We employ two efficient parallel approaches to reduce a model arising from a semi-discretization of a controlled heat transfer process for optimal cooling of a steel profile. Both algorithms are based on balanced truncation but differ in the numerical method that is used to solve two dual generalized Lyapunov equations, which is the major computational task. Experimental results on a cluster of Intel Xeon processors compare the efficacy of the parallel model reduction algorithms.

Kinematics based guidance laws like the proportional navigation (PN) and many other linear optimal guidance laws perform well in near-collision course conditions. These have been studied thoroughly in the literature from all aspects, ranging from optimality to capturability, for planar or two dimensional interceptor-target engagements, and to a lesser extent, for three dimensional engagements. But guidance in widely off-collision course conditions like high initial heading errors has been relatively less studied. This is probably due to the inherently high nonlinearity of the problem, which makes it a far more difficult problem to solve. However, with increasing speed and agility of interceptors and targets, solutions of such problems have acquired an increased urgency, as has been reflected in the recent literature. This thesis proposes a guidance law based on differential evolution (DE), a member of the evolutionary algorithms (EA) family. While EAs have been applied extensively to static optimization problems, they have been considered unsuitable for solving dynamic optimization or optimal control problems, due to their computationally intensive nature, and their consequent inability to produce solutions online in real-time, except for systems with very slow dynamics. This thesis proposes an online-implementable optimal control for interceptor guidance, a problem with inherently fast dynamics. The proposed law is applicable to all initial geometries including those that involve high to very high heading errors. While interception by itself is a challenging task in the presence of high heading errors, an additional requirement of optimality is also imposed. The first part of the thesis considers only the 2-D kinematic model with high heading errors. In the second part, a 3-D realistic dynamic model, which includes a time-varying interceptor speed, thrust, drag and mass, besides gravity in the vertical plane of motion, and upper bound on the lateral acceleration, is considered, in addition to high heading errors. It is shown that the same structure of the law that is proposed for the 2-D kinematic model can also be used for the 3-D realistic model, if the rest of the complexities of moving from 2-D space to 3-D space, and from kinematics to dynamics is duly addressed. The guidance law proposed does not require time-to-go, the estimation of which can be a difficult problem in high heading error scenarios in which the closing velocity can be negative. Easy to compute and simple to implement in practice, the proposed law does not need any of the techniques or methods from classical optimal control theory, which are complicated and suffer from several limitations. The empirical pure PN (PPN) law is augmented with a term that is a polynomial function of the heading error. The values of the coefficients of the polynomial are found by using the DE. The computational effort required for this low dimensional polynomial optimization problem is shown to be low enough to enable online implementation in real-time. The performance of the proposed law in nominal and off-nominal conditions is validated through several simulations for the 2-D kinematic model, and the 3-D realistic dynamic model. The results are compared with the PPN, augmented PPN and the all-aspect proportional navigation (AAPN) laws in the literature, as per several criteria like optimality, peak latax required and robustness to off-nominal conditions. A successful online implementation of the proposed law for application in practice is also demonstrated. An obvious limitation of optimization by soft computation methods like differential evolution is that no rigorous proof of either convergence or optimality exists for such methods. A fallback option in the form of a conventional guidance law is included in the scheme in case of failure of convergence, and an indirect proof of optimality is provided in the third and final part of the thesis. The same guidance problem is solved by direct multiple shooting method, and it is shown that the numerical results of the two methods compare favourably. The solution by the shooting method is optimal, but computationally far more intensive and takes a computation time of an order of magnitude that is at least one or two times that of the simulation time of the plant. It also needs a good initial guess solution that lies within the region of convergence, which can be a difficult task by itself. Moreover, the shooting method solution is only open loop, and hence applicable for the given model and initial conditions only. Whereas, the simplicity of the method proposed in the thesis makes the solution or guidance law computable in a fraction of the flight time of the engagement, thereby making it online implementable. Equally important, is the fact that it is closed loop, and hence robust to off-nominal conditions like variations in the plant model and parameters assumed in its design.

No description available.

