fuzzy model validation using the local statistical approach the local statistical approach for fault detection and isolation is applied to fuzzy models validation the method detects the inconsistencies between a fuzzy rule base and the modelled system it can also identify which are the faulty parameters of the fuzzy model the fisher information matrix explains the detectability of changes in the parameters of the fuzzy model simulation tests illustrate the method s credibility

on residual generation by observer and parity space approaches a unifying framework for observer design by eigenstructure assignment is described a new technique for structured residual generation based on this framework is proposed one of the main features of this technique is that the equivalence between residual generation by means of observers or parity space devices are made conspicuous more precisely from a computational point of view the equations to solve in both cases are shown to be similar and for implementation both devices are shown to be identical a necessary and sufficient condition for the existence of structured residuals is given finally the sensitivity of structured residuals to nondecoupled failures is studied and a procedure for maximizing this sensitivity is described

transport upscaling in heterogeneous aquifers what physical parameters control memory functions 1 power law tailing is often observed in the breakthrough curves btcs of tracer tests tailing is attributed to heterogeneity of aquifer properties and cannot be properly modeled by means of the homogeneous advection dispersion equation mass transfer models e g continuous time random walk method multirate mass transfer or fractional order advection dispersion equations using memory have been widely applied for reproducing observed tails the relationship between memory parameters obtained from btc fitting and the parameters characterizing the heterogeneity of hydraulic properties is still unclear here we investigate the conditions under which heterogeneity produces the type of tailing observed in the field and how memory functions are influenced by measurable heterogeneity parameters e g variance variogram or integral scale of the underlying transmissivity field we find that the slope of a btc in a log log plot is mainly influenced by the connectivity of the underlying permeability field but is insensitive to its variance the slope btc reaches asymptotically 2 as connectivity increases we conclude that an appropriate choice of the memory function allows reproducing the spreading caused by hydraulic heterogeneity but not necessarily the rate of mixing

diagnosis of unknown parametric faults in non linear stochastic dynamical systems a new detection and isolation scheme for unknown parametric faults in non linear stochastic systems is presented that is particularly suited for small parametric changes the proposed residual is the moving angle between two stochastic processes the error derived from the reference model and the expected error in case a certain fault has occurred since the fault is unknown fault classes are defined most of the faults that belong to such a fault class can be detected and isolated by just testing one representative of this fault class as the moving angle itself is a stochastic process an estimator is designed and characterised conditions for the detectability and isolability of fault classes are given for this estimator based on hypotheses tests finally the theoretical results are confirmed by simulations and monte carlo tests

adaptive observers with arbitrary exponential rate of convergence for nonlinear systems concerns the same class of linearly parameterized single output nonlinear systems that the authors previously identified in 1992 in terms of differential geometric conditions when persistency of excitation conditions are satisfied the adaptive observers presented in this note guarantee arbitrarily fast exponential convergence both of parameter and state estimates to actual parameters and states while previous adaptive observers guarantee only exponential not arbitrarily fast convergence this extends earlier results for linear systems

fault estimation for a class of nonlinear systems based on intermediate estimator this technical note investigates the problem of fault estimation for a class of nonlinear systems with lipschitzian nonlinearities in most of the existing fault estimation approaches the observer matching condition should be satisfied however this condition is hard to meet for many systems to overcome this restriction a new fault estimation method is proposed where an intermediate variable is introduced and a specially designed intermediate estimator is proposed to estimate the state and the faults simultaneously by exploiting the properties of fault distribution matrix it is proved that the states of the error system are uniformly ultimately bounded simulation examples verify the effectiveness of the proposed method

sensor fault reconstruction and observability for unknown inputs with an application to wastewater treatment plants in this article we propose a general methodology for identifying and reconstructing sensor faults on dynamical processes this methodology is issued from the general identification theory developed in the previous papers busvelle e and gauthier j p 2003 on determining unknown functions in differential systems with an application to biological reactor esaim control optimisation and calculus of variations 9 509 553 busvelle e and gauthier j p 2004 new results on identifiability of nonlinear systems in 2nd symposium on systems structure and control oaxaca mexico busvelle e and gauthier j p 2005 observation and identification tools for non linear systems application to a fluid catalytic cracker international journal of control 78 208 234 in fact this identification theory also provides a general framework for the problem of observability with unknown inputs indeed many problems of fault detection can be formulated as such observability problems the e

a geometric approach to the synthesis of failure detection filters a geometric formulation of beard s failure detection filter problem is stated using the concepts of c a invariant and unobservability subspaces the notions of output separable and mutually detectable families of subspaces introduced by beard are also clarified it is shown that mutual detectability is a necessary and sufficient condition for the existence of a detection filter with arbitrarily assignable spectrum moreover it is shown that the failure detection falter problem has a computationally simple solution when the failure events satisfy some mild restrictions finally the complete duality between a generalization of beard s detection filter problem and the restricted control decoupling problem is illustrated

robust inversion based fault estimation for discrete time lpv systems the article presents a state space based fault diagnosis fd method for discrete time affine linear parameter varying lpv systems the goal of the technical note is to develop a robust and dynamic inversion based technique for systems with parameter varying representations when an additive exogenous disturbance signal perturbs the system after applying geometric concepts for explicit fault inversion a robust strategy is proposed to attenuate the effect of the unknown disturbance input signal on the fault estimation error the proposed robust observer is derived as a solution of off line linear matrix inequality lmi conditions the technical note demonstrates the viability of the novel methodology through a numerical example

approximate solutions for diffusive fracture matrix transfer application to storage of dissolved co2 in fractured rocks author s zhou q oldenburg cm spangler lh birkholzer jt abstract 2017 american geophysical union all rights reserved analytical solutions with infinite exponential series are available to calculate the rate of diffusive transfer between low permeability blocks and high permeability zones in the subsurface truncation of these series is often employed by neglecting the early time regime in this paper we present unified form approximate solutions in which the early time and the late time solutions are continuous at a switchover time the early time solutions are based on three term polynomial functions in terms of square root of dimensionless time with the first coefficient dependent only on the dimensionless area to volume ratio the last two coefficients are either determined analytically for isotropic blocks e g spheres and slabs or obtained by fitting the exact solutions and they solely depend on the aspect ratios for rectangular columns and parallelepipeds for the late time solutions only the leading exponential term is needed for isotropic blocks while a few additional exponential terms are needed for highly anisotropic rectangular blocks the optimal switchover time is between 0 157 and 0 229 with highest relative approximation error less than 0 2 the solutions are used to demonstrate the storage of dissolved co2 in fractured reservoirs with low permeability matrix blocks of single and multiple shapes and sizes these approximate solutions are building blocks for development of analytical and numerical tools for hydraulic solute and thermal diffusion processes in low permeability matrix blocks

