stochastic theory of continuous time state space identification this paper presents theory algorithms and validation results for system identification of continuous time state space models from finite input output sequences the algorithms developed are methods of subspace model identification and stochastic realization adapted to the continuous time context the resulting model can be decomposed into an input output model and a stochastic innovations model using the riccati equation we have designed a procedure to provide a reduced order stochastic model that is minimal with respect to system order as well as the number of stochastic inputs thereby avoiding several problems appearing in standard application of stochastic realization to the model validation problem

identification of continuous time models the paper considers the problem of estimation of the transfer function of a continuous time dynamic system in the presence of colored noise the author introduces an operator transformation that allows for keeping a continuous time parametrization whereas the parameter estimation can be made by means of a discrete time maximum likelihood algorithm a comparison is made between the performance of the new method in comparison with a standard identification of an armax model the method is useful in cases where it is important to estimate the coefficients of a continuous time transfer function and where it is important to maintain a physical interpretation of the transfer function results

a sampling theory approach for continuous arma identification the problem of estimating continuous domain autoregressive moving average processes from sampled data is considered the proposed approach incorporates the sampling process into the problem formulation while introducing exponential models for both the continuous and the sampled processes we derive an exact evaluation of the discrete domain power spectrum using exponential b splines and further suggest an estimation approach that is based on digitally filtering the available data the proposed functional which is related to whittle s likelihood function exhibits several local minima that originate from aliasing the global minimum however corresponds to a maximum likelihood estimator regardless of the sampling step experimental results indicate that the proposed approach closely follows the cramer rao bound for various aliasing configurations

discontinuous displacement approximation for capturing plastic localization it is proposed to capture localized plastic deformation via the inclusion of regularized displacement discontinuities at element boundaries interfaces of the finite element subdivision the regularization is based on a kinematic assumption for an interface that resembles that which is pertinent to the classical shear band concept as a by product of the regularization an intrinsic band width is introduced as a constitutive property rather than a geometric feature of the finite element mesh in this way the spurious mesh sensitivity which is obtained when the displacement approximation is continuous can be avoided another consequence is that the interfacial relation between the elements is derived directly from the conventional constitutive properties of the continuously deforming material an interesting feature is that the acoustic tensor will not only play a role for diagnosing discontinuous bifurcation but will also serve as the tangent stiffness tensor of the interface up to within a scalar factor an analytical investigation of the behaviour of the interface is carried out and it is shown that dilatation may indeed accompany slip within a shear band for a general plasticity model the significance of proper mesh alignment is demonstrated for a simple problem in plane strain and plane stress it is shown that a unique structural post peak response in accordance with non linear fracture mechanics can be achieved when the plastic softening modulus is properly related to the bandwidth the paper concludes with a numerical simulation of the gradual development of a shear band in a soil slope

rigorous time space trade offs for inverting functions we provide rigorous time space trade offs for inverting any function given a function f we give a time space trade off of t s2 n3 q f where q f is the probability that two random elements taken with replacement are mapped to the same image under f we also give a more general trade off t s3 n3 that can invert any function at any point

membership in constant time and almost minimum space this paper deals with the problem of storing a subset of elements from the bounded universe mathcal m 0 ldots m 1 so that membership queries can be performed efficiently in particular we introduce a data structure to represent a subset of n elements of mathcal m in a number of bits close to the information theoretic minimum b left lceil lg m choose n right rceil and use the structure to answer membership queries in constant time

brief paper stochastic system transformation using generalized orthonormal basis functions with applications to continuous time system identification this paper studies the system transformation using generalized orthonormal basis functions that include the laguerre basis as a special case the transformation of the deterministic systems is studied in the literature which is called the hambo transform the aim of the paper is to develop a transformation theory for stochastic systems the paper establishes the equivalence of continuous and transformed discrete time stochastic systems in terms of solutions the method is applied to the continuous time system identification problem it is shown that using the transformed signals the po moesp subspace identification algorithm yields consistent estimates for system matrices an example is included to illustrate the efficacy of the proposed identification method and to make a comparison with the method using the laguerre filter

