Representation and properties of para-Bose oscillator operators. II. Coherent states and the minimum uncertainty states

The energy, position, and momentum eigenstates of a para-Bose oscillator system were considered in paper I. Here we consider the Bargmann or the analytic function description of the para-Bose system. This brings in, in a natural way, the coherent states ||z;alpha> defined as the eigenstates of the annihilation operator ?. The transformation functions relating this description to the energy, position, and momentum eigenstates are explicitly obtained. Possible resolution of the identity operator using coherent states is examined. A particular resolution contains two integrals, one containing the diagonal basis ||z;alpha><−z;alpha||. We briefly consider the normal and antinormal ordering of the operators and their diagonal and discrete diagonal coherent state approximations. The problem of constructing states with a minimum value of the product of the position and momentum uncertainties and the possible alpha dependence of this minimum value is considered. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Relaxation Labeling with Learning Automata

Relaxation labeling processes are a class of mechanisms that solve the problem of assigning labels to objects in a manner that is consistent with respect to some domain-specific constraints. We reformulate this using the model of a team of learning automata interacting with an environment or a high-level critic that gives noisy responses as to the consistency of a tentative labeling selected by the automata. This results in an iterative linear algorithm that is itself probabilistic. Using an explicit definition of consistency we give a complete analysis of this probabilistic relaxation process using weak convergence results for stochastic algorithms. Our model can accommodate a range of uncertainties in the compatibility functions. We prove a local convergence result and show that the point of convergence depends both on the initial labeling and the constraints. The algorithm is implementable in a highly parallel fashion.

Damage assessment of structures with uncertainty by using mode-shape curvatures and fuzzy logic

Uncertainties associated with the structural model and measured vibration data may lead to unreliable damage detection. In this paper, we show that geometric and measurement uncertainty cause considerable problem in damage assessment which can be alleviated by using a fuzzy logic-based approach for damage detection. Curvature damage factor (CDF) of a tapered cantilever beam are used as damage indicators. Monte Carlo simulation (MCS) is used to study the changes in the damage indicator due to uncertainty in the geometric properties of the beam. Variation in these CDF measures due to randomness in structural parameter, further contaminated with measurement noise, are used for developing and testing a fuzzy logic system (FLS). Results show that the method correctly identifies both single and multiple damages in the structure. For example, the FLS detects damage with an average accuracy of about 95 percent in a beam having geometric uncertainty of 1 percent COV and measurement noise of 10 percent in single damage scenario. For multiple damage case, the FLS identifies damages in the beam with an average accuracy of about 94 percent in the presence of above mentioned uncertainties. The paper brings together the disparate areas of probabilistic analysis and fuzzy logic to address uncertainty in structural damage detection.

Design of laterally loaded piles in clays based on cone penetration test data: a reliability-based approach

The behaviour of laterally loaded piles is considerably influenced by the uncertainties in soil properties. Hence probabilistic models for assessment of allowable lateral load are necessary. Cone penetration test (CPT) data are often used to determine soil strength parameters, whereby the allowable lateral load of the pile is computed. In the present study, the maximum lateral displacement and moment of the pile are obtained based on the coefficient of subgrade reaction approach, considering the nonlinear soil behaviour in undrained clay. The coefficient of subgrade reaction is related to the undrained shear strength of soil, which can be obtained from CPT data. The soil medium is modelled as a one-dimensional random field along the depth, and it is described by the standard deviation and scale of fluctuation of the undrained shear strength of soil. Inherent soil variability, measurement uncertainty and transformation uncertainty are taken into consideration. The statistics of maximum lateral deflection and moment are obtained using the first-order, second-moment technique. Hasofer-Lind reliability indices for component and system failure criteria, based on the allowable lateral displacement and moment capacity of the pile section, are evaluated. The geotechnical database from the Konaseema site in India is used as a case example. It is shown that the reliability-based design approach for pile foundations, considering the spatial variability of soil, permits a rational choice of allowable lateral loads.