Interconnects in power module result in thermal interfaces. The thermal interfaces degrade under thermal cycling, or chemical loading. Moreover, the reliability of thermal interfaces can be especially problematic when the interconnecting area is large, which increases its predisposition to generate defects (voids, delamination, or nonuniform quality) during processing. In order to improve the quality of the bonding process, as well as to be able to accurately assess interface reliability, it would be desirable to have a simple, reliable, and nondestructive measurement technique that would produce a 2-d map of the interface thermal resistance across a large bonded area. Based on the transient thermal method of JEDEC standard 51-14, we developed a measurement technique that involves moving a thermal sensor discretely across a large-area bonded substrate and acquiring the interface thermal resistance at each location. As detailed herein, the sensor was fabricated by packaging an IGBT bare die. An analytical thermal model was built to investigate the effects of thermal sensor packaging materials and structural parameters on the sensitivity of the measurement technique. Based on this model, we increased the detection sensitivity of the sensor by modifying the size of the sensor substrate, the material of the sensor substrate, the size of the IGBT bare die, the size of the heat sink, and the thermal resistance between sample and the heat sink. The prototype of the thermal sensor was fabricated by mounting Si IGBT on copper substrate, after which the Al wires were ultrasonic bonded to connect the terminals to the electrodes. The sensor was also well protected with a 3-d printed fixture. Then the edge effect was investigated, indicating the application of the thermal sensor is suitable for samples thinner than the value in TABLE 2 3. The working principle of the movable thermal sensor – Zth measurement and its structure function analysis – was then evaluated by sequence. The Zth measurement was evaluated by measuring the Zth change of devices induced by degradation in sintered silver die-attach layer during temperature cycling. At the end of the temperature cycling, failure modes of the sintered silver layer were investigated by scanning electron microscope (SEM) and X-ray scanning, to construct a thermal model for FEA simulation. The simulation results showed good agreement with the measured Zth result, which verified the accuracy of the test setup. The sensitivity of structure function analysis was then evaluated by measuring thermal resistance (Rth) of interface layers with different thermal properties. The structure function analysis approach successfully detected the Rth change in the thermal interface layer. The movable thermal sensor was then applied for 2d-mapping of the interface Rth of a large-area bonded substrate. Examining the test coupons bonded by sintered silver showed good and uniform bonding quality. The standard deviation of Rth is about 0.005 K/W, indicating the 95% confidence interval is about 0.01 K/W, which is commonly chosen as the error of measurement. The sensitivity of the movable thermal sensor was evaluated by detecting defects/heat channels of differing sizes. The 2-d mapping confirmed that the thermal sensor was able to detect defect/heat channel sizes larger than 1x1 mm2. The accuracy of the sensitivity was verified by FEA simulation. Moreover, the simulated results were consistent with the measured results, which indicates that the movable sensor is accurate for assessing interface thermal resistance. In summary, based on structure function analysis of the transient thermal impedance, the concept of a movable thermal sensor was proposed for two-dimensional mapping of interface thermal resistance. (1) Preliminary evaluation of this method indicated both transient thermal impedance and structure function analysis were sensitive enough to detect the thermal resistance change of thermal interface layers. With the help of transient thermal impedance measurement, we non-destructively tested the reliability of sintered silver die-attach layer bonded on either Si3N4 AMB or AlN DBA substrates. (2) An analytical thermal model was constructed to evaluate the design parameters on the sensitivity and resolution of the movable thermal sensor. A detailed design flow chart was provided in this thesis. To avoid edge effect, requirements on thickness and materials of test coupon also existed. Test coupon with smaller thermal conductivity and larger thickness had a more severe edge effect. (3) The application of the movable sensor was demonstrated by measuring the 2-d thermal resistance map of interface layers. The results indicated for bonded copper plates (k = 400 W/mK) with thickness of 2 mm, the sensor was able to detect defect/heat channel with size larger than 1x1 mm2. / Doctor of Philosophy / Interconnects in power module result in thermal interfaces. The thermal interfaces degrade during operation and their reliability can be especially problematic when the interconnecting area is large. In order to improve the quality of the bonding process, as well as to be able to accurately assess interface reliability, it would be desirable to have a simple, reliable, and nondestructive measurement technique that would produce a 2-d map of the interface thermal resistance across a large bonded area. Based on the transient thermal method of JEDEC standard 51-14, we developed a measurement technique that involves moving a thermal sensor discretely across a large-area bonded substrate and acquiring the interface thermal resistance at each location. As detailed herein, the sensor was fabricated by packaging an IGBT bare die, which allowed us to get a 2-d map of the interface thermal resistance. A thermal model was also constructed to guide the design of the sensor, to increase its performance. Moreover, the preliminary test of the test setup was conducted to prove its feasibility for the sensor. Eventually, the sensor’s performance and application was demonstrated by measuring the 2-d thermal resistance map of the bonded interfaces.

