Interval Analysis Algorithm Research Articles

Dynamic identification of axial force and boundary restraints in tie rods and cables with uncertainty quantification using Set Inversion Via Interval Analysis

A methodology is developed for the estimation of internal axial force and boundary restraints within in-service, prismatic axial force members of structural systems using interval arithmetic and contractor programming. The determination of the internal axial force and end restraints in tie rods and cables using vibration-based methods has been a long standing problem in the area of structural health monitoring and performance assessment. However, for structural members with low slenderness where the dynamics are significantly affected by the boundary conditions, few existing approaches allow for simultaneous identification of internal axial force and end restraints and none permit for quantifying the uncertainties in the parameter estimates due to measurement uncertainties. This paper proposes a new technique for approaching this challenging inverse problem that leverages the Set Inversion Via Interval Analysis algorithm to solve for the unknown axial forces and end restraints using natural frequency measurements. The framework developed offers the ability to completely enclose the feasible solutions to the parameter identification problem, given specified measurement uncertainties for the natural frequencies. This ability to propagate measurement uncertainty into the parameter space is critical towards quantifying the confidence in the individual parameter estimates to inform decision-making within structural health diagnosis and prognostication applications. The methodology is first verified with simulated data for a case with unknown rotational end restraints and then extended to a case with unknown translational and rotational end restraints. A laboratory experiment is then presented to demonstrate the application of the methodology to an axially loaded rod with progressively increased end restraint at one end.

Parameter identification for structural dynamics based on interval analysis algorithm

A parameter identification method using interval analysis algorithm for structural dynamics is presented in this paper. The proposed uncertain identification method is investigated by using central difference method and ARMA system. With the help of the fixed memory least square method and matrix inverse lemma, a set-membership identification technology is applied to obtain the best estimation of the identified parameters in a tight and accurate region. To overcome the lack of insufficient statistical description of the uncertain parameters, this paper treats uncertainties as non-probabilistic intervals. As long as we know the bounds of uncertainties, this algorithm can obtain not only the center estimations of parameters, but also the bounds of errors. To improve the efficiency of the proposed method, a time-saving algorithm is presented by recursive formula. At last, to verify the accuracy of the proposed method, two numerical examples are applied and evaluated by three identification criteria respectively.

High dimensional model representation for hybrid reliability analysis with dependent interval variables constrained within ellipsoids

Random variables could be dependent, and so could interval variables. To accommodate dependent interval variables, this work develops an efficient hybrid reliability analysis method to handle both random and dependent interval input variables. Due to the dependent interval variables, the reliability analysis needs to perform the probability analysis for every combination of dependent interval variables. This involves a nested double-loop procedure and dramatically decreases the efficiency. The proposed method decomposes the nested double loops into sequential probability analysis (PA) loop and interval analysis (IA) loop. An efficient IA algorithm based on the cut-HDMR (High Dimensional Model Representation) expansion is developed and a sampling strategy with the leave-one-out technique without extra calls of the limit-state function is proposed. The proposed method has good accuracy and efficiency as demonstrated by two engineering examples.

An interval space reducing method for constrained problems with particle swarm optimization

In this paper, we propose a method for solving constrained optimization problems using interval analysis combined with particle swarm optimization. A set inverter via interval analysis algorithm is used to handle constraints in order to reduce constrained optimization to quasi unconstrained one. The algorithm is useful in the detection of empty search spaces, preventing useless executions of the optimization process. To improve computational efficiency, a space cleaning algorithm is used to remove solutions that are certainly not optimal. As a result, the search space becomes smaller at each step of the optimization procedure. After completing pre-processing, a modified particle swarm optimization algorithm is applied to the reduced search space to find the global optimum. The efficiency of the proposed approach is demonstrated through comprehensive experimentation involving 100000 runs on a set of well-known benchmark constrained engineering design problems. The computational efficiency of the new method is quantified by comparing its results with other PSO variants found in the literature.

