a geometric optimization approach to detecting and intercepting dynamic targets using a mobile sensor network a methodology is developed to deploy a mobile sensor network for the purpose of detecting and capturing mobile targets in the plane the sensing pursuit problem considered in this paper is analogous to the marco polo game in which a pursuer marco must capture multiple mobile targets that are sensed intermittently and with very limited information the competing objectives exhibited by this problem arise in a number of surveillance and monitoring applications in this paper the mobile sensor network consists of a set of robotic sensors that must track and capture mobile targets based on the information obtained through cooperative detections when these detections form a satisfactory target track a mobile sensor is switched to pursuit mode and deployed to capture the target in minimum time since the sensors are installed on robotic platforms and have limited range the geometry of the platforms and of the sensors fields of view play a key role in obstacle avoidance and target detection a new cell decomposition approach is presented to determine the probability of detection and the cost of operating the sensors from the geometric properties of the network and its workspace the correctness and complexity of the algorithm are analyzed proving that the termination time is a function of the network parameters and of the number of required detections

influence of errors on the two microphone method for measuring acoustic properties in ducts using the two microphone method acoustic properties in ducts as for example reflection coefficient and acoustic impedance can be calculated from a transfer function measurement between two microphones in this paper a systematic investigation of the various measurement errors that can occur and their effect on the calculated quantities is made the input data for the calculations are the measured transfer function the microphone separation and the distance between one microphone and the sample first errors in the estimate of the transfer function are treated conclusions concerning the most favorable measurement configuration to avoid these errors are drawn next the length measurement errors are treated measurements were made to study the question of microphone interference the influence of errors on the calculated quantities has been investigated by numerical simulation from this conclusions are drawn on the useful frequency range for a given microphone separation and on the magnitude of errors to expect for different cases

input impedance in flow ducts theory and measurement this paper presents both a theoretical and an experimental investigation of the influence of the mean flow on the input impedance of a duct the input impedance of an axisymetrical flow duct is calculated taking into account the convective effect of a uniform flow the dissipative effect of a turbulent flow and the radiation in an open jet each of these effects is separately studied an experimental apparatus has been specifically designed to lower flow noise on the transducers taking advantage of the two microphone three calibration tmtc method v gibiat and f laloe j acoust soc am 88 2533 2545 1990 whose full calibration process allows any geometry for the measurement head theory and experiments are compared for a 1 m long cylindrical duct carrying a flow whose mach number equals up to 0 15 the resonant frequencies are in close agreement within 3 the relative evolution of the magnitude maxima with increasing flow are in good agreement within 10 despite similar tendencies when modifying the mean flow velocity the amplitude of variation of the magnitude is 2 to 5 times smaller in the experiments this paper presents both a theoretical and an experimental investigation of the influence of the mean flow on the input impedance of a duct the input impedance of an axisymetrical flow duct is calculated taking into account the convective effect of a uniform flow the dissipative effect of a turbulent flow and the radiation in an open jet each of these effects is separately studied an experimental apparatus has been specifically designed to lower flow noise on the transducers taking advantage of the two microphone three calibration tmtc method v gibiat and f laloe j acoust soc am 88 2533 2545 1990 whose full calibration process allows any geometry for the measurement head theory and experiments are compared for a 1 m long cylindrical duct carrying a flow whose mach number equals up to 0 15 the resonant frequencies are in close agreement within 3 the relative evolution of the magnitude maxima with increasing flow are in good agreement within 10 despite similar tendencies when mo

experimental evaluation of inverse filtering using physical systems with known glottal flow and tract characteristics the technique presented here uses an impedance head to measure the input impedance spectrum of a physical model of a vocal tract and then to inject a known glottal flow waveform into the tract the sound measured outside the mouth is used to evaluate inverse filtering techniques by comparison with the known glottal flow and measured acoustical properties of the tract the normalized least square errors in the glottal flow were typically a percent or less in the time domain and several percent in the frequency domain accurate determination of resonance frequencies and bandwidths required a suitable order of inverse filter

