Sequential Quadratic Programming Algorithm Research Articles

Optimal process parameter determination in selective laser melting via machine learning-guided sequential quadratic programing

Selective Laser Melting (SLM) is a widely used additive manufacturing method with critical processing parameters such as Laser Power, Scanning Speed, Hatch Distance, and Laser Beam Diameter, which significantly impact process quality and mechanical properties of fabricated parts like Relative Density, Hardness, and Surface Roughness. This study investigates an effective approach to modeling the SLM process for predicting and optimizing processing parameters using a combination of Machine Learning (ML) and Sequential Quadratic Programing (SQP). The proposed method aims to predict the mechanical properties of SLM-produced AlSi10Mg parts using Machine Learning techniques and then transform the process into a constrained multiple-objective optimization model employing the SQP algorithm to determine optimal process parameters. Artificial Neural Networks (ANN), Gaussian Process Regression (GPR), and Support Vector Machine (SVM) algorithms are applied to establish correlations between process parameters and mechanical properties, represented as mathematical functions. A cost function is formulated using these functions and minimized using the SQP method. Statistical analysis is implemented to validate the influence of processing parameters on mechanical properties accordingly. The outcomes of the method are verified through additional experiments and analyses using Micro-CT scanning techniques. The results demonstrate that processing parameters have a significant impact on part properties across different scales, with Micro-CT scanning proving instrumental in validating mechanical properties. Overall, this study establishes that multiple objectives can be efficiently optimized through the integration of ML and SQP methods, complemented by a judicious number of experiments.

A unified calibration method for robot manipulators: hand-eye parameters, kinematic parameters and TCP position calibration

PurposeThe purpose of the paper is to propose an efficient, simple and concise unified robot calibration method that simultaneously considers errors in hand-eye parameters, kinematic parameters and tool center point (TCP) position.Design/methodology/approachThis paper proposes a unified robot calibration method. First, the initial hand-eye matrix and TCP position are computed without considering kinematic parameter errors. Second, the nominal TCP positions in the laser tracker coordinate system {S} are computed. The actual TCP positions in {S} are directly measured. Third, a unified parameter error calibration model is established, and the sequential quadratic programming algorithm is used for error identification. Finally, the identified errors are used for direct error compensation.FindingsSimulation results prove that the proposed scheme can accurately calibrate the hand-eye parameters, kinematic parameters and TCP position simultaneously. Experimental results reveal that the maximum value of the absolute positioning errors is reduced from 5.4725 mm to 0.4095 mm (reduced by 92.52%). Thus, the proposed approach meets the accuracy requirements of most robotic applications.Originality/valueThe main contributions of this paper are: (1) this scheme is efficient. The method can achieve fully automatic calibration by incorporating Kronecker products for the initial hand-eye matrix and TCP position computation. Thereby significantly improving the calibration efficiency and liberating the labor force. (2) This scheme is simple and concise. The hand-eye parameters, kinematic parameters and TCP position errors are modeled in a unified framework. Furthermore, the related redundant parameters are deleted.

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.

Energy Consumption Minimization with SNR Constraint for Wireless Powered Communication Networks.

The article addresses the energy consumption minimization problem in wireless powered communication networks (WPCNs) and proposes a time allocation scheme, named DaTA, which is based on the Different Target Simultaneous Wireless Information and Power Transfer (DT-SWIPT) scheme such that the wireless station can share the remaining energy after transmission to the Hybrid Access Point (HAP) to those who have not transmitted to the HAP to minimize the energy consumption of the WPCN. In addition to proposing a new frame structure, the article also considers the Signal-to-Noise (SNR) constraint to guarantee that the HAP can successfully receive data from wireless stations. In the article, the problem of minimization of energy consumption is formulated as a nonlinear programming model. We employ the SQP (Sequential Quadratic Programming) algorithm to figure out the optimal solution. Moreover, a heuristic method is proposed as well to obtain a near-optimal solution in a shorter time. The simulation results showed that the proposed scheme outperforms the related work in terms of energy consumption and energy efficiency.

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.

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.

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.

A Stochastic Inexact Sequential Quadratic Optimization Algorithm for Nonlinear Equality-Constrained Optimization

A stochastic algorithm is proposed, analyzed, and tested experimentally for solving continuous optimization problems with nonlinear equality constraints. It is assumed that constraint function and derivative values can be computed but that only stochastic approximations are available for the objective function and its derivatives. The algorithm is of the sequential quadratic optimization variety. Distinguishing features of the algorithm are that it only employs stochastic objective gradient estimates that satisfy a relatively weak set of assumptions (while using neither objective function values nor estimates of them) and that it allows inexact subproblem solutions to be employed, the latter of which is particularly useful in large-scale settings when the matrices defining the subproblems are too large to form and/or factorize. Conditions are imposed on the inexact subproblem solutions that account for the fact that only stochastic objective gradient estimates are employed. Convergence results are established for the method. Numerical experiments show that the proposed method vastly outperforms a stochastic subgradient method and can outperform an alternative sequential quadratic programming algorithm that employs highly accurate subproblem solutions in every iteration. Funding: This material is based upon work supported by the National Science Foundation [Awards CCF-1740796 and CCF-2139735] and the Office of Naval Research [Award N00014-21-1-2532].

