Design Optimization Formulation Research Articles

Progress and Opportunities for Machine Learning in Materials and Processes of Additive Manufacturing.

In recent years, there has been widespread adoption of machine learning (ML) technologies to unravel intricate relationships among diverse parameters in various additive manufacturing (AM) techniques. These ML models excel at recognizing complex patterns from extensive, well-curated datasets, thereby unveiling latent knowledge crucial for informed decision-making during the AM process. The collaborative synergy between ML and AM holds the potential to revolutionize the design and production of AM-printed parts. This review delves into the challenges and opportunities emerging at the intersection of these two dynamic fields. It provides a comprehensive analysis of the publication landscape for ML-related research in the field of AM, explores common ML applications in AM research (such as quality control, process optimization, design optimization, microstructure analysis, and material formulation), and concludes by presenting an outlook that underscores the utilization of advanced ML models, the development of emerging sensors, and ML applications in emerging AM-related fields. Notably, ML has garnered increased attention in AM due to its superior performance across various AM-related applications. It is envisioned that the integration of ML into AM processes will significantly enhance 3D printing capabilities across diverse AM-related research areas.

Enhancing seismic resilience of nonlinear structures through optimally designed additional mass dampers

Reducing dynamic responses in structures subjected to external excitations like earthquakes and strong winds is crucial for ensuring safety and serviceability. Conventional tuned mass dampers (CTMDs) have limitations in mitigating nonlinear vibrations efficiently. This research proposes the use of additional mass dissipation (AMD) devices to control nonlinear dynamic responses more effectively than CTMDs. The AMD concept involves installing an auxiliary mass–damper system atop the primary structure. An analytical approach is developed to determine the optimal design parameters of AMDs for linear and nonlinear single-degree-of-freedom systems using H2 and H∞ optimization techniques. Transfer function and harmonic balance methods are employed to evaluate the dynamic response reduction capabilities. Compared to optimally designed CTMDs, the proposed H2 and H∞ optimized AMDs demonstrate remarkably superior vibration mitigation achieving up to 77 % and 73.71 % greater reductions in dynamic responses, respectively. The Newmark-beta numerical validation confirms AMDs outperforming CTMDs by 16.06 % in minimizing structural vibrations. The novel AMD concept, coupled with the derived optimal design formulations, offers a highly effective vibration control strategy for both linear and nonlinear structural systems under harmonic and random excitations. This analytical solution paves the way for implementing AMDs in practice to enhance structural safety and longevity against external dynamic loads.

Effect of climate on the optimal sizing and operation of seasonal ice storage systems

Seasonal thermal storage systems can reduce the temporal mismatch between renewable energy availability and energy demand. Ice storage systems exhibit a non-linear behaviour in the heat exchange and storage processes, complicating the formulation of optimal design and operation problems. In this work, we propose a mixed-integer quadratically-constrained programming formulation, which minimizes the Levelized Cost of Energy for space heating and cooling, including sizing of a supporting PV array. The optimization was repeated for different storage volumes, finding the system optimal operation in each case –and thereby the optimal system sizing. The heating and cooling demands were computed from an archetypal office building, placed in three reference locations with cold and semi-arid, warm and humid continental, and temperate and humid continental climates. Results show that the optimal PV size decreases with growing ice storage volume, and an ice storage works best in a temperate continental climate, covering up to 47% of the cooling demand with a 250 m 3 storage.

