Search results for: equation error

Authors: Nanine Fouche

Abstract:

The Cape Flats is a low-lying sand-covered expanse of approximately 460 square kilometres, situated to the southeast of the central business district of Cape Town in the Western Cape of South Africa. The aeolian sands masking this area are often loose and compressible in the upper 1m to 1.5m of the surface, and there is a general exceedance of the maximum allowable settlement in these sands. The settlement of shallow foundations on Cape Flats sands is commonly predicted using the results of in-situ tests such as the SPT or DPSH due to the difficulty of retrieving undisturbed samples for laboratory testing. Varying degrees of accuracy and reliability are associated with these methods. More recently, shear wave velocity (Vs) profiles obtained from seismic testing, such as continuous surface wave tests (CSW), are being used for settlement prediction. Such predictions have the advantage of considering non-linear stress-strain behaviour of soil and the degradation of stiffness with increasing strain. CSW tests are rarely executed in the Cape Flats, whereas SPT’s are commonly performed. For this reason, and to facilitate better settlement predictions in Cape Flats sand, equations representing shear wave velocity (Vs) as a function of SPT blow count (N60) and vertical effective stress (v’) were generated by statistical regression of site investigation data. To reveal the most appropriate method of overburden correction, analyses were performed with a separate overburden term (Pa/σ’v) as well as using stress corrected shear wave velocity and SPT blow counts (correcting Vs. and N60 to Vs1and (N1)60respectively). Shear wave velocity profiles and SPT blow count data from three sites masked by Cape Flats sands were utilised to generate 80 Vs-SPT N data pairs for analysis. Investigated terrains included sites in the suburbs of Athlone, Muizenburg, and Atlantis, all underlain by windblown deposits comprising fine and medium sand with varying fines contents. Elastic settlement analysis was also undertaken for the Cape Flats sands, using a non-linear stepwise method based on small-strain stiffness estimates, which was obtained from the best Vs-N60 model and compared to settlement estimates using the general elastic solution with stiffness profiles determined using Stroud’s (1989) and Webb’s (1969) SPT N60-E transformation models. Stroud’s method considers strain level indirectly whereasWebb’smethod does not take account of the variation in elastic modulus with strain. The expression of Vs. in terms of N60 and Pa/σv’ derived from the Atlantis data set revealed the best fit with R2 = 0.83 and a standard error of 83.5m/s. Less accurate Vs-SPT N relations associated with the combined data set is presumably the result of inversion routines used in the analysis of the CSW results showcasing significant variation in relative density and stiffness with depth. The regression analyses revealed that the inclusion of a separate overburden term in the regression of Vs and N60, produces improved fits, as opposed to the stress corrected equations in which the R2 of the regression is notably lower. It is the correction of Vs and N60 to Vs1 and (N1)60 with empirical constants ‘n’ and ‘m’ prior to regression, that introduces bias with respect to overburden pressure. When comparing settlement prediction methods, both Stroud’s method (considering strain level indirectly) and the small strain stiffness method predict higher stiffnesses for medium dense and dense profiles than Webb’s method, which takes no account of strain level in the determination of soil stiffness. Webb’s method appears to be suitable for loose sands only. The Versak software appears to underestimate differences in settlement between square and strip footings of similar width. In conclusion, settlement analysis using small-strain stiffness data from the proposed Vs-N60 model for Cape Flats sands provides a way to take account of the non-linear stress-strain behaviour of the sands when calculating settlement.

Keywords: sands, settlement prediction, continuous surface wave test, small-strain stiffness, shear wave velocity, penetration resistance

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Authors: Riccardo Fratini, Riccardo Santini, Jacopo Serafini, Massimo Gennaretti, Stefano Panzieri

Abstract:

