Characteristics Of Error Propagation Research Articles

The improved backward compatible physics-informed neural networks for reducing error accumulation and applications in data-driven higher-order rogue waves.

Due to the dynamic characteristics of instantaneity and steepness, employing domain decomposition techniques for simulating rogue wave solutions is highly appropriate. Wherein, the backward compatible physics-informed neural network (bc-PINN) is a temporally sequential scheme to solve PDEs over successive time segments while satisfying all previously obtained solutions. In this work, we propose improvements to the original bc-PINN algorithm in two aspects based on the characteristics of error propagation. One is to modify the loss term for ensuring backward compatibility by selecting the earliest learned solution for each sub-domain as pseudo-reference solution. The other is to adopt the concatenation of solutions obtained from individual subnetworks as the final form of the predicted solution. The improved backward compatible PINN (Ibc-PINN) is applied to study data-driven higher-order rogue waves for the nonlinear Schrödinger (NLS) equation and the AB system to demonstrate the effectiveness and advantages. Transfer learning and initial condition guided learning (ICGL) techniques are also utilized to accelerate the training. Moreover, the error analysis is conducted on each sub-domain, and it turns out that the slowdown of Ibc-PINN in error accumulation speed can yield greater advantages in accuracy. In short, numerical results fully indicate that Ibc-PINN significantly outperforms bc-PINN in terms of accuracy and stability without sacrificing efficiency.

Predictive analysis of the precision remaining useful life of CNC machine tools based on meta-action unit

Taking into consideration the dynamic characteristics of motion error propagation in CNC machine tools, in order to enhance the accuracy of PRUL (precision remaining useful life) prediction analysis, this paper presents a precision degradation modeling approach based on MAU (meta-action unit) for CNC machine tools. Firstly, from the perspective of motion, the CNC machine tool is divided into the smallest unit by the decomposition of FMA (Function-Motion-Action). Secondly, the MBS (multi-body systems) theory is used to topologically describe the motion relationship between the MAU, and the spinor theory is used to model the motion error. Thirdly, considering the influence of multiple error sources on the PRUL of the CNC machine tool MAU, the motion transmission ratio is used to synthesize multiple error sources, and combined with the constructed error model, the precision degradation model of MAU is constructed, and its PRUL is accurately predicted. Finally, the CNC turntable is selected as the experimental subject to compare the proposed method with commonly used methods in terms of rationality, applicability, and simplicity, and the results verify the applicability and correctness of the method proposed in this paper.

Flexible assembly research for cylindrical interference fit with form error in shaft-hole structures

The interference fit has been widely used for torque transmission and assembly stability in the modern machinery industry. The form error of cylindrical feature is propagated during the interference fit of shaft-hole assembly, which causes the translation and rotation of following structures. Therefore, the overall precision variation is difficult to be predicted. In this paper, an error computational model of interference fit stage is proposed to represent the form error propagation of cylindrical features in the shaft-hole assembly. The characteristic parameter of form error is obtained by the minimum zone cylinder method and integrated into the small displacement torsor. The deformation behavior of interference fit with form error is described as a weakening propagation of error. An interference fit error propagation coefficient is introduced to quantify the phenomenon of weakening propagation of error, which depends on particular fit conditions such as materials, sizes, and interference range of parts. The error computational model for interference fit with form feature is deduced by using the Jacobian-Torsor theory. The characteristic of deformation flexibility in the interference fit is well considered comparing to the simple rigidity analysis in the traditional Jacobian-Torsor model. An error analysis of a shaft-hole structure deciding the symmetry and sensibility performance in the servo valve is conducted to verify the applicability. The cylindrical feature error and deformation during the interference fit are included. The results show that the new error model may represent characteristics of interference fit error propagation with form feature and has a higher reliability than the traditional error models.

