lower bounds on the localization errors of a moving source observed by a passive array the cramer rao inequality is used to set absolute bounds on the accuracy of location and velocity estimates obtainable by observing the signal radiated from a moving acoustic source at an array of stationary sensors the source radiates a zero mean gaussian random process and the observations are made in a background of spatially incoherent gaussian noise results are first obtained for the error covariance matrix of a set of parameters characterizing the time variable differential delays observed at various sensor pairs these are then translated into bounds on the error covariance matrix of a set of parameters describing source location and track numerical results are presented for the specific case of a source moving in a straight line course at constant velocity

an accurate algebraic solution for moving source location using tdoa and fdoa measurements this paper proposes an algebraic solution for the position and velocity of a moving source using the time differences of arrival tdoas and frequency differences of arrival fdoas of a signal received at a number of receivers the method employs several weighted least squares minimizations only and does not require initial solution guesses to obtain a location estimate it does not have the initialization and local convergence problem as in the conventional linear iterative method the estimated accuracy of the source position and velocity is shown to achieve the crame spl acute r rao lower bound for gaussian tdoa and fdoa noise at moderate noise level before the thresholding effect occurs simulations are included to examine the algorithm s performance and compare it with the taylor series iterative method

alleviating sensor position error in source localization using calibration emitters at inaccurate locations a previous study shows that the use of a calibration emitter whose position is known exactly can significantly reduce the loss in time differences of arrival tdoa based source localization accuracy when the available sensor positions have random errors this paper extends the previous work to a more practical scenario where the exact position of a calibration emitter is not known by modeling the calibration position error as additive gaussian noise the amount of reduction in localization accuracy due to calibration position error is derived through cramer rao lower bound crlb analysis in addition the analysis also affirms the previous studies on bayesian sensor network localization that it remains possible to improve the localization accuracy even if the calibration position is completely unknown next a performance analysis illustrates that the penalty could be very high if one simply pretends the calibration position is accurate and ignores its error a closed form solution is then developed by accounting for the calibration position error and it is proved analytically to reach the crlb accuracy when the sensor and calibration position errors are small relative to the distance between the calibration emitter and the sensor finally the results are generalized to the case where multiple calibration emitters are available when deploying multiple calibration emitters although their positions may not be known exactly we show that it is possible to completely eliminate the sensor position error and recover the best localization accuracy that is limited by the measurement noise in tdoas only all the theoretical developments are corroborated by simulations

structural optimization under uncertain loads and nodal locations this paper presents algorithms for solving structural topology optimization problems with uncertainty in the magnitude and location of the applied loads and with small uncertainty in the location of the structural nodes the second type of uncertainty would typically arise from fabrication errors where the tolerances for the node locations are small in relation to the length scale of the structural elements we first review the discrete form of the uncertain loads problem which has been previously solved using a weighted average of multiple load patterns with minor modifications we extend this solution to include loads described by continuous joint probability density functions we then proceed to the main contribution of this paper structural optimization under uncertainty in the nodal locations this optimization problem is computationally difficult because it involves variations of the inverse of the structural stiffness matrix it is shown however that for small uncertainties the problem can be recast into a simpler but equivalent structural optimization problem with equivalent uncertain loads by expressing these equivalent loads in terms of continuous random variables we are able to make use of the extended form of the uncertain loads problem presented in the first part of this paper the optimization algorithms are developed in the context of minimum compliance maximum stiffness design simple examples are presented the results demonstrate that load and nodal uncertainties can have dramatic impact on optimal design for structures containing thin substructures under axial loads it is shown that these uncertainties a are of first order significance influencing the linear elastic response quantities and b can affect designs by avoiding unrealistically optimistic and potentially unstable structures the additional computational cost associated with the uncertainties scales linearly with the number of uncertainties and is insignificant compared to the cost associated with solving the deterministic structural optimization problem