Queuing Models for Estimating Aircraft Fleet Availability

The availability of a small fleet of aircraft in a flying-base, repair-depot combination is modeled and studied. First, a deterministic flow model relates parameters of interest and represents the state-of-the art in the planning of such systems. Second, a cyclic queue model shows the effect of the principal uncertainties in operation and repair and shows the consequent decrease in the availability of aircraft at the flying-base. Several options such as increasing fleet size, investments in additional repair facilities, or building reliability and maintainability into the individual aircraft during its life-cycle are open for increasing the availability. A life-cycle cost criterion brings out some of these features. Numerical results confirm Rose's prediction that there exists a minimal cost combination of end products and repair-depot capability to achieve a prescribed operational availability.

An imprecise fuzzy risk approach for water quality management of a river system

Uncertainty plays an important role in water quality management problems. The major sources of uncertainty in a water quality management problem are the random nature of hydrologic variables and imprecision (fuzziness) associated with goals of the dischargers and pollution control agencies (PCA). Many Waste Load Allocation (WLA)problems are solved by considering these two sources of uncertainty. Apart from randomness and fuzziness, missing data in the time series of a hydrologic variable may result in additional uncertainty due to partial ignorance. These uncertainties render the input parameters as imprecise parameters in water quality decision making. In this paper an Imprecise Fuzzy Waste Load Allocation Model (IFWLAM) is developed for water quality management of a river system subject to uncertainty arising from partial ignorance. In a WLA problem, both randomness and imprecision can be addressed simultaneously by fuzzy risk of low water quality. A methodology is developed for the computation of imprecise fuzzy risk of low water quality, when the parameters are characterized by uncertainty due to partial ignorance. A Monte-Carlo simulation is performed to evaluate the imprecise fuzzy risk of low water quality by considering the input variables as imprecise. Fuzzy multiobjective optimization is used to formulate the multiobjective model. The model developed is based on a fuzzy multiobjective optimization problem with max-min as the operator. This usually does not result in a unique solution but gives multiple solutions. Two optimization models are developed to capture all the decision alternatives or multiple solutions. The objective of the two optimization models is to obtain a range of fractional removal levels for the dischargers, such that the resultant fuzzy risk will be within acceptable limits. Specification of a range for fractional removal levels enhances flexibility in decision making. The methodology is demonstrated with a case study of the Tunga-Bhadra river system in India.

Climate-change and agriculture - an indian perspective

In this paper, we examine the major predictions made so far regarding the nature of climate change and its impacts on our region in the light of the known errors of the set of models and the observations over this century. The major predictions of the climate models about the impact of increased concentration of greenhouse gases ave at variance with the observations over the Indian region during the last century characterized by such increases and global warming. It is important to note that as far as the Indian region is concerned, the impact of year-to-year variation of the monsoon will continue to be dominant over longer period changes even in the presence of global warming. Recent studies have also brought out the uncertainties in the yields simulated by crop models. It is suggested that a deeper understanding of the links between climate and agricultural productivity is essential for generating reliable predictions of impact of climate change. Such an insight is also required for identifying cropping patterns and management practices which are tailored for sustained maximum yield in the face of the vagaries of the monsoon.

An adaptive drug delivery design using neural networks for effective treatment of infectious diseases: A simulation study

An adaptive drug delivery design is presented in this paper using neural networks for effective treatment of infectious diseases. The generic mathematical model used describes the coupled evolution of concentration of pathogens, plasma cells, antibodies and a numerical value that indicates the relative characteristic of a damaged organ due to the disease under the influence of external drugs. From a system theoretic point of view, the external drugs can be interpreted as control inputs, which can be designed based on control theoretic concepts. In this study, assuming a set of nominal parameters in the mathematical model, first a nonlinear controller (drug administration) is designed based on the principle of dynamic inversion. This nominal drug administration plan was found to be effective in curing "nominal model patients" (patients whose immunological dynamics conform to the mathematical model used for the control design exactly. However, it was found to be ineffective in curing "realistic model patients" (patients whose immunological dynamics may have off-nominal parameter values and possibly unwanted inputs) in general. Hence, to make the drug delivery dosage design more effective for realistic model patients, a model-following adaptive control design is carried out next by taking the help of neural networks, that are trained online. Simulation studies indicate that the adaptive controller proposed in this paper holds promise in killing the invading pathogens and healing the damaged organ even in the presence of parameter uncertainties and continued pathogen attack. Note that the computational requirements for computing the control are very minimal and all associated computations (including the training of neural networks) can be carried out online. However it assumes that the required diagnosis process can be carried out at a sufficient faster rate so that all the states are available for control computation.

