Generalized State Estimation and Model Predictive Guidance for Spiraling and Ballistic Targets

An extended Kalman filter based generalized state estimation approach is presented in this paper for accurately estimating the states of incoming high-speed targets such as ballistic missiles. A key advantage of this nine-state problem formulation is that it is very much generic and can capture spiraling as well as pure ballistic motion of targets without any change of the target model and the tuning parameters. A new nonlinear model predictive zero-effort-miss based guidance algorithm is also presented in this paper, in which both the zero-effort-miss as well as the time-to-go are predicted more accurately by first propagating the nonlinear target model (with estimated states) and zero-effort interceptor model simultaneously. This information is then used for computing the necessary lateral acceleration. Extensive six-degrees-of-freedom simulation experiments, which include noisy seeker measurements, a nonlinear dynamic inversion based autopilot for the interceptor along with appropriate actuator and sensor models and magnitude and rate saturation limits for the fin deflections, show that near-zero miss distance (i.e., hit-to-kill level performance) can be obtained when these two new techniques are applied together. Comparison studies with an augmented proportional navigation based guidance shows that the proposed model predictive guidance leads to a substantial amount of conservation in the control energy as well.

Estimation of time variant reliability of randomly parametered non-linear vibrating systems

The problem of time variant reliability analysis of randomly parametered and randomly driven nonlinear vibrating systems is considered. The study combines two Monte Carlo variance reduction strategies into a single framework to tackle the problem. The first of these strategies is based on the application of the Girsanov transformation to account for the randomness in dynamic excitations, and the second approach is fashioned after the subset simulation method to deal with randomness in system parameters. Illustrative examples include study of single/multi degree of freedom linear/non-linear inelastic randomly parametered building frame models driven by stationary/non-stationary, white/filtered white noise support acceleration. The estimated reliability measures are demonstrated to compare well with results from direct Monte Carlo simulations. (C) 2014 Elsevier Ltd. All rights reserved.

Reliability-based load and resistance factor design approach for external seismic stability of reinforced soil walls

Load and resistance factor design (LRFD) approach for the design of reinforced soil walls is presented to produce designs with consistent and uniform levels of risk for the whole range of design applications. The evaluation of load and resistance factors for the reinforced soil walls based on reliability theory is presented. A first order reliability method (FORM) is used to determine appropriate ranges for the values of the load and resistance factors. Using pseudo-static limit equilibrium method, analysis is conducted to evaluate the external stability of reinforced soil walls subjected to earthquake loading. The potential failure mechanisms considered in the analysis are sliding failure, eccentricity failure of resultant force (or overturning failure) and bearing capacity failure. The proposed procedure includes the variability associated with reinforced backfill, retained backfill, foundation soil, horizontal seismic acceleration and surcharge load acting on the wall. Partial factors needed to maintain the stability against three modes of failure by targeting component reliability index of 3.0 are obtained for various values of coefficients of variation (COV) of friction angle of backfill and foundation soil, distributed dead load surcharge, cohesion of the foundation soil and horizontal seismic acceleration. A comparative study between LRFD and allowable stress design (ASD) is also presented with a design example. (C) 2014 Elsevier Ltd. All rights reserved.

Hysteresis current controller for a general n-level inverter fed drive with online current error boundary computation and nearly constant switching frequency

A space vector-based hysteresis current controller for any general n-level three phase inverter fed induction motor drive is proposed in this study. It offers fast dynamics, inherent overload protection and low harmonic distortion for the phase voltages and currents. The controller performs online current error boundary calculations and a nearly constant switching frequency is obtained throughout the linear modulation range. The proposed scheme uses only the adjacent voltage vectors of the present sector, similar to space vector pulse-width modulation and exhibits fast dynamic behaviour under different transient conditions. The steps involved in the boundary calculation include the estimation of phase voltages from the current ripple, computation of switching time and voltage error vectors. Experimental results are given to show the performance of the drive at various speeds, effect of sudden change of the load, acceleration, speed reversal and validate the proposed advantages.

