Applied Mathematical Modelling最新文献_第10页

A hybrid bayesian calibrated grey model for robust lubricant wear debris forecasting 基于混合贝叶斯校正灰色模型的润滑油磨损磨损预测

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2026-01-14 DOI: 10.1016/j.apm.2026.116776

Xiaoyu Yang , Zhigeng Fang

To address the challenges of data fluctuations and sparse sampling in prognostic and health management, this paper proposes a hybrid Bayesian-calibrated grey model that enhances prediction robustness and accuracy by systematically integrating prior evolution knowledge from homogeneous historical samples into the grey modeling framework. The model incorporates a Bayesian calibration mechanism implemented through three key steps: first, constructing a prior distribution for the development coefficient based on historically similar samples; second, deriving a posterior estimate of the development coefficient via Bayesian inference to mitigate the impact of sampling data fluctuations; third, obtaining the prediction results from the general solution of the grey differential equation. The model’s performance is evaluated through numerical experiments and a practical task of predicting lubricant iron content in wind turbine gearboxes. Experimental results demonstrate that the proposed model exhibits excellent anti-interference capability, significantly improves prediction accuracy and robustness compared to conventional grey models, while also providing reliable interval forecasts. This framework offers a novel and robust solution for forecasting under data-sparse conditions, advancing the application of grey models in engineering prognostics.

为了解决预测和健康管理中数据波动和稀疏采样的挑战，本文提出了一种混合贝叶斯校准灰色模型，该模型通过系统地将来自同质历史样本的先验进化知识集成到灰色建模框架中，提高了预测的鲁棒性和准确性。该模型采用贝叶斯校准机制，通过三个关键步骤实现：首先，基于历史相似样本构建发展系数的先验分布；其次，通过贝叶斯推理得到发展系数的后验估计，以减轻抽样数据波动的影响；第三，由灰色微分方程的通解得到预测结果。通过数值实验和风电齿轮箱润滑油铁含量预测的实际任务，对该模型的性能进行了评价。实验结果表明，该模型具有良好的抗干扰能力，与传统灰色模型相比，预测精度和鲁棒性显著提高，同时提供了可靠的区间预测。该框架为数据稀疏条件下的预测提供了一种新颖、鲁棒的解决方案，促进了灰色模型在工程预测中的应用。

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引用次数: 0

Fractal invariance-constrained deep learning for spatial-temporal prediction of turbulent flows 湍流时空预测的分形不变性约束深度学习

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2026-01-13 DOI: 10.1016/j.apm.2026.116754

Min Luo , Jiaxin Wu

Spatial-temporal prediction of turbulence remains an important and challenging task in fluid dynamics. This study proposes a fractal invariance-constrained deep learning model, which is characterized by two novel components: (1) a main network equipped with a multi-scale feature reuse mechanism for reduced-order modelling and flow state prediction; and (2) a physical constraint derived from the fractal theory to quantify and regularize scale-invariant self-similarities of fluid dynamic systems. The proposed physical constraint is then embedded into the main network, leading to the proposed model that integrates the efficiency of a deep learning network and the accuracy of physical constraints for flow state prediction. Moreover, a novel learning strategy is proposed to learn turbulence fluctuations at high frequencies and improve the training efficiency of the proposed model. Results on five self-affine fractal images and two turbulence cases demonstrate that the proposed model has achieved a threefold higher efficiency and 40 times improvement in prediction accuracy compared to the purely data-driven methods. Particularly in reconstructing physical quantities, such as the energy spectra and probability density functions of flow fields, the proposed model achieves up to a hundredfold improvement in accuracy. These results highlight the role of constraint in guiding the main network to accurately capture scale invariances and predict kinetic energy within high-frequency subranges.

