Error Propagation Research Articles

Improving the accuracy of interferometer testing with absolute surface calibration and power spectral density analysis

A novel absolute surface calibration method for interferometer testing based on power spectral density analysis has been proposed. The method involves obtaining the loss of signal at different frequencies as a function of various rotation angles by signal analysis to choose the rotation angle for calibration. A model is developed to evaluate the calibration method by creating random surface shapes based on the Power Spectral Density. Using this algorithm, the precision of the absolute testing method during the testing process exceeds 0.28 %. Error propagation during the experimental process, such as testing optic clamping, angular errors, eccentricity, vibrations and airflow disturbances, were calibrated. Ultimately, the absolute detection test results were verified using high-precision flat mirrors. The experimental result indicates an RMS of 4.275 nm, 4.263 nm, and 4.265 nm in different rotation angle, and the calibrated result shows an RMS of 4.880 nm. The shape of surface errors in the absolute test results and calibration results is consistent.

Research on Optimization of Nonlinear Extended State Observer for the Upper-Limb Rehabilitation Robot Controller

Background: In recent years, patents have shown that upper-limb rehabilitation robots play a significant role in home-based rehabilitation training for stroke hemiplegia patients. Changes in muscle tension during the flaccid paralysis phase cause the rehabilitation robot to deviate from the predetermined motion trajectory. This poses a challenge to the mathematical modeling of the rehabilitation robot and the design of the nonlinear extended state observer (NESO). Objective: To address the problem of trajectory tracking errors caused by the rehabilitation robot when the patient's muscle tension changes, a method based on optimizing the nonlinear function within the NESO is proposed. Methods: First, a mathematical model of the upper-limb rehabilitation robot is established to obtain the dynamic relationship between the robot's velocity and the input voltage. Second, the nonlinear function of NESO is optimized by adjusting the gain values of the sine and tangent functions to effectively estimate the muscle tension and reduce the problem of accumulative error due to changes in muscle tension. Finally, comparative simulations of trajectory tracking including the optimized nonlinear function as well as the sine, tangent and power functions are performed on the MATLAB platform. Results: NESO is constructed to estimate changes in muscle tension based on sine, tangent, and power functions, as well as optimized nonlinear functions. The equivalent gain values of each function and the muscle tension estimation curves of NESO are compared. The simulation results show that the equivalent gain value of the optimized nonlinear function acting in NESO is increased to more than 8 and the convergence time is reduced by 11.9% accordingly. This conclusion is validated by simulations and practical tests. Conclusion: The optimized nonlinear function shortens the estimation time of the NESO for changes in muscle tension, which can provide a reference value for the design of observers for upper-limb rehabilitation robots of patients in the flaccid paralysis stage.

Thermal characterization of thin films: A chip-based approach for in-plane property analysis

Accurate measurement of thermal properties in thin films is crucial for optimizing devices and deepening our understanding of heat transfer at nano and micro scales. This study presents a combined experimental and computational investigation on a chip-integrated technique for the assessment of in-plane thermal properties of thin films. This method stands out by incorporating inherent error cancelation to lessen the impact of radiative heat loss and allows simultaneous, independent determination of both thermal conductivity and diffusivity through straightforward linear fittings from the same dataset, reducing error propagation. We examine an 84 nm thick SiNx membrane over a temperature range from 100 K to nearly 500 K, aligning with previous studies. Further investigations into a conducting polymer film post-doping demonstrate a notable increase in both thermal conductivity and diffusivity, corroborating scanning thermal microscopy observations, confirming the technique's efficacy and reliability.