Robust optimization of the design of monopropellant propulsion control systems using an advanced teaching-learning-based optimization method

This research proposes a novel approach for the robust optimization of the design of hydrogen peroxide propulsion control systems using the efficient and advanced Teaching-Learning-Based Optimization (TLBO) method. This study adopts a robust design optimization (RDO) formulation that considers both epistemic and aleatory uncertainties, including sparse points and interval data, and uses the Johnson distribution family for uncertainty representation. The maximum likelihood estimation method is applied to determine the distribution parameters, also considering interval data with a nested optimization technique. A novel advanced TLBO method with high accuracy and convergence rate is employed to optimization of this robust design approach. The method’s originality and advancement come from two categories of modifications to the original framework: the structure of the teaching and learning phases and the initialization and search approach. The efficacy and applicability of the proposed Ad-TLBO, respectively, were evaluated using benchmark problems from the CEC2020 competition and three real-world engineering problems, with a comparison to some recently published and the CEC competition’s top-ranked algorithms. The results and statistical analyses of the Quade test, Wilcoxon signed-rank test, and Friedman test show that the proposed Ad-TLBO method outperforms the other algorithms. The proposed optimization method is eventually applied to design a monopropellant propulsion system as the control actuator of a satellite orbital transfer system. It is found that the proposed advanced TLBO is effective in handling uncertainty in real design problems and improves both the convergence rate and accuracy of the optimization process.

Exploring the impact of excitation and structural response/performance modeling fidelity in the design of seismic protective devices

The design of seismic protective devices (SPDs), such as fluid viscous dampers (VDs), and inertial vibration absorbers (IVAs), requires the adoption of appropriate models for: (i) the earthquake excitation description (e.g. stochastic stationary/non-stationary versus recorded ground motions); (ii) the seismic structural response estimation (e.g. linear versus nonlinear/hysteretic); and (iii) the seismic performance quantification (e.g. average response versus risk-based performance description). This paper pursues a novel, detailed investigation of the impact of modeling fidelity in the design process of SPDs, by examining different combinations of models with different levels of sophistication for each of the aforementioned aspects. In this manner, a large model hierarchy is established, resulting in multiple SPD design variants. A bi-objective optimal design formulation is adopted, considering the structural vibration suppression (building performance) and device control forces as distinct, competing performance objectives (POs). Comprehensive comparisons are reported for a 3-storey and a 9-storey steel benchmark building, equipped with distributed VDs in all floors and with different types of single-device IVAs including the tuned-inerter-damper (TID), the tuned-mass-damper-inerter (TMDI) and the tuned-mass-damper (TMD). An innovative methodological approach is established to gauge the impact of the model fidelity by examining the deviation of POs achieved by lower fidelity SPD designs versus the Pareto-optimal fronts corresponding to POs consistent with the higher fidelity assumptions. The study overall stresses that that the use of lower fidelity models may provide sub-optimal performance in certain settings, and that comparison across the model hierarchy can be leveraged to obtain key insights of the SPD behavior. Additional key findings pertain to the robustness characteristics of the different type of SPDs to the modeling assumptions utilized for the device design.

Design Optimization of a Miniaturized Pneumatic Artificial Muscle and Experimental Validation

Miniaturized pneumatic artificial muscles (MPAMs) are widely utilized in various applications due to their unique characteristics, such as a high power-to-weight ratio, flexibility, and compatibility with the human environment, as well as being compact enough to fit within small-scale mechanical systems. Maximizing the amount of force generated by these actuators while keeping their dimensions minimized can greatly affect their efficiency. In this study, a formal design optimization problem was formulated to identify optimal sizes of MPAMs while maximizing their blocked force as a novel approach to address the issue of low force outputs of these actuators. A force model for an MPAM including various correction terms was derived to better predict the response behavior of the actuator. The optimization results reveal that an MPAM with a bladder that has an outer diameter of 6 mm and a thickness of 0.7 mm, as well as a braid angle of 72 degrees, can produce up to almost 239 N of blocked force if the inlet pressure is increased to 600 kPa. An MPAM with optimal parameters was subsequently fabricated and experimentally tested to evaluate its quasi-static response behavior and to validate the theoretical optimization results. Experimental tests were conducted under a wide range of pressures (0–300 kPa) to evaluate the variation of the generated blocked force versus inlet pressure. The overall error between the simulation and the experimental blocked forces was found to be less than 10%. This study represents a significant contribution to the design optimization of MPAMs, and the resulting optimal design offers potential applications in various fields, from soft robots to medical devices.

