Discrete Modelling of Continuous-Time Systems Having Interval Uncertainties Using Genetic Algorithms

In this paper, a higher-order integrator approach is proposed to obtain an approximate discrete-time transfer function for uncertain continuous systems having interval uncertainties. Because of the simple algebraic operations of this approach, the resulting discrete model is a rational function of the uncertain parameters. The problem of non-linearly coupled coefficients with exponential nature occurring in the exact discretetime transfer function is therefore circumvented. Furthermore, the interval structure of the uncertain continuous-time system is preserved in the resulting discrete model by using this approach. Formulae to obtain the lower and upper bounds for the coefficients of the discrete interval system are derived, so that digital simulation and design for the uncertain continuous systems can be performed by using the available robustness results in the discrete-time domain.

Numerical simulation of a fractured-vuggy porous medium is a challenging problem. One reason is the coexistence of matrix, fractures and vugs on multiple scales that need to be coupled, and the other reason is that the high-resolution fractured-vuggy model may contain up to several millions of gridcells in applications, which brings severe computational challenges into the numerical methods. Therefore, the requirement for accurate and efficient technique is widely increasing. Fractured-vuggy porous medium is generally represented by triple-continuum model in which the matrix system, fracture system and vug system each are treated as a parallel continuous system. Although triple-continuum model is widely used because of its easy-implementation and high efficiency, it fails to capture the detailed flow patterns of reservoir with disconnected long fractures. Discrete fracture-vug network (DFVN) model can precisely model the fluid flow in fractures and vugs. However, the simulation of this model is deemed intractable even with the advent of supercomputers because of the large amount of calculation. In view of the fact that the multigrid method is now well known as one of the fastest method of solving elliptic problems, in this paper we introduce a nearly linear complexity multiresolution decomposition method for fluid flow in a fractured-vuggy reservoir. The detailed flow patterns are described by combing the advantages of continuum model and discrete model. That is, the homogenization theory is used to construct an equivalent permeability in each coarse grid block in which the vugs and small-scale fractures are represented by discrete fracture-vug network model. We decompose the solution space into several subspaces and then we compute the corresponding solutions of heterogeneous discrete fracture network model in each subspace. Gamblets are constructed and they are elementary solutions of hierarchical information games associated with the process of computing with partial information and limited resources. These gamblets have a natural Bayesian interpretation under the mixed strategy emerging from the game theoretic formulation. This method could realize its fast simulation by decomposing the solution space into a direct sum of linear subspaces that are orthogonal to each other. Finally, the pressure difference distribution of fractured-vuggy porous medium is obtained by combing the DFVN solutions of all subspaces. Numerical results are presented to demonstrate the accuracy and efficiency of the proposed multiresolution decomposition method. The results show that this method is a promising method of numerically simulating the fractured-vuggy porous medium.

The chapter concerns numerical issues encountered when the pipeline flow process is modeled as a discrete-time state-space model . In particular, issues related to computational complexity and computability are discussed, i.e., simulation feasibility which is connected to the notions of singularity and stability of the model. These properties are critical if a diagnostic system is based on a discrete mathematical model of the flow process. The starting point of the study is determined by the partial differential equations obtained from the momentum and mass conservation laws by using physical principles. A realizable computational model is developed by approximation of the principal equations using the finite difference method. This model is expressed in terms of the recombination matrix A which is the key of the analysis by taking into account its possible singularity and stability . The nonsingularity of the matrix A for nonzero and finite, time and spatial steps is proven by the Lower–Upper decomposition. A feature of the discrete model allows the derivation of a nonsingular aggregated model, whose stability can be analyzed. By considering the Courant–Friedrichs–Lewy condition and data from experimental studies, numerical stability conditions are derived and limitations for the feasible discretized grid are obtained. Moreover, the optimal relationship between the time and space steps which ensures a maximum stability margin is derived. Because the inverse of matrix A, composed of four tridiagonal matrices, is required for the main diagnosis methods, two analytical methods for the inversion are discussed which reduce the system’s initialization time and allow designing an accurate and fast diagnosis algorithm. By considering that each inversion method generates its particular structure, two different flow models are generated: one based on auxiliary variables and the other suitable if the stability condition of A is satisfied. The applicability of the two models is shown by considering the norm of the difference between their behaviors for a finer discretization grid . A similarity measure is proposed which considers the number of pipeline segments as well as the ratio between the time and spatial steps . Thus, the system’s computational efficiency is improved and satisfactory results are shown with respect to the base model, if a highly dimensional model with the approximated diagonal matrix is considered.

This paper shows that the analysis and the design of discrete-time models of continuous-time systems can be carried out within a single framework. Briefly, all classes of discrete-time models, namely the invariant models, the mapping models and the matched pole-zero models, are shown to incorporate the common structure of a hold followed by a continuous-time system and the ideal sampler. This interpretation of discrete-time models of continuous-time systems facilitates the understanding of the differences and similarities among the various discrete-time models. A numerical example illustrates the concepts involved.

A procedure for identifying linear continuous-time multivariable systems is presented. The scheme is based on a discrete identification method which requires no structural identification. This is accomplished by the use of pseudo-observable forms whose structure is defined by their corresponding pseudo-observability indices. A First-Order Hold transformation of this discrete-time model to an equivalent continuous-time model is then performed. First, the state transition matrix is transformed to an equivalent continuous-time system matrix using a procedure which is insensitive to the size of the spectral radii of the system. The remaining system matrices are then transformed using a generalized First-Order Hold transformation technique which places no restrictions on the singularity of the continuous-time system.