bias reduction for an explicit solution of source localization using tdoa this paper proposes two methods to reduce the bias of the well known algebraic explicit solution chan and ho a simple and efficient estimator for hyperbolic location ieee trans signal process vol 42 pp 1905 1915 aug 1994 for source localization using tdoa bias of a source location estimate is significant when the measurement noise is large and the geolocation geometry is poor bias also dominates performance when multiple times of independent measurements are available such as in uwb localization or in target tracking the paper starts by deriving the bias of the source location estimate from chan and ho the bias is found to be considerably larger than that of the maximum likelihood estimator two methods called biassub and biasred are developed to reduce the bias the biassub method subtracts the expected bias from the solution of chan and ho s work where the expected bias is approximated by the theoretical bias using the estimated source location and noisy data measurements the biasred method augments the equation error formulation and imposes a constraint to improve the source location estimate the biassub method requires the exact knowledge of the noise covariance matrix and biasred only needs the structure of it analysis shows that both methods reduce the bias considerably and achieve the crlb performance for distant source when the noise is gaussian and small the biassub method can nearly eliminate the bias and the biasred method is able to lower the bias to the same level as the maximum likelihood estimator the biasred method is extended for tdoa and fdoa positioning simulations corroborate the performance of the proposed methods

robust topology optimization of structures with imperfect geometry based on geometric nonlinear analysis abstract topology optimization often leads to structures consisting of slender elements which are particularly sensitive to geometric imperfections such imperfections might affect the structural stability and induce large displacement effects in these slender structures this paper therefore presents a robust approach to topology optimization which accounts for geometric imperfections and their potentially detrimental influence on the structural stability geometric nonlinear effects are incorporated in the optimization by means of a total lagrangian finite element formulation in the minimization of end compliance geometric imperfections are modeled as a vector valued random field in the design domain the resulting uncertain performance of the design is taken into account by minimizing a weighted sum of the mean and standard deviation of the compliance in the robust optimization problem these stochastic moments are typically estimated by means of sampling methods such as monte carlo simulation however these methods require multiple independent nonlinear finite element analyses in each design iteration of the optimization algorithm an efficient solution algorithm which uses adjoint differentiation in a second order perturbation method is therefore developed to estimate the stochastic moments during the optimization two applications with structures that exhibit different types of structural instabilities are examined in both cases it is demonstrated by means of an extensive monte carlo simulation that the deterministic design is very sensitive to imperfections while the design obtained by means of the proposed method is much more robust

measurement of the differential doppler shift doppler shifts between narrow band signals observed at one or more pairs of receivers and originated from a remote source of radiation are useful for estimating source location and track this paper deals with an instrumentationally attractive approach of estimating differential doppler shifts by making center frequency measurements at each receiver output and subtracting them in a pairwise fashion for low in band signal to noise ratio conditions center frequency measurements at different receiver outputs are weakly correlated in this mode of operation therefore the mean square error in the differential doppler estimate equals the pairwise sum of the mean square errors in each of the center frequency measurement for high signal to noise ratio conditions the various center frequency estimates are strongly correlated in this mode of operation the accuracy of the resulting differential doppler estimate improves with the first power of the signal to noise ratio even though the accuracy of each center frequency estimate approaches an absolute bound independent of the noise spectrum the optimal minimum mean square error differential doppler shift estimate is obtained by simultaneous processing of the receiver outputs jointly comparison between the former indirect and the latter direct estimation techniques yields some interesting insights the accuracy of the direct estimation procedure is proportional to t 3where t is the observation period it is basically a coherent procedure center frequency measurement and the differential doppler shift estimate derived from it are basically incoherent procedures and obey the well known t 1dependence under high signal to noise ratio conditions the estimation error in both methods decreases with the first power of the signal to noise ratio under low signal to noise ratio conditions the accuracy of the suboptimal indirect method is inferior to the optimal direct method by a factor proportional to the inverse first power of the individual signal to noise ratio

statistical estimation of the parameters of a moving source from array data on propose une methode d estimation des parametres d un modele de retard temporel lineaire la methode compare les transformees de fourier a differentes frequences

delay and doppler estimation by time space partition of the array data an instrumentationally attractive technique for estimating the doppler time compression and its time derivatives is proposed and analyzed in this paper the basic scheme consists of m 1 generalized cross correlators gcc s in parallel where m is the number of sensors in the receiving array each of which is implemented successively to generate a sequence of differential delay measurements the resulting spatial temporal differential delay data are then compressed into the estimates of the doppler and its derivatives using a least squares ls filter it is shown that for signal to noise ratio snr conditions above the threshold level the indicated two step estimation procedure is very nearly optimal when operating near the threshold point however the proposed scheme is only distinctly suboptimal

