Fractal analysis of polyferric chloride-humic acid(PFC-HA) flocs in different topological spaces

The fractal dimensions in different topological spaces of polyferric chloride-humic acid （PFC-HA） flocs, formed in flocculating different kinds of humic acids （HA） water at different initial pH （9.0, 7.0, 5.0） and PFC dosages, were calculated by effective densitymaximum diameter, image analysis, and N2 absorption-desorption methods, respectively. The mass fractal dimensions （De） of PFC-HA floes were calculated by bi-logarithm relation of effective density with maximum diameter and Logan empirical equation. The Df value was more than 2.0 at initial pH of 7,0, which was 11% and 13% higher than those at pH 9.0 and 5.0, respecively, indicating the most compact flocs formed in flocculated HA water at initial pH of 7.0. The image analysis for those flocs indicates that after flocculating the HA water at initial pH greater than 7.0 with PFC flocculant, the fractal dimensions of D2 （logA vs. logdL） and D3 （logVsphere vs. logdL） of PFC-HA floes decreased with the increase of PFC dosages, and PFC-HA floes showed a gradually looser structure. At the optimum dosage of PFC, the D2 （logA vs. logdL） values of the flocs show 14%-43% difference with their corresponding Dr, and they even had different tendency with the change of initial pH values. However, the D2 values of the floes formed at three different initial pH in HA solution had a same tendency with the corresponding Df. Based on fractal Frenkel-Halsey-HiU （FHH） adsorption and desorption equations, the pore surface fractal dimensions （Ds） for dried powders of PFC-HA flocs formed in HA water with initial pH 9.0 and 7.0 were all close to 2.9421, and the Ds values of flocs formed at initial pH 5.0 were less than 2.3746. It indicated that the pore surface fractal dimensions of PFC-HA floes dried powder mainly show the irregularity from the mesopore-size distribution and marcopore-size distribution.

AN APPLICATION OF TOPOLOGICAL ANALYSIS TO STUDYING THE THREE-DIMENSIONAL FLOW IN CASCADES;PART I—TOPOLOGICAL RULES FOR SKIN-FRICTION LINES AND SECTION STREAMLINES

Based on the working of Lighthill and Hunt et al., in the present paper the author has established the topological rules adapting to analysing the skin-friction lines and the section streamlines in cascades. These rules are (1) for a rotor cascade without shroud band, the total number of nodal points equals that the saddle points on the skin-friction line vector fields in eachpitch range; (2) for an annular or straight cascade with no-clearances at blade ends, the total number of saddle points is two more than that of nodal points on the skin-friction line fields in a pitch; (3) the total number of saddles in the secondary flow fields on cross-sections in cascade is one less than that of nodes; (4) in the section streamline vector fields on a meridian surface penetrating a flow passage, and on leading and trailing edge sections, the total number of nodes is equal to that of saddles; (5) on the streamline vector fields of a blade-to-blade surface, the total number of nodes is one less than that of saddles.

AN APPLICATION OF TOPOLOGICAL METHOD TO ANALYSING THE THREE-DIMENSIONAL FLOW IN CASCADES(Ⅱ)-TOPOLOGICAL ANALYSIS ON THE VECTOR FIELD PATTERNS OF SKINFRICTIONS AND SECTION STREAMLINES

With an application of topological analysis, in this paper the skin-friction line patterns on compressor and turbine cascade surfaces are depicted and the streamline patterns of the secondary flow fields in the cross-section of a curved pipe and a turbine cascade are drawn under given conditions. In addition the structures of vortices within three-dimensional viscous flow fields in cascades are analysed.

