Legendre-Weighted Residual Methods for System of Fractional Order Differential Equations

The numerical approach for finding the solution of fractional order systems of boundary value problems (BPVs) is derived in this paper. The implementation of the weighted residuals such as Galerkin, Least Square, and Collocation methods are included for solving fractional order differential equations, which is broadened to acquire the approximate solutions of fractional order systems with differentiable polynomials, namely Legendre polynomials, as basis functions. The algorithm of the residual formulations of matrix form can be coded efficiently. The interpretation of Caputo fractional derivatives is employed here. We have demonstrated these methods numerically through a few examples of linear and nonlinear BVPs. The results in absolute errors show that the present method efficiently finds the numerical solutions of fractional order systems of differential equations.

Structural and microwave absorption properties of CoFe_(2)O_(4)/residual carbon composites

Electromagnetic interference,which necessitates the rapid advancement of substances with exceptional capabilities for bsorbing electromagnetic waves,is of urgent concern in contemporary society.In this work,CoFe_(2)O_(4)/residual carbon from coal gasification fine slag(CFO/RC)composites were created using a novel hydrothermal method.Various mechanisms for microwave absorption,including conductive loss,natural resonance,interfacial dipole polarization,and magnetic flux loss,are involved in these composites.Consequently,compared with pure residual carbon materials,this composite offers superior capabilities in microwave absorption.At 7.76GHz,the CFO/RC-2 composite achieves an impressive minimum reflection loss(RL_(min))of-43.99 dB with a thickness of 2.44 mm.Moreover,CFO/RC-3 demonstrates an effective absorption bandwidth(EAB)of up to 4.16 GHz,accompanied by a thickness of 1.18mm.This study revealed the remarkable capability of the composite to diminish electromagnetic waves,providing a new generation method for microwave absorbing materials of superior quality.

Internal residual stress measurement on linear friction welding of titanium alloy plates with contour method

The internal residual stress within a TC 17 titanium alloy joint welded by linear friction welding （LFW） was measured by the contour method, which is a relatively new and destructive technique to obtain a full map of internal residual stress. The specimen was first cut into two parts; the out-of-plane displacement contour formed by the release of the residual stress was then measured; finally, taking the measured contour of the cut plane as the boundary conditions, a linear elastic finite element analysis was carried out to calculate the corresponding distribution of residual stress normal to the cut plane. The internal stress distribution of the TC 17 titanium alloy LFWjoint was also analyzed. The results show that the tensile residual stress in the TC17 LFW weld is mainly present within a region about 12 mm from the weld centerline; the peak tensile residual stress occurs at the weld centerline and reaches 360 MPa （about one third of the yield strength of TC17 alloy）; within the weld zone of the TC17 LFW weld, the through-thickness stress is not uniform, and the internal stress is larger than that near the top or bottom surface.

Additive manufacturing of Ni-based superalloys: Residual stress, mechanisms of crack formation and strategies for crack inhibition

The additive manufacturing(AM)of Ni-based superalloys has attracted extensive interest from both academia and industry due to its unique capabilities to fabricate complex and high-performance components for use in high-end industrial systems.However,the intense temperature gradient induced by the rapid heating and cooling processes of AM can generate high levels of residual stress and metastable chemical and structural states,inevitably leading to severe metallurgical defects in Ni-based superalloys.Cracks are the greatest threat to these materials’integrity as they can rapidly propagate and thereby cause sudden and non-predictable failure.Consequently,there is a need for a deeper understanding of residual stress and cracking mechanisms in additively manufactured Ni-based superalloys and ways to potentially prevent cracking,as this knowledge will enable the wider application of these unique materials.To this end,this paper comprehensively reviews the residual stress and the various mechanisms of crack formation in Ni-based superalloys during AM.In addition,several common methods for inhibiting crack formation are presented to assist the research community to develop methods for the fabrication of crack-free additively manufactured components.