A Novel Structural Decomposition Method for Error Propagation Mechanism Analysis Based on Meta-Action Unit Theory

A reasonable structural decomposition method is the foundation of studying the error propagation mechanism precisely. In this paper, a new Function-Motion-Action-Part (FMAP) structural decomposition method is proposed to analyze the mapping model between the geometric dimension of part and output errors of a mechanical product. First, the meta-action unit (MAU) theory is extended to the part layer, and the MAU structure and the MAU chain are redefined. Second, according to the coordination characteristics of the parts in MAU, the error expression model of the parts and the error propagation model of the MAU assembly process are established. The state-space model of the MAU output error is further established so as to complete the mapping model from the geometric dimension of manufactured parts to the precision of the MAU. Then, according to the characteristics of the kinematic error propagation between the MAUs, the input and output error indexes of the MAU chain are determined, and the error propagation model in the MAU chain is established based on the radial basis function network. Finally, the methodology is applied to a numerical control rotary table to verify the effectiveness of the FMAP structural decomposition method for the error propagation mechanism analysis.

A General Euler Angle Error Model of Strapdown Inertial Navigation Systems

Attitude error models play an important role in analyzing the characteristics of navigation error propagation for the design and operation of strapdown inertial navigation systems (SINS). However, the majority of existing attitude error models focus on misalignment, rather than Euler angle errors. Misalignment cannot directly describe attitude error propagation, which is an indirect measurement. To solve the problem, a general Euler angle error model of SINS is proposed. Based on Euler angle error propagation analysis, relative Euler angle errors, and convected Euler angle errors are introduced to compose the general Euler angle error model. Simulation experiments are carried out to verify the proposed model.

Error Propagation Analysis in Three-Dimensional Coseismic Displacement Inversion

Using the Bam earthquake as an example, we apply the multiple-aperture interferometry (MAI) algorithm to measure the azimuth (AZI) displacement with multiple mode synthetic aperture radar (SAR) images (ScanSAR and image modes) and further on produce the 3-D coseismic displacement maps using well-known models: multiple independent interferometric SAR (InSAR) with different viewing angles and combining MAI with conventional InSAR. The 3-D displacement maps show that, besides accuracy of SAR observation, inversion model is another major perturbing factor limiting the accuracy of 3-D component reconstruction. That is, in the former model, the smaller the difference of incidence angles is, the more easily influenced by ill-conditioned systems the estimated parameters are. Based on characteristics of error sources of SAR observations, we classify observation errors into random error, systematic error, and gross error. Moreover, their characteristics of error propagation are analyzed in the two models, respectively. Error propagation analysis indicates that random errors only affect variability of inversion result, while systematic error and gross error cause not only variability but also bias or uncertainty in estimated parameters. The presented error analysis method provides a more comprehensive understanding of bias or uncertainty of 3-D estimated components, which will be a useful tool for evaluating errors in displacement fields obtained from SAR observations. In this letter, we also group multiple InSAR and MAI observations to estimate 3-D components using weighted least squares whose weights are given by the Forstner posterior variance estimation, which may avoid an ill-conditioned system, reducing line-of-sight and AZI random noises and improving accuracies of estimated 3-D components.

An algorithm for geometrical uncertainty analysis in planar truss structures

An algorithm is proposed for description of error accumulation during assembly process of planar truss structures. Specifically, given the tolerances of pre-fabricated members, the uncertainty in the position of nodes is calculated in terms of variances and covariances. Twoconstituent elements of planar trusses (i.e. two-bar unit cell and redundant member) are formulated based on linear models of kinematics and deformation mechanics. Subsequently, these models are combined together in a single algorithm to construct a suitable procedure for estimation of uncertainty zone of each node. Accuracy of the developed method is verified by comparing its results with outcomes of Monte Carlo simulations. Also, appropriate numerical examples are presented to investigate important characteristics of error propagation in planar truss structures and obtain configurations with minimum shape deviation.

Method of change management based on dynamic machining error propagation

In multistage machining processes (MMPs), the final quality of a part is influenced by a series of machining processes, which are complex correlations. So it is necessary to research the rule of machining error propagation to ensure the machining quality. For this issue, a change management method of quality control nodes (i.e., QC-nodes) for machining error propagation is proposed. A new framework of QC-nodes is proposed including association analysis of quality attributes, quality closed-loop control, error tracing and error coordination optimization. And the weighted directed network is introduced to describe and analyze the correlativity among the machining processes. In order to establish the dynamic machining error propagation network (D-MEPN), QC-nodes are defined as the network nodes, and the correlation among the QC-nodes is mapped onto the network. Based on the network analysis, the dynamic characteristics of machining error propagation are explored. An adaptive control method based on the stability theory is introduced for error coordination optimization. At last, a simple example is used to verify the proposed method.