Quadratic Programming Algorithm Research Articles

Adaptive projected SOR algorithms for nonnegative quadratic programming

Adaptive projected SOR algorithms for nonnegative quadratic programming

Environmental sustainability and nutritional quality of different diets considering nutritional adequacy

This study examines how four diets change nutritionally and environmentally when the diets are nutritionally adjusted. Data on individual Belgian diets of omnivores (n = 131), pescovegetarians (n = 159), vegetarians (n = 494), and vegans (n = 78) were obtained, called non-adjusted diets. We assessed if diets met energy and nutrient intake requirements and calculated the Alternative Healthy Eating Index (AHEI)-2010. The environmental impact was evaluated by a cradle-to-grave life cycle assessment considering all midpoint indicators of the Environmental Footprint 3.0 and expressing the impact per “daily food and supplement intake by one Belgian adult”. The individual dietary intakes were adjusted nutritionally to meet the recommended energy and nutrition intakes using a quadratic programming algorithm. All diets had a significantly improved AHEI score but also a significantly increased water use (WU) when adjusting. The omnivore's diet demonstrated a significantly decreased carbon footprint (CF) while it significantly (except for vegans) raised for the restrictive diets due to adjustment. The omnivorous diet had the greatest improvements in AHEI (15.4), while WU increased the most among all diets (3.7 m3), primarily due to elevated fruit intake. The CF was reduced with 1.2 kg CO2 due to decreased red meat consumption. The AHEI of the vegan diet improved the second most of all diets (13.2) due to the intake of omega-3 supplements, while its WU rose the least of all diets (2.4 m3), and its CF barely increased (0.1 kg CO2-eq). The AHEI improvements of the vegetarian diet were similar to those of the vegan diet (12.5), while the one of the pescovegetarian diet was limited (3.5). The (pesco)vegetarian diet had an increase in WU (2.5 and 2.7 m3) and the highest increase in the CF (0.3 kg CO2-eq). Since nutritionally adjusted diets do not lead to similar nutritional and environmental improvements, this research highlights the need to assess both metrics.

Data-Driven Model-Free Adaptive Containment Control for Uncertain Rehabilitation Exoskeleton Robots with Input Constraints

This paper presents a data-driven model-free adaptive containment control (MFACC) scheme for uncertain rehabilitation exoskeleton robots, where the robotic exoskeleton dynamics are uncertain with saturation constraints. To handle uncertainties of the robotic dynamics, a model-free adaptive control (MFAC) strategy is established by linearizing the robotic exoskeleton dynamics into an equivalent data model. Considering the integral additive effect of the traditional MFAC method, an improved MFAC controller is designed in this paper. Since actuators with saturation constraints constantly affect the safety of patients during rehabilitation training, we construct a new criterion function with active constraints for the critical function of the MFAC algorithm and adopt the Hildreth quadratic programming algorithm to find the constrained optimal solution to overcome this limitation. The proposed MFACC scheme is rigorously proven by the compression mapping method to demonstrate model-free stability. Finally, the proposed control scheme is verified to be effective by simulation studies of the robotic SimMechanics model.

Hybrid TBETI domain decomposition for huge 2D scalar variational inequalities

AbstractThe unpreconditioned H‐TFETI‐DP (hybrid total finite element tearing and interconnecting dual‐primal) domain decomposition method introduced by Klawonn and Rheinbach turned out to be an effective solver for variational inequalities discretized by huge structured grids. The basic idea is to decompose the domain into non‐overlapping subdomains, interconnect some adjacent subdomains into clusters on a primal level, and enforce the continuity of the solution across both the subdomain and cluster interfaces by Lagrange multipliers. After eliminating the primal variables, we get a reasonably conditioned quadratic programming (QP) problem with bound and equality constraints. Here, we first reduce the continuous problem to the subdomains' boundaries, then discretize it using the boundary element method, and finally interconnect the subdomains by the averages of adjacent edges. The resulting QP problem in multipliers with a small coarse grid is solved by specialized QP algorithms with optimal complexity. The method can be considered as a three‐level multigrid with the coarse grids split between primal and dual variables. Numerical experiments illustrate the efficiency of the presented H‐TBETI‐DP (hybrid total boundary element tearing and interconnecting dual‐primal) method and nice spectral properties of the discretized Steklov–Poincaré operators as compared with their finite element counterparts.

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.

