Interval-based Algorithm Research Articles

Evolving fuzzy prediction interval for fault detection in a heat exchanger

The objective of this work is to design a novel evolving fuzzy prediction interval for modeling a nonlinear system and to implement a novel interval-based algorithm for fault detection. To achieve these goals, three frameworks are studied to provide the basis for the ideas to be proposed. First, the prediction intervals developed in the literature to characterize the uncertainties in modeling systems. Second, the evolving intelligence systems presented in the literature to improve the predictive models through adaptability to temporal changes. Third, the model-based error detection algorithms that detect anomalies in system behavior based on the error of the models. This work proposes a complete recursive design of the evolving fuzzy prediction interval based on interval coverage estimation. This estimation is based on the accumulated number of past time points in which the interval contained the measurements of the modeled system. Additionally, a new interval-based fault detection algorithm is proposed in this work that determines the activation of alarms based on the increment of the proposed interval failure index. This novel index is similar in structure to the interval coverage estimation. The proposed recursively evolving fuzzy prediction interval and interval-based fault detection algorithm were tested on a heat exchanger system whose characteristics were affected by external changes. The experimental results show the effectiveness of the proposed interval model in representing the dynamics of the heat exchanger. Furthermore, the experiment shows that the proposed fault detection algorithm achieves comparable accurate performance to the results of a previous model-based fault detection method.

Inner and outer characterization of the projection of polynomial equations using symmetries, quotients and intervals

In this paper, we propose a new approach to compute the projection of a set defined by polynomial equations. It assumes that the polynomial equations have some nice symmetries and that a solution of the projection problem is already available in the case where the variables along which we project are all positive. A new interval-based algorithm which combines symmetry operators and set quotient is proposed. Symmetries are used to move from one part of the space to another. The set quotient is needed to avoid redundant symmetries. The projection procedure yields an inner and an outer approximations of the projected set. Two applications are considered. The first one corresponds to the characterization of the space occupied by a rotating polygon, and the second one deals with the estimation of the speed of a moving object observed by several robots with uncertain orientations.

An interval-based nested optimization framework for deriving flexibility from smart buildings and electric vehicle fleets in the TSO-DSO coordination

Emerging renewable-based transmission and distribution systems, despite many environmental and economic benefits, due to the intermittent nature of their production resources, compared to traditional systems, need more flexibility capacities, which necessitates the need for more suppliers of flexibility. To deal with these challenges, a nested framework is presented to derive the required flexibility of the transmission system operator (TSO) from distributed energy resources (DERs) and active end-users such as smart buildings (SBs) and electric vehicle (EV) fleets at the distribution level. To this end, a novel mechanism to design the demand response program (DRP) is introduced in which tariffs with time-varying rewards are built based on flexibility requirements. The coordination between TSO and distribution system operator (DSO) is initially modeled as a bi-level non-linear programming (NLP) problem, in which the upper-level is day-ahead (DA) operational planning of DS considering the schedules received from SBs, while the lower-level is DA operational planning of the TS. The bi-level NIL problem is transformed into a single-level linear programming (LP) problem by Krush Kuhn Tucker (KKT) conditions, Big-M method and Strong Duality Theory (SDT), which makes it computationally tractable. Finally, a two-stage interval-based algorithm solves the obtained single-level problem to secure the planning against uncertainties where battery energy storage systems (BESSs) are responsible for dealing with extreme conditions. The simulation results testify that the proposed interval-based nested framework has improved the economic, technical and security aspects of the TSO-DSO coordination since it has reduced the daily costs of the energy and flexibility markets, relieved lines congestion and improved voltage characteristics.