Scaling of pressure spectrum in turbulent boundary layers

Scaling of pressure spectrum in zero-pressure-gradient turbulent boundary layers is discussed. Spatial DNS data of boundary layer at one time instant (Re-theta = 4500) are used for the analysis. It is observed that in the outer regions the pressure spectra tends towards the -7/3 law predicted by Kolmogorov's theory of small-scale turbulence. The slope in the pressure spectra varies from -1 close to the wall to a value close to -7/3 in the outer region. The streamwise velocity spectra also show a -5/3 trend in the outer region of the flow. The exercise carried out to study the amplitude modulation effect of the large scales on the smaller ones in the near-wall region reveals a strong modulation effect for the streamwise velocity, but not for the pressure fluctuations. The skewness of the pressure follows the same trend as the amplitude modulation coefficient, as is the case for the velocity. In the inner region, pressure spectra were seen to collapse better when normalized with the local Reynolds stress (-(u'v') over bar) than when scaled with the local turbulent kinetic energy (q(2) = (u'(2)) over bar + (v'(2)) over bar + (w'(2)) over bar)

A performance-based framework for assessing liquefaction potential based on CPT data

This article describes a new performance-based approach for evaluating the return period of seismic soil liquefaction based on standard penetration test (SPT) and cone penetration test (CPT) data. The conventional liquefaction evaluation methods consider a single acceleration level and magnitude and these approaches fail to take into account the uncertainty in earthquake loading. The seismic hazard analysis based on the probabilistic method clearly shows that a particular acceleration value is being contributed by different magnitudes with varying probability. In the new method presented in this article, the entire range of ground shaking and the entire range of earthquake magnitude are considered and the liquefaction return period is evaluated based on the SPT and CPT data. This article explains the performance-based methodology for the liquefaction analysis – starting from probabilistic seismic hazard analysis (PSHA) for the evaluation of seismic hazard and the performance-based method to evaluate the liquefaction return period. A case study has been done for Bangalore, India, based on SPT data and converted CPT values. The comparison of results obtained from both the methods have been presented. In an area of 220 km2 in Bangalore city, the site class was assessed based on large number of borehole data and 58 Multi-channel analysis of surface wave survey. Using the site class and peak acceleration at rock depth from PSHA, the peak ground acceleration at the ground surface was estimated using probabilistic approach. The liquefaction analysis was done based on 450 borehole data obtained in the study area. The results of CPT match well with the results obtained from similar analysis with SPT data.

Design of fully rotatable, roller-crank-driven, cam mechanisms for arbitrary motion specifications

The design of a non-traditional cam and roller-follower mechanism is described here. In this mechanism, the roller-crank rather than the cam is used as the continuous input member, while both complete a full rotation in each revolution and remain in contact throughout. It is noted that in order to have the cam fully rotate for every full rotation of the roller-crank, the cam cannot be a closed profile, rather the roller traverses the open cam profile twice in each cycle. Using kinematic analysis, the angular velocity of the cam when the roller traverses the cam profile in one direction, is related to the angular velocity of the cam when the roller retraces its path on the cam in the other direction. Thus, one can specify any arbitrary function relating the motion of the cam to the motion of the roller-crank for only 180 degrees of rotation in the angular velocity space. The motion of the cam in the remaining portion is then automatically determined. In specifying the arbitrary motion, many desirable characteristics such as multiple dwells, low acceleration and jerk, etc., can be obtained. Useful design equations are derived for this purpose. Using the kinematic inversion technique, the cam profile is readily obtained once the motion is specified in the angular velocity space. The only limitation to the arbitrary motion specification is making sure that the transmission angle never gets too low, so that the force will be transmitted efficiently from roller to cam. This is addressed by incorporating a transmission index into the motion specification in the synthesis process. Consequently, in this method we can specify any arbitrary motion within a permissible rone, such that the transmission index is higher than the specified minimum value. Single-dwell, double-dwell and a long hesitation motion are used as examples to demonstrate the ffectiveness of the design method. Force closure using an optimally located spring and quasi-kinetostatic analysis are also discussed. (C) 2001 Elsevier Science Ltd. All rights reserved.

Stability of a circular tunnel in presence of pseudostatic seismic body forces

The stability of a long circular tunnel in a cohesive frictional soil medium has been determined in the presence of horizontal pseudo-static seismic body forces. The tunnel is supported by means of lining and anchorage system which is assumed to exert uniform internal compressive normal pressure on its periphery. The upper bound finite element limit analysis has been performed to compute the magnitude of the internal compressive pressure required to support the tunnel. The results have been presented in terms of normalized compressive normal stress, defined in terms of sigma(i)/c; where sigma(i) is the magnitude of the compressive normal pressure on the periphery of the tunnel and c refers to soil cohesion. The variation of sigma(i)/c with horizontal earthquake acceleration coefficient (alpha(h)) has been established for different combinations of H/D, gamma D/c and phi where (i) H and D refers to tunnel cover and diameter, respectively, and (ii) gamma and phi correspond to unit weight and internal friction angle of soil mass, respectively. Nodal velocity patterns have also been plotted for assessing the zones of significant plastic deformation. The analysis clearly reveals that an increase in the magnitude of the earthquake acceleration leads to a significant increment in the magnitude of internal compressive pressure. (C) 2014 Elsevier Ltd. All rights reserved.