nonlinear robust optimization via sequential convex bilevel programming in this paper we present a novel sequential convex bilevel programming algorithm for the numerical solution of structured nonlinear min max problems which arise in the context of semi infinite programming here our main motivation are nonlinear inequality constrained robust optimization problems in the first part of the paper we propose a conservative approximation strategy for such nonlinear and non convex robust optimization problems under the assumption that an upper bound for the curvature of the inequality constraints with respect to the uncertainty is given we show how to formulate a lower level concave min max problem which approximates the robust counterpart in a conservative way this approximation turns out to be exact in some relevant special cases and can be proven to be less conservative than existing approximation techniques that are based on linearization with respect to the uncertainties in the second part of the paper we review existing theory on optimality conditions for nonlinear lower level concave min max problems which arise in the context of semi infinite programming regarding the optimality conditions for the concave lower level maximization problems as a constraint of the upper level minimization problem we end up with a structured mathematical program with complementarity constraints mpcc the special hierarchical structure of this mpcc can be exploited in a novel sequential convex bilevel programming algorithm we discuss the surprisingly strong global and locally quadratic convergence properties of this method which can in this form neither be obtained with existing sqp methods nor with interior point relaxation techniques for general mpccs finally we discuss the application fields and implementation details of the new method and demonstrate the performance with a numerical example

an approximately efficient tdoa localization algorithm in closed form for locating multiple disjoint sources with erroneous sensor positions this paper considers the problem of time difference of arrival tdoa source localization when the tdoa measurements from multiple disjoint sources are subject to the same sensor position displacements from the available sensor positions this is a challenging problem and closed form solution with good localization accuracy has yet to be found this paper proposes an estimator that can achieve this purpose the proposed algorithm jointly estimates the unknown source and sensor positions to take the advantage that the tdoas from different sources have the same sensor position displacements the joint estimation is a highly nonlinear problem due to the coupling of source and sensor positions in the measurement equations we introduce the novel idea of hypothesized source locations in the algorithm development to enable the formulation of psuedolinear equations thereby leading to the establishment of closed form solution for source location estimates besides the advantage of closed form the newly developed algorithm is shown analytically under the condition that the tdoa measurement noise and the sensor position errors are sufficiently small to reach the crlb accuracy for clarity the localization of two disjoint sources is used in the algorithm development the developed algorithm is then examined under the special case of a single source and extended to the more general case of more than two unknown sources the theoretical developments are supported by simulations

optimal design of trusses with geometric imperfections accounting for global instability abstract a topology optimization method is proposed for the design of trusses with random geometric imperfections due to fabrication errors this method is a generalization of a previously developed perturbation approach to topology optimization under geometric uncertainties the main novelty in the present paper is that the objective function includes the nonlinear effects of potential buckling due to misaligned structural members solutions are therefore dependent on the magnitude of applied loads and the direction of resulting internal member forces whether they are compression or tension direct differentiation is used in the sensitivity analysis and analytical expressions for the associated derivatives are derived in a form that is computationally efficient a series of examples illustrate how the effects of geometric imperfections and buckling may have substantial influence on truss design monte carlo simulation together with second order elastic analysis is used to verify that solutions offer improved performance in the presence of geometric uncertainties

delay estimation using narrow band processes array processing of narrow band gaussian signals is studied with emphasis on delay estimation the barankin bound is used to examine the effect of ambiguity on mean square measurement error when the bound is plotted as a function of signal to noise ratio one observes a distinct threshold above the critical signal to noise ratio the lower bound on mean square error is given by the cramer rao inequality which is approached by the barankin inequality under these conditions below the threshold the barankin bound can exceed the cramer rao bound by large factors the relative magnitude of the bounds in that region depends critically on the ratio of signal center frequency to signal bandwidth

