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Structural and Multidisciplinary Optimization
Journal Prestige (SJR): 1.458
Citation Impact (citeScore): 3
Number of Followers: 12  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1615-1488 - ISSN (Online) 1615-147X
Published by Springer-Verlag Homepage  [2467 journals]
  • Multi-objective robust optimization using adaptive surrogate models for
           problems with mixed continuous-categorical parameters

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      Abstract: Explicitly accounting for uncertainties is paramount to the safety of engineering structures. Optimization which is often carried out at the early stage of the structural design offers an ideal framework for this task. When the uncertainties are mainly affecting the objective function, robust design optimization is traditionally considered. This work further assumes the existence of multiple and competing objective functions that need to be dealt with simultaneously. The optimization problem is formulated by considering quantiles of the objective functions which allows for the combination of both optimality and robustness in a single metric. By introducing the concept of common random numbers, the resulting nested optimization problem may be solved using a general-purpose solver, herein the non-dominated sorting genetic algorithm (NSGA-II). The computational cost of such an approach is however a serious hurdle to its application in real-world problems. We therefore propose a surrogate-assisted approach using Kriging as an inexpensive approximation of the associated computational model. The proposed approach consists of sequentially carrying out NSGA-II while using an adaptively built Kriging model to estimate the quantiles. Finally, the methodology is adapted to account for mixed categorical-continuous parameters as the applications involve the selection of qualitative design parameters as well. The methodology is first applied to two analytical examples showing its efficiency. The third application relates to the selection of optimal renovation scenarios of a building considering both its life cycle cost and environmental impact. It shows that when it comes to renovation, the heating system replacement should be the priority.
      PubDate: 2022-12-01
       
  • Single-objective aerodynamic optimization of a streamlined bridge deck
           subjected to shape modification using a polynomial emulator and genetic
           algorithm

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      Abstract: Traditional approach based on wind tunnel tests used in bridge wind-resistant design is no more efficient since long-span bridges require an iterative process involving multiple design variables and processes. To ease the design process, scholars have proposed aerodynamic shape optimization based on the Kriging surrogate model. Despite the prowess of the Kriging model, it is accurate only when using high-fidelity data (experimental or Large Eddy Simulation data) and is not suitable for noisy datasets, making this model costly and hindering its practical use. To tackle this issue, the present study proposed a polynomial surrogate combined with a genetic algorithm to determine the optimal shape of a streamlined bridge deck cross-section. First, a uniform sampling plan considering 57 different geometries was generated. Then, the polynomial surrogate was used to predict the aerodynamic coefficients and the flutter velocity based on the dataset obtained from the unsteady Reynolds-average Navier–Stokes computational fluid dynamics simulations. The accuracy of the surrogate model is evaluated using error metrics, such as the sum-squared error, R-squared, and the root mean squared error. The results obtained from the statistical metrics demonstrate that the proposed polynomial surrogate provides an accurate prediction of the force coefficients and their derivatives, as well as the critical flutter velocity. A benchmark example is used to demonstrate the efficiency of the proposed model. Finally, a genetic algorithm was introduced to determine an optimal shape, and the results demonstrate that the proposed optimization framework can improve the design process remarkably.
      PubDate: 2022-11-30
       
  • Metamaterials design with a desired thermal expansion using a
           multi-material BESO method

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      Abstract: The use of computational evolutionary strategies in the design of metamaterials with desired thermal expansion coefficients is uncommon due to the discrete nature of the design variables. This work presents a Bi-directional Evolutionary Structural Optimization (BESO) based methodology for designing orthotropic metamaterials with a specific thermal expansion coefficient using an objective function considering only the thermal expansion coefficients, with no constraints on geometry or stiffness. Topologies of the metamaterials, composed of two material phases and a void, are obtained using a material interpolation between neighboring material phases and three easy-to-implement numerical strategies to stabilize the evolutionary process. Two are on the sensitivity calculation and one is on the addition ratio’s value. The strategies applied to the sensitivity numbers are proposed to avoid the positive and negative values of the elemental sensitivity numbers and the element change between no neighboring materials. Additionally, the addition ratio’s value reduction strategy assures the convergence of the thermal expansion properties to the desired value. The homogenization method is used to obtain the equivalent thermal expansion properties of the designed materials. Some numerical examples are presented to show the potential and effectiveness of the proposed methodology.
      PubDate: 2022-11-30
       