unique permutation hashing we propose a new hash function the unique permutation hash function and a performance analysis of its hash computation we denote the cost of a hash function h by c h k n which stands for the expected number of table entries that are checked when inserting the k 1 s t key into a hash table of size n where k out of n table entries are filled by previous insertions a hash function maps a key to a permutation of the table locations a hash function h is simple uniform if items are equally likely to be hashed to any table location in the first trial a hash function h is random or strong uniform if the probability of any permutation to be a probe sequence when using h is 1n where n is the size of the table we show that the unique permutation hash function is not only a simple uniform hash function but also a random hash function i e strong uniform and therefore has the optimal cost namely each probe sequence is equally likely to be chosen when the keys are uniformly chosen our hash function ensures that each empty table location has the same probability to be assigned by a uniformly chosen key we also show that the expected time for computing the unique permutation hash function is o 1 and the expected number of table locations that are checked before an empty location is found during insertion or search is also o 1 for constant load factors a 1 where the load factor a is the ratio between the number of inserted items and the table size

an analysis of strong discontinuities in multiplicative finite strain plasticity and their relation with the numerical simulation of strain localization in solids abstract this paper presents an analysis of strong discontinuities in inelastic solids at finite strains solutions exhibiting this type of discontinuities characterized by a discontinuous displacement field are shown to make physical and mathematical sense in a classical multiplicative plasticity continuum model if the softening modulus is reinterpreted as a singular distribution physically the strainsoftening is localized along the discontinuity conditions for the appearance of strong discontinuities in the geometrically nonlinear range are characterized as it is the response of the material during localization in addition these analytical results are exploited in the design of a new class of finite element methods the proposed methods fall within the class of enhanced strain methods and lead to solutions independent of the mesh size and insensitive to mesh alignment without requiring any regularization of the solutions by numerical parameters like a characteristic length

on the unique identification of continuous time autoregressive models from sampled data in this work we investigate the relationship between continuous time autoregressive ar models and their sampled version we consider uniform sampling and derive criteria for uniquely determining the continuous time parameters from sampled data the model order is assumed to be known we achieve this by removing a set of measure zero from the collection of all ar models and by investigating the asymptotic behavior of the remaining set of autocorrelation functions we provide necessary and sufficient conditions for uniqueness of general ar models and we demonstrate the usefulness of this result by considering particular examples we further exploit our theory and introduce an estimation algorithm that recovers continuous time ar parameters from sampled data regardless of the sampling interval we demonstrate the usefulness of our algorithm for various gaussian and non gaussian ar processes

batch scheme recursive parameter estimation of continuous time systems using the modulating functions method abstract the modulating functions method is a very effective method for parameter estimation of continuous time systems that are linear in their parameters one efficient implementation developed by pearson and lee involves the use of trigonometric functions and fast computations offered by fpt techniques in this paper a recursive implementation of the method is developed for on line parameter estimation of a continuous time system by shifting a fixed window of time series data one step forward at each sampling instant the resulting recursion algorithms are fast and use the identities of discrete fourier transforms along with some inherent commutative properties a simulation example with a van der pol oscillator is included to investigate the performance of the proposed estimation method