robust nonlinear optimization with conic representable uncertainty set the robust optimization methodology is known as a popular method dealing with optimization problems with uncertain data and hard constraints this methodology has been applied so far to various convex conic optimization problems where only their inequality constraints are subject to uncertainty in this paper the robust optimization methodology is applied to the general nonlinear programming nlp problem involving both uncertain inequality and equality constraints the uncertainty set is defined by conic representable sets the proposed uncertainty set is general enough to include many uncertainty sets which have been used in literature as special cases the robust counterpart rc of the general nlp problem is approximated under this uncertainty set it is shown that the resulting approximate rc of the general nlp problem is valid in a small neighborhood of the nominal value furthermore a rather general class of programming problems is posed that the robust counterparts of its problems can be derived exactly under the proposed uncertainty set our results show the applicability of robust optimization to a wider area of real applications and theoretical problems with more general uncertainty sets than those considered so far the resulting robust counterparts which are traditional optimization problems make it possible to use existing algorithms of mathematical optimization to solve more complicated and general robust optimization problems

passive localization from doppler shifted frequency measurements the position and speed of a moving source that radiates a pure tone can be determined by measurements of doppler shifted frequencies at five or more different locations the equations relating to the measured frequencies to the localization parameters are nonlinear and there is no closed form solution solving nonlinear equations by a grid search whereby all possible combination of source parameters are entered into the equation to see if they constitute a solution would require a five dimensional search a more efficient search scheme that uses intermediate variables which are products of some of the unknowns is introduced the search dimension is two the resultant intermediate equations become linear and are easier to solve the major calculation at each grid point requires only an inversion of a 3 3 matrix the cramer rao bound for localization is given together with simulation results that verify the method

estimation of time differences of arrival by pole decomposition time differences of arrival tdoa s of emitter wave fronts to a spatially distributed array of sensors can be used to determine the source location in this paper we suggest a new method of tdoa estimation for multiple unknown autoregressive moving average arma sources and additive noise that may be correlated between the sensors we derive a theoretical formula that only uses the receiver cross spectra and the source poles for the tdoa determination the poles are estimated by a least squares technique and two methods are suggested for the estimation of the cross spectra which allow tradeoffs between computational complexity and accuracy a new time delay model is derived and used to show the applicability of the methods for noninteger tdoa s results from simulations illustrate the performance of the algorithm by monte carlo trials and compare it to the cramer rao bound

robust truss topology design via semidefinite programming we present and motivate a new model of the truss topology design problem where the rigidity of the resulting truss with respect both to given loading scenarios and small occasional loads is optimized it is shown that the resulting optimization problem is a semidefinite program we derive and analyze several equivalent reformulations of the problem and present illustrative numerical examples

a new method for optimal truss topology design truss topology optimization formulated in terms of displacements and bar volumes results in a large nonconvex optimization problem for the case of maximization of stiffness for a prescribed volume this paper presents a new equivalent an unconstrained and convex minimization problem in displacements only where the function to be minimized is the sum of terms each of which is the maximum of two convex quadratic functions existence of solutions is proved as is the convergence of a nonsmooth steepest descent type algorithm for solving the topology optimization problem the algorithm is computationally attractive and has been tested on a large number of examples some of which are presented

potential reduction polynomial time method for truss topology design the multiload truss topology design problem is modeled as a minimization of the maximum with respect to k loading scenarios compliance subject to equilibium constraints and restrictions on the bar volumes the problem may involve a very large number of potential bars so as to allow a rich variety of topologies the original formulation is in terms of two sets of variables m bar volumes and n nodal displacements several equivalent convex reformulations of this problem are presented these convex problems although highly nonlinear possess nice analytical structure and therefore can be solved by an interior point potential reduction method associated with appropriate logarithmic barrier for the feasible domain of the problem for this method to improve the accuracy of the current a proximate solution by an absolute constant factor it suffices in the worst case to perform o sqrt km newton steps with o k 3 n 3 k 2 n 2 m operations per step

robustness analysis of trusses with separable load and structural uncertainties this paper discusses evaluation techniques of the robustness function of trusses which is regarded as one of measures of structural robustness under the uncertainties of member stiffnesses and external forces by using quadratic embedding of the uncertainty and the s procedure we formulate a quasiconvex optimization problem which provides lower bounds of the robustness functions a bisection method is proposed where we solve a finite number of semidefinite programming problems in order to obtain a global optimal solution to the proposed quasiconvex optimization problem the lower bounds of the robustness functions are computed for various trusses under several uncertainty circumstances