revisiting the fundamental analytical solutions of heat and mass transfer the kernel of multirate and multidimensional diffusion there are two types of analytical solutions of temperature concentration in and heat mass transfer through boundaries of regularly shaped 1 d 2 d and 3 d blocks these infinite series solutions with either error functions or exponentials exhibit highly irregular but complementary convergence at different dimensionless times td in this paper approximate solutions were developed by combining the error function series solutions for early times and the exponential series solutions for late times and by using time partitioning at the switchover time td0 the combined solutions contain either the leading term of both series for normal accuracy approximations with less than 0 003 relative error or the first two terms for high accuracy approximations with less than 10 7 relative error for 1 d isotropic spheres cylinders slabs and 2 d 3 d rectangular blocks squares cubes rectangles and rectangular parallelepipeds this rapid and uniform convergence for rectangular blocks was achieved by employing the same time partitioning with individual dimensionless times for different directions and the product of their combined 1 d slab solutions the switchover dimensionless time was determined to minimize the maximum approximation errors furthermore the analytical solutions of first order heat mass flux for 2 d 3 d rectangular blocks were derived for normal accuracy approximations these flux equations contain the early time solution with a three term polynomial in td and the late time solution with the limited term exponentials for rectangular blocks the heat mass flux equations and the combined temperature concentration solutions form the ultimate kernel for fast simulations of multirate and multidimensional heat mass transfer in porous fractured media with millions of low permeability blocks of varying shapes and sizes

a geometric approach to nonlinear fault detection and isolation we present a differential geometric approach to the problem of fault detection and isolation for nonlinear systems a necessary condition for the problem to be solvable is derived in terms of an unobservability distribution which is computable by means of suitable algorithms the existence and regularity of such a distribution implies the existence of changes of coordinates in the state and in the output space which induce an observable quotient subsystem unaffected by all fault signals but one for this subsystem a fault detection filter is designed

analytical relationship between gaussian and transformed gaussian spatially distributed fields 1 a transformation of a gaussian random field results in a change of the spatial dependence in simple terms the range and the shape of a variogram are different between an underlying gaussian and a transformed gaussian field there is a relationship between the underlying and the transformed spatial dependence this paper shows how this relationship can be expressed analytically rather than generating multidimensional random fields and conducting spatial statistical analysis we develop an accurate and efficient approach based on a unique mapping of the correlation coefficients of the original multi gaussian fields to the transformed correlation coefficients to evaluate the spatial correlation of transformed non gaussian random fields for any type of geostatistical parameterization such a mapping can also yield accurate estimation of the spatial correlation of the underlying gaussian field given the spatial correlation of the transformed field results indicate that 1 a nonlinear transformation of spatially distributed fields usually changes the spatial dependence structure and 2 the relationship between the dependence structures of the underlying and the transformed field can be expressed analytically and it is sufficient to do this in one dimension we use the developed approach to investigate the change of correlations of connected random fields generated by the absolute value transformation results show 1 the correlation lengths of the underlying gaussian fields are 1 67 and 2 64 times of those of transformed non gaussian fields for gaussian and exponential covariance models respectively 2 the anisotropic ratio does not change and 3 the anticorrelation in hole effect correlation models disappear

conditional stochastic mapping of transport connectivity 1 we present a method for the stochastic simulation of point to point transport connectivity honoring data from three types of information 1 travel time estimates obtained from field tracer tests 2 estimates of flow connectivity indicators obtained from the relatively fast or slow flow response that is observed at a point location given the flow impulse at another location and 3 measurements of transmissivity at a local scale the method thus efficiently integrates data obtained from different hydraulic tests each sampling different areas within the aquifer to achieve this we first extend the concept of point to point flow connectivity and transport connectivity mathematically formulated by trinchero et al 2008 for pumping conditions to support a more general flow configuration interestingly point to point flow connectivity can be generally seen as a weighted integral of transmissivity over the entire domain the weighting function being proportional to the sensitivity of heads with respect to the natural log of transmissivity per unit of aquifer volume on the contrary point to point transport connectivity is a weighted integral along the particle path of the solute mass that involves two variables transmissivity and flow connectivity each variable has its own distinct weighting function the weighting function of transmissivity is inversely proportional to both the homogeneous travel time and the point velocity sampled along the travel path on this basis we show how to generate conditional point to point transport connectivity maps the method avoids the inference of cross covariance functions between variables measured over different scales and sampled areas which cannot be otherwise estimated with a few data measurements by expressing them as a function of the local transmissivity covariance function an example of the method is provided to evaluate the worth of including tracer data to delineate capture zones of abstraction wells originally defined from local transmissivity measurements monte carlo simulations reveal that the impact of including tracer data is a maximum when the travel time data are obtained at a location different than that of transmissivity measurements the reason is that weighting functions give larger weights to the injection location so introducing tracer test data at points where transmissivity is already known is somewhat redundant

on the formation of multiple local peaks in breakthrough curves the analysis of breakthrough curves btcs is of interest in hydrogeology as a way to parameterize and explain processes related to anomalous transport classical btcs assume the presence of a single peak in the curve where the location and size of the peak and the slope of the receding limb has been of particular interest as more information is incorporated into btcs for example with high frequency data collection supercomputing efforts it is likely that classical definitions of btc shapes will no longer be adequate descriptors for contaminant transport problems we contend that individual btcs may display multiple local peaks depending on the hydrogeologic conditions and the solute travel distance in such cases classical definitions should be reconsidered in this work the presence of local peaks in btcs is quantified from high resolution numerical simulations in synthetic fields with a particle tracking technique and a kernel density estimator to avoid either overly jagged or smoothed curves that could mask the results individual btcs from three dimensional heterogeneous hydraulic conductivity fields with varying combinations of statistical anisotropy heterogeneity models and local dispersivity are assessed as a function of travel distance the number of local peaks their corresponding slopes and a transport connectivity index are shown to strongly depend on statistical anisotropy and travel distance results show that the choice of heterogeneity model also affects the frequency of local peaks but the slope is less sensitive to model selection we also discuss how solute shearing and rerouting can be determined from local peak quantification

coupled estimation of flow and solute transport parameters a methodology for solving the coupled linear flow and transport inverse problem is presented it allows the estimation of aquifer parameters transmissivity storativity recharge boundary heads and flows leakage dispersivity molecular diffusion porosity retardation linear decay boundary concentrations using their prior estimates as well as head and concentration measurements as basic information transient flow and transport equations are solved using the finite element method in space and a weighted finite difference scheme in time flow and transport domains can be one two or quasi three dimensional applying linear one dimensional elements linear two dimensional triangles or bilinear two dimensional rectangles mixed at will time regimes can be transient or steady state in any equation flow or transport parameters are estimated on the basis of maximum likelihood theory which allows us to obtain information about parameters uncertainty minimization of the negative log likelihood is performed using marquardt s method the applicability of the method is shown by means of two real examples they illustrate that the proposed approach can successfully address model selection parameter uncertainty and nontrivial identifiability problems estimation of time dependent sources and the role of prior estimates are also addressed in the examples while the formulation of the problem leaves room for both stochastic and deterministic treatment of hydraulic parameters the latter has been adopted in both examples limitations of the approach are also apparent

geological entropy and solute transport in heterogeneous porous media we propose a novel approach to link solute transport behavior to the physical heterogeneity of the aquifer which we fully characterize with two measurable parameters the variance of the log k values math formula and a new indicator hr that integrates multiple properties of the k field into a global measure of spatial disorder or geological entropy from the results of a detailed numerical experiment considering solute transport in k fields representing realistic distributions of hydrofacies in alluvial aquifers we identify empirical relationship between the two parameters and the first three central moments of the distributions of arrival times of solute particles at a selected control plane the analysis of experimental data indicates that the mean and the variance of the solutes arrival times tend to increase with spatial disorder i e hr increasing while highly skewed distributions are observed in more orderly structures i e hr decreasing or at higher math formula we found that simple closed form empirical expressions of the bivariate dependency of skewness on hr and math formula can be used to predict the emergence of non fickian transport in k fields considering a range of structures and heterogeneity levels some of which based on documented real aquifers the accuracy of these predictions and in general the results from this study indicate that a description of the global variability and structure of the k field in terms of variance and geological entropy offers a valid and broadly applicable approach for the interpretation and prediction of transport in heterogeneous porous media