Water balance modelling in a tropical watershed under deciduous forest (Mule Hole, India): Regolith matric storage buffers the groundwater recharge process

Accurate estimations of water balance are needed in semi-arid and sub-humid tropical regions, where water resources are scarce compared to water demand. Evapotranspiration plays a major role in this context, and the difficulty to quantify it precisely leads to major uncertainties in the groundwater recharge assessment, especially in forested catchments. In this paper, we propose to assess the importance of deep unsaturated regolith and water uptake by deep tree roots on the groundwater recharge process by using a lumped conceptual model (COMFORT). The model is calibrated using a 5 year hydrological monitoring of an experimental watershed under dry deciduous forest in South India (Mule Hole watershed). The model was able to simulate the stream discharge as well as the contrasted behaviour of groundwater table along the hillslope. Water balance simulated for a 32 year climatic time series displayed a large year-to-year variability, with alternance of dry and wet phases with a time period of approximately 14 years. On an average, input by the rainfall was 1090 mm year(-1) and the evapotranspiration was about 900 mm year(-1) out of which 100 mm year(-1) was uptake from the deep saprolite horizons. The stream flow was 100 mm year(-1) while the groundwater underflow was 80 mm year(-1). The simulation results suggest that (i) deciduous trees can uptake a significant amount of water from the deep regolith, (ii) this uptake, combined with the spatial variability of regolith depth, can account for the variable lag time between drainage events and groundwater rise observed for the different piezometers and (iii) water table response to recharge is buffered due to the long vertical travel time through the deep vadose zone, which constitutes a major water reservoir. This study stresses the importance of long term observations for the understanding of hydrological processes in tropical forested ecosystems. (C) 2009 Elsevier B.V. All rights reserved.

Optimum Design of Bridge Abutments under Seismic Conditions: Reliability-Based Approach

The paper focuses on the reliability-based design optimization of gravity wall bridge abutments when subjected to active condition during earthquakes. An analytical study considering the effect of uncertainties in the seismic analysis of bridge abutments is presented. Planar failure surface has been considered in conjunction with the pseudostatic limit equilibrium method for the calculation of the seismic active earth pressure. Analysis is conducted to evaluate the external stability of bridge abutments when subjected to earthquake loads. Reliability analysis is used to estimate the probability of failure in three modes of failure viz. sliding failure of the wall on its base, overturning failure about its toe (or eccentricity failure of the resultant force) and bearing failure of foundation soil below the base of wall. The properties of backfill and foundation soil below the base of abutment are treated as random variables. In addition, the uncertainties associated with characteristics of earthquake ground motions such as horizontal seismic acceleration and shear wave velocity propagating through backfill soil are considered. The optimum proportions of the abutment needed to maintain the stability are obtained against three modes of failure by targeting various component and system reliability indices. Studies have also been made to study the influence of various parameters on the seismic stability.

Low power pipelined TCAM employing mismatch dependent power allocation technique

This paper presents design of a Low power 256x72 bit TCAM in 0.13um CMOS technology. In contrast to conventional Match line (ML) sensing scheme in which equal power is consumed irrespective of match or mismatch, the ML scheme employed in this design allocates less power to match decisions involving a large number of mismatched bits. Typically, the probability of mismatch is high so this scheme results in significant CAM power reduction. We propose to use this technique along with pipelining of search operation in which the MLs are broken into several segments. Since most words fail to match in first segment, the search operation for subsequent segments is discontinued, resulting in further reduction in power consumption. The above architecture provides 70% power reduction while performing search in 3ns.

Modelling of solute transport in a mild heterogeneous porous medium using stochastic finite element method: Effects of random source conditions

Randomness in the source condition other than the heterogeneity in the system parameters can also be a major source of uncertainty in the concentration field. Hence, a more general form of the problem formulation is necessary to consider randomness in both source condition and system parameters. When the source varies with time, the unsteady problem, can be solved using the unit response function. In the case of random system parameters, the response function becomes a random function and depends on the randomness in the system parameters. In the present study, the source is modelled as a random discrete process with either a fixed interval or a random interval (the Poisson process). In this study, an attempt is made to assess the relative effects of various types of source uncertainties on the probabilistic behaviour of the concentration in a porous medium while the system parameters are also modelled as random fields. Analytical expressions of mean and covariance of concentration due to random discrete source are derived in terms of mean and covariance of unit response function. The probabilistic behaviour of the random response function is obtained by using a perturbation-based stochastic finite element method (SFEM), which performs well for mild heterogeneity. The proposed method is applied for analysing both the 1-D as well as the 3-D solute transport problems. The results obtained with SFEM are compared with the Monte Carlo simulation for 1-D problems.

