Worst-case Deviation Research Articles

Lower bounds for the trade-off between bias and mean absolute deviation

In nonparametric statistics, rate-optimal estimators typically balance bias and stochastic error. The recent work on overparametrization raises the question whether rate-optimal estimators exist that do not obey this trade-off. In this work we consider pointwise estimation in the Gaussian white noise model with regression function f in a class of β-Hölder smooth functions. Let ’worst-case’ refer to the supremum over all functions f in the Hölder class. It is shown that any estimator with worst-case bias ≲n−β/(2β+1)≕ψn must necessarily also have a worst-case mean absolute deviation that is lower bounded by ≳ψn. To derive the result, we establish abstract inequalities relating the change of expectation for two probability measures to the mean absolute deviation.

Helically Coiled Tube Flocculators in Water Clarification Systems: Optimal Length Evaluation and Process Efficiency Probabilistic Analysis

New sustainable technologies have been explored as potential solutions to address the global issue of water scarcity by enhancing water treatment processes. In this context, an innovative coagulation/flocculation unit known as the helically coiled tube flocculator (HCTF) has emerged, offering notable advantages such as high process efficiency, short detention time, and cost-effectiveness compared to conventional hydraulic units. The HCTF harnesses its flow energy to disperse coagulation/flocculation agents and facilitate the formation of flocs through collisions between destabilized particles. This paper introduces an assessment of the process efficiency, geometric properties, and hydraulic characteristics of an alternative and sustainable water clarification system incorporating an HCTF, with the aim of determining its optimal length. In HCTFs, the flocculator’s length (referred to as L) can exert a significant influence on process efficiency, necessitating a comprehensive evaluation of this parameter for the rational design of such units. To accomplish this, the paper scrutinizes physical experimental findings from previous research articles, which are related to the efficiency of flocculation (indirectly estimated by analyzing turbidity removal efficiency). Additionally, it examines the geometric and hydraulic attributes across 48 distinct variations of HCTFs. This study culminates in the development of a model for determining the optimal length for HCTFs. Furthermore, it includes a probabilistic assessment that establishes a connection between the optimal length and other parameters involved in the clarification process—whether deterministic or probabilistic—and their impact on the final process efficiency, all with a 90% confidence level. This paper stands out by pioneering the determination of the optimal length of HCTFs, filling a gap in the existing literature, which previously only mentioned the importance of this parameter in process efficiency without providing a predictive model. The results highlight the robustness of the proposed alternative clarification system. Even in scenarios with substantial variations in dimensional hydraulic parameters (such as a worst-case relative standard deviation of 20%), the process efficiency fluctuations range between 1.3% and 5.2%. These outcomes lend support to the adoption of such alternative water clarification systems. They also underscore the potential of probabilistic evaluation as a valuable tool for investigating novel water and wastewater treatment units and enhancing existing ones.

Material uncertainty quantification for optimized composite structures with failure criteria

We propose a method to analyze effects of material uncertainty in composite laminate structures optimized using a simultaneous topology and material optimization approach. The method is based on computing worst-case values for the material properties and provides an efficient way of handling variation in material properties of composites for stiffness driven optimization problems. An analysis is performed to evaluate the impact of material uncertainty on designs from two design problems: Maximization of stiffness and minimization of a failure criteria index, respectively. The design problems are solved using different loads, boundary conditions and manufacturing constraints. The analysis indicates that the influence of material uncertainty is dependent on the type of optimization problem. For compliance problems the impact on the objective value is proportional to the changes of the constitutive properties and the effect of material uncertainty is consistent and predictable for the generated designs. The strength-based problem shows that material uncertainty has a significant impact on the response, and the effects of material uncertainty is not consistent and changes for different design requirements. In addition, the results show an increase of up to 25% of the maximum failure index when considering the worst-case deviation of the constitutive properties from their nominal values.

User-segregation based channel estimation in the MIMO system

In a multi-user multi-cell massive Multiple Input Multiple Output (MIMO) system, pilot contamination is a challenge of channel estimation. Traditional channel gain estimation follows pilot-based estimation, which is processed with the contamination and degrades the spectral efficiency. In order to overcome the above-stated problem, this work proposes User Segregation-Based Channel Estimation (USCE) improve spectral efficiency. The estimation process considers the prior minimization of pilot contamination. Hence the convergence of the proposed model with minimal contamination is validated. Moreover, the proposed user segregation method includes knowledge of both large-scale fading and small-scale fading. In order to do the analysis, the number of users is changed from N=100, 500, and 1000 to fix τd=200. The worst-case, best-case, mean, median, and Standard deviation (SD) case scenarios are all taken into account during this study. When compared to alternative methods such as Blind downlink channel estimation (BDCE) and Orthogonal pilot reuse sequence-based channel estimation (OPRSCE), the simulated results show that the suggested approach regularly produces accurate estimation. Accordingly, the NMSE value attained by the proposed work is −14.254 dB, whereas the other models achieve the NMSE values of −32.453 dB, and −54.764 dB, respectively.