The operation of digital systems are based on time slotting and it finds many applications particularly in communication networks. It is important to analyze a digital network on some digital concepts. In this paper we analyze the network buffer through discrete time queueing system in which queue is discrete in nature and it is used to analyze the performance of the communication networks buffer. Discrete time models can be used to represents such type of systems in terms of slotted time units to models any physical system. More than one state changes in discrete time models from one time unit to another. Discrete time markov chains are used to describes the behavior of the network under the specific conditions and various performance measures are evaluated such as queue length, mean waiting time and mean number in the system.

Background and Purpose— Observational studies suggest that platelet inhibitors reduce the risk of delayed cerebral ischemia (DCI) after aneurysmal subarachnoid hemorrhage and thereby have a beneficial effect on clinical outcome. Robust evidence, however, is lacking. We performed a systematic meta-analysis to determine whether antiplatelet therapy has a beneficial effect after SAH. Methods— We searched Medline and the Cochrane Library to identify all randomized controlled trials of antiplatelet drugs versus control and calculated relative risks with corresponding 95% confidence intervals (CIs) for poor outcome (dependence or death), the occurrence of DCI, and the occurrence of any intracranial hemorrhage. Results— We included 5 trials totaling 699 patients. The overall relative risk for poor outcome was 0.87 (95% CI, 0.65 to 1.17); for the occurrence of DCI (reported in 3 of the 5 studies), 0.65 (95% CI, 0.47 to 0.89); and for the occurrence of intracranial hemorrhage, 1.19 (reported in 4 of the 5 studies)...

Complex patterns in a space–time discrete mathematical model of antibiotic resistance in hospitals with self-diffusion

A higher-order integrator approach is proposed to obtain an approximate discrete-time transfer function for uncertain continuous systems having interval uncertainties. Thanks to simple algebraic operations of this approach, the resulting discrete model is a rational function of the uncertain parameters. The problem of non-linearly coupled coefficients of exponential nature in the exact discrete-time transfer function is therefore circumvented. Furthermore, interval structure of the uncertain continuous-time system is preserved in the resulting discrete model by using this approach. Formulas to obtain the lower and upper bounds for the discrete interval system are derived, so that existing robust results in the discrete-time domain can be easily applied to the discretized system. Digital simulation and design for the continuous-time interval plant can then be performed based on the obtained discrete-time interval model.

Using the bilinear and tuning bilinear approximation together with the interval arithmetic operation, the discrete-time uncertain model and robust digital redesign of sampled-data uncertain system with input time delay are presented. The system matrices characterizing the stale-space representation of the original uncertain system are assumed to be interval matrices. The developed discrete-time interval model tightly encloses the exactly discretized continuous-time input time-delay uncertain system, and it can be utilized for digital simulation. Based on bilinear approximation, a tuning bilinear approximation is presented to find the digitally redesign controller of the digitally controlled sampled-data uncertain system with input time delay. The digitally redesigned predictor controller is able to closely match the states of the digitally redesigned uncertain sampled-data system with those of the original continuous-time predictor controlled uncertain system.

Ahlstrom Corp, Finland

In this paper, a least-mean-squares (LMS) finite memory (FM) estimator for a stochastic discrete-time state space model is obtained by taking the conditional expectation of the estimated state given a finite number of inputs and outputs measured on the recent finite horizon. Any a priori state information is not involved and any arbitrary constraints are not imposed. For a general discrete-time state space model with both system and measurement noises, the LMS FM estimator is represented in a closed-form. It turns out that the proposed LMS FM estimator has the unbiased property and the linear structure with respect to inputs and outputs on the recent finite horizon.

Schematic-level optimization and steady-state loss modeling play a vital role in the design of advanced power converters. Recently, discrete time state-space modeling has shown merits in rapid analysis and generality to arbitrary circuit topologies but has not yet been utilized under rapid optimization techniques. In this work, we investigate methods for the incorporation of rapid gradient-based optimization techniques leveraging discrete time state-space modeling and showcase the utility of the approach for use in the converter design process.

The effectiveness of intradiscal biologic treatments for discogenic low back pain: a systematic review

In patients with aneurysmal subarachnoid hemorrhage (aSAH), it is unclear whether aneurysm treatment <24 h after ictus results in better outcomes than treatment 24-72 h after aSAH. We studied whether aneurysm occlusion <24 h is associated with better outcomes than occlusion 24-72 h after aSAH. We used two cohorts of patients with aSAH: (1) the UMC Utrecht cohort with patients admitted between 2008 and 2012 and (2) the International Subarachnoid Aneurysm Trial cohort. Aneurysm treatment was categorized into <24 h and 24-72 h after ictus. We calculated adjusted risk ratios (aRRs) with 95% confidence intervals (CIs) using Poisson regression analyses for poor functional outcome (death or dependency) for both cohorts separately, and performed a pooled analysis based on individual patient data. We also performed a worst-case scenario analysis wherein all patients with rebleeding >3 h after admission were re-categorized into the group with aneurysm treatment 24-72 h after aSAH. We included 1,238 patients (UMC Utrecht cohort: n = 330; ISAT: n = 908). The aRR for poor outcome after treatment <24 h was in the UMC Utrecht cohort 1.84 (95% CI: 1.25-2.70), in ISAT 1.14 (95% CI 0.84-1.55), in the pooled analysis 1.37 (95% CI 1.11-1.68), and in the worst-case scenario pooled analysis 1.24 (95% CI 1.01-1.52). Our results suggest that aneurysm occlusion can be performed in day time within 72 h after ictus, instead of on an emergency basis. However, due to the retrospective, non-randomized design of our study, our results cannot be considered as definitive evidence.