Sequential Quadratic Programming Research Articles

Optimization of reduction gear in anchor winch based on modal analysis

In order to achieve more scientific design of the reduction gear and reduce material waste, pre-stressed modal analysis method was combined with multi-objective optimization algorithm to optimize the structure of the reduction gear basic body. The model was simplified and parameterized and the maximum stress and equivalent stiffness under different parameter size combinations were obtained through finite element analysis. Separately, genetic clustering method, neural network method, and Kriging method were used to construct the response surface function. Through error verification and comparison, it was found that the Kriging method was more suitable for the gear model. In the design of variable extremum search, multi-objective genetic algorithm and sequential quadratic programming were compared and analyzed. The results show that the mass of the gear can be reduced by 39.9 %, while the maximum stress remains unchanged, the equivalent stiffness is not reduced, and a good optimization design effect is achieved.

An Efficient Algorithm for Constrained CASSCF(1,2) and CASSCF(3,2) Simulations as Relevant to Electron and Hole Transfer Problems.

We propose an efficient algorithm for the recently published electron/hole-transfer Dynamical-weighted State-averaged Constrained CASSCF (eDSC/hDSC) method studying charge transfer states and D1-D0 crossings for systems with odd numbers of electrons. By separating the constrained minimization problem into an unconstrained self-consistent-field (SCF) problem and a constrained nonself-consistent-field (nSCF) problem, as well as accelerating the direct inversion in the iterative subspace (DIIS) technique to solve the SCF problem, the overall computational cost is reduced by a factor of 8-20 compared with directly using sequential quadratic programming (SQP). This approach should be applicable for other constrained minimization problems, and in the immediate future, once gradients are available, the present eDSC/hDSC algorithm should allow for speedy nonadiabatic dynamics simulations.

Intelligent computing framework to analyze the transmission risk of COVID-19: Meyer wavelet artificial neural networks

The optimum control methods for the epidemiology of the COVID-19 model are acknowledged using a novel advanced intelligent computing infrastructure that joins artificial neural networks with unsupervised learning-based optimizers i.e., Genetic Algorithms (GA) and sequential quadratic programming (SQP). Unsupervised learning strategy is provided which depends on the wavelet basis's sequential deconstruction of stochastic data. The weights or selection values of neural networks are utilizing cumulative algorithms of Meyer wavelet artificial neural networks (MWANNs) optimized with global search Genetic Algorithms (GAs) and Sequential Quadratic Programming (SQP), referred to as MWANNs-GA-SQP and the design technique is utilized to determine the COVID-19 model for five different scenarios employing different step sizes and input intervals. The findings of this research article examined that in order to minimize the total disease transmission at the lowest cost and complexity, safety, focused medical care, and exterior sterilization methods applicability. The provided data is validated through various graphical simulations, which surely authenticate the effectiveness and robustness of the proposed solver. The suggested solver, MWANNs-GA-SQP, is tested in a variety of circumstances to examine that how reliable, safe, and tolerant. Using the proposed MWANNs hubristic intelligent approach, an objective optimization function is created in feed forward neural networking to minimize the mean square error. An investigation of the hybrid GA-SQP is used to confirm the accuracy and dependability of the MWANNs model results. Mean absolute graphs have been constructed to assess the integrity and efficiency of the proposed methodology. The accuracy and reliability of the suggested method are demonstrated by constantly achieving maximum variables of analytical assessment criteria computed for a large appropriate variety of distinct trials.