Hierarchical Motion Planning for Autonomous Vehicles in Unstructured Dynamic Environments

This letter presents a hierarchical motion planner for generating smooth and feasible trajectories for autonomous vehicles in unstructured environments with static and moving obstacles. The framework enables real-time computation by progressively shrinking the solution space. First, a graph searcher based on combined heuristic and partial motion planning is proposed for finding coarse trajectories in spatiotemporal space. To enable fast online planning, a time interval-based algorithm that considers obstacle prediction trajectories is proposed, which uses line segment intersection detection to check for collisions. Second, to practically smooth the coarse trajectory, a continuous optimizer is implemented in three layers, corresponding to the whole path, the near-future path and the speed profile. We use discrete points to represent the far-future path and parametric curves to represent the near-future path and the whole speed profile. The approach is validated in both simulations and real-world off-road environments based on representative scenarios, including the “wait and go” scenario. The experimental results show that the proposed method improves the success rate and travel efficiency while actively avoiding static and moving obstacles.

Demonstration and Performance Evaluation of Two Novel Algorithms for Removing Artifacts From Automated Intraoperative Temperature Data Sets: Multicenter, Observational, Retrospective Study.

BackgroundThe automated acquisition of intraoperative patient temperature data via temperature probes leads to the possibility of producing a number of artifacts related to probe positioning that may impact these probes’ utility for observational research.ObjectiveWe sought to compare the performance of two de novo algorithms for filtering such artifacts.MethodsIn this observational retrospective study, the intraoperative temperature data of adults who received general anesthesia for noncardiac surgery were extracted from the Multicenter Perioperative Outcomes Group registry. Two algorithms were developed and then compared to the reference standard—anesthesiologists’ manual artifact detection process. Algorithm 1 (a slope-based algorithm) was based on the linear curve fit of 3 adjacent temperature data points. Algorithm 2 (an interval-based algorithm) assessed for time gaps between contiguous temperature recordings. Sensitivity and specificity values for artifact detection were calculated for each algorithm, as were mean temperatures and areas under the curve for hypothermia (temperatures below 36 °C) for each patient, after artifact removal via each methodology.ResultsA total of 27,683 temperature readings from 200 anesthetic records were analyzed. The overall agreement among the anesthesiologists was 92.1%. Both algorithms had high specificity but moderate sensitivity (specificity: 99.02% for algorithm 1 vs 99.54% for algorithm 2; sensitivity: 49.13% for algorithm 1 vs 37.72% for algorithm 2; F-score: 0.65 for algorithm 1 vs 0.55 for algorithm 2). The areas under the curve for time × hypothermic temperature and the mean temperatures recorded for each case after artifact removal were similar between the algorithms and the anesthesiologists.ConclusionsThe tested algorithms provide an automated way to filter intraoperative temperature artifacts that closely approximates manual sorting by anesthesiologists. Our study provides evidence demonstrating the efficacy of highly generalizable artifact reduction algorithms that can be readily used by observational studies that rely on automated intraoperative data acquisition.

Interval-Based LDA Algorithm for Electrocardiograms for Individual Verification

This paper presents an interval-based LDA (Linear Discriminant Analysis) algorithm for individual verification using ECG (Electrocardiogram). In this algorithm, at first, unwanted noise and power-line interference are removed from the ECG signal. Then, the autocorrelation profile (ACP) of the ECG signal, which is a mathematical representation of the degree of similarity between a given time series and a lagged version of itself over successive time intervals, is calculated. Finally, the interval-based LDA algorithm is applied to extract unique individual feature vectors that represent distance and angle characteristics on short ACP segments. These feature vectors are used during the processes of enrollment and verification of individual identification. To validate our algorithm, we conducted experiments using the MIT-BIH ECG and achieved EERs (Equal Error Rate) of 0.143%, showing that the proposed algorithm is practically effective and robust in verifying the individual’s identity.