Nonsingular Terminal Sliding Mode Guidance with Impact Angle Constraints

Guidance laws based on a conventional sliding mode ensures only asymptotic convergence. However, convergence to the desired impact angle within a finite time is important in most practical guidance applications. These finite time convergent guidance laws suffer from singularity leading to control saturation. In this paper, guidance laws to intercept targets at a desired impact angle, from any initial heading angle, without exhibiting any singularity, are presented. The desired impact angle, which is defined in terms of a desired line-of-sight angle, is achieved in finite time by selecting the interceptor's lateral acceleration to enforce nonsingular terminal sliding mode on a switching surface designed using nonlinear engagement dynamics. Numerical simulation results are presented to validate the proposed guidance laws for different initial engagement geometries and impact angles. Although the guidance laws are designed for constant speed interceptors, its robustness against the time-varying speed of interceptors is also evaluated through extensive simulation results.

Comprehensive seismic hazard assessment of Tripura and Mizoram states

Northeast India is one of the most highly seismically active regions in the world with more than seven earthquakes on an average per year of magnitude 5.0 and above. Reliable seismic hazard assessment could provide the necessary design inputs for earthquake resistant design of structures in this' region. In this study, deterministic as well as probabilistic methods have been attempted for seismic hazard assessment of Tripura and Mizoram states at bedrock level condition. An updated earthquake catalogue was collected from various national and international seismological agencies for the period from 1731 to 2011. The homogenization, declustering and data completeness analysis of events have been carried out before hazard evaluation. Seismicity parameters have been estimated using G R relationship for each source zone. Based on the seismicity, tectonic features and fault rupture mechanism, this region was divided into six major subzones. Region specific correlations were used for magnitude conversion for homogenization of earthquake size. Ground motion equations (Atkinson and Boore 2003; Gupta 2010) were validated with the observed PGA (peak ground acceleration) values before use in the hazard evaluation. In this study, the hazard is estimated using linear sources, identified in and around the study area. Results are presented in the form of PGA using both DSHA (deterministic seismic hazard analysis) and PSHA (probabilistic seismic hazard analysis) with 2 and 10% probability of exceedance in 50 years, and spectral acceleration (T = 0. 2 s, 1.0 s) for both the states (2% probability of exceedance in 50 years). The results are important to provide inputs for planning risk reduction strategies, for developing risk acceptance criteria and financial analysis for possible damages in the study area with a comprehensive analysis and higher resolution hazard mapping.

Shaking table tests to investigate the influence of various factors on the liquefaction resistance of sands

This paper presents the shaking table studies to investigate the factors that influence the liquefaction resistance of sand. A uniaxial shaking table with a perspex model container was used for the model tests, and saturated sand beds were prepared using wet pluviation method. The models were subjected to horizontal base shaking, and the variation of pore water pressure was measured. Three series of tests varying the acceleration and frequency of base shaking and density of the soil were carried out on sand beds simulating free field condition. Liquefaction was visualized in some model tests, which was also established through pore water pressure ratios. Effective stress was calculated at the point of pore water pressure measurement, and the number of cycles required to liquefy the sand bed were estimated and matched with visual observations. It was observed that there was a gradual variation in pore water pressure with change in base acceleration at a given frequency of shaking. The variation in pore water pressure is not significant for the range of frequency used in the tests. The frequency of base shaking at which the sand starts to liquefy when the sand bed is subjected to any specific base acceleration depends on the density of sand, and it was observed that the sand does not liquefy at any other frequency less than this. A substantial improvement in liquefaction resistance of the sand was observed with the increase in soil density, inferring that soil densification is a simple technique that can be applied to increase the liquefaction resistance.