Swarm intelligence hybridized with genetic search in multi-objective design optimization under constrained-Pareto dominance

The inclusion of uncertainty in structural design optimization led to more complex design optimization formulations, where uncertainty quantification has significant influence on solution methods and computing times. Designs maintaining steady levels of performance, under uncertainty, are called robust and the combination of both robustness and performance optimality leads to a methodology called Robust Design Optimization (RDO). In this work a new approach to the RDO of angle-ply composite laminate structures is proposed. The key concept of this methodology is the hybridization between the principles of Particle Swarm Optimization and Genetic Algorithms, through the evolution of multiple populations based on local and global constrain-dominance. The RDO problem is here defined as the bi-objective minimization of the structural weight (optimality) and the determinant of the variance–covariance matrix (robustness) of the system’s response functionals, subject to stress and displacement constraints. A numerical structural design problem, representing a composite laminate engine hood shell, shows the capabilities of the proposed approach. Results display the good convergence properties of the proposed hybridizations both in the search and objective spaces.

Modeling and Design Optimization of an Electric Environmental Control System for Commercial Passenger Aircraft

The aircraft environmental control system (ECS) is the second-highest fuel consumer system, behind the propulsion system. To reduce fuel consumption, one research direction intends to replace conventional aircraft with more electric aircraft. Thus, new electric architectures have to be designed for each system, such as for the ECS. In this paper, an electric ECS is modeled and then sized and optimized for different sizing scenarios with the aim of minimizing fuel consumption at the aircraft level. For the system and for each component, such as air inlets and heat exchangers, parametric models are developed to allow the prediction of relevant characteristics. These models, developed in order to be adapted to aircraft design issues, are of different types, such as scaling laws and surrogate models. They are then assembled to build a preliminary sizing procedure for the ECS by using a multidisciplinary design analysis and optimization (MDAO) formulation. Results show that the ECS design is highly dependent on the sizing scenario considered. An approach to size the ECS globally with respect to all the sizing scenarios leads to an ECS that accounts for around 200 N of drag, 190 kW of electric power, and 1500 kg of mass for the CeRAS aircraft.

Single-Loop Multi-Objective Reliability-Based Design Optimization Using Chaos Control Theory and Shifting Vector with Differential Evolution

Multi-objective reliability-based design optimization (MORBDO) is an efficient tool for generating reliable Pareto-optimal (PO) solutions. However, generating such PO solutions requires many function evaluations for reliability analysis, thereby increasing the computational cost. In this paper, a single-loop multi-objective reliability-based design optimization formulation is proposed that approximates reliability analysis using Karush-Kuhn Tucker (KKT) optimality conditions. Further, chaos control theory is used for updating the point that is estimated through KKT conditions for avoiding any convergence issues. In order to generate the reliable point in the feasible region, the proposed formulation also incorporates the shifting vector approach. The proposed MORBDO formulation is solved using differential evolution (DE) that uses a heuristic convergence parameter based on hypervolume indicator for performing different mutation operators. DE incorporating the proposed formulation is tested on two mathematical and one engineering examples. The results demonstrate the generation of a better set of reliable PO solutions using the proposed method over the double-loop variant of multi-objective DE. Moreover, the proposed method requires 6×–377× less functional evaluations than the double-loop-based DE.