Self-measurement and calibration of amplitude-frequency response for coherent optical transmitters with limited DAC resolution

Precise measurement and calibration of the amplitude-frequency response (AFR) of coherent optical transmitters (Tx) are paramount for generating high-quality signals, especially when the transmitter has insufficient bandwidth. The previously proposed self-measurement and calibration (SMC) method based on multi-tone signals (MTS) is cost-effective, fast, and convenient. However, this method exhibits a compromised AFR measurement precision in high-frequency regions, especially when the digital-to-analog converters (DAC) of the Tx have a limited resolution. To solve this problem, we optimize the amplitudes and phases of the MTS by pre-emphasis and the sequential quadratic programming (SQP) algorithm to improve the accuracy in the high-frequency region. Numerical simulations show a notable reduction in AFR measurement error, from about 4 dB to 0.8 dB, when employing a DAC with a four-bit resolution. Additionally, experiments utilizing a 22 GHz 3-dB bandwidth transmitter to generate 61 GBaud dual-polarization 16QAM signals demonstrate a 60% BER reduction. The proposed SMC method is attractive for high-baud rate systems employing Tx with limited bandwidth and DAC resolution.

Hispanic Thrifty Food Plan (H-TFP): Healthy, Affordable, and Culturally Relevant.

The USDA Thrifty Food Plan (TFP) is a federal estimate of a healthy diet at lowest cost for US population groups defined by gender and age. The present goal was to develop a version of the TFP that was more tailored to the observed dietary patterns of self-identified Hispanic participants in NHANES 2013-16. Analyses used the same national food prices and nutrient composition data as the TFP 2021. Diet quality was measured using the Healthy Eating Index 2015. The new Hispanic TFP (H-TFP) was cost-neutral with respect to TFP 2021 and fixed at $186/week for a family of four. Two H-TFP models were created using a quadratic programming (QP) algorithm. Fresh pork was modeled separately from other red meats. Hispanic NHANES participants were younger, had lower education and incomes, but had similar or higher HEI 2015 scores than non-Hispanics. Their diet included more pulses, beans, fruit, 100% juice, grain-based dishes, and soups, but less pizza, coffee, candy, and desserts. The H-TFP market basket featured more pork, whole grains, 100% fruit juice, and cheese. The second TFP model showed that pork could replace both poultry and red meat, while satisfying all nutrient needs. A vegetarian H-TFP proved infeasible for most age-gender groups. Healthy, affordable, and culturally relevant food plans can be developed for US population subgroups.

On the impact of B0 shimming algorithms on single-voxel MR spectroscopy.

To assess the impact of different B0 shimming algorithms on MRS. B0 field maps and single-voxel MR spectroscopy were acquired in the prefrontal cortex of five volunteers at 3 T using five different B0 shimming approaches. B0 shimming was achieved using Siemens' proprietary shim algorithm, in addition to the Pseudo-Inverse (PI), Quadratic Programming (QuadProg), Least Squares (LSq), and Gradient optimization (Grad) algorithms. The standard deviation of the shimmed B0 field, as well as the SNR and FWHM of the measured metabolites, was used to evaluate the performance of each B0 shimming algorithm. Compared to Siemens's shim, significant reductions (p < 0.01) in the standard deviation of the B0 field distribution within the MRS voxel were observed for the PI, QuadProg, and Grad algorithms (3.8 Hz, 7.3 Hz, and 3.9 Hz respectively, compared to 11.5 Hz for Siemens), but not for the LSq (12.9 Hz) algorithm. Moreover, significantly increased SNR and reduced FWHM for the N-acetylaspartate metabolite were consistent with the improvement in B0 homogeneity for the aforementioned shimming algorithms. Here, we demonstrate that the choice of B0 shimming algorithm can have a significant impact on the quality of MR spectra and that significant improvements in spectrum quality could be achieved by using alternatives to the default vendor approach.

On optimizing the sensor spacing for pressure measurements on wind turbine airfoils

Abstract. This research article presents a robust approach to optimizing the layout of pressure sensors around an airfoil. A genetic algorithm and a sequential quadratic programming algorithm are employed to derive a sensor layout best suited to represent the expected pressure distribution and, thus, the lift force. The fact that both optimization routines converge to almost identical sensor layouts suggests that an optimum exists and is reached. By comparing against a cosine-spaced sensor layout, it is demonstrated that the underlying pressure distribution can be captured more accurately with the presented layout optimization approach. Conversely, a 39 %–55 % reduction in the number of sensors compared to cosine spacing is achievable without loss in lift prediction accuracy. Given these benefits, an optimized sensor layout improves the data quality, reduces unnecessary equipment and saves cost in experimental setups. While the optimization routine is demonstrated based on the generic example of the IEA 15 MW reference wind turbine, it is suitable for a wide range of applications requiring pressure measurements around airfoils.

