Analysis of two degrees of freedom systems through weighted mean square linearization approach

In this paper a study of the free, forced and self-excited vibrations of non-linear, two degrees of freedom systems is reported. The responses are obtained by linearizing the nonlinear equations using the weighted mean square linearization approach. The scope of this approach, in terms of the type of non-linearities the method can tackle, is also discussed.

Analysis of two degrees of freedom systems through weighted mean square linearization approach

In this paper a study of the free, forced and self-excited vibrations of non-linear, two degrees of freedom systems is reported. The responses are obtained by linearizing the nonlinear equations using the weighted mean square linearization approach. The scope of this approach, in terms of the type of non-linearities the method can tackle, is also discussed.

A weighted mean square method of linearization in non-linear oscillations

The paper deals with a linearization technique in non-linear oscillations for systems which are governed by second-order non-linear ordinary differential equations. The method is based on approximation of the non-linear function by a linear function such that the error is least in the weighted mean square sense. The method has been applied to cubic, sine, hyperbolic sine, and odd polynomial types of non-linearities and the results obtained are more accurate than those given by existing linearization methods.

Vertical uplift capacity of two interfering horizontal anchors in sand using an upper bound limit analysis

The vertical uplift resistance of two interfering rigid rough strip anchors embedded horizontally in sand at shallow depths has been examined. The analysis is performed by using an upper bound theorem o limit analysis in combination with finite elements and linear programming. It is specified that both the anchors are loaded to failure simultaneously at the same magnitude of the failure load. For different clear spacing (S) between the anchors, the magnitude of the efficiency factor (xi(gamma)) is determined. On account of interference, the magnitude of xi(gamma) is found to reduce continuously with a decrease in the spacing between the anchors. The results from the numerical analysis were found to compare reasonably well with the available theoretical data from the literature.

Impulse Voltage Breakdown Characteristics of Point-Plane Gaps at Low Pressures

Practical applications of vacuum as an insulator necessitated determining the low-pressure breakdown characteristics of long gap lengths of a point-plane electrode system. The breakdown voltage has been found to vary as the square root of the gap length. Further, with the point electrode as the anode, the values of the breakdown voltages obtained have been found to be larger than those obtained with a plane-parallel electrode system at a corresponding gap length. By applying the theory of the anode heating mechanism as the cause for breakdown, the results have been justified, and by utilizing a field efficiency factor which is the ratio of the average to maximum field, an empirical criterion has been developed. This criterion helps in calculating the breakdown voltage of a nonuniform gap system by the knowledge of the breakdown voltage of a plane-parallel electrode system.

Climate change impact assessment: Uncertainty modeling with imprecise probability

Hydrologic impacts of climate change are usually assessed by downscaling the General Circulation Model (GCM) output of large-scale climate variables to local-scale hydrologic variables. Such an assessment is characterized by uncertainty resulting from the ensembles of projections generated with multiple GCMs, which is known as intermodel or GCM uncertainty. Ensemble averaging with the assignment of weights to GCMs based on model evaluation is one of the methods to address such uncertainty and is used in the present study for regional-scale impact assessment. GCM outputs of large-scale climate variables are downscaled to subdivisional-scale monsoon rainfall. Weights are assigned to the GCMs on the basis of model performance and model convergence, which are evaluated with the Cumulative Distribution Functions (CDFs) generated from the downscaled GCM output (for both 20th Century [20C3M] and future scenarios) and observed data. Ensemble averaging approach, with the assignment of weights to GCMs, is characterized by the uncertainty caused by partial ignorance, which stems from nonavailability of the outputs of some of the GCMs for a few scenarios (in Intergovernmental Panel on Climate Change [IPCC] data distribution center for Assessment Report 4 [AR4]). This uncertainty is modeled with imprecise probability, i.e., the probability being represented as an interval gray number. Furthermore, the CDF generated with one GCM is entirely different from that with another and therefore the use of multiple GCMs results in a band of CDFs. Representing this band of CDFs with a single valued weighted mean CDF may be misleading. Such a band of CDFs can only be represented with an envelope that contains all the CDFs generated with a number of GCMs. Imprecise CDF represents such an envelope, which not only contains the CDFs generated with all the available GCMs but also to an extent accounts for the uncertainty resulting from the missing GCM output. This concept of imprecise probability is also validated in the present study. The imprecise CDFs of monsoon rainfall are derived for three 30-year time slices, 2020s, 2050s and 2080s, with A1B, A2 and B1 scenarios. The model is demonstrated with the prediction of monsoon rainfall in Orissa meteorological subdivision, which shows a possible decreasing trend in the future.