An improved manifold-projection trajectory based method for chemical kinetic mechanism reduction

An improved manifold-projection trajectory based dimension reduction algorithm (MTDR) to automatically generate skeletal chemical kinetic mechanisms was proposed and validated in this study. This algorithm is implemented by constructing an approximate manifold-based trajectory of the combustion system using Euclidean distances between two adjacent points and cosine similarities between two adjacent vectors in the manifold space, and then evaluating the importance of species by calculating the error of manifold-based trajectories before and after the projection of the manifold. In this method, the nature of the combustion system is well reflected since the combustion process information can be captured by the location of the state point in the manifold space. The calculation during the reduction process is simplified by using the manifold-based trajectory instead of the complex differential equations. Compared to our previous work, this study improves the prediction accuracy of the reduced mechanisms through a more comprehensive error evaluation in the mechanism reduction process. The detailed mechanisms of fuels including iso-cetane, iso-octane and gasoline surrogate mixtures of toluene, iso-octane and n-heptane were reduced to portray the prowess of the algorithm. It’s demonstrated that the number of species of the fuels is reduced from 492, 254 and 1389 to 95, 87 and 427 within an acceptable error, respectively. Meanwhile, the case of iso-octane mechanism reduction was chosen to compare the performance of MTDR with traditional methods including path flux analysis (PFA) and directed relation graph with error propagation and sensitivity analysis (DRGEPSA), and it is shown that the MDTR can generate more compact mechanism under a broad range of error limits.

Temporal feature decomposition fusion network for building energy multi-step prediction

Accurate building energy prediction methods have become a key factor in achieving energy-saving goals. Traditional methods for building energy multi-step prediction often use recursive or direct strategies to address time series prediction problems, which may neglect the data sequence correlation and result in the cumulative error. To solve the above problem, this paper proposed a Temporal Feature Decomposition Fusion Network (TFDFNet) model for building energy consumption multi-step prediction, with an encoder-decoder architecture. In the encoder, feature fusion layers is employed to consider the influence of different feature sequences on the predicted sequence. Through the decomposition of historical load data sequences, different hierarchical sequence structures are constructed to enhance the interpretability and predictability of the data. In the decoder, a simple and efficient network is constructed using MLP to decode the encoded information and obtain the prediction results. Experimental results show that, the proposed model achieves higher prediction accuracy and more stable convergence than the other five comparable methods, which also indicates the potential of achieving excellent building energy consumption multi-step prediction results with a simple model design.

Towards high‐definition vector map construction based on multi‐sensor integration for intelligent vehicles: Systems and error quantification

AbstractA lightweight, high‐definition vector map (HDVM) enables fully autonomous vehicles. However, the generation of HDVM remains a challenging problem, especially in complex urban scenarios. Moreover, numerous factors in the urban environment can degrade the accuracy of HDVM, necessitating a reliable error quantification. To address these challenges, this paper presents an open‐source and generic HDVM generation pipeline that integrates the global navigation satellite system (GNSS), inertial navigation system (INS), light detection and ranging (LiDAR), and camera. The pipeline begins by extracting semantic information from raw images using the Swin Transformer. The absolute 3D information of semantic objects is then retrieved using depth from the 3D LiDAR, and pose estimation from GNSS/INS integrated navigation system. Vector information (VI), such as lane lines, is extracted from the semantic information to construct the HDVM. To assess the potential error of the HDVM, this paper systematically quantifies the impacts of two key error sources, segmentation and LiDAR‐camera extrinsic parameter error. An error propagation scheme is first formed to illustrate how these errors fundamentally influence the accuracy of the HDVM. The effectiveness of the proposed pipeline is demonstrated through our codeavailable at https://github.com/ebhrz/HDMap. The performance is verified using typical datasets, including indoor garages and complex urban scenarios.

Robust Online Estimation of State of Health for Lithium-Ion Batteries Based on Capacities under Dynamical Operation Conditions

