Error Propagation Research Articles

Development of backward compatible physics-informed neural networks to reduce error accumulation based on a nested framework

Physical information neural network (PINN) provides an effective method for solving partial differential equations, and many variants have been derived, the most representative of which is backward compatible physical information neural network (BC-PINN). The core of BC-PINN is to use the prediction of the previous time period as the label data of the current time period, which leads to error accumulation in the process of backward compatibility. To solve this problem, a nested backward compatible physical information neural network (NBC-PINN) is proposed in this paper. NBC-PINN has an overlap region between the computation domain of the previous time period and the computation domain of the current time period, which is trained twice in total. Numerical experiments on four representative time-varying partial differential equations show that NBC-PINN can effectively reduce error accumulation, improve computational efficiency and accuracy, and improve the L2 relative error of the numerical solution with fewer residual allocation points. The development of NBC-PINN provides a theoretical basis for the scientific calculation of partial differential equations, and promotes the progress of PINN to a certain extent.

Research on Multi cabin Collaborative Assembly Method Based on Multi Agent Reinforcement Learning

Abstract In the domain of multi-cabin assembly, the prevailing method entails step-by-step docking assembly, which often leads to the accumulation of errors throughout the assembly process. This paper employs multi-agent reinforcement learning techniques to facilitate collaborative assembly of the lateral force device assembly, thereby enhancing assembly quality. Initially, the assembly process of the final assembly is scrutinized to establish a conducive learning environment. Subsequently, a novel agent configuration is proposed, wherein two agents are deployed to represent a single motion unit. Following this, a diverse range of algorithms is employed to train the model, enabling the selection of the most appropriate algorithm and optimization of pertinent parameters. The resultant multi-agent assembly paths are then generated for comprehensive analysis and comparison. Finally, simulation verification of the paths is conducted, accompanied by an analysis of the assembly-induced stress during the assembly process.

An IMFO-LSTM_BIGRU combined network for long-term multiple battery states prediction for electric vehicles

Predicting the state of power batteries is crucial for ensuring the safe and reliable operation of electric vehicles. However, accurately forecasting multiple battery parameters under full operating conditions remains challenging. Traditional prediction models struggle to accurately represent the actual battery behavior due to irregular vehicle driving patterns. Furthermore, long-term prediction of battery states, essential for potential fault diagnosis, poses significant difficulties for conventional neural networks. To address the issue of error accumulation in recurrent neural networks (RNNs) during multi-parameter battery prediction across various operating conditions, we propose a combined model featuring multi-level feature extraction. This model integrates Long Short-Term Memory (LSTM) and Bidirectional Gated Recurrent Unit (BiGRU) networks, where the LSTM layer employs forget gates to filter out unnecessary data while preserving valuable information. The bidirectional update gate in the BiGRU layer effectively combines historical and future data to enhance time series modeling. This comprehensive approach improves sequence modeling efficiency, thereby increasing reliability. However, the multi-level feature extraction structure introduces higher-dimensional hyperparameters, complicating the optimization process. To maintain prediction accuracy across multiple battery parameters, we propose an improved moth-flame optimization (IMFO) algorithm to optimize the complex hyperparameters of the LSTM_BiGRU model. Extensive experiments conducted on a real-world vehicle dataset demonstrate that the IMFO-LSTM_BiGRU combined network surpasses existing state-of-the-art methods in terms of accuracy and stability.