湍流的时空预测仍然是流体动力学中一项重要而富有挑战性的任务。本文提出了一种分形不变性约束深度学习模型，该模型具有两个新的组成部分：(1)主网络具有多尺度特征重用机制，用于降阶建模和流状态预测；(2)由分形理论导出的物理约束，用于量化和正则化流体动力系统的尺度不变自相似。然后将所提出的物理约束嵌入到主网络中，从而产生将深度学习网络的效率和流状态预测物理约束的准确性集成在一起的所提出的模型。此外，提出了一种新的学习策略来学习高频湍流波动，提高了模型的训练效率。在5张自仿射分形图像和2个湍流情况下的实验结果表明，该模型的预测效率比纯数据驱动的方法提高了3倍，预测精度提高了40倍。特别是在重建物理量时，如流场的能谱和概率密度函数，该模型的精度提高了一百倍。这些结果突出了约束在指导主网络准确捕获尺度不变性和预测高频子范围内动能方面的作用。

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引用次数: 0

Autonomous drone model: A mathematical study 自主无人机模型：一个数学研究

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2026-01-12 DOI: 10.1016/j.apm.2026.116750

Agata Lonc, Barbara Domżała, Monika J. Piotrowska

In this paper, we propose a novel model that describes the movement of a group of n drones in an air corridor, where overtaking is allowed. The model combines main ideas from car-following traffic models with macroscopic concepts, such as the congestion of the air corridor. Furthermore, it incorporates the heterogeneity of drones through varying parameters, such as size, maximum velocity, and maximum acceleration. Apart from interactions between drones, the model allows for the wind compound to be taken into account. We prove the essential mathematical properties of the proposed model. Moreover, we derive the necessary conditions for all drones to move at the same constant speed and analyse the stability of such a situation. The process of overtaking is examined in two examples. In particular, we present all possible long-term scenarios for a special case of two drones. Then, we analyse the model with non-zero wind force, showing that wind strongly affects the dynamics of the whole system. Finally, we perform numerical simulations to illustrate the theoretical properties of the model.

在本文中，我们提出了一个新的模型来描述一组n架无人机在允许超车的空中走廊中的运动。该模型结合了汽车跟随交通模型的主要思想和宏观概念，如空中走廊的拥堵。此外，它通过不同的参数，如尺寸、最大速度和最大加速度，结合了无人机的异质性。除了无人机之间的相互作用外，该模型还考虑了风的化合物。我们证明了所提模型的基本数学性质。此外，我们推导了所有无人机以相同恒定速度移动的必要条件，并分析了这种情况的稳定性。通过两个实例分析了超车过程。特别是，我们提出了所有可能的长期情况下，两个无人机的特殊情况。然后，我们分析了非零风力的模型，表明风对整个系统的动力学影响很大。最后，我们进行了数值模拟来说明模型的理论性质。

引用次数: 0

Adaptive finite-time second-order sliding mode attitude control for fixed-wing UAVs 固定翼无人机自适应有限时间二阶滑模姿态控制

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2026-01-11 DOI: 10.1016/j.apm.2026.116745

MohammadReza Ebrahimpour , Mihai Lungu , Saleh Mobayen , Rui Wang

Fixed-wing unmanned aerial vehicles are widely used in applications such as environmental monitoring, surveillance, and aerial mapping, where accurate attitude control is essential for flight stability and mission success. However, external disturbances, parametric uncertainties, and actuator dynamics with saturation and faults pose significant challenges to control performance and reliability. This paper proposes a robust and adaptive attitude-control strategy that addresses these challenges while maintaining low computational complexity. A fast finite-time second-order sliding-mode control method is designed by combining backstepping and sliding mode control techniques, providing enhanced robustness and effective suppression of chattering. The method is further augmented with an adaptive radial basis function neural network law and an auxiliary compensation system: the adaptive law updates only a single learning parameter, reducing computational load by approximately 53 % compared with conventional neural network–based adaptive methods, while the auxiliary system mitigates actuator saturation. Numerical simulations demonstrate that the proposed methods reduce tracking errors by up to 77 % relative to conventional approaches, maintain performance under severe disturbances and uncertainties, and achieve low computational overhead, highlighting their practical applicability in real-world unmanned aerial vehicle operations.

