Conservative Bound Research Articles

Optimizing decision-making in uncertain environments through analysis of stochastic stationary Multi-Armed Bandit algorithms

Reinforcement learning traditionally plays a pivotal role in artificial intelligence and various practical applications, focusing on the interaction between an agent and its environment. Within this broad field, the multi-armed bandit (MAB) problem represents a specific subset, characterized by a sequential interaction between a learner and an environment where the agents actions do not alter the environment or reward distributions. MABs are prevalent in recommendation systems and advertising and are increasingly applied in sectors like agriculture and adaptive clinical trials. The stochastic stationary bandit problem, a fundamental category of MAB, is the primary focus of this article. Here, we delve into the implementation and analytical comparison of several key bandit algorithmsincluding Explore-then-Commit (ETC), Upper Confidence Bound (UCB), Thompson Sampling (TS), Epsilon-Greedy (-Greedy), SoftMax, and Conservative Lower Confidence Bound (CON-LCB)across various datasets. These datasets vary in the number of options (arms), reward distributions, and specific parameters, offering a broad testing ground. Additionally, this work provides an overview of the diverse applications of bandit problems across different fields, highlighting their versatility and broad impact.

Two-Phase Non-Singular Terminal Sliding Mode Control of Nonlinear Systems

This paper presents a two-phase non-singular terminal sliding mode control scheme for a class of nonlinear systems in the presence of external disturbances. A two-phase terminal sliding mode surface is constructed and utilized, such that our control scheme achieves fast finite-duration convergence in regions both close to and far away from the control objective, by which the transition state is set and a less conservative bound of the settling time is obtained and superior to the existing results. Meanwhile, the singularity is avoided by the utilization of the saturation function, with the simplicity of structure and implementation. Extensions to multi-input multi-output systems are carried out further. The numerical simulation of the single inverted pendulum and the industrial manipulator are conducted to verify the effectiveness of the proposed control strategy.

Fixed-time fault-tolerant attitude control for rigid spacecraft with torque saturation

This paper investigates the fixed-time attitude control problem for spacecraft under input saturation, actuator faults, and system uncertainties. Three novel saturated fixed-time nonsingular terminal sliding mode surfaces (NTSMSs) are designed, which can keep the system states fixed-time stable after the establishment of their sliding manifolds. Two of them are time-varying and firstly designed. Each of the two NTSMSs has an adjustment parameter that is adjusted dynamically and used to handle saturation and cancel the attitude dynamics. According to other related predesigned parameters, a conservative lower bound of this parameter is obtained. A saturated control scheme is then designed in conjunction with a newly proposed saturated reaching law. A modification strategy is carried out to facilitate the engineering applications of our methods. The fixed-time stability of the closed-loop systems is validated by Lyapunov stable theory. Simulation results validate the effectiveness and superiority of the proposed control scheme.

Urban Road Safety Prediction: A Satellite Navigation Perspective

Predicting the safety of urban roads for navigation via global navigation satellite systems (GNSS) signals is considered. To ensure safe driving of automated vehicles, the vehicle must plan its trajectory to avoid navigating on unsafe roads (e.g., icy conditions, construction zones, narrow streets, etc.). Such information can be derived from the roads' physical properties, vehicle's capabilities, and weather conditions. From a GNSS-based navigation perspective, the reliability of GNSS signals in different locales, which is heavily dependent on the road layout within the surrounding environment, is crucial to ensure safe automated driving. An urban road environment surrounded by tall objects can significantly degrade the accuracy and availability of GNSS signals. This article proposes an approach to predict the reliability of GNSS-based navigation to ensure safe urban navigation. Satellite navigation reliability at a given location and time on a road is determined based on the probabilistic position error bound of the vehicle-mounted GNSS receiver. A metric for GNSS reliability for ground vehicles is suggested, and a method to predict the conservative probabilistic error bound of the GNSS navigation solution is proposed. A satellite navigation reliability map is generated for various navigation applications. As a case study, the reliability map is used in the proposed optimization problem formulation for automated ground vehicle safety-constrained path planning.

Specified-time group consensus for general linear systems over directed graphs

This paper studies the distributed specified-time group consensus control with hard settling-time constraint and milder communication topology constraint. To this end, we propose two distributed control schemes by employing a motion planning approach for the single- and double-integrator systems. Compared with the most existing works over undirected communication topologies, the underlying topology of each group is required to be directed graphs in our proposed distributed controllers. Furthermore, the root vertex of one group is allowed to belong to the other group. The convergence analysis is performed via the algebraic graph theory and matrix theory. The results show that the agents in the same group can reach consensus within any prespecified settling-time instead of a conservative upper bound of the settling-time. Moreover, the designed specified-time group consensus protocols do not require continuous information exchange. Finally, simulation results are provided to illustrate the effectiveness of the proposed methods.

