Performance of transducers with segmented piezoelectric stacks using materials with high electromechanical coupling coefficient

Underwater acoustic transducers often include a stack of thickness polarized piezoelectric material pieces of alternating polarity interspersed with electrodes, bonded together and electrically connected in parallel. The stack is normally much shorter than a quarter wavelength at the fundamental resonance frequency, so that the mechanical behavior of the transducer is not affected by the segmentation. When the transducer bandwidth is less than a half octave, as has conventionally been the case, stack segmentation has no significant effect on the mechanical behavior of the device. However, when a high coupling coefficient material such as PMN-PT is used to achieve a wider bandwidth, the difference between a segmented stack and a similar piezoelectric section with electrodes only at the two ends can be significant. This paper investigates the effects of stack segmentation on the performance of wideband underwater acoustic transducers, particularly tonpilz transducer elements. Included is discussion of transducer designs using single crystal piezoelectric material with high coupling coefficient compared with more traditional PZT ceramics.Comment: 26 pages including 14 figures, one table and one appendi

Strain and Volume Loss in a Second Order Buckle Fold, Central Appalachian Valley and Ridge, U.S.A.

Large scale thrusts and imbricates overlain by folded sedimentary strata characterize structure in the Valley and Ridge Province of the Central Appalachians. The Cambrian Waynesboro Formation is a decollement zone that detached an imbricated Cambro-Ordovician sequence from an unfaulted Pre-Cambrian basement. The Ordovician Martinsburg Shale is a second zone of major detachment that de-coupled the blind thrust system in the Cambro-Ordovician carbonates from the overlying orogenic wedge. Thus, the Central Valley and Ridge deformed during the late Paleozoic Alleghenian orogeny as a three tiered system consisting of the undeformed basement, the imbricated stiff layer, and the primarily folded cover layer. A road cut along the eastern side of Martin Mountain exposes a smaller (probably second-order) fold in the Silurian Tonoloway limestone that belongs to the cover layer. This anticline is one of a train of regular folds with wavelengths of 150 to 250 m. A small hinge region and symmetrical planar limbs characterize this angular, open anticline. Bed thickness remains relatively constant throughout the fold, making it a class IB (parallel) or IC fold. The anticlinal hinge trends 28° east of north and dips 8° to the north. A poorly exposed, smaller syncline flanks its eastern limb. The Tonoloway Limestone formed during the late Silurian on a carbonate platform. During Paleozoic deformation, it lay under 3 km of sediments at a temperature of 250°C. This outcrop exposes only 80 m of the 550 m thick formation. Cathodoluminescence reveals that the sediments comprise only calcite, dolomite, organic rich clays, and trace amounts of quartz. These fine-grained arenites and lutites display neither noteworthy fossil content nor sedimentary structures oblique to bedding. Bed thicknesses vary from 0.5 m. to 2 m.; planar lamination defined by grain size and clay content occurs in most beds. Slickensides on primary bedding surfaces indicate that flexural slip was an important mechanism during folding. Mesoscopic and microscopic structures accommodate strain within the layers. Two morphologically distinct cleavages within the fold are non-coaxial. Clay selvage seams indicate that both cleavages resulted from pressure solution. Whereas one spaced cleavage fans convergently around the fold hinge in the more competent beds, the second, more penetrative cleavage fans divergently around the fold hinge in the less competent beds. The non-coaxiality of these two cleavages helps define the chronology of and tectonic stress field during the shortening event that produced the cleavages and the fold. In addition to establishing a deformation history of folding, mesoscopic and microscopic structures speak to the question of strain behavior and layer rheology of the folded Tonoloway Limestone. The persistence of pressure solution surfaces and fibrous veins throughout the fold suggest linear or Newtonian behavior in the deformed strata. In the fold limbs, twinning and undulose extinction patterns in calcite crystals signal power law or plastic behavior. Fold geometry, layer rheology, and geologic setting suggest that buckling best defines the mechanism of folding here. In the Central Valley and Ridge, new cross sections show that the stiff tier of thrusts and imbricates controls megascopic structural morphologies in the cover layer. Regional anticlinoria and synclinoria formed by either fault bend folding or passive kinking during emplacement of imbricates in the stiff layer. The train of second order buckles, in which this exposed anticline formed, occurs, however, in a smaller scale environment, which, although it allowed for local buckling, results from the geometry of regional imbrication in the stiff layer. Traditionally, cross sections of this region fail to provide a long enough cover layer to blanket the unthrusted stiff layer. Volume loss strain (i.e. loss through percolating meteoric fluids) in shallow deformed rocks may account for one element of this problem with balancing the two tiers together. If volume loss strain is more significant in one layer than in the other, an unraveled cross section naturally displays an unbalance between the two. Although volume loss strain directly relates to structures and strain patterns, this phenomenon has interested geologists only recently. As a result, no general methodology exists for measuring it. Volume loss strain challenges the notion that structures such as folds and cleavages develop within a closed system, in which material dissolved in areas of high stress reprecipitates locally in areas of low stress. Volume loss strain, however, requires an open system from which foreign fluids introduced by significant dewatering or infiltration remove material

Strain and Volume Loss in a Second Order Buckle Fold, Central Appalachian Valley and Ridge, U.S.A.