Lithium-ion batteries, as the main energy storage component of electric vehicles (EVs), play a crucial role in ensuring the safe and reliable operation of the battery systems through monitoring their state of health (SOH). However, temperature variations and battery aging have significant impacts on the internal parameters of lithium-ion batteries, and these changes directly correlate with the accuracy of battery SOH estimation. To address these issues, this paper proposes an estimation method for lithium-ion battery SOH that considers the impact of temperature. The method begins with reconstructing a second-order hybrid equivalent circuit model for lithium-ion batteries, through which an adaptive update rate for battery model parameters is designed. On this basis, a nonlinear observer for battery states is introduced by integrating filters to estimate SOH. The proposed method considers the impact of capacity in the design of the parameter adaptive update rate, enabling the capacity to be dynamically adjusted based on the actual state of the batteries. This reduces the cumulative error in the SOC observer and improves the modeling accuracy of battery models. Experimental results demonstrate that the method proposed in this paper exhibits exceptional performance in SOH estimation under different temperature conditions. The mean absolute error for SOH estimation does not exceed 0.5%, and the root mean square error does not exceed 0.2%. This method can significantly improve the estimation accuracy of SOH, providing a more efficient and accurate solution for battery management systems in EVs.

Modified (n+1)D Laplacian for smooth pressure reconstruction based on time-resolved velocimetry (1): analysis and numerics

Abstract We analyze a smooth pressure solver based on the "modified Poisson equation": ∇2 p +ξ 2∂2 p/∂ t 2 = f(u(t)), where p is the pressure field, u (t) is the velocity field measured by time-resolved image velocimetry, and ξ 2 is a tunable parameter to control the solver's diffusive behavior in time. This modified Poisson equation aims at obtaining smooth pressure fields from potentially noisy image velocimetry measurements, and is a part of the current four-dimensional (4D) pressure solver (implemented in, for example, DaVis 10.2) by LaVision. This work focuses on investigating three aspects of the "modified Poisson equation": smoothing effect, error propagation, and drift in time. We first provide rigorous analysis and validate that this solver can sufficiently smooth the computed pressure field by setting a large enough ξ 2. However, a large value of ξ 2 may cause large errors in the reconstructed pressure fields. Then we introduce an upper bound on the error in the reconstructed pressure fields to quantify the error propagation dynamics. Finally, we discuss the potential drift due to the partitioning in time, which is an optional strategy used in LaVision's current 4D pressure solver to reduce computational costs. Our analysis and validation not only show that careful choice of the parameters (e.g., ξ 2) is needed for smooth and accurate pressure field reconstruction but provide theoretical guidelines for parameter tuning when similar pressure solvers are used for time-resolved image velocimetry data.

Three-Dimensional Dead-Reckoning Based on Lie Theory for Overcoming Approximation Errors

This paper proposes a dead-reckoning (DR) method for vehicles using Lie theory. This approach treats the pose (position and attitude) and velocity of the vehicle as elements of the Lie group SE2(3) and follows the computations based on Lie theory. Previously employed DR methods, which have been widely used, suffer from cumulative errors over time due to inaccuracies in the calculated changes from velocity during the motion of the vehicle or small errors in modeling assumptions. Consequently, this results in significant discrepancies between the estimated and actual positions over time. However, by treating the pose and velocity of the vehicle as elements of the Lie group, the proposed method allows for accurate solutions without the errors introduced by linearization. The incremental updates for pose and velocity in the DR computation are represented in the Lie algebra. Experimental results confirm that the proposed method improves the accuracy of DR. In particular, as the motion prediction time interval of the vehicle increases, the proposed method demonstrates a more pronounced improvement in positional accuracy.

Stereologically corrected particle size distributions for polymer-mounted additive manufacturing powders

Well-defined particle size distributions are required for good flowability and powder packing properties of additive manufacturing powders. Mounting powders within a polymer and using standard metallurgical preparation techniques to cross-section and prepare powder particles for optical analysis allows for simple characterisation processes. However, measured diameters of cross-sectioned particles are typically underestimates of actual particle diameters and hence require stereological correction. The effectiveness of three stereological corrections are investigated in this work, namely the Scheil-Schwartz-Saltykov method, the Goldsmith-Cruz-Orive method and a Finite Difference Method. These methods are investigated against plasma-atomised, gas-atomised and ultrasonically processed Ti-6Al-4V powders. The corrected outputs are compared to laser size diffraction, benchmark data for each powder. Although all three stereological corrections produce improved estimations of the particle size distributions, the Finite Difference Method is recommended producing cumulative mean absolute error values of 2.4%, 3.1% and 7.5% for the plasma-atomised, gas-atomised and ultrasonically processed powders respectively.