A matheuristic for the robust integrated airline fleet assignment, aircraft routing, and crew pairing problem

We address an integrated airline scheduling problem that combines three airline planning processes: fleet assignment, aircraft routing, and crew pairing. For a given daily flight schedule, the problem requires simultaneously assigning aircraft and crews to each scheduled flight, taking into account aircraft maintenance restrictions and crew work rules. We propose to solve this complex problem of integrated flight planning while taking into account robustness considerations. In this regard, robustness is achieved by restricting tight connections in the schedule and increasing the number of connections where crews follow the aircraft. We formulate the problem using a very large-scale, yet compact, mixed-integer programming model, and we propose a matheuristic consisting of a decomposition approach and a proximity search algorithm. Computational experiments carried out on real instances from a major airline and having up to 14,014 itineraries, 646 flights, and 202 aircraft provide evidence of the proposed approach’s efficacy. In particular, we find that the average deviation from a conservative bound is at most equal to 0.6%.

Efficient Estimation for Models With Nonlinear Heteroscedasticity

We study efficient estimation for models with nonlinear heteroscedasticity. In two-step quantile regression for heteroscedastic models, motivated by several undesirable issues caused by the preliminary estimator, we propose an efficient estimator by constrainedly weighting information across quantiles. When the weights are optimally chosen under certain constraints, the new estimator can simultaneously eliminate the effect of preliminary estimator as well as achieve good estimation efficiency. When compared to the Cramér-Rao lower bound, the relative efficiency loss of the new estimator has a conservative upper bound, regardless of the model design structure. The upper bound is close to zero for practical situations. In particular, the new estimator can asymptotically achieve the optimal Cramér-Rao lower bound if the noise has either a symmetric density or the asymmetric Laplace density. Monte Carlo studies show that the proposed method has substantial efficiency gain over existing ones. In an empirical application to GDP and inflation rate modeling, the proposed method has better prediction performance than existing methods.

Impact of anomalous ionospheric gradients on GBAS in the low-latitude region of China

The ionospheric gradient caused by spatial decorrelation is a crucial factor affecting the integrity of a ground-based augmentation system (GBAS). We processed GPS data from the Crustal Movement Observation Network of China from 2008 to 2018 with the long-term ionospheric anomaly monitoring method and then analyzed and verified a typical anomalous event. Compared with the wedge, plasma bubbles in the low-latitude region can be better described by the trapezoid. The largest detected anomalous gradient in China was 196 mm/km, and the conservative upper bound of anomalous gradients was determined to be 300 mm/km. Wedge and trapezoid were applied to establish GBAS threat models for China. Based on these threat models, we analyzed the impact of anomalous ionospheric gradients on GBAS in the low-latitude region of China. The results show that the performances of ionospheric anomaly monitors satisfy the requirements of GBAS approach service type D when the wedge is applied. However, the performances do not satisfy the requirements under the trapezoid for the following scenarios: When the speed and direction of the aircraft are similar to the threat model with a narrower slope width, the aircraft is affected by anomalies before the time that the GBAS facilities are affected; moreover, the monitor performance decreases sharply, and large differential range errors may occur. Finally, the high-risk approach conditions were analyzed in detail, and we provided recommendations for conducting aircraft approaches at low latitudes.

Calculation of decay heat rate in VVER-1000 spent fuel pool including uncertainties

