Search results for: Laplacian eigenvalues

Authors: Jurriaan Gillissen

Abstract:

This work is concerned with stabilizing the numerical integration of the Navier-Stokes equation (NSE), backwards in time. Applications involve the detection of sources of, e.g., sound, heat, and pollutants. Stable reverse numerical integration of parabolic differential equations is also relevant for image de-blurring. While the literature addresses the reverse integration problem of the advection-diffusion equation, the problem of numerical reverse integration of the NSE has, to our knowledge, not yet been addressed. Owing to the presence of viscosity, the NSE is irreversible, i.e., when going backwards in time, the fluid behaves, as if it had a negative viscosity. As an effect, perturbations from the perfect solution, due to round off errors or discretization errors, grow exponentially in time, and reverse integration of the NSE is inherently unstable, regardless of using an implicit time integration scheme. Consequently, some sort of filtering is required, in order to achieve a stable, numerical, reversed integration. The challenge is to find a filter with a minimal adverse affect on the accuracy of the reversed integration. In the present work, we explore an adjoint gradient method (AGM) to achieve this goal, and we apply this technique to two-dimensional (2D), decaying turbulence. The AGM solves for the initial velocity field u0 at t = 0, that, when integrated forward in time, produces a final velocity field u1 at t = 1, that is as close as is feasibly possible to some specified target field v1. The initial field u0 defines a minimum of a cost-functional J, that measures the distance between u1 and v1. In the minimization procedure, the u0 is updated iteratively along the gradient of J w.r.t. u0, where the gradient is obtained by transporting J backwards in time from t = 1 to t = 0, using the adjoint NSE. The AGM thus effectively replaces the backward integration by multiple forward and backward adjoint integrations. Since the viscosity is negative in the adjoint NSE, each step of the AGM is numerically stable. Nevertheless, when applied to turbulence, the AGM develops instabilities, which limit the backward integration to small times. This is due to the exponential divergence of phase space trajectories in turbulent flow, which produces a multitude of local minima in J, when the integration time is large. As an effect, the AGM may select unphysical, noisy initial conditions. In order to improve this situation, we propose two remedies. First, we replace the integration by a sequence of smaller integrations, i.e., we divide the integration time into segments, where in each segment the target field v1 is taken as the initial field u0 from the previous segment. Second, we add an additional term (regularizer) to J, which is proportional to a high-order Laplacian of u0, and which dampens the gradients of u0. We show that suitable values for the segment size and for the regularizer, allow a stable reverse integration of 2D decaying turbulence, with accurate results for more then O(10) turbulent, integral time scales.

Keywords: time reversed integration, parabolic differential equations, adjoint gradient method, two dimensional turbulence

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Authors: M. Maier, I. Dedigama, J. Majasan, Y. Wu, Q. Meyer, L. Castanheira, G. Hinds, P. R. Shearing, D. J. L. Brett

Abstract:

Increasing the efficiency of electrolyser technology is commonly seen as one of the main challenges on the way to the Hydrogen Economy. There is a significant lack of understanding of the different states of operation of polymer electrolyte membrane water electrolysers (PEMWE) and how these influence the overall efficiency. This in particular means the two-phase flow through the membrane, gas diffusion layers (GDL) and flow channels. In order to increase the efficiency of PEMWE and facilitate their spread as commercial hydrogen production technology, new analytic approaches have to be found. Acoustic emission (AE) offers the possibility to analyse the processes within a PEMWE in a non-destructive, fast and cheap in-situ way. This work describes the generation and analysis of AE data coming from a PEM water electrolyser, for, to the best of our knowledge, the first time in literature. Different experiments are carried out. Each experiment is designed so that only specific physical processes occur and AE solely related to one process can be measured. Therefore, a range of experimental conditions is used to induce different flow regimes within flow channels and GDL. The resulting AE data is first separated into different events, which are defined by exceeding the noise threshold. Each acoustic event consists of a number of consequent peaks and ends when the wave diminishes under the noise threshold. For all these acoustic events the following key attributes are extracted: maximum peak amplitude, duration, number of peaks, peaks before the maximum, average intensity of a peak and time till the maximum is reached. Each event is then expressed as a vector containing the normalized values for all criteria. Principal Component Analysis is performed on the resulting data, which orders the criteria by the eigenvalues of their covariance matrix. This can be used as an easy way of determining which criteria convey the most information on the acoustic data. In the following, the data is ordered in the two- or three-dimensional space formed by the most relevant criteria axes. By finding spaces in the two- or three-dimensional space only occupied by acoustic events originating from one of the three experiments it is possible to relate physical processes to certain acoustic patterns. Due to the complex nature of the AE data modern machine learning techniques are needed to recognize these patterns in-situ. Using the AE data produced before allows to train a self-learning algorithm and develop an analytical tool to diagnose different operational states in a PEMWE. Combining this technique with the measurement of polarization curves and electrochemical impedance spectroscopy allows for in-situ optimization and recognition of suboptimal states of operation.

