Multi-Material and Multiscale Topology Design Optimization of Thermoelastic Lattice Structures

This study establishes amultiscale andmulti-material topology optimization model for thermoelastic lattice structures(TLSs)consideringmechanical and thermal loading based on the ExtendedMultiscale Finite ElementMethod(EMsFEM).The corresponding multi-material and multiscale mathematical formulation have been established with minimizing strain energy and structural mass as the objective function and constraint,respectively.The Solid Isotropic Material with Penalization(SIMP)interpolation scheme has been adopted to realize micro-scale multi-material selection of truss microstructure.The modified volume preserving Heaviside function(VPHF)is utilized to obtain a clear 0/1 material of truss microstructure.Compared with the classic topology optimization of single-material TLSs,multi-material topology optimization can get a better structural design of the TLS.The effects of temperatures,size factor,and mass fraction on optimization results have been presented and discussed in the numerical examples.

Design of Lattice Structures Using Local Relative Density Mapping Method

In order to solve the problem of substantial computational resources of lattice structure during optimization, a local relative density mapping(LRDM) method is proposed. The proposed method uses solid isotropic microstructures with penalization to optimize a model at the macroscopic scale. The local relative density information is obtained from the topology optimization result. The contour lines of an optimized model are extracted using a density contour approach, and the triangular mesh is generated using a mesh generator. A local mapping relationship between the elements’ relative density and the struts’ relative cross?sectional area is established to automatically determine the diameter of each individual strut in the lattice structures. The proposed LRDM method can be applied to local finite element meshes and local density elements, but it is also suitable for global ones. In addition, some cases are con?sidered in order to test the e ectiveness of the LRDM method. The results show that the solution time of the LRDM is lower than the RDM method by approximately 50%. The proposed method provides instructions for the design of more complex lattice structures.

Parameter Estimation and Topology Identification of Uncertain General Fractional-order Complex Dynamical Networks with Time Delay

Complex networks have attracted much attention from various fields of sciences and engineering in recent years. However, many complex networks have various uncertain information, such as unknown or uncertain system parameters and topological structure, which greatly affects the system dynamics. Thus, the parameter estimation and structure identification problem has theoretical and practical importance for uncertain complex dynamical networks. This paper investigates identification of unknown system parameters and network topologies in uncertain fractional-order complex network with time delays (including coupling delay and node delay). Based on the stability theorem of fractional-order differential system and the adaptive control technique, a novel and general method is proposed to address this challenge. Finally two representative examples are given to verify the effectiveness of the proposed approach. © 2014 Chinese Association of Automation.

Robust topology optimization of multi-material lattice structures under material and load uncertainties

Enabled by advancements in multi-material additive manufacturing,lightweight lattice structures consisting of networks of periodic unit cells have gained popularity due to their extraordinary performance and wide array of functions.This work proposes a density-based robust topology optimization method for meso-or macroscale multi-material lattice structures under any combination of material and load uncertainties.The method utilizes a new generalized material interpolation scheme for an arbitrary number of materials,and employs univariate dimension reduction and Gauss-type quadrature to quantify and propagate uncertainty.By formulating the objective function as a weighted sum of the mean and standard deviation of compliance,the tradeoff between optimality and robustness can be studied and controlled.Examples of a cantilever beam lattice structure under various material and load uncertainty cases exhibit the efficiency and flexibility of the approach.The accuracy of univariate dimension reduction is validated by comparing the results to the Monte Carlo approach.

Layout design of thin-walled structures with lattices and stiffeners using multi-material topology optimization

In this paper,the thin-walled structures with lattices and stiffeners manufactured by additive manufacturing are investigated.A design method based on the multi-material topology optimization is proposed for the simultaneous layout optimization of the lattices and stiffeners in thin-walled structures.First,the representative lattice units of the selected lattices are equivalent to the virtual homogeneous materials whose effective elastic matrixes are achieved by the energy-based homogenization method.Meanwhile,the stiffeners are modelled using the solid material.Subsequently,the multi-material topology optimization formulation is established for both the virtual homogeneous materials and solid material to minimize the structural compliance under mass constraint.Thus,the optimal layout of both the lattices and stiffeners could be simultaneously attained by the optimization procedure.Two applications,the aircraft panel structure and the equipment mounting plate,are dealt with to demonstrate the detailed design procedure and reveal the effect of the proposed method.According to numerical comparisons and experimental results,the thin-walled structures with lattices and stiffeners have significant advantages over the traditional stiffened thin-walled structures and lattice sandwich structures in terms of static,dynamic and anti-instability performance.