固定翼无人机广泛应用于环境监测、监视和航空测绘等领域，精确的姿态控制对飞行稳定和任务成功至关重要。然而，外部干扰、参数不确定性以及执行器的饱和和故障动力学对控制性能和可靠性提出了重大挑战。本文提出了一种鲁棒的自适应姿态控制策略，以解决这些挑战，同时保持较低的计算复杂度。将反步控制技术与滑模控制技术相结合，设计了一种快速有限时间二阶滑模控制方法，增强了鲁棒性，有效抑制了抖振。该方法进一步增强了自适应径向基函数神经网络律和辅助补偿系统：自适应律只更新单个学习参数，与传统的基于神经网络的自适应方法相比，计算负荷减少了约53%，而辅助系统减轻了执行器的饱和。数值模拟表明，与传统方法相比，所提出的方法将跟踪误差降低了77%，在严重干扰和不确定性下保持性能，并且实现了较低的计算开销，突出了其在实际无人机操作中的实用性。

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引用次数: 0

Recursive modeling and trajectory optimization of space manipulator mounted on flexible structure 柔性结构空间机械臂递归建模与轨迹优化

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2026-01-11 DOI: 10.1016/j.apm.2026.116741

Yixing Gong, Hao Wen

Manipulators mounted on flexible bases are widely used in space missions. However, their control is complicated by the dynamic coupling between the manipulator and the flexible base. The control objective of such a system is to simultaneously suppress the base’s vibrations and control the manipulator to move to its target configuration. Most existing approaches either use simplified mass-spring models that fail to capture complex dynamics or high-fidelity methods that are computationally expensive. This study focuses on manipulators mounted on large slender truss structures and presents a trajectory optimization scheme to accomplish the control task. To simplify analysis, the large slender truss is modeled as an Euler-Bernoulli beam with dynamics derived via the finite element method. For efficiency, the manipulator-truss dynamics is derived using recursive modeling. Subsequently, a trajectory optimization problem is formulated, in which the system’s implicit dynamics are employed as constraints. Afterwards, The trajectory optimization problem is subsequently transcribed into a nonlinear programming formulation and solved to generate optimal trajectories for feedback-based online tracking. Finally, numerical simulations using an Absolute Nodal Coordinate Formulation beam as reference demonstrate the effectiveness of the proposed trajectory optimization scheme, achieving the control tasks in both Absolute Nodal Coordinate Formulation- and Euler-Bernoulli-based models.

安装在柔性基座上的机械臂在航天任务中有着广泛的应用。然而，由于机械臂与柔性基座之间的动态耦合，使其控制变得复杂。该系统的控制目标是在抑制基座振动的同时控制机械手运动到目标位形。大多数现有的方法要么使用简化的质量-弹簧模型，无法捕获复杂的动力学，要么使用计算成本高的高保真方法。针对安装在大型细长桁架结构上的机械臂，提出了一种轨迹优化方案来完成控制任务。为了简化分析，将大型细长桁架建模为欧拉-伯努利梁，并通过有限元法推导其动力学。为提高效率，采用递归建模方法推导了机械臂桁架动力学。在此基础上，提出了以系统隐式动力学为约束条件的轨迹优化问题。然后，将轨迹优化问题转化为非线性规划公式求解，生成基于反馈的在线跟踪的最优轨迹。最后，以绝对节点坐标公式光束为参考的数值仿真验证了所提出的轨迹优化方案的有效性，实现了绝对节点坐标公式和基于euler - bernoulli模型的控制任务。

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引用次数: 0

Hodograph transformation and cuspon localized wave solutions for the modified complex short pulse equation 修正复短脉冲方程的矢状变换与cuson局域波解

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2026-01-10 DOI: 10.1016/j.apm.2026.116747