the fuzzy two load method for measurement of ducted one port source characteristics abstract knowledge of source characteristics is important for the calculation of sound pressure level and insertion loss of a silencer in sourced ducts measurement is usually the only feasible approach for the determination of source characteristics the present paper is concerned with the measurement methods based on the helmholtz thevenin equivalent of ducted one port plane wave sources existing methods are classified as crisp and over determined methods in the crisp methods the measured data are just sufficient for unique characterization of the source this calls for two loads if their phase relative to the source is known otherwise three loads are required over determined methods use more number of loads than the crisp methods and are motivated for possible minimization of variations due to measurement errors the point estimates for the source parameters are however still subject to some uncertainty but estimation of confidence intervals is not feasible because the loads do not constitute a probability sample the present paper proposes an approach which can yield the source characteristics in intervals from auto power spectral density measurements with only two loads the method is based on a novel apollonian circle formulation it is called the fuzzy two load method because uncertainty inherent to measurements is modelled by fuzzification of a characteristic parameter of the apollonian circle of two loads fuzzy number transformations leading to the source pressure strength sound pressure level and insertion loss interval predictions are discussed in depth the paper includes an application showing the working features of the fuzzy two load method

an exact two dimensional non guillotine cutting tree search procedure we consider the two dimensional cutting problem of cutting a number of rectangular pieces from a single large rectangle so as to maximize the value of the pieces cut we develop a lagrangean relaxation of a zero one integer programming formulation of the problem and use it as a bound in a tree search procedure subgradient optimization is used to optimize the bound derived from the lagrangean relaxation problem reduction tests derived from both the original problem and the lagrangean relaxation are given incorporating the bound and the reduction tests into a tree search procedure enables moderately sized problems to be solved

application of multivariate uncertainty analysis to frequency response function estimates uncertainty estimation is an important part of any measurement but is often neglected for complex valued or multivariate data e g vectors this paper presents a methodology for estimating the uncertainty in multivariate experimental data and applies it to the measurement of the frequency response function obtained when using a periodic random input signal this multivariate uncertainty method is an extension of classical uncertainty methods used for scalar variables and tracks the correlation between all variates along with the sample variance instead of just tracking the standard uncertainty the method is used in this paper to propagate the sample covariance matrix from spectral density estimates to the uncertainty in the frequency response function estimate for two different system models in the first model the case when only the output signal is corrupted by noise is considered while in the second model both the input and output signals are corrupted by uncorrelated noise sources the results for the single noise model are verified by comparing them to published expressions in the literature while the results for the two noise model are verified by using a direct computation of the statistics finally the method is applied to experimental data from two microphone measurements within an acoustic waveguide the random uncertainty estimates in the frequency response function from the multivariate method agree well with the results from a direct computation of the statistics

error analysis of two microphone measurements in ducts with flow in an earlier work h boden and m abom j acoust soc am 79 541 549 1986 the influence of errors on two microphone measurements in ducts without flow has been studied the aim of this article is mainly to extend the earlier work to include the effects of mean flow and also of attenuation during the sound propagation first a short review of the various existing two microphone methods is made the errors in the measured input data are then analyzed and special attention is paid to the effects of neglected attenuation nonideal microphones and flow noise the influence of errors on the calculated quantities has been investigated and the conclusions from the earlier work have been extended to the case with flow it is also shown that the neglect of attenuation between the microphones leads to a low frequency limit for the applicability of the two microphone method finally a new technique for measuring the mach number using a two microphone method is suggested

a mathematical model and a solution method for the problem of placing various sized circles into a strip abstract a mathematical model of the problem of placing different radii circles into a strip is constructed several peculiarities of the mathematical model are considered on the ground of these peculiarities an original method of transition from one local minimum to another one to provide a decrease of the objective function value is suggested the method is based on the idea of increasing the problem dimension and a reduced gradient method as well as on the concept of active inequalities and the newton method an algorithm to solve the problem is described in detail numerical examples which demonstrate the possibilities of the method are also given

