Variability of sif and cod of stochastic structural systems

Stochastic structural systems having a stochastic distribution of material properties and stochastic external loadings in space are analysed when a crack of deterministic size is present. The material properties and external loadings are considered to constitute independent, two-dimensional, univariate, real, homogeneous stochastic fields. The stochastic fields are characterized by their means, variances, autocorrelation functions or the equivalent power spectral density functions, and scale fluctuations. The Young's modulus and Poisson's ratio are treated to be stochastic quantities. The external loading is treated to be a stochastic field in space. The energy release rate is derived using the method of virtual crack extension. The deterministic relationship is derived to represent the sensitivities of energy release rate with respect to both virtual crack extension and real system parameter fluctuations. Taylor series expansion is used and truncation is made to the first order. This leads to the determination of second-order properties of the output quantities to the first order. Using the linear perturbations about the mean values of the output quantities, the statistical information about the energy release rates, SIF and crack opening displacements are obtained. Both plane stress and plane strain cases are considered. The general expressions for the SIF in all the three fracture modes are derived and a more detailed analysis is conducted for a mode I situation. A numerical example is given.

Modeling stochastic hybrid systems

Stochastic hybrid systems arise in numerous applications of systems with multiple models; e.g., air traffc management, flexible manufacturing systems, fault tolerant control systems etc. In a typical hybrid system, the state space is hybrid in the sense that some components take values in a Euclidean space, while some other components are discrete. In this paper we propose two stochastic hybrid models, both of which permit diffusion and hybrid jump. Such models are essential for studying air traffic management in a stochastic framework.

Doubly spectral stochastic finite element method (DSSFEM) for random field problems

Uncertainties in complex dynamic systems play an important role in the prediction of a dynamic response in the mid- and high-frequency ranges. For distributed parameter systems, parametric uncertainties can be represented by random fields leading to stochastic partial differential equations. Over the past two decades, the spectral stochastic finite-element method has been developed to discretize the random fields and solve such problems. On the other hand, for deterministic distributed parameter linear dynamic systems, the spectral finite-element method has been developed to efficiently solve the problem in the frequency domain. In spite of the fact that both approaches use spectral decomposition (one for the random fields and the other for the dynamic displacement fields), very little overlap between them has been reported in literature. In this paper, these two spectral techniques are unified with the aim that the unified approach would outperform any of the spectral methods considered on their own. An exponential autocorrelation function for the random fields, a frequency-dependent stochastic element stiffness, and mass matrices are derived for the axial and bending vibration of rods. Closed-form exact expressions are derived by using the Karhunen-Loève expansion. Numerical examples are given to illustrate the unified spectral approach.

Basin Scale Water Resources Systems Modeling Under Cascading Uncertainties

Global change in climate and consequent large impacts on regional hydrologic systems have, in recent years, motivated significant research efforts in water resources modeling under climate change. In an integrated future hydrologic scenario, it is likely that water availability and demands will change significantly due to modifications in hydro-climatic variables such as rainfall, reservoir inflows, temperature, net radiation, wind speed and humidity. An integrated regional water resources management model should capture the likely impacts of climate change on water demands and water availability along with uncertainties associated with climate change impacts and with management goals and objectives under non-stationary conditions. Uncertainties in an integrated regional water resources management model, accumulating from various stages of decision making include climate model and scenario uncertainty in the hydro-climatic impact assessment, uncertainty due to conflicting interests of the water users and uncertainty due to inherent variability of the reservoir inflows. This paper presents an integrated regional water resources management modeling approach considering uncertainties at various stages of decision making by an integration of a hydro-climatic variable projection model, a water demand quantification model, a water quantity management model and a water quality control model. Modeling tools of canonical correlation analysis, stochastic dynamic programming and fuzzy optimization are used in an integrated framework, in the approach presented here. The proposed modeling approach is demonstrated with the case study of the Bhadra Reservoir system in Karnataka, India.

Pole placement in multi-input systems via elementary transformations

This paper is concerned with the development of an algorithm for pole placement in multi-input dynamic systems. The algorithm which uses a series of elementary transformations is believed to be simpler, computationally more efficient and numerically stable when compared with earlier methods. In this paper two methods have been presented.

Pole placement in multi-input systems via elementary transformations

This paper is concerned with the development of an algorithm for pole placement in multi-input dynamic systems. The algorithm which uses a series of elementary transformations is believed to be simpler, computationally more efficient and numerically stable when compared with earlier methods. In this paper two methods have been presented.