  • Scenario-based multidisciplinary optimization for a new accelerated life
           testing of electric traction motor and inverter system

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      Abstract: With the electrification of automobiles, the importance of an electric traction motor and inverter system is increasing. Durability and reliability tests are crucial in the development process of electric vehicle (EV) systems. To reduce the time and cost of durability and reliability tests, accelerated life testing (ALT) that applies high-stress conditions in a short time needs to be carried out. Because the electric traction motor and inverter system have been combined as vehicles have become smaller, it is necessary to concurrently test these parts. This study proposes a scenario-based multidisciplinary optimization (SBMO) method to develop a new ALT that simultaneously assesses the mechanical damage to the electric traction motor and the electrical damage to the inverter system. First, four driving scenarios for the ALT are extracted by analyzing the driving conditions of various field tests. Second, a methodology for EV modeling and lifespan prediction of the electric traction motor and inverter system based on the analytical mechanics is proposed. Third, discrete scenario variables corresponding to the four driving scenarios are defined. Fourth, a new SBMO problem is formulated to generate a new ALT. The test requirements of an ALT are reflected in the SBMO constraints to be employed in the development of EVs. Finally, a genetic algorithm is used to solve the SBMO problem. The SBMO successfully obtains the optimum ALT cycle satisfying the test requirements for designing an electric traction motor and inverter system in the early design stage.
      PubDate: 2022-11-28
       
  • Multi-material topology optimization using Wachspress interpolations for
           designing a 3-phase electrical machine stator

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      Abstract: This work uses multi-material topology optimization (MMTO) to maximize the average torque of a 3-phase permanent magnet synchronous machine (PMSM). Eight materials are considered in the stator: air, soft magnetic steel, three electric phases, and their three returns. To address the challenge of designing a 3-phase PMSM stator, a generalized density-based framework is used. The proposed methodology places the prescribed material candidates on the vertices of a convex polytope, interpolates material properties using Wachspress shape functions, and defines Cartesian coordinates inside polytopes as design variables. A rational function is used as penalization to ensure convergence towards meaningful structures, without the use of a filtering process. The influences of different polytopes and penalization parameters are investigated. The results indicate that a hexagonal-based diamond polytope is a better choice than the classical orthogonal domains for this MMTO problem. In addition, the proposed methodology yields high-performance designs for 3-phase PMSM stators by implementing a continuation method on the electric load angle.
      PubDate: 2022-11-28
       
  • A comprehensive review of digital twin — part 1: modeling and twinning
           enabling technologies

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      Abstract: As an emerging technology in the era of Industry 4.0, digital twin is gaining unprecedented attention because of its promise to further optimize process design, quality control, health monitoring, decision and policy making, and more, by comprehensively modeling the physical world as a group of interconnected digital models. In a two-part series of papers, we examine the fundamental role of different modeling techniques, twinning enabling technologies, and uncertainty quantification and optimization methods commonly used in digital twins. This first paper presents a thorough literature review of digital twin trends across many disciplines currently pursuing this area of research. Then, digital twin modeling and twinning enabling technologies are further analyzed by classifying them into two main categories: physical-to-virtual, and virtual-to-physical, based on the direction in which data flows. Finally, this paper provides perspectives on the trajectory of digital twin technology over the next decade, and introduces a few emerging areas of research which will likely be of great use in future digital twin research. In part two of this review, the role of uncertainty quantification and optimization are discussed, a battery digital twin is demonstrated, and more perspectives on the future of digital twin are shared. Code and preprocessed data for generating all the results and figures presented in the battery digital twin case study in part 2 of this review are available on Github.
      PubDate: 2022-11-28
       
