Model-based Optimization Method Research Articles

Artificial neural network-based control of powered knee exoskeletons for lifting tasks: design and experimental validation

Abstract This study introduces a hybrid model that utilizes a model-based optimization method to generate training data and an artificial neural network (ANN)-based learning method to offer real-time exoskeleton support in lifting activities. For the model-based optimization method, the torque of the knee exoskeleton and the optimal lifting motion are predicted utilizing a two-dimensional (2D) human–exoskeleton model. The control points for exoskeleton motor current profiles and human joint angle profiles from cubic B-spline interpolation represent the design variables. Minimizing the square of the normalized human joint torque is considered as the cost function. Subsequently, the lifting optimization problem is tackled using a sequential quadratic programming (SQP) algorithm in sparse nonlinear optimizer (SNOPT). For the learning-based approach, the learning-based control model is trained using the general regression neural network (GRNN). The anthropometric parameters of the human subjects and lifting boundary postures are used as input parameters, while the control points for exoskeleton torque are treated as output parameters. Once trained, the learning-based control model can provide exoskeleton assistive torque in real time for lifting tasks. Two test subjects’ joint angles and ground reaction forces (GRFs) comparisons are presented between the experimental and simulation results. Furthermore, the utilization of exoskeletons significantly reduces activations of the four knee extensor and flexor muscles compared to lifting without the exoskeletons for both subjects. Overall, the learning-based control method can generate assistive torque profiles in real time and faster than the model-based optimal control approach.

ROM-based stochastic optimization for a continuous manufacturing process

This paper proposes a model-based optimization method for the production of automotive seals in an extrusion process. The high production throughput, coupled with quality constraints and the inherent uncertainty of the process, encourages the search for operating conditions that minimize nonconformities. The main uncertainties arise from the process variability and from the raw material itself. The proposed method, which is based on Bayesian optimization, takes these factors into account and obtains a robust set of process parameters. Due to the high computational cost and complexity of performing detailed simulations, a reduced order model is used to address the optimization. The proposal has been evaluated in a virtual environment, where it has been verified that it is able to minimize the impact of process uncertainties. In particular, it would significantly improve the quality of the product without incurring additional costs, achieving a 50% tighter dimensional tolerance compared to a solution obtained by a deterministic optimization algorithm.

A coordinated active and reactive power optimization approach for multi-microgrids connected to distribution networks with multi-actor-attention-critic deep reinforcement learning

As a promising approach to managing distributed energy, the use of microgrids has attracted significant attention among those managing continuous connections to distribution networks. However, the barriers of the data sharing among different microgrids, the uncertainty of the distributed renewable sources and loads, and the nonlinear optimization of power flow make traditional model-based optimization methods difficult to be applied. In this paper, a data-driven coordinated active and reactive power optimization method is proposed for distribution networks with multi-microgrids. A multi-agent deep reinforcement learning (MADRL) method is used to protect the data privacy of each microgrids. Moreover, attention mechanism, which pays attention to crucial information, is presented to overcome the problem of slow convergence caused by the dimensionality explosion of the optimized variables. Two types of agents, controlling discrete action and continuous action devices, respectively, are formulated in coordinated optimization, which reduces voltage violations and improves the system operation efficiency. In addition, in order to improve the performance of the online agent model under variable operation conditions, the transfer learning is embedded in the training process of the MADRL. The proposed method is verified on a modified IEEE 33-bus distribution network with nine microgrids.

Model-based design optimization for motion decoupling in dual-segment flexible robots

The design of a multiple-segment notched tube is distinctively appropriate for miniature surgical robots, attributing to its superior structural compliance and the provision of a substantial lumen within a constrained diameter. However, the cable-driven mechanism commonly adopted in this design naturally leads to inter-segment motion coupling, limiting its clinical potential. This study introduces a model-based design optimization method aimed at concurrently minimizing the coupled motion of a two-segment notched flexible robot and meeting diverse design and performance criteria. In the design optimization framework, a single-segment mechanics model, a 3-dimensional (3D) coupled mechanics model, and a 3D stiffness model have been developed and integrated to simultaneously minimize the coupled bending angle and satisfy surgery-specific performance requirements. A back propagation neural network (BPNN) has also been adopted to achieve computationally efficient optimization process. A case study is conducted on two-segment notched flexible robot optimization design for maxillary sinus surgery, with the mechanics models being verified experimentally. Ultimately, the optimized robot demonstrates its ability to provide visualization of the maxillary sinus cavity, including the blind spots. The proposed robot design optimization approach offers a systematic and efficient methodology to minimize motion coupling without compromising robot performance, thus fundamentally enabling procedure-specific design of multi-segment flexible surgical robots.