A collaborative navigation algorithm for UAV Ad Hoc network based on improved sequence quadratic programming and unscented Kalman filtering in GNSS denied area

In global navigation satellite system (GNSS) denied area, collaborative positioning precision is important for unmanned aerial vehicle (UAV) to perform collaborative tasks in Ad Hoc network. Continuous optimization of algorithm complexity and parameter setting has long been a focal point in the field of collaborative positioning research. An algorithm of UAVs collaborative positioning based on improved sequential quadratic programming (SQP) and unscented kalman filter (UKF) is proposed. By optimizing the parameter constraints of SQP, parameters are controlled within certain conditions. The convergence speed of SQP is improved, and more accurate filtering parameters are obtained. The improved SQP and UKF are combined to optimize the location data of UAVs, which improves the precision of collaborative positioning. The simulation results show that the positioning precision can be greatly enhanced by approximately 25% when using the proposed algorithm, as compared to the traditional algorithm. The influence of the collaborative UAV number also is simulated. The positioning performance improve slowly when more than five UAVs are used for collaborative positioning. Therefore, the positioning performance cannot be improved only by increasing the number of UAVs, but also by improving the performance of collaborative positioning algorithm.

Intelligent Design of Street Lamp in Rural Areas Based on an Improved Genetic Algorithm

This study addresses the demand for more efficient streetlight designs in rural areas by introducing an improved genetic algorithm (GA) to optimize the geometry and placement of streetlight poles. Conventional GAs frequently suffer from premature convergence and becoming trapped in local optima, reducing their effectiveness. To mitigate these issues, this research integrates the genetic algorithm with Sequential Quadratic Programming (SQP), using the quasi-optimal solution generated by the GA as the initial input for the SQP, enhancing both accuracy and stability. The methodology includes developing a geometric model of streetlight poles utilizing point cloud data and extracting the centerline via the optimized GA-SQP approach. Additionally, the study examines the effects of random errors, gross errors, incomplete point cloud data, and centerline deviations on the algorithm's performance.

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.

AXIAL DEFORMATION OF SPINEBIO-TENSEGRITY MODELAT DIFFERENT DEPLOYABLE SCHEMES

The study presents the axial deformation of a spine bio-tensegrity model through a shape change strategy with different deployment schemes. The spine bio-tensegrity model mimics the total height, tapered form and natural curvature of a human spine. Three deployable schemes S1-S3 with a different combination of cables at alterable and fixed lengths (at the lower, middle and upper part of the model, respectively) were investigated to achieve a series of axial displacements at 200 mm, 400 mm and 600 mm in the z-direction. The shape change algorithm was developed to optimise the forced elongation of cables, incorporating an objective function designed for monitored nodes in the system to reach their prescribed targets during the optimisation process. Sequential quadratic programming was employed to solve a nonlinear optimisation problem in the shape change analysis involving inequality constraints. The efficiency of the deployable schemes was evaluated based on the deformed shapes, convergence curve and axial forces of the spine bio-tensegrity model. The finding shows in addition to axial deformation, the model in deployment scheme S1 preserves the slenderness characteristic of the spine. In contrast, the model exhibits excessive expansion in the thoracic region in schemes S2 and S3. Greater total computational steps in deployment scheme S3, followed by S2 and S1, reveal that the active cables set near the monitored nodes allow the model to sense and act faster to reach their targets. The study contributes to understanding the structural behaviour and deployment strategy for a structure mimicking a biological system.

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.

Deep contextual reinforcement learning algorithm for scalable power scheduling

This article introduces a deep contextual reinforcement learning (DCRL) optimization algorithm to tackle the NP-hard power scheduling problem. The algorithm is based on a multi-agent simulation environment that decomposes the power scheduling problem into sequential Markov decision processes (MDPs). The simulation environment inherently corrects incorrect decisions and adjusts supply capacities so that the MDPs adhere to the optimization constraints. A deep reinforcement learning (DRL) model is trained on these MDPs to provide optimal solutions. Demonstrating its applicability and effectiveness, the proposed method is evaluated on various test systems with different unit numbers, constraints, and production cost functions. The experimental results show that the proposed method has better performance relative to alternative methods, such as binary alternative moth-flame optimization (BAMFO), binary particle swarm optimization (BPSO), teaching learning-based optimization (TLBO), new binary particle swarm optimization (NBPSO), binary learning particle swarm optimization (BLPSO), quasi-oppositional teaching learning-based algorithm (QOTLBO), binary-real-coded genetic algorithm (BRCGA), hybrid genetic-imperialist competitive algorithm (HGICA), three-stage priority list (TSPL), and hybridized evolutionary algorithm and sequential quadratic programming (HEPSQP). The novelties of the proposed method lie in its adaptability to longer planning horizons and linear dimensionality complexity, rendering it suitable for large-scale power systems.