Flood inundation monitoring using multi-source satellite imagery: a knowledge transfer strategy for heterogeneous image change detection

Flood emergency mapping is essential for flood management, often requiring near real-time extraction of large-scale flood extents by combining pre- and post-event multi-source remote sensing images. Pre-event optical imagery delineates the normal water extent, providing a benchmark for estimation of post-flood changes. Synthetic aperture radar (SAR) imagery provides rapid and accurate interpretation of flood inundation extent during the rainy period. Post-classification comparison is one of the fundamental methods for flood mapping of multi-source imagery, as the image characteristics of SAR and optical imagery are inherently different. However, the accuracy of flood mapping depends on the accuracy of water body delineation from single temporal imagery, which can lead to error propagation in flood extent determination. Change detection methods can extract flood extent directly from pre- and post-event imagery, but the models need to learn a consistent flood feature description between optical and SAR imagery from a limited flood dataset. Here, we propose an automatic method for flood inundation extent extraction using pre- and post-event multi-source imagery that requires only a small number of pseudo-change labels. The methodology adopts a pseudo-Siamese network framework as a Heterogeneous - Flood Inundation Extraction Network (H-FIENet), to detect flood extent between the pre‐ and post-event heterogeneous images. Spatially inconsistent multi-source pre- and post-event imagery was used to create a pseudo flood dataset, and this dataset was used to transfer water body feature knowledge from the pre-trained model to the flood extraction model using a cross-task knowledge transfer strategy. Pre- and post-event images from different satellite sources and different flood scenarios were used to evaluate the performance of H-FIENet. We found that: (1) The methodology produced an overall accuracy of over 0.94 for flood inundation extraction from multi-source heterogeneous pre- and post-event imagery. (2) H-FIENet can detect both expansion and recession of the flood extent using any dual-temporal imagery. Our work makes it possible to automate time-series flood monitoring from multi-source remote sensing imagery.

Digital image correlation calculation method for RGB-D camera multi-view matching using variable template

Multi-view matching is an indispensable method for digital image correlation 3D reconstruction. However, as the camera viewing angle changes, traditional DIC methods can lead to the accumulation of matching errors and an increase in mismatches, thereby affecting the 3D reconstruction quality. This paper proposes a digital image correlation method for multi-view RGB-D images based on variable template matching. Initial positioning is achieved by dynamically adjusting the size and sampling direction of the variable template. Sub-pixel registration is then performed using the inverse compositional algorithm, followed by multi-view point cloud fusion using the Iterative Closest Point (ICP) registration method. Experimental results show that the iteration speed of point cloud registration is increased by 30%, and the cumulative error is reduced by 62.5%. These improvements demonstrate that the proposed method is suitable for multi-viewpoint matching scenarios, achieving excellent results in multi-view feature point matching and multi-view point cloud fusion, significantly enhancing 3D reconstruction accuracy and efficiency.

A near real-time carbon accounting framework for the decarbonization of maritime transport

The recently proposed marine greenhouse gas (GHG) emission pricing mechanism has pressured shipping companies and regulators to adopt effective methods for the real-time monitoring of carbon emissions. This study proposes a Near Real-Time (NRT) carbon accounting framework that leverages machine learning models to enable carbon emission tracking at a 15-minute time interval. The framework incorporates critical factors, such as ship navigation characteristics, weather, and sea conditions to achieve accurate carbon accounting. We validate the framework’s efficacy through a case study of four mega-container ships of varying sizes and navigation scenarios. Our results show a maximum cumulative error of 5.83% for all ship navigation scenarios, even without critical data, and during the most extended voyages of their respective services. The proposed framework provides a new perspective on the decarbonization application of ship energy efficiency prediction research. By integrating it with a cloud-computing platform, shipping companies can enhance their voyage planning and route adjustment to optimize operational efficiency and reduce carbon footprints. Using this framework, international maritime transport regulators can develop an early warning system for carbon emissions to coordinate and improve environmental sustainability practices in the shipping industry.