This paper presents a decay heat rate analysis of the VVER-1000 (unit 6 in “Kozloduy NPP” Plc.) spent fuel pool (SFP) using the method outlined by the United States (US) Nuclear Regulatory Commission (NRC) Regulatory Guide (RG) 3.54 (Revision 2, 2018), titled “Spent Fuel Heat Generation in an Independent Spent Fuel Storage Installation.” The usage of RG 3.54 for SFP calculations is extremely attractive because it enables fast determination of the decay status of a large number of stored fuel assemblies (FAs) in an SFP and further evaluation of their uncertainties.Two batches of fuel FAs in an SFP were analyzed in the study: The first batch consisted of 402 FAs that were stored for 321 days of reactor power operation from 2014 to 2015. The second batch consisted of 355 FAs that were stored for 326 days of reactor power operation from 2018 to 2019. The total decay heat rate and the corresponding decay heat rates of the FA that was placed in each of three VVER-1000 SFP sections were evaluated. Additionally, the propagation of the input uncertainties introduced by the initial fuel mass, burnup, and operation time on full power effective days was estimated.The applied method was derived from the uncertainty method, which was previously introduced by Gesellschaft für Anlagen-und Reaktorsicherheit (GRS), for free from deliberate pessimism safety analyses (named best estimate). The variation in the selected input parameters produced decay heat generation uncertainty as follows: ±73.2 kW (2014)/±59.1 kW (2018) at the beginning of each batch storage, and correspondingly, ±12.0 kW (2015)/±10.7 kW (2019) at the end of each batch storage. The results indicate that the method is sufficiently sensitive to the initial mass variation and irradiation uncertainties.The degree of conservatism (via a parameter referred to as a ‘safety factor’), introduced in RG 3.54 to address the numerical and nuclear data uncertainties in pressurized water reactor (PWR) decay heat calculations, was calculated for the stored VVER-1000 FA. An original approach for calculation of the scaling coefficient kcorr is suggested in the paper for estimation of the level of conservatism using the safety factor in RG 3.54 and other sources. The obtained results are reported.The recommendations by RG 3.54 were implemented in an input script for the MAXIMA Computer Algebra System (CAS). The MAXIMA CAS calculations of the VVER-1000 SFP decay heat rate were verified with the corresponding Oak Ridge Isotope Generation (ORIGEN) (SCALE 6.1) data at the beginning and end of the analyzed time periods. The authors determined that the obtained values of kcorr = 0.91–0.93 are useful in the re-evaluation of the RG 3.54 degree of conservatism. Furthermore, the scaled safety factor decay heat generation output was replaced with the calculated upper uncertainty bound. The upper boundary values in the decay heat rate uncertainty range showed flexibility and reduced conservatism in comparison with the upper 10% of the conservative bound of the nominal values.

Natural Sources of Ionization and Their Impact on Atmospheric Electricity

AbstractWe present a study of atmospheric electricity using the chemistry‐climate model SOCOL considering ionization by solar energetic particles during an extreme solar proton event (SPE), galactic cosmic rays (GCR), and terrestrial radon (Rn‐222). We calculate the global distribution of the atmospheric conductivity and fair‐weather downward current density (Jz) using atmospheric ionization rates from all sources. We found that Jz is enhanced (by more than 3.5 pA/m2) in radon source and polar regions. Contribution of Rn‐222 is essential at middle and low latitudes/altitudes where GCR‐induced air conductivity is reduced. The model results are in good agreement with the available observations. We also studied the effects of an extreme SPE, corresponding to the 774 AD event, on the atmospheric electricity and found that it would lead to a large increase of Jz on a global scale. The magnitude of the effects depends on location and can exceed background value more than 30 times over the high latitudes (a conservative upper bound). Such an assessment has been performed for the first time.

Buckling severity measurement of axially compressed cylindrical structures with periodic buckling pattern

We introduced a simplified method to measure the buckling severity of the cylindrical structures subjected to axial compression. The method is intended for the cylindrical structures with a buckling mode comprising a repetition of similar single tiers, and estimates an upper bound of the deformed surface shape of the structure from measurements of a few data points. Moreover, this method helps monitor the magnitude of surface distortion of the large-sized buckled cylindrical structures with full-field surface shapes that are usually problematic for measurement. The discussion of classical buckling theory reveals that the point-to-point variation of radial displacements on cylindrical structures with periodic buckling pattern is similarly distributed even when the buckling mode changes depending on the structure’s size. A fundamental probability distribution model governing the point-to-point variation of the radial displacements is established from the results. A computation procedure for the conservative upper bound (CUB) of radial displacements from measurements at a few data points is proposed. A buckling experiment on cylindrical structures under axial compression demonstrated that the CUB from the proposed method appropriately envelopes the radial displacement of the buckled cylindrical structure within a designated probability, confirming the effectiveness of the proposed method. The study offers a novel method to compute the magnitude of the surface distortion of buckled cylindrical structures from a few measurements.