Method for Measuring Residual Stresses Induced by Boring in Internal Surface of Tube and Its Validation with XRD Method

Residual stresses can have a strong effect on the usability of machined parts,and the X-ray diffraction(XRD)measuring equipment,which is commonly used to measure residual stresses,is very expensive.This paper presents a method of measuring the residual stresses induced by boring in the internal surface of a tube with much cheaper equipment.The method,called the strain-based method is mainly based on the strains measured on the external surface of the tube.It is proposed on the basis of the very long tube assumption.The finite element method(FEM)analysis is thus used to validate the length of the tube.Guided by the FEM results,an appropriate length of the tube is chosen,and the residual stresses are obtained from both the strain-based method and the XRD method.Stress profiles obtained from both two methods are compared.The comparison result indicates that the profiles of the two methods agree well with each other.Therefore,it can be concluded that the accuracy of the strain-based method is high enough,and it can be applied to residual stress measurement in practice.

Measuring internal residual stress in Al-Cu alloy forgings by crack compliance method with optimized parameters

Measuring the internal stress of Al alloy forgings accurately is critical for controlling the deformation during the subsequent machine process.In this work,the crack compliance method was used to calculate the internal residual stress of Al-Cu high strength alloys,and the effect of various model parameters of crack compliance method on the calculated precision was studied by combining the numerical simulation and experimental method.The results show that the precision first increased and then decreased with increasing the crack range.The decreased precision when using a high crack range was due to the strain fluctuation during the machining process,and the optimized crack range was 71%of the thickness of forgings.Low orders of Legendre polynomial can result in residual stress curve more smooth,while high orders led to the occurrence of distortion.The Tikhonov regularization method effectively suppressed the distortion of residual stress caused by the fluctuation of strain data,which significantly improved the precision.In addition,The crack compliance method with optimized parameters was used to measure the residual stress of Al-Cu alloy with different quenching methods.The calculated results demonstrated that the distribution of residual stress was obtained accurately.

Use of Plastic Correction Formula to Improve Accuracy of Welding Residual Stress Test with Blind-Hole Method

The blind-hole method is the most widely used approach to experimentally determine the distribution of residual stress. This paper aims to improve test accuracy of welding residual stress and conducts an experimental study on the strain release factors involved when using the blind-hole method for Q235 and Q345, two steels commonly used in building structures. The ranges of strain release factors A and B in the elastic stage, the effects of strain release factors on residual stress calculated values, and the plastic corrected strain release factors are analyzed considering of the effect of plastic deformation around the blind hole on measurement accuracy. Finally, a simplified calculation formula to determine strain release factors is proposed for use with the blind-hole method. Results show that in the elastic stage, strain release factor A for Q235 and Q345 ranges from-0.399 to-0.525 and strain release factor B from-0.791 to-0.960. Changing the strain release factors A and B shows that calculated residual tensile stress varies in relation to a decrease in both factor values. However, there is a increase in calculated residual compressive stress with a decrease in the strain release factor A value, but there is an decrease with a decrease in strain release factor B value. Calculated residual stress applied to elastic strain release factors is compared with that applied to amended plastic strain release factors for Q235 steel. The maximum deviation between calculated residual stress and test stress is reduced from 21.1 to 1.0%,and for Q345 steel from 26.5 to 1.2%. It is thus evident that the plastic correction formula proposed in this paper can be used in calculations when conducting a residual stress test.

MODIFIED LAYER REMOVAL METHOD FOR MEASUREMENT OF RESIDUAL STRESS DISTRIBUTION IN THICK PRE-STRETCHED ALUMINUM PLATE

The integrated structure parts are widely used in aircraft. The distortion caused by residual stresses in thick pre-stretched aluminum plates during machining integrated parts is a common and serious problem. To predict and control the machining distortion, the residual stress distribution in the thick plate must be measured firstly. The modified removal method for measuring residual stress in thick pre-stretched aluminum plates is proposed and the stress-strain relation matrix is deduced by elasticity theory. The residual stress distribution in specimen of 7050T7451 plate is measured by using the method, and measurement results are analyzed and compared with data obtained by other methods. The method is effective to measure the residual stress.