Keywords: acoustic emission, gas diffusion layers, in-situ diagnosis, PEM water electrolyser

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Authors: Getachew Weldemichael, Sentayehu Alamerew, Leta Tulu, Gezahegn Berecha

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Coffee quality improvement program is becoming the focus of coffee research, as the world coffee consumption pattern shifted to high-quality coffee. However, there is limited information on the genetic variation of C. Arabica for quality improvement in potential specialty coffee growing areas of Ethiopia. Therefore, this experiment was conducted with the objectives of determining the magnitude of variation among 105 coffee accessions collected from east Wollega coffee growing areas and assessing correlations between the different coffee qualities attributes. It was conducted in RCRD with three replications. Data on green bean physical characters (shape and make, bean color and odor) and organoleptic cup quality traits (aromatic intensity, aromatic quality, acidity, astringency, bitterness, body, flavor, and overall standard of the liquor) were recorded. Analysis of variance, clustering, genetic divergence, principal component and correlation analysis was performed using SAS software. The result revealed that there were highly significant differences (P<0.01) among the accessions for all quality attributes except for odor and bitterness. Among the tested accessions, EW104 /09, EW101 /09, EW58/09, EW77/09, EW35/09, EW71/09, EW68/09, EW96 /09, EW83/09 and EW72/09 had the highest total coffee quality values (the sum of bean physical and cup quality attributes). These genotypes could serve as a source of genes for green bean physical characters and cup quality improvement in Arabica coffee. Furthermore, cluster analysis grouped the coffee accessions into five clusters with significant inter-cluster distances implying that there is moderate diversity among the accessions and crossing accessions from these divergent inter-clusters would result in hetrosis and recombinants in segregating generations. The principal component analysis revealed that the first three principal components with eigenvalues greater than unity accounted for 83.1% of the total variability due to the variation of nine quality attributes considered for PC analysis, indicating that all quality attributes equally contribute to a grouping of the accessions in different clusters. Organoleptic cup quality attributes showed positive and significant correlations both at the genotypic and phenotypic levels, demonstrating the possibility of simultaneous improvement of the traits. Path coefficient analysis revealed that acidity, flavor, and body had a high positive direct effect on overall cup quality, implying that these traits can be used as indirect criteria to improve overall coffee quality. Therefore, it was concluded that there is considerable variation among the accessions, which need to be properly conserved for future improvement of the coffee quality. However, the variability observed for quality attributes must be further verified using biochemical and molecular analysis.

Keywords: accessions, Coffea arabica, cluster analysis, correlation, principal component

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Authors: Ali H. Daraji, Jack M. Hale, Ye Jianqiao

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With the extensive use of high specific strength structures to optimise the loading capacity and material cost in aerospace and most engineering applications, much effort has been expended to develop intelligent structures for active vibration reduction and structural health monitoring. These structures are highly flexible, inherently low internal damping and associated with large vibration and long decay time. The modification of such structures by adding lightweight piezoelectric sensors and actuators at efficient locations integrated with an optimal control scheme is considered an effective solution for structural vibration monitoring and controlling. The size and location of sensor and actuator are important research topics to investigate their effects on the level of vibration detection and reduction and the amount of energy provided by a controller. Several methodologies have been presented to determine the optimal location of a limited number of sensors and actuators for small-scale structures. However, these studies have tackled this problem directly, measuring the fitness function based on eigenvalues and eigenvectors achieved with numerous combinations of sensor/actuator pair locations and converging on an optimal set using heuristic optimisation techniques such as the genetic algorithms. This is computationally expensive for small- and large-scale structures subject to optimise a number of s/a pairs to suppress multiple vibration modes. This paper proposes an efficient method to determine optimal locations for a limited number of sensor/actuator pairs for active vibration reduction of a flexible structure based on finite element method and Hamilton’s principle. The current work takes the simplified approach of modelling a structure with sensors at all locations, subjecting it to an external force to excite the various modes of interest and noting the locations of sensors giving the largest average percentage sensors effectiveness measured by dividing all sensor output voltage over the maximum for each mode. The methodology was implemented for a cantilever plate under external force excitation to find the optimal distribution of six sensor/actuator pairs to suppress the first six modes of vibration. It is shown that the results of the optimal sensor locations give good agreement with published optimal locations, but with very much reduced computational effort and higher effectiveness. Furthermore, it is shown that collocated sensor/actuator pairs placed in these locations give very effective active vibration reduction using optimal linear quadratic control scheme.