Development of an efficient design optimization strategy for thick-walled cylinders treated with combinations of autofrettage, shrink-fit and wire-winding processes

Shrink-fit, wire-winding, and autofrettage processes are commonly utilized to enhance fatigue strength and durability of thick-walled cylinders across various mechanical applications. In this study, a novel practical design optimization methodology has been developed to determine the optimal configuration of a thick-walled cylinder, incorporating different combinations of shrink-fit, wire-winding, and autofrettage techniques. The objective is to identify the optimal layer thickness, shrink-fit interference, conventional autofrettage pressure, and reverse autofrettage pressure, if applicable, to maximize the compressive residual stress and minimize the tensile residual stress, thereby extending fatigue lifetime of the cylinder. First, different configurations of thick-walled cylinders, subjected to various combinations of reinforcement processes, are identified. A dataset of residual hoop stress profiles through the cylinder thickness is subsequently generated for these configurations based on the same manufacturing process. Neural network regression is effectively utilized to construct a single fitting function for the residual hoop stress profiles. A parametric study is performed to determine the optimal training functions, activation functions, and hyperparameters, achieving a remarkable agreement with the dataset, indicated by a coefficient of determination of over 0.97. A combination of Genetic Algorithm and Sequential Quadratic Programming algorithms is utilized to determine the accurate optimal values. Fatigue life analysis is subsequently conducted to estimate the fatigue lifetime of the optimal configuration. Results suggest that the optimal configuration, involving conventional autofrettage of the inner layer followed by shrink-fitting with a virgin layer and wire-winding the entire assembly, achieves a maximum fatigue life of 88 × 10⁶ cycles under cyclic pressure load of 300 MPa.

Nonlinear Quadratic Programming Algorithm Modelling for Operation of The Off-Grid Energy Resources System with Backup Storage System

Nonlinear Quadratic Programming Algorithm Modelling for Operation of The Off-Grid Energy Resources System with Backup Storage System

A computational approach for phase-field model of quasi-brittle fracture under dynamic loading

AbstractA computational model is formulated for studying dynamic crack propagation in quasi-brittle materials exposed to time-dependent loading conditions. Under such conditions, inertial effects of structural components play an important role in modelling crack propagation problems. The computational model is proposed within the theory of regularised cracks which uses a damage-like internal variable. Here, fracture considers phase-field damage which gives rise to a material degradation in a narrow material strip defining the regularised crack. Based on the energy formulation using the Lagrangian of the system, the proposed computational approach introduces a staggered scheme adopted to solve the coupled system and providing it in a variational form within the time stepping procedure. The numerical data are obtained by quadratic programming algorithms implemented together with a finite element code.

Event-Triggered Neural Adaptive Distributed Cooperative Control for the Multi-Tug Towing of Unactuated Offshore Platform with Uncertainties and Unknown Disturbances

An event-triggered neural adaptive cooperative control is proposed for the towing system (TS) with model parameter uncertainties and unknown disturbances. Different from ordinary multi-vessel formation control, the tugs and unactuated offshore platform in the TS are connected together by towlines, and the resultant tension of the towlines serves as the actual drag force for the platform. Initially, based on the radial basis function neural network (RBFNN), an adaptive RBFNN is designed to compensate unknown disturbances and model parameter uncertainties of the TS, and we use minimal learning parameter (MLP) algorithm to reduce the online learning parameters of adaptive RBFNN. Combined with dynamic surface technology and event-triggered control (ETC) mechanism, an event-triggered neural adaptive virtual controller is designed to obtain the desired drag force of the platform. According to the quadratic programming algorithm, the desired drag force is allocated as the desired tensions of towlines. Subsequently, the desired towline length and the desired position information of the tugs are obtained sequentially through the towline model and the position relationship between the tugs and the platform. Then, according to the desired positions of tugs, an event-triggered neural adaptive distributed cooperative controller is designed for achieving the multi-tug towing of the offshore platform. The ETC mechanism is introduced to reduce the communication burden within the TS and the execution frequency of the tugs’ thrusters. Finally, the stability of the closed-loop system is proven using the Lyapunov theory, and the ETC mechanism proves that no Zeno behavior occurs. The effectiveness of the ETC mechanism and the MLP-based adaptive RBFNN on the controllers of TS is verified through simulations and comparison analysis.