linear hash functions consider the set h of all linear or affine transformations between two vector spaces over a finite field f we study how good h is as a class of hash functions namely we consider hashing a set s of size n into a range having the same cardinality n by a randomly chosen function from h and look at the expected size of the largest hash bucket h is a universal class of hash functions for any finite field but with respect to our measure different fields behave differently if the finite field f has n elements then there is a bad set s f 2 of size n with expected maximal bucket size h n 1 3 if n is a perfect square then there is even a bad set with largest bucket size always at least n this is worst possible since with respect to a universal class of hash functions every set of size n has expected largest bucket size below n 1 2 if however we consider the field of two elements then we get much better bounds the best previously known upper bound on the expected size of the largest bucket for this class was o 2 log n we reduce this upper bound to o log n log log n note that this is not far from the guarantee for a random function there the average largest bucket would be t log n log log n in the course of our proof we develop a tool which may be of independent interest suppose we have a subset s of a vector space d over z 2 and consider a random linear mapping of d to a smaller vector space r if the cardinality of s is larger than c e r log r then with probability 1 e the image of s will cover all elements in the range

subspace identification for continuous time stochastic systems via distribution based approach this paper presents a novel approach for system identification of continuous time stochastic state space models from random input output continuous data the approach is based on the introduction of random distribution theory in describing higher time derivatives of stochastic processes and the input output algebraic relationship is derived which is treated in the time domain the efficacy of the approach is examined by comparing with other approaches employing the filters

principal component analysis in linear systems controllability observability and model reduction kalman s minimal realization theory involves geometric objects controllable unobservable subspaces which are subject to structural instability specifically arbitrarily small perturbations in a model may cause a change in the dimensions of the associated subspaces this situation is manifested in computational difficulties which arise in attempts to apply textbook algorithms for computing a minimal realization structural instability associated with geometric theories is not unique to control it arises in the theory of linear equations as well in this setting the computational problems have been studied for decades and excellent tools have been developed for coping with the situation one of the main goals of this paper is to call attention to principal component analysis hotelling 1933 and an algorithm golub and reinsch 1970 for computing the singular value decompositon of a matrix together they form a powerful tool for coping with structural instability in dynamic systems as developed in this paper principal component analysis is a technique for analyzing signals singular value decomposition provides the computational machinery for this reason kalman s minimal realization theory is recast in terms of responses to injected signals application of the signal analysis to controllability and observability leads to a coordinate system in which the internally balanced model has special properties for asymptotically stable systems this yields working approximations of x c x bar o the controllable and unobservable subspaces it is proposed that a natural first step in model reduction is to apply the mechanics of minimal realization using these working subspaces

frequency domain identification of continuous time arma models from sampled data the subject of this paper is the direct identification of continuous time autoregressive moving average carma models the topic is viewed from the frequency domain perspective which then turns the reconstruction of the continuous time power spectral density ct psd into a key issue the first part of the paper therefore concerns the approximate estimation of the ct psd from uniformly sampled data under the assumption that the model has a certain relative degree the approach has its point of origin in the frequency domain whittle likelihood estimator the discrete or continuous time spectral densities are estimated from equidistant samples of the output for low sampling rates the discrete time spectral density is modeled directly by its continuous time spectral density using the poisson summation formula in the case of rapid sampling the continuous time spectral density is estimated directly by modifying its discrete time counterpart

numerical integration approach to on line identification of continuous time systems abstract the problem of estimating the parameters in linear continuous differential equation models from sampled data is treated using a linear integral filter we can obtain an identification model that is parametrized directly in the continuous time model parameters the unknown initial states of the system do not require estimation the choice of the sampling interval and the design of the linear integral filter are discussed considering the accuracy of parameter estimates and the computational burden by applying the results from discrete time model identification with the obtained identification model a discrete time parameter estimation method is developed and the necessary condition as well as the sufficient condition on the input for consistency are explicitly derived and discussed in particular situations a simulation study is also included to confirm the theoretical results

dynamic perfect hashing upper and lower bounds the dynamic dictionary problem is considered provide an algorithm for storing a dynamic set allowing the operations insert delete and lookup a dynamic perfect hashing strategy is given a randomized algorithm for the dynamic dictionary problem that takes o 1 worst case time for lookups and o 1 amortized expected time for insertions and deletions it uses space proportional to the size of the set stored furthermore lower bounds for the time complexity of a class of deterministic algorithms for the dictionary problem are proved this class encompasses realistic hashing based schemes that use linear space such algorithms have amortized worst case time complexity omega log n for a sequence of n insertions and lookups if the worst case lookup time is restricted to k then the lower bound becomes omega k cdot n 1 k