Large scale thrusts and imbricates overlain by folded sedimentary strata characterize structure in the Valley and Ridge Province of the Central Appalachians. The Cambrian Waynesboro Formation is a decollement zone that detached an imbricated Cambro-Ordovician sequence from an unfaulted Pre-Cambrian basement. The Ordovician Martinsburg Shale is a second zone of major detachment that de-coupled the blind thrust system in the Cambro-Ordovician carbonates from the overlying orogenic wedge. Thus, the Central Valley and Ridge deformed during the late Paleozoic Alleghenian orogeny as a three tiered system consisting of the undeformed basement, the imbricated stiff layer, and the primarily folded cover layer. A road cut along the eastern side of Martin Mountain exposes a smaller (probably second-order) fold in the Silurian Tonoloway limestone that belongs to the cover layer. This anticline is one of a train of regular folds with wavelengths of 150 to 250 m. A small hinge region and symmetrical planar limbs characterize this angular, open anticline. Bed thickness remains relatively constant throughout the fold, making it a class IB (parallel) or IC fold. The anticlinal hinge trends 28° east of north and dips 8° to the north. A poorly exposed, smaller syncline flanks its eastern limb. The Tonoloway Limestone formed during the late Silurian on a carbonate platform. During Paleozoic deformation, it lay under 3 km of sediments at a temperature of 250°C. This outcrop exposes only 80 m of the 550 m thick formation. Cathodoluminescence reveals that the sediments comprise only calcite, dolomite, organic rich clays, and trace amounts of quartz. These fine-grained arenites and lutites display neither noteworthy fossil content nor sedimentary structures oblique to bedding. Bed thicknesses vary from 0.5 m. to 2 m.; planar lamination defined by grain size and clay content occurs in most beds. Slickensides on primary bedding surfaces indicate that flexural slip was an important mechanism during folding. Mesoscopic and microscopic structures accommodate strain within the layers. Two morphologically distinct cleavages within the fold are non-coaxial. Clay selvage seams indicate that both cleavages resulted from pressure solution. Whereas one spaced cleavage fans convergently around the fold hinge in the more competent beds, the second, more penetrative cleavage fans divergently around the fold hinge in the less competent beds. The non-coaxiality of these two cleavages helps define the chronology of and tectonic stress field during the shortening event that produced the cleavages and the fold. In addition to establishing a deformation history of folding, mesoscopic and microscopic structures speak to the question of strain behavior and layer rheology of the folded Tonoloway Limestone. The persistence of pressure solution surfaces and fibrous veins throughout the fold suggest linear or Newtonian behavior in the deformed strata. In the fold limbs, twinning and undulose extinction patterns in calcite crystals signal power law or plastic behavior. Fold geometry, layer rheology, and geologic setting suggest that buckling best defines the mechanism of folding here. In the Central Valley and Ridge, new cross sections show that the stiff tier of thrusts and imbricates controls megascopic structural morphologies in the cover layer. Regional anticlinoria and synclinoria formed by either fault bend folding or passive kinking during emplacement of imbricates in the stiff layer. The train of second order buckles, in which this exposed anticline formed, occurs, however, in a smaller scale environment, which, although it allowed for local buckling, results from the geometry of regional imbrication in the stiff layer. Traditionally, cross sections of this region fail to provide a long enough cover layer to blanket the unthrusted stiff layer. Volume loss strain (i.e. loss through percolating meteoric fluids) in shallow deformed rocks may account for one element of this problem with balancing the two tiers together. If volume loss strain is more significant in one layer than in the other, an unraveled cross section naturally displays an unbalance between the two. Although volume loss strain directly relates to structures and strain patterns, this phenomenon has interested geologists only recently. As a result, no general methodology exists for measuring it. Volume loss strain challenges the notion that structures such as folds and cleavages develop within a closed system, in which material dissolved in areas of high stress reprecipitates locally in areas of low stress. Volume loss strain, however, requires an open system from which foreign fluids introduced by significant dewatering or infiltration remove material

Understanding the barriers to the implementation of precision agriculture in the central region