Lightweight topology optimization of graded lattice structures with displacement constraints based on an independent continuous mapping method

This paper presents a novel topology optimization method to design graded lattice structures to minimize the volume subject to displacement constraints based on the independent continuous mapping(ICM)method.First,the effective elastic properties of graded unit cells are analyzed by the strain energy-based homogenization method.A surrogate model using quartic polynomial interpolation is built to map the independent continuous topological variable to the effective elastic matrix of the unit cell and set up the relationship between the macroscale structure and microscale unit cells.Second,a lightweight topology optimization model is established,which can be transformed into an explicitly standard quadratic programming problem by sensitivity analysis and solved by dual sequential quadratic programming.Third,several numerical examples demonstrate that graded lattice structures have a better lightweight effect than uniform lattice structures,which validates the effectiveness and feasibility of the proposed method.The results show that graded lattice structures become lighter with increasing displacement constraints.In addition,some diverse topological configurations are obtained.This method provides a reference for the graded lattice structure design and expands the application of the ICM method.

Three-dimensional spatial structure of the macro-pores and flow simulation in anthracite coal based on X-ray μ-CT scanning data

The three-dimensional(3 D) structures of pores directly affect the CH4 flow.Therefore,it is very important to analyze the3 D spatial structure of pores and to simulate the CH4 flow with the connected pores as the carrier.The result shows that the equivalent radius of pores and throats are 1-16 μm and 1.03-8.9 μm,respectively,and the throat length is 3.28-231.25 μm.The coordination number of pores concentrates around three,and the intersection point between the connectivity function and the X-axis is 3-4 μm,which indicate the macro-pores have good connectivity.During the single-channel flow,the pressure decreases along the direction of CH4 flow,and the flow velocity of CH4 decreases from the pore center to the wall.Under the dual-channel and the multi-channel flows,the pressure also decreases along the CH4 flow direction,while the velocity increases.The mean flow pressure gradually decreases with the increase of the distance from the inlet slice.The change of mean flow pressure is relatively stable in the direction horizontal to the bedding plane,while it is relatively large in the direction perpendicular to the bedding plane.The mean flow velocity in the direction horizontal to the bedding plane(Y-axis) is the largest,followed by that in the direction horizontal to the bedding plane(X-axis),and the mean flow velocity in the direction perpendicular to the bedding plane is the smallest.

A systematic design of multifunctional lattice structures with energy absorption and phononic bandgap by topology and parameter optimization

Lattice structure can realize excellent multifunctional charac-teristics because of its huge design space,and the cellular configuration directly affects the lattice structural performance and lightweight.A novel energy-absorbing multifunctional lat-tice structure with phononic bandgap is presented by topol-ogy and parameter optimization in this paper.First,the two-dimensional(2D)cellular configuration is lightweight designed by using independent continuous mapping(ICM)topology optimization method.The 2D cell is reconstructed by geo-metric parameters and rotated into a three-dimensional(3D)cell by using chiral shape to achieve bandgap.Subsequently,the surrogated model with energy absorption as the object and first-order natural frequency as the constraint is estab-lished to optimize a parametric 3D cell based on the Response Surface Methodology(RSM).Finally,the lattice struc-tures are assembled with dodecagonal staggered arrange-ments to avoid the deformation interference among the adjacent cells.In addition,the lattice structural energy absorp-tion and bandgap characteristics are analyzed and discussed.Compared to Kelvin lattice structure,the optimal lattice struc-ture shows significant improvement in energy absorption effi-ciency.Besides,the proposed design also performs well in damping characteristics of the high-frequency and wide-bandgap.The lattice structural optimization design framework has great meaning to achieve the equipment structural light-weight and multi-function in the aerospace field.

Topology Optimization for Design of Hybrid Lattice Structures with Multiple Microstructure Configurations

Hybrid lattice structures consisting of multiple microstructures have drawn much attention due to their excellent performance and extraordinary designability.This work puts forward a novel design scheme of lightweight hybrid lattice structures based on independent continuous mapping(ICM)method.First,the effective elastic properties of various microstructure configurations serve as a bridge between the macrostructure and the multiple microstructures by the homogenization theory.Second,a concurrent topology optimization model for seeking optimized macroscale topology and the specified microstructures is established and solved by a generalized multi-material interpolation formulation and sensitivity analysis.Third,several numerical examples show that hybrid lattice structures with different anisotropic configurations accomplish a better lightweight effect than those with various orthogonal configurations,which verifies the feasibility of the presented method.Hence,anisotropic configurations are more conducive to the sufficient utilization of constitutive material.The proposed scheme supplies a reference for the design of hybrid lattice structures and extends the application field of the ICM method.