This paper presents a nonlinear differential model, for a three-bladed horizontal axis wind turbine (HAWT) suited for control applications. It is based on a 8-dofs, lumped parameters structural dynamics coupled with a quasi-steady sectional aerodynamics. In particular, using the Euler-Lagrange Equation (Energetic Variation approach), the authors derive, and successively validate, such model. For the derivation of the aerodynamic model, the Greenbergs theory, an extension of the theory proposed by Theodorsen to the case of thin airfoils undergoing pulsating flows, is used. Specifically, in this work, the authors restricted that theory under the hypothesis of low perturbation reduced frequency k, which causes the lift deficiency function C(k) to be real and equal to 1. Furthermore, the expressions of the aerodynamic loads are obtained using the quasi-steady strip theory (Hodges and Ormiston), as a function of the chordwise and normal components of relative velocity between flow and airfoil Ut, Up, their derivatives, and section angular velocity ε˙. For the validation of the proposed model, the authors carried out open and closed-loop simulations of a 5 MW HAWT, characterized by radius R =61.5 m and by mean chord c = 3 m, with a nominal angular velocity Ωn = 1.266rad/sec. The first analysis performed is the steady state solution, where a uniform wind Vw = 11.4 m/s is considered and a collective pitch angle θ = 0.88◦ is imposed. During this step, the authors noticed that the proposed model is intrinsically periodic due to the effect of the wind and of the gravitational force. In order to reject this periodic trend in the model dynamics, the authors propose a collective repetitive control algorithm coupled with a PD controller. In particular, when the reference command to be tracked and/or the disturbance to be rejected are periodic signals with a fixed period, the repetitive control strategies can be applied due to their high precision, simple implementation and little performance dependency on system parameters. The functional scheme of a repetitive controller is quite simple and, given a periodic reference command, is composed of a control block Crc(s) usually added to an existing feedback control system. The control block contains and a free time-delay system eτs in a positive feedback loop, and a low-pass filter q(s). It should be noticed that, while the time delay term reduces the stability margin, on the other hand the low pass filter is added to ensure stability. It is worth noting that, in this work, the authors propose a phase shifting for the controller and the delay system has been modified as e^(−(T−γk)), where T is the period of the signal and γk is a phase shifting of k samples of the same periodic signal. It should be noticed that, the phase shifting technique is particularly useful in non-minimum phase systems, such as flexible structures. In fact, using the phase shifting, the iterative algorithm could reach the convergence also at high frequencies. Notice that, in our case study, the shifting of k samples depends both on the rotor angular velocity Ω and on the rotor azimuth angle Ψ: we refer to this controller as a spatial repetitive controller. The collective repetitive controller has also been coupled with a C(s) = PD(s), in order to dampen oscillations of the blades. The performance of the spatial repetitive controller is compared with an industrial PI controller. In particular, starting from wind speed velocity Vw = 11.4 m/s the controller is asked to maintain the nominal angular velocity Ωn = 1.266rad/s after an instantaneous increase of wind speed (Vw = 15 m/s). Then, a purely periodic external disturbance is introduced in order to stress the capabilities of the repetitive controller. The results of the simulations show that, contrary to a simple PI controller, the spatial repetitive-PD controller has the capability to reject both external disturbances and periodic trend in the model dynamics. Finally, the nominal value of the angular velocity is reached, in accordance with results obtained with commercial software for a turbine of the same type.

Keywords: wind turbines, aeroelasticity, repetitive control, periodic systems

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Authors: Ali Kazemi

Abstract:

Those within the volatile and interconnected international economic markets, appropriately predicting market trends, hold substantial fees for traders and financial establishments. Traditional device mastering strategies have made full-size strides in forecasting marketplace movements; however, monetary data's complicated and networked nature calls for extra sophisticated processes. This observation offers a groundbreaking method for monetary marketplace prediction that leverages the synergistic capability of Graph Convolutional Networks (GCNs) and Long Short-Term Memory (LSTM) networks. Our suggested algorithm is meticulously designed to forecast the traits of inventory market indices and cryptocurrency costs, utilizing a comprehensive dataset spanning from January 1, 2015, to December 31, 2023. This era, marked by sizable volatility and transformation in financial markets, affords a solid basis for schooling and checking out our predictive version. Our algorithm integrates diverse facts to construct a dynamic economic graph that correctly reflects market intricacies. We meticulously collect opening, closing, and high and low costs daily for key inventory marketplace indices (e.g., S&P 500, NASDAQ) and widespread cryptocurrencies (e.g., Bitcoin, Ethereum), ensuring a holistic view of marketplace traits. Daily trading volumes are also incorporated to seize marketplace pastime and liquidity, providing critical insights into the market's shopping for and selling dynamics. Furthermore, recognizing the profound influence of the monetary surroundings on financial markets, we integrate critical macroeconomic signs with hobby fees, inflation rates, GDP increase, and unemployment costs into our model. Our GCN algorithm is adept at learning the relational patterns amongst specific financial devices represented as nodes in a comprehensive market graph. Edges in this graph encapsulate the relationships based totally on co-movement styles and sentiment correlations, enabling our version to grasp the complicated community of influences governing marketplace moves. Complementing this, our LSTM algorithm is trained on sequences of the spatial-temporal illustration discovered through the GCN, enriched with historic fee and extent records. This lets the LSTM seize and expect temporal marketplace developments accurately. Inside the complete assessment of our GCN-LSTM algorithm across the inventory marketplace and cryptocurrency datasets, the version confirmed advanced predictive accuracy and profitability compared to conventional and opportunity machine learning to know benchmarks. Specifically, the model performed a Mean Absolute Error (MAE) of 0.85%, indicating high precision in predicting day-by-day charge movements. The RMSE was recorded at 1.2%, underscoring the model's effectiveness in minimizing tremendous prediction mistakes, which is vital in volatile markets. Furthermore, when assessing the model's predictive performance on directional market movements, it achieved an accuracy rate of 78%, significantly outperforming the benchmark models, averaging an accuracy of 65%. This high degree of accuracy is instrumental for techniques that predict the course of price moves. This study showcases the efficacy of mixing graph-based totally and sequential deep learning knowledge in economic marketplace prediction and highlights the fee of a comprehensive, records-pushed evaluation framework. Our findings promise to revolutionize investment techniques and hazard management practices, offering investors and economic analysts a powerful device to navigate the complexities of cutting-edge economic markets.