A review of welding residual stress test methods

Due to local uneven heating during the welding process,the residual stress of the structure after welding affects the reliability of it.In order to ensure the reliability,it is of great significance to test the residual stress distribution of the welded joint.It has always been the focus to find a simple and feasible method for residual stress testing to quickly and accurately obtain the residual stress distribution of welded joints.The mechanical measurement method has high measurement accuracy,convenient and easy operation,but it will cause certain damage to the components.Physical measurement method can avoid damage to components,but its test cost is usually high,and its measurement accuracy can also be affected by the material microstructure characteristics of welded components.Based on the advantages and disadvantages of these two residual stress test methods,a modal test method is proposed.This method is a non-destructive measurement method.Based on the mathematical relationship between the residual stress of the welded structure and the natural frequency(mathematical model),the natural frequency is measured through the modal test to calculate the residual stress quickly.However,it is difficult to establish a mathematical model with this method,and it is not suitable for realization.

Method of Semi Analytic Perturbation Weighted Residuals for Nonlinear Bending of Shallow Shells

The semi? analytic perturbation weighted residuals method was used to solve the nonlinear bending problem of shallow shells, and the fifth order B spline was taken as trial function to seek an efficient method for nonlinear bending problem of shallow shells. The results from the present method are in good agreement with those derived from other methods. The present method is of higher accuracy, lower computing time and wider adaptability. In addition, the design of computer program is simple and it is easy to be programmed.

Residual stress with asymmetric spray quenching for thick aluminum alloy plates

Solution and quenching heat treatments are generally carried out in a roller hearth furnace for large-scale thick aluminum alloy plates.However,the asymmetric or uneven spray water flow rate is inevitable under industrial production conditions,which leads to an asymmetric residual stress distribution.The spray quenching treatment was conducted on self-designed spray equipment,and the residual stress along the thickness direction was measured by a layer removal method based on deflections.Under the asymmetric spray quenching condition,the subsurface stress of the high-flow rate surface was lower than that of the low-flow rate surface,and the difference between the two subsurface stresses increased with the increase in the difference in water flow rates.The subsurface stress underneath the surface with a water flow rate of 0.60 m^(3)/h was 15.38 MPa less than that of 0.15 m^(3)/h.The simulated residual stress by finite element(FE)method of the high heat transfer coefficient(HTC)surface was less than that of the low HTC surface,which is consistent with the experimental results.The FE model can be used to analyze the strain and stress evolution and predict the quenched stress magnitude and distribution.

A time domain induced polarization relaxation time spectrum inversion method based on a damping factor and residual correction

Relaxation time spectra （RTS） derived from time domain induced polarization data （TDIP） are helpful to assess oil reservoir pore structures. However, due to the sensitivity to the signal-to-noise ratio （SNR）, the inversion accuracy of the traditional singular value decomposition （SVD） inversion method reduces with a decrease of SNR. In order to enhance the inversion accuracy and improve robustness of the inversion method to the SNR, an improved inversion method, based on damping factor and spectrum component residual correction, is proposed in this study. The numerical inversion results show that the oscillation of the RTS derived from the SVD method increased with a decrease of SNR, which makes it impossible to get accurate inversion components. However, the SNR has little influence on inversion components of the improved method, and the RTS has high inversion accuracy and robustness. Moreover, RTS derived from core sample data is basically in accord with the pore-size distribution curve, and the RTS derived from the actual induced polarization logging data is smooth and continuous, which indicates that the improved method is practicable.

Speech Enhancement via Mask-Mapping Based Residual Dense Network

Masking-based and spectrum mapping-based methods are the two main algorithms of speech enhancement with deep neural network(DNN).But the mapping-based methods only utilizes the phase of noisy speech,which limits the upper bound of speech enhancement performance.Maskingbased methods need to accurately estimate the masking which is still the key problem.Combining the advantages of above two types of methods,this paper proposes the speech enhancement algorithm MM-RDN(maskingmapping residual dense network)based on masking-mapping(MM)and residual dense network(RDN).Using the logarithmic power spectrogram(LPS)of consecutive frames,MM estimates the ideal ratio masking(IRM)matrix of consecutive frames.RDN can make full use of feature maps of all layers.Meanwhile,using the global residual learning to combine the shallow features and deep features,RDN obtains the global dense features from the LPS,thereby improves estimated accuracy of the IRM matrix.Simulations show that the proposed method achieves attractive speech enhancement performance in various acoustic environments.Specifically,in the untrained acoustic test with limited priors,e.g.,unmatched signal-to-noise ratio(SNR)and unmatched noise category,MM-RDN can still outperform the existing convolutional recurrent network(CRN)method in themeasures of perceptual evaluation of speech quality(PESQ)and other evaluation indexes.It indicates that the proposed algorithm is more generalized in untrained conditions.