Certifiable Robustness to Adversarial State Uncertainty in Deep Reinforcement Learning.

Deep neural network-based systems are now state-of-the-art in many robotics tasks, but their application in safety-critical domains remains dangerous without formal guarantees on network robustness. Small perturbations to sensor inputs (from noise or adversarial examples) are often enough to change network-based decisions, which was recently shown to cause an autonomous vehicle to swerve into another lane. In light of these dangers, numerous algorithms have been developed as defensive mechanisms from these adversarial inputs, some of which provide formal robustness guarantees or certificates. This work leverages research on certified adversarial robustness to develop an online certifiably robust for deep reinforcement learning algorithms. The proposed defense computes guaranteed lower bounds on state-action values during execution to identify and choose a robust action under a worst case deviation in input space due to possible adversaries or noise. Moreover, the resulting policy comes with a certificate of solution quality, even though the true state and optimal action are unknown to the certifier due to the perturbations. The approach is demonstrated on a deep Q-network (DQN) policy and is shown to increase robustness to noise and adversaries in pedestrian collision avoidance scenarios, a classic control task, and Atari Pong. This article extends our prior work with new performance guarantees, extensions to other reinforcement learning algorithms, expanded results aggregated across more scenarios, an extension into scenarios with adversarial behavior, comparisons with a more computationally expensive method, and visualizations that provide intuition about the robustness algorithm.

A Parallel Approach to Perform Threshold Value and Propagation Delay Analyses of Genetic Logic Circuit Models.

Experiments with synthetic genetic logic circuits can be time-consuming and expensive. Accordingly, advances in the field of computer-aided design and simulation of genetic circuits have reduced the cost and time required for experimentation. D-VASim is the first genetic circuit simulation tool that allows users to interact with the model during run-time. In contrast to electronic circuits, genetic circuits have different threshold values for different circuits, which need to be estimated prior to simulation. D-VASim allows the user to perform threshold concentration and propagation delay analysis before simulating the circuit. The algorithm currently used in D-VASim has considerable scope for improvements. Thus, we propose a parallel implementation of the algorithm, significantly faster by up to 16 times. In adddition, we improve the algorithm for consistent runtimes across multiple simulation runs under the same parameter settings, reducing the worst-case standard deviation in runtime from 6.637 to 1.841. Our algorithm also estimates the threshold value more accurately, as evident from experimentation for long runtimes. With these modifications, the utility of D-VASim as a virtual laboratory environment has been significantly enhanced.

A Comparison of Front-End Amplifiers for Tetrapolar Bioimpedance Measurements

Many commercial benchtop impedance analyzers are incapable of acquiring accurate tetrapolar measurements, when large electrode contact impedances are present, as in bioimpedance measurements using electrodes with micrometer-sized features. External front-end amplifiers can help overcome this issue and provide high common-mode rejection ratio (CMRR) and input impedance. Several discrete component-based topologies are proposed in the literature. In this article, these are compared with new alternatives with regard to their performance in measuring known loads in the presence of electrode contact impedance models, to emulate tetrapolar bioimpedance measurements. These models are derived from bipolar impedance measurements taken from the electrodes of a tetrapolar bioimpedance sensor. Comparison with other electrode models used in the literature established that this is a good and challenging model for bioimpedance front-end amplifier evaluation. Among the examined amplifiers, one of the best performances is achieved with one of the proposed topologies based on a custom front-end with no external resistors (AD8066/AD8130). Under the specific testing conditions, it achieved an uncalibrated worst-case absolute measurement deviation of 4.4% magnitude and 4° at 20 Hz, and 2.2% and 7° at 1 MHz accordingly with loads between $10~\Omega $ and 10 $\text{k}\Omega $ . Finally, the practical use of the front-end with the impedance analyzer is demonstrated in the characterization of the bioimpedance sensor, in saline solutions of varying conductivities (2.5–20 mS/cm) to obtain its cell constant. This article serves as a guide for evaluating and choosing front-end amplifiers for tetrapolar bioimpedance measurements both with and without impedance analyzers for practical/clinical applications and material/sensor characterization.