Keywords: financial market prediction, graph convolutional networks (GCNs), long short-term memory (LSTM), cryptocurrency forecasting

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Authors: Katerina Zaharieva, Katya Milenova, Zara Cherkezova-Zheleva, Alexander Eliyas, Boris Kunev, Ivan Mitov

Abstract:

The synthesized nanosized manganese ferrite-type of samples have been tested as photocatalysts in the reaction of oxidative degradation of model contaminant Reactive Black 5 (RB5) dye in aqueous solutions under UV irradiation. As it is known this azo dye is applied in the textile-coloring industry and it is discharged into the waterways causing pollution. The co-precipitation procedure has been used for the synthesis of manganese ferrite-type of materials: Sample 1 - Mn0.25Fe2.75O4, Sample 2 - Mn0.5Fe2.5O4 and Sample 3 - MnFe2O4 from 0.03M aqueous solutions of MnCl2•4H2O, FeCl2•4H2O and/or FeCl3•6H2O and 0.3M NaOH in appropriate amounts. The mechanochemical activation of co-precipitated ferrite-type of samples has been performed in argon (Samples 1 and 2) or in air atmosphere (Sample 3) for 2 hours at a milling speed of 500 rpm. The mechano-chemical treatment has been carried out in a high energy planetary ball mill type PM 100, Retsch, Germany. The mass ratio between balls and powder was 30:1. As a result mechanochemically activated Sample 4 - Mn0.25Fe2.75O4, Sample 5 - Mn0.5Fe2.5O4 and Sample 6 - MnFe2O4 have been obtained. The synthesized manganese ferrite-type photocatalysts have been characterized by X-ray diffraction method and Moessbauer spectroscopy. The registered X-ray diffraction patterns and Moessbauer spectra of co-precipitated ferrite-type of materials show the presence of manganese ferrite and additional akaganeite phase. The presence of manganese ferrite and small amounts of iron phases is established in the mechanochemically treated samples. The calculated average crystallite size of manganese ferrites varies within the range 7 – 13 nm. This result is confirmed by Moessbauer study. The registered spectra show superparamagnetic behavior of the prepared materials at room temperature. The photocatalytic investigations have been made using polychromatic UV-A light lamp (Sylvania BLB, 18 W) illumination with wavelength maximum at 365 nm. The intensity of light irradiation upon the manganese ferrite-type photocatalysts was 0.66 mW.cm-2. The photocatalytic reaction of oxidative degradation of RB5 dye was carried out in a semi-batch slurry photocatalytic reactor with 0.15 g of ferrite-type powder, 150 ml of 20 ppm dye aqueous solution under magnetic stirring at rate 400 rpm and continuously feeding air flow. The samples achieved adsorption-desorption equilibrium in the dark period for 30 min and then the UV-light was turned on. After regular time intervals aliquot parts from the suspension were taken out and centrifuged to separate the powder from solution. The residual concentrations of dye were established by a UV-Vis absorbance single beam spectrophotometer CamSpec M501 (UK) measuring in the wavelength region from 190 to 800 nm. The photocatalytic measurements determined that the apparent pseudo-first-order rate constants calculated by linear slopes approximating to first order kinetic equation, increase in following order: Sample 3 (1.1х10-3 min-1) < Sample 1 (2.2х10-3 min-1) < Sample 2 (3.3 х10-3 min-1) < Sample 4 (3.8х10-3 min-1) < Sample 6 (11х10-3 min-1) < Sample 5 (15.2х10-3 min-1). The mechanochemically activated manganese ferrite-type of photocatalyst samples show significantly higher degree of oxidative degradation of RB5 dye after 120 minutes of UV light illumination in comparison with co-precipitated ferrite-type samples: Sample 5 (92%) > Sample 6 (91%) > Sample 4 (63%) > Sample 2 (53%) > Sample 1 (42%) > Sample 3 (15%). Summarizing the obtained results we conclude that the mechanochemical activation leads to a significant enhancement of the degree of oxidative degradation of the RB5 dye and photocatalytic activity of tested manganese ferrite-type of catalyst samples under our experimental conditions. The mechanochemically activated Mn0.5Fe2.5O4 ferrite-type of material displays the highest photocatalytic activity (15.2х10-3 min-1) and degree of oxidative degradation of the RB5 dye (92%) compared to the other synthesized samples. Especially a significant improvement in the degree of oxidative degradation of RB5 dye (91%) has been determined for mechanochemically treated MnFe2O4 ferrite-type of sample with the highest extent of substitution of iron ions by manganese ions than in the case of the co-precipitated MnFe2O4 sample (15%). The mechanochemically activated manganese ferrite-type of samples show good photocatalytic properties in the reaction of oxidative degradation of RB5 azo dye in aqueous solutions and it could find potential application for dye removal from wastewaters originating from textile industry.

Keywords: nanostructured manganese ferrite-type materials, photocatalytic activity, Reactive Black 5, water treatment

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