There is an increasing requirement for more astute land resource management through efficiencies in agricultural inputs in a sugar cane production system. A precision agriculture (PA) approach can provide a pathway for a sustainable sugarcane production system. One of the impediments to the adoption of PA practices is access to paddock-scale mapping layers displaying variability in soil properties, crop growth and surface drainage. Variable rate application (VRA) of nutrients is an important component of PA. However, agronomic expertise within PA systems has fallen well behind significant advances in PA technologies. Generally, advisers in the sugar industry have a poor comprehension of the complex interaction of variables that contribute to within-paddock variations in crop growth. This is regarded as a significant impediment to the progression of PA in sugarcane and is one of the reasons for the poor adoption of VRA of nutrients in a PA approach to improved sugar cane production. This project therefore has established a number of key objectives which will contribute to the adoption of PA and the staged progression of VRA supported by relevant and practical agronomic expertise. These objectives include provision of base soils attribute mapping that can be determined using Veris 3100 Electrical Conductivity (EC) and digital elevation datasets using GPS mapping technology for a large sector of the central cane growing region using analysis of archived satellite imagery to determine the location and stability of yield patterns over time and in varying seasonal conditions on selected project study sites. They also include the stablishment of experiments to determine appropriate VRA nitrogen rates on various soil types subjected to extended anaerobic conditions, and the establishment of trials to determine nitrogen rates applicable to a declining yield potential associated with the aging of ratoons in the crop cycle. Preliminary analysis of archived yield estimation data indicates that yield patterns remain relatively stable overtime. Results also indicate the where there is considerable variability in EC values there is also significant variation in yield

Quaternion normalization in spacecraft attitude determination

Attitude determination of spacecraft usually utilizes vector measurements such as Sun, center of Earth, star, and magnetic field direction to update the quaternion which determines the spacecraft orientation with respect to some reference coordinates in the three dimensional space. These measurements are usually processed by an extended Kalman filter (EKF) which yields an estimate of the attitude quaternion. Two EKF versions for quaternion estimation were presented in the literature; namely, the multiplicative EKF (MEKF) and the additive EKF (AEKF). In the multiplicative EKF, it is assumed that the error between the correct quaternion and its a-priori estimate is, by itself, a quaternion that represents the rotation necessary to bring the attitude which corresponds to the a-priori estimate of the quaternion into coincidence with the correct attitude. The EKF basically estimates this quotient quaternion and then the updated quaternion estimate is obtained by the product of the a-priori quaternion estimate and the estimate of the difference quaternion. In the additive EKF, it is assumed that the error between the a-priori quaternion estimate and the correct one is an algebraic difference between two four-tuple elements and thus the EKF is set to estimate this difference. The updated quaternion is then computed by adding the estimate of the difference to the a-priori quaternion estimate. If the quaternion estimate converges to the correct quaternion, then, naturally, the quaternion estimate has unity norm. This fact was utilized in the past to obtain superior filter performance by applying normalization to the filter measurement update of the quaternion. It was observed for the AEKF that when the attitude changed very slowly between measurements, normalization merely resulted in a faster convergence; however, when the attitude changed considerably between measurements, without filter tuning or normalization, the quaternion estimate diverged. However, when the quaternion estimate was normalized, the estimate converged faster and to a lower error than with tuning only. In last years, symposium we presented three new AEKF normalization techniques and we compared them to the brute force method presented in the literature. The present paper presents the issue of normalization of the MEKF and examines several MEKF normalization techniques

Quaternion normalization in additive EKF for spacecraft attitude determination

This work introduces, examines, and compares several quaternion normalization algorithms, which are shown to be an effective stage in the application of the additive extended Kalman filter (EKF) to spacecraft attitude determination, which is based on vector measurements. Two new normalization schemes are introduced. They are compared with one another and with the known brute force normalization scheme, and their efficiency is examined. Simulated satellite data are used to demonstrate the performance of all three schemes. A fourth scheme is suggested for future research. Although the schemes were tested for spacecraft attitude determination, the conclusions are general and hold for attitude determination of any three dimensional body when based on vector measurements, and use an additive EKF for estimation, and the quaternion for specifying the attitude

Generalized Linear Covariance Analysis

We review and extend in two directions the results of prior work on generalized covariance analysis methods. This prior work allowed for partitioning of the state space into "solve-for" and "consider" parameters, allowed for differences between the formal values and the true values of the measurement noise, process noise, and a priori solve-for and consider covariances, and explicitly partitioned the errors into subspaces containing only the influence of the measurement noise, process noise, and a priori solve-for and consider covariances. In this work, we explicitly add sensitivity analysis to this prior work, and relax an implicit assumption that the batch estimator s anchor time occurs prior to the definitive span. We also apply the method to an integrated orbit and attitude problem, in which gyro and accelerometer errors, though not estimated, influence the orbit determination performance. We illustrate our results using two graphical presentations, which we call the "variance sandpile" and the "sensitivity mosaic," and we compare the linear covariance results to confidence intervals associated with ensemble statistics from a Monte Carlo analysis