Determination of optimal potential parameters for the self-assembly of various lattice structures

We present a gradient-based optimization method that precisely designs simplified isotropic potentials for self-assembly of targeted lattice structures. An ansatz potential and its constraints are constructed to directly reflect the characteristics of a Bravais lattice for the target crystal, and the method is able to design the simplified potential systematically and smoothly. The potential is simplified with a Gaussian function in reciprocal space to minimize the information loss caused by Fourier transform in each design update. Design optimization formulation is derived using design sensitivity to relative entropy, employing a Fourier-Filtered Relative Entropy Minimization (FF-REM) formulation embedded in LAMMPS code to be used as an optimization tool. The potential obtained through this optimization method can successfully self-assemble low-coordinated crystals, such as square, triangle, honeycomb, and Kagome lattices, without further smoothing techniques. It turns out that completely removing the competitive alternative structures is an important condition for improving stability in self-assembling the target lattice in various density ranges.

Probabilistic framework for reliable optimal design of gearboxes in general-purpose industrial robots considering random use conditions

AbstractA vertically articulated robot with 6-degrees of freedom (DoF), called a general-purpose robot, can perform a myriad of different tasks within a workspace. This paper newly presents a probabilistic framework for the reliable optimal design of gearboxes used in general-purpose industrial robots, which considers random use conditions. To account for random use conditions, the start and end positions of a single motion profile are described as the random variable, which is statistically modeled as a uniform distribution based on the assumption that we have no information about the robot use pattern. Then, each sample of the random variable is converted to the corresponding motion profile by using an on-line trajectory planner. Monte Carlo simulation is implemented for the uncertainty propagation analysis, due to the heuristic feature of the on-line trajectory planner. In the design optimization formulation, the peak torque constraint and maximum bending moment constraint are described in a probabilistic manner. The system-level lifetime is calculated by combining component scale factors. The effectiveness of the proposed framework is demonstrated by examining a case study of a gearbox size problem for a 6-DoF serial industrial robot. The benefits of this study are as follows: Firstly, the proposed framework can evaluate the performance considering random use conditions. Secondly, torque reliability and bending moment reliability are newly proposed to ensure the dynamic performance of an industrial robot. Thirdly, the system-level lifetime by combining component scale factors gives more user-oriented and intuitive measure in an industrial robot design.

An augmented formulation for robust design optimization of structures using stochastic simulation method

An augmented formulation for robust design optimization of structures using stochastic simulation method

Probabilistic Digital Twin for Additive Manufacturing Process Design and Control

Abstract This paper proposes a detailed methodology for constructing an additive manufacturing (AM) digital twin for the laser powder bed fusion (LPBF) process. An important aspect of the proposed digital twin is the incorporation of model uncertainty and process variability. A virtual representation of the LPBF process is first constructed using a physics-based model. To enable faster computation required in uncertainty analysis and decision-making, the physics-based model is replaced by a cheaper surrogate model. A two-step surrogate model is proposed when the quantity of interest is not directly observable during manufacturing. The data collected from the monitoring sensors are used for diagnosis (of current part quality) and passed on to the virtual representation for model updating. The model updating consists of Bayesian calibration of the uncertain parameters and the discrepancy term representing the model prediction error. The resulting digital twin is thus tailored for the particular individual part being produced and is used for probabilistic process parameter optimization (initial, before starting the printing) and online, real-time adjustment of the LPBF process parameters, in order to control the porosity in the manufactured part. A robust design optimization formulation is used to minimize the mean and standard deviation of the difference between the target porosity and the predicted porosity. The proposed methodology includes validation of the digital twin in two stages. Validation of the initial model in the digital twin is performed using available data, whereas data collected during manufacturing are used to validate the overall digital twin.

Explainable machine learning in image classification models: An uncertainty quantification perspective