Jian-Yu Liu, Xiao-Yong Wen

This work employs the modified complex short pulse equation to model the nonlinear propagation of ultrashort optical pulses in fibers. Based on the hodograph transformation and the generalized Darboux transformation, four types of position-controlled cuspon localized wave solutions are constructed, comprising cuspon semi-rational soliton, cuspon rogue wave, cuspon periodic wave, and their cuspon hybrid interaction solutions, all of which are illustrated graphically. Unlike traditional single-valued smooth structures, we demonstrate single-valued, non-smooth cuspon-type localized wave structures with sharp peaks. Furthermore, by adjusting specific parameters, we can effectively control the spatial positions and shapes of these localized wave solutions. These results not only enrich the understanding of cuspon localized wave structures but also offer valuable tools for interpreting ultrashort optical pulse propagation under nonlinear conditions.

本文采用修正的复短脉冲方程来模拟超短光脉冲在光纤中的非线性传播。基于hodograph变换和广义Darboux变换，构造了四种位置控制的cuspon局域波解，包括cuspon半有理孤子、cuspon流氓波、cuspon周期波及其cuspon混合相互作用解，并给出了图解。与传统的单值光滑结构不同，我们展示了具有尖峰的单值非光滑cuscustype局域波结构。此外，通过调整特定参数，我们可以有效地控制这些局部波解的空间位置和形状。这些结果不仅丰富了对cuspon局域波结构的理解，而且为解释非线性条件下的超短光脉冲传播提供了有价值的工具。

引用次数: 0

A new method of specifying parameter bounds for optimization of reduced-order models and application in design of controllers 一种确定降阶模型优化参数界的新方法及其在控制器设计中的应用

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2026-01-10 DOI: 10.1016/j.apm.2026.116751

Anuj Goel , Amit Kumar Manocha , Parveen Bajaj , George Uwadiegwu Alaneme

In the present work, a new framework is proposed to design controllers using model order reduction techniques for linear time invariant complex engineering systems. The proposed model order reduction methodology employs optimization-based techniques namely ant lion optimization and moth flame optimization for which boundary conditions are systematically procured from an interim model derived using balancing free square-root algorithm. An area control coefficient is introduced to adjust the exploration range of the optimization process around the coefficients of the interim reduced-order model. The numerator as well as denominator coefficients of the desired reduced-order models are optimized to retain the performance characteristics of the original high-order systems. The effectiveness of the proposed approach is assessed based on different error metrics and unit step response plots. To validate the performance, seven benchmark systems of different pole configurations have been considered from the literature. It has been found that proposed approach provides reduced-systems with significant improvement in error and transient performance when compared to the literature work. The suggested model order reduction approach is further extended to design proportional-integral-derivative controller and fractional-order proportional-integral-derivative controller for an 84th-order benchmark system and a mechanical ventilator system respectively. The results demonstrate that the proposed model order reduction-based controller design approach achieves high-performance control with lesser steady-state error, improved time-domain specifications and robust disturbance rejection capability.

本文提出了一种利用模型降阶技术设计线性时不变复杂工程系统控制器的新框架。所提出的模型降阶方法采用基于优化的技术，即蚁狮优化和蛾焰优化，其边界条件是系统地从使用平衡自由平方根算法导出的临时模型中获得的。在中间降阶模型系数周围引入面积控制系数来调整优化过程的勘探范围。对期望的降阶模型的分子和分母系数进行了优化，以保持原高阶系统的性能特征。基于不同的误差度量和单位阶跃响应图对所提方法的有效性进行了评估。为了验证性能，从文献中考虑了七个不同极点配置的基准系统。研究发现，与文献相比，本文提出的方法在误差和瞬态性能方面提供了显著改善的简化系统。将模型降阶方法进一步推广到84阶基准系统和机械通风机系统的比例-积分-导数控制器和分数阶比例-积分-导数控制器的设计中。结果表明，所提出的基于模型阶数约简的控制器设计方法具有较小的稳态误差、较好的时域参数和鲁棒抗扰能力，实现了高性能的控制。