Optimal topology design of replaceable bar dampers of a reticulated shell based on sensitivity analysis

In this study,a method for control of reticulated shells is proposed and its practicality is demonstrated.The control is implemented by replacing selected bars of the shell with passive viscoelastic dampers.By applying the eigenvalue perturbation technique and the earthquake spectrum concept,the sensitivities of various topologies of the shell are analyzed,and the optimal topology is determined by taking their symmetries into consideration.The results of this research show that common damper topologies are not effective for all types of responses and recorded earthquakes.The optimal topology identifi ed requires a minimal number of dampers for each type of earthquake record.The displacement control effect of the dynamic responses of the optimal topology is 10% – 20%; the acceleration control effect is also about 10% – 20%; and the axial force control effect is as much as 30% – 45%.Furthermore,the incremental dynamic analysis(IDA) method is used to investigate the stability of the controlled shell.The results show that the dynamic stability of the controlled shell is well preserved when it is vibrated under vibration and is better than the uncontrolled shell.The ultimate load increased by 10% and the elements entered into the plastic stage when the peak acceleration reached 580 Gal,which is 200 Gal larger than the uncontrolled shell.

THE SATELLITE STRUCTURE TOPOLOGY OPTIMIZATION BASED ON HOMOGENIZATION METHOD AND ITS SIZE SENSITIVITY ANALYSIS

With the development of satellite structure technology, more and more design parameters will affect its structural performance. It is desirable to obtain an optimal structure design with a minimum weight, including optimal configuration and sizes. The present paper aims to describe an optimization analysis for a satellite structure, including topology optimization and size optimization. Based on the homogenization method, the topology optimization is carried out for the main supporting frame of service module under given constraints and load conditions, and then the sensitivity analysis is made of 15 structural size parameters of the whole satellite and the optimal sizes are obtained. The numerical result shows that the present optimization design method is very effective.

A non-probabilistic reliability topology optimization method based on aggregation function and matrix multiplication considering buckling response constraints

A non-probabilistic reliability topology optimization method is proposed based on the aggregation function and matrix multiplication.The expression of the geometric stiffness matrix is derived,the finite element linear buckling analysis is conducted,and the sensitivity solution of the linear buckling factor is achieved.For a specific problem in linear buckling topology optimization,a Heaviside projection function based on the exponential smooth growth is developed to eliminate the gray cells.The aggregation function method is used to consider the high-order eigenvalues,so as to obtain continuous sensitivity information and refined structural design.With cyclic matrix programming,a fast topology optimization method that can be used to efficiently obtain the unit assembly and sensitivity solution is conducted.To maximize the buckling load,under the constraint of the given buckling load,two types of topological optimization columns are constructed.The variable density method is used to achieve the topology optimization solution along with the moving asymptote optimization algorithm.The vertex method and the matching point method are used to carry out an uncertainty propagation analysis,and the non-probability reliability topology optimization method considering buckling responses is developed based on the transformation of non-probability reliability indices based on the characteristic distance.Finally,the differences in the structural topology optimization under different reliability degrees are illustrated by examples.

Probabilistic-Ellipsoid Hybrid Reliability Multi-Material Topology Optimization Method Based on Stress Constraint

This paper proposes a multi-material topology optimization method based on the hybrid reliability of the probability-ellipsoid model with stress constraint for the stochastic uncertainty and epistemic uncertainty of mechanical loads in optimization design.The probabilistic model is combined with the ellipsoidal model to describe the uncertainty of mechanical loads.The topology optimization formula is combined with the ordered solid isotropic material with penalization(ordered-SIMP)multi-material interpolation model.The stresses of all elements are integrated into a global stress measurement that approximates the maximum stress using the normalized p-norm function.Furthermore,the sequential optimization and reliability assessment(SORA)is applied to transform the original uncertainty optimization problem into an equivalent deterministic topology optimization(DTO)problem.Stochastic response surface and sparse grid technique are combined with SORA to get accurate information on the most probable failure point(MPP).In each cycle,the equivalent topology optimization formula is updated according to the MPP information obtained in the previous cycle.The adjoint variable method is used for deriving the sensitivity of the stress constraint and the moving asymptote method(MMA)is used to update design variables.Finally,the validity and feasibility of the method are verified by the numerical example of L-shape beam design,T-shape structure design,steering knuckle,and 3D T-shaped beam.