A Deep Reinforcement Learning Model-based Optimization Method for Graphic Design

A Deep Reinforcement Learning Model-based Optimization Method for Graphic Design

An optimal interpolation set for model-based derivative-free optimization methods

This paper demonstrates the optimality of an interpolation set employed in derivative-free trust-region methods. This set is optimal in the sense that it minimizes the constant of well-poisedness in a ball centred at the starting point. It is chosen as the default initial interpolation set by many derivative-free trust-region methods based on underdetermined quadratic interpolation, including NEWUOA, BOBYQA, LINCOA, and COBYQA. Our analysis provides a theoretical justification for this choice.

Electrochemical aging model of lithium-ion battery with impedance output and its parameter sensitivity analysis and identification

The electrochemical model of the battery has gained widespread recognition due to its clear physical interpretability. However, achieving an accurate electrochemical model heavily relies on precise parameter settings. To address this challenge, various model-based parameter optimization methods have been developed. Currently, most research relies on model reduction techniques and heuristic random search methods for parameter identification. These approaches often lead to time-consuming processes and a loss of physical interpretability in the electrochemical model. To overcome these limitations, we propose a novel technical framework that directly parametrizes the electrochemical model. First, we establish a battery electrochemical model that accounts for lithium plating and SEI film thickening, serving as the main focus of this study. Secondly, in order to expedite parameter identification without compromising the model's physical interpretability, we innovate by performing comprehensive sensitivity analysis using voltage and impedance characteristics. This allows us to identify the most influential parameters, which become the key for subsequent research. Finally, to ensure reasonable initialization of finite element computations and to avoid convergence issues in the identification algorithm, we combine machine learning and optimization algorithms into a two-step parameter identification method. By utilizing the proposed method to identify the model parameters, the simulations exhibit high accuracy.

Self-Supervised Deep Unrolled Reconstruction Using Regularization by Denoising.

Deep learning methods have been successfully used in various computer vision tasks. Inspired by that success, deep learning has been explored in magnetic resonance imaging (MRI) reconstruction. In particular, integrating deep learning and model-based optimization methods has shown considerable advantages. However, a large amount of labeled training data is typically needed for high reconstruction quality, which is challenging for some MRI applications. In this paper, we propose a novel reconstruction method, named DURED-Net, that enables interpretable self-supervised learning for MR image reconstruction by combining a self-supervised denoising network and a plug-and-play method. We aim to boost the reconstruction performance of Noise2Noise in MR reconstruction by adding an explicit prior that utilizes imaging physics. Specifically, the leverage of a denoising network for MRI reconstruction is achieved using Regularization by Denoising (RED). Experiment results demonstrate that the proposed method requires a reduced amount of training data to achieve high reconstruction quality among the state-of-the-art approaches utilizing Noise2Noise.

Optimization-Driven DRL-Based Joint Beamformer Design for IRS-Aided ITSN Against Smart Jamming Attacks

This paper investigates an intelligent reflecting surfaces (IRS) aided anti-jamming communication strategy in the integrated terrestrial-satellite network (ITSN), where the IRS is exploited to mitigate jamming interference and enhance the integrated system communication performance. In such a network, the terrestrial network and satellite network are co-existing with a spectrum-sharing scheme in the presence of a multi-antenna jammer. We aim at maximizing the weighted sum rate (WSR) of all users by jointly optimizing the terrestrial beamformers and IRS phase shifts while considering the signal-to-interference-plus-noise ratio (SINR) requirements of legitimate users. Different from the non-convex optimization techniques utilized in the IRS-related problem, a novel optimization-driven deep reinforcement learning (DRL) algorithm is proposed, which leverages both the robustness of model-free learning approaches and the efficiency of model-based optimization methods. In the optimization module of the proposed algorithm, we analyze the smart jammer under the unknown jamming model and derive a lower bound of the anti-jamming uncertainty, such that the IRS-aided anti-jamming problem can be solved by alteration method with second-order cone programming (SOCP) algorithm and semidefinite relaxation (SDR) technique. Simulation results demonstrate that the IRS can enhance the anti-jamming performance efficiently, and the proposed optimization-driven DRL algorithm can improve both the learning rate and the system performance compared with existing solutions.