A hybrid, nonlinear programming approach for optimizing passive shimming in MRI.

In magnetic resonance imaging (MRI), maintaining a highly uniform main magnetic field (B0) is essential for producing detailed images of human anatomy. Passive shimming (PS) is a technique used to enhance B0 uniformity by strategically arranging shimming iron pieces inside the magnet bore. Traditionally, PS optimization has been implemented using linear programming (LP), posing challenges in balancing field quality with the quantity of iron used for shimming. In this work, we aimed to improve the efficacy of passive shimming that has the advantages of balancing field quality, iron usage, and harmonics in an optimal manner and leads to a smoother field profile. This study introduces a hybrid algorithm that combines particle swarm optimization with sequential quadratic programming (PSO-SQP) to enhance shimming performance. Additionally, a regularization method is employed to reduce the iron pieces' weight effectively. The simulation study demonstrated that the magnetic field was improved from 462 to 3.6ppm, utilizing merely 1.2kg of iron in a 40cm diameter spherical volume (DSV) of a 7T MRI magnet. Compared to traditional optimization techniques, this method notably enhanced magnetic field uniformity by 96.7% and reduced the iron weight requirement by 81.8%. The results indicated that the proposed method is expected to be effective for passive shimming.

CO2 emissions of fuel-cell battery hybrid system for large ships

ABSTRACT The needs of solid oxide fuel cells (SOFC) and batteries in large ships are analyzed by estimating the amount of fuel consumption and CO2 emissions. Three types of systems are proposed: 1) fuel cells-battery-generator engine system, 2) battery-generator engine system, and 3) generator engine system. This study is based on the time-varying electric power demand and adopted the sequential quadratic programming (SQP) method to find the optimal power distribution of mixed power sources. CO2 emissions in the SOFC hybrid system are 11.6% lower than in the conventional generator engine system, and those in the battery-generator engine system are 5.1% lower than in the conventional system. The reduction of CO2 emissions come from three factors: the operation of the generator engine at a relatively high load rate, the battery sharing the operation of the generator engine, and the high efficiency of the SOFC running. The SOFC hybrid system can be a sustainable technology in large vessels.

Deformation mitigation and twisting moment control in space frames

Over the last five decades, space frames have centered on the modernization of touristic zones in view of architectural attractions. Although attempts to control joint movement and minimize axial force and bending moment in such structures were made sufficiently, twisting moments in space frames have been underestimated so far. In space frames, external load or restoring the misshapen shape may cause twisting in members. We herein developed a robust computational algorithm to reduce the induced torsional moment through shape restoration within a desired limit by changing the length of active bars that are placed in space frames. Applying optimization algorithms like interior-point and Sequential quadratic programming (SQP), a direct correlation was pursued between bar length alteration and twisting in structural members. A numerical model of a single-layer space frame resembling an egg captures the twisting moment in all members, achieving a specified limit. The overall length change of the active members using an iterative process based on a heuristic that considers a threshold on the minimum length change of the active members.

Modeling magnetic soft continuum robot in nonuniform magnetic fields via energy minimization