Testing and Modeling of MR Damper and Its Application to SDOF Systems Using Integral Backstepping Technique

Magnetorheological dampers are intrinsically nonlinear devices, which make the modeling and design of a suitable control algorithm an interesting and challenging task. To evaluate the potential of magnetorheological (MR) dampers in control applications and to take full advantages of its unique features, a mathematical model to accurately reproduce its dynamic behavior has to be developed and then a proper control strategy has to be taken that is implementable and can fully utilize their capabilities as a semi-active control device. The present paper focuses on both the aspects. First, the paper reports the testing of a magnetorheological damper with an universal testing machine, for a set of frequency, amplitude, and current. A modified Bouc-Wen model considering the amplitude and input current dependence of the damper parameters has been proposed. It has been shown that the damper response can be satisfactorily predicted with this model. Second, a backstepping based nonlinear current monitoring of magnetorheological dampers for semi-active control of structures under earthquakes has been developed. It provides a stable nonlinear magnetorheological damper current monitoring directly based on system feedback such that current change in magnetorheological damper is gradual. Unlike other MR damper control techniques available in literature, the main advantage of the proposed technique lies in its current input prediction directly based on system feedback and smooth update of input current. Furthermore, while developing the proposed semi-active algorithm, the dynamics of the supplied and commanded current to the damper has been considered. The efficiency of the proposed technique has been shown taking a base isolated three story building under a set of seismic excitation. Comparison with widely used clipped-optimal strategy has also been shown.

Online client-AP association in WLANs

In many IEEE 802.11 WLAN deployments, wireless clients have a choice of access points (AP) to connect to. In current systems, clients associate with the access point with the strongest signal to noise ratio. However, such an association mechanism can lead to unequal load sharing, resulting in diminished system performance. In this paper, we first provide a numerical approach based on stochastic dynamic programming to find the optimal client-AP association algorithm for a small topology consisting of two access points. Using the value iteration algorithm, we determine the optimal association rule for the two-AP topology. Next, utilizing the insights obtained from the optimal association ride for the two-AP case, we propose a near-optimal heuristic that we call RAT. We test the efficacy of RAT by considering more realistic arrival patterns and a larger topology. Our results show that RAT performs very well in these scenarios as well. Moreover, RAT lends itself to a fairly simple implementation.

Foaming of slags under dynamic conditions

Slag foaming under dynamic conditions has been studied in laboratory scale to examine the influence of properties commonly used to describe the foaminess and foam stability of slags under steady-state conditions. Synthetically produced slags with compositions relevant to tool steel and stainless steel production were studied through X-ray equipment in measurements simulating the dynamic conditions found in real processes. It is found that the dynamic systems display a more complex behavior than systems Under steady state. Traditional theories for foaming do not seem to be valid for slag foaming under dynamic conditions. The foam displays a fluctuating behavior, which the presently available models are not able to take into account. The concept of a foaming index does not seem to be applicable, resulting in the need for alternative models.

On Optimal Performance in Mobile Ad-Hoc Networks

In this paper we are concerned with finding the maximum throughput that a mobile ad hoc network can support. Even when nodes are stationary, the problem of determining the capacity region has long been known to be NP-hard. Mobility introduces an additional dimension of complexity because nodes now also have to decide when they should initiate route discovery. Since route discovery involves communication and computation overhead, it should not be invoked very often. On the other hand, mobility implies that routes are bound to become stale resulting in sub-optimal performance if routes are not updated. We attempt to gain some understanding of these effects by considering a simple one-dimensional network model. The simplicity of our model allows us to use stochastic dynamic programming (SDP) to find the maximum possible network throughput with ideal routing and medium access control (MAC) scheduling. Using the optimal value as a benchmark, we also propose and evaluate the performance of a simple threshold-based heuristic. Unlike the optimal policy which requires considerable state information, the heuristic is very simple to implement and is not overly sensitive to the threshold value used. We find empirical conditions for our heuristic to be near-optimal as well as network scenarios when our simple heuristic does not perform very well. We provide extensive numerical and simulation results for different parameter settings of our model.