delineation of connectivity structures in 2 d heterogeneous hydraulic conductivity fields connectivity is a critical aquifer property controlling anomalous transport behavior at large scales but connectivity cannot be easily defined in a continuous field based on information of the hydraulic conductivity alone we conceptualize it as a connecting structure a connected subset of a continuous hydraulic conductivity field that consists of paths of least hydraulic resistance we develop a simple and robust numerical method to delineate the connectivity structure using information of the hydraulic conductivity field only first the topology of the connectivity structure is determined by finding the path s of least resistance between two opposite boundaries and second a series of connectivity structures are created by inflating and shrinking the individual channels finally we apply this methodology to different heterogeneous fields we show that our method captures the main flow channels as well as the pathways of early time solute arrivals we find our method informative to study connectivity in 2 d heterogeneous hydraulic conductivity fields

a new methodology for observer design and implementation observers are usually formulated as explicit systems of differential equations and implemented using standard ode solvers in this paper we show that there can be advantages in formulating the observer as a differential algebraic equation dae we propose a canonical dae observer and show that it can be implemented using standard dae solvers the dae implementation of the observer can be considered regardless of the design philosophy used we present a simple design strategy for this canonical dae observer based on the extended linearization method

brief paper adaptive observers for nonlinearly parameterized class of nonlinear systems in this paper one proposes adaptive observers for a class of uniformly observable mimo nonlinear systems with general nonlinear parameterizations the state and the unknown parameters of the considered systems are supposed to lie in bounded domains which size can be arbitrarily large and the exponential convergence of the observers is shown to result under a well defined persistent excitation condition moreover the gain of the observers involves a design function that has to satisfy a simple condition which is given different expressions of such a function are proposed and it is shown that adaptive high gain like observers and adaptive sliding mode like observers can be derived by considering particular expressions of the design function the theory is supported by simulation results related to the estimation of the biomass concentration and the contois model parameters in a bioreactor

a continuous time random walk approach to transient flow in heterogeneous porous media 1 we propose a new physical interpretation of the diffusion process for the piezometric head h x t in heterogeneous aquifers based on the continuous time random walk ctrw theory for the typical heterogeneities considered in this work we find that a ctrw based diffusion equation for h x t provides better fits to the transient flow simulations than the classical diffusion equation de the de is found to be a special case of the ctrw diffusion equation the results of this work have clear implications for the interpretation of pumping tests and what information can be extracted from them 2 well testing is an essential tool for groundwater aquifer assessment the key idea being that hydraulic properties can be derived by means of transient drawdown and or flux measurements the commonly accepted mathematical model for groundwater flow in porous formations is based on the well known darcy law which relates the fluid flow to the gradient of the piezometric head h x t l together with a mass balance and the assumptions of small compressibility constant porosity and permeability and small head gradients it is possible to derive a partial differential equation of parabolic type diffusion equation for h th x t r a x rh x t

design of a unified adaptive fuzzy observer for uncertain nonlinear systems this paper presents an adaptive fuzzy observer for a class of uncertain nonlinear systems more precisely we propose a unified approach for designing such an observer with some design flexibility so that it can be easily adaptable and employed either as a high gain or a sliding mode observer by selecting its gain appropriately additionally we derive a suitable parameter adaptation law so that the proposed observer is robust with respect to ubiquitous fuzzy approximation errors and external disturbances we also show that the observation error is ultimately bounded using a lyapunov approach without having recourse to the usual strictly positive real spr condition or a suitable observation error filtering the effectiveness of the proposed observers is illustrated through two simulation case studies taken from the adaptive fuzzy control literature

krein space based h adaptive smoother design for a class of lipschitz nonlinear discrete time systems in this paper the problem of h adaptive smoother design is addressed for a class of lipschitz nonlinear discrete time systems with l2 bounded disturbance input by comprehensively analyzing the h performance lipschitz conditions and unknown parameter s bounded condition a positive minimum problem for an indefinite quadratic form is introduced such that the h adaptive smoothing problem is achieved a krein space stochastic system with multiple fictitious outputs is constructed by associating with the minimum problem of the introduced indefinite quadratic form the minimum of indefinite quadratic form is derived in the form of innovations through utilizing krein space orthogonal projection and innovation analysis approach via choosing the suitable fictitious outputs to guarantee the minimum of indefinite quadratic form is positive the existence condition of the adaptive smoother and its analytical solutions are obtained in virtue of nonstandard riccati difference equations the quality of the estimator is checked on an example

non negative matrix tri factorization for co clustering non negative dyadic data that is data representing observations which relate two finite sets of objects appear in several domain applications such as text mining based information retrieval collaborative filtering and recommender systems micro array analysis and computer vision discovering latent subgroups among data is a fundamental task to be performed on dyadic data in this context clustering and co clustering techniques are relevant tools for extracting and representing latent information in high dimensional data recently non negative matrix factorizations attracted a great interest as clustering methods due to their capability of performing a parts based decomposition of data in this paper we focus our attention on how nmf with additional constraints can be properly applied for co clustering non negative dyadic data in particular we present a process which aims at enhancing the performance of 3 factors nmf as a co clustering method by identifying a clearer correlation structure represented by the block matrix experimental evaluation performed on some common datasets by applying the proposed approach on two different nmf algorithms shows that in most cases the quality of the obtained clustering increases especially in terms of average inter cluster similarity

conditioned invariant and locally conditioned invariant distributions abstract we define the concepts of conditioned invariant and locally conditioned invariant distributions for nonlinear system and show how they can be used to solve the problem of tracking an output signal of a nonlinear system in spite of unknown disturbances

spatial markov processes for modeling lagrangian particle dynamics in heterogeneous porous media we investigate the representation of lagrangian velocities in heterogeneous porous media as markov processes we use numerical simulations to show that classical descriptions of particle velocities using markov processes in time fail because low velocities are much more strongly correlated in time than high velocities we demonstrate that lagrangian velocities describe a markov process at fixed distances along the particle trajectories i e a spatial markov process this remarkable property has significant implications for modeling effective transport in heterogeneous velocity fields i the spatial lagrangian velocity transition densities are sufficient to fully characterize these complex velocity field organizations ii classical effective transport descriptions that rely on markov processes in time for the particle velocities are not suited for describing transport in heterogeneous porous media and iii an alternative effective transport description derives from the markovian nature of the spatial velocity transitions it expresses particle movements as a random walk in space time characterized by a correlated random temporal increment and thus generalizes the continuous time random walk model to transport in correlated velocity fields

nonlinear system fault diagnosis based on adaptive estimation an approach to fault diagnosis for a class of nonlinear systems is proposed in this paper it is based on a new adaptive estimation algorithm for recursive estimation of the parameters related to faults this algorithm is designed in a constructive manner through a nontrivial combination of a high gain observer and a recently developed linear adaptive observer without resort to any linearization its global exponential convergence is ensured by an easy to check persistent excitation condition a numerical example is presented for illustration

