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The geometric parameters of the compressor blade have a noteworthy influence on compressor stability, which should be meticulously designed. However, machining inaccuracies cause the blade geometric parameters to deviate from the ideal design, and the geometric deviation exhibits high randomness. Therefore, the purpose of this study is to quantify the uncertainty and analyze the sensitivity of the impact of blade geometric deviation on compressor stability.

In this work, the influence of blade geometric deviation is analyzed based on a subsonic compressor rotor stage, and three-dimensional numerical simulations are used to compute samples with different geometric features. A method of combining Halton sequence and non-intrusive polynomial chaos is adopted to carry out uncertainty quantitative analysis. Sobol’ index and Spearman correlation coefficient are used to analysis the sensitivity and correlation between compressor stability and blade geometric deviation, respectively.

The results show that the compressor stability is most sensitive to the tip clearance deviation, whereas deviations in the leading edge radius, trailing edge radius and chord length have minimal impact on the compressor stability. And, the effects of various blade geometric deviations on the compressor stability are basically independent and linearly superimposed.

This work provided a new approach for uncertainty quantification in compressor stability analysis. The conclusions obtained in this work provide some reference value for the manufacturing and maintenance of rotor blades.

Ensuring the safety of structures is important. However, when a structure possesses both an implicit performance function and an extremely small failure probability, traditional methods struggle to conduct a reliability analysis. Therefore, this paper proposes a reliability analysis method aimed at enhancing the efficiency of rare event analysis, using the widely recognized Relevant Vector Machine (RVM).

Drawing from the principles of importance sampling (IS), this paper employs Harris Hawks Optimization (HHO) to ascertain the optimal design point. This approach not only guarantees precision but also facilitates the RVM in approximating the limit state surface. When the U learning function, designed for Kriging, is applied to RVM, it results in sample clustering in the design of experiment (DoE). Therefore, this paper proposes a FU learning function, which is more suitable for RVM.

Three numerical examples and two engineering problem demonstrate the effectiveness of the proposed method.

By employing the HHO algorithm, this paper innovatively applies RVM in IS reliability analysis, proposing a novel method termed RVM-HIS. The RVM-HIS demonstrates exceptional computational efficiency, making it eminently suitable for rare events reliability analysis with implicit performance function. Moreover, the computational efficiency of RVM-HIS has been significantly enhanced through the improvement of the U learning function.

The prolonged training time of the neural network (NN) has sparked considerable debate regarding their application in the field of optimization. The purpose of this paper is to explore the beneficial assistance of NN-based alternative models in inductance design, with a particular focus on multi-objective optimization and uncertainty analysis processes.

Under Gaussian-distributed manufacturing errors, this study predicts error intervals for Pareto points and select robust solutions with minimal error margins. Furthermore, this study establishes correlations between manufacturing errors and inductance value discrepancies, offering a practical means of determining permissible manufacturing errors tailored to varying accuracy requirements.

The NN-assisted methods are demonstrated to offer a substantial time advantage in multi-objective optimization compared to conventional approaches, particularly in scenarios where the trained NN is repeatedly used. Also, NN models allow for extensive data-driven uncertainty quantification, which is challenging for traditional methods.

Three objectives including saturation current are considered in the multi-optimization, and the time advantages of the NN are thoroughly discussed by comparing scenarios involving single optimization, multiple optimizations, bi-objective optimization and tri-objective optimization. This study proposes direct error interval prediction on the Pareto front, using extensive data to predict the response of the Pareto front to random errors following a Gaussian distribution. This approach circumvents the compromises inherent in constrained robust optimization for inductance design and allows for a direct assessment of robustness that can be applied to account for manufacturing errors with complex distributions.

The current analysis produces the fractional sample of non-Newtonian Casson and Williamson boundary layer flow considering the heat flux and the slip velocity. An extended sheet with a nonuniform thickness causes the steady boundary layer flow’s temperature and velocity fields. Our purpose in this research is to use Akbari Ganji method (AGM) to solve equations and compare the accuracy of this method with the spectral collocation method.

The trial polynomials that will be utilized to carry out the AGM are then used to solve the nonlinear governing system of the PDEs, which has been transformed into a nonlinear collection of linked ODEs.

The profile of temperature and dimensionless velocity for different parameters were displayed graphically. Also, the effect of two different parameters simultaneously on the temperature is displayed in three dimensions. The results demonstrate that the skin-friction coefficient rises with growing magnetic numbers, whereas the Casson and the local Williamson parameters show reverse manners.

Moreover, the usefulness and precision of the presented approach are pleasing, as can be seen by comparing the results with previous research. Also, the calculated solutions utilizing the provided procedure were physically sufficient and precise.

A time-varying grey Fourier model (TVGFM(1,1,N)) is proposed for the simulation of variable amplitude seasonal fluctuation time series, as the performance of traditional grey models can't catch the time-varying trend well.

The proposed model couples Fourier series and linear time-varying terms as the grey action, to describe the characteristics of variable amplitude and seasonality. The truncated Fourier order N is preselected from the alternative order set by Nyquist-Shannon sampling theorem and the principle of simplicity, then the optimal Fourier order is determined by hold-out method to improve the robustness of the proposed model. Initial value correction and the multiple transformation are also studied to improve the precision.

The new model has a broader applicability range as a result of the new grey action, attaining higher fitting and forecasting accuracy. The numerical experiment of a generated monthly time series indicates the proposed model can accurately fit the variable amplitude seasonal sequence, in which the mean absolute percentage error (MAPE) is only 0.01%, and the complex simulations based on Monte-Carlo method testify the validity of the proposed model. The results of monthly electricity consumption in China's primary industry, demonstrate the proposed model catches the time-varying trend and has good performances, where MAPE_F and MAPE_T are below 5%. Moreover, the proposed TVGFM(1,1,N) model is superior to the benchmark models, grey polynomial model (GMP(1,1,N)), grey Fourier model (GFM(1,1,N)), seasonal grey model (SGM(1,1)), seasonal ARIMA model seasonal autoregressive integrated moving average model (SARIMA) and support vector regression (SVR).

The parameter estimates and forecasting of the new proposed TVGFM are studied, and the good fitting and forecasting accuracy of time-varying amplitude seasonal fluctuation series are testified by numerical simulations and a case study.

This paper intends to construct a new adaptive grey seasonal model (AGSM) to promote the application of the grey forecasting model in quarterly GDP.

Firstly, this paper constructs a new accumulation operation that embodies the new information priority by using a hyperparameter. Then, a new AGSM is constructed by using a new grey action quantity, nonlinear Bernoulli operator, discretization operation, moving average trend elimination method and the proposed new accumulation operation. Subsequently, the marine predators algorithm is used to quickly obtain the hyperparameters used to build the AGSM. Finally, comparative analysis experiments and ablation experiments based on China's quarterly GDP confirm the validity of the proposed model.

AGSM can be degraded to some classical grey prediction models by replacing its own structural parameters. The proposed accumulation operation satisfies the new information priority rule. In the comparative analysis experiments, AGSM shows better prediction performance than other competitive algorithms, and the proposed accumulation operation is also better than the existing accumulation operations. Ablation experiments show that each component in the AGSM is effective in enhancing the predictive performance of the model.

A new AGSM with new information priority accumulation operation is proposed.

This study aims to investigate two newly developed (3 + 1)-dimensional Kairat-II and Kairat-X equations that illustrate relations with the differential geometry of curves and equivalence aspects.

The Painlevé analysis confirms the complete integrability of both Kairat-II and Kairat-X equations.

This study explores multiple soliton solutions for the two examined models. Moreover, the author showed that only Kairat-X give lump solutions and breather wave solutions.

The Hirota’s bilinear algorithm is used to furnish a variety of solitonic solutions with useful physical structures.

This study also furnishes a variety of numerous periodic solutions, kink solutions and singular solutions for Kairat-II equation. In addition, lump solutions and breather wave solutions were achieved from Kairat-X model.

The work formally furnishes algorithms for studying newly constructed systems that examine plasma physics, optical communications, oceans and seas and the differential geometry of curves, among others.

This paper presents an original work that presents two newly developed Painlev\'{e} integrable models with insightful findings.

This study aims to reduce the redundant weight of the anti-roll torsion bar brought by the traditional empirical design and improving its strength and stiffness.

Based on the finite element approach coupled with the improved beluga whale optimization (IBWO) algorithm, a collaborative optimization method is suggested to optimize the design of the anti-roll torsion bar structure and weight. The dimensions and material properties of the torsion bar were defined as random variables, and the torsion bar's mass and strength were investigated using finite elements. Then, chaotic mapping and differential evolution (DE) operators are introduced to improve the beluga whale optimization (BWO) algorithm and run case studies.

The findings demonstrate that the IBWO has superior solution set distribution uniformity, convergence speed, solution correctness and stability than the BWO. The IBWO algorithm is used to optimize the anti-roll torsion bar design. The error between the optimization and finite element simulation results was less than 1%. The weight of the optimized anti-roll torsion bar was lessened by 4%, the maximum stress was reduced by 35% and the stiffness was increased by 1.9%.

The study provides a methodological reference for the simulation optimization process of the lateral anti-roll torsion bar.

Robotic arms’ interactions with the external environment are growing more intricate, demanding higher control precision. This study aims to enhance control precision by establishing a dynamic model through the identification of the dynamic parameters of a self-designed robotic arm.

This study proposes an improved particle swarm optimization (IPSO) method for parameter identification, which comprehensively improves particle initialization diversity, dynamic adjustment of inertia weight, dynamic adjustment of local and global learning factors and global search capabilities. To reduce the number of particles and improve identification accuracy, a step-by-step dynamic parameter identification method was also proposed. Simultaneously, to fully unleash the dynamic characteristics of a robotic arm, and satisfy boundary conditions, a combination of high-order differentiable natural exponential functions and traditional Fourier series is used to develop an excitation trajectory. Finally, an arbitrary verification trajectory was planned using the IPSO to verify the accuracy of the dynamical parameter identification.

Experiments conducted on a self-designed robotic arm validate the proposed parameter identification method. By comparing it with IPSO1, IPSO2, IPSOd and least-square algorithms using the criteria of torque error and root mean square for each joint, the superiority of the IPSO algorithm in parameter identification becomes evident. In this case, the dynamic parameter results of each link are significantly improved.

A new parameter identification model was proposed and validated. Based on the experimental results, the stability of the identification results was improved, providing more accurate parameter identification for further applications.

In this paper we talk about complex matrix quaternions (biquaternions) and we deal with some abstract methods in mathematical complex matrix analysis.

We introduce and investigate the complex space HC consisting of all 2 × 2 complex matrices of the form ξ=z1+iw1z2+iw2−z‾2−iw‾2z‾1+iw‾1, (z1,w1,z2,w2)∈C4.

We develop on HC a new matrix holomorphic structure for which we provide the fundamental operational calculus properties.

We give sufficient and necessary conditions in terms of Cauchy–Riemann type quaternionic differential equations for holomorphicity of a function of one complex matrix variable ξ∈HC. In particular, we show that we have a lot of holomorphic functions of one matrix quaternion variable.