Training mode of university dance performers based on sequential quadratic programming algorithm

Dance performance is an art form, which needs to cultivate students’ dance skills, artistic accomplishment and stage performance ability. Sequential quadratic programming algorithm is an optimization algorithm that can be used to solve complex optimization problems. In this paper, Sequential Quadratic Programming (SQP) is applied to explore the training mode of dance performers in colleges to help dance performers develop the optimal training plan and program. Aiming at the problems existing in the training mode of dance performance talents in colleges, this paper put forward an optimization method based on SQP algorithm, and implemented its optimization scheme in actual colleges. In the planning of dance performance talent training mode, particle swarm optimization (PSO) is used to optimize SQP algorithm, so that it can have higher planning efficiency. This paper studied the goal and index system of the training of dance performance talents in colleges, generated a personalized training program, and further improved the scientific and practical effectiveness of the training mode. This paper investigated the current situation of dance performance talent training in several dance schools in a certain province of China. The survey data include practical curriculum planning, teachers’ teaching philosophy and teaching content. Combined with SQP algorithm, the teaching and training program is optimized. After evaluation, it can be concluded that the SQP algorithm optimized by PSO shows good stability and accuracy. It can calculate the optimal solution of the cultivation scheme, and when calculating the optimal solution, the running time of the Central Processing Unit (CPU) was only 5.6 s, which can further improve the efficiency of the planning. Finally, through the satisfaction and resource utilization test, it can be found that the number of people who are very satisfied with the teaching content of the dance performance talent training program optimized by SQP increased from 38.4% to 52.4%. After optimization, the average utilization rate of teaching resources reached 88.1%. It can be concluded that SQP algorithm can provide scientific basis for dance education institutions to improve the training mode of dance talents. This can help dance education institutions better improve the training mode, and improve the overall quality and dance skills of dance students.

A Reentry Trajectory Planning Algorithm via Pseudo-Spectral Convexification and Method of Multipliers

The reentry trajectory planning problem of hypersonic vehicles is generally a continuous and nonconvex optimization problem, and it constitutes a critical challenge within the field of aerospace engineering. In this paper, an improved sequential convexification algorithm is proposed to solve it and achieve online trajectory planning. In the proposed algorithm, the Chebyshev pseudo-spectral method with high-accuracy approximation performance is first employed to discretize the continuous dynamic equations. Subsequently, based on the multipliers and linearization methods, the original nonconvex trajectory planning problem is transformed into a series of relaxed convex subproblems in the form of an augmented Lagrange function. Then, the interior point method is utilized to iteratively solve the relaxed convex subproblem until the expected convergence precision is achieved. The convex-optimization-based and multipliers methods guarantee the promotion of fast convergence precision, making it suitable for online trajectory planning applications. Finally, numerical simulations are conducted to verify the performance of the proposed algorithm. The simulation results show that the algorithm possesses better convergence performance, and the solution time can reach the level of seconds, which is more than 97% less than nonlinear programming algorithms, such as the sequential quadratic programming algorithm.

Surge-Elimination Strategy for Aero-Engine Transient Control

Abstract The fundamental principle of the transient state control method for turbofan engines, which is based on the acceleration ratio of high-pressure rotational speed (N-dot), involves sacrificing a portion of the safety margin to obtain satisfactory acceleration performance. However, it could induce surge in the engine's compressor. To prevent the destructive damage caused by surge to both the engine and its components, a surge-elimination control strategy for the engine based on an N-dot controller is proposed. First, the engine mathematical model, which incorporates the effects of engine volumetric dynamics, stall zone characteristics, and combustion chamber flameout characteristics, is established to simulate surge mechanism. Subsequently, the acceleration schedule of the N-dot is calculated by employing sequential quadratic programming (SQP) algorithm to solve the multiconstraint optimization problem, while designing the transition state controller of N-dot based on a high-order filter. Finally, the surge detection logic and surge-elimination strategy based on the μ-correction method are proposed and designed to realize active control of surge elimination. The simulation results demonstrate that the N-dot control method offers significant advantages in mitigating the steady-state errors resulting from inevitable engine degradations. The surge state is effectively suppressed by the proposed surge-elimination control method, and the surge duration is significantly shorten during the acceleration phases. Furthermore, compared to the one without any surge-elimination control, the proposed method decreases the acceleration time by 5.53%.