observer based residual generation for fault diagnosis for non affine non linear polynomial systems this paper proposes an observer based residual generator obrg for diagnosing faults in a continuous non affine system with polynomial non linearities up to any finite degree where the fault and an unknown input affect both the system and part of the output firstly given certain assumptions and the use of defined extended vectors a parameterized polynomial system is considerred for which a compact set of sufficient conditions is given for the existence of a candidate obrg conditions for error stability by a lyapunov method and detectability are given the calculation steps in the design of the obrg are shown to involve the solution of three linear equations with parameterizations and the calculation of a set of constant matrices for detectability of faults a result is then given establishing that the design holds for a much wider class of systems the residual design is applied to a real three tank system

a game theoretic fault detection filter the fault detection process is approximated with a disturbance attenuation problem the solution to this problem for both linear time varying and time invariant systems leads to a game theoretic filter which bounds the transmission of all exogenous signals except the fault to be detected in the limit when the disturbance attenuation bound is brought to zero a complete transmission block is achieved by embedding the nuisance inputs into an unobservable invariant subspace since this is the same invariant subspace structure seen in some types of detection filters we can claim that the asymptotic game filter is itself a detection filter one can also make use of this subspace structure to reduce the order of the limiting game theoretic filter by factoring this invariant subspace out of the state space the resulting lower dimensional filter will then be sensitive only to the failure to be detected a pair of examples given at the end of the paper demonstrate the effectiveness of the filter for time invariant and time varying problems in both full order and reduced order forms

disturbance decoupling by measurement feedback with stability or pole placement in this paper we solve the disturbance decoupling problem by measurement feedback and requiring stability or pole placement on the closed loop system the problem is attacked using the geometric approach through the concepts of a bmod mathcal b invariant and controllability subspaces and their duals a mid k invariant and complementary observability subspaces the solution of this problem has an interesting structure consisting of a feedback processor which decomposes into i a disturbance decoupling loop ii a disturbance input stabilization or pole placement loop and iii a controlled output stabilization or pole placement loop

statistical formulation of generalized tracer retention in fractured rock we study tracer retention in fractured rock by combing lagrangian and time domain random walk frameworks as well as a statistical representation of the retention process mass transfer is quantified by the retention time distribution that follows from a lagrangian coupling between advective transport and mass exchange processes applicable for advection dominated transport a unifying parametrisation is presented for generalised diffusion using two rates denoted by k1 and k2 where k1 is a forward rate and k2 a reverse rate plus an exponent as an additional parameter for the fickian diffusion model k1 and k2 are related to measurable retention properties of the fracture matrix by the method of moments whereas for the non fickian case dimensional analysis is used the derived retention time distributions are exemplified for interpreting tracer tests as well as for predictive modelling of expected tracer breakthrough we show that non fickian effects can be notable when transport is upscaled based on a non fickian interpretation of a tracer test for which deviations from fickianity are relatively small the statistical representation of retention clearly shows the significance of the forward rate k1 which depends on the active specific surface area and is the most difficult parameter to characterise in the field

improving non negative matrix factorizations through structured initialization in this paper we explore a recent iterative compression technique called non negative matrix factorization nmf several special properties are obtained as a result of the constrained optimization problem of nmf for facial images the additive nature of nmf results in a basis of features such as eyes noses and lips we explore various methods for efficiently computing nmf placing particular emphasis on the initialization of current algorithms we propose using spherical k means clustering to produce a structured initialization for nmf we demonstrate some of the properties that result from this initialization and develop an efficient way of choosing the rank of the low dimensional nmf representation

subtractive clustering for seeding non negative matrix factorizations non negative matrix factorization is a multivariate analysis method which is proven to be useful in many areas such as bio informatics molecular pattern discovery pattern recognition document clustering and so on it seeks a reduced representation of a multivariate data matrix into the product of basis and encoding matrices possessing only non negative elements in order to learn the so called part based representations of data all algorithms for computing non negative matrix factorization are iterative therefore particular emphasis must be placed on a proper initialization of nmf because of its local convergence the problem of selecting appropriate starting matrices becomes more complex when data possess special meaning as in document clustering in this paper we propose the adoption of the subtractive clustering algorithm as a scheme to generate initial matrices for non negative matrix factorization algorithms comparisons with other commonly adopted initializations of non negative matrix factorization algorithms have been performed and the proposed scheme reveals to be a good trade off between effectiveness and speed moreover the effectiveness of the proposed initialization to suggest a number of basis for nmf when data distances are estimated is illustrated when nmf is used for solving clustering problems where the number of groups in which the data are grouped is not known a priori the influence of a proper rank factor on the interpretability and the effectiveness of the results are also discussed

solute transport in low heterogeneity sandboxes the role of correlation length and permeability variance this work examines how heterogeneity structure in particular correlation length controls flow and solute transport we used two dimensional 2d sandboxes 21 9 cm 20 6 cm and four modeling approaches including 2d advection dispersion equation ade with explicit heterogeneity structure 1d ade with average properties and nonlocal continuous time random walk ctrw and fractional ade fade the goal is to answer two questions 1 how and to what extent does correlation length control effective permeability and breakthrough curves btc 2 which model can best reproduce data under what conditions sandboxes were packed with the same 20 v v fine and 80 v v coarse sands in three patterns that differ in correlation length the mixed cases contain uniformly distributed fine and coarse grains the four zone and one zone cases have four and one square fine zones respectively a total of seven experiments were carried out with permeability variance of 0 10 lc 0 22 mc and 0 43 hc experimental data show that the btc curves depend strongly on correlation length especially in the hc cases the hc one zone hco case shows distinct breakthrough steps arising from fast advection in the coarse zone slow advection in the fine zone and slow diffusion while the lco and mco btcs do not exhibit such behavior with explicit representation of heterogeneity structure 2d ade reproduces btcs well in all cases ctrw reproduces temporal moments with smaller deviation from data than fade in all cases except hco where fade has the lowest deviation

origins of anomalous transport in heterogeneous media structural and dynamic controls anomalous or non fickian transport is ubiquitous in the context of tracer migration in geological formations we quantitatively identify the origin of anomalous transport in a representative model of a heterogeneous porous medium under uniform in the mean flow conditions we focus on anomalous transport which arises in the complex flow patterns of lognormally distributed hydraulic conductivity k fields with several decades of k values transport in the domains is determined by a particle tracking technique and characterized by breakthrough curves btcs the btc averaged over multiple realizations demonstrates anomalous transport in all cases which is accounted for entirely by a power law distribution t 1 of local transition times the latter is contained in the probability density function t of transition times embedded in the framework of a continuous time random walk ctrw a unique feature of our analysis is the derivation of t as a function of parameters quantifying the heterogeneity of the domain in this context we first establish the dominance of preferential pathways across each domain and characterize the statistics of these pathways by forming a particle visitation weighted histogram hw k of the hydraulic conductivity by converting the ln k dependence of hw k into time we demonstrate the equivalence of hw k and t and delineate the region of hw k that forms the power law of t this thus defines the origin of anomalous transport analysis of the preferential pathways clearly demonstrates the limitations of critical path analysis and percolation theory as a basis for determining the origin of anomalous transport furthermore we derive an expression defining the power law exponent in terms of the hw k parameters the equivalence between hw k and t is a remarkable result particularly given the nature of the k heterogeneity the complexity of the flow field within each realization and the statistics of the particle transitions