Capturability of Augmented Pure Proportional Navigation Guidance Against Time-Varying Target Maneuvers

This paper proposes a variation of the pure proportional navigation guidance law, called augmented pure proportional navigation, to account for target maneuvers, in a realistic nonlinear engagement geometry, and presents its capturability analysis. These results are in contrast to most work in the literature on augmented proportional navigation laws that consider a linearized geometry imposed upon the true proportional navigation guidance law. Because pure proportional navigation guidance law is closer to a realistic implementation of proportional navigation than true proportional navigation law, and any engagement process is predominantly nonlinear, the results obtained in this paper are more realistic than any available in the literature. Sufficient conditions on speed ratio, navigation gain, and augmentation parameter for capturability, and boundedness of lateral acceleration, against targets executing piecewise continuous maneuvers with time, are obtained. Further, based on a priori knowledge of the maximum maneuver capability of the target, a significant simplification of the guidance law is proposed in this paper. The proposed guidance law is also shown to require a shorter time of interception than standard pure proportional navigation and augmented proportional navigation. To remove chattering in the interceptor maneuver at the end phase of the engagement, a hybrid guidance law using augmented pure proportional navigation and pure proportional navigation is also proposed. Finally, the guaranteed capture zones of standard and augmented pure proportional navigation guidance laws against maneuvering targets are analyzed and compared in the normalized relative velocity space. It is shown that the guaranteed capture zone expands significantly when augmented pure proportional navigation is used instead of pure proportional navigation. Simulation results are given to support the theoretical findings.

Generalized Model Predictive Static Programming and Angle-Constrained Guidance of Air-to-Ground Missiles

A new generalized model predictive static programming technique is presented for rapidly solving a class of finite-horizon nonlinear optimal control problems with hard terminal constraints. Two key features for its high computational efficiency include one-time backward integration of a small-dimensional weighting matrix dynamics, followed bya static optimization formulation that requires only a static Lagrange multiplier to update the control history. It turns out that under Euler integration and rectangular approximation of finite integrals it is equivalent to the existing model predictive static programming technique. In addition to the benchmark double integrator problem, usefulness of the proposed technique is demonstrated by solving a three-dimensional angle-constrained guidance problem for an air-to-ground missile, which demands that the missile must meet constraints on both azimuth and elevation angles at the impact point in addition to achieving near-zero miss distance, while minimizing the lateral acceleration demand throughout its flight path. Simulation studies include maneuvering ground targets along with a first-order autopilot lag. Comparison studies with classical augmented proportional navigation guidance and modern general explicit guidance lead to the conclusion that the proposed guidance is superior to both and has a larger capture region as well.

Uplift Resistance of Long Pipelines in the Presence of Seismic Forces

The vertical uplift resistance of long pipes buried in sands and subjected to pseudostatic seismic forces has been computed by using the lower-bound theorem of the limit analysis in conjunction with finite elements and nonlinear optimization. The soil mass is assumed to follow the Mohr-Coulomb failure criterion and an associated flow rule. The failure load is expressed in the form of a nondimensional uplift factor F-gamma. The variation of F-gamma is plotted as a function of the embedment ratio of the pipe, horizontal seismic acceleration coefficient (k(h)), and soil friction angle (phi). The magnitude of F-gamma is found to decrease continuously with an increase in the horizontal seismic acceleration coefficient. The reduction in the uplift resistance becomes quite significant, especially for greater values of embedment ratios and lower values of friction angle. The predicted uplift resistance was found to compare well with the existing results reported from the literature. (C) 2014 American Society of Civil Engineers.

Seismic Bearing Capacity of Shallow Embedded Foundations on a Sloping Ground Surface

By using the lower-bound theorem of the limit analysis in conjunction with finite elements and nonlinear optimization, bearing-capacity factors, N-c and N-gamma q, with an inclusion of pseudostatic horizontal seismic body forces, have been determined for a shallow embedded horizontal strip footing placed on sloping ground surface. The variation of N-c and N-gamma q with changes in slope angle (beta) for different values of seismic acceleration coefficient (k(h)) has been obtained. The analysis reveals that irrespective of ground inclination and the embedment depth of the footing, the factors N-c and N-gamma q decrease quite considerably with an increase in k(h). As compared with N-c, the factor N-gamma q is affected more extensively with changes in k(h) and beta. Unlike most of the results reported in literature for the seismic case, the present computational results take into account the shear resistance of soil mass above the footing level. An increase in the depth of the embedment leads to an increase in the magnitudes of both N-c and N-gamma q. (C) 2014 American Society of Civil Engineers.