on uniqueness transfer and combination of acoustic sources in one dimensional systems the use of electroacoustic analogies suggests that a source of acoustical energy such as an engine compressor blower turbine loudspeaker etc can be characterized by an acoustic source pressure ps and internal source impedance zs analogous to the open circuit voltage and internal impedance of an electrical source the present paper shows analytically that the source characteristics evaluated by means of the indirect methods are independent of the loads selected that is the evaluated values of ps and zs are unique and that the results of the different methods including the direct method are identical in addition general relations have been derived here for the transfer of source characteristics from one station to another station across one or more acoustical elements and also for combining several sources into a single equivalent source finally all the conclusions are extended to the case of a uniformly moving medium incorporating the convective as well as dissipative effects of the mean flow

on the multiple microphone method for measuring in duct acoustic properties in the presence of mean flow nowadays the two microphone method is accepted as the standard as specified in astm e1050 90 for measuring in duct acoustic properties however research results on using the least square method with multiple measurement points and broadband excitation have been reported for enhancing the frequency response of the two microphone method in this paper the effects of varying the relative measurement positions on errors in the estimation of the acoustic quantities is studied for the multiple microphone method both the theoretical and experimental results show that among possible sensor positioning configurations the equidistant positioning of sensors yields the smallest error within the effective measurement frequency range in addition it is noted that the measurement accuracy can be increased and the effective frequency range can be widened by increasing the number of equidistant sensors measurement examples are shown and the results support the findings

lebesgue function for multivariate interpolation by radial basis functions multivariate interpolation and approximation is a powerful tool for intuition of real world in this paper we study lebesgue function and lebesgue constant for multivariate interpolation by conditionally positive definite rbfs also we give a conjecture about similar bernstein and erdos problem to multivariate case

a geometric transversals approach to sensor motion planning for tracking maneuvering targets this paper presents a geometric transversals approach for representing the probability of track detection as an analytic function of time and target motion parameters by this approach the optimization of the detection probability subject to sensor kinodynamic constraints can be formulated as an optimal control problem using the proposed detection probability function the necessary conditions for optimality can be derived using calculus of variations and solved numerically using a variational iteration method vim the simulation results show that sensor state and control trajectories obtained by this approach bring about a significant increase in detection probability compared to existing strategies and require a computation that is significantly reduced compared to direct methods

interpolation in the limit of increasingly flat radial basis functions abstract many types of radial basis functions such as multiquadrics contain a free parameter in the limit where the basis functions become increasingly flat the linear system to solve becomes highly ill conditioned and the expansion coefficients diverge nevertheless we find in this study that limiting interpolants often exist and take the form of polynomials in the 1 d case we prove that with simple conditions on the basis function the interpolants converge to the lagrange interpolating polynomial hence differentiation of this limit is equivalent to the standard finite difference method we also summarize some preliminary observations regarding the limit in 2 d

error analysis of spectral estimates with application to the measurement of acoustic parameters using random sound fields in ducts several methods have been proposed using multiple point pressure measurement of random sound fields in ducts to determine acoustic properties of materials and systems this paper presents an error analysis of the spectral estimates used in these techniques expressions for the normal acoustic absorption coefficient and impedance are derived for a random sound field in a duct theory is developed to determine the bias and random errors in estimating the spectral density function for plane wave propagation in the duct a bivariate stochastic process has been employed to model the acoustic system experimental and theoretical calculations show that minimum bias error can be achieved by using a small bandwidth in estimating the spectra and by locating the microphones close to the sample furthermore random error can be minimized by maintaining a high coherence between microphone signals this implies that the microphones should have a small spacing however high coherence may not be realized when a microphone location coincides with a node point in the sound field