Tolerance Analysis of Antenna Array Pattern and Array Synthesis in the Presence of Excitation Errors

This paper analyzes array pattern tolerance against excitation errors. The nonprobabilistic interval analysis algorithm is used for tolerance analysis of the nonideal uniform linear array in this work. Toward this purpose, corresponding interval models of the power pattern functions are established, respectively, with the consideration of the amplitude errors, phase errors, or both simultaneously, in antenna arrays. The tolerance for the amplitude-phase error of the main function parameters including the beamwidth, sidelobe level, and the directivity is simulated by computer according to the indicators and the actual requirements. Accordingly, the worst admissible performance of an array can be evaluated, which may provide theoretical reference for optimal antenna array design. As for the problem of array synthesis in the presence of various array errors, interval analysis-convex programming (IA-CP) is presented. Simulation results show that the proposed IA-CP based synthesis technique is robust for the amplitude and phase errors.

Electrophysiologic Characteristics of Complex Fractionated Atrial Electrograms in Patients with Atrial Fibrillation

The underlying mechanisms of complex fractionated atrial electrogram (CFAE) during radiofrequency catheter ablation (RFCA) of atrial fibrillation (AF) have not yet been clearly elucidated. We explored the relationships between CFAE and left atrial (LA) voltage, or conduction velocity (CV). In 50 patients with AF (23 paroxysmal AF [PAF], 41 males, mean age 55.76 +/- 10.16 years), the CFAE (average index of fractionation of electrograms during AF by interval-analysis algorithm, cycle length [CL]<or= 120 ms) areas, voltage, and CV were measured at eight different quadrants in each patient's LA by analyzing a NavX-guided, color-coded CFAE CL map, a voltage map, and an isochronal map (500 ms pacing) generated by contact bipolar electrograms (70-100 points in the LA). The results were: (1) CFAE areas were predominantly located in the septum, roof, and LA appendage; (2) CFAE area had lower voltage than those in non-CFAE area and was surrounded by the areas of high voltage (P < 0.0001); (3) The CFAE areas had low CVs compared with non-CFAE areas (P < 0.001); and (4) The percentage of CFAE area was lower in patients with persistent atrial fibrillation (PeAF) compared with those with PAF (P < 0.05). The CFAE area, which is primarily located at the septum, has a low voltage with a lower CV, and is surrounded by high-voltage areas. Underlying electroanatomical complexity is associated with clustering of CFAEs.

Coordinated basal-bolus infusion for tighter postprandial glucose control in insulin pump therapy.

Basal and bolus insulin determination in intensive insulin therapy for type 1 diabetes mellitus (T1DM) are currently considered independently of each other. A new strategy that coordinates basal and bolus insulin infusion to cope with postprandial glycemia in pump therapy is proposed. Superior performance of this new strategy is demonstrated through a formal analysis of attainable performances in an in silico study. The set inversion via interval analysis algorithm has been applied to obtain the feasible set of basal and bolus doses that, for a given meal, mathematically guarantee a postprandial response fulfilling the International Diabetes Federation (IDF) guidelines (i.e., no hypoglycemia and 2 h postprandial glucose below 140 mg/dl). Hypoglycemia has been defined as a glucose value below 70 mg/dl. A 5 h time horizon has been considered for a 70 kg in silico T1DM subject consuming meals in the range of 30 to 80 g of carbohydrates. The computed feasible sets demonstrate that current separated basal/bolus strategy dramatically limits the attainable performance. For a nominal basal of 0.8 IU/h leading to a basal glucose of approximately 100 mg/dl, IDF guidelines cannot be fulfilled for meals greater than 50 g of carbohydrates, independent of the bolus insulin computed. However, coordinating the basal and bolus insulin delivery can achieve this. A decrement of basal insulin during the postprandial period is required together with an increase in bolus insulin, in appropriate percentages, which is meal dependent. After 3 h, basal insulin can be restored to its nominal value. The new strategy meets IDF guidelines in a typical day, contrary to the standard basal/bolus strategy, yielding a mean 2 h postprandial glucose reduction of 36.4 mg/dl without late hypoglycemia. The application of interval analysis for the computation of feasible sets is demonstrated to be a powerful tool for the analysis of attainable performance in glucose control.