Design and Evaluation of an Adjustable Compliant Constant-Force Microgripper.

Precise control of the manipulating force within an appropriate range is crucial to prevent potential damage to the operating object. However, achieving accurate force control through force feedback is challenging in micro-scale applications. This study presents the design of a quasi-zero stiffness-compliant constant-force microgripper with adjustable force output. The parameters of the constant-force mechanism are designed using a model-based optimization method. By utilizing this mechanism, a compliant microgripper capable of providing adjustable constant-force output is developed to overcome the limitation of traditional grippers that offer only a single constant force. Finite element analysis is performed to simulate the behavior and verify the stability of the constant-force output. Furthermore, an experimental platform is constructed to validate the mechanical properties of the developed microgripper. The experimental results demonstrate that the automatically optimized structural parameters enable the microgripper to achieve the desired constant-force value of 2 N with an adjustable range of 0.15 N. These findings provide a further basis for the application and promotion of compliant constant-force structures.

A Sparse Model-Inspired Deep Thresholding Network for Exponential Signal Reconstruction-Application in Fast Biological Spectroscopy.

The nonuniform sampling (NUS) is a powerful approach to enable fast acquisition but requires sophisticated reconstruction algorithms. Faithful reconstruction from partially sampled exponentials is highly expected in general signal processing and many applications. Deep learning (DL) has shown astonishing potential in this field, but many existing problems, such as lack of robustness and explainability, greatly limit its applications. In this work, by combining the merits of the sparse model-based optimization method and data-driven DL, we propose a DL architecture for spectra reconstruction from undersampled data, called MoDern. It follows the iterative reconstruction in solving a sparse model to build the neural network, and we elaborately design a learnable soft-thresholding to adaptively eliminate the spectrum artifacts introduced by undersampling. Extensive results on both synthetic and biological data show that MoDern enables more robust, high-fidelity, and ultrafast reconstruction than the state-of-the-art methods. Remarkably, MoDern has a small number of network parameters and is trained on solely synthetic data while generalizing well to biological data in various scenarios. Furthermore, we extend it to an open-access and easy-to-use cloud computing platform (XCloud-MoDern), contributing a promising strategy for further development of biological applications.

Nonlinear Dynamic Model-Based Position Control Parameter Optimization Method of Planar Switched Reluctance Motors

Currently, there are few systematic position control parameter optimization methods for planar switched reluctance motors (PSRMs); how to effectively optimize the control parameters of PSRMs is one of the critical issues that needs to be urgently solved. Therefore, a nonlinear dynamic model-based position control parameter optimization method of PSRMs is proposed in this paper. First, to improve the accuracy of the motor dynamics model, a Hammerstein–Wiener model based on the BP neural network input–output nonlinear module is established by combining the linear model and nonlinear model structures so that the nonlinear and linear characteristics of the system are characterized simultaneously. Then, a position control parameter optimization system of PSRMs is developed using the established Hammerstein–Wiener model. In addition, with a self-designed simulated annealing adaptive particle swarm optimization algorithm (SAAPSO), the position control parameter optimization system is performed offline iteratively to obtain the optimal position control parameters. Simulations and experiments are carried out and the corresponding results show that the optimal position control parameters obtained by the proposed method can be directly applied in the actual control system of PSRMs and the control performance is improved effectively using the obtained optimal control parameters.

A Multi-objective Optimization Planning Framework for Active Distribution System Via Reinforcement Learning

The effective planning of active distribution networks is crucial for utility companies to make informed decisions regarding investments in distributed generation, reliability assessment, reactive power planning, substation revisions, and feeder repositioning. However, the dynamic nature of the solution space makes it challenging for model-based optimization methods to ensure computational performance in active distribution network planning. To address this issue, this study proposes a planning method that focuses on improving computational performance through the continuous updating of the planning model’s solution space during the reinforcement learning training process. Based on simulations conducted on the IEEE 33-bus test system, the proposed planning strategy successfully enhances computational performance while minimizing investment costs compared to other strategies. With the proposed method, the investment cost and the operation cost are reduced by 32.42% and 23.91%, respectively.