fault detection and isolation in nonlinear dynamic systems a combined input output and local approach the problem of fault detection and isolation fdi is addressed for nonlinear dynamic systems modeled by polynomial differential algebraic equations ritt s algorithm is used to obtain an input output representation of the monitored system by eliminating unknown variables a local approach to change detection is then applied to the input output representation for fdi residual generation and evaluation simulation results on a microbial growth process are provided which illustrate the relevance of the proposed fdi method

on board component fault detection and isolation using the statistical local approach we describe both the key principles and real application examples of a unified theory which allows us to perform the on board incipient fault detection and isolation tasks involved in monitoring for condition based maintenance this theory is known under the name of local approach and it is especially suited to component faults it aims at transforming complex detection problems concerning a parameterized stochastic process into the universal problem of monitoring the mean of a gaussian vector based on a small deviation assumption the key tools are the first order taylor expansion and the asymptotic gaussianity of a convenient parameter estimating function ml ls iv and subspace identification methods are addressed in this perspective in the case of dynamic processes given in state space form the approach may also call for observer based state estimation or state elimination experiments concerning both simulated and real data for linear and nonlinear dynamical processes are reported how the key principles and features of the local approach compare with those of other approaches is discussed

projective robust nonnegative factorization nonnegative matrix factorization nmf has been successfully used in many fields as a low dimensional representation method projective nonnegative matrix factorization pnmf is a variant of nmf that was proposed to learn a subspace for feature extraction however both original nmf and pnmf are sensitive to noise and are unsuitable for feature extraction if data is grossly corrupted in order to improve the robustness of nmf a framework named projective robust nonnegative factorization prnf is proposed in this paper for robust image feature extraction and classification since learned projections can weaken noise disturbances prnf is more suitable for classification and feature extraction in order to preserve the geometrical structure of original data prnf introduces a graph regularization term which encodes geometrical structure in the prnf framework three algorithms are proposed that add a sparsity constraint on the noise matrix based on l1 2 norm l1 norm and l2 1 norm respectively robustness and classification performance of the three proposed algorithms are verified with experiments on four face image databases and results are compared with state of the art robust nmf based algorithms experimental results demonstrate the robustness and effectiveness of the algorithms for image classification and feature extraction

additive change detection in nonlinear systems with unknown change parameters we study the change detection problem in partially observed nonlinear systems which satisfy the hidden markov model hmm property the change parameters are assumed unknown and the changes can be slow or sudden a partially observed system needs to be tracked first before changes can be detected sudden changes result in significant loss of track these can be detected easily using the increase in tracking error te or observation likelihood ol or using a cusum type method applied to either of these however slow changes which result in small loss of track often get missed we propose here a statistic that uses the tracked component of the change to detect it and hence detects slow changes faster than te or ol we show both analytically and through simulations that this statistic complements ol and te for change detection

adaptive approximation for multiple sensor fault detection and isolation of nonlinear uncertain systems this paper presents an adaptive approximation based design methodology and analytical results for distributed detection and isolation of multiple sensor faults in a class of nonlinear uncertain systems during the initial stage of the nonlinear system operation adaptive approximation is used for online learning of the modeling uncertainty then local sensor fault detection and isolation sfdi modules are designed using a dedicated nonlinear observer scheme the multiple sensor fault isolation process is enhanced by deriving a combinatorial decision logic that integrates information from local sfdi modules the performance of the proposed diagnostic scheme is analyzed in terms of conditions for ensuring fault detectability and isolability a simulation example of a single link robotic arm is used to illustrate the application of the adaptive approximation based sfdi methodology and its effectiveness in detecting and isolating multiple sensor faults

nonlinear decoupling via feedback a differential geometric approach the paper deals with the nonlinear decoupling and noninteracting control problems a complete solution to those problems is made possible via a suitable nonlinear generalization of several powerful geometric concepts already introduced in studying linear multivariable control systems the paper also includes algorithms concerned with the actual construction of the appropriate control laws

clustering based initialization for non negative matrix factorization non negative matrix factorization nmf is an unsupervised learning algorithm that can extract parts from visual data the goal of this technique is to find intuitive basis such that training examples can be faithfully reconstructed using linear combination of basis images which are restricted to non negative values thus nmf basis images can be understood as localized features that correspond better with intuitive notions of parts of images however there has been few systematic study to explore various methods for initialization of nmf algorithm which is crucial for the performance of nmf algorithm in data analysis in this paper we discuss a structured nmf initialization scheme based on the clustering method comparing with the random initialization in common use our method achieved faster convergence while maintaining the data structure and also obtained good result for the face recognition task furthermore we also proposed to use a normalized aic incorporated with our nmf initialization for rank selection of traditional nmf at the cost of much less computational load while obtaining a good performance in face recognition

on global identifiability for arbitrary model parametrizations it is a fundamental problem of identification to be able even before the data have been analyzed to decide if all the free parameters of a model structure can be uniquely recovered from data this is the issue of global identifiability in this contribution we show how global identifiability for an arbitrary model structure basically with analytic non linearities can be analyzed using concepts and algorithms from differential algebra it is shown how the question of global structural identifiability is reduced to the question of whether the given model structure can be rearranged as a linear regression an explicit algorithm to test this is also given furthermore the question of persistent excitation for the input can also be tested explicitly is a similar fashion the algorithms involved are very well suited for implementation in computer algebra one such implementation is also described

adaptive observer for multiple input multiple output mimo linear time varying systems for joint state parameter estimation in linear time varying ltv multiple input multiple output mimo systems an approach to the design of adaptive observers is proposed it is conceptually simple and computationally efficient its global exponential convergence is established for noise free systems in the presence of noises it is proved that the estimation errors are bounded and converge in the mean to zero if the noises are bounded and have zero means potential applications are fault detection and isolation and adaptive control

validity of the local equilibrium assumption for modeling sorbing solute transport through homogeneous soils sorption processes that occur during reactive solute movement through porous media can be modeled using either an equilibrium or kinetic approach because of the resulting conceptual and mathematical simplification many transport models assume local chemical equilibrium is valid for describing sorption reactions this paper presents quantitative criteria to assess the validity of the local equilibrium assumption for one dimensional steady flow through homogeneous soils a method is described whereby formulas for solute breakthrough curve time moments can be determined without knowledge of the nalytical solution to the mass transport model this method is applied to several commonly used nonequilibrium formulations as well as the standard linear equilibrium model the formulations considered include both the physical nonequilibrium models where the sorption rate is controlled by diffusive solute transfer between mobile and stagnant fluid zones and the chemical nonequilibrium models where the overall sorption rate is governed by the rate of reaction at the soil solution interfaces criteria for local equilibrium to be valid are derived by comparing the time moment formulas for the nonequilibrium and equilibrium models these criteria explicitly show that basic system parameters e g seepage velocity dispersion coefficient distribution coefficient sorption rate boundary conditions have a significant influence on the attainment of local equilibrium

