation-based predictor approach computing a guaranteed set of admissible state values when the uncertainties (i.e. measurement noises and system disturbances) are considered unknown but bounded with a priori known bounds. The state prediction strategy is used to compensate the effect of transmission delays. Finally, the theoretical results are validated through a numerical example. [ABSTRACT FROM AUTHOR]

Cast blasting–dragline stripping technology is the most advanced mining technology used in open-pit mines. For a long time, however, its precision has been hindered. In this paper, we aim to improve the precision of cast blasting–dragline stripping technology and promote its intelligent design. We present a method to determine cast blasting stockpile forms. First, the 3D point cloud data for the Heidaigou open-pit mine from recent years were collected and counted, and a 3D mathematical model of overcasting stripping steps was constructed. Then, data classification and multivariate statistical analysis were used to establish a cast blasting stockpile characteristic parameter database. Next, locally weighted linear regression was used as the fitting method to achieve shape fitting under different cast blasting step heights. Finally, interval estimation was used as the fitting result test method to verify the morphology of the acquired cast blasting stockpile form. The research results show that the cast blasting stockpile form obtained by fitting can truly reflect the cast blasting effect of the Heidaigou open-pit mine and ensure the reliability and accuracy of the subsequent design of cast blasting–dragline stripping technology. [ABSTRACT FROM AUTHOR]

Two- and three-level designs in educational and psychological research can involve entire populations of Level-3 and possibly Level-2 units, such as schools and educational districts nested within a given state, or neighborhoods and counties in a state. Such a design is of increasing relevance in empirical research owing to the growing popularity of large-scale studies in these and cognate disciplines. The present note discusses a readily applicable procedure for point-and-interval estimation of the proportions of second- and third-level variances in such multilevel settings, which may also be employed in model choice considerations regarding ensuing analyses for response variables of interest. The method is developed within the framework of the latent variable modeling methodology, is readily utilized with widely used software, and is illustrated with an example. [ABSTRACT FROM AUTHOR]

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This paper investigates the problem of interval estimation for discrete-time linear descriptor systems subject to unknown-but-bounded uncertainties. Based on prediction-correction mechanism, we proposed a two-step interval estimator to over-estimate the bounds of the system states. To reduce the conservatism, a novel parameterization-based approach is presented. Besides, by using a Frobenius norm-based minimization approach, optimal correction is calculated. Compared to the volume criterion, the computational efficiency is greatly enhanced. Finally, two numerical examples are presented to illustrate the efficiency and potential application of the proposed approach. [ABSTRACT FROM AUTHOR]