  • An adaptive ensemble of surrogate models based on heuristic model
           screening

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      Abstract: Ensembles of surrogate models have received increasing attention due to their more robust performance than that of individual surrogate models (ISMs) in the face of different problems. In this work, a novel adaptive ensemble of surrogate models based on heuristic model screening (AE-HMS) is proposed. First, a performance index (PI) combining a distance measure (DM) and cross validation (CV) is employed to determine the performance of the ISMs. Second, a heuristic model screening method based on the PI is used to select acceptable ISMs and eliminate poor ISMs. Compared with previous model screening methods, the proposed heuristic model screening method can better eliminate ISMs with poor performance. Finally, the weight factor of the baseline model (the ISM with the smallest PI) is adaptively allocated according to its PI, and the weight factors of the other ISMs are calculated in a point-by-point manner to complete the ensemble construction process. Based on this process and three representative DMs, three variations of the AE-HMS are proposed. A total of 42 test functions are used to select the appropriate AE-HMS hyperparameters and evaluate its accuracy and robustness. The results show that the AE-HMS has higher accuracy and stronger robustness than the ISMs and other ensembles. More importantly, the same results are obtained in an optimization problem concerning a safety valve, indicating that this model can provide an effective design optimization method for engineering problems.
      PubDate: 2022-11-24
       
  • Wing jig shape optimisation with gradient-assisted metamodel building in a
           trust-region optimisation framework

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      Abstract: Significant computational resources are required to obtain an optimised wing jig shape by solving a high-fidelity large-scale aero-structural design optimisation problem. Gradient-based methods are efficient; however, some of the features of real-life engineering problems including numerical noise that pollutes the function values and occurrences of failed evaluations in the optimisation may limit their performance. To address these issues, this paper presents the latest developments in the multipoint approximation method (MAM) based on a gradient-assisted metamodel assembly technique within a trust-region optimisation framework. The proposed method is tested by a benchmark case first, and then, an aircraft wing jig shape optimisation problem is offered to demonstrate its performance. The gradient-based optimisation is used as a benchmark case, and the metamodel-based optimisation utilises the latest developments in MAM to solve the same problem. The results show that the proposed method can achieve the same design goal as the gradient-based method but with enhanced robustness and efficient performance. In the wing jig shape optimisation, the difference in the design objective, the global equivalent drag coefficient, between the two aforementioned optimisation approaches is 0.20 counts, whose relative difference is approximately 0.10%. Three approximate sub-optimisations have been conducted in every iteration of the metamodel-based optimisation to reduce the possibility of local optimality, while the overall elapsed time of the metamodel-based optimisation is approximately 1.98 times that of one gradient-based optimisation, which confirms the competitiveness of the proposed method bearing in mind the added safeguards for numerical noise, failed evaluations and possible local optimality.
      PubDate: 2022-11-24
       
  • Health index construction with feature fusion optimization for predictive
           maintenance of physical systems

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      Abstract: In any prognostics and health management framework, the key to accurate remaining useful life prediction is finding a signal that directly quantifies the health status of a physical asset. When a direct measurement of an asset’s health is not available, researchers and practitioners develop virtual health indices, fused from many different signals, to quantify a unit’s health status. However, current metrics and methods used to engineer virtual health indices struggle to deal with large signal noises and do not consider health index performance on a population of units wholistically. In response to these challenges, we propose a new trend metric, which more accurately quantifies the monotonicity of a signal in the presence of noise, as well as a new probabilistic method, called meta-probability, for comparing health indices across a population of units to better understand the unit-to-unit variation in health index performance. To demonstrate the utility of our proposed trend metric and probabilistic comparison tool, we formulate a multi-objective optimization problem with the goal of creating the best virtual health index across a population of units by fusing many sensor signals and derived features. The proposed metrics and optimization scheme are evaluated in two case studies considering rolling element bearing run-to-failure data. The proposed optimization method, which considers the newly proposed monotonicity metric as one of the objectives, is found to create a health index that is more optimal for a larger percentage of the units in the population than five existing health index construction methodologies reported in the literature.
      PubDate: 2022-11-23
       