robust optimization of sums of piecewise linear functions with application to inventory problems robust optimization is a methodology that has gained a lot of attention in the recent years this is mainly due to the simplicity of the modeling process and ease of resolution even for large scale models unfortunately the second property is usually lost when the cost function that needs to be robustified is not concave or linear with respect to the perturbing parameters in this paper we study robust optimization of sums of piecewise linear functions over polyhedral uncertainty set given that these problems are known to be intractable we propose a new scheme for constructing conservative approximations based on the relaxation of an embedded mixed integer linear program and relate this scheme to methods that are based on exploiting affine decision rules our new scheme gives rise to two tractable models that respectively take the shape of a linear program and a semidefinite program with the latter having the potential to provide solutions of better quality than the former at the price of heavie

on safe tractable approximations of chance constrained linear matrix inequalities in the paper we consider the chance constrained version of an affinely perturbed linear matrix inequality lmi constraint assuming the primitive perturbations to be independent with light tail distributions e g bounded or gaussian constraints of this type playing a central role in chance constrained linear conic quadratic semidefinite programming are typically computationally intractable the goal of this paper is to develop a tractable approximation to these chance constraints our approximation is based on measure concentration results and is given by an explicit system of lmis thus the approximation is computationally tractable moreover it is also safe meaning that a feasible solution of the approximation is feasible for the chance constraint

transient three dimensional rayleigh and stoneley signal effects in thermoelastic solids a transient 3d study of surface rayleigh and interface stoneley signals in fully coupled thermolastic solids begins by obtaining analytical expressions for the zeroes of the corresponding rayleigh stoneley functions that arise in the integral transforms of the solutions the expressions locate the zeroes as functions of the temporal transform variable in a complex plane defined by a scalar resultant of spatial transform variables expressions for the change in surface temperature caused by the rayleigh signal are then derived for cases of normal traction surface loading by using long time asymptotic results the expressions can be obtained analytically and they show that rayleigh stoneley signal induced thermal effects can be important the long time asymptotic results also show that rayleigh stoneley zeroes reduce to the thermally modified inverses of the classical non thermal rayleigh stoneley wave speeds this result agrees with 2d predictions that can be made on the basis of low frequency asymptotic harmonic wave studies the long time results are not restrictive because time is scaled by a small i e o 10 4 m thermoelastic characteristic length

estimation of the speed of moving source from time delay estimate this work studies the situation in which a signal emitted by a moving source was received by an array of sensors the particular cases of interest are those in which the time delay between sensors can be approximated by a linear function the procedure for estimating linear time delay functions is discussed based on the time delay estimate a procedure for estimating the speed of the moving source is proposed simulations are carried out the results show that the procedure gives an unbiased estimate of the speed and the estimates are asymptotically normal distributed

optimal source localization and tracking from passive array measurements if the signal of a moving source is observed at several spatially separated locations during a common time interval the received signals exhibit differential delays and doppler shifts which provide information about source location and velocity this paper deals with the optimal in the minimum mean square error sense source localization and tracking by utilizing differential delay and doppler observations at a linear array of receivers we shall be concerned with source ranges large compared with array baseline and with the distance traversed by the source during the observation interval it is shown that the optimal estimation procedure can be carried out in two sequential steps without any loss in performance in the first step source location is estimated from the differential delay group of measurements in the second step source velocity is estimated from the differential doppler group of measurements and the outcome of the first step furthermore by employing an intermediate track dependent parameter set the two step algorithm yields a closed form solution of the estimation problem

robust topology optimization under multiple independent unknown but bounded loads abstract the optimal designs obtained from the deterministic topology optimization without considering the loading uncertainties may become vulnerable or even lead to catastrophic failures a two level optimization formulation is often used in the robust topology optimization rto under uncertain loads various approaches have been reported to identify the critical loads associated with the worst structure responses because convex model approaches apply convex approximations to the original non convex model at the lower level the optimal designs obtained by these methods are greatly dependent on the quality of the approximation in this paper a new formulation based on the wolfe duality for the rto problems with multiple independent unknown but bounded loads is proposed following the two level formulation the lower level optimization problem for the worst multiple independent uncertain loading case is transformed by the wolfe duality both the first order necessary conditions and the second order sufficient conditions are derived rigorously to validate the solution optimality despite of the non convexity associated with the lower level formulation numerical examples are also presented to demonstrate the proposed approach