transport behavior of a passive solute in continuous time random walks and multirate mass transfer 1 we consider the transport behavior of a passive solute in a heterogeneous medium modeled by continuous time random walks ctrw and linear multirate mass transfer mrmt within the ctrw framework we formulate a transport model which is formally equivalent to mrmt in both approaches the total concentration is divided into mobile and immobile parts the immobile concentration is given by the convolution in time of the mobile concentration and a memory function the memory function is a functional of the distribution of transition and trapping times for the ctrw and the mrmt approach respectively and determines the transport behavior of the solute based on different expressions for the memory function in the two frameworks we derive conditions for which both approaches describe the same transport behavior we focus on anomalous transport behavior that can arise if the transition and trapping time distributions behave algebraically in a given time regime using an expansion of the laplace transform of the memory function we develop explicit expressions for the time behavior of the flux concentration as well as for the center of mass velocity and the macro dispersion coefficients of the solute distribution we observe anomalous power law as well as normal fickian transport behavior depending on the exponents that dominate the trapping and transition time distributions respectively the results show that the character of the anomalous transport does not depend on the details of the transport model but only on the exponents dominating the transition or trapping time distributions the unified transport framework presented here comprising ctrw and mrmt shows new aspects and opens new perspectives for the modeling of transport in heterogeneous media

on the complexity of nonnegative matrix factorization nonnegative matrix factorization nmf has become a prominent technique for the analysis of image databases text databases and other information retrieval and clustering applications the problem is most naturally posed as continuous optimization in this report we define an exact version of nmf then we establish several results about exact nmf i that it is equivalent to a problem in polyhedral combinatorics ii that it is np hard and iii that a polynomial time local search heuristic exists

nonlinear black box models in system identification mathematical foundations we discuss several aspects of the mathematical foundations of the nonlinear black box identification problem we shall see that the quality of the identification procedure is always a result of a certain trade off between the expressive power of the model we try to identify the larger the number of parameters used to describe the model the more flexible is the approximation and the stochastic error which is proportional to the number of parameters a consequence of this trade off is the simple fact that a good approximation technique can be the basis of a good identification algorithm from this point of view we consider different approximation methods and pay special attention to spatially adaptive approximants we introduce wavelet and neuron approximations and show that they are spatially adaptive then we apply the acquired approximation experience to estimation problems finally we consider some implications of these theoretical developments for the practically implemented versions of the spatially adaptive algorithms

on observer based fault detection for nonlinear systems abstract this paper addresses analysis and integrated design of observer based fault detection fd for nonlinear systems to gain a deeper insight into the observer based fd framework definitions and existence conditions for nonlinear observer based fd systems are studied first then a scheme for an integrated design of observer based fd systems for affine nonlinear systems is proposed our work is considerably inspired by the study on input output stability and stabilization of nonlinear systems examples are given at the end of the paper to illustrate the theoretical results

stable adaptive observers for nonlinear time varying systems an adaptive observer identifier for single input single output observable nonlinear systems that can be transformed to a certain observable canonical form is described sufficient conditions for stability of this observer are provided these conditions are in terms of the structure of the system and canonical form the boundedness of the parameter variations and the sufficient richness of some signals the scope of the canonical form and the use of the observer identifier is motivated by the presentation of applications to time invariant bilinear systems nonlinear systems in phase variable form a biotechnological process and a robot manipulator in each case the specific stability conditions are presented

universal scaling of hydraulic conductivities and dispersivities in geologic media an interpretation is offered for the observation that dispersivities increase with scale apparent longitudinal dispersivity data from a variety of hydrogeologic settings are assumed to represent a continuous hierarchy of log hydraulic conductivity fields with mutually uncorrelated increments each field having its own exponential autocovariance associated integral scale and variance that increases as a power of scale such a hierarchy is shown theoretically to form a self similar random field with homogeneous increments regardless of whether or not the underlying assumption is valid one can justify interpreting the apparent dispersivities in a manner consistent with a recent quasi linear theory of non fickian and fickian dispersion in homogeneous media which supports the notion of a self similar hierarchy a posteriori the hierarchy is revealed to possess a semivariogram s cs where c is a constant and a fractal dimension d e 0 75 where e is the topological dimension of interest this can be viewed as a universal scaling rule about which large deviations occur due to local influences including the existence of discrete natural scales at which log hydraulic conductivity is statistically homogeneous as such homogeneity is at best a local phenomenon occurring intermittently over narrow bands of the scale spectrum one must question the utility of associating medium properties with representative elementary volumes and relying on fickian models of dispersion over more than relatively narrow scale intervals porous and fractured media appear to follow the same idealized scaling rule for both flow and transport raising a question about the validity of many distinctions commonly drawn between such media finally the data suggest that conditioning transport models through calibration against hydraulic measurements has the effect of filtering out large scale modes from the hierarchy

lagrangian statistical model for transport in highly heterogeneous velocity fields we define an effective lagrangian statistical model in phase space x t v for describing transport in highly heterogeneous velocity fields with complex spatial organizations the spatial markovian nature and temporal non markovian nature of lagrangian velocities leads to an effective transport description that turns out to be a correlated continuous time random walk this model correctly captures the lagrangian velocity correlation properties and is demonstrated to represent a forward model for predicting transport in highly heterogeneous porous media for different types of velocity organizations

theory of anomalous chemical transport in random fracture networks we show that dominant aspects of chemical particle transport in fracture networks char22 non gaussian propagation char22 result from subtle features of the steady flow field distribution through the network this is an outcome of a theory based on a continuous time random walk formalism structured to retain the key space time correlations of particles as they are advected across each fracture segment the approach is designed to treat the complex geometries of a large variety of fracture networks and multiscale interactions monte carlo simulations of steady flow in these networks are used to determine the distribution of velocities in individual fractures as a function of their orientation the geometry and velocity distributions are used in conjunction with particle mixing rules to map the particle movement between fracture intersections onto a joint probability density ensuremath psi mathbf r t the chemical concentration plume and breakthrough curves can then be calculated analytically particle tracking simulations on these networks exhibit the same non gaussian profiles demonstrating quantitative agreement with the theory the analytic plume shapes display the same basic behavior as extensive field observations at the columbus air force base mississippi the quantitative correlation between the time dependence of the mean and standard deviation of the field plumes and their shape is predicted by the theory

fault detection schemes for continuous time stochastic dynamical systems in this paper the fault detection fd task in stochastic continuous time dynamical systems is addressed a new family of fd approaches is presented which is based on the application of hypothesis testing on continuous time estimators the given fd schemes are widely analyzed in the framework of their characteristics such as fault detectability false alarms and missed detection a collection of sufficient detectability conditions are given for a class of faults referred here as generic characterizing the faults which can be detected with certain formalized guarantee by the given fd schemes and providing also an upper bound for the detection time in a probabilistic sense the application and comparative performance of these fd approaches is illustrated for different faults in a simulation example

remarks on nonlinear adaptive observer design abstract a solution to the problem of state estimation for systems with unknown parameters is to use some on line adaptation of the observer parameters on the basis of various existing results for such adaptive observer designs a unifying adaptive observer form is proposed in this paper this form indeed emphasizes properties allowing some asymptotic state estimation in spite of unknown parameters as well as additional properties which further allow parameter estimation as an example it is shown how an adaptive observer can be designed for a class of state affine systems