An Interval Analysis Algorithm for Automated Controller Synthesis in QFT Designs

In this paper, an interval analysis algorithm is proposed for the automatic synthesis of fixed structure controllers in quantitative feedback theory (QFT). The proposed algorithm is tested on several examples and compared with the controller designs given in the QFT literature. Compared to the existing methods for QFT controller synthesis, the proposed algorithm yields considerable improvement in the high frequency gain of the controller in all examples, and improvements in the cutoff frequency of the controller in all but one examples. Notation: R denotes the field of real numbers, Rn is the vector space of column vectors of length n with real entries. A real closed nonempty interval is a one-dimensional box, i.e., a pair x=[x̱,x¯] consisting of two real numbers x̱ and x¯ with x̱⩽x¯. The set of all intervals is IR. A box may be considered as an interval vector x=(x1,…,xn)T with components xk=[x̱k,x¯k]. A box x can also be identified as a pair x=[x̱,x¯] consisting of two real column vectors x̱ and x¯ of length n with x̱⩽x¯. A vector x∊Rn is contained in a box x, i.e., x∊x iff x̱⩽x⩽x¯. The set of all boxes of dimension n is IRn. The width of a box x is wid x=x¯−x̱. The range of a function f:Rn→R over a box x is range(f,x)={f(x)∣x∊x}. A natural interval extension of f on the box x is obtained by replacing in the expression for f, all occurrences of reals xi with intervals xi and all real operations with the corresponding interval operations. The natural interval evaluation of f on x is written as f(x). The interval function f(x) is said to be of convergent of order α if widf(x)−wid{range(f,x)}⩽c{widx}α. By the inclusion property of interval arithmetic, range (f,x)⊆f(x).

SET-MEMBERSHIP IDENTIFICATION OF CONTINUOUS-TIME SYSTEMS

The identification of continuous-time systems from discrete-time data is investigated in a bounded-error context. Errors are taken as a discrete time signal, additive on output, unknown but bounded with known bounds. The set inversion via interval analysis algorithm is used with validated numerical integration methods. The theory of monotone cooperative systems is also introduced in order to derive tighter enclosures for the solution of the differential equations. Via an illustrative example with simulated data, it is shown that for systems modelled by parabolic differential equations, the cooperativity property only makes it possible to obtain results in a reasonable computation time.

SENSOR BASED ROBOT LOCALISATION AND NAVIGATION: USING INTERVAL ANALYSIS AND NONLINEAR KALMAN FILTERS.

Multiple sensor fusion for robot localisation and navigation has attracted a lot of interest in recent years. This paper describes a sensor based navigation and localisation approach for an autonomous mobile robot using an interval analysis (IA) based adaptive mechanism for the non-linear Kalman filter namely the Extended Kalman filter (EKF). The map used for this study is two-dimensional and assumed to be known a priori. The robot is equipped with inertial sensors (INS), encoders and ultrasonic sensors. A non-linear Kalman filter is used to estimate the robots position using the inertial sensors and encoders. The ultrasonic sensors use an Interval Analysis (IA) algorithm for guaranteed robot localisation. Since the Kalman Filter estimates may be affected by bias, drift etc. we propose an adaptive mechanism using IA to correct these defects in estimates. In the presence of landmarks the complementary interval robot position information from the IA algorithm with uniform distribution using ultrasonic sensors is used to estimate and bound the errors in the non-linear Kalman filter robot position estimate with a Gaussian distribution.

A Simple Algorithm for Global Data Flow Analysis Problems

A simple, iterative bit propagation algorithm for solving global data flow analysis problems such as “available expressions” and “live variables” is presented and shown to be quite comparable in speed to the corresponding interval analysis algorithm. This comparison is facilitated by a result relating two parameters of a reducible flow graph (rfg). Namely, if G is an rfg, d is the largest number of back edges found in any cycle-free path in G, and k is the length of the interval derived sequence of G, then $k \geqq d$. (Intuitively, k is the maximum nesting depth of loops in a computer program, while d is a measure of the maximum loop-interconnectedness.) The node ordering employed by the simple algorithm is the reverse of the order in which a node is last visited while growing any depth-first spanning tree of the flow graph. In addition, a dominator algorithm for an rfg is presented which takes O(edges) bit vector steps.