Beyond fractional derivatives: local approximation of other convolution integrals

Dynamic systems involving convolution integrals with decaying kernels, of which fractionally damped systems form a special case, are non-local in time and hence infinite dimensional. Straightforward numerical solution of such systems up to time t needs O(t(2)) computations owing to the repeated evaluation of integrals over intervals that grow like t. Finite-dimensional and local approximations are thus desirable. We present here an approximation method which first rewrites the evolution equation as a coupled in finite-dimensional system with no convolution, and then uses Galerkin approximation with finite elements to obtain linear, finite-dimensional, constant coefficient approximations for the convolution. This paper is a broad generalization, based on a new insight, of our prior work with fractional order derivatives (Singh & Chatterjee 2006 Nonlinear Dyn. 45, 183-206). In particular, the decaying kernels we can address are now generalized to the Laplace transforms of known functions; of these, the power law kernel of fractional order differentiation is a special case. The approximation can be refined easily. The local nature of the approximation allows numerical solution up to time t with O(t) computations. Examples with several different kernels show excellent performance. A key feature of our approach is that the dynamic system in which the convolution integral appears is itself approximated using another system, as distinct from numerically approximating just the solution for the given initial values; this allows non-standard uses of the approximation, e. g. in stability analyses.

A Combinatorial Optimization Problem for High Order PODs with Few Sensors

Experimental characterization of high dimensional dynamic systems sometimes uses the proper orthogonal decomposition (POD). If there are many measurement locations and relatively fewer sensors, then steady-state behavior can still be studied by sequentially taking several sets of simultaneous measurements. The number required of such sets of measurements can be minimized if we solve a combinatorial optimization problem. We aim to bring this problem to the attention of engineering audiences, summarize some known mathematical results about this problem, and present a heuristic (suboptimal) calculation that gives reasonable, if not stellar, results.

Reservoir performance under uncertainty in hydrologic impacts of climate change

Relatively few studies have addressed water management and adaptation measures in the face of changing water balances due to climate change. The current work studies climate change impact on a multipurpose reservoir performance and derives adaptive policies for possible futurescenarios. The method developed in this work is illustrated with a case study of Hirakud reservoir on the Mahanadi river in Orissa, India,which is a multipurpose reservoir serving flood control, irrigation and power generation. Climate change effects on annual hydropower generation and four performance indices (reliability with respect to three reservoir functions, viz. hydropower, irrigation and flood control, resiliency, vulnerability and deficit ratio with respect to hydropower) are studied. Outputs from three general circulation models (GCMs) for three scenarios each are downscaled to monsoon streamflow in the Mahanadi river for two future time slices, 2045-65 and 2075-95. Increased irrigation demands, rule curves dictated by increased need for flood storage and downscaled projections of streamflow from the ensemble of GCMs and scenarios are used for projecting future hydrologic scenarios. It is seen that hydropower generation and reliability with respect to hydropower and irrigation are likely to show a decrease in future in most scenarios, whereas the deficit ratio and vulnerability are likely to increase as a result of climate change if the standard operating policy (SOP) using current rule curves for flood protection is employed. An optimal monthly operating policy is then derived using stochastic dynamic programming (SDP) as an adaptive policy for mitigating impacts of climate change on reservoir operation. The objective of this policy is to maximize reliabilities with respect to multiple reservoir functions of hydropower, irrigation and flood control. In variations to this adaptive policy, increasingly more weightage is given to the purpose of maximizing reliability with respect to hydropower for two extreme scenarios. It is seen that by marginally sacrificing reliability with respect to irrigation and flood control, hydropower reliability and generation can be increased for future scenarios. This suggests that reservoir rules for flood control may have to be revised in basins where climate change projects an increasing probability of droughts. However, it is also seen that power generation is unable to be restored to current levels, due in part to the large projected increases in irrigation demand. This suggests that future water balance deficits may limit the success of adaptive policy options. (C) 2010 Elsevier Ltd. All rights reserved.

Robust multivariable controllers for a tublar ammonia reactor

The specific objective of this paper is to develop multivariable controllers that would achieve asymptotic regulation in the presence of parameter variations and disturbance inputs for a tubular reactor used in ammonia synthesis. A ninth order state space model with three control inputs and two disturbance inputs is generated from the nonlinear distributed model using linearization and lumping approximations. Using this model, an approach for control system design is developed keeping in view the imperfections of the model and the measurability of the state variables. Specifically, the design of feedforward and robust integral controllers using state and output feedback is considered. Also, the design of robust multiloop proportional integral controllers is presented. Finally the performance of these controllers is evaluated through simulation.