  • An adaptive and scalable artificial neural network-based
           model-order-reduction method for large-scale topology optimization designs
           

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      Abstract: Topology optimization (TO) provides a systematic approach for obtaining structure design with optimum performance of interest. However, the process requires the numerical evaluation of the objective function and constraints at each iteration, which is computationally expensive, especially for large-scale designs. Deep learning-based models have been developed to accelerate the process either by acting as surrogate models replacing the simulation process, or completely replacing the optimization process. However, most of them require a large set of labelled training data, which is generated mostly through simulations. The data generation time scales rapidly with the design size, decreasing the efficiency of the method itself. Another major issue is the weak generalizability of deep learning models. Most models are trained to work with the design problem similar to that used for data generation and require retraining if the design problem changes. In this work an adaptive, scalable deep learning-based model-order-reduction method is proposed to accelerate large-scale TO process, by utilizing MapNet, a neural network which maps the field of interest from coarse-scale to fine-scale. The proposed method allows for each simulation of the TO process to be performed at a coarser mesh, thereby greatly reducing the total computational time. More importantly, a crucial element, domain fragmentation, is introduced and integrated into the method, which greatly improves the transferability and scalability of the method. It has been demonstrated that the MapNet trained using data from one cantilever beam design with a specific loading condition can be directly applied to other structure design problems with different domain shapes, sizes, boundary and loading conditions.
      PubDate: 2022-11-23
       
  • Seismic fragility analysis of deteriorated bridge structures employing a
           UAV inspection-based updated digital twin

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      Abstract: Aging bridges require regular inspection due to performance deterioration. For this purpose, numerous researchers have considered the use of unmanned aerial vehicle (UAV) systems for structural health monitoring and inspection. However, present UAV-based inspection methods only represent the type and extent of external damage, but does not assess the seismic performance. In this study, a seismic fragility analysis of deteriorated bridges employing a UAV inspection-based updated digital twin is proposed. The proposed method consists of two phases: (1) bridge condition assessment using UAV inspection for updating the digital twin and (2) seismic fragility analysis based on the updated digital twin. To update the digital twin, the bridge damage grade is assigned based on the UAV inspection, and subsequently, the corresponding damage index is calculated. The damage index is utilized as a percentage reduction in the stiffness of finite element (FE) model, based on a previously proposed research. Using the updated digital twin, the seismic fragility analysis is conducted with different earthquake motions and magnitudes. To demonstrate the proposed method, an inservice pre-stressed concrete box bridge is examined. In particular, the seismic fragility curves of deteriorated bridges are compared with those of intact bridges. The numerical results show that the maximum failure probability of the deteriorated bridges is 3.6% higher than that of intact bridges. Therefore, the proposed method has the potential to updated the digital twin effectively using UAV inspection, allowing for seismic fragility analysis of deteriorated bridges to be conducted.
      PubDate: 2022-11-22
       
  • Crashworthiness optimization of thin-walled tube structures with
           tailor-welded blank using targeting force–displacement method