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引用次数: 0

Efficient simulation method of non-stationary non-Gaussian stochastic ground motions based on adaptive interpolation strategy 基于自适应插值策略的非平稳非高斯随机地震动高效模拟方法

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2026-01-10 DOI: 10.1016/j.apm.2026.116746

Xiangqian Sheng , Kuahai Yu , Wenliang Fan , Baiwan Su

The translation process-based spectral representation method is widely used to simulate the non-stationary non-Gaussian stochastic ground motions. However, the computation of the underlying evolutionary power spectral density matrix and its decomposition require substantial computational effort at discrete time-frequency points. To address this problem, this paper proposes an adaptive interpolation strategy for selecting the time-frequency interpolation points to improve the simulation efficiency. Firstly, the correlation function equations between non-Gaussian stochastic processes and the underlying Gaussian stochastic processes are constructed using Mehler's formula. A fast calculation method for the evolutionary power spectral density of the underlying Gaussian processes is introduced based on the interpolation technique. Secondly, the discrete time-frequency interpolation points are determined based on the amplitude information of the evolutionary power spectral density of the underlying Gaussian stochastic processes. The evolutionary power spectral density matrix is decomposed at these time-frequency interpolation points. The decomposed spectrum is then expressed as a sum of products of various time and frequency components. Spline interpolation is applied to these components at the discrete time-frequency points to approximate the matrix decomposition required by the spectral representation method, improving the efficiency of the decomposition. Additionally, the Fast Fourier Transform further accelerates simulation efficiency. Finally, the accuracy and efficiency of the proposed method for simulating non-stationary non-Gaussian stochastic ground motions are verified by considering the real ground motion record, stochastic vector processes, different probability distribution types, different power spectrum density types, and the number of variates.

基于平移过程的谱表示方法被广泛用于模拟非平稳非高斯随机地震动。然而，底层进化功率谱密度矩阵的计算及其分解需要在离散时频点进行大量的计算。针对这一问题，本文提出了一种选择时频插值点的自适应插值策略，以提高仿真效率。首先，利用梅勒公式建立了非高斯随机过程与底层高斯随机过程的相关函数方程；介绍了一种基于插值技术的高斯过程演化功率谱密度的快速计算方法。其次，根据高斯随机过程演化功率谱密度的幅值信息确定离散时频插值点；在这些时频插值点处对演化功率谱密度矩阵进行分解。然后将分解后的频谱表示为各种时间和频率分量的乘积和。在离散时频点对这些分量进行样条插值，逼近谱表示法所需的矩阵分解，提高了分解效率。此外，快速傅里叶变换进一步提高了仿真效率。最后，通过考虑实际地震动记录、随机矢量过程、不同概率分布类型、不同功率谱密度类型和变量数量，验证了所提方法模拟非平稳非高斯随机地震动的准确性和效率。

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引用次数: 0

An efficient adaptive time-integration method for second-order nonlinear dynamics 二阶非线性动力学的一种有效自适应时间积分方法

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2026-01-09 DOI: 10.1016/j.apm.2026.116740

Zhi Duan , Xiaohui Liu , Hongbing Guo , Chuan Wu , Zhongfei Ye , Zhongbin Lu

Achieving an optimal balance among computational efficiency, robustness, and accuracy is a central challenge in simulating second-order nonlinear dynamical systems. While the existing parameterized two-sub-step composite integrator provides rigorous nonlinear stability and controllable dissipation, its fixed-step formulation limits efficiency in simulations with strongly varying dynamics. This paper presents a novel adaptive time integration method that augments the second-order base scheme with an explicit auxiliary stage for efficient error estimation. Its key innovation is a cost-free, direct error estimator, constructed by rigorously deriving the embedding coefficients via order conditions and analytically combining the implicit base stages with an extrapolated explicit stage to derive a local error estimate based on a third-order embedding without additional nonlinear iterations or matrix operations. Combined with a proportional–integral–derivative-like step-size controller, systematic numerical tests show that the proposed method achieves a significantly better computational cost-to-accuracy trade-off than high-order algebraically stable singly diagonally implicit Runge–Kutta methods. The algorithm demonstrates strong robustness in stiff and large-scale nonlinear problems while preserving the unconditional nonlinear stability and controllable dissipation of the base scheme. In summary, the proposed adaptive method offers an efficient, reliable, and self-starting tool for simulating large-scale, long-duration, strongly nonlinear systems.