Mahanadi streamflow: climate change impact assessment and adaptive strategies

Impacts of climate change on hydrology are assessed by downscaling large scale general circulation model (GCM) outputs of climate variables to local scale hydrologic variables. This modelling approach is characterized by uncertainties resulting from the use of different models, different scenarios, etc. Modelling uncertainty in climate change impact assessment includes assigning weights to GCMs and scenarios, based on their performances, and providing weighted mean projection for the future. This projection is further used for water resources planning and adaptation to combat the adverse impacts of climate change. The present article summarizes the recent published work of the authors on uncertainty modelling and development of adaptation strategies to climate change for the Mahanadi river in India.

Bearing capacity of interfering multiple strip footings by using lower bound finite elements limit analysis

The ultimate bearing capacity of a number of multiple strip footings, identically spaced and equally loaded to failure at the same time,is computed by using the lower bound limit analysis in combination with finite elements. The efficiency factor due to the component of soil unit weight, is computed with respect to changes in the clear spacing (xi(gamma)) between the footings. It is noted that the failure load for a footing in the group becomes always greater than that of a single isolated footing. The values of xi(gamma) for the smooth footings are found to be always lower than the rough footings. The values ofxi(gamma) are found to increase continuously with a decrease in the spacing between footings. As compared to the available theoretical and experimental results reported in literature, the present analysis provides generally a little lower values of xi(gamma). (C) 2010 Elsevier Ltd. All rights reserved.

Receiver-only optimized Vector Quantization for fading channels

This paper considers the design and analysis of a filter at the receiver of a source coding system to mitigate the excess distortion caused due to channel errors. The index output by the source encoder is sent over a fading discrete binary symmetric channel and the possibly incorrect received index is mapped to the corresponding codeword by a Vector Quantization (VQ) decoder at the receiver. The output of the VQ decoder is then processed by a receive filter to obtain an estimate of the source instantiation. The distortion performance is analyzed for weighted mean square error (WMSE) and the optimum receive filter that minimizes the expected distortion is derived for two different cases of fading. It is shown that the performance of the system with the receive filter is strictly better than that of a conventional VQ and the difference becomes more significant as the number of bits transmitted increases. Theoretical expressions for an upper and lower bound on the WMSE performance of the system with the receive filter and a Rayleigh flat fading channel are derived. The design of a receive filter in the presence of channel mismatch is also studied and it is shown that a minimax solution is the one obtained by designing the receive filter for the worst possible channel. Simulation results are presented to validate the theoretical expressions and illustrate the benefits of receive filtering.

An Area-Efficient Noise-Adaptive Neural Amplifier in 130 nm CMOS Technology

Chronic recording of neural signals is indispensable in designing efficient brain–machine interfaces and to elucidate human neurophysiology. The advent of multichannel micro-electrode arrays has driven the need for electronics to record neural signals from many neurons. The dynamic range of the system can vary over time due to change in electrode–neuron distance and background noise. We propose a neural amplifier in UMC 130 nm, 1P8M complementary metal–oxide–semiconductor (CMOS) technology. It can be biased adaptively from 200 nA to 2 $mu{rm A}$, modulating input referred noise from 9.92 $mu{rm V}$ to 3.9 $mu{rm V}$. We also describe a low noise design technique which minimizes the noise contribution of the load circuitry. Optimum sizing of the input transistors minimizes the accentuation of the input referred noise of the amplifier and obviates the need of large input capacitance. The amplifier achieves a noise efficiency factor of 2.58. The amplifier can pass signal from 5 Hz to 7 kHz and the bandwidth of the amplifier can be tuned for rejecting low field potentials (LFP) and power line interference. The amplifier achieves a mid-band voltage gain of 37 dB. In vitro experiments are performed to validate the applicability of the neural low noise amplifier in neural recording systems.

Experiments and zero D modeling studies using specific Wiebe coefficients for producer gas as fuel in spark-ignited engines