Towards Robotic-Assisted Subretinal Injection: A Hybrid Parallel–Serial Robot System Design and Preliminary Evaluation

Subretinal injection is a delicate and complex microsurgery. The main surgical difficulties come from the surgeon's hand tremor, dexterous motion, and insufficient visual feedback. In order to begin addressing these challenges, this article presents a robot system for subretinal insertion integrated with intraoperative optical coherence tomography (OCT). The surgical workflow using this system consists of two main parts. The first part is the manual robot control, which aims the target before approaching the retinal surface, while considering the remote center of motion (RCM) constraint. When the injection area has been located precisely, needle is inserted into retina. To ensure surgical safety, needle insertion depth is estimated using OCT images on a continuous basis. A soft RCM control method is designed and integrated for the controller of our hybrid parallel–serial surgical robot. Safety and accuracy performance evaluation with a 15-ms control loop shows that the worst-case RCM deviation error is within 1 mm. Experimental results demonstrated that the proposed system has the ability to improve surgical outcomes by surgeons overcoming their physical limitations in order to enable a better dexterous motion, and furthermore enhancing their visual feedback for a better intraocular perception.

Robust evaluation of chatter stability for milling process with uncertainties based on optimal configuration of machining position and spindle speed

Chatter vibration in milling process is a major obstacle that limits the machining quality and productivity, which may be avoided by using stability lobe diagrams (SLDs). Many traditional models developed to predict chatter stability assume that dynamic parameters of the machine tool remain constant under operational conditions. However, these parameters such as natural frequencies, damping ratios, stiffness, and cutting force coefficients vary depending upon different aspects including spindle speed, tool wear, and machining position, reducing the accuracy of chatter prediction. In this study, a robust chatter prediction method based on conventional analytical milling stability models is presented by employing the Edge theorem and Zero Exclusion condition. In this method, optimal combinations of spindle speeds and machining positions are firstly researched to obtain higher critical depths of cut, based on the conventional stability model, modal fitting technique, Kriging model, and improved particle swarm optimization. At each combination, related nominal modal parameters and cutting force coefficients are identified, and their left and right worst-case deviations are also determined. Critical stable condition for each combination is detected by a graphic approach within the minimum and maximum bounds of uncertainties. Accordingly, a robust stability lobe diagram is obtained with related spindle speeds and critical cutting depths. The proposed method was verified by chatter tests on a real vertical machining center, demonstrating its reliability in chatter prediction compared to the conventional stability lobe diagram.

Coordinate control of air movement for optimal thermal comfort

Personally controlled air movement can maintain or enhance thermal comfort in warm environments and reduce energy consumption. Unlike controlling a personal fan, using a system of fans for multiple occupants is difficult as it is hard to find an appropriate fan speed setting that maximizes occupants' satisfaction. Since limited work has been carried out on this issue, in this paper, a novel cooperative control approach for a system of fans is proposed to provide optimized air movement for multiple occupants. This is the first time that a system of fans is controlled cooperatively in the research of built environment. The proposed approach predicts airflow in a cost-effective manner by calibrating the fans in the real environment. The operation of the fans is optimized by minimizing the worst-case deviation between the actual air speed and the desired air speed, which can be determined based on either the PMV – SET model or the occupants' feedback. This minimax-error problem is formulated as an equivalent linear programming problem which can be solved using standard methods. The proposed approach was tested in two different indoor scenarios respectively by 1) measuring air speed directly in a business conference room and 2) involving human subject surveys in a university classroom. In the first experiment, the measured air speeds after optimization are closer to the target values at all tested temperature levels (26°C, 27.5°C, and 29°C) indicating improved thermal comfort. In the second experiment, only 62% of the occupants (totally 34) are satisfied with slightly increased room temperature (around 26.5°C) before optimization, while this number increased to 94% after optimization.

Robust location of new housing developments using a choice model

We consider the issue of choosing a subset of locations to construct new housing developments maximizing the satisfaction of potential buyers, which has not been previously studied in the literature. The allocation of demands to the selected locations is modeled by a choice model, based on the distance to the location, real-estate prices and incomes. We study two robust counterparts of the optimal location problem, where uncertainty lies on demand volumes for the first one, and on customer preferences for the second one. In both cases, the parameters subject to uncertainty appear both in the objective function and constraints. The second robust model combines a scenario-based approach with nominal, price-centric and distance-centric scenarios on customers preferences, and an uncertainty budget approach that limits the number of customers that can deviate from the nominal scenario. We show that the subproblem of finding the worst-case deviation of parameters subject to uncertainty is tractable and leads to linear formulations of the robust problem. Computational experiments conducted on instances of the Paris region show that the average loss of value of the robust solution is reasonably low when compared to the optimal solution of deviated instances. We also derive insights for the new housing development issue.