Full-period operation optimization of the semi-regenerative reactor based on dehydrogenation reaction and deactivation kinetics

Semi-regenerative reactors are adopted in many catalytic processes. Based on industrial data, a one-dimensional pseudo-homogeneous reactor model was established for the semi-regenerative reactor of the dehydrogenation of heavy paraffins. The validation results show high accuracy of the model prediction. The Sequential Quadratic Programming (SQP) algorithm was employed for the full-period operation optimization of the reactor, resulting in a 3.04% increase in the yield of mono-olefins, but the optimized operation conditions are not consistent with common combination according to the practical production experience described in the literature. Further investigations for semi-regenerative reactors with different dehydrogenation systems show that the optimized combination of operation conditions in a full period is dependent on the depth of dehydrogenation, the rate of catalyst deactivation, and the duration of the period.

Optimizing heat source distribution in sintering molds: Integrating response surface model with sequential quadratic programming

The sintering mold imposes strict requirements for temperature uniformity. The mold geometric parameters and the power configuration of heating elements exert substantial influence. In this paper, we introduce an optimization approach that combines response surface models with the sequential quadratic programming algorithm to optimize the geometric parameters and heating power configuration of a heating system for sintering mold. The response surface models of the maximum temperature difference, maximum temperature, and minimum temperature of the sintering area are constructed utilizing the central composite design method. The model's reliability is rigorously confirmed through variance analysis, residual analysis, and generalization capability validation. The models demonstrate remarkable predictive accuracy within the design space. A nonlinear constrained optimization model is established based on the response surface models, and the optimal parameters are obtained after 9 iterations using the sequential quadratic programming algorithm. Under the optimal parameters, the maximum temperature difference is maintained at less than 5 °C, confirming exceptional temperature uniformity. We conduct parameter analysis based on standardized effects to determine the main influencing factors of temperature uniformity, revealing that the distance between adjacent heating rods and the power density of the inner heating rods exert significant influence. Enhanced temperature uniformity can be achieved by adopting a larger distance between heating rods and configuring the power density of the heating rods to a relatively modest level. This work introduces a practical approach to optimize the heating systems for sintering molds, with potential applications in various industrial mold optimization.

A Robot Positional Error Compensation Method Based on Improved Kriging Interpolation and Kronecker Products

This paper proposes a stable and high-accuracy model-free calibration method for unopened robotic systems, which can significantly improve the robot positional accuracy. Two improvements are made to the existing kriging-based error compensation method to achieve robustness/practicality enhancement goals: (1) The semi-variogram model is solved using the sequential quadratic programming (SQP) algorithm, and the distance weight coefficients are added to the objective function. The accuracy of semi-variogram modeling is guaranteed, thereby improving the performance and stability of error compensation. (2) The hand-eye (the pose matrix between the robot base and the laser tracker) and the tool center point (TCP) position are calibrated based on Kronecker products without relying on the spatial analyzer (SA) software to construct the robot base coordinate system separately. Thus, the calibration accuracy and efficiency are significantly improved. Experiments have been conducted, and the results reveal that the proposed method can significantly reduce the robot positional error. Furthermore, the proposed approach performs better than the existing kriging-based error compensation method without Kronecker products. The maximum, mean, and root mean square (RMS) values of the absolute positional errors are reduced by 34.48%, 8.09%, and 10.05%, respectively.

Optimization of surface texture distribution on the thrust bearing using the mass-conserving cavitation boundary condition: Theory and experiments

This study developed a numerical optimization model for the texture distribution in thrust bearings, employing the flat-headed chevron and circular dimple, and utilizing a mass-conserving cavitation boundary. A hybrid of the genetic algorithm and sequential quadratic programming algorithm is utilized. The results indicate the highest load-carrying capacity can be obtained by optimizing the texture distribution based on the flat-headed chevron. The primary mechanism is that the optimal distribution can efficiently harness the collective effect of texture, thereby effectively building up pressure. The optimal distributions of the flat-headed chevron and circular dimples exhibit asymmetric chevron and herringbone shapes, respectively. Furthermore, verification experiments show that the optimal distribution can shift the transition point to a lower rotation speed and higher normal load.

MIMO radar partially correlated waveform design based on chirp rate diversity

Waveform design is a significant topic in multiple-input-multiple-output (MIMO) radar. In this paper, we address the problem of waveform design for colocated narrowband MIMO radar transmit beampattern synthesis. The existing methods have not comprehensively considered the transmit beampattern synthesis under multiple practical constraints, such as constant modulus constraint, Doppler tolerance, high range resolution and low auto-correlation sidelobe. We consider these practical constraints and propose a novel chirp rate diversity-based linear frequency modulated (CRD-LFM) waveform design for approximating the desired MIMO radar transmit beampattern. To tackle the problem, we improve the classical two-step approach. Firstly we design the covariance matrix using the existing closed-form solution. Then we model the problem of obtaining the waveforms from the covariance matrix as a nonlinear optimization problem, and we utilize the Sequential Quadratic Programming (SQP) algorithm to solve it. The simulations demonstrate that the waveforms obtained by this method can well approximate the desired transmit beampattern and have higher range resolution. Furthermore, we verify that the suppression of auto-correlation sidelobe can be achieved using amplitude weighting, which is easily realizable in practical engineering.