brief parameter identification with derivative shift operator parametrization a way of parametrizing linear systems using an operator which combines the two commonly used operators the shift q and the delta d operators is proposed it is shown that the proposed parametrization improves the numerical property of parameter identification process by using the proposed operator the condition number of the information matrix in the identification algorithm is significantly lower than that using the q or d operator it is also shown that accurate and fast converging parameter identification can be achieved by using the new operator at fast sampling rates especially for systems with relatively wide bandwidth the numerical superiority of the new parametrization is demonstrated by simulation results

transdichotomous results in computational geometry i point location in sublogarithmic time given a planar subdivision whose coordinates are integers bounded by u leq2 w we present a linear space data structure that can answer point location queries in o min lg n lg lg n sqrt lg u lg lg u time on the unit cost random access machine ram with word size w this is the first result to beat the standard theta lg n bound for infinite precision models as a consequence we obtain the first o n lg n randomized algorithms for many fundamental problems in computational geometry for arbitrary integer input on the word ram including constructing the convex hull of a three dimensional 3d point set computing the voronoi diagram or the euclidean minimum spanning tree of a planar point set triangulating a polygon with holes and finding intersections among a set of line segments higher dimensional extensions and applications are also discussed though computational geometry with bounded precision input has been investigated for a long time improvements have been limited largely to problems of an orthogonal flavor our results surpass this long standing limitation answering for example a question of willard soda 92

embedded localization band in undrained soil based on regularized strong discontinuity theory and fe analysis abstract the paper presents a novel approach to the analysis of a developing localization zone in undrained soil considered as a mixture of a solid skeleton and fluid filled pores where the solid phase is considered as elastic plastic the basic feature is the concept of regularized displacement and pore pressure discontinuities which are assumed to occur across an internal discontinuity surface in this respect the present developments are extensions of those suggested by simo et al 1993 comput mech 12 277 296 and more recently by larsson and runesson 1995 j engng mech asce in press a finite element formulation is proposed on the basis of a mixed variational formulation in the spirit of the enhanced strain concept by simo and rifai 1990 int j numer meth engng 29 1595 1638 in this fashion the localization zone is embedded into a base element for the ordinary analysis of the non localized mixture problem

order preserving indexing kubica et al 33 and kim et al 29 introduced order preserving pattern matching for a given text the goal is to find its factors having the same shape as a given pattern known results include a linear time algorithm for this problem in case of polynomially bounded alphabet and a generalization to multiple patterns we propose an index that enables order preserving pattern matching queries in time proportional to pattern length the index can be constructed in o n log log n expected time or in o n log 2 log n log log log n worst case time it is an incomplete order preserving suffix tree which may miss a single edge label at each branching node for most applications such incomplete suffix trees provide the same functional power as the complete ones we show a number of their applications including computation of longest common factors longest previously occurring factors and squares in a string in the order preserving setting we also give an o n log n time algorithm constructing complete order preserving suffix trees

brief performance evaluation of methods for identifying continuous time autoregressive processes identification of continuous time autoregressive processes from discrete time data by replacing the differentiation operator by an approximation is considered a linear regression model can then be formulated the least squares method and the instrumental variables method must be used with some care to get parameter estimates of good quality the bias is studied explicitly in the paper together with the asymptotic distribution and expressions are presented for the covariance matrix of the estimated parameters it turns out that there are small differences in the dominating bias term for the different methods whereas the statistical properties are comparable overall the performance is similar to that of a prediction error method for short sampling intervals