Worst-case large deviations upper bounds for i.i.d. sequencesunder ambiguity

An introductory study of large deviations upper bounds from a worst-case perspective under parameter uncertainty (referred to as ambiguity) of the underlying distributions is given. Borrowing ideas from robust optimization, suitable sets of ambiguity are defined for imprecise parameters of underlying distributions. Both univariate and multivariate i.i.d. sequences of random variables are considered. The resulting optimization problems are challenging min‒max (or max‒min) problems that admit some simplifications and some explicit results, mostly in the case of the normal probability law.

The Impact of Worst-Case Deviations in Non-Atomic Network Routing Games

We introduce a unifying model to study the impact of worst-case latency deviations in non-atomic selfish routing games. In our model, latencies are subject to (bounded) deviations which are taken into account by the players. The quality deterioration caused by such deviations is assessed by the Deviation Ratio, i.e., the worst case ratio of the cost of a Nash flow with respect to deviated latencies and the cost of a Nash flow with respect to the unaltered latencies. This notion is inspired by the Price of Risk Aversion recently studied by Nikolova and Stier-Moses (Nikolova and Stier-Moses 2015). Here we generalize their model and results. In particular, we derive tight bounds on the Deviation Ratio for multi-commodity instances with a common source and arbitrary non-negative and non-decreasing latency functions. These bounds exhibit a linear dependency on the size of the network (besides other parameters). In contrast, we show that for general multi-commodity networks an exponential dependency is inevitable. We also improve recent smoothness results to bound the Price of Risk Aversion.

A pulse oximeter system, OxiSense, with embedded signal processing using an ultra-low power ASIC designed for testability

This paper presents a complete IoT enabled pulse oximeter (PO) system, called OxiSense, made using a custom designed low power application specific integrated circuit (ASIC) for signal conditioning. One of the novel aspects of the developed system is the testability of all the important modules of the ASIC (both analog and digital) using auxiliary circuits implemented in the ASIC. Another novel aspect is a new embedded and efficient signal processing algorithm which is robust to small motion artifacts. This new algorithm has been implemented on a low-power micro-controller (embedded processing mode) as well as on PC using Python (remote processing mode). The PO ASIC is fabricated in 180 nm mixed-mode CMOS technology and it works at 1.8 V supply voltage. The average power consumption of the analog front-end is 176 µW and that of the digital module controlling the analog front-end is 23 µW. The prototype PO system made using the custom ASIC operates from a 3.7 V lithium ion battery and consumes about 8 mW power. The prototype is housed in a 3D printed casing and it connects with a display device via USB or wirelessly to laptop/smartphone/tablet. Readings on 20 subjects, both in the lab and in hospital, show less than 2% deviation in the measured SpO2 level and worst case deviation of 2.7 beats per minute for the measured heart rate, when compared with the commercial POs.

A new robust criterion for the vehicle routing problem with uncertain travel time

This article investigates a new robust criterion for the vehicle routing problem with uncertainty on the travel time. The objective of the proposed criterion is to find a robust solution which displays better behaviour on a majority of scenarios, where each scenario represents a potential state of an uncertain event. In order to highlight the robustness of the proposed approach, the new robust criterion is compared with the classical robust criteria, such as best-case, worst-case and min-max deviation. Inspired from the mechanism developed by B. Roy for evaluating the robustness, this paper focuses on providing two robust conclusions for the new robust criterion: perfectly robust and pseudo robust. For the perfectly robust, the robust criterion is evaluated by using an exact method on a set of 480 small-scale instances generated from Solomon’s benchmark instances. For the pseudo robust, the robust criterion is evaluated by using a metaheuristic on a set of 54 medium-scale and large-scale instances. The numerical results show that the new approach is able to produce the robust solutions in a majority of cases.