Stratification structures on a kind of completely distributive lattices and their applications in theory of topological molecular lattices

A completely distributive lattice is also called a molecular lattice.The least and the greatestelements in a lattice are denoted by 0 and 1,respectively.For the empty subset L of alattice L,we assume that V=0 and ∧=1.The set of all the molecules（i.e.non-zero∨-irreducible elements）in a lattice L is denoted by M（L）. Let L1 and L2 be completely distributive lattices,f:L1→L2 and g:L2→L1 be order-preserving maps.If for any a∈L1 and any b∈L2,f（a）≤b if and only if a≤g（b）,then fis called the left adjoint of g,or g is called the right adjoint of f.The right adjoint of f

An efficient reliability evaluation method for industrial wireless sensor networks

Aimed at the difficulties in accurately, comprehensively and systematically evaluating the reliability of industrial wireless sensor networks （WSNs）, a time-evolving state transition-Monte Carlo （TEST-MC） evaluation method and a novel network function value representation method are proposed to evaluate the reliability of the IWSNs. First, the adjacency matrix method is used to characterize three typical topologies of WSNs including the mesh network, tree network and ribbon network. Secondly, the network function value method is used to evaluate the network connectivity, and the TEST-MC evaluation method is used to evaluate network reliability and availability. Finally, the variations in the reliability, connectivity and availability of these three topologies are presented. Simulation results show that the proposed method can quickly analyze the reliability of the networks containing typical WSN topologies, which provides an effective method for the comprehensive and accurate evaluation of the reliability of WSNs.

Calculation connectivity reliability of road networks based on recursive decomposition arithmetic

In order to decrease the calculation complexity of connectivity reliability of road networks, an improved recursive decomposition arithmetic is proposed. First, the basic theory of recursive decomposition arithmetic is reviewed. Then the characteristics of road networks, which are different from general networks, are analyzed. Under this condition, an improved recursive decomposition arithmetic is put forward which fits road networks better. Furthermore, detailed calculation steps are presented which are convenient for the computer, and the advantage of the approximate arithmetic is analyzed based on this improved arithmetic. This improved recursive decomposition arithmetic directly produces disjoint minipaths and avoids the non-polynomial increasing problems. And because the characteristics of road networks are considered, this arithmetic is greatly simplified. Finally, an example is given to prove its validity.

Study of the topological quantities of lattice QCD using a modified DCGAN frame

A modified deep convolutional generative adversarial network(M-DCGAN)frame is proposed to study the N-dimensional(ND)topological quantities in lattice QCD based on Monte Carlo(MC)simulations.We construct a new scaling structure including fully connected layers to support the generation of high-quality high-dimensional images for the M-DCGAN.Our results suggest that the M-DCGAN scheme of machine learning will help to more efficiently calculate the 1D distribution of topological charge and the 4D topological charge density compared with MC simulation alone.

Analytical and Experimental Study on Complex Compressed Air Pipe Network

To analyze the working characteristics of complex compressed air networks, numerical methods are widely used which are based on finite element technology or intelligent algorithms. However, the effectiveness of the numerical methods is limited. In this paper, to provide a new method to optimize the design and the air supply strategy of the complex compressed air pipe network, firstly, a novel method to analyze the topology structure of the compressed air flow in the pipe network is initially proposed. A matrix is used to describe the topology structure of the compressed air flow. Moreover, based on the analysis of the pressure loss of the pipe network, the relationship between the pressure and the flow of the compressed air is derived, and a prediction method of pressure fluctuation and air flow in a segment in a complex pipe network is proposed. Finally, to inspect the effectiveness of the method, an experiment with a complex network is designed. The pressure and the flow of airflow in the network are measured and studied. The results of the study show that, the predicted results with the proposed method have a good consistency with the experimental results, and that verifies the air flow prediction method of the complex pipe network. This research proposes a new method to analyze the compressed air network and a prediction method of pressure fluctuation and air flow in a segment, which can predicate the fluctuation of the pressure according to the flow of compressed air, and predicate the fluctuation of the flow according to the pressure in a segment of a complex pipe network.