Utilizing multiple inputs autoregressive models for bearing remaining useful life prediction

Accurate prediction of the remaining useful life (RUL) of rolling bearings is crucial in industrial production, yet existing models often struggle with limited generalization capabilities due to their inability to fully process all vibration signal patterns. We introduce a novel multi-input autoregressive model to address this challenge in RUL prediction for bearings. Our approach uniquely integrates vibration signals with previously predicted RUL values, employing feature fusion to output current window RUL values. Through autoregressive iterations, the model attains a global receptive field, effectively overcoming the limitations in generalization. Furthermore, we innovatively incorporate a segmentation method and multiple training iterations to mitigate error accumulation in autoregressive models. Empirical evaluation on the PMH2012 dataset demonstrates that our model, compared to other backbone networks using similar autoregressive approaches, achieves significantly lower root mean square error (RMSE) and Score. Notably, it outperforms traditional autoregressive models that use label values as inputs and non-autoregressive networks, showing superior generalization abilities with a marked lead in RMSE and Score metrics.

Model-free aperiodic tracking for discrete-time systems using hierarchical reinforcement learning

In the operation of practical systems, it is often a challenging task to deal with limited knowledge of the system dynamics, therefore, it is needed to obtain a framework for the simultaneous learning and control of dynamic systems, able to cope with uncertain dynamics. This paper proposes a model-free aperiodic tracking control method based on MAXQ hierarchical reinforcement learning for unknown dynamics in discrete-time systems. Firstly, a MAXQ hierarchical framework is developed for aperiodic tracking control that decomposes the task into pre-control and accurate control subtasks. The former achieves sub-optimal tracking which prompts the implementation of accurate control. The latter implements aperiodic tracking based on the pre-control result to reduce resource occupation. The structure of the MAXQ framework simplifies the complexity of the tracking task, and the incorporation of pre-control accelerates the learning process in the formal control stage. Secondly, considering the disparities between the control inputs and the control update instants, pre-control is decomposed to learn the triggering strategy and control policy, respectively. Meanwhile, the control policy learns optimal control inputs by minimizing the cost function. Similarly, the triggering strategy and control policy are also separately learned in accurate control. In contrast to traditional aperiodic triggering mechanisms, in accurate control stage, the triggering strategy is developed based on the cumulative error of the pre-control result, thus avoiding the influence of accidental factors and the cumulative effects of errors, enhancing system robustness. Thirdly, the proposed tracking control is derived by using only the input, output, and reference signal data from the system, without relying on system dynamics. It is applicable to both linear and nonlinear systems, demonstrating strong generalizability. Finally, simulation examples are provided to validate the effectiveness and superiority of the proposed method.

基于扫描上下文和 NDT-ICP 融合方案的果园同步定位与绘图方法研究

Simultaneous localization and mapping (SLAM) is one of the key technologies for agricultural robots to build maps and localize in complex orchard environments and realize unmanned autonomous operations. Due to the complexity of the orchard environment, the single canopy feature and the diffuse reflection of light caused by the leaves, etc., the map construction process of the orchard environment leads to mismatch and increases the cumulative error of the map construction. Aiming at the above problems, this paper propose a navigation map construction method for orchard environment based on the fusion of Scan Context and NDT-ICP. The method firstly searches the Ring key quickly to get the candidate frames, and scores the similarity between the candidate frames and the current frame, and effectively detects the loopbacks by two-stage searching algorithm to reduce the false matches in the map of orchard environment. Meanwhile, a point cloud alignment method based on the fusion of normal distribution transform coarse alignment and iterative nearest point exact alignment is used to reduce the cumulative error of the orchard environment map. The results show that the improved algorithm compensates the drift of the point cloud map with higher mapping accuracy, better real-time performance, lower resource utilization, higher overlap between the trajectory estimation and the real trajectory, smoother loops, and a 4% reduction in CPU occupancy. In the complex orchard environment, the root mean square error and standard deviation of the trajectories of this paper's algorithm are 0.57 m and 0.19 m, which are 68% and 83% higher than those of the loop detection algorithms in the Lightweight Ground Optimized Lidar Trajectory Measurement and Multivariate Terrain Mapping (LeGO-LOAM), respectively. Accurate map construction and low drift pose estimation can be performed.The research algorithm effectively reduces the influence of mis-matching and large cumulative error in the process of map construction in