Sensitivity to Serial Dependency of Input Processes: A Robust Approach

Procedures in assessing the impact of serial dependency on performance analysis are usually built on parametrically specified models. In this paper, we propose a robust, nonparametric approach to carry out this assessment, by computing the worst-case deviation of the performance measure due to arbitrary dependence. The approach is based on optimizations, posited on the model space, that have constraints specifying the level of dependency measured by a nonparametric distance to some nominal independent and identically distributed input model. We study approximation methods for these optimizations via simulation and analysis of variance. Numerical experiments demonstrate how the proposed approach can discover the hidden impacts of dependency beyond those revealed by conventional parametric modeling and correlation studies. The online appendix is available at https://doi.org/10.1287/mnsc.2016.2667 . This paper was accepted by Assaf Zeevi, stochastic models and simulation.

Design of a fast response time single-phase PLL with dc offset rejection capability

Second-order generalized integrator (SOGI) based phase-locked loops (PLLs) are commonly used for grid voltage synchronization in single-phase grid-connected power converters. SOGI-PLLs are attractive because of their simple structure that makes them suitable for implementation even in low-end digital controllers. In this paper, an SOGI based fixed-parameter PLL structure with full dc offset rejection capability is presented. This PLL uses two cascaded SOGI structures and it is termed as cascaded generalized integrator PLL (CGI-PLL). A systematic design procedure is proposed for the CGI-PLL that minimizes the response time and unit vector harmonic distortion. This design achieves minimum settling time for any given worst-case frequency deviation in the grid voltage and ensures that the unit vector THD is less than 1%. The PLL designed using the proposed method has good harmonic attenuation capability. The steady-state and transient response of this PLL have been validated experimentally and are found to agree with the theoretical analysis.

Forensic Analysis of Packet Losses in Wireless Networks

Due to the lossy nature of wireless links, it is difficult to determine if packet losses are due to wireless-induced effects or from malicious discarding. Many prior efforts on detecting malicious packet drops rely on evidence collected via passive monitoring by neighbor nodes. However, they do not analyze the cause of packet losses. In this paper, we ask: 1) Given certain macroscopic parameters of the network (like traffic intensity and node density) what is the likelihood that evidence exists with respect to a transmission? 2) How can these parameters be used to perform a forensic analysis of the reason for the losses? Toward answering the above questions, we first build an analytical framework that computes the likelihood that evidence (we call this transmission evidence, or TE for short) exists with respect to transmissions, in terms of a set of network parameters. We validate our analytical framework via both simulations as well as real-world experiments on two different wireless testbeds. The analytical framework is then used as a basis for a protocol within a forensic analyzer to assess the cause of packet losses and determine the likelihood of forwarding misbehaviors. Through simulations, we find that our assessments are close to the ground truth in all examined cases, with an average deviation of 2.3% from the ground truth and a worst case deviation of 15.0%.

Mathematical modeling and a memetic algorithm for the integration of process planning and scheduling considering uncertain processing times

The integration of process planning and scheduling is important for an efficient utilization of manufacturing resources. However, the focus of existing works is mainly on deterministic constraints of jobs. This article proposes a novel memetic algorithm for the integrated process planning and scheduling problem with processing time uncertainty based on processing time scenarios. First, a mathematical model for the stochastic integrated process planning and scheduling problem based on the network graph is established. Due to the nonlinearity in the model and the complexity of the problem, a memetic algorithm is then suggested for this problem. A novel local search (variable neighborhood search) algorithm is incorporated into the memetic algorithm. Two effective neighborhood structures are employed in the variable neighborhood search algorithm to improve the overall performance of the population. Furthermore, for the uncertainty in processing times, a set of scenarios have been generated to evaluate each individual. Finally, two performance measures—the expected performance measure and the worst-case deviation measure—are introduced and compared. In the experimental studies, the proposed memetic algorithm is tested on typical benchmark instances. Computational results show that the expected makespan measure performs better than the worst-case deviation measure and the proposed method exhibits high performance especially for large-scale instances. In addition, the results obtained by the proposed memetic algorithm are more satisfactory than those obtained by the algorithm that considers deterministic processing times only.

Model predictive load–frequency control taking into account imbalance uncertainty

Nonlinear model predictive control (NMPC) is investigated for load frequency control (LFC) of an interconnected power system which is exposed to increasing wind power penetration. The robustified NMPC (RNMPC) proposed here uses knowledge of the estimated worst-case deviation in wind-power production to make the NMPC more robust. The NMPC is based on a simplified system model that is updated using state- and parameter estimation by Kalman filters, and it takes into account limitations on among others tie-line power flow. Tests on a proxy of the Nordic power system show that the RNMPC is able to fulfill system constraints under worst-case deviations in wind-power production, where the nominal NMPC is not.