The emerging magnetic soft continuum robots (MSCRs) – a type of slender and soft rods with embedded hard-magnetic particles – hold great promise in endovascular intervention via remote magnetic actuation. Although numerous advantages of using permanent magnets have been demonstrated for manipulating MSCRs (e.g., simple systems with high actuation force, large operating workspace), the magneto-mechanical behavior of MSCRs in nonuniform magnetic fields, particularly those generated by permanent magnets, remains largely unexplored. In this work, a systematic study of MSCRs in the nonuniform field is presented, which includes theoretical modeling using hard-magnetic elastica theory, numerical analyses by energy minimization method, finite element simulations using ABAQUS user element (UEL), and experimental validation. Without solving governing differential equations, the large deflection of MSCRs is efficiently obtained via the minimization of the total potential energy using sequential quadratic programming (SQP). This efficient modeling method offers insights into the control of MSCRs using nonuniform magnetic fields. Two practical strategies are provided for precisely controlling MSCRs by manipulating a cubic magnet through the adjustment of the actuation distance, rotation angle, and spin angle, laying the foundation for applications of magnetically-assisted endovascular intervention.

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.

Optimized Longitudinal and Lateral Control Strategy of Intelligent Vehicles Based on Adaptive Sliding Mode Control

To improve the tracking accuracy and robustness of the path-tracking control model for intelligent vehicles under longitudinal and lateral coupling constraints, this paper utilizes the Kalman filter algorithm to design a longitudinal and lateral coordinated control (LLCC) strategy optimized by adaptive sliding mode control (ASMC). First, a three-degree-of-freedom (3-DOF) vehicle dynamics model was established. Next, under the fuzzy adaptive Unscented Kalman filter (UKF) theory, the vehicle state parameter estimation and road adhesion coefficient (RAC) observer were designed to estimate vehicle speed (VS), yaw rate (YR), sideslip angle (SA), and RAC. Then, a layered control concept was adopted to design the path-tracking controller, with a target VS, YR, and SA as control objectives. An upper-level adaptive sliding mode controller was designed using RBF neural networks, while a lower-level tire force distribution controller was designed using distributed sequential quadratic programming (DSQP) to obtain an optimal tire driving force. Finally, the control strategy was validated using Carsim and Matlab/Simulink software under different road adhesion coefficients and speeds. The findings indicate that the optimized control strategy is capable of adaptively adjusting control parameters to accommodate various complex conditions, enhancing the tracking precision and robustness of vehicles even further.

Comparative study of kernel- and deep learning-based proxy models for nonlinearly constrained life-cycle production optimization

This study presents a comparative study for the application of deep learning–based and kernel-based proxy models in hydrocarbon production optimization with nonlinear constraints, comparing their performance against high-fidelity simulators (HFS) in terms of computational efficiency and the quality of the results achieved. One of the proxy models employed is referred to as embed to control and observe (E2CO), a deep learning–based model. The other model is a kernel-based proxy model known as least-squares support-vector regression (LS-SVR). Both proxy models can predict production/injection outputs for each well. We use the sequential quadratic programming (SQP) method for nonlinearly constrained production optimization. Our optimization objective revolves around the net present value (NPV), while the nonlinear state constraints involve field liquid production rate (FLPR) and field water production rate (FWPR). NPV, FLPR, and FWPR are estimated using two different types of proxy models. The gradient of the objective function and the Jacobian matrix of constraints are computed analytically for LS-SVR. In contrast, the method of stochastic simplex approximated gradient (StoSAG) is employed for optimization with E2CO and HFS. The reservoir model considered in this study is a two-phase, three-dimensional reservoir characterized by channelized and heterogeneous permeability, sourced from the SPE10 benchmark case. We optimize well controls to maximize NPV in an oil-water waterflooding scenario. All proxy models can achieve optimal NPV results like those obtained through HFS but with significantly lower computational resources. Both proxy models are found to be approximately 15-fold more efficient than using HFS when the number of simulation runs is compared. Forward prediction results show that both proxy models outperform numerical simulator, and the E2CO can predict up to 2400 times faster than HFS whereas speedups gained over HFS go up to 5000-fold with LS-SVR. The training time required for E2CO is at least an order of magnitude longer than that for LS-SVR. The main contributions of the paper are (i) development of a novel methodology that uses an E2CO proxy model within a gradient-based iterative retraining proxy approach for life-cycle production optimization with nonlinear state constraints, (ii) comparison of this methodology in terms of computational cost and accuracy with an LS-SVR proxy model, and (iii) new insights into the accuracy and prediction performances of these machine learning-based proxy models for 3D oil-water systems as well as their efficiency in nonlinearly constrained production optimization for waterflooding applications.