a least squares method for evaluation of characteristics of acoustical sources abstract a multi load method to determine source characteristics is presented here the method is simple only one microphone is used and no second noise source is needed it is shown that a larger amount of information gained from the system due to more loads avoids stability problems the validity of the source parameters obtained by the method is compared with the prediction of insertion loss and of the noise production at the output of a known load both theoretical predictions and experimental results are compared the agreement is good further explanations are given regarding stability problems occurring in the so called four load method the method gives better results for relatively complex sources non constant impedance than the four load method although consuming more time in measurement because of the extra loads

solving circle packing problems by global optimization numerical results and industrial applications abstract a general circle packing is an optimized arrangement of n arbitrary sized circles inside a container e g a rectangle or a circle such that no two circles overlap in this paper we present several circle packing problems review their industrial applications and some exact and heuristic strategies for their solution we also present illustrative numerical results using generic global optimization software packages our work highlights the relevance of global optimization in solving circle packing problems and points towards the necessary advancements in both theory and numerical practice

on the reconstruction of the vibro acoustic field over the surface enclosing an interior space using the boundary element method the vibrational velocity sound pressure and acoustic power on the vibrating boundary comprising an enclosed space are reconstructed by the boundary element method based on the measured field pressures the singular value decomposition is used to obtain the inverse solution in the least square sense and to express the acoustic modal expansion between the measurement and source fields in general such an inverse operation has been considered an ill posed problem having a divergence phenomenon involved with extremely small measurement errors the ill conditioned nature of the acoustic inverse problem is caused by the singularity of the transfer matrix which produces nonradiating wave components in order to minimize the singularity and to also reduce the number of measurement points optimal measurement positions are determined by the effective independence method regularization methods are used to stabilize the reconstructed field by suppressing nonradiating components resulting in the singular transfer

iterated tabu search for the circular open dimension problem abstract this paper investigates the circular open dimension problem codp which consists of packing a set of circles of known radii into a strip of fixed width and unlimited length without overlapping the objective is to minimize the length of the strip in this paper codp is solved by a series of sub problems each corresponding to a fixed strip length for each sub problem an iterated tabu search approach named its is proposed its starts from a randomly generated solution and attempts to gain improvements by a tabu search procedure after that if the obtained solution is not feasible a perturbation operator is subsequently employed to reconstruct the incumbent solution and an acceptance criterion is implemented to determine whether or not accept the perturbed solution as a supplementary method the length of the strip is determined in monotonously decreasing way with the aid of some post processing techniques the search terminates and returns the best found solution after the allowed computation time has been elapsed computational experiments based on numerous well known benchmark instances show that its produces quite competitive results with respect to the best known results while the computational time remains reasonable for each instance

a geometric transversal approach to analyzing track coverage in sensor networks this paper presents a new coverage formulation addressing the quality of service of sensor networks that cooperatively detect targets traversing a region of interest the problem of track coverage consists of finding the positions of n sensors such that a lebesgue measure on the set of tracks detected by at least k sensors is optimized this paper studies the geometric properties of the network addressing a deterministic track coverage formulation and binary sensor models it is shown that the tracks detected by a network of heterogeneous omnidirectional sensors are the geometric transversals of non translates families of circles a novel methodology based on cone theory is presented for representing and measuring sets of transversals in closed form then the solution of the track coverage problem can be formulated as a nonlinear program nlp the numerical results show that this approach can improve track coverage by up to two orders of magnitude compared to grid and random deployments also it can be used to reduce the number of sensors required to achieve a desired detection performance by up to 50 and to optimally replenish or reposition existing sensor networks

fuzzy plane geometry ii circles and polygons abstract this paper continues our research in fuzzy plane geometry previously we studied fuzzy points and fuzzy lines now we investigate fuzzy circles and fuzzy polygons we show that the fuzzy area of a fuzzy circle or a fuzzy polygon is a fuzzy number we also argue that the fuzzy perimeter of a fuzzy circle or a fuzzy polygon is a fuzzy number