nonlinear black box modeling in system identification a unified overview a nonlinear black box structure for a dynamical system is a model structure that is prepared to describe virtually any nonlinear dynamics there has been considerable recent interest in this area with structures based on neural networks radial basis networks wavelet networks and hinging hyperplanes as well as wavelet transform based methods and models based on fuzzy sets and fuzzy rules this paper describes all these approaches in a common framework from a user s perspective it focuses on what are the common features in the different approaches the choices that have to be made and what considerations are relevant for a successful system identification application of these techniques it is pointed out that the nonlinear structures can be seen as a concatenation of a mapping form observed data to a regression vector and a nonlinear mapping from the regressor space to the output space these mappings are discussed separately the latter mapping is usually formed as a basis function expansion the basis functions are typically formed from one simple scalar function which is modified in terms of scale and location the expansion from the scalar argument to the regressor space is achieved by a radial or a ridge type approach basic techniques for estimating the parameters in the structures are criterion minimization as well as two step procedures where first the relevant basis functions are determined using data and then a linear least squares step to determine the coordinates of the function approximation a particular problem is to deal with the large number of potentially necessary parameters this is handled by making the number of used parameters considerably less than the number of offered parameters by regularization shrinking pruning or regressor selection

a systematic approach to adaptive observer synthesis for nonlinear systems geometric techniques of controller design for nonlinear systems have enjoyed great success a serious shortcoming however has been the need for access to full state feedback this paper addresses the issue of state estimation from limited sensor measurements in the presence of parameter uncertainty an adaptive nonlinear observer is suggested for lipschitz nonlinear systems and the stability of this observer is shown to be related to finding solutions to a quadratic inequality involving two variables a coordinate transformation is used to reformulate this inequality as a linear matrix inequality a systematic algorithm is presented which checks for feasibility of a solution to the quadratic inequality and yields an observer whenever the solution is feasible the state estimation errors then are guaranteed to converge to zero asymptotically the convergence of the parameters however is determined by a persistence of excitation type constraint

invariant subspaces for lpv systems and their applications the aim of this paper is to extend the notion of invariant subspaces known in the geometric control theory of the linear time invariant systems to the linear parameter varying lpv systems by introducing the concept of parameter varying invariant subspaces for lpv systems affine in their parameters algorithms are given to compute many parameter varying subspaces relevant in the solution of state feedback and observer design problems

pore scale modeling and continuous time random walk analysis of dispersion in porous media 1 we provide a physically based explanation for the complex macroscopic behavior of dispersion in porous media as a function of peclet number pe using a pore scale network model that accurately predicts the experimental dependence of the longitudinal dispersion coefficient dl on pe the asymptotic dispersion coefficient is only reached after the solute has traveled through a large number of pores at high pe this implies that preasymptotic dispersion is the norm even in experiments in statistically homogeneous media interpreting transport as a continuous time random walk we show that 1 the power law dispersion regime is controlled by the variation in average velocity between throats the distribution of local pe giving dl pe with 3 1 2 where is an exponent characterizing the distribution of transit times between pores 2 the crossover to a linear regime dl pe for pe pecrit 400 is due to a transition from a diffusion controlled late time cutoff to transport governed by advective movement and 3 the transverse dispersion coefficient dt pe for all pe 1

observer design for nonlinear systems with discrete time measurements this paper focuses on the development of asymptotic observers for nonlinear discrete time systems it is argued that instead of trying to imitate the linear observer theory the problem of constructing a nonlinear observer can be more fruitfully studied in the context of solving simultaneous nonlinear equations in particular it is shown that the discrete newton method properly interpreted yields an asymptotic observer for a large class of discrete time systems while the continuous newton method may be employed to obtain a global observer furthermore it is analyzed how the use of broyden s method in the observer structure affects the observer s performance and its computational complexity an example illustrates some aspects of the proposed methods moreover it serves to show that these methods apply equally well to discrete time systems and to continuous time systems with sampled outputs

brief paper fault isolation for multivariate nonlinear non gaussian systems using generalized entropy optimization principle this paper is concerned with the fault isolation fi problem for multivariate nonlinear non gaussian systems by using a novel filtering method the generalized entropy optimization principle geop is established for non gaussian systems with multiple faults and disturbances where the statistic information including entropy and mean of the residual variable is maximized in the presence of the target fault as well as all the nuisance faults and disturbances and is minimized in the absence of the target fault but in the presence of the nuisance faults and disturbances different from the existing results where the output is measurable for feedback the fault isolation filter is designed and driven by the joint output stochastic distributions rather than its deterministic value the error dynamics is represented by a multivariate nonlinear non gaussian system for which new recursive relationships are proposed to formulate the joint probability density functions jpdfs of the residual variable in terms of the jpdfs of the noises and the faults finally a simulation example is given to demonstrate the effectiveness of the proposed multivariate fi algorithms

the fractional order governing equation of levy motion a governing equation of stable random walks is developed in one dimension this fokker planck equation is similar to and contains as a subset the second order advection dispersion equation ade except that the order a of the highest derivative is fractional e g the 1 65th derivative fundamental solutions are levy s a stable densities that resemble the gaussian except that they spread proportional to time 1 a have heavier tails and incorporate any degree of skewness the measured variance of a plume undergoing levy motion would grow faster than fickian plume at a rate of time 2 a where 0 a 2 the equation is parsimonious since the parameters are not functions of time or distance the scaling behavior of plumes that undergo levy motion is accounted for by the fractional derivatives which are appropriate measures of fractal functions in real space the fractional derivatives are integrodifferential operators so the fractional ade describes a spatially nonlocal process that is ergodic and has analytic solutions for all time and space

a mathematical framework for new fault detection schemes in nonlinear stochastic continuous time dynamical systems in this work a mathematical unifying framework for designing new fault detection schemes in nonlinear stochastic continuous time dynamical systems is developed these schemes are based on a stochastic process called the residual which reflects the system behavior and whose changes are to be detected a quickest detection scheme for the residual is proposed which is based on the computed likelihood ratios for time varying statistical changes in the ornstein uhlenbeck process several expressions are provided depending on a priori knowledge of the fault which can be employed in a proposed cusum type approximated scheme this general setting gathers different existing fault detection schemes within a unifying framework and allows for the definition of new ones a comparative simulation example illustrates the behavior of the proposed schemes

on the observability codistributions of a nonlinear system abstract the purpose of this is to introduce the notion of observability codistribution for a nonlinear system which extends the dual of the notion of unobservability subspace then we study its properties which bear important similarities with a number of properties which render the notion of unobservability subspace powerful in the solution of certain design problems

analytical redundancy relations for fault detection and isolation in algebraic dynamic systems this paper extends the analytical redundancy techniques well developed for linear systems to fdi in non linear dynamic systems modeled by polynomial differential algebraic equations the residual evaluation form is developed for sensor actuator and process component faults fault detectability and isolability conditions are given and the design of robust structured residuals is addressed

svd based initialization a head start for nonnegative matrix factorization we describe nonnegative double singular value decomposition nndsvd a new method designed to enhance the initialization stage of nonnegative matrix factorization nmf nndsvd can readily be combined with existing nmf algorithms the basic algorithm contains no randomization and is based on two svd processes one approximating the data matrix the other approximating positive sections of the resulting partial svd factors utilizing an algebraic property of unit rank matrices simple practical variants for nmf with dense factors are described nndsvd is also well suited to initialize nmf algorithms with sparse factors many numerical examples suggest that nndsvd leads to rapid reduction of the approximation error of many nmf algorithms