Vulnerability analysis of multimodal transport networks based on complex network theory

To explore the structural characteristics and vulnerability of multimodal transport networks,this study identifies the structural characteristics of a multimodal transport network on the basis of the complex network theory.Key nodes are clarified from the analysis of the structural characteristics.The characteristic path length and percentage of the largest subgraph are applied to analyze the vulnerability of the multimodal transport network after random and intentional attacks on the nodes.The network of a multimodal transport company is taken as an example in the empirical analysis.Results show that with more than ten nodes under a random attack,the percentage of the largest subgraph is less than 20%,and the characteristic path length is less than 2.The same performance is observed for more than seven nodes under an intentional attack.The multimodal transport network is more vulnerable under an international attack against key nodes.The results of the topology and node failure under random or intentional attacks would support the management of the multimodal transport network.Suggestions for the emergency transportation organization of enterprises under attacks are proposed accordingly.These suggestions should help improve network invulnerability and recovery from node failure.

T_2 Separation Subsets and T_2 Separateness in L-fuzzy Topological Spaces

The concept of α-CT2 separation L-fuzzy subsets in L-fuzzy topological spaces is presented by taking the stratiform structure of L-fuzzy subsets as the point of departure,and its basic characterizations and some topological properties are discussed,and the relation between it and other separateness is exposed,and the action is studied of α-CT2 separateness in N-compact spaces and N-paracompact spaces.

Prediction of preferential fluid flow in porous structures based on topological network models: Algorithm and experimental validation

The understanding and prediction of preferential fluid flow in porous media have attracted considerable attention in various engineering fields because of the implications of such flows in leading to a non-equilibrium fluid flow in the subsurface. In this study, a novel algorithm is proposed to predict preferential flow paths based on the topologically equivalent network of a porous structure and the flow resistance of flow paths. The equivalent flow network was constructed using Poiseuille's law and the maximal inscribed sphere algorithm. The flow resistance of each path was then determined based on Darcy's law. It was determined that fluid tends to follow paths with lower flow resistance. A computer program was developed and applied to an actual porous structure. To validate the algorithm and program, we tested and recorded two-dimensional(2 D) water flow using an ablated Perspex sheet featuring the same porous structure investigated using the analytical calculations. The results show that the measured preferential flow paths are consistent with the predictions.

Brain networks modeling for studying the mechanism underlying the development of Alzheimer’s disease

Alzheimer’s disease is a primary age-related neurodegenerative disorder that can result in impaired cognitive and memory functions.Although connections between changes in brain networks of Alzheimer’s disease patients have been established,the mechanisms that drive these alterations remain incompletely understood.This study,which was conducted in 2018 at Northeastern University in China,included data from 97 participants of the Alzheimer’s Disease Neuroimaging Initiative(ADNI)dataset covering genetics,imaging,and clinical data.All participants were divided into two groups:normal control(n=52;20 males and 32 females;mean age 73.90±4.72 years)and Alzheimer’s disease(n=45,23 males and 22 females;mean age 74.85±5.66).To uncover the wiring mechanisms that shaped changes in the topology of human brain networks of Alzheimer’s disease patients,we proposed a local naive Bayes brain network model based on graph theory.Our results showed that the proposed model provided an excellent fit to observe networks in all properties examined,including clustering coefficient,modularity,characteristic path length,network efficiency,betweenness,and degree distribution compared with empirical methods.This proposed model simulated the wiring changes in human brain networks between controls and Alzheimer’s disease patients.Our results demonstrate its utility in understanding relationships between brain tissue structure and cognitive or behavioral functions.The ADNI was performed in accordance with the Good Clinical Practice guidelines,US 21 CFR Part 50-Protection of Human Subjects,and Part 56-Institutional Review Boards(IRBs)/Research Good Clinical Practice guidelines Institutional Review Boards(IRBs)/Research Ethics Boards(REBs).

Optimal control of end-port glass tank furnace regenerator temperature based on artificial neural network

In the paper, an artificial neural network (ANN) method is put forward to optimize melting temperature control, which reveals the nonlinear relationships of tank melting temperature disturbances with secondary wind flow and fuel pressure, implements dynamic feed-forward complementation and dynamic correctional ratio between air and fuel in the main control system. The application to Anhui Fuyang Glass Factory improved the control character of the melting temperature greatly.

Fuzzy adaptive learning control network with sigmoid membership function

To get simpler operation in modified fuzzy adaptive learning control network （FALCON） in some engineering application, sigmoid nonlinear function is employed as a substitute of traditional Gaussian membership function. For making the modified FALCON learning more efficient and stable, a simulated annealing （SA） learning coefficient is introduced into learning algorithm. At first, the basic concepts and main advantages of FALCON were briefly reviewed. Subsequently, the topological structure and nodes operation were illustrated; the gradient-descent learning algorithm with SA learning coefficient was derived; and the distinctions between the archetype and the modification were analyzed. Eventually, the significance and worthiness of the modified FALCON were validated by its application to probability prediction of anode effect in aluminium electrolysis cells.