packing different sized circles into a rectangular container abstract this paper is motivated by the problem of fitting pipes of different diameters into a shipping container here we study the subproblem of fitting circles of different sizes into a rectangle since that problem is a central part of the larger problem we formulate this situation as a nonlinear mixed integer programming problem and develop a number of heuristic procedures for approximately solving this problem the heuristics are based on a variety of solution building rules that emulate the process of packing a container some of these methods including a genetic algorithm were based on a more structured design intended to provide solutions which are stable from a stowage viewpoint these heuristics are described in detail and their relative performances are compared for a sample set of 66 randomly generated problems based on this sample the best performing heuristic methods were a quasi random technique and a genetic algorithm of the stable solution structure

some observations regarding interpolants in the limit of flat radial basis functions abstract radial basis functions rbfs form a primary tool for multivariate interpolation some of the most commonly used radial functions feature a shape parameter allowing them to vary from being nearly flat e small to sharply peaked e large the former limit can be particularly accurate when interpolating a smooth function based on scattered data this study discusses theoretical and computational aspects of the e 0 limit and includes the conjecture that gaussian rbf interpolants will never diverge in this limit

cutting stock problems and solution procedures this paper discusses some of the basic formulation issues and solution procedures for solving one and two dimensional cutting stock problems linear programming sequential heuristic and hybrid solution procedures are described for two dimensional cutting stock problems with rectangular shapes we also propose an approach for solving large problems with limits on the number of times an ordered size may appear in a pattern

improved precision in measurements of acoustic impedance spectra using resonance free calibration loads and controlled error distribution resonances and or singularities during measurement and calibration often limit the precision of acoustic impedance spectra this paper reviews and compares several established techniques and describes a technique that incorporates three features that considerably improve precision the first feature is to minimize problems due to resonances by calibrating the instrument using up to three different acoustic reference impedances that do not themselves exhibit resonances the second involves using multiple pressure transducers to reduce the effects of measurement singularities the third involves iteratively tailoring the spectrum of the stimulus signal to control the distribution of errors across the particular measured impedance spectrum examples are given of the performance of the technique on simple cylindrical waveguides

a geometric transversals approach to analyzing the probability of track detection for maneuvering targets there is considerable precedence in the sensor tracking and estimation literature for modeling maneuvering targets by markov motion models in order to estimate the target state from multiple distributed sensor measurements although the transition probability density functions of these markov models are routinely outputted by tracking and estimation algorithms little work has been done to use them in sensor coordination and control algorithms this paper presents a geometric transversals approach for representing the probability of track detection by multiple distributed sensors as a function of the markov model transition probabilities by this approach the markov parameters of maneuvering targets that may be detected by the sensors are represented by three dimensional cones that are finitely generated by the sensors fields of view in a spatiotemporal euclidian space then the problem of deploying a sensor network for the purpose of maximizing the expected number of target detections can be formulated as a nonlinear program that can be solved numerically for the optimal sensor placement numerical results show that the optimal sensor placements obtained by this geometric transversals approach significantly outperform greedy grid or randomized sensor deployments

optimizing the packing of cylinders into a rectangular container a nonlinear approach abstract the container loading problem has important industrial and commercial applications an increase in the number of items in a container leads to a decrease in cost for this reason the related optimization problem is of economic importance in this work a procedure based on a nonlinear decision problem to solve the cylinder packing problem with identical diameters is presented this formulation is based on the fact that the centers of the cylinders have to be inside the rectangular box defined by the base of the container a radius far from the frontier and far from each other at least one diameter with this basic premise the procedure tries to find the maximum number of cylinder centers that satisfy these restrictions the continuous nature of the problem is one of the reasons that motivated this study a comparative study with other methods of the literature is presented and better results are achieved