The poor explainability of deep learning models has hindered their adoption in safety and quality-critical applications. This paper focuses on image classification models and aims to enhance the explainability of deep learning models through the development of an uncertainty quantification-based framework. The proposed methodology consists of three major steps. In the first step, we adopt dropout-based Bayesian neural network to characterize the structure and parameter uncertainty inherent in deep learning models, propagate and represent such uncertainties to the model prediction as a distribution. Next, we employ entropy as a quantitative indicator to measure the uncertainty in model prediction, and develop an Empirical Cumulative Distribution Function (ECDF)-based approach to determine an appropriate threshold value for the purpose of deciding when to accept or reject the model prediction. Secondly, in the cases with high model prediction uncertainty, we combine the prediction difference analysis (PDA) approach with dropout-based Bayesian neural network to quantify the uncertainty in pixel-wise feature importance, and identify the locations in the input image that highly correlate with the model prediction uncertainty. In the third step, we develop a robustness-based design optimization formulation to enhance the relevance between input features and model prediction, and leverage a differential evolution approach to optimize the pixels in the input image with high uncertainty in feature importance. Experimental studies in MNIST and CIFAR-10 image classifications are included to demonstrate the effectiveness of the proposed approach in increasing the explainability of deep learning models.

Design of shell and tube heat exchangers considering the interaction of fouling and hydraulics

AbstractWe extend a formulation of the heat exchanger design optimization with fouling modeling to consider the effect of fouling on hydraulics. A shell‐side fouling model was added so the optimization can consider cases with fouling in the tube and shell sides. The focus is the design of heat exchangers with fouling behavior associated with a threshold model, like in crude preheat trains. We solve the optimization problem by using a newly proposed Set Trimming technique. We compare our results with the traditional approach of using fixed fouling factors and the previous approach of not considering the hydraulic impact of fouling. We conclude that considering the deposit thickness leads to more realistic results that are different than the ones obtained using the previous approaches. Moreover, we show that previous approaches can render designs with larger pressure drops than the maximum imposed by the constraints, as well as exchangers with higher areas.

Multi-Objective Optimization Under Uncertainty of Part Quality in Fused Filament Fabrication

Abstract This work presents a data-driven methodology for multi-objective optimization under uncertainty of process parameters in the fused filament fabrication (FFF) process. The proposed approach optimizes the process parameters with the objectives of minimizing the geometric inaccuracy and maximizing the filament bond quality of the manufactured part. First, experiments are conducted to collect data pertaining to the part quality. Then, Bayesian neural network (BNN) models are constructed to predict the geometric inaccuracy and bond quality as functions of the process parameters. The BNN model captures the model uncertainty caused by the lack of knowledge about model parameters (neuron weights) and the input variability due to the intrinsic randomness in the input parameters. Using the stochastic predictions from these models, different robustness-based design optimization formulations are investigated, wherein process parameters such as nozzle temperature, nozzle speed, and layer thickness are optimized under uncertainty for different multi-objective scenarios. Epistemic uncertainty in the prediction model and the aleatory uncertainty in the input is considered in the optimization. Finally, Pareto surfaces are constructed to estimate the tradeoffs between the objectives. Both the BNN models and the effectiveness of the proposed optimization methodology are validated using the actual manufacturing of the parts.

Jaya algorithm for design optimization of planar steel frames

An efficient metaheuristic optimization method called Jaya Algorithm (JA) has gained wide acceptance among optimization researchers in various engineering problems recently. The main feature of JA is that it does not use algorithm-specific parameters and has a very simple formulation based on the concept of approaching the best solution and moving away from the worst solution. This study presents the JA formulation for design optimization of planar steel frames under strength and displacement constraints. The validity of JA is investigated by solving two benchmark design examples. The results demonstrated the superiority of JA over other state-of-the-art metaheuristic optimization methods in terms of optimized weight, number of structural analyses and several statistical parameters.