A performance indicator-based evolutionary algorithm for expensive high-dimensional multi-/many-objective optimization

Surrogate-assisted multi-objective evolutionary algorithms have shown considerable potential for solving optimization problems in which only a small number of expensive function evaluations are available. However, most existing research remains restricted to low-/medium-dimensional problems, with very little attention paid to addressing problems involving decision variables with more than 100 dimensions. In this study, a performance indicator-based evolutionary algorithm (PIEA) is proposed for expensive high-dimensional multi-/many-objective optimization. A surrogate model is employed to approximate the performance indicator rather than directly predicting the objective function, thus simplifying the optimization complexity and mitigating the impact of cumulative errors. An efficient indicator-based optimization strategy emphasising the balance between exploration and exploitation is designed for surrogate-assisted evolution and infill sampling. A history-based selection strategy is implemented to select a suitable indicator from the preset pool for each optimization cycle. An empirical study was conducted on two well-known benchmark suites, and the results demonstrate the superiority of the proposed algorithm over several state-of-the-art algorithms. Moreover, we integrate this concept into a classification-based framework, which further verifies its effectiveness.

A novel adaptive PID controller with new seesaw algorithms using alternative derivatives

ABSTRACT The PID controller is present in at least 90% of industrial applications due to its simplicity and robustness to control linear and non-linear systems. Its main drawbacks include difficulty in achieving proper gains tuning for complex systems and lack of adaptability attributed to its fixed gains when system dynamics change. Despite the emergence of promising controllers like Neural Networks, Fuzzy Logic, Sliding Modes, or Genetic Algorithms, diverse research efforts focus on using these to improve the PID rather than replacing it, aiming for either ideal fixed gains or adaptive gains. Nevertheless, while some require system models, training data, rules establishment, extensive iterations, and demanding computational resources, the PID and the novel APID controller do not. The new seesaw algorithms propose alternative behaviours based on the current error and its derivative, which are dynamic parameters that change over time. These behaviours can be inserted into the PID to imbue it with adaptive characteristics, achieving adaptive PID ( SeesawAPID ) controllers with faster signal rise and stabilization times, reduction of the maximum peak, and less error accumulation compared to conventional PID .

Stochastic analysis of drift error of gyroscope in the single-axis attitude determination

Understanding and mitigating the various stochastic errors in gyroscope measurements is crucial for accurate attitude determination. White noise and bias instability can introduce drift errors, reducing the system’s accuracy. Efficient sensor selection and algorithm design necessitate a thorough understanding of these influences and how they propagate throughout the system. This paper addresses the propagation of significant stochastic errors in the attitude determination system, including white noise (angle random walk), bias instability, rate random walk, and correlated noise. The paper discusses the modeling strategy and statistical characteristics of these error contributors. It then evaluates the variance propagation of these errors within the output of a single-axis attitude determination system. The presented analysis calculates and compares the impact of each source of error on the system’s precision over time. Experiments with the MPU6050 and L3G4200D sensors are conducted to validate the analytical results.

Artificial neural network based on strong track and square root UKF for INS/GNSS intelligence integrated system during GPS outage

When INS/GNSS (inertial navigation system/global navigation satellite system) integrated system is applied, it will be affected by the insufficient number of visible satellites, and even the satellite signal will be lost completely. At this time, the positioning error of INS accumulates with time, and the navigation accuracy decreases rapidly. Therefore, in order to improve the performance of INS/GNSS integration during the satellite signals interruption, a novel learning algorithm for neural network has been presented and used for intelligence integrated system in this article. First of all, determine the input and output of neural network for intelligent integrated system and a nonlinear model for weighs updating during neural network learning has been established. Then, the neural network learning based on strong tracking and square root UKF (unscented Kalman filter) is proposed for iterations of the nonlinear model. In this algorithm, the square root of the state covariance matrix is used to replace the covariance matrix in the classical UKF to avoid the filter divergence caused by the negative definite state covariance matrix. Meanwhile, the strong tracking coefficient is introduced to adjust the filter gain in real-time and improve the tracking capability to mutation state. Finally, an improved calculation method of strong tracking coefficient is presented to reduce the computational complexity in this algorithm. The results of the simulation test and the field-positioning data show that the proposed learning algorithm could improve the calculation stability and robustness of neural network. Therefore, the error accumulation of INS/GNSS integration is effectively compensated, and then the positioning accuracy of INS/GNSS intelligence integrated system has been improved.

GFN: A novel joint entity and relation extraction model with redundancy and denoising strategies

Joint entity and relation extraction refers to the extraction of entities and their corresponding relationships in the given sentence, which has gained increasing attention in recent years. Some joint extraction models utilize a shared encoder to model the interactions between named entity recognition and relation extraction subtasks. Despite achieving decent performance, they inevitably face the issue of error propagation. One-step exhaustive methods can mitigate the error propagation problem to some extent, but they suffer from issues such as huge computation complexity and a proliferation of negative samples. Therefore, addressing the problems mentioned above, we propose a Greedy Filter Network that combines Greedy-NER and Filter-RE. GFN employs the Greedy-NER with a redundancy strategy to prioritize recall, thereby reducing error propagation between subtasks. To reduce the computational complexity, we design an innovative approach to represent and store spans in Greedy-NER. In Filter-RE, we traverse all pairwise combinations of candidate entities. To address the issue of widespread negative samples, we design a denoising strategy with two filters, effectively filtering out entity pairs without relations, which can eliminate noise and alleviate the issue of negative sample proliferation. Finally, to enable flexible control over the redundancy strategy, we design two misclassifying penalty parameters for each module. The experimental results indicate that GFN achieves the state-of-the-art F1-score on the CoNLL04 and NYT datasets, with a notable 2.0% improvement observed specifically on CoNLL04.

A hybrid numerical model for horizontal ground heat exchanger

The horizontal ground heat exchanger (HGHE) possesses a complicated heat transfer mechanism as its extensive spatial scale, long operational duration, and vulnerability to meteorological conditions. Consequently, the long-period simulations of HGHE usually involve significant computational costs, posing challenges for its dynamic optimization implementation. Therefore, this study initially established and validated a conventional numerical (full-order) model for HGHE as the reference model. Subsequently, a hybrid model was developed using the proposed adaptive proper orthogonal decomposition (POD) method. By analyzing the influential characteristics, the study identified the solution strategy and the key parameter values for adaptive POD, followed by the generality tests. The hybrid model proved to successfully mitigate the issue of error accumulation commonly associated with native POD extrapolation. Finally, employing a long-running engineering case study, the accuracy and the solution efficiency of the hybrid model were compared against those of the conventional (full-order) model. The results demonstrated that the hybrid model maintained computational accuracy at a comparable level while exhibiting a computational efficiency 326 % higher than that of the conventional (full-order) model, without requiring additional computational resources. This study can provide efficient modeling support for the dynamic optimization design of HGHE.

GWSM4C: A global wave surrogate model for climate simulation based on a convolutional architecture

Accurate and rapid ocean surface wave simulations are essential for navigation safety, marine activity, and climate change research. However, traditional numerical wave models incur substantial computational costs, especially in long-term simulations for climatology research. Deep-learning methods have shown promise in enabling faster simulations with fewer computational resources. However, the cumulative error in current deep-learning wave models limits their use as surrogate component models in climate modeling. In this work, a deep-learning model, named the Global Wave Surrogate Model for Climate simulation (GWSM4C), was developed based on a convolutional architecture, which accounts for the physical processes (wind waves and swells) of waves. Because GWSM4C can automatically generate initial conditions for each simulation moment depending only on historical wind fields, the accumulation of errors from previous simulated wave states can be avoided. The experimental results demonstrated that simulated global significant wave height produced by GWSM4C exhibited a correlation coefficient of 0.94 and a root-mean-square error of 0.21 m compared with the traditional numerical wave model. Furthermore, the generalization test of the GWSM4C indicates that it is feasible to use GWSM4C for long-term wave simulation in climatology-related studies or to integrate it into a coupled climate model as a surrogate wave component model.

Nonlinear Regularization Decoding Method for Speech Recognition.

Existing end-to-end speech recognition methods typically employ hybrid decoders based on CTC and Transformer. However, the issue of error accumulation in these hybrid decoders hinders further improvements in accuracy. Additionally, most existing models are built upon Transformer architecture, which tends to be complex and unfriendly to small datasets. Hence, we propose a Nonlinear Regularization Decoding Method for Speech Recognition. Firstly, we introduce the nonlinear Transformer decoder, breaking away from traditional left-to-right or right-to-left decoding orders and enabling associations between any characters, mitigating the limitations of Transformer architectures on small datasets. Secondly, we propose a novel regularization attention module to optimize the attention score matrix, reducing the impact of early errors on later outputs. Finally, we introduce the tiny model to address the challenge of overly large model parameters. The experimental results indicate that our model demonstrates good performance. Compared to the baseline, our model achieves recognition improvements of 0.12%, 0.54%, 0.51%, and 1.2% on the Aishell1, Primewords, Free ST Chinese Corpus, and Common Voice 16.1 datasets of Uyghur, respectively.

Stable predictive control of continuous stirred-tank reactors using deep learning

In this work, a Lyapunov-based predictive control method utilizing deep learning techniques is proposed for driving continuous-time nonlinear processes towards the desired equilibrium point. Initially, a neural ordinary differential equation model is developed to learn the continuous-time dynamics from discrete-time sampling data. Subsequently, the theoretical conditions that the control Lyapunov function (CLF) developed on the learned continuous-time system is feasible to act on the actual system through a zero-order-holder are analyzed. Building upon the theoretical analysis and the constructed continuous-time dynamics, a deep neural network control Lyapunov function (DNN-CLF) controller is developed. Importantly, the DNN-CLF is independent of the affine system formulation, effectively addressing the challenge of designing the CLF. Benefiting from the stability guarantee provided by the established DNN-CLF, it is integrated into the model predictive control (MPC) framework to develop Lyapunov-based MPC to further improve the control performance. To ensure safety, considering error propagation and associated risks with enlarging the feasible region of the CLF, tubes are constructed and integrated into the MPC scheme. Finally, a numerical simulation of a chemical process is conducted to validate the efficiency of the proposed method.

Enhancing multivariate, multi-step residential load forecasting with spatiotemporal graph attention-enabled transformer

Short-term residential load forecasting (STRLF) holds great significance for the stable and economic operation of distributed power systems. Different households in the same region may exhibit similar consumption patterns owing to the analogous environmental parameters. Incorporating the spatiotemporal correlations can enhance the load forecasting performance of individual households. To this end, a spatiotemporal graph attention (STGA)-enabled Transformer is proposed for multivariate, multi-step residential load forecasting in this paper. Specifically, the multiple residential loads are cast to a graph and a Transformer with a graph sequence-to-sequence (Seq2Seq) structure is employed to model the multi-step load forecasting problem. Gated fusion-based STGA blocks are embedded in the encoder and decoder of the Transformer to extract dynamic spatial correlations and non-linear temporal patterns among multiple residential loads. A transform attention block is further designed to transfer historical graph observations into future graph predictions and alleviate the error propagation between the encoder and decoder. The embedding of multiple attention modules in the Seq2Seq framework allows us to capture the spatiotemporal correlations between residents and achieve confident inference of load values several steps ahead. Numerical simulations on residential data from three different regions demonstrate that the developed Transformer method improves multi-step load forecasting by 14.7% at least, compared to the state-of-the-art benchmarks.