Optimum design of cantilever sheet pile walls in sandy soils using inverse reliability approach

In this paper an approach for obtaining depth and section modulus of the cantilever sheet pile wall using inverse reliability method is described. The proposed procedure employs inverse first order reliability method to obtain the design penetration depth and section modulus of the steel sheet pile wall in order that the reliability of the wall against failure modes must meet a desired level of safety. Sensitivity analysis is conducted to assess the effect of uncertainties in design parameters on the reliability of cantilever sheet pile walls. The analysis is performed by treating back fill soil properties, depth of the water table from the top of the sheet pile wall, yield strength of steel and section modulus of steel pile as random variables. Two limit states, viz., rotational and flexural failure of sheet pile wall are considered. The results using this approach are used to develop a set of reliability based design charts for different coefficients of variation of friction angle of the backfill (5%, 10% and 15%). System reliability considerations in terms of series and parallel systems are also studied.

Self-regularized pseudo time-marching schemes for structural system identification with static measurements

We explore the application of pseudo time marching schemes, involving either deterministic integration or stochastic filtering, to solve the inverse problem of parameter identification of large dimensional structural systems from partial and noisy measurements of strictly static response. Solutions of such non-linear inverse problems could provide useful local stiffness variations and do not have to confront modeling uncertainties in damping, an important, yet inadequately understood, aspect in dynamic system identification problems. The usual method of least-square solution is through a regularized Gauss-Newton method (GNM) whose results are known to be sensitively dependent on the regularization parameter and data noise intensity. Finite time,recursive integration of the pseudo-dynamical GNM (PD-GNM) update equation addresses the major numerical difficulty associated with the near-zero singular values of the linearized operator and gives results that are not sensitive to the time step of integration. Therefore, we also propose a pseudo-dynamic stochastic filtering approach for the same problem using a parsimonious representation of states and specifically solve the linearized filtering equations through a pseudo-dynamic ensemble Kalman filter (PD-EnKF). For multiple sets of measurements involving various load cases, we expedite the speed of thePD-EnKF by proposing an inner iteration within every time step. Results using the pseudo-dynamic strategy obtained through PD-EnKF and recursive integration are compared with those from the conventional GNM, which prove that the PD-EnKF is the best performer showing little sensitivity to process noise covariance and yielding reconstructions with less artifacts even when the ensemble size is small.

Self-regularized pseudo time-marching schemes for structural system identification with static measurements

We explore the application of pseudo time marching schemes, involving either deterministic integration or stochastic filtering, to solve the inverse problem of parameter identification of large dimensional structural systems from partial and noisy measurements of strictly static response. Solutions of such non-linear inverse problems could provide useful local stiffness variations and do not have to confront modeling uncertainties in damping, an important, yet inadequately understood, aspect in dynamic system identification problems. The usual method of least-square solution is through a regularized Gauss-Newton method (GNM) whose results are known to be sensitively dependent on the regularization parameter and data noise intensity. Finite time, recursive integration of the pseudo-dynamical GNM (PD-GNM) update equation addresses the major numerical difficulty associated with the near-zero singular values of the linearized operator and gives results that are not sensitive to the time step of integration. Therefore, we also propose a pseudo-dynamic stochastic filtering approach for the same problem using a parsimonious representation of states and specifically solve the linearized filtering equations through apseudo-dynamic ensemble Kalman filter (PD-EnKF). For multiple sets ofmeasurements involving various load cases, we expedite the speed of the PD-EnKF by proposing an inner iteration within every time step. Results using the pseudo-dynamic strategy obtained through PD-EnKF and recursive integration are compared with those from the conventional GNM, which prove that the PD-EnKF is the best performer showing little sensitivity to process noise covariance and yielding reconstructions with less artifacts even when the ensemble size is small. Copyright (C) 2009 John Wiley & Sons, Ltd.