A Reliability-Based Formulation for Simulation-Based Control Co-Design Using Generalized Polynomial Chaos Expansion

Abstract Combined plant and control design (control co-design (CCD)) methods are often used during product development to address the synergistic coupling between the plant and control parts of a dynamic system. Recently, a few studies have started applying CCD to stochastic dynamic systems. In their most rigorous approach, reliability-based design optimization (RBDO) principles have been used to ensure solution feasibility under uncertainty. However, since existing reliability-based CCD (RBCCD) algorithms use all-at-once formulations, only most-probable-point (MPP) methods can be used as reliability analysis techniques. Though effective for linear/quadratic RBCCD problems, the use of such methods for highly nonlinear RBCCD problems introduces solution error that could lead to system failure. A multidisciplinary feasible (MDF) formulation for RBCCD problems would eliminate this issue by removing the dynamic equality constraints and instead enforcing them through forward simulation. Since the RBCCD problem structure would be similar to traditional RBDO problems, any of the well-established reliability analysis methods could be used. Therefore, in this work, a novel reliability-based MDF formulation of multidisciplinary dynamic system design optimization has been proposed for RBCCD. To quantify the uncertainty propagated by the random decision variables, Monte Carlo simulation has been applied to the generalized polynomial chaos expansion of the probabilistic constraints. The proposed formulation is applied to two engineering test problems, with the results indicating the effectiveness of both the overall formulation as well as the reliability analysis technique for RBCCD.

Analysis, optimization and control of an adaptive tuned vibration absorber featuring magnetoactive materials

Excessive vibration may cause premature fatigue failure on structural components if it is not properly controlled. One effective way to attenuate vibration is to attach a tuned vibration absorber to the main structural component. Passive tuned vibration absorbers are mainly effective to attenuate vibration at a specific range of frequencies and thus they become infective under varied environmental conditions which can significantly alter the tuning frequencies. The present study aims at development of a wide-bandwidth and light-weight adaptive tuned vibration absorber (ATVA) featuring a magnetorheological elastomer (MRE) which is tuned to absorb the vibrations of a flexible beam. The accelerance transfer function is derived for both beam with and without ATVA. The effectiveness of the ATVA to control vibration of the flexible beam caused by external excitation under wide range of frequencies is demonstrated. The proposed ATVA consists of C-Shape frame with winding coils, two isometric MRE specimens with 40% volume fraction, and active mass. An empirical model for the MRE has been developed through an experimental identification method in order to predict the MRE's elastic modulus under various levels of excitation frequencies and applied magnetic fields. Using MRE models and magneto-circuit analysis, the frequency bandwidth of the ATVA is analytically obtained. The analytical model is then used to develop a multidisciplinary design optimization formulation to minimize the mass and maximize the frequency bandwidth of an ATVA featuring MRE given several geometrical and physical constraints. Finally, a tuning algorithm has been presented to determine the required applied magnetic flux density to the MRE layers based on the identified phase difference between the absolute acceleration of the host and relative acceleration of the host and ATVA's resonator.

Kinematic Analysis and Optimal Design of a Novel Schönflies-Motion Parallel Manipulator With Rotational Pitch Motion for Assembly Operations

Abstract This paper presents a novel Schönflies-motion Parallel Manipulator with RotationalPitch motion (SPM-RP) based on a single-platform fully parallel mechanism. An analysis of the position, workspace, velocity, and singularity of the SPM-RP is carried out in detail, and a dimensionless Jacobian is proposed to evaluate the manipulability of the SPM-RP. The analysis shows that the SPM-RP is with position-decoupled kinematics, a large singularity-free workspace, and excellent manipulability. The SPM-RP is actuated by four parallel prismatic actuators, enabling the manipulator to provide the identical kinematic performance at all generic cross sections perpendicular to the prismatic joint axes within its workspace. This paper thus proposes a reduced design optimization formulation, where the traditional optimization over the entire workspace is reduced to the optimization on a representative workspace cross section of the SPM-RP. According to this approach, the design optimization of the SPM-RP is carried out by maximizing its manipulability over the total orientation workspace, which is crucial for precision assembly. Based on the achieved optimal design, an SPM-RP prototype is developed. The mobility, orientation capability, total orientation workspace, and repeatability of the optimal design are tested and verified by the developed SPM-RP prototype. Experiments show that the SPM-RP can achieve a large total orientation workspace with excellent precision performance.