robust solutions of uncertain quadratic and conic quadratic problems we consider a conic quadratic and in particular a quadratically constrained optimization problem with uncertain data known only to reside in some uncertainty set cal u the robust counterpart of such a problem leads usually to an np hard semidefinite problem this is the case for example when cal u is given as the intersection of ellipsoids or as an n dimensional box for these cases we build a single explicit semidefinite program which approximates the np hard robust counterpart and we derive an estimate on the quality of the approximation which is essentially independent of the dimensions of the underlying conic quadratic problem

design of planar articulated mechanisms using branch and bound this paper considers an optimization model and a solution method for the design of two dimensional mechanical mechanisms the mechanism design problem is modeled as a nonconvex mixed integer program which allows the optimal topology and geometry of the mechanism to be determined simultaneously the underlying mechanical analysis model is based on a truss representation allowing for large displacements for mechanisms undergoing large displacements elastic stability is of major concern we derive conditions modeled by nonlinear matrix inequalities which guarantee that a stable equilibrium is found and that buckling is prevented the feasible set of the design problem is described by nonlinear differentiable and non differentiable constraints as well as nonlinear matrix inequalities to solve the mechanism design problem a branch and bound method based on convex relaxations is developed to guarantee convergence of the method two different types of convex relaxations are derived the relaxations are strengthened by adding valid inequalities to the feasible set and by solving bound contraction sub problems encouraging computational results indicate that the branch and bound method can reliably solve mechanism design problems of realistic size to global optimality

transient thermal effects in edge dislocation generation near a crack edge abstract a transient 2 d study of edge dislocation generation near a crack in a fully coupled thermoelastic solid loaded by sv wave diffraction is considered exact solutions to the mixed boundary initial value problem in the integral transform space are obtained and inversions valid for short times performed the solution behavior indicates that the generation process requires only a short time period and that thermal effects might be important in particular a thermally sensitive dislocation takes longer to be emitted from the crack edge region than one described in a non thermal analysis but on the other hand does not arrest moreover in contrast to the simple relaxation effect seen in non thermal analyses dislocation generation here causes oscillations in the dynamic stress intensity factor finally the average temperature gradient across the dislocation cut is large enough to suggest that generation may be a potential source of local material disorder

some statistical methods for random process data from seismology and neurophysiology examples are presented of statistical techniques for the analysis of random process data and of their uses in the substantive fields of seismology and neurophysiology the problems addressed include frequency estimation for decaying cosinusoids signal estimation association measurement causal connection assessment estimation of speed and direction and structural modeling the techniques employed include complex demodulation nonlinear regression probit analysis deconvolution maximum likelihood singular value decomposition fourier analysis and averaging

spectral analysis for harmonizable processes spectral estimation of nonstationary but harmonizable processes is considered given a single realization of the process periodogram like and consistent estimators are proposed for spectral mass estimation when the spectral support of the process consists of lines such a process can arise in signals of a moving source from array data or multipath signals with doppler stretch from a single receiver such processes also include periodically correlated or cyclostationary and almost periodically correlated processes as special cases we give detailed analysis on aliasing bias and covariances of various estimators it is shown that dividing a single long realization of the process into nonoverlapping subsections and then averaging periodogram like estimates formed from each subsection will not yield meaningful results if one is estimating spectral mass with support on lines with slope not equal to 1 if the slope of a spectral support line is irrational then spectral masses do not fold on top of each other in estimation even if the data are equally spaced simulation examples are given to illustrate various theoretical results

estimating partial group delay summary the partial group delay between two channels of a multiple time series has an interpretation as the time lag between frequency components of the two channels after adjustments have been made for the influence of the remaining channels a procedure for estimating partial group delay is proposed and conditions for consistency and asymptotic normality of the estimating sequence are obtained

optimal delay estimation in a multiple sensor array having spatially correlated noise the maximal likelihood ml estimation of time of arrival differences for signals from a single source or target arriving at m geq 2 sensors has been the subject of a large number of papers in recent years these time differences or delays enable target location nearly all previous work has assumed noises which are independent among all sensors herein noises are taken to have complex correlation between sensors a set of nonlinear equations in the unknown delays is derived and the fisher information matrix fim for the estimates is also derived the cramer rao matrix bound crmb which is the inverse of fim shows optimal estimator covariances computer evaluations are plotted for crmb elements with varied snr and noise covariance values typical of turbulent boundary layer noise in towed arrays and signal sources at infinite range plane wave fronts maximum changes in the bound are within 3 db for complex noise correlations with magnitudes up to 0 4 which we tested