∇-Prox: Differentiable Proximal Algorithm Modeling for Large-Scale Optimization

Tasks across diverse application domains can be posed as large-scale optimization problems, these include graphics, vision, machine learning, imaging, health, scheduling, planning, and energy system forecasting. Independently of the application domain, proximal algorithms have emerged as a formal optimization method that successfully solves a wide array of existing problems, often exploiting problem-specific structures in the optimization. Although model-based formal optimization provides a principled approach to problem modeling with convergence guarantees, at first glance, this seems to be at odds with black-box deep learning methods. A recent line of work shows that, when combined with learning-based ingredients, model-based optimization methods are effective, interpretable, and allow for generalization to a wide spectrum of applications with little or no extra training data. However, experimenting with such hybrid approaches for different tasks by hand requires domain expertise in both proximal optimization and deep learning, which is often error-prone and time-consuming. Moreover, naively unrolling these iterative methods produces lengthy compute graphs, which when differentiated via autograd techniques results in exploding memory consumption, making batch-based training challenging. In this work, we introduce ∇-Prox, a domain-specific modeling language and compiler for large-scale optimization problems using differentiable proximal algorithms. ∇-Prox allows users to specify optimization objective functions of unknowns concisely at a high level, and intelligently compiles the problem into compute and memory-efficient differentiable solvers. One of the core features of ∇-Prox is its full differentiability, which supports hybrid model- and learning-based solvers integrating proximal optimization with neural network pipelines. Example applications of this methodology include learning-based priors and/or sample-dependent inner-loop optimization schedulers, learned with deep equilibrium learning or deep reinforcement learning. With a few lines of code, we show ∇-Prox can generate performant solvers for a range of image optimization problems, including end-to-end computational optics, image deraining, and compressive magnetic resonance imaging. We also demonstrate ∇-Prox can be used in a completely orthogonal application domain of energy system planning, an essential task in the energy crisis and the clean energy transition, where it outperforms state-of-the-art CVXPY and commercial Gurobi solvers.

Pretraining Graph Neural Networks for Few-Shot Analog Circuit Modeling and Design

Being able to predict the performance of circuits without running expensive simulations is a desired capability that can catalyze automated design. In this paper, we present a supervised pretraining approach to learn circuit representations that can be adapted to new circuit topologies or unseen prediction tasks. We hypothesize that if we train a neural network (NN) that can predict the output direct current (DC) voltages of a wide range of circuit instances it will be forced to learn generalizable knowledge about the role of each circuit element and how they interact with each other. The dataset for this supervised learning objective can be easily collected at scale since the required DC simulation to get ground truth labels is relatively cheap. This representation would then be helpful for few-shot generalization to unseen circuit metrics that require more time consuming simulations for obtaining the ground-truth labels. To cope with the variable topological structure of different circuits we describe each circuit as a graph and use graph neural networks (GNNs) to learn node embeddings. We show that pretraining GNNs on prediction of output node voltages can encourage learning representations that can be adapted to new unseen topologies or prediction of new circuit level properties with up to 10x more sample efficiency compared to a randomly initialized model. We further show that we can improve sample efficiency of prior SoTA model-based optimization methods by 2x (almost as good as using an oracle model) via fintuning pretrained GNNs as the feature extractor of the learned models.

A Surrogate Modeling Space Definition Method for Efficient Filter Yield Optimization

Surrogate models are widely used in filter yield optimization methods to improve efficiency, which can be divided into online and offline. State-of-the-art offline surrogate model-based filter yield optimization methods are shown to be effective for filter cases with more than ten sensitive design variables. In these methods, a keystone is the appropriate definition of the space for building the surrogate model, deciding success/failure, or at least the efficiency of the yield optimization. However, there is a lack of systematic methods to achieve it. To address this challenge, a new method, called pattern search optimization-based surrogate modeling space definition method (PSOMSD), is proposed. The performance of PSOMSD is demonstrated by a real-world filter case with 14 sensitive design variables. Analysis shows the appropriateness of the defined surrogate modeling space and advantages compared to empirical methods.