An Obstacle Avoidance Trajectory Planning Methodology Based on Energy Minimization (OTPEM) for the Tilt-Wing eVTOL in the Takeoff Phase

Electric tilt-wing flying cars are an efficient, economical, and environmentally friendly solution to urban traffic congestion and travel efficiency issues. This article addresses the high energy consumption and obstacle interference during the takeoff phase of the tilt-wing eVTOL (electric Vertical Takeoff and Landing), proposing a trajectory planning method based on energy minimization and obstacle avoidance. Firstly, based on the dynamics analysis, the relationship between energy consumption, spatial trajectory, and obstacles is sorted out and the decision variables for the trajectory planning problem with obstacle avoidance are determined. Secondly, based on the power discretization during the takeoff phase, the energy minimization objective function is established and the constraints of performance limitations and spatial obstacles are derived. Thirdly, by integrating the optimization model with the SLSQP (Sequential Least Squares Quadratic Programming algorithm), the second-order sequential quadratic programming model and decision variable update equations are derived, establishing the solution process for the trajectory planning problem of the tilt-wing eVTOL takeoff with obstacle avoidance. Finally, the Airbus Vahana A3 is taken as an example to verify and validate the effectiveness, stability, and robustness of the model and optimization algorithm proposed. The validation results show that the OTPEM (obstacle avoidance trajectory planning methodology based on energy minimization) can effectively handle changes in the takeoff end state and exhibits good stability and robustness in different obstacle environments. It can provide a certain reference for the three-dimensional obstacle avoidance trajectory planning of Airbus Vahana A3 and other tilt-wing eVTOL trajectory planning problems.

Design and Research of a Strain Elastic Element with a Double-Layer Cross Floating Beam for Strain Gauge Wireless Rotating Dynamometers.

Cutting force is one of the most basic signals that can reflect the information of the cutting process, so it is very necessary to study the strain elastic element of strain gauge wireless rotating dynamometers. This paper proposes a strain elastic element with a double-layer cross floating beam that can be applied to the strain gauge wireless rotating dynamometer, which can simultaneously obtain the four-component cutting force/torque information of FX, FY, FZ, and MZ. Based on the proposed strain elastic element, a compact strain gauge wireless rotating dynamometer is designed, which is composed of a tool holder, upper connection flange, strain elastic element, lower connection flange, tool base, and data acquisition and wireless transmission system. The static model of the double-layer cross floating beam on the strain elastic element is established by the segmented rigid body method, and the relationships between the material, force, structural parameters, and the strain and deformation of the floating beam are obtained. The static model is consistent with the finite element solution, which proves the rationality of the static model. Based on the established static model, the sequential quadratic programming algorithm is used to optimize the structural parameters of the double-layer cross floating beam to maximize the sensitivity of the floating beam. The overall structure of the strain elastic element is analyzed by finite element software, and the strain of the structure under simulation conditions is obtained, which provides a reference for subsequent calibration tests and circuit design. The calibration matrix and dynamic performance of the strain elastic element are obtained by the static calibration test, dynamic calibration test, and cutting test. The results show that the proposed strain elastic element has high sensitivity and low cross-sensitivity error, and can be applied to the strain gauge wireless rotating dynamometer to measure medium- and low-speed cutting forces.

Research on performance seeking control of turbofan engine in minimum hot spot temperature mode

Abstract The uneven temperature distribution at the combustion chamber outlet seriously affects the working life of the engine. In order to reduce the heat spot temperature at the combustion chamber outlet, a performance optimization control method of the engine minimum heat spot temperature pattern is proposed. Firstly, based on CFD method, the temperature distribution characteristics of combustion chamber outlet under different working conditions were obtained, and a component-level model of turbofan engine was established to characterize the heat spot temperature at combustion chamber outlet. Secondly, the high precision and high real-time engine on-board model is established by deep neural network. Compared with the component-level model, the average relative error of each performance parameter is less than 0.3 %, and the real-time performance is improved by 12 times. Finally, based on the feasible sequential quadratic programming algorithm, the performance optimization control of the minimum hot spot temperature model in the typical flight envelope is simulated and verified. The simulation results show that under the condition of ensuring the safe and stable operation of the engine and constant thrust, the heat spot temperature at the combustion chamber outlet decreases by 21 K maximum. Compared with the conventional minimum turbine front temperature optimization mode, the minimum heat spot temperature mode significantly reduces the heat spot temperature at the combustion chamber outlet.