brief identification of continuous time ar processes from unevenly sampled data when identifying a continuous time ar process from discrete time data an obvious approach is to replace the derivative operator in the continuous time model by an approximation in some cases a linear regression model can then be formulated the well known least squares method would be very desirable to apply since it enjoy good numerical properties and low computational complexity in particular for fast or nonuniform sampling the focus of this paper is the latter i e nonuniform sampling two consistent least squares schemes for the case of unevenly sampled data are presented the precise choice of derivative approximation turns out to be crucial the obtained results are compared to a prediction error method

on the localization properties of multiplicative hyperelasto plastic continua with strong discontinuities abstract the objective of this work is to examine the large strain localization properties of hyperelasto plastic materials which are based on the multiplicative decomposition of the deformation gradient thereby the case of strong discontinuities is investigated to this end first an explicit expression for the spatial tangent operator is given taking into account anisotropic as well as nonassociated material behaviour then the structure of a regularized discontinuous velocity gradient is elaborated and discussed in detail based on these two results the localization condition is derived with special emphasis on the loading conditions inside and outside an anticipated localization band thereby the intriguingly simple structure of the tangent operator which resembles the structure of the geometrically linear theory is extensively exploited this similarity carries over to the general representation for the critical hardening modulus which is exemplified for isotropic materials as a result analytical solutions are available under the assumption of small elastic strains which is justified for metals finally examples are given for the special case of the associated von mises flow rule to this end the critical localization direction and the critical hardening modulus are investigated with respect to the amount of finite elastic strain within different modes of homogeneous elasto plastic deformations

two way chaining with reassignment we present an algorithm for hashing lfloor alpha n rfloor elements into a table with n separate chains that requires o 1 deterministic worst case insert time and o 1 expected worst case search time for constant alpha we exploit the connection between two way chaining and random graph theory in our techniques

system identification using laguerre models the traditional approach of expanding transfer functions and noise models in the delay operator to obtain linear in the parameters predictor models leads to approximations of very high order in cases of rapid sampling and or dispersion in time constants by using prior information about the time constants of the system more appropriate expansions related to laguerre networks are introduced and analyzed it is shown that the model order can be reduced compared to arx fir ar modeling by using laguerre models furthermore the numerical accuracy of the corresponding linear regression estimation problem is improved by a suitable choice of the laguerre parameter consistency error bounds persistence of excitation conditions and asymptotic statistical properties are investigated this analysis is based on the result that the covariance matrix of the regression vector of a laguerre model has a toeplitz structure

brief box jenkins continuous time modeling this paper treats the identification of continuous time models using arbitrary band limited excitation signals a modeling approach is presented that has the following two advantages 1 asymptotically the amount of data tends to infinity there is no approximation error over the complete frequency band from dc to nyquist 2 it allows to identify general parametric noise models the key idea is to combine a continuous time plant model with a discrete time noise model hybrid box jenkins model structure

a simple parallel algorithm for the maximal independent set problem two basic design strategies are used to develop a very simple and fast parallel algorithms for the maximal independent set mis problem the first strategy consists of assigning identical copies o

modeling strong discontinuities at finite strains a novel numerical implementation abstract in this paper a finite element formulation suitable for the modeling of locally embedded strong discontinuities at finite strains is presented following the enhanced assumed strain concept eas the proposed numerical model is based on an additive decomposition of the displacement gradient into a conforming and an enhanced part the enhanced part is associated with the final failure kinematics of solids which are approximated by means of a discontinuous displacement field strong discontinuities referring to the displacement jump no special assumption such as purely mode i or mode ii failure is made the same holds for the class of interface laws considered which govern the evolution of the displacement discontinuity in terms of the traction vector acting at the surface of strong discontinuities consequently the suggested numerical framework can be applied to a broad range of different interface laws including damage based models in contrast to previous works the presented finite element formulation does not require the static condensation technique to be employed more precisely instead of computing the conforming part of deformation and the displacement jump simultaneously from the weak form of equilibrium and the weak form of traction continuity the different parts of the local deformation are decomposed according to a predictor corrector algorithm the proposed predictor and the corrector step are formally identical to that of classical computational plasticity models hence subroutines designed for standard models continuous deformation can be applied with only minor modifications necessary the applicability as well as the performance of the resulting finite element formulation are demonstrated by means of a fully three dimensional analysis of shear band formation in a bar made of a ductile material