A Combination of Residual Distribution and the Active Flux Formulations or a New Class of Schemes That Can Combine Several Writings of the Same Hyperbolic Problem:Application to the 1D Euler Equations

We show how to combine in a natural way(i.e.,without any test nor switch)the conservative and non-conservative formulations of an hyperbolic system that has a conservative form.This is inspired from two different classes of schemes:the residual distribution one(Abgrall in Commun Appl Math Comput 2(3):341–368,2020),and the active flux formulations(Eyman and Roe in 49th AIAA Aerospace Science Meeting,2011;Eyman in active flux.PhD thesis,University of Michigan,2013;Helzel et al.in J Sci Comput 80(3):35–61,2019;Barsukow in J Sci Comput 86(1):paper No.3,34,2021;Roe in J Sci Comput 73:1094–1114,2017).The solution is globally continuous,and as in the active flux method,described by a combination of point values and average values.Unlike the“classical”active flux methods,the meaning of the point-wise and cell average degrees of freedom is different,and hence follow different forms of PDEs;it is a conservative version of the cell average,and a possibly non-conservative one for the points.This new class of scheme is proved to satisfy a Lax-Wendroff-like theorem.We also develop a method to perform nonlinear stability.We illustrate the behaviour on several benchmarks,some quite challenging.

Defending Adversarial Examples by a Clipped Residual U-Net Model

Deep learning-based systems have succeeded in many computer vision tasks.However,it is found that the latest study indicates that these systems are in danger in the presence of adversarial attacks.These attacks can quickly spoil deep learning models,e.g.,different convolutional neural networks(CNNs),used in various computer vision tasks from image classification to object detection.The adversarial examples are carefully designed by injecting a slight perturbation into the clean images.The proposed CRU-Net defense model is inspired by state-of-the-art defense mechanisms such as MagNet defense,Generative Adversarial Net-work Defense,Deep Regret Analytic Generative Adversarial Networks Defense,Deep Denoising Sparse Autoencoder Defense,and Condtional Generattive Adversarial Network Defense.We have experimentally proved that our approach is better than previous defensive techniques.Our proposed CRU-Net model maps the adversarial image examples into clean images by eliminating the adversarial perturbation.The proposed defensive approach is based on residual and U-Net learning.Many experiments are done on the datasets MNIST and CIFAR10 to prove that our proposed CRU-Net defense model prevents adversarial example attacks in WhiteBox and BlackBox settings and improves the robustness of the deep learning algorithms especially in the computer visionfield.We have also reported similarity(SSIM and PSNR)between the original and restored clean image examples by the proposed CRU-Net defense model.

Numerical simulation on residual stress and deformation for WAAM parts of aluminum alloy based on temperature function method

Wire arc additive manufacture(WAAM) is a new technique to fabricate large-scale complex aluminum alloy components.However, the performance of the parts is critically influenced by residual stresses and deformation. A sequentially thermal-mechanical coupled model of residual stress and deformation for aluminum alloy WAAM parts was established based on commercial FE software ABAQUS. The temperature field was calculated by the moving heat source(MHS) method. The temperature function was obtained according to the distribution of the peak temperature. Furthermore, the MHS method and segmented temperature function(STF) method were used to calculate the residual stress and deformation. The results show that the STF method satisfies both the efficiency and accuracy requirements. 1-segment, 3-segment, and 5-segment STF methods can shorten the time for mechanical analysis by 91%, 79%, 63%, respectively.The error of the residual stress and deformation are all less than 20%. STF method provides an effective way to predict the residual stress and deformation of large-scale WAAM parts.