Enhancing Power Supply Flexibility in Renewable Energy Systems with Optimized Energy Dispatch in Coupled CHP, Heat Pump, and Thermal Storage

The use of renewable energy by converting it into heat is an important form of storing energy in a usable form and improving the energy supply flexibility; therefore, the electricity–heating system (EHS) can cope with load fluctuations. However, relevant research is lacking on improving the energy supply limitations by the optimal dispatch of energy flow at the typical EHS, such as the coupled CHP–heat pump–thermal storage system (CCHTS). Based on the study of the energy supply characteristics of the CCHTS for extending the energy supply limitation, this study develops an optimal dispatch method using a heat pump (HP) and the thermal storage (TS) of heating networks to improve the flexibility of the CCHTS and the accommodation capacity of renewable energy. The maximum and minimum energy supply limitation model of the CCHTS and the output power characteristic model are established. Based on the piecewise power supply constraint, the energy flow of the EHS is optimized by using the quadratic programming algorithm. The CCHTS can significantly improve the energy supply flexibility; both coupled combined heat and power (CHP) + HP and coupled CHP + TS can improve the power supply flexibility, but the enhanced effect of CHP + HP is better than that of CHP + TS. An increase of 7.6% in wind power consumption is achieved. The consumption of renewable energy increases by 17.9% in the energy flow optimization results.

Improved SQP and SLSQP algorithms for feasible path-based process optimisation

Feasible path algorithms have been widely used for process optimisation due to its good convergence. The sequential quadratic programming (SQP) algorithm is usually used to drive the feasible path algorithms towards optimality. However, existing SQP algorithms may suffer from inconsistent quadratic programming (QP) subproblems and numerical noise, especially for ill-conditioned process optimisation problems, leading to a suboptimal or infeasible solution. In this work, we propose an improved SQP algorithm (I-SQP) and an improved sequential least squares programming algorithm (I-SLSQP) that solves a least squares (LSQ) subproblem at each major iteration. A hybrid method through the combination of two existing relaxations is proposed to solve the inconsistent subproblems for better convergence and higher efficiency. We find that a certain part of the dual LSQ algorithm suffers from serious cancellation errors, resulting in an inaccurate search direction or no viable search direction generated. Therefore, the QP solver is used to solve LSQ subproblems in such a situation. The computational results indicates that I-SLSQP is more robust than fmincon in MATLAB, IPOPT, Py-SLSQP and I-SQP. It is also shown that I-SLSQP and Py-SLSQP is superior to I-SQP for ill-conditioned process optimisation problems, whilst I-SQP is more computationally efficient than I-SLSQP and Py-SLSQP for well-conditioned problems.

A PWR core power control using optimized PID controller with SQP based on control rod positioning and variable coolant flow rate

To ensure safety and stability, it is optimal for nuclear power plants to operate at their nominal power level. However, to meet the needs of power systems, NPPs must also be able to adjust their output for load-following purposes. This necessitates finding an effective control algorithmto maintain stable/safe operating conditions. The current study investigates the performance of PID controllersoptimized using Sequential Quadratic Programming algorithm and applied using two control techniques: control rod positioning and variable coolant flow rate. Simulation is done using model of four-loop Westinghouse PWR-1200 MW nuclear reactor. The proposed controller’s performance is evaluated in three scenarios:sudden control rod withdrawal, sudden change in coolant inlet temperature, and linear load tracking. The influences of model parametric uncertainty are also investigated. Simulation results revealed that the performance of the control algorithm applied using variable coolant flow rate was superior to the one usingcontrol rod positioning.

Fatigue-resistant design of carbon/epoxy composites based on a failure tensor polynomial model by particle swarm optimization-sequential quadratic programming algorithm

This article introduces a design procedure to find the optimum fiber orientations of carbon/epoxy composite laminates for fatigue life advancement. The approach incorporates a fatigue failure tensor polynomial model and employs a hybrid algorithm, combining particle swarm optimization and sequential quadratic programming. Firstly, material properties of quasi-static and fatigue of the carbon/epoxy composites, fabricated by the vacuum-assisted resin transfer molding method, were determined to be used in the model. Various design problems involving two optimization scenarios were then solved using the hybrid algorithm. The algorithm’s performance was also evaluated by specific test problems, confirming its speed and robustness. The optimally fiber-oriented carbon/epoxy composite laminates having maximum fatigue lives were obtained for many critical in-plane cyclic loading cases. To validate the proposed design procedure, two optimum designs were experimentally verified under uniaxial loading conditions. The results indicated a good correlation between the estimated fatigue life of the optimally designed laminates and experimental data. This methodology offers a promising approach for the design of carbon/epoxy composite laminates with superior fatigue strength, particularly significant in specific industrial applications.