Cosmological implications of Standard Model criticality and Higgs inflation

The observed Higgs mass indicates that the Standard Model can be valid up to near the Planck scale MP. Within this framework, it is important to examine how little modification is necessary to fit the recent experimental results in particle physics and cosmology. As a minimal extension, we consider the possibility that the Higgs field plays the role of inflaton and that the dark matter is the Higgs-portal scalar field. We assume that the extended Standard Model is valid up to the string scale 1017GeV. (This translates to the assumption that all the non-minimal couplings are not particularly large, ξ≲102, as in the critical Higgs inflation, since MP/102∼1017GeV.) We find a correlated theoretical bound on the tensor-to-scalar ratio r and the dark matter mass mDM. As a result, the Planck bound r<0.09 implies that the dark-matter mass must be smaller than 1.1 TeV, while the PandaX-II bound on the dark-matter mass mDM>0.7±0.2TeV leads to r≳2×10−3. Both are within the range of near-future detection. When we include the right-handed neutrinos of mass MR∼1014 GeV, the allowed region becomes wider, but we still predict r≳10−3 in the most of the parameter space. The most conservative bound becomes r>10−5 if we allow three-parameter tuning of mDM, MR, and the top-quark mass.

Design and Analysis of New Zeroing Neural Network Models With Improved Finite-Time Convergence for Time-Varying Reciprocal of Complex Matrix

In this article, two improved finite-time convergent complex-valued zeroing neural network (IFTCVZNN) models are presented and investigated for real-time solution of time-varying reciprocal of complex matrices on account of two equivalent processing ways of complex calculations for nonlinear activation functions. Furthermore, a novel nonlinear activation function is explored to modify the comprehensive performance of such two IFTCVZNN models. Compared with existing complex-valued neural networks converging within the limited time, the proposed IFTCVZNN models with the new activation function have better finite-time convergence and less conservative upper bound. Numerical simulations verify that the maximum of convergence time estimated via Lyapunov stability is theoretically much closer to the actual convergence time.

Bounding Integrity Risk and False Alert Probability Over Exposure Time Intervals

This paper investigates the impact of the autocorrelations of monitor test statistics on navigation integrity and continuity. General analytical methods are rigorously developed to evaluate the actual integrity risk and false alert probability over the exposure interval. Prior to this work, the probabilities computed based on one-sample test have been widely applied in aviation navigation. However, it will be shown that using the one-sample probability may lead to overly optimistic results, because the actual risk can be significantly higher, especially for false alert. The new methods are applied to an example problem of advanced receiver autonomous integrity monitoring. To quantify integrity, a simple but conservative upper bound is derived. As for continuity, both analytical and experimental results show that the actual false alert probability is two orders of magnitude higher than previously thought, due to the time-correlation effects. A feasible solution to mitigate this impact is provided, without degrading navigation availability.

Robust fault tolerance for continuous-variable cluster states with excess antisqueezing

The immense scalability of continuous-variable cluster states motivates their study as a platform for quantum computing, with fault tolerance possible given sufficient squeezing and appropriately encoded qubits [Menicucci, PRL 112, 120504 (2014)]. Here, we expand the scope of that result by showing that additional anti-squeezing has no effect on the fault-tolerance threshold, removing the purity requirement for experimental continuous-variable cluster-state quantum computing. We emphasize that the appropriate experimental target for fault-tolerant applications is to directly measure 15-17 dB of squeezing in the cluster state rather than the more conservative upper bound of 20.5 dB.

Fuel Quantity Estimation of Aircraft Supplementary Tank Using Markov Chain Monte Carlo Method

This paper presents an aircraft fuel quantity estimation method using the Markov Chain Monte Carlo (MCMC) method. Using the proposed method, fuel quantity uncertainty of an aircraft supplementary tank can be estimated when the roll and pitch attitudes of an aircraft change. Through reflecting uncertainties, the conservative bound of fuel quantity estimation results can be found, which is necessary for a reliable aircraft operation. The first step of the estimation process is a mathematical modeling of the fuel quantity in a supplementary tank. In the model, the fuel quantity is represented as a multivariate polynomial function of sensor output (i.e., frequency), aircraft roll and pitch angles. The parameter of the mathematical model is then estimated using the MCMC method. As an estimation result, the probability density function of the fuel quantity is provided, which accounts for the uncertainties caused from the developed mathematical model and measured data. The lower bound in the estimation result can be utilized as a conservative fuel quantity value for a reliable operation. To validate the proposed fuel quantity estimation approach, a test with known fuel quantity is performed.