A Multifractal Detrended Fluctuation Analysis of the Ising Financial Markets Model with Small World Topology

We present a multifractal detrended fluctuation analysis （MFDFA） of the time series of return generated by our recently-proposed Ising financial market model with underlying small world topology. The result of the MFDFA shows that there exists obvious multifractal scaling behavior in produced time series. We compare the MFDFA results for original time series with those for shuffled series, and find that its multifractal nature is due to two factors： broadness of probability density function of the series and different correlations in small- and large-scale fluctuations. This may provide new insight to the problem of the origin of multifractality in financial time series.

Multi-Material Topology Optimization of 2D Structures Using Convolutional Neural Networks

In recent years,there has been significant research on the application of deep learning(DL)in topology optimization(TO)to accelerate structural design.However,these methods have primarily focused on solving binary TO problems,and effective solutions for multi-material topology optimization(MMTO)which requires a lot of computing resources are still lacking.Therefore,this paper proposes the framework of multiphase topology optimization using deep learning to accelerate MMTO design.The framework employs convolutional neural network(CNN)to construct a surrogate model for solving MMTO,and the obtained surrogate model can rapidly generate multi-material structure topologies in negligible time without any iterations.The performance evaluation results show that the proposed method not only outputs multi-material topologies with clear material boundary but also reduces the calculation cost with high prediction accuracy.Additionally,in order to find a more reasonable modeling method for MMTO,this paper studies the characteristics of surrogate modeling as regression task and classification task.Through the training of 297 models,our findings show that the regression task yields slightly better results than the classification task in most cases.Furthermore,The results indicate that the prediction accuracy is primarily influenced by factors such as the TO problem,material category,and data scale.Conversely,factors such as the domain size and the material property have minimal impact on the accuracy.

A Hybrid Parallel Strategy for Isogeometric Topology Optimization via CPU/GPU Heterogeneous Computing

This paper aims to solve large-scale and complex isogeometric topology optimization problems that consumesignificant computational resources. A novel isogeometric topology optimization method with a hybrid parallelstrategy of CPU/GPU is proposed, while the hybrid parallel strategies for stiffness matrix assembly, equationsolving, sensitivity analysis, and design variable update are discussed in detail. To ensure the high efficiency ofCPU/GPU computing, a workload balancing strategy is presented for optimally distributing the workload betweenCPU and GPU. To illustrate the advantages of the proposedmethod, three benchmark examples are tested to verifythe hybrid parallel strategy in this paper. The results show that the efficiency of the hybrid method is faster thanserial CPU and parallel GPU, while the speedups can be up to two orders of magnitude.

Full-Scale Isogeometric Topology Optimization of Cellular Structures Based on Kirchhoff-Love Shells

Cellular thin-shell structures are widely applied in ultralightweight designs due to their high bearing capacity and strength-to-weight ratio.In this paper,a full-scale isogeometric topology optimization(ITO)method based on Kirchhoff-Love shells for designing cellular tshin-shell structures with excellent damage tolerance ability is proposed.This method utilizes high-order continuous nonuniform rational B-splines(NURBS)as basis functions for Kirchhoff-Love shell elements.The geometric and analysis models of thin shells are unified by isogeometric analysis(IGA)to avoid geometric approximation error and improve computational accuracy.The topological configurations of thin-shell structures are described by constructing the effective density field on the controlmesh.Local volume constraints are imposed in the proximity of each control point to obtain bone-like cellular structures.To facilitate numerical implementation,the p-norm function is used to aggregate local volume constraints into an equivalent global constraint.Several numerical examples are provided to demonstrate the effectiveness of the proposed method.After simulation and comparative analysis,the results indicate that the cellular thin-shell structures optimized by the proposed method exhibit great load-carrying behavior and high damage robustness.

Toward a Neurophysiological Measure of Image Quality Perception Based on Algebraic Topology Analysis

The bandwidth of internet connections is still a bottleneck when transmitting large amounts of images,making the image quality assessment essential.Neurophysiological assessment of image quality has highlight advantages for it does not interfere with natural viewing behavior.However,in JPEG compression,the previous study is hard to tell the difference between the electroencephalogram(EEG)evoked by different quality images.In this paper,we propose an EEG analysis approach based on algebraic topology analysis,and the result shows that the difference between Euler characteristics of EEG evoked by different distortion images is striking both in the alpha and beta band.Moreover,we further discuss the relationship between the images and the EEG signals,and the results implied that the algebraic topological properties of images are consistent with that of brain perception,which is possible to give birth to braininspired image compression based on algebraic topological features.In general,an algebraic topologybased approach was proposed in this paper to analyze the perceptual characteristics of image quality,which will be beneficial to provide a reliable score for data compression in the network and improve the network transmission capacity.