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      Abstract: Tailor-welded blank (TWB), one of the representative technologies in the modern manufacturing process, has the vast applied foreground in energy absorbers of automotive industries due to its significant advantages in better load-bearing capacity and lightweight. The mechanical performance of TWB structures is closely related to its thickness distribution and its location of weld lines. However, so far good algorithm has not been developed to design TWB structure considering concurrently these two aspects due to the time-consuming nature of impact dynamics and the complexity of TWB structure. To find its optimal thickness distribution and optimal location of weld lines, an optimization strategy is proposed to improve crashworthiness of the TWB structures. Firstly, the target force–displacement method is used to find thickness distribution of initial structures. Then, a finite element modeling technology of TWB developed to obtain the finite element model of TWB structures is automatically converted from that of the initial structures according to the results of the fore step. Finally, set uniform thicknesses constraint and find optimal thickness distribution of the TWB structure by using TFD method again. Compared with the existing methods, the proposed method comprehensively considers two important design objectives of TWB structures. Numerical results demonstrate the effectiveness of this method because it can obtain thickness distribution and location of weld lines of the TWB structure, and tailor the force–displacement response of the designed structure to closer a targeting force–displacement curve.
      PubDate: 2022-11-22
       
  • An application of dependent Kriging combined with spherical decomposition
           sampling for the system reliability analysis of flap mechanism

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      Abstract: Reliability analysis for complex systems is a challenging problem, because of complex failure regions and frequently time-consuming simulations. Especially for complex systems with extremely rare events, it is of great significance to evaluate the reliability efficiently and accurately. Therefore, a novel reliability analysis method that combines the dependent Kriging method and adaptive spherical decomposition sampling for the rare event is proposed in this work to solve these problems. It makes full use of the mean and variance information of the Kriging predicted responses and the covariance information between the responses. In addition, the stopping criterion is directly related to the accuracy of failure probability rather than the accuracy of model construction. Furthermore, spherical decomposition sampling is used to estimate the small failure probability and improve sampling efficiency. Three test examples are presented to illustrate the accuracy and efficiency of the proposed method. Meanwhile, the flap motion mechanism is used as the research object to verify the application of the proposed method.
      PubDate: 2022-11-21
       
  • Thermo-elastic topology optimization of continuum structures subjected to
           load allocation constraints

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      Abstract: This paper is aimed to develop a load allocation topology optimization approach to meet the design requirement of thermo-elastic structures in engineering practice. To formulate the optimization problem, load allocation constraint is proposed by constraining the ratio of considered reaction forces to a proper range. The average displacement at the prescribed region is taken as the objective function. Based on the adjoint method, sensitivity analyses of the average displacement and the load allocation constraint are carried out and used in combination with the gradient-based algorithm. Numerical examples are presented to demonstrate the validity of the proposed approach. Comparisons are made with solutions of standard topology optimization to highlight the coupling effect between the load allocation constraint and the temperature field.
      PubDate: 2022-11-21
       
  • 3D shape optimization of loudspeaker cabinets for uniform directivity

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      Abstract: This paper presents a method to perform gradient-based shape optimization to minimize the root mean square deviation of the exterior acoustic sound pressure level distribution in front of an initially spherically shaped loudspeaker. The work includes several examples of how different multi-frequency optimization strategies can affect the final optimized design performance. This includes testing, averaging, and weighting of multi-frequency cost functions or using a minimax formulation. The shape optimization technique is based on an acoustic Boundary Element Method coupled to a Lumped Parameter loudspeaker model. To control and alter the deformation of the loudspeaker cabinet the optimization method adapts a spherical free-form deformation approach based on Bernstein polynomials. For the particular optimization problems presented, it is shown that improvements in the root mean square deviation of the sound pressure level in front of the loudspeaker can be achieved between 1 and 5 kHz. In the best-case scenario, less than a 1 dB sound pressure level (SPL) variation is observed between on-axis and a 70° off-axis response in the range 2 to 5 kHz. The widest frequency bandwidth and smoothest response of the root mean square deviation is found by utilizing the minimax formulation.
      PubDate: 2022-11-19
       
  • Correction: MILP-based discrete sizing and topology optimization of truss
           structures: new formulation and benchmarking

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      PubDate: 2022-11-17
       
  • Correction: An efficient 137-line MATLAB code for geometrically nonlinear
           topology optimization using bi-directional evolutionary structural
           optimization method