Applicability of Empirical Tolerance Limit for Wrinkled-Membrane Distortions

This paper evaluates the applicability of the stochastic method to membrane-wrinkling problems. The stochastic method is used to compute a conservative upper bound of structural responses for membrane-wrinkling problems based on measurements at selected points. An empirical tolerance limit, which is defined as the value that exceeds the possible structural responses for at least a proportion of among all values with a confidence level of 50% , was applied. The spatial distribution of the wrinkled-membrane distortion, presented by point-to-point variation in the out-of-plane displacement at various points on the membrane surface, was investigated through a wrinkling analysis based on shell theory. A practical method for computing a conservative upper bound of the wrinkled-membrane distortions based on measurements at selected points was then proposed and evaluated for the wrinkling phenomena in three membrane models: a rectangular membrane under shear and tension loadings, a stretched circular membrane with a rotating center hub, and a square membrane subjected to corner tension loads. The calculated upper bounds approximately enveloped the wrinkled-membrane profile, confirming that this method provides a new and simple statistical approach for estimating highly nonlinear wrinkling behavior.

The global equity premium revisited: What human rights imply for assets' purchasing power

In this paper, we argue that past computations of the equity risk premium did not properly account for the financial implications of political collapse on property, civil and human rights. Accordingly, we argue past calculations overstated the equity risk premium. In their stead, we argue a conservative lower bound is to set the value of equity to zero when confronted with the total absence of human, civil and property rights which negate the purchasing power of financial investments. In doing so, we provide a valid lower-bound estimate of the equity risk premium that is corrected for lack of such basic rights, demonstrating the important changes in this estimate over time.

Individual wave height and wave crest distributions based on field measurements from the northern North Sea

This paper concerns full-scale wave measurements of individual wave heights and crest heights at one location with water depth 190 m in the northern North Sea from 2004 up to date. The surface elevation was recorded by a Saab WaveRadar REX from one location in the northern North Sea. The measured individual wave heights and crest heights have been compared to well-known theoretical distributions. For wave heights, the Rayleigh distribution is found to form a conservative upper bound, whilst the Forristall distribution is considered to show a good accuracy, though somewhat conservative in the most severe sea states. For crest heights, the Rayleigh distribution is found to be nonconservative, whilst the Forristall distributions for long- and short-crested sea both provide reasonable descriptions. Based on the present study, the Forristall distributions for individual wave height and crest heights in long-crested seas are considered to provide the most appropriate descriptions of these measured wave data.

Springtime Beryllium-7, meteorology, and ozone variability in the southeastern United States

Ground level 24 h average observations of 7Be activity, combined with continuous ozone (O3), carbon monoxide (CO) and minimum relative humidity (minRH) measurements, were conducted at two non-urban sites in the Deep South of the United States. One site is inland at Yorkville, Georgia, YRK (33°55′27″N; 84°59′44″W); the other is near the coast of the Gulf of Mexico outside Pensacola, Florida, OLF (30°25′N:87°13′W). The objective of the measurements was to explore the potential for estimating a contribution to surface O3 from stratospheric and upper tropospheric air for during the springtime months from April 2 to June 13, 2015 using 7Be as a tracer. The observed 24 h average 7Be activities were 1.88 ± 0.66 mBq/m3 at YRK and 1.99 ± 0.68 mBq/m3 at OLF. Corresponding means of 24 h average O3 mixing ratios were 38.3 ± 10.1 ppbv for YRK and 28.7 ± 8.9 ppbv at OLF. A weak statistically significant O37Be regression based estimate of O3 from the stratosphere and upper troposphere was constrained to a conservative upper bound of 14 ± 4 (1σ) ppbv. From daily inspection of meteorological features, a lower bound of 3–7 ppbv was estimated. A multiple regression of O3 versus 7Be and daily minimum relative humidity (minRH) improved the statistical fit and indicated stratosphere-upper troposphere contributions of 8.6 ± 4.0 ppbv for YRK and 6.6 ± 3.3 ppbv for OLF. Daily variability of 7Be and O3 was explored with respect to meteorological variability. 7BeO3 relationships in this experiment were examined using (a) ozonesonde and vertical dew point temperature profiles, inferring very dry air as an upper atmosphere tracer descending into the boundary layer, (b) backward air trajectories, identifying 7Be spatial and temporal variation, and (c) precipitation, indicating 7Be scavenging and lowered O3 with suppression of photochemistry. The average 7Be measurements at the ground during the study are useful for helping estimate the long-term O3 contributions from the upper atmosphere. However, the day-to-day 7Be observations had limited value for determining the contributions of upper air O3 to daily O3 mixing ratios. Conventional surface and upper-air meteorological data could be used effectively as an alternative.