The present study deals with the effects of sparsely distributed three-dimensional elements on two-dimensional (2-D) and three-dimensional (3-D) turbulent boundary layers (TBL) such as those that occur on submarines, ship hulls, etc. This study was achieved in three parts: Part 1 dealt with the cylinders when placed individually in the turbulent boundary layers, thereby considering the effect of a single perturbation on the TBL; Part 2 considered the effects when the same individual elements were placed in a sparse and regular distribution, thus studying the response of the flow to a sequence of perturbations; and in Part 3, the distributions were subjected to 3-D turbulent boundary layers, thus examining the effects of streamwise and spanwise pressure gradients on the same perturbed flows as considered in Part 2. The 3-D turbulent boundary layers were generated by an idealized wing-body junction flow. Detailed 3-velocity-component Laser-Doppler Velocimetry (LDV) and other measurements were carried out to understand and describe the rough-wall flow structure. The measurements include mean velocities, turbulence quantities (Reynolds stresses and triple products), skin friction, surface pressure and oil flow visualizations in 2-D and 3-D rough-wall flows for Reynolds numbers, based on momentum thickness, greater than 7000. Very uniform circular cylindrical roughness elements of 0.38mm, 0.76mm and 1.52mm height (k) were used in square and diagonal patterns, yielding six different roughness geometries of rough-wall surface. For the 2-D rough-wall flows, the roughness Reynolds numbers, based on the element height (k) and the friction velocity, range from 26 to 131. Results for the 2-D rough-wall flows reveal that the velocity-defect law is similar for both smooth and rough surfaces, and the semi-logarithmic velocity-distribution curve is shifted by an amount depending on the height of the roughness element, showing that this amount is a function of roughness Reynolds number and the wall geometry. For the 3-D flows, the data show that the surface pressure gradient is not strongly influenced by the roughness elements. In general, for both 2-D and 3-D rough-wall TBL, the differences between the two roughness patterns (straight and diagonal), as regards the mean velocities and the Reynolds stresses, are limited to about 3 roughness element heights from the wall. The study on single elements revealed that the separated shear layers emanating from the top of the elements form a pair of counter rotating vortices that dominate the downstream flow structure. These vortices, termed as the roughness top vortex structure (RTVS), in conjunction with mean flow, forced over and around the elements, are responsible for the production of large Reynolds stresses in the neighborhood of the element height aft of the elements. When these elements are placed in a distribution, the effects of RTVS are not apparent. The roughness elements create a large region of back flow behind them which is continuously replenished by faster moving fluid flowing through the gaps in the rough-wall. The fluid in the back flow region moves upward as low speed ejections where it collides with the inrushing high speed flow, thus, leading to a strong mixing of shear layers. This is responsible for the generation of large levels of turbulent kinetic energy (TKE) in the vicinity of the element height which is transported, primarily, by turbulent diffusion. As regards the 3-D rough-wall TBL, the effect of flow three-dimensionality is seen in the large skewing of the distributions of mean velocities, Reynolds stresses and TKE, aft of the elements. In general, the regions of large TKE production-rates seem to propagate in the direction of the local velocity vector at the element height. The data-sets also enable the extraction of the turbulent flow structure to better describe the flow physics of these rough-wall turbulent boundary layers. / Ph. D.

No description available.

No description available.

no / The interface tribo-layer (ITL) in an automotive brake friction pair is a layer of material created from transfer films, wear particles, and surface transformations between the rotor and stator. Its presence in a brake friction interface has been proven, e.g. by the existence of a temperature ‘jump’ across the friction interface. In this paper two static transient heat transfer models which force one dimensional heat flow, have been used to investigate the ITL behaviour and obtain an equivalent thermal conductance value. The ITL equivalent thermal conductance value is important as it reduces computational requirements and software restrictions encountered in the physical model of the ITL. This approach is developed into a more realistic two-dimensional coupled temperature-displacement model using commercial FEA software (ABAQUS). A newly developed relationship that utilises the contact pressure, real contact area, and the ITL equivalent thermal conductance, has been used to estimate the effective thermal conductance at the friction interface. Subsequently the effective thermal conductance relationship is combined with the 2-D coupled temperaturedisplacement model. The combination of this relationship with the 2D FE model provides a new method of heat partition prediction in brake friction pairs. Heat partition at a brake friction interface is confirmed to be neither uniform nor constant with time. / IMechE / The full text will not be made available in Bradford Scholars due to the publisher's copyright policies.