efficient convex relaxation methods for robust target localization by a sensor network using time differences of arrivals we consider the problem of target localization by a network of passive sensors when an unknown target emits an acoustic or a radio signal its position can be localized with multiple sensors using the time difference of arrival tdoa information in this paper we consider the maximum likelihood formulation of this target localization problem and provide efficient convex relaxations for this nonconvex optimization problem we also propose a formulation for robust target localization in the presence of sensor location errors two cramer rao bounds are derived corresponding to situations with and without sensor node location errors simulation results confirm the efficiency and superior performance of the convex relaxation approach as compared to the existing least squares based approach when large sensor node location errors are present

an asymptotically efficient estimator for tdoa and fdoa positioning of multiple disjoint sources in the presence of sensor location uncertainties this correspondence considers the problem of locating multiple disjoint sources using time differences of arrival tdoas and frequency differences of arrival fdoas in the presence of sensor position and velocity errors previous work applies to one source only with suboptimum performance for near source or requires joint estimation of the source and sensor locations that could be computation demanding through nonlinearly transforming the measurements and converting them with respect to the inaccurate sensor locations we have developed an algebraic solution to this problem the solution is shown analytically to achieve the cramer rao lower bound crlb performance over small noise region and does not require joint estimation with sensor locations

effects of crack surface convection for rapid crack growth in a thermoelastic solid abstract as a green s function for rapid steady state crack growth with crack surface convection semi infinite mode i crack growth at subcritical speeds in an unbounded solid under the action of compressive line loads moving on the crack surfaces is considered a standard convection law that relates heat flux to change in temperature is employed and the solid obeys the fully coupled dynamic equations of thermoelasticity the use of robust asymptotic forms reduces the problem to the solution of coupled integral equations these exhibit both cauchy and abel operators but an exact solution is possible the solution indicates that convection can give rise to temperature changes in the crack plane that are both more prominent and extensive than those that occur for an insulated crack surface exact expressions for the thermoelastic rayleigh speed which is the critical crack speed and for speeds that arise for a particular value of an important characteristic parameter are also presented

the nominal force method for truss geometry and topology optimization incorporating stability considerations abstract this paper presents a computationally efficient method for truss layout optimization with stability constraints previously proposed approaches that ensure stability of optimal frameworks are first reviewed showing that existing studies are generally restricted to topology optimization the present contribution aims to generalize the approach to simultaneous geometry and topology optimization a lower bound plastic design formulation under multiple loading will serve as basis for this purpose the numerical difficulties associated with geometrical variations are identified and the parametrization is adapted accordingly to avoid nodal instability the nominal force method is adopted which introduces artificial loading cases to simulate the effect of geometric imperfections hence the truss systems with unstable nodes are eliminated from the set of optimal solutions at the same time the local stability of structural members is ensured via a consistent local buckling criterion this novel formulation leads to optimal configurations that can be practically used for the preliminary design of structural frameworks four applications illustrate the impact of stability constraints on the solution the importance of geometry optimization is also pointed out by comparing with results that would be unattainable by topology optimization only

response of welded thermoelastic solids to the rapid motion of thermomechanical sources parallel to the interface abstract the analysis of rapidly moving thermomechanical surface sources is extended to the study of buried thermomechanical sources that move parallel to the interface of two welded dissimilar thermoelastic half spaces at a constant subcritical speed the sources are manifest as body force line loads in the coupled equations of thermoelasticity and a 2 d steady state situation is treated exact integral transform solutions are obtained and expressions for the displacements and temperature changes are generated by analytical inversion of robust asymptotic versions of the transforms these expressions show that thermoelastic coupling effects increase with source speed and that the thermal source is always manifest in combination with a component of the mechanical source i e an effective thermal source term exists the expressions also exhibit component functions that are in effect hybrids of functions that are seen in purely thermal and isothermal elastic solutions the critical source speed is defined as the minimum of the two asymptotic thermoelastic rayleigh speeds in the half spaces and when it exists the asymptotic thermoelastic stoneley speed exact expressions for these speeds are given and used to present some typical values