A Causal Fusion Inference Method for Industrial Alarm Root Cause Analysis Based on Process Topology and Alarm Event Data

Modern industrial systems are usually in large scale,consisting of massive components and variables that form a complex system topology.Owing to the interconnections among devices,a fault may occur and propagate to exert widespread influences and lead to a variety of alarms.Obtaining the root causes of alarms is beneficial to the decision supports in making corrective alarm responses.Existing data-driven methods for alarm root cause analysis detect causal relations among alarms mainly based on historical alarm event data.To improve the accuracy,this paper proposes a causal fusion inference method for industrial alarm root cause analysis based on process topology and alarm events.A Granger causality inference method considering process topology is exploited to find out the causal relations among alarms.The topological nodes are used as the inputs of the model,and the alarm causal adjacency matrix between alarm variables is obtained by calculating the likelihood of the topological Hawkes process.The root cause is then obtained from the directed acyclic graph(DAG)among alarm variables.The effectiveness of the proposed method is verified by simulations based on both a numerical example and the Tennessee Eastman process(TEP)model.

The Hidden-Layers Topology Analysis of Deep Learning Models in Survey for Forecasting and Generation of the Wind Power and Photovoltaic Energy

As wind and photovoltaic energy become more prevalent,the optimization of power systems is becoming increasingly crucial.The current state of research in renewable generation and power forecasting technology,such as wind and photovoltaic power(PV),is described in this paper,with a focus on the ensemble sequential LSTMs approach with optimized hidden-layers topology for short-term multivariable wind power forecasting.The methods for forecasting wind power and PV production.The physical model,statistical learningmethod,andmachine learning approaches based on historical data are all evaluated for the forecasting of wind power and PV production.Moreover,the experiments demonstrated that cloud map identification has a significant impact on PV generation.With a focus on the impact of photovoltaic and wind power generation systems on power grid operation and its causes,this paper summarizes the classification of wind power and PV generation systems,as well as the benefits and drawbacks of PV systems and wind power forecasting methods based on various typologies and analysis methods.

The Topology Optimization of Oil Cylinder Mounting

The method of the structural topology optimization is often used to design machine in the early stage of the mechanical design.And the mechanical structures use the topology design to produce a new still and lightweight part with the different loading.A new structure is created through overlapping these new optimized structure.

Structural Design Optimization Using Isogeometric Analysis: A Comprehensive Review

Isogeometric analysis(IGA),an approach that integrates CAE into conventional CAD design tools,has been used in structural optimization for 10 years,with plenty of excellent research results.This paper provides a comprehensive review on isogeometric shape and topology optimization,with a brief coverage of size optimization.For isogeometric shape optimization,attention is focused on the parametrization methods,mesh updating schemes and shape sensitivity analyses.Some interesting observations,e.g.the popularity of using direct(differential)method for shape sensitivity analysis and the possibility of developing a large scale,seamlessly integrated analysis-design platform,are discussed in the framework of isogeometric shape optimization.For isogeometric topology optimization(ITO),we discuss different types of ITOs,e.g.ITO using SIMP(Solid Isotropic Material with Penalization)method,ITO using level set method,ITO using moving morphable com-ponents(MMC),ITO with phase field model,etc.,their technical details and applications such as the spline filter,multi-resolution approach,multi-material problems and stress con-strained problems.In addition to the review in the last 10 years,the current developmental trend of isogeometric structural optimization is discussed.