Background: Pelvic floor muscle (PFM) training is recommended as first line conservative management for stress urinary incontinence (SUI). The fundamental issue of how to optimally contract the PFM has not previously been investigated. An effective voluntary PFM contraction is known to positively influence the bladder neck and urethra which are urethrovesical (UV) structures associated with continence. The PFM may be globally or selectively contracted according to cue to instruction. The main research question was to investigate which cue to instruction for a PFM contraction has the potential to optimise position of UVSs following a brief period of practice in continent nulliparous pre-menopausal women (aiming to provide normative data) and parous menopausal women with previously unreported SUI. Hypotheses: Posterior or combined cues for instruction of PFM contraction are more influential in optimising UV position (UVP) during PFMC following brief practice than an anterior cue. Posterior or combined cues are equally influential in altering UVP. Aims: Preliminary aim was to investigate the reliability and suitability of 2-DRTUS and angle of urethral inclination (AUI) for imaging of selective contraction of the PFM and ease of reading images by a non diagnostic imaging researcher. Principal aim was to investigate if there is an optimal cue to instruction for a PFM contraction in two groups of women. Study 1: pre menopausal nulliparous continent women (to provide normative data) and Study 2: post menopausal parous stress incontinent women. Secondary aims were investigation of posture; ability to selectively contract the PFM contraction; and cue preference. Method: Study 1: Twenty women who were able to effectively and selectively contract were taught the following cues: anterior; posterior; anterior and posterior combined. Following 4 weeks of practice, perineal 2-D RTUS images of three PFMC for each cue were captured in supine and standing twice (for repeatability analysis) five minutes apart. Two raters measured AUI. Data analysis was undertaken using a Customized General Linear Model (GLM) ANOVA with Bonferroni correction for interactions between all variables; subject, cue, posture and test. Seventeen data sets were available for analysis. Study 2: Methodology was based on Study 1. Twenty-one women were taught the study cues, followed the practice protocol and underwent data collection in the supine position. Twenty-one sets of data were available for analysis. Results: Reliability: ICC [1,3] for intra rater reliability was 0.957 [CI 95%: 0.946 to 0.967 p=0.000], inter rater reliability [2,1] 0.820 [CI 95%: 0.768 to 0.861] and for repeatability [1,3] 0.781 [CI 95%: 0.690 to 0.849 p=0.000] (continent) and 0.954 [CI 95%:0.931 to 0.971 p=0.000] (incontinent). Principal results Study 1: anterior vs posterior cues (difference) 3.979˚ (CI 95%: [0.503 to 7.455 p=0.021]); anterior vs combined 3.777˚ (CI 95%: [-0.099 to 6.853 p= 0.059]) posterior vs combined cues -0.602˚ (CI 95%: [-2.874- 4.078 p=1.00]). Aggregated data from tests 1 and 2: anterior vs posterior 4.240° (CI 95%: [1.213 to 7.267 p=0.003]); anterior vs posterior 3.756° (95%CI: [0.729 to 6.783 p=0.009]); posterior vs combined-6.48° (95% CI: [-3.511 to 2.542 p=1.000]). Principal results Study 2: anterior vs posterior 3.936˚ (95%CI: [0.863 to 7.008p=0.008]; 4.946˚ anterior vs combined (95%CI: [1.873 to 8.018 p=0.001]); posterior vs combined 1.010° (95%CI: -[2.062 to 4.082 p=1.000]). Aggregated analysis was anterior vs posterior 3.703˚ (95%CI: [1.639 to 5.761 p=0.000]); anterior vs combined 5.089˚ (95%CI: [3.0287 to 7.1503 p=0.000]) and posterior and combined 1.389° (95%CI: [-0.672 to 3.450 p=0.309]). Secondary results: 2-D RTUS and the AUI were found to be suitable for investigating selective PFM contraction. Posture: supine vs standing (difference) 9.496˚ (p=0.000); (posture did not affect absolute AUI). Three continent (13%) and 2 incontinent (7%) subjects were unable to selectively contract the PFM. Cue preference in both studies was posterior or combined. Conclusions: AUI was significantly narrower/optimal when instruction for PFM contraction included a posterior cue, in both continent and stress incontinent women. This is proposed to be due to optimal recruitment of puborectalis. Puborectalis may be more important in urinary continence than widely recognized. This study has provided seminal information with respect to optimal cue to contraction for a PFM contraction and will change practice. Investigation of the potential impact of these findings clinically is required. It is proposed that further understanding will lead to standardisation of PFM instruction, ease of comparability between PFM research studies, and will clarify PFM instructions for the media and lay public.

The purpose of this paper is to give a historical and stylistic analysis of the Sonata, Op.31, No.2 in D minor of Beethoven. The historical background of Beethoven, the time period the sonata was written, and the influence that the piano of the time had on the sonata is first discussed. The author then discusses the general aspects of Beethoven's style followed by a detailed analysis of the sonata.