Keywords: optimisation, plate, sensor effectiveness, vibration control

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Authors: Dragan Ribarić

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We employ the so-called problem-dependent linked interpolation concept to develop two cubic 4-node quadrilateral Mindlin plate finite elements with 12 external degrees of freedom. In the problem-independent linked interpolation, the interpolation functions are independent of any problem material parameters and the rotation fields are not expressed in terms of the nodal displacement parameters. On the contrary, in the problem-dependent linked interpolation, the interpolation functions depend on the material parameters and the rotation fields are expressed in terms of the nodal displacement parameters. Two cubic 4-node quadrilateral plate elements are presented, named Q4-U3 and Q4-U3R5. The first one is modelled with one displacement and two rotation degrees of freedom in every of the four element nodes and the second element has five additional internal degrees of freedom to get polynomial completeness of the cubic form and which can be statically condensed within the element. Both elements are able to pass the constant-bending patch test exactly as well as the non-zero constant-shear patch test on the oriented regular mesh geometry in the case of cylindrical bending. In any mesh shape, the elements have the correct rank and only the three eigenvalues, corresponding to the solid body motions are zero. There are no additional spurious zero modes responsible for instability of the finite element models. In comparison with the problem-independent cubic linked interpolation implemented in Q9-U3, the nine-node plate element, significantly less degrees of freedom are employed in the model while retaining the interpolation conformity between adjacent elements. The presented elements are also compared to the existing problem-independent quadratic linked-interpolation element Q4-U2 and to the other known elements that also use the quadratic or the cubic linked interpolation, by testing them on several benchmark examples. Simple functional upgrading from the quadratic to the cubic linked interpolation, implemented in Q4-U3 element, showed no significant improvement compared to the quadratic linked form of the Q4-U2 element. Only when the additional bubble terms are incorporated in the displacement and rotation function fields, which complete the full cubic linked interpolation form, qualitative improvement is fulfilled in the Q4-U3R5 element. Nevertheless, the locking problem exists even for the both presented elements, like in all pure displacement elements when applied to very thin plates modelled by coarse meshes. But good and even slightly better performance can be noticed for the Q4-U3R5 element when compared with elements from the literature, if the model meshes are moderately dense and the plate thickness not extremely thin. In some cases, it is comparable to or even better than Q9-U3 element which has as many as 12 more external degrees of freedom. A significant improvement can be noticed in particular when modeling very skew plates and models with singularities in the stress fields as well as circular plates with distorted meshes.

Keywords: Mindlin plate theory, problem-independent linked interpolation, problem-dependent interpolation, quadrilateral displacement-based plate finite elements

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Authors: Kaleeswari R. K., Seevagan L .

Abstract:

Soil quality in an agroecosystem is influenced by the cropping system, water and soil fertility management. A valid soil quality index would help to assess the soil and crop management practices for desired productivity and soil health. The soil quality indices also provide an early indication of soil degradation and needy remedial and rehabilitation measures. Imbalanced fertilization and inadequate organic carbon dynamics deteriorate soil quality in an intensive cropping system. The rice soil ecosystem is different from other arable systems since rice is grown under submergence, which requires a different set of key soil attributes for enhancing soil quality and productivity. Assessment of the soil quality index involves indicator selection, indicator scoring and comprehensive score into one index. The most appropriate indicator to evaluate soil quality can be selected by establishing the minimum data set, which can be screened by linear and multiple regression factor analysis and score function. This investigation was carried out in intensive rice cultivating regions (having >1.0 lakh hectares) of Tamil Nadu viz., Thanjavur, Thiruvarur, Nagapattinam, Villupuram, Thiruvannamalai, Cuddalore and Ramanathapuram districts. In each district, intensive rice growing block was identified. In each block, two sampling grids (10 x 10 sq.km) were used with a sampling depth of 10 – 15 cm. Using GIS coordinates, and soil sampling was carried out at various locations in the study area. The number of soil sampling points were 41, 28, 28, 32, 37, 29 and 29 in Thanjavur, Thiruvarur, Nagapattinam, Cuddalore, Villupuram, Thiruvannamalai and Ramanathapuram districts, respectively. Principal Component Analysis is a data reduction tool to select some of the potential indicators. Principal Component is a linear combination of different variables that represents the maximum variance of the dataset. Principal Component that has eigenvalues equal or higher than 1.0 was taken as the minimum data set. Principal Component Analysis was used to select the representative soil quality indicators in rice soils based on factor loading values and contribution percent values. Variables having significant differences within the production system were used for the preparation of the minimum data set. Each Principal Component explained a certain amount of variation (%) in the total dataset. This percentage provided the weight for variables. The final Principal Component Analysis based soil quality equation is SQI = ∑ i=1 (W ᵢ x S ᵢ); where S- score for the subscripted variable; W-weighing factor derived from PCA. Higher index scores meant better soil quality. Soil respiration, Soil available Nitrogen and Potentially Mineralizable Nitrogen were assessed as soil quality indicators in rice soil of the Cauvery Delta zone covering Thanjavur, Thiruvavur and Nagapattinam districts. Soil available phosphorus could be used as a soil quality indicator of rice soils in the Cuddalore district. In rain-fed rice ecosystems of coastal sandy soil, DTPA – Zn could be used as an effective soil quality indicator. Among the soil parameters selected from Principal Component Analysis, Microbial Biomass Nitrogen could be used quality indicator for rice soils of the Villupuram district. Cauvery Delta zone has better SQI as compared with other intensive rice growing zone of Tamil Nadu.

Keywords: soil quality index, soil attributes, soil mapping, and rice soil

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