Two-Step Quadratic Programming for Physically Meaningful Smoothing of Longitudinal Vehicle Trajectories

Longitudinal vehicle trajectories suffer from errors and noise because of detection and extraction techniques, challenging their applications. Existing smoothing methods either lack physical meaning or cannot ensure solution existence and uniqueness. To address this, we propose a two-step quadratic programming method that aligns smoothed speeds and higher-order derivatives with physical laws, drivers’ behaviors, and vehicle characteristics. Unlike the well-known smoothing splines method, which minimizes a weighted sum of discrepancy and roughness in a single quadratic programming problem, our method incorporates prior knowledge of position errors into two sequential quadratic programming problems. Step 1 solves half-smoothed positions by minimizing the discrepancy between them and raw positions, subject to physically meaningful bounds on speeds and higher-order derivatives of half-smoothed positions. Step 2 solves smoothed positions by minimizing the roughness while maintaining physically meaningful bounds and allowing the deviations from raw data of smoothed positions by at most those of the half-smoothed positions and prior position errors. The second step’s coefficient matrix is not positive definite, necessitating the matching of the first few smoothed positions with corresponding half-smoothed ones, with equality constraints equaling the highest order of derivatives. We establish the solution existence and uniqueness for both problems, ensuring their well-defined nature. Numerical experiments using Next Generation Simulation (NGSIM) data demonstrate that a third-order derivative constraint yields an efficient method and produces smoothed trajectories comparable with manually re-extracted ones, consistent with the minimum jerk principle for human movements. Comparisons with an existing approach and application to the Highway Drone data set further validate our method’s efficacy. Notably, our method is a postprocessing smoothing technique based on trajectory data and is not intended for systematic errors. Future work will extend this method to lateral vehicle trajectories and trajectory prediction and planning for both human-driven and automated vehicles. This approach also holds potential for broader smoothing problems with known average error in raw data. History: This paper has been accepted for the Transportation Science Special Issue on ISTTT25 Conference. Funding: The authors extend their gratitude to the Pacific Southwest Region University Transportation Center and the University of California Institute of Transportation Studies (UC ITS) Statewide Transportation Research Program (STRP) for their valuable financial support.

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.

Self-learning Markov prediction algorithm based aging-oriented gradient drop power control strategy for the transient modes of fuel cell hybrid electric vehicles

The power transients caused by switching from drive mode to brake mode in fuel cell hybrid electric vehicles (FCHEV) can result in significant degradation cost losses to the fuel cell. To address this issue, this study proposes a self-learning Markov prediction algorithm based aging-oriented gradient drop power control strategy. First, a real-time self-learning Markov predictor (SLMP) based on the traditional offline training Markov improvement is designed to predict the demand power and combined with the sequential quadratic programming (SQP) optimization algorithm to solve for the inner optimal demand power based on its global cost function minimization characteristic. On this basis, the fuel cell gradient drop power (FGDP) strategy is proposed to optimize the operating state of the vehicle powertrain under vehicle mode switching. This involves establishing a power gradient drop step based on considering the fuel cell hydrogen consumption cost and its lifetime degradation cost to further obtain the outer fuel cell demand power at the optimal step. And three execution modes are designed to trigger the FGDP strategy. Finally, by combining the above efforts, the SLMP-FGDP optimization control strategy is constructed. The numerical verification and hardware in loop experiments results show that the proposed improved SLMP can predict the vehicle demand power more accurately. Compared with the non-FGDP system, the SLMP-FGDP strategy can effectively near-eliminate the fuel cell power transient due to any braking scenario, thus effectively controlling the fuel cell lifetime degradation cost in a lower range and realizing a reduction of up to 52.21% of the fuel cell usage costs without significantly sacrificing the hydrogen fuel economy.

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.