a localization capturing fe interface based on regularized strong discontinuities at large inelastic strains the objective of this work is the development of a finite element interface formulation tailored to capture localization within geometrically nonlinear solid mechanics in this context strong discontinuities are considered as the final failure mechanism within localization problems the failure kinematics are governed by a jump in the nonlinear deformation map across a discontinuity surface in the finite element discretization the interface element is endowed with these kinematics as a consequence the interface stiffness is dominated by the weighted spatial localization tensor based on these developments a localization capturing procedure is advocated and is computationally highlighted

simple fast parallel hashing by oblivious execution a hash table is a representation of a set in a linear size data structure that supports constant time membership queries we show how to construct a hash table for any given set of n keys in o lg lg n parallel time with high probability using n processors on a weak version of a concurrent read concurrent write parallel random access machine crcw pram our algorithm uses a novel approach of hashing by oblivious execution based on probabilistic analysis the algorithm is simple and has the following structure partition the input set into buckets by a random polynomial of constant degree for t 1 to o lg lg n do allocate mt memory blocks each of size kt let each bucket select a block at random and try to injectively map its keys into the block using a random linear function buckets that fail carry on to the next iteration the crux of the algorithm is a careful a priori selection of the parameters mt and kt the algorithm uses only o lg lg n random words and can be implemented in a work efficient manner

continuous time identification of siso systems using laguerre functions this paper looks at the problem of estimating the coefficients of a continuous time transfer function given samples of its input and output data we first prove that any nth order continuous time transfer function can be written as a fraction of the form spl sigma sub k 0 sup n b sub k l sub k s spl sigma sub k 0 sup n a sub k l sub k s where l sub k s denotes the continuous time laguerre basis functions based on this model we derive an asymptotically consistent parameter estimation scheme that consists of the following two steps 1 filter both the input and output data by l sub k s and 2 estimate a sub k b sub k and relate them to the coefficients of the transfer function for practical implementation we require the discrete time approximation of l sub k s since only sampled data is available we propose a scheme that is based on higher order pade approximations and we prove that this scheme produces discrete time filters that are approximately orthogonal and consequently a well conditioned numerical problem some other features of this new algorithm include the possibility to implement it as either an off line or a quasi on line algorithm and the incorporation of constraints on the transfer function coefficients a simple example is given to illustrate the properties of the proposed algorithm

an algebraic theory for design of controllers for linear multivariable systems part ii feedback realizations and feedback design the study of general linear multivariable systems with possibly different controlled and measured outputs is continued in this part of the paper the structure matrices defined in part i are used to solve the feedback realization problem feedback realizable transfer functions are then used to solve problems of regulator type it is shown that the solutions to problems like disturbance deeoupling output regulation and pole placement are all special cases of the solution to a more general problem finally it is shown how the results of part i and part ii can be combined to solve problems of servo type and of regulator type simultaneously

a construction method for optimally universal hash families and its consequences for the existence of rbibds we introduce a method for constructing optimally universal hash families and equivalently rbibds as a consequence of our construction we obtain minimal optimally universal hash families if the cardinalities of the universe and the range are powers of the same prime a corollary of this result is that the necessary conditions for the existence of an rbibd with parameters v k namely v 0 mod k and v 1 0 mod k 1 are sufficient if v and k are powers of the same prime as an application of our construction we show that the k maxcut algorithm of hofmeister and lefmann a combinatorial design approach to maxcut random struct algorithms 9 1996 163 173 can be implemented such that it has a polynomial running time in the case that the number of vertices and k are powers of the same prime