实现计算效率、鲁棒性和准确性之间的最佳平衡是模拟二阶非线性动力系统的核心挑战。虽然现有的参数化两子步复合积分器提供了严格的非线性稳定性和可控耗散，但其定步式限制了其在强动态变化模拟中的效率。本文提出了一种新的自适应时间积分方法，该方法在二阶基格式的基础上增加了一个显式的辅助阶段，以实现有效的误差估计。它的关键创新是一种无成本的直接误差估计器，该估计器通过严格地根据阶条件推导嵌入系数，并将隐式基本阶段与外推的显式阶段解析地结合起来，从而基于三阶嵌入推导出局部误差估计，而无需额外的非线性迭代或矩阵运算。结合比例-积分-导数类步长控制器，系统数值试验表明，与高阶代数稳定的单对角隐式龙格-库塔方法相比，该方法具有更好的计算成本-精度权衡。该算法对刚性和大规模非线性问题具有较强的鲁棒性，同时保持了基本方案的无条件非线性稳定性和可控耗散。总之，所提出的自适应方法为模拟大规模、长时间、强非线性系统提供了一种高效、可靠和自启动的工具。

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引用次数: 0

Interval theory-embedded data-driven identification framework for uncertain thermo-elastic parameters 区间理论嵌入的数据驱动不确定热弹性参数识别框架

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2026-01-09 DOI: 10.1016/j.apm.2026.116743

Xin Qiang , Chong Wang , Huanyu Zhang

Since system parameters can reflect fluctuations in structural performance, identifying the thermo-elastic parameters based on measured responses is becoming increasingly important for health monitoring of thermo-mechanical systems. To avoid the drawback of traditional probabilistic methods in handling limited experimental samples, this paper proposes a novel interval theory-integrated computational framework for efficient and robust identification of uncertain thermo-elastic parameters. For the coupled thermo-mechanical problem, the thermo-elastic governing equation is derived and the thermal stress effect is discussed. In view of the limitation of extremum searching in capturing potential supplementary data, a confidence-based unbiased interval estimation method is introduced to quantify experimental response bounds of limited experimental samples. Subsequently, a gene expression programming support vector regression (GEP-SVR) metamodel is constructed to replace the full-scale finite element simulations, thereby alleviating the computational burden of the nested dual-loop optimization in interval parameter identification. The effectiveness of the proposed framework is demonstrated through three case studies. Numerical results show that the proposed method achieves identification errors below 3.0% while improving computational efficiency by 87.08% compared to full-scale finite element simulation, providing a practical and efficient tool for uncertainty-aware parameter identification of thermo-mechanical systems.

由于系统参数可以反映结构性能的波动，因此基于测量响应识别热弹性参数对于热机械系统的健康监测变得越来越重要。为了避免传统概率方法在处理有限实验样本时的缺点，提出了一种新的区间理论集成计算框架，用于高效、鲁棒地识别不确定热弹性参数。对于热-力耦合问题，推导了热弹性控制方程，讨论了热应力效应。针对极值搜索在获取潜在补充数据方面的局限性，提出了一种基于置信度的无偏区间估计方法来量化有限实验样本的实验响应界。随后，构建基因表达编程支持向量回归（GEP-SVR）元模型取代全尺寸有限元模拟，减轻了区间参数辨识中嵌套双环优化的计算负担。通过三个案例研究证明了所提出框架的有效性。数值结果表明，与全尺寸有限元模拟相比，该方法辨识误差在3.0%以下，计算效率提高87.08%，为热机械系统的不确定性参数辨识提供了实用、高效的工具。

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引用次数: 0