DVFS Algorithms of GPU and Memory for Mobile GPGPU Applications: A case study

Although both OpenCL and RenderScript have allowed the General-Purpose Graphics Processing Unit (GPGPU) to be used even for mobile GPUs, it is still difficult for mobile applications to use the GPGPU for several reasons. One of the reasons is that mobile devices place restrictions on GPU performance through power-saving technologies such as Dynamic Voltage and Frequency Scaling (DVFS). DVFS tries to control the balance between performance and energy consumption based on the application’s requirements. This technology has been successful in many cases and is widely used; however, it significantly decreases the performance of GPGPU applications. In this paper, we propose novel DVFS algorithms for GPU and memory when the GPGPU applications run. The suggested algorithms decreased the energy consumption by more than 0.7 times without any algorithm changes, and improved the energy efficiency (performance per watt) by more than 3.42 times in comparison with the conventional interval-based algorithm.

QoS-Guaranted Slot Allocation Algorithm for Efficient Medium Access in HR-WPAN

It is very important to provide a parameterized quality of service (QoS) using traffic specification (TSPEC), such as mean data rate, maximum burst size, and peak data rate, when packets from the application layer need to be transmitted with guaranteed services in a high-rate wireless personal area network (HR-WPAN). As medium resources are limited, the optimal medium time required for each device needs to be estimated to share the resources efficiently among devices. This paper proposes a variable-service interval-based resource allocation algorithm to efficiently make a reservation of medium resources based on a parameterized QoS. In other words, the proposed algorithm calculates the number of medium access slots (MASs) based on TSPEC, local resources, and local conditions and determines suitable locations for the MASs within a superframe to accommodate more devices. The simulation results show that the proposed algorithm can accommodate more devices and has greater than 10% resource allocation efficiency in an HR-WPAN compared to existing schemes.

An interval-based algorithm to represent conformational states of experimentally determined polypeptide templates and fast prediction of approximated 3D protein structures

Predicting the three-dimensional (3-D) structure of a protein that has no templates in the Protein Data Bank (PDB) is a very hard, still an impossible task. Computational prediction methods have been developed during the last years, but the problem still remains challenging. In this paper we present a new strategy based on Interval Arithmetic to store structural information obtained from experimental protein templates and predict native-like approximate three-dimensional structures of proteins. Our objective is to perform the prediction in a very fast manner and predict native-like structures that can be used as starting point structures to ab initio methods. We illustrate the efficacy of our method in five case studies of polypeptides.

Assessing optimal assignment under uncertainty: An interval-based algorithm

We consider the problem of multi-robot task-allocation when robots have to deal with uncertain utility estimates. Typically an allocation is performed to maximize expected utility; we consider a means for measuring the robustness of a given optimal allocation when robots have some measure of the uncertainty (e.g. a probability distribution, or moments of such distributions). We introduce the interval Hungarian algorithm, a new algorithm that extends the classic Kuhn—Munkres Hungarian algorithm to compute the maximum interval of deviation, for each entry in the assignment matrix, which will retain the same optimal assignment. The algorithm has a worst-case time complexity of O(n 4); we also introduce a parallel variant with O(n 3) running time, which is able to exploit the concurrent computing capabilities of distributed multi-robot systems. This provides an efficient measurement of the tolerance of the allocation to the uncertainties and dynamics, for both a specific interval and a set of interrelated intervals. We conduct experiments both in simulation and with physical robots to validate the approach and to gain insight into the effect of location uncertainty on allocations for multi-robot multi-target navigation tasks.

An interval-based congestion control algorithm under varying network conditions

A new IRED (interval random early detection) congestion control algorithm is proposed for network congestion avoidance and resource management. Different to the traditional AQM (active queue management) algorithms, the control parameters of IRED are not configured statically, and is setting as a parameter interval according to the changes of network environment. By the interval parameter design, the IRED alleviates the tuning difficulty of RED (random early detection) and shows a robust performance than RED under varying network conditions. It is proved that the stability and stability margin of the IRED control system can be guaranteed. A systematic design method for the configuration of parameter interval is proposed. Simulation studies show the proposed IRED algorithm achieves a robust control performance in varying network environment, which is superior to the RED and Gentle-RED algorithm.