observer design based on triangular form generated by injective map a procedure is provided for constructing an injective map as a generalized coordinate change for triangular form transformation based on the triangular form a method is developed for designing nonlinear state observers

non negative matrix factorization with sparseness constraints non negative matrix factorization nmf is a recently developed technique for finding parts based linear representations of non negative data although it has successfully been applied in several applications it does not always result in parts based representations in this paper we show how explicitly incorporating the notion of sparseness improves the found decompositions additionally we provide complete matlab code both for standard nmf and for our extension our hope is that this will further the application of these methods to solving novel data analysis problems

a convex semi nonnegative matrix factorisation approach to fuzzy c means clustering we propose an alternative approach to fuzzy c means clustering which eliminates the weighting exponent parameter of conventional algorithms it is based on a particular convex factorisation of data matrix the proposed method is invariant under certain linear transformations of the data including principal component analysis we tested its accuracy using both synthetic data and real datasets and compared it to that provided by the usual fuzzy c means algorithm we were able to ascertain that our proposal can be a credible yet easier alternative to this approach to fuzzy clustering moreover it showed no noticeable sensitivity to the initial guess of the partition matrix

brief paper redesign of adaptive observers for improved parameter identification in nonlinear systems we propose a method for redesigning adaptive observers for nonlinear systems the redesign uses an adaptive law that is based on delayed observers this increases the computational burden but gives significantly better parameter identification and robustness properties in particular given that a special persistency of excitation condition is satisfied we prove uniform global asymptotic stability and semi global exponential stability of the origin of the state and parameter estimation error and give explicit lower bounds on the convergence rate of both the state and parameter estimation error dynamics for initial conditions with a known upper bound we prove tunable exponential convergence rate to illustrate the use of the proposed method we apply it to estimate the unmeasured flow rate and the uncertain friction parameters in a model of a managed pressure drilling system the simulation results clearly show the improved performance of the redesigned adaptive observer compared to a traditional design

how to design a fuzzy adaptive controller based on observers for uncertain affine nonlinear systems this paper focuses on the construction of a fuzzy adaptive output feedback control based on any observer high gain hg observer sliding mode like observer etc for a class of single input single output siso uncertain or ill defined affine nonlinear systems indeed the corrective term of the proposed observer involves a well defined design function which is shown to be satisfied by the commonly used hg based observers namely for the usual hg observers and the sliding mode observers together with their implementable versions the design of the underlying update law as well as the robust control term is based on an appropriate filtering of the output tracking error this particularly allows to overcome the output observation error filtering or the necessity of the famous strictly positive real spr condition

upscaling transport with mass transfer models mean behavior and propagation of uncertainty 1 the choice of an adequate large scale conceptual transport model constitutes a major challenge associated with the upscaling of solute transport among the different alternatives to the classical advection dispersion model the multirate mass transfer model has been proposed as a valuable and convenient alternative to model the large scale behavior of solute transport this paper evaluates the use of mass transfer models as a constitutive equation for upscaling solute transport to achieve this we compare monte carlo simulations of solute transport at two different support scales transport simulations performed at the smallest scale represent a set of reference transport solutions described at a high resolution which are contrasted against transport simulations obtained using an upscaled model low resolution several formulations of the multirate mass transfer model which differ in the type of memory function single rate double rate and truncated power law are used as a constitutive transport equation the large scale scenario represents a simplified model obtained by partially homogenizing the reference solution results show that the double rate and the truncated power law mass transfer models are capable of properly describing the ensemble average behavior of the main features associated with the integrated breakthrough curves however the uncertainty associated with the upscaled mass transfer models was substantially smaller than that attributed to the reference solution importantly the cumulative distribution function of concentrations associated with the upscaled model follows a distribution similar to the reference solution but with smaller statistical dispersion the reason is that while appropriate memory functions can be used to preserve the residence time distribution of mass particles during upscaling the lack of memory in space prevents the model from reproducing mass fluxes in all directions specifically the reproduction of mass fluxes taking place at the interface between two homogenized blocks of the upscaled model is not satisfied thus providing a poor description of the spatial distribution of mass particles in a given realization

comparative study of non linear state observation techniques abstract this paper contains a comparative study of four techniques for observing the slates of non linear systems the first technique examined is inspired by bestle and zeitz and icrener and respondek in this method a non linear transformation is found that brings the system into a canonical form from where observer design is facilitated the second technique is attributable to thau in this method the error between the system s true state and the output of the observer is shown to be asymptotically convergent to zero provided that an additional assumption is valid the third technique is due to baumann and rugh in this method extended or pseudolinearization of the error differential equation about a family of equilibrium points results in an observer design such that the eigenvalues of the linearized error equation are locally invariant finally techniques from variable structure systems are utilized to design an observer that yields an exponentially decaying error like thau s observer but unl

observability and observers for nonlinear systems this paper deals with observability and observers for general nonlinear systems in the non control affine case we characterize systems that are observable independently of the inputs an exponential observer for these systems is also exhibited

information criteria for residual generation and fault detection and isolation using an information point of view we discuss deterministic versus stochastic tools for residual generation and evaluation for fault detection and isolation fdi in linear time invariant lti state space systems in both types of approaches to off line fdi residual generation can be viewed as the design of a linear transformation of a gaussian vector the finite window input adjusted observations several statistical isolation methods are revisited using both a linear transform formulation and the information content of the corresponding residuals we formally state several multiple fault cases with or without causality assumptions and discuss an optimality criterion for the most general one new information criteria are proposed for investigating the residual optimization problem

underdetermined reverberant acoustic source separation using weighted full rank nonnegative tensor models in this paper a fusion of k models of full rank weighted nonnegative tensor factor two dimensional deconvolution k wntf2d is proposed to separate the acoustic sources that have been mixed in an underdetermined reverberant environment the model is adapted in an unsupervised manner under the hybrid framework of the generalized expectation maximization and multiplicative update algorithms the derivation of the algorithm and the development of proposed full rank k wntf2d will be shown the algorithm also encodes a set of variable sparsity parameters derived from gibbs distribution into the k wntf2d model this optimizes each sub model in k wntf2d with the required sparsity to model the time varying variances of the sources in the spectrogram in addition an initialization method is proposed to initialize the parameters in the k wntf2d experimental results on the underdetermined reverberant mixing environment have shown that the proposed algorithm is effective at separating the mixture with an average signal to distortion ratio of 3 db

geometric tools for solving the fdi problem for linear periodic discrete time systems this paper studies the problem of detecting and isolating faults in linear periodic discrete time systems the aim is to design an observer based residual generator where each residual is sensitive to one fault whilst remaining insensitive to the other faults that can affect the system making use of the geometric tools and in particular of the outer observable subspace notion the fault detection and isolation fdi problem is formulated and necessary and solvability conditions are given an algorithmic procedure is described to determine the solution of the fdi problem

failure detection and identification using the geometric concept of an unobservability subspace a solution is given to the problem of detecting and identifying control system component failures in linear time invariant systems conditions are developed for the existence of a causal linear time invariant processor that can detect and uniquely identify a component failure first for the case where components can fail simultaneously and then for the case where they fail only one at a time explicit design algorithms are provided when these conditions are satisfied in addition to time domain solvability conditions frequency domain interpretations of the results are given and connections are drawn with results already available in the literature