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      PubDate: 2022-11-17
       
  • Multi-fidelity neural optimization machine for Digital Twins

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      Abstract: Digital Twins (DTs) are widely used for design, manufacturing, prognostics, and decision support for operations. One critical challenge in optimizing DTs usually involves multi-fidelity (MF) models and data, such as multi-resolution computational simulation and experimental testing. The MF strategies provide advantages of high accuracy with low computational and experimental cost in DTs. A novel MF optimization framework is proposed in this paper to demonstrate and validate its potential application in DTs. First, MF data aggregation using convolutional neural networks (MDACNN) is introduced to integrate low-fidelity (LF) and high-fidelity (HF) models and data. It can fully utilize the LF data to learn the relationship across multiple fidelities. With MDACNN, predictions can be made with high accuracy compared to HF models. Next, MDACNN is integrated into the neural optimization machine (NOM), an optimization framework based on NNs. NOM is explicitly designed for optimizing NN objective functions based on the stochastic gradient descent method. The integrated model is named MF neural optimization machine (MFNOM). A numerical example is presented to illustrate the procedure of implementing MFNOM. Two engineering applications are presented for both MF simulation models and experimental data. The first problem focuses on the multi-resolution finite element simulation for structures and materials. Coarse and fine meshes are applied for simulation. The properties of multi-phase heterogeneous materials are optimized to minimize the stress in the simulation domain. The second problem investigates the internal defects in additively manufacturing. Low/high resolution and full/partial field scanning data are utilized to build DTs. MFNOM is used to design pore size and orientation to reduce the risk caused by irregular pores.
      PubDate: 2022-11-16
       
  • Topology optimization of stationary fluid–structure interaction problems
           including large displacements via the TOBS-GT method

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      Abstract: This paper addresses the topology optimization of fluid–structure interaction (FSI) systems considering large displacements. We consider the steady-state analysis of flexible structures in contact with a fluid flow governed by the incompressible Navier–Stokes equations. The optimization method used in this work considers the physical analysis and optimization module in a decoupled form. The decoupled analysis allows the finite element problem to be meshed and solved accordingly to the physics requirements. Optimized geometry is constructed by reading and trimming out from an optimization grid described by a set of binary \(\{0,1\}\) design variables. The method is so-called TOBS (Topology Optimization of Binary Structures) with geometry trimming (TOBS-GT). Displacements are resolved using an elastic formulation with geometrical nonlinearities to allow for large deformations. The FSI system is solved by using finite elements and the Arbitrary Lagrangian–Eulerian (ALE) method. Low Reynolds numbers are assumed. The sensitivities are calculated using semi-automatic differentiation and interpolated to optimization grid points. In order to consider large displacements, a mapping between material and spatial coordinates is used to identify and track the deformed configuration of the structure. The optimized binary topology is found by using the standard TOBS approach (Sivapuram and Picelli in Finite Elem Anal Des 139:49–61, 2018) based on sequential integer linear programming. Numerical examples show that the TOBS-GT method can be effectively applied to design 2D and 3D structures in FSI problems including nonlinear structural responses.
      PubDate: 2022-11-15
       
  • Non-probabilistic reliability-based topology optimization against loading
           uncertainty field with a bounded field model

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      Abstract: This paper presents a non-probabilistic reliability-based topology optimization under the distributed loading uncertainty, in which the loading uncertainty is described as the non-probability bounded field model. The reliability-based optimization model is a nested optimization process, in which the inner-loop optimization problem is to evaluate the structural reliability under the loading field uncertainty. Based on material-field series-expansion (MFSE) optimization method, the outer-loop optimization problem is expressed as determining the optimum structural topology that minimizes structural volume under the non-probability reliability index constraint. The nested optimization problem is solved via a gradient-based optimization algorithm. To reduce the computational cost of the optimization model, the concerned performance approach is employed to transform the non-probabilistic reliability-based optimization model equivalently. Three numerical examples considering uncertain loading field (including 2D and 3D structures) are given to illustrate the validity of the proposed method.
      PubDate: 2022-11-15
       
 
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