A fast memoryless interval-based algorithm for global optimization

We present a global optimization algorithm of the interval type that does not require a lot of memory and treats standard constraints. The algorithm is shown to be able to find one globally optimal solution under certain conditions. It has been tested with many examples with various degrees of complexity and a large variety of dimensions ranging from 1 to 2,000 merely in a basic personal computer. The extensive numerical experiments have indicated that the algorithm would have a good chance to successfully find a good approximation of a globally optimal solution. More importantly, it finds such a solution much more quickly and using much less memory space than a conventional interval method. The new algorithm is also compared with several noninterval global optimization methods in our numerical experiments, again showing its clear superiority in most cases.

Improving inter-block backtracking with interval Newton

Inter-block backtracking (IBB) computes all the solutions of sparse systems of nonlinear equations over the reals. This algorithm, introduced by Bliek et al. (1998) handles a system of equations previously decomposed into a set of (small) k ×k sub-systems, called blocks. Partial solutions are computed in the different blocks in a certain order and combined together to obtain the set of global solutions. When solutions inside blocks are computed with interval-based techniques, IBB can be viewed as a new interval-based algorithm for solving decomposed systems of nonlinear equations. Previous implementations used Ilog Solver and its IlcInterval library as a black box, which implied several strong limitations. New versions come from the integration of IBB with the interval-based library Ibex. IBB is now reliable (no solution is lost) while still gaining at least one order of magnitude w.r.t. solving the entire system. On a sample of benchmarks, we have compared several variants of IBB that differ in the way the contraction/filtering is performed inside blocks and is shared between blocks. We have observed that the use of interval Newton inside blocks has the most positive impact on the robustness and performance of IBB. This modifies the influence of other features, such as intelligent backtracking. Also, an incremental variant of inter-block filtering makes this feature more often fruitful.

Design Strategy of Serial Manipulators With Certified Constraint Satisfaction

This paper presents the design strategy of serial manipulators with constraint satisfaction. The algorithm provides certified solutions to the range of values of the manipulator design parameters that satisfy the given constraints for all points inside a desired workspace. Alternatively, it can also be used to obtain the achievable workspace of a particular manipulator topology within which a set of given constraints are satisfied. This strategy can therefore be applied to the general case of a serial manipulator design problem, robots of adjustable parameters, or even reconfigurable robot strategy to obtain a suitable topology. The interval-based algorithm was implemented on an example serial anthropomorphic manipulator with joint displacement constraints and obtains the possible variations to the manipulator topology that allow the required workspace to be achievable under the given joint displacement constraints. Results are presented and discussed.

Interval based off-line clock synchronization for wireless mesh networks

Wireless mesh networks suffer from various problems like congestion or packet collisions. To identify and overcome these problems an exact global view of the communication is required. However, it is not possible to observe the whole network from a single location. Instead, a distributed monitoring is necessary, which has to include clock synchronization. We present a new interval-based algorithm for the off-line synchronization of passively monitored network events. It calculates the worst-case time interval for every event on a global clock, while considering inaccuracies caused by processing jitter and non-uniform clock drifts. The experimental evaluation on a live mesh network shows an accuracy of better than 130μ s over a four-hop distance, which is below the minimum transmission time of data packets. Thereby, our algorithm creates a highly precise global view of the network, which allows a detailed diagnosis of wireless mesh networks.

Modeling measurement errors and missing initial values in freeway dynamic origin–destination estimation systems

Most existing dynamic origin–destination (O–D) estimation approaches are grounded on the assumption that a reliable initial O–D set is available and traffic volume data from detectors are accurate. However, in most traffic systems, both types of critical information are either not available or subjected to some level of measurement errors such as traffic counts and speed measurement from sensors. To contend with those critical issues, this study presents two robust algorithms, one for estimation of an initial O–D set and the other for tackling the input measurement errors with an extended estimation algorithm. The core concept of the initial O–D estimation algorithm is to decompose the target network in a number of sub-networks based on proposed rules, and then execute the estimation of the initial O–D set iteratively with the observable information at the first time interval. To contend with the inevitable detector measurement error, this study proposes an interval-based estimation algorithm that converts each model input data as an interval with its boundaries being set based on some prior knowledge. The performance of both proposed algorithms has been tested with a simulated system, the I-95 freeway corridor between I-495 and I-695, and the results are quite promising.