Kinetic modeling of dynamically operated heterogeneously catalyzed reactions: Microkinetic model reduction and semi-mechanistic approach on the example of the CO[formula omitted] methanation

As the production of green hydrogen from fluctuating resources and the use of Power-to-X technologies become more and more important in the energy sector and the chemical process industries, the interest in dynamically operated reactors is increasing. In order to apply model-based optimization methods for process intensification the dynamic reactor behavior needs to be predicted sufficiently accurate by the underlying model equations, in which the reaction kinetics play a key role. Microkinetic elementary step models are able to describe the dynamic behavior on the catalyst surface. However, these models are laborious to derive, parameterize and require comparably high computational effort to solve. For these reasons, simpler semi-mechanistic kinetic models based on a rate determining step at steady state conditions are much more frequently applied in numerical studies. However, the underlying assumptions of these models are questionable for dynamic operation since sorption processes and possible changes in the reaction mechanisms are not considered. We present a semi-mechanistic kinetic model approach based on so called rate-affecting steps and the dynamic change in surface coverages, which is able to describe the dynamic behavior of the catalyst surface. The applicability of our approach is demonstrated for model reduction of an elementary step mechanism developed for the COx methanation and for kinetic model development with synthetic experimental data. Both methods result in a kinetic expression that can accurately reproduce the dynamic kinetic behavior predicted by the elementary step model, with a significant reduction in computational effort for our new semi-mechanistic model, making this new class of model approach attractive for model-based optimization applications.

Coordinated real-time power dispatch for integrated transmission and distribution networks based on model-based optimization and deep reinforcement learning

As massive distributed energy resources are connected to the distribution networks, the distribution networks are gradually transforming into active distribution networks, and the transmission and distribution networks become more coupled. To make the most of these distributed energy resources and improve the safety of the coupled power system, coordinated real-time power dispatch is indispensable. And for privacy protection and actual engineering needs, the real-time power dispatch problem should be optimized in a decentralized manner by different control centers. In this paper, we decompose the global objective function into local ones, which can be locally optimized by control centers of transmission and distribution networks. The coordination is then realized by introducing the alternating direction method of multipliers (ADMM). Based on the decomposition, we design a novel communication architecture, in which only the boundary variables are exchanged, effectively protecting private information. Additionally, in the real power system, the transmission networks have credible models, while the maintenance of accurate models for distribution networks is usually unaffordable. Therefore, this paper also proposes a hybrid real-time power dispatch method: a model-based optimization method for the transmission network and model-free deep reinforcement learning for each subordinate distribution network. This hybrid method not only overcomes the model incompleteness of the distribution networks but also accelerates and stabilizes the learning process. Numerical test results on three different cases justify the effectiveness of the proposed communication architecture and hybrid real-time power dispatch method.

Hybrid Surrogate Model-Based Multi-Objective Lightweight Optimization of Spherical Fuel Element Canister

A number of canisters need to be lightweight designed to store the spherical fuel elements (SFE) used in high-temperature gas-cooled reactors (HTGR). The main challenge for engineering is pursuing high-accuracy and high-efficiency optimization simultaneously. Accordingly, a hybrid surrogate model-based multi-objective optimization method with the numerical method for the lightweight and safe design of the SFE canister is proposed. To be specific, the drop analysis model of the SFE canister is firstly established where the finite element method—discrete element method (FEM–DEM) coupled method is integrated to simulate the interaction force between the SFE and canister. Through simulation, the design variables, optimization objectives, and constraints are identified. Then the hybrid radial basis function—response surface method (RBF–RSM) surrogate method is carried out to approximate and simplify the accurate numerical model. A non-dominated sorting genetic algorithm (NSGA-II) is used for resolving this multi-objective model. Optimal design is validated using comprehensive comparison, and the reduction of weight and maximum strain can be up to 2.46% and 44.65%, respectively. High-accuracy simulation with high-efficiency optimization is successfully demonstrated to perform the lightweight design on nuclear facilities.

Energy-saving potential analysis for a 24-hour operating chiller plant using the model-based global optimization method

Various studies have been conducted to develop energy efficient measures for chiller plants. In these studies, much attention has been paid to equipment retrofits and various optimal operation strategies, while some measures may interfere with building normal use, like conflicting with the factory's 24-hour production schedule. How much energy saving potential could be obtained from non-interfere measures remains unknown. Therefore, a full-performance simulation chiller plant model was first built based on the Modelica language and then hierarchically calibrated using measured data. Subsequently, the optimization variables were selected based on three principles proposed in this study. An optimization framework based on GenOpt-Dymola was established for the holistic optimization problem, and a chiller plant located in Shanghai, China was used to investigate the energy-saving potential. The results showed that the average global energy-saving rate of the chiller plant reached 8.5% just by optimizing the setpoints in the original control strategy. The largest contribution to energy savings came from the water pumps, which benefited from lowering the chilled water supply temperature, although this reduced the chiller efficiency. Overall, this work can help engineers select appropriate optimization variables that can be easily deployed and can achieve significant energy savings.