A Single Image Derain Method Based on Residue Channel Decomposition in Edge Computing

The numerous photos captured by low-price Internet of Things(IoT)sensors are frequently affected by meteorological factors,especially rainfall.It causes varying sizes of white streaks on the image,destroying the image texture and ruining the performance of the outdoor computer vision system.Existing methods utilise training with pairs of images,which is difficult to cover all scenes and leads to domain gaps.In addition,the network structures adopt deep learning to map rain images to rain-free images,failing to use prior knowledge effectively.To solve these problems,we introduce a single image derain model in edge computing that combines prior knowledge of rain patterns with the learning capability of the neural network.Specifically,the algorithm first uses Residue Channel Prior to filter out the rainfall textural features then it uses the Feature Fusion Module to fuse the original image with the background feature information.This results in a pre-processed image which is fed into Half Instance Net(HINet)to recover a high-quality rain-free image with a clear and accurate structure,and the model does not rely on any rainfall assumptions.Experimental results on synthetic and real-world datasets show that the average peak signal-to-noise ratio of the model decreases by 0.37 dB on the synthetic dataset and increases by 0.43 dB on the real-world dataset,demonstrating that a combined model reduces the gap between synthetic data and natural rain scenes,improves the generalization ability of the derain network,and alleviates the overfitting problem.

De-Noising Brain MRI Images by Mixing Concatenation and Residual Learning(MCR)

Brain magnetic resonance images(MRI)are used to diagnose the different diseases of the brain,such as swelling and tumor detection.The quality of the brain MR images is degraded by different noises,usually salt&pepper and Gaussian noises,which are added to the MR images during the acquisition process.In the presence of these noises,medical experts are facing problems in diagnosing diseases from noisy brain MR images.Therefore,we have proposed a de-noising method by mixing concatenation,and residual deep learning techniques called the MCR de-noising method.Our proposed MCR method is to eliminate salt&pepper and gaussian noises as much as possible from the brain MRI images.The MCR method has been trained and tested on the noise quantity levels 2%to 20%for both salt&pepper and gaussian noise.The experiments have been done on publically available brain MRI image datasets,which can easily be accessible in the experiments and result section.The Structure Similarity Index Measure(SSIM)and Peak Signal-to-Noise Ratio(PSNR)calculate the similarity score between the denoised images by the proposed MCR method and the original clean images.Also,the Mean Squared Error(MSE)measures the error or difference between generated denoised and the original images.The proposed MCR denoising method has a 0.9763 SSIM score,84.3182 PSNR,and 0.0004 MSE for salt&pepper noise;similarly,0.7402 SSIM score,72.7601 PSNR,and 0.0041 MSE for Gaussian noise at the highest level of 20%noise.In the end,we have compared the MCR method with the state-of-the-art de-noising filters such as median and wiener de-noising filters.

Hyperstatic reaction method for calculations of tunnels with horseshoe-shaped cross-section under the impact of earthquakes

Tunnels are now an integral part of the infrastructure in major cities around the world. For many reasons, these tunnels have horseshoe-shaped cross-sections with round top and flat bottom. This paper presents some improvements to the use of the Hyperstatic Reaction Method-HRM for analysing tunnels with horseshoe-shaped cross-sections when these tunnels operate under the influence of earthquakes, particularly in cases when the tunnel lining is a continuous lining. The analysis used parameters of a tunnel from the Hanoi metro system, as well as parameters of the strongest earthquake that may occur in the central Hanoi area in the improved HRM and 2 D numerical methods using the ABAQUS software. On the basis of the results obtained, the paper gives conclusions about the HRM methodology when it is used to calculate tunnels that have horseshoe cross-sections operating under the influence of earthquakes.

Modified Layer-Removal Method for Measurement of Residual Stress in Pre-stretched Aluminium Alloy Plate

Residual stress is one of the factors affecting the machining deformation of monolithic structure parts in the aviation industry. Thus, the studies on machining deformation rules induced by residual stresses largely depend on correctly and efficiently measuring the residual stresses of workpieccs. A modified layer-removal method is proposed to measure residual stress by analysing the characteristics of a traditional, layer-removal method. The coefficients of strain release are then deduced according to the simulation results using the finite element method （FEM）. Moreover, the residual stress in a 7075T651 aluminium alloy plate is measured using the proposed method, and the results are then analyzed and compared with the data obtained by the traditional methods. The analysis indicates that the modified layer-removal method is effective and practical for measuring the residual stress distribution in pre-stretched aluminium alloy plates.