The paper addresses experiments and modeling studies on the use of producer gas, a bio-derived low energy content fuel in a spark-ignited engine. Producer gas, generated in situ, has thermo-physical properties different from those of fossil fuel(s). Experiments on naturally aspirated and turbo-charged engine operation and subsequent analysis of the cylinder pressure traces reveal significant differences in the heat release pattern within the cylinder compared with a typical fossil fuel. The heat release patterns for gasoline and producer gas compare well in the initial 50% but beyond this, producer gas combustion tends to be sluggish leading to an overall increase in the combustion duration. This is rather unexpected considering that producer gas with nearly 20% hydrogen has higher flame speeds than gasoline. The influence of hydrogen on the initial flame kernel development period and the combustion duration and hence on the overall heat release pattern is addressed. The significant deviations in the heat release profiles between conventional fuels and producer gas necessitates the estimation of producer gas-specific Wiebe coefficients. The experimental heat release profiles are used for estimating the Wiebe coefficients. Experimental evidence of lower fuel conversion efficiency based on the chemical and thermal analysis of the engine exhaust gas is used to arrive at the Wiebe coefficients. The efficiency factor a is found to be 2.4 while the shape factor m is estimated at 0.7 for 2% to 90% burn duration. The standard Wiebe coefficients for conventional fuels and fuel-specific coefficients for producer gas are used in a zero D model to predict the performance of a 6-cylinder gas engine under naturally aspirated and turbo-charged conditions. While simulation results with standard Wiebe coefficients result in excessive deviations from the experimental results, excellent match is observed when producer gas-specific coefficients are used. Predictions using the same coefficients on a 3-cylinder gas engine having different geometry and compression ratio(s) indicate close match with the experimental traces highlighting the versatility of the coefficients.

Horizontal pullout resistance of a group of two vertical anchors in sand

The horizontal pullout capacity of a group of two vertical strip anchors placed along the same vertical plane in sand has been determined by using the upper bound finite elements limit analysis. The variation of the efficiency factor (xi (gamma) ) with changes in clear spacing (S) between the anchors has been established to evaluate the total group failure load for different values of (i) embedment ratio (H/B), (ii) soil internal friction angle (phi), and (iii) anchor-soil interface friction angle (delta). The total group failure load, for a given H/B, becomes always maximum corresponding to a certain optimal spacing (S-opt). The value of S-opt/B was found to lie in a range of 0.5-1.4. The maximum magnitude of xi (gamma) increases generally with increases in H/B, phi and delta.

Vertical uplift resistance of two closely spaced horizontal strip anchors embedded in cohesive-frictional weightless medium

The vertical uplift resistance of two closely spaced horizontal strip plate anchors has been investigated by using lower and upper bound theorems of the limit analysis in combination with finite elements and linear optimization. The interference effect on uplift resistance of the two anchors is evaluated in terms of a nondimensional efficiency factor (eta(c)). The variation of eta(c) with changes in the clear spacing (S) between the two anchors has been established for different combinations of embedment ratio (H/B) and angle of internal friction of the soil (phi). An interference of the anchors leads to a continuous reduction in uplift resistance with a decrease in spacing between the anchors. The uplift resistance becomes a minimum when the two anchors are placed next to each other without any gap. The critical spacing (S-cr) between the two anchors required to eliminate the interference effect increases with an increase in the values of both H/B and phi. The value of S-cr was found to lie approximately in the range 0.65B-1.5B with H/B = 1 and 11B-14B with H/B = 7 for phi varying from 0 degrees to 30 degrees.

Spatially Adaptive Kernel Regression Using Risk Estimation

An important question in kernel regression is one of estimating the order and bandwidth parameters from available noisy data. We propose to solve the problem within a risk estimation framework. Considering an independent and identically distributed (i.i.d.) Gaussian observations model, we use Stein's unbiased risk estimator (SURE) to estimate a weighted mean-square error (MSE) risk, and optimize it with respect to the order and bandwidth parameters. The two parameters are thus spatially adapted in such a manner that noise smoothing and fine structure preservation are simultaneously achieved. On the application side, we consider the problem of image restoration from uniform/non-uniform data, and show that the SURE approach to spatially adaptive kernel regression results in better quality estimation compared with its spatially non-adaptive counterparts. The denoising results obtained are comparable to those obtained using other state-of-the-art techniques, and in some scenarios, superior.

Vertical Uplift Resistance of Two Interfering Horizontal Anchors in Clay

The vertical uplift resistance of two interfering rigid strip plate anchors embedded horizontally at the same level in clay has been examined. The lower and upper bound theorems of the limit analysis in combination with finite-elements and linear optimization have been employed to compute the failure load in a bound form. The analysis is meant for an undrained condition and it incorporates the increase of cohesion with depth. For different clear spacing (S) between the anchors, the magnitude of the efficiency factor (eta c gamma) resulting from the combined components of soil cohesion (c) and soil unit weight (gamma), has been computed for different values of embedment ratio (H/B), the rate of linear increase of cohesion with depth (m) and normalized unit weight (gamma H/c). The magnitude of eta c gamma has been found to reduce continuously with a decrease in the spacing between the anchors, and the uplift resistance becomes minimum for S/B=0. It has been noted that the critical spacing between the anchors required to eliminate the interference effect increases continuously with (1) an increase in H/B, and (2) a decrease in m.