A New Efficient Block-Matching Algorithm for Motion Estimation

This paper presents a new full-search block-matching algorithm: Multi-stage Interval-based Motion Estimation algorithm (MIME). The proposed algorithm is a block based motion estimation algorithm that utilizes successive elimination technique. We define two approximate functions, as the upper and lower boundaries of the interval that includes the Conventional distortion metric SAD. Each stage in the proposed algorithm; except for the last stage; incorporates low resolution pixels for the boundary functions calculations. The final stage is a full resolution block matching stage. MIME has a high probability of finding the optimal motion vector at any stage of the algorithm. The proposed algorithm reduces the computational complexity by successively eliminating non-candidate blocks from the search window at each stage. This computational reduction leads to enhanced performance in terms of low power consumption and fast motion vector estimation. A low power VLSI implementation of the algorithm is also presented in this paper. Simulation results on benchmark video sequences shows that MIME algorithm eliminates almost 88% of the candidate blocks after only two interval based stages.

Interval-based clock synchronization with optimal precision

We present description and analysis of a novel optimal precision clock synchronization algorithm (OP), which takes care of both precision and accuracy with respect to external time. It relies upon the generic interval-based algorithm of Schmid and Schossmaier [Real-Time Syst. 12 (2) (1997) 173] and utilizes a convergence function based on the orthogonal accuracy algorithm of Schmid [Chicago J. Theor. Comput. Sci. 3 (2000) 3]. As far as precision is concerned, we show that OP achieves optimal worst case precision, optimal maximum clock adjustment, and optimal rate, as does the algorithm of Fetzer and Cristian [Proceedings 10th Annual IEEE Conference on Computer Assurance, Gaithersburg, MD, 1995]. However, relying upon a perception-based hybrid fault model and a fairly realistic system model, our results are valid for a wide variety of node and link faults and apply to very high-precision applications as well: Impairments due to clock granularity and discrete rate adjustment cannot be ignored here anymore. Our accuracy analysis focuses on the nodes’ local accuracy interval, which provides the atop running application with an on-line bound on the current deviation from external time. We show that this bound could get larger than twice the necessary lower bound (“traditional accuracy”), hence OP is considerably suboptimal in this respect.

A new interval bounding algorithm for parameter estimation from bounded-error data

A new interval-based algorithm for parameter estimation from bounded-error data is proposed. The new algorithm utilizes interval mathematics to calculate axis-aligned orthotopic (boxes) outer bounds on the set of feasible parameters. The outer bounds are then revised recursively using this new information. Examples are provided to illustrate the new method.

Interval-based Clock Synchronization

In this paper, we develop and analyze a simple interval-based algorithm suitable for fault-tolerant external clock synchronization. Unlike usual internal synchronization approaches, our convergence function-based algorithm provides approximately synchronized clocks maintaining both precision and accuracy w.r.t. external time. This is accomplished by means of a time representation relying on intervals that capture external time, providing accuracy information encoded in interval lengths. The algorithm, which is generic w.r.t. the convergence function and relies on either instantaneous correction or continuous amortization for clock adjustment, is analyzed by utilizing a novel, interval-based framework for establishing worst-case precision and accuracy bounds subject to a fairly detailed system model. Apart from individual clock rate and transmission delay bounds, our system model incorporates non-standard features like clock granularity and broadcast latencies as well. Relying on a suitable notion of internal global time, our analysis unifies treatment of precision and accuracy, ending up in striking conceptual beauty and expressive power.