Optimization Design and Performance Analysis of Vehicle Powertrain Mounting System

The design strategies for powertrain mounting systems play an important role in the reduction of vehicular vibration and noise. As stiffness and damping elements connecting the transmission system and vehicle body, the rubber mount exhibits better vibration isolation performance than the rigid connection. This paper presents a complete design process of the mounting system, including the vibration decoupling, vibration simulation analysis, topology optimization, and experimental verification. Based on the 6?degrees?of?freedom vibration coupling model of the powertrain mounting system, an optimization algorithm is used to extract the best design parameters of each mount, thus rendering the mounting system fully decoupled and the natural frequency well configured, and the optimal parameters are used to design the mounting system. Subsequently, vibration simulation analysis is applied to the mounting system, considering both transmission and road excitations. According to the results of finite element analysis, the topological structure of the metal frame of the front mount is optimized to improve the strength and dynamic characteristics of the mounting system. Finally, the vibration bench test is used to verify the availability of the optimization design with the analysis of acceleration response and vibration transmissibility of the mounting system. The results show that the vibration isolation performance of the mounting system can be improved effectively using the vibration optimal decoupling method, and the structural modification of the metal frame can well promote the dynamic characteristics of the mounting system.

Customized reconstructive prosthesis design based on topological optimization to treat severe proximal tibia defect

A novel reconstructive prosthesis was designed with topological optimization(TO)and a lattice structure to enhance biomechanical and biological properties in the proximal tibia.The biomechanical performance was validated through finite element analysis(FEA)and biomechanical tests.The tibia with inhomogeneous material properties was reconstructed according to computed tomography images,and different components were designed to simulate the operation.Minimum compliance TO subject to a volume fraction constraint combined with a graded lattice structure was utilized to redesign the prosthesis.FEA was performed to evaluate the mechanical performances of the tibia and implants after optimization,including stress,micromotion,and strain energy.The results were analyzed by paired-samples t tests,and p<0.05 was considered significant.Biomechanical testing was used to verify the tibial stresses.Compared to the original group(OG),the TO group(TOG)exhibited lower stress on the stem,and the maximum von Mises stresses were 87.2 and 53.1 MPa,respectively,a 39.1%reduction(p<0.05).Conversely,the stress and strain energy on the tibia increased in the TOG.The maximum von Mises stress values were 16.4 MPa in the OG and 22.9 MPa in the TOG with a 39.6%increase(p<0.05),and the maximum SED value was 0.026 MPa in the OG and 0.042 MPa in the TOG,corresponding to an increase of 61.5%(p<0.05).The maximum micromotions in the distal end of the stem were 135μm in the OG and 68μm in the TOG,almost a 50%reduction.The stress curves of the biomechanical test coincided well with the FEA results.The TO approach can effectively reduce the whole weight of the prosthesis and improve the biomechanical environment of the tibia.It could also pave the way for next-generation applications in orthopedics surgery.

An XBi-CFAO Method for the Optimization of Multi-Layered Variable Stiffness Composites Using Isogeometric Analysis

This paper presents an effective fiber angle optimization method for two and multi-layered variable stiffness composites.A gradient-based fiber angle optimization method is developed based on isogeometric analysis(IGA).Firstly,the element densities and fiber angles for two and multi-layered composites are synchronously optimized using an extended Bi-layered continuous fiber angle optimization method(XBi-CFAO).The densities and fiber angles in the base layer are attached to the control points.The structure response and sensitivity analysis are accomplished using the non-uniform rational B-spline(NURBS)based IGA.By the benefit of the B-spline space,this method is free from checkerboards,and no additional filtering is needed to smooth the sensitivity numbers.Then the curved fiber paths are generated using the streamline method and the discontinuous fiber paths are smoothed using a partitioned selection process.The proposed method in the paper can alleviate the phenomenon of fiber discontinuity,enhance information retention for the optimized fiber angles of the singular points and save calculating resources effectively.

M-P INVERSE TOPOLOGICAL VARIATION METHODOF FINITE ELEMENT STRUCTURES

Using Moore-Penrose inverse theory, a set of formulations for calculating the static responses of a changed finite element structure are given in this paper. Using these formulations by structural analysis may eliminate the need of assembling the stiffness matrix and solving a set of simultaneous equations.