refined multiload method for measuring acoustical source characteristics of an intake or exhaust system the one port source characteristics in a duct system viz source impedance and strength can be determined by using the four load method in this paper to avoid the instability problem of the conventional four load method a new formulation for the multiload method has been proposed which employs an error function based on the linear time invariant source model it is shown that the method is less sensitive to input errors compared to the previous methods for a 10 input error the proposed method yields a relative error in the source resistance that is about 1 100 times smaller than for the conventional method the effectiveness of the present method is demonstrated by two test examples a loudspeaker and a blower each operating in a duct it is observed that the conventional and least squares methods result in large errors whereas the present method yields far better agreement with the actual source parameters as measured by the direct method the present method is then used to obtain the source parameters on the exhaust side of an operating internal combustion engine the radiated sound spectrum from the exhaust opening is predicted by using the measured source parameters and the calculated result agrees very well with the measured one

an improved algorithm for the packing of unequal circles within a larger containing circle abstract this paper describes an approved algorithm for the problems of unequal circle packing the quasi physical quasi human algorithm first the quasi physical approach for the general packing problems is described in solving the pure problems of unequal circle packing the method is an analogy to the physical model in which a number of smooth cylinders are packed inside a container a quasi human strategy is then proposed to trigger a jump for a stuck object in order to get out of local minima our method has been tested in numerical experiments the computational results are presented showing the merits of the proposed method our algorithm can be thought as an adoptive algorithm of the tabu search

uncertainty analysis of the two microphone method accurate duct acoustic propagation models are required to characterize and subsequently reduce aircraft engine noise the boundary conditions for these models ultimately rely on accurate measurements of the acoustic impedance for candidate nacelle liners the standard two microphone method is widely used to estimate acoustic impedance but does not provide uncertainty estimates that are essential for data quality assessment and model validation a systematic framework is presented in this paper to propagate the experimental 95 confidence interval uncertainty estimates in the measured quantities to the calculated acoustic impedance data using the two microphone method for small and large input uncertainties one method is an analytical small perturbation technique using multivariate statistics this method provides useful analytical scaling information a second monte carlo method is utilized to validate the analytical multivariate method both methods are applied to the two microphone method for simulated data representative of sound hard and sound soft acoustic materials the results indicate that for realistic experimental parameters the uncertainty in the input measurements results in nonlinear perturbations therefore the small perturbation technique fails and the monte carlo method should be used to obtain uncertainty estimates furthermore the nonlinear perturbations also distort the output statistical distributions of the calculated acoustic impedance and reflection coefficient which results in significant deviation from gaussian behavior the distortion is a function of the acoustic impedance of the specimen itself finally the monte carlo method is applied to experimental data for a ceramic tubular specimen and compared to the multivariate results to demonstrate the implementation and usefulness of the technique

error analysis for the four load method used to measure the source impedance in ducts the impedance of a sound source can be measured using direct approaches such as the standing wave and transfer function methods or indirect approaches such as two load three load and four load methods unlike the direct and two load methods the three load and four load methods do not require the measurement of a complex quantity such as the acoustic transfer function therefore a single channel signal analyzer can be used to measure the autospectra needed in the case of the three load and four load methods the formulation for the source impedance gives two and three second order nonlinear algebraic equations for the three load and four load methods the unknowns in these equations are the real and imaginary parts of the source impedance the two nonlinear equations in the three load method can be solved graphically for each frequency of interest or by using well known mathematical methods however in the four load method there are three nonlinear equations in terms of two unknowns which means one of the equations is redundant the three nonlinear equations could also be reduced to two linear equations and the two equations could be solved for the real and imaginary parts of the source impedance the accuracy of the solutions depends on how accurately the original nonlinear equations are satisfied when the real and imaginary parts are substituted into these equations an error analysis of the formulation in the four load method of source impedance measurement was done it was found that the error due to apparent reduction of the nonlinear equations to linear equations was very large the source impedance values computed using the four load method were compared with those obtained from the direct transfer function method although the formulation of the four load method satisfies the mathematical procedure the error due to computation could be large and further work is needed in the application of the three load and the four load methods