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Non-null tests are more versatile than null tests and could give fast, generic tests with sufficient performance. The non-null testing methods are able to measure aspheric surfaces with substantial deviations from a reference sphere. The ray will return along a different path and interfere with a separate reference ray in a non-null arrangement. The retrace error occurs because of the significant disparity between the aspheric and the reference. To correct retracing errors and replicate aspheric fabrication imperfections, complex systems modelling and simulations are required. We propose a ray-tracing-based technique for simulating the non-null interferometer that estimates the optical path differences by tracking lasers across the reference and testing paths. An error correction method is used by ray trace analysis to correct the retracing errors in non-null tests of aspheric surfaces. Experiments were conducted to demonstrate the effectiveness of this strategy. The result of the study shows that the proposed system successfully and effectively rectifies the retracing error compared to other practical findings and computer simulation methods. It is more versatile, faster, and provides adequate aspheric assessment performance. [ABSTRACT FROM AUTHOR]

• This paper suggests a grating Moiré fringe-based error correction approach that uses an artificial neural network (ANN) and the quartile method (QM). • The approach uses QM for data cleaning operations to eliminate outliers and creates the ANN model with a structure of fully connected layer-normalization layer-fully connected layer for regression training in order to achieve lightweight and stability. • The proposed QM-ANN error correction model's mean absolute error (MAE) can reach 3.3 nm once the QM data has been cleaned and the ANN model has been trained. Many interference factors of the complex and changeable working environment of the grating sensor are the main factors affecting the accuracy; a grating Moiré fringe error correction model based on the quartile method (QM) and artificial neural network (ANN) is proposed in this paper. Firstly, the grating sensor's signals in the working process are collected, and three kinds of interference signals (temperature, humidity and vibration) from the grating sensor working environment are collected simultaneously. Secondly, the QM is used to detect outliers from the collected data and delete data outliers directly. Subsequently, the processed data are input into the ANN model for training. The model is lightweight and stable, because it adopts the cascaded structure of full connection layer-normalization layer-full connection layer, which does not need deploy the complex convolution layer module etc. Finally, the corrected data are output after being processed by the QM-ANN error correction model. The experimental results show that the mean absolute error (MAE) of the proposed QM-ANN error correction model is better than QM-convolutional neural network (CNN), QM-long short-term memory (LSTM) and ANN, CNN, LSTM models without QM. It shows that the proposed model has better robustness and practicability. [ABSTRACT FROM AUTHOR]

• This paper presents an error correction method for curved rail profile measurement based on selective focus, without adding additional hardware. • This paper proposes a method for solving the optimal auxiliary plane through the objective function of the overlap between virtual 3D rail and actual rail. Its advantage is that the optimal auxiliary plane can be solved through a single line laser. • Laboratory experiments have shown that the rail wear error has been reduced to 0.1 mm, while vehicle dynamic experiments have shown that the rail wear error has been reduced to within 0.2 mm. • This paper proposes a virtual 3D rail creation method based on the center of the light strip, providing a new insight into future work on rail profile measurement error correction. Rail profile detection is an important means of railway operation and maintenance. Currently, structured light profile measurement technology is mainly used for vehicle-mounted rail profile measurement. The body attitude of the vehicle will change as it passes by a curve, and the laser plane of the rail profile measurement device would be non-perpendicular to the rail in the local longitudinal direction, resulting in errors in rail profile measurement. To address this issue, an error correction method based on selective focus for curved rail profile measurement is proposed. The virtual 3D rail is generated with the section image of a single-beam laser and projected onto the image plane, which is then combined with the projection data of virtual 3D rail and the actual rail from the rail image to build the optimization function. The optimal auxiliary plane perpendicular to the rail's longitudinal direction is then determined. Finally, error correction is achieved by projecting the measured data onto the optimal auxiliary plane. The effectiveness and accuracy of the proposed method are validated through experiments, demonstrating that regardless of the laser plane's relative pitch or yaw motion with respect to the rail, the corrected profile wear measurement error was under 0.10 mm, satisfying the requirement for rail wear measurement accuracy. In this study, the plane perpendicular to the longitudinal direction of the rail was obtained through selective focus, thus providing a new insight into future work on rail profile measurement error correction. [ABSTRACT FROM AUTHOR]

Wind power forecasting can effectively improve the energy utilization efficiency of a power system and ensure its stable operation. In this study, a novel hybrid multistep prediction model, including the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), variational mode decomposition (VMD), the kernel principal component analysis (KPCA), an enhanced arithmetic optimization algorithm (ENAOA), a bidirectional long short-term memory (BILSTM) neural network, and error correction, was designed for short-term wind power forecasting. First, the collected original wind power data were decomposed into multiple intrinsic mode functions (IMFs) through a secondary decomposition composed of the CEEMDAN and VMD, which eliminated the interactions between different components to achieve denoising. Second, the KPCA was adopted to reduce the dimensionality of the multiple IMFs by extracting the principal components, effectively reducing the complexity of the multidimensional IMF data and improving the forecasting efficiency of the proposed prediction model. Subsequently, an ENAOA was proposed based on the Sobol sequence, adaptive T-distribution, and random walk strategy to optimize the BILSTM parameters. Finally, multiple preprocessed components were predicted by the optimized BILSTM, after which error correction was performed to obtain the final prediction results, which could further reduce the forecast error of the designed prediction model. Based on two sets of data collected from a wind farm in northwest China, the simulation results of 1-step, 4-step, 7-step, and 10-step forecasting revealed that compared with other incomplete models, the various algorithms adopted in the hybrid forecasting model reduced the prediction errors to different degrees, significantly enhanced the wind power prediction performance, and validated the effectiveness and feasibility of the proposed model. • Original wind power data is preprocessed through CEEMNAN and VMD. • KPCA is adopted to extract principal components of several IMFs. • Propose an improved ENAOA optimization algorithm through three improvements. • Error correction is employed to further increase the forecast accuracy. • The hybrid multi-step forecasting model greatly reduces the prediction error. [ABSTRACT FROM AUTHOR]

Accurate day-ahead wind power prediction is the basis for scheduling next-day generation in power systems with a high proportion of wind power. In this study, to overcome the adverse effects of changeable weather conditions and inaccurate numerical weather prediction data on day-ahead wind power prediction, a novel ensemble model considering multiple indicators combined with error correction was proposed. Four representative models that are frequently used for day-ahead wind power forecasting served as benchmark models. Then, considering the mean and variance of prediction errors, the nondominated sorting genetic algorithm was utilized to assemble the forecast outcomes from four benchmark models. Lastly, a statistics-based algorithm for error correction that considered temporal correlation was proposed to enhance prediction accuracy. The effectiveness of the proposed model was verified using data from a real wind farm. In a month of performing the successive day-ahead prediction task, the average errors of the proposed ensemble model were 0.1301 for the root mean square error and 0.1076 for the mean absolute error, which were 1.89%–14.52% and 2.62%–15.54% lower, respectively, than those of other models, including four other individual models and three ensemble models. Through error correction, the average forecast errors decreased to 0.1182 for the root mean square error and 0.0915 for the mean absolute error, indicating 9.14% and 14.96% reductions, respectively. • A novel and feasible framework for day-ahead wind power prediction using NWP data was proposed. • An ensemble model considering multiple indicators was proposed to reduce the uncertainty of prediction. • A statistics-based error correction method considering temporal correlation was proposed. • The effectiveness of the proposed model was verified in a month of successive day-ahead prediction task. [ABSTRACT FROM AUTHOR]

Accurate prognostic for the remaining useful life (RUL) of lithium-ion batteries (LIBs) is extremely crucial to the stable operation and timely maintenance of a battery system. Nevertheless, battery lifespan is difficult to measure due to the capacity regeneration in non-linear and unstable degradation trend. To increase the prediction accuracy, the Time Varying Filter-based Empirical Mode Decomposition (TVF-EMD) is innovatively introduced to decompose the original capacity data into subseries. Meanwhile, the complexities of the subseries are measured by the Box-counting dimension (BCD). Moreover, Fast Ensemble Empirical Mode Decomposition (FEEMD) is exploited to further decompose the most complex subseries. Additionally, Bidirectional Gated Recurrent Unit (BiGRU) is established for (sub-)subseries prognosis. The prediction performance is further strengthened by an error correction method (ECM). Eventually, the effectiveness of the proposed prognosis framework is verified on two battery datasets. The experimental results illustrate that the maximum root mean squared error (RMSE), mean absolute error (MAE) and mean absolute percentage error (MAPE) of the proposed hybrid framework are merely 1.917, 0.434 and 0.706% respectively. Compared with two decomposition methods, MAE can be reduced by at least 22.73%, and a reduction of not less than 7.4% in RMSE is achieved. • A new hybrid methodis proposed for the remaining useful life forecasting. • The secondary decomposition method employed can enhance the composition ability. • The box-counting dimension is utilized to choose the most complicated sub-layers. • An error correction scheme is proposed to further enhance prediction performance. [ABSTRACT FROM AUTHOR]

[Display omitted] • A stepwise hybrid model is proposed for hourly solar irradiance forecasting. • The correction errors are used by a step-by-step approach. • The VMD method is proposed to reduce non-stationarity of irradiance series. • The CNN-LSTM-MLP and DBN are combined. • The feature of high and low frequencies are predicted separately. Accurate and reliable solar irradiance forecasting is critical for distribution planning and modern smart grid management and dispatch. However, due to the time series of solar irradiance with the nonlinearity and nonstationarity, some researches up to now are still unsatisfactory in terms of prediction accuracy and model generalization ability. Therefore, to improve the comprehensive performance of the model, a novel forecasting framework of hourly stepwise forecasting for solar irradiance using integrated hybrid models CNN-LSTM-MLP combined with error correction and variational mode decomposition (VMD) was proposed. In this paper, three different datasets were pre-processed and then the step-by-step predictions of seven different methods were completed based on the proposed procedures. Finally, comprehensive analysis results of the model indicated that the prediction scheme proposed in this paper made full use of, step-by-step prediction, VMD method, integrated hybrid model, and error correction four major advantages greatly improved the anti-interference ability of the model, so that the average performance metrics RMSE, nRMSE, MAE, and R2 of the three datasets reach to 12.53 W/m2, 6.04 %, 7.65 W/m2, and 99.79 %, respectively. Moreover, the optimal promoting percentages of the R2(P R 2 )indicator compared to the persistence model (Per) is by 20.17 %. It is found that the model is superior to a large number of traditional alternative approaches in terms of accuracy and robustness, which may provide a reference for comprehensive performance optimization of the model in the future. [ABSTRACT FROM AUTHOR]

• A unified error model of the geomagnetic measurement data was established. • A two-stage Kalman filter method was proposed to perform data fusion. • An adaptive attitude updating algorithm is proposed to eliminate data interference. • The high-precision geomagnetic directional technology was achieved. Low-cost magnetic and inertial sensors based on micro-electro-mechanical systems (MEMS) are extensively used for navigation systems. However, measurements of the magnetometer are very susceptible to different factors, resulting in low accuracy when used for attitude estimation. To solve these problems, a novel method is proposed for geomagnetic directional technology based on sensor error correction and adaptive hybrid filter. In the dynamic directional accuracy test with the turntable rotating speed of 40°/s, the maximum error and RMSE of the yaw angle is 1.00° and 0.63°, respectively. When magnetic interference exists, this algorithm dynamically adjusts the weighting of the magnetometer data by information entropy and RMSE. The experimental results show that the adaptive attitude updating algorithm can reduce the directional error by 90.61% in the environment of magnetic interference. It can meet the overall demand for high-precision attitude calculation of different carriers. [ABSTRACT FROM AUTHOR]

• A novel signal decomposition algorithm based on FPA-VMD is proposed. • BiLSTM neural network is employed to capture the deep temporal features. • Multiple meteorological factors are considered to improve the model's performance. • The proposed model can perform better for multi-step ahead wind power forecasting. To reduce the effect of nonlinearity and volatility in the wind power time sequence, a two-stage short-term wind power forecasting method based on optimized decomposition prediction and error correction is proposed. In the first stage, in order to improve the decomposition effect of variational mode decomposition (VMD), the decomposition loss is defined as the evaluation criterion to guide the parameter setting of VMD, and flower pollination algorithm (FPA) is utilized to automatically optimize the parameters of VMD. Then the complex wind power sequence is decomposed into simple intrinsic mode functions (IMFs). Besides, bi-directional long short-term memory (BiLSTM) neural network is built for each IMF to explore the deep time-series features of wind power in both past and future directions. In the second stage, to reduce the correlation among meteorological factors, principal component analysis (PCA) is employed to convert the multi-dimensional meteorological factors into low-dimensional principal components. Then, with the input of IMFs and principal component, an error correction model based on BiLSTM neural network is established to reduce the inherent error of the model. The experimental results show that the proposed method has higher prediction accuracy than the traditional methods in single-step and multi-step ahead forecasting. [ABSTRACT FROM AUTHOR]

Carbon price forecasting is an important component of a sound carbon price market mechanism. The accurate prediction of carbon prices is an active topic of research. However, many previous studies have focused on the application of a single model, ignoring the application of combination strategies. In this study, a hybrid forecasting system that includes error correction strategy and divide-conquer strategy is designed to predict the carbon price series accurately. Specifically, the main framework of this article comprises four modules. Data preprocessing module of the divide and conquer strategy is proposed. Next, the optimization module uses a multi-objective grasshopper optimization algorithm to enhance the performance of the prediction module. Then, the error correction module predicts the error sequence and corrects the model results. To verify the performance of the established hybrid forecasting system, experiments were performed using two real carbon price series from China and European Union emissions trading schemes, and the results showed that the mean absolute percentage errors of the system were 2.7793% and 0.6720%, respectively, which are better than the other benchmark methods considered. Moreover, it was proved that the designed forecasting system provides a new, effective, and feasible solution for carbon price forecasting. • An advanced preprocessing strategy is applied to process the signal. • ORELM model is improved by multi-objective optimization strategy. • Datasets for different regions are used in the experiment. • Multiple evaluation metrics for testing system performance. [ABSTRACT FROM AUTHOR]

Cyclic redundancy checks (CRC) are widely used in transmission protocols to detect whether errors have altered a transmitted packet. It has been demonstrated in the literature that CRC can also be used to correct transmission errors. In this paper, we propose an improvement of the state-of-the-art CRC-based error correction method. The proposed approach is designed to significantly increase the error correction capabilities of the previous method, by handling a greater part of error cases through the management of candidate lists and using additional validations. Simulations and results for wireless video communications over 802.11p and Bluetooth Low Energy illustrate the Peak Signal-to-Noise Ratio (PSNR) and visual quality gains achieved with the proposed approach versus the state-of-the-art and traditional approaches. These gains range on average from 1.6 dB to 7.3 dB over Bluetooth Low Energy channels with Eb/No ratio of 10 dB and 8 dB, respectively. • The addition of validation steps can enhance the CRC-based error correction. • Adding checksum validation greatly reduces the candidate's list size. • The parity of the CRC syndrome can avoid unnecessary computations. • The CRC-based correction can improve the quality of wireless video transmissions. • The error distribution has a significant impact on the proposed method's gains. [ABSTRACT FROM AUTHOR]