Most researches focused on the analytical stabilized algorithm for the modular simulation of single domain,e.g.,pure mechanical systems.Only little work has been performed on the problem of multi-domain simulation stability influenced by algebraic loops.In this paper,the algebraic loop problem is studied by a composite simulation method to reveal the internal relationship between simulation stability and system topologies and simulation unit models.A stability criterion of multi-domain composite simulation is established,and two algebraic loop compensation algorithms are proposed using numerical iteration and approximate function in multi-domain simulation.The numerical stabilized algorithm is the Newton method for the solution of the set of nonlinear equations,and it is used here in simulation of the system composed of mechanical system and hydraulic system.The approximate stabilized algorithm is the construction of response surface for inputs and outputs of unknown unit model,and it is utilized here in simulation of the system composed of forging system,mechanical and hydraulic system.The effectiveness of the algorithms is verified by a case study of multi-domain simulation for forging system composed of thermoplastic deformation of workpieces,mechanical system and hydraulic system of a manipulator.The system dynamics simulation results show that curves of motion and force are continuous and convergent.This paper presents two algorithms,which are applied to virtual reality simulation of forging process in a simulation platform for a manipulator,and play a key role in simulation efficiency and stability.
In this paper, the eigenvalue problem with multiple uncertain parameters is analyzed by the sparse grid stochastic collocation method. This method provides an interpolation approach to approximate eigenvalues and eigenvectors' functional dependencies on uncertain parameters. This method repetitively evaluates the deterministic solutions at the pre-selected nodal set to construct a highdimensional interpolation formula of the result. Taking advantage of the smoothness of the solution in the uncertain space, the sparse grid collocation method can achieve a high order accuracy with a small nodal set. Compared with other sampling based methods, this method converges fast with the increase of the number of points. Some numerical examples with different dimensions are presented to demonstrate the accuracy and efficien y of the sparse grid stochastic collocation method.
Volterra series is a powerful mathematical tool for nonlinear system analysis,and there is a wide range of nonlinear engineering systems and structures that can be represented by a Volterra series model.In the present study,the random vibration of nonlinear systems is investigated using Volterra series.Analytical expressions were derived for the calculation of the output power spectral density(PSD) and input-output cross-PSD for nonlinear systems subjected to Gaussian excitation.Based on these expressions,it was revealed that both the output PSD and the input-output crossPSD can be expressed as polynomial functions of the nonlinear characteristic parameters or the input intensity.Numerical studies were carried out to verify the theoretical analysis result and to demonstrate the effectiveness of the derived relationship.The results reached in this study are of significance to the analysis and design of the nonlinear engineering systems and structures which can be represented by a Volterra series model.
Deep learning algorithms based on neural networks make remarkable achievements in machine fault diagnosis,while the noise mixed in measured signals harms the prediction accuracy of networks.Existing denoising methods in neural networks,such as using complex network architectures and introducing sparse techniques,always suffer from the difficulty of estimating hyperparameters and the lack of physical interpretability.To address this issue,this paper proposes a novel interpretable denoising layer based on reproducing kernel Hilbert space(RKHS)as the first layer for standard neural networks,with the aim to combine the advantages of both traditional signal processing technology with physical interpretation and network modeling strategy with parameter adaption.By investigating the influencing mechanism of parameters on the regularization procedure in RKHS,the key parameter that dynamically controls the signal smoothness with low computational cost is selected as the only trainable parameter of the proposed layer.Besides,the forward and backward propagation algorithms of the designed layer are formulated to ensure that the selected parameter can be automatically updated together with other parameters in the neural network.Moreover,exponential and piecewise functions are introduced in the weight updating process to keep the trainable weight within a reasonable range and avoid the ill-conditioned problem.Experiment studies verify the effectiveness and compatibility of the proposed layer design method in intelligent fault diagnosis of machinery in noisy environments.
