Table of Content

25 December 2024, Volume 52 Issue 12

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Mechanical Engineering

Optimization Design and Experiment of XY Compliant Platform with Local Resonance Damping



CHEN Zhong, QIU Yuliang, ZHANG Xianmin

2024, 52(12):  1-13.  doi:10.12141/j.issn.1000-565X.240007

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A compliant precision positioning platform is a core component of precision equipment. The high-speed and high-precision positioning operation requires the platform to possess high response speed and good regulation capabilities. Passive damping can effectively enhance the platform’s rapid response capabilities. To improve the rapid response capability of an XY compliant positioning platform with local resonance damping, this paper proposes an optimization design method that comprehensively enhances modal damping and natural frequency. In the investigation, firstly, based on elasticity theory and Castigliano’s second theorem, the platform stiffness is analytically modeled and synthesized, and the expression for the platform’s natural frequency is derived. Subsequently, aiming at the maximum control gain, a single-objective optimization function composed of natural frequency and the frequency response curve area of the resonant region is formulated, along with the mathematical expression for the platform optimization design problem and a ABAQUS-Python-Matlab joint optimization model. Then, to simplify the complexity of finite element calculations, an equivalent structure for the optimized platform based on the first-order fixed frequency equivalence is established. Moreover, simulation analysis of the optimized platform is conducted, and the optimization design results are compared and analyzed to verify the correctness of the natural frequency analytical expression. Finally, an experimental platform is constructed to perform static, dynamic and trajectory tracking experiments on the XY compliant platform with local resonance damping. The results demonstrate that the proposed comprehensive optimization method can increase the X-axis and Y-axis control bandwidths of the platform respectively by 7.42% and 24.70%, and effectively enhance the trajectory tracking performance of the system.

Calculation of Fatigue Life of Rubber Vibration Isolators Under Random Vibration Loads

LI Min, YAO Qishui

2024, 52(12):  14-21.  doi:10.12141/j.issn.1000-565X.240118

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In order to effectively calculate the fatigue life of rubber vibration isolator under random vibration loads, a rubber vibration isolator for air conditioning compressor of an electric vehicle was taken as the research object, and the road spectrum acquisition of rubber vibration isolator was carried out, by which the acceleration signals versus time of rubber vibration isolator were obtained. Then, Fourier transform was used to transform the acceleration signals into the acceleration power spectral density as load input, and a random vibration test of rubber vibration isolator for compressor was carried out under variable temperature and constant humidity conditions, with the cracking of main spring of rubber vibration isolator being observed. Moreover, a finite element model of rubber vibration isolator was established, with its validity being verified by static characteristic tests as the relative error between simulation value and test value is within ±5%. In addition, frequency response of rubber vibration isolator under unit load was analyzed by ABAQUS, that is, extracting and importing stress response PSD of rubber element into Fe-safe, and using acceleration PSD as load input to calculate the fatigue life. The calculated results were compared with the random vibration test results, finding that the predicted life is consistent with test data, with a relative error of only 2.5%, and that fatigue danger position of rubber vibration isolator unit can be effectively predicted. Finally, the structure of rubber vibration isolator was improved, through which the fatigue life of rubber vibration isolator is 2.8 times that before the improvement, meaning that the fatigue life design requirements are successfully met. This study helps to shorten the design cycle of rubber vibration isolator and reduce the cost of sample test.

Coupled Analysis of Dynamic Contact and Dynamics of Gear System Considering Tooth Back Meshing

CHANG Lehao, WANG Peilin, HUANG Qidi, YUAN Bing, SU Jinzhan

2024, 52(12):  22-31.  doi:10.12141/j.issn.1000-565X.230682

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In order to study the effect of tooth back meshing on the nonlinear dynamic response of the gear system more deeply, a method of analyzing the coupling of tooth transient contact and system dynamics considering the tooth back meshing is proposed. First, the differences in dynamic model and the phase relationship between tooth back meshing and normal meshing are analyzed by studying the mechanism of tooth back meshing. Next, a dynamic model of the gear system considering tooth back meshing is established. Then, a closed-loop “excitation-response-feedback” coupled method is proposed by combining with the dynamic loaded tooth contact analysis (DLTCA). The proposed method can not only can consider the inverse effect of dynamic displacement on the dynamic contact state of the tooth surface, but also can factor in the tooth backlash, flank errors and modification, thus helping obtain more actual dynamic mesh stiffness and system response. The results show that the tooth back meshing mainly affects the nonlinear vibration responses in the speed-down process, while the effect on the speed-up process is not obvious; that increasing the tooth clearance may increase the main resonance speed range of the gear system, while the sensitivity of system vibration to the change of tooth clearance may decrease; that the tooth clearance with small value mainly affects the system nonlinear vibration through the tooth back meshing; and that considering the tooth back meshing may not only change the chaotic rotational speeds, but also change the chaotic state at the same rotational speed. This research provides some theoretical guidance for the nonlinear dynamic control of gear system.

Analysis and Control of Assembly Deviation of Large-Size Thin-Walled Shell Based on Improved Jacobian-Torsor Model

YI Yali, YANG Zeyu, WEI Rui, ZHAO Minjie, JIN Herong

2024, 52(12):  32-42.  doi:10.12141/j.issn.1000-565X.230636

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The large-size thin-walled shell has large size and mass, and is easy to deform with strict assembly accuracy requirement. In order to meet the high-precision requirement of spacecraft shell docking assembly, it is necessary to actively predict and control the shell assembly deviation. In this paper, a large thin-walled shell is taken as the research object. Based on the small displacement spinor method, the key characteristic errors of cabin are characterized, the geometric error spinor expression of the cabin and the constraint relationship between the spinor parameters are obtained. Then, the cumulative paths of parallel and series assembly chains considering the key feature errors of the shell are established, the assembly deviation of the cabin is characterized based on the Jacobian spinor theory, and an assembly deviation transfer model of the cabin based on the improved Jacobian spinor is obtained. Moreover, the Monte Carlo simulation method is used to numerically simulate the shell assembly step difference qualification rate of the improved Jacobian-Torsor model, with the results being compared with the simulation analysis results. Based on which, a calculation method for quantifying the contributions of various errors is proposed. Finally, by taking the minimum total processing cost as the optimization objective, and the variation relationship of various errors as well as the requirements of assembly order difference as the constraint conditions, an optimal allocation strategy for cabin tolerance considering the error contribution is proposed. The success rate of cabin assembly and the qualified rate of assembly order difference before and after the optimization are then compared, finding that the proposed method increases the qualified rate from the original 88.12% to 99.56%. The research method proposed in this paper provides theoretical reference for designers to carry out active tolerance design.

Optimization Design of Battery Box of Electric Vehicles Based on Response Surface Model

WANG Ningzhen, QIN Kangjie, TANG Liang, SHANGGUAN Lijian, ZHOU Fupeng, SHANGGUAN Wenbin

2024, 52(12):  43-51.  doi:10.12141/j.issn.1000-565X.230737

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In order to improve the performance of the battery box of electric vehicles and strengthen the safety and reliability of each component, the acceleration response of the battery modules at different positions inside the box was investigated with the battery box body of an electric vehicle, finding that the calculation results of the power spectral density curves of the three groups of battery modules in the z direction are in good agreement with the test results. Then, by considering the dimensional parameters, such as the top cover of the box, the front end parts of the box, the rear end parts of the box, the middle parts of the box, the module fixing brackets and the reinforcement parts, a response surface proxy model, which describes the relationship between the dimensional parameters of the battery box’s main parts and the intrinsic frequency, deformation as well as vibration response, was established, and the random vibration and the mechanical shock of the box were calculated, with the results verifying the correctness of the model. Based on the Box-Behnken response surface method for designing tests, several combinations of tests with six design variables and three levels were obtained, and the corresponding test design matrices were obtained. A polynomial response surface approximation model was fitted using multiple regression analysis, and the model was iterated and optimized using a multi-objective genetic algorithm to obtain the optimal dimensional parameters of the battery box. Experimental results show that, as compared with the original model, the first-order intrinsic frequency in the optimized case increases by 29.12%, the deformation reduces by 29.39%, and the vibration response reduces by 40.31%, which means a successful lightweighting. The modelling and analyzing methods in this paper can be used to calculate the influence of the battery box components on the overall structure of the battery box, improve the performance of the battery box through optimized design, and strengthen the safety and reliability of each component.

Excavation Trajectory Planning with Optimal Energy Consumption for Mining Electric Shovel

WANG Wei, ZHANG Yuan, SHI Shaoyu, SHEN Gang, YANG Wenqing

2024, 52(12):  52-64.  doi:10.12141/j.issn.1000-565X.230668

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The mining and loading operations are the central link in the open-pit coal mining process, and its energy consumption accounts more than half of the total energy consumption of open-pit coal mining and loading, which determines the mining efficiency and equipment energy consumption. Traditional open-pit coal mining and loading operations are completed by manually operating mining electric shovels, and the process is of low excavation full-bucket rate and high energy consumption. To further reduce the energy consumption and meet the requirements of unmanned and intelligent electric shovels, this paper deals with the optimal excavation trajectory of mining electric shovels. In the research, firstly, a kinematic analysis was conducted on the working device, and the relationship between the pose space and joint space of the working device was revealed through kinematic forward and inverse solutions. Secondly, a dynamic analysis was conducted on the working device of the mining electric shovel. Based on the static analysis of the working device during the excavation process, as well as the analysis of dynamic excavation resistance and material gravity, the Lagrange dynamic equation of the working device was constructed. Then, based on the particle swarm optimization algorithm and the optimization design model of trajectory planning, the optimal excavation trajectory for excavation energy consumption per unit material volume was obtained. Moreover, the effects of material pile surface characteristics, operating parameters and fitting functions on the energy consumption and operation stability of the working device were analyzed, and an excavation trajectory planning strategy that balances energy conservation and stability was proposed. Finally, an experimental study was conducted on the optimal excavation trajectory planning. The results show that the proposed excavation trajectory planning method based on the optimal energy consumption per unit material volume can ensure the efficiency and energy-saving requirement during the excavation with mining electric shovel.

Mechanics

Method of Imposing Local Fixed Constraints Exactly in Isogeometric Analysis

WANG Yingjun, LI Jinghui

2024, 52(12):  65-78.  doi:10.12141/j.issn.1000-565X.230749

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Isogeometric analysis uses computer splines such as non-uniform rational B-splines as the basis functions. When the order of the basis function is 2 or greater, the control points do not coincide with the element nodes and the support domain of the basis function spans multiple elements, which makes it difficult to impose local fixed constraints precisely in isogeometric analysis. To solve this problem, this paper uses a step function to modify the displacement interpolation function of isogeometric analysis. The step function takes a value of 0 in the locally fixed constraint region and 1 in the other region, so that the displacement value in the fixed constraint region is forced to be 0, and the displacement interpolation function in other region is revert to the original form. In order to minimize the influence of step function on the analysis domain, the rising interval of the step function is set to be small. Meanwhile, the hierarchical spline is used to subdivide the elements in the rising interval locally, therefore, the Gaussian points of the subdivided elements fall into the rising interval of the step function as well as the step function has an effect on the stiffness matrix. In addition, the element subdivision also effectively improves the solution accuracy in the local constraint region where large strains are present. Finally, the method mentioned above is compared with analytical solution and the finite element method to verify its accuracy, flexibility and reliability, finding that the results of calculation coincide with the analytical solution. Finally, by considering the situations with different fixed constrains that vary in shape, area and location., the finite element method with coarse mesh and fine mesh are used to calculate the examples, finding that the displacement and stress obtained by the proposed method are closer to those obtained by the fine mesh finite element method, which illustrates that the solution accuracy can be achieved with fewer elements; and that the proposed method is of good accuracy, flexibility and reliability.

Molecular Simulation of Interaction Behavior Between Asphalt Components and Waste Wood Oil

ZHENG Zhi, GUO Naisheng, YOU Zhanping

2024, 52(12):  79-86.  doi:10.12141/j.issn.1000-565X.240112

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To clarify the interaction mechanism between asphalt components and waste wood oil (WWO) in waste sawdust-based bio-asphalts in a molecular scale, five molecular models including virgin asphalt and four kinds of bio-asphalts were established based on the SARA theory by using molecular dynamics (MD) method, and their validity was verified by using the radial distribution function (RDF), energy, density, and solubility parameters. The interaction behavior between WWO and asphalt components was tracked through the analysis of interaction energy, RDF, and snapshots of stable configurations. The results show that the interaction energies between WWO and asphalt components in different bio-asphalt systems are negative, indicating that they attract each other. The order of interaction energies is WWO-resin>WWO-aromatic>WWO-asphaltene>WWO-saturate, which suggests that WWO has the largest interaction force with the resin molecules and the smallest interaction force with the saturate. The intermolecular RDF curves between WWO and four asphalt components stabilize with increasing distance and eventually converge to 1.0, indicating that the molecules within the system show a disordered distribution over a long range. The RDF curves of WWO-resin, WWO-aromatic, and WWO-asphaltene are flat, and there are no significant peaks. However, the RDF curve of WWO-saturate has obvious fluctuations in the range of 0.5~1.5 nm, and the maximum peak intensity is only 1.24, indicating that there are molecular aggregation phenomena in some regions. In addition, similar conclusions to the interaction energy and RDF analyses were found by analyzing the MD snapshots of the stable configurations. The findings demonstrate at the molecular level that WWO is compatible with asphalt components.

Investigation into Critical Depth in Silo-Grains-Lifting Rod Systems Based on Janssen's Continuum Model

ZHANG Xinggang, CUI Jinqin, HE Ninghuai, TANG Yan, CUI Jinhe, WANG Feng

2024, 52(12):  87-92.  doi:10.12141/j.issn.1000-565X.230752

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Granular matter is widely present in nature and human production and life. It exhibits many mechanical properties that differ from those of conventional solids and liquids. Janssen effect is one of the important and well-known phenomena that demonstrates the unique static mechanical properties of granular matter. Researchers have conducted in-depth studies on this effect from various perspectives, including theoretical models and computer simulations. “Chopstick rice-lifting” is an interesting physical phenomenon closely related to the Janssen effect. However, existing research lacks a quantitative analysis of this phenomenon, particularly regarding the discussion of the critical depth. In this paper, the actual system involved in “chopstick rice-lifting” is simplified into a system composed of a silo, grains, and a lifting rod, and the Janssen continuum model is employed to conduct a static mechanical analysis of this system, leading to the theoretical derivation of a transcendental equation concerning the critical depth. Subsequently, by combining experimental data with the numerical solution of this transcendental equation, the authors explore how the Janssen coefficient and critical depth of the granular system in the experiment vary with relevant physical quantities. The results indicate that the Janssen coefficient under different experimental conditions fluctuates slightly around an average value 1.16; and that, when the diameter of the lifting rod is held constant, an increase in the diameter and mass of the silo results in a higher total mass of both the grains and the silo, thereby increasing the critical depth. Conversely, when the diameter of the silo is constant, an increase in the diameter of the lifting rod leads to a decrease in the total mass and an increase in the contact area between the lifting rod and the grains, resulting in a decrease in the critical depth. The theoretical calculation results are generally consistent with the experimental measurement results.

Fluid Power & Mechatronic Control Engineering

Review of Driving Technology for Permanent Magnet Synchronous Motors Without Electrolytic Capacitor

WANG Xiaohong, LIANG Yu, PAN Zhifeng, LU Mingqing, LIU Manxi

2024, 52(12):  93-108.  doi:10.12141/j.issn.1000-565X.240274

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Due to their small size, low cost and high reliability, permanent magnet synchronous motors have been widely used in the fields of industrial production, transportation and household appliances. Electrolytic capacitor is the middle part of drive system connecting the power grid and the motor. Its life is easily affected by external factors such as environmental temperature and humidity, which seriously restricts the stability and reliability of the motor products. Therefore, the drive system without electrolytic capacitor has become the research hotspot at home and abroad. Scholars have proposed various control strategies for achieving high power factor, suppressing current harmonics, and stabling motor operation. In this paper, the factors affecting the power quality and motor performance of drive system without electrolytic capacitor are analyzed, the advantages and disadvantages of different control strategies are compared, the control strategies for optimizing system performance are summarized, and the driving technology of permanent magnet synchronous motor without electrolytic capacitor is prospected. There comes to the following conclusions: at present, the current power quality is improved mainly through the optimization of motor control algorithm, but the existing methods, such as indirect power control, direct power control, compensation phase current’s non-ideal characteristics and regenerative energy control, all have some limitations; the improvement of motor performance is mainly carried out by the traditional control strategies based on constant bus voltage, such as weak magnetic control and over-modulation, while simultaneously suppressing beat phenomenon and ensuring stable operation of the motor, thus, it is necessary to further consider whether the power factor and current harmonics meet the standards in the subsequent research. Moreover, it is pointed that the comprehensive performance control of non-electrolytic capacitor motor, which takes into account both power quality and motor performance, is the biggest problem faced by the current non-electrolytic capacitor control system. Therefore, it is necessary to carry out a collaborative control for the power grid and the motor to rationally allocate functions and avoid conflicts.

Simulated and Experimental Investigation into Coupled Wear of Cavitation and Erosion in Regulating Valves

LIU Xiumei, MA Xuemin, LI Beibei, ZHAO Qiao, LI Shiyang, WU Siyu, HAN Rui

2024, 52(12):  109-118.  doi:10.12141/j.issn.1000-565X.240304

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In order to reveal the influence factors of regulating valve’s service life in coal liquefaction, and ensure the safety and stability of coal liquefaction system operation, numerical simulations were carried out based on turbulence model, cavitation model and discrete phase model to address the complex multiphase flow problem of gas liquid solid. In the investigation, the distribution characteristics of erosion wear and cavitation inside the valve were studied, and the coupled damage rate of cavitation erosion in key parts of the valve core was obtained. Then, the coupled cavitation erosion wear behavior of solid multiphase flow in the flow channel during the operation of the regulating valve was reproduced through experiments, and the damage morphology of the metal tin valve core under continuous cavitation erosion composite action was analyzed. Finally, the damage degree of tin valve cores under different working conditions was quantitatively evaluated using roughness values, and the impact fatigue and composite damage mechanism of valve core surfaces were explored. The results show that the main area where cavitation occurs in the coal liquefaction regulating valve is from the throttle port to the head of the valve core. The range of cavitation increases with the increase of inlet pressure, and the cavitation intensity also increases accordingly. Under different import pressures, the extreme value of the surface erosion rate of the valve core appears at the head of the valve core, with a maximum erosion wear rate of 1.42 × 10^-4 kg/(m²·s), which is more than 10 times that of other erosion areas. The reason is that the high-speed fluid backflow at the head of the valve core carries particles and impacts the head of the valve core, while the collapse of bubbles impacts the surface of the valve core. In addition, it is also found that the surface of the regulating valve core, which works for a long time under the coupling effect of erosion and cavitation, exhibits characteristic morphology such as grooves and corrosion points.

BP Neural Network Prediction Model for Turbulent Noise Intensity in Gas/Water Medium

ZHU Rui, LIU Yu, LIANG Yuying, SHEN Chuanpeng

2024, 52(12):  119-126.  doi:10.12141/j.issn.1000-565X.240077

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Addressing the issues of long computation time and low efficiency in numerical solutions for turbulent noise intensity in conventional air/water medium, a neural network prediction model for bluff body/cavity turbulent noise intensity in air/water medium under similar flow conditions was established. This model efficiently predicts aerodynamic noise intensity at the same Reynolds number based on underwater noise intensity, providing technical support for the efficient prediction and control methods of turbulent noise intensity in air/water medium, as well as the research on the interchangeability of noise testing medium. Particle image velocimetry experiments were conducted to measure the flow velocity around open-slot cylinders, validating the effectiveness of the numerical methods. A numerical model for turbulent noise intensity in air/water medium was constructed using the large eddy simulation method, achieving an average velocity calculation error of less than 2.25% and a Strouhal number error of 0.89% between test and simulated values. The numerical model generated 1 338 data points, which were used to construct a training sample dataset. Then, a backpropagation (BP) neural network was built based on key flow parameters to map the relationship between turbulent noise in air/water medium. The Levenberg-Marquardt algorithm was employed to train the predictive model, with the Sigmoid function selected as the activation function. The network comprises 8 input neurons, 1 output neuron, and a single hidden layer. The results demonstrate that the proposed BP neural network prediction model can predict aerodynamic noise intensity at the same Reynolds number as underwater noise intensity, with a maximum prediction error of less than 6.21 dB and an average error of 0.44 dB; that the model exhibits good generalization ability, with an error of 0.27 dB at irregular points in the test set; and that, under comparable hardware conditions, the numerical solution method required approximately 30 hours for computation, while the BP neural network prediction model took only 70 seconds, significantly improving the computational efficiency.

Vibration Diagnosis and Vibration Damping Optimization of Large-Caliber Wedge Gate Valve

ZHANG Weizheng, HUANG Wenbin, ZHANG Juntao, LIU Jingwei, LIN Hua, HAN Dongmin

2024, 52(12):  127-138.  doi:10.12141/j.issn.1000-565X.240044

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Large diameter wedge gate valves are commonly used in petroleum and chemical pipeline systems, where they endure a coupled load of dynamic pressure from the medium and thermal loads. This coupled load not only exacerbates the structural deformation of the valve but also increases the friction wear between the valve stem and the valve cover. Additionally, it may affect the fluid flow pattern, and, in severe cases, may induce flow-induced vibration, leading to valve stem fracture issues. Aiming at the problem of valve stem fracture in the practical engineering application of DN1 200 mm large-caliber gate valve, this paper uses the process discrete analysis method to divide the position of multi-valve plate, adopts ANSYS numerical simulation technology to visualize the flow characteristics of flow field in the gate valve, and employs Fourier signal analysis method to reveal the pressure pulsation response in fluid domain. Then, the modal analysis and harmonic response analysis of the valve pipeline flow system are carried out, and the resonance characteristics of valve stem and gate plate with multi-physical field coupling under specific stroke are studied. The results show that, when the gate valve opens/closes and the stroke is small, the large Karman vortex street and backflow phenomenon are generated due to the disturbance of the gate plate after the valve, the fluid pressure pulsation increases and the flow condition is disordered, which induces the valve pipeline flow system to produce a large common amplitude value, resulting in the fracture of the valve stem. Therefore, this paper proposes and verifies that the addition of expansion pipe can alleviate the vortex and backflow behind the valve, reduce the pressure pulsation and avoid the flow-induced resonance. Qualitative and quantitative analyses are finally performed to determine the expansion pipe size to weaken the fluid pressure pulsation and the common amplitude value. The comparative study shows that the vibration reduction effect is the best when the diameter of the expansion pipe is 1.3 times that of the pipe (1 560 mm) and when the length of the expansion pipe equals the diameter of the pipe (1 200 mm). The obtained results have certain guiding significance for the vibration reduction optimization research of large-caliber gate valves.

Construction of Upper Boundary Model Based on Least Squares Support Vector Regression

LIU Xiaoyong, ZENG Chengbin, LIU Yun, HE Guofeng, YAN Genglong

2024, 52(12):  139-150.  doi:10.12141/j.issn.1000-565X.240283

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At present, traditional data-driven nonlinear system modeling methods primarily focus on model fitting and application. In this context, this paper constructs an upper boundary model based on least squares support vector regression (LSSVR) for the maximum tolerable output of a critical parameter from the system, which is influenced by uncertainty. The study delves into the relationship between the balance of model accuracy and sparsity, and its effect on the model output. First, by utilizing the optimization problem of LSSVR, the original equality linear constraints are transformed into inequality constraints that satisfy the upper boundary model. Next, to improve the model’s accuracy, an inequality constraint based on the approximation error between the predicted output of the upper bound model and the actual output is introduced. Meanwhile, the LSSVR’s weight L₂-norm is employed to control the complexity of the upper boundary model’s structure, thereby constructing a new objective function and establishing a new optimization problem that satisfies the inequality constraints of the upper bound model. Finally, the Lagrangian function is introduced into the optimization problem, and the Karush-Kuhn-Tucker conditions are used to derive the corresponding dual optimization problem, which is then converted into a standard quadratic programming problem to solve for the parameters of the upper bound model. Since the new optimization problem satisfies convexity, the solution for the model coefficients is globally optimal. The effectiveness and superiority of the proposed method are validated through experimental analysis, where the maximum approximation error, root mean square error, and sparsity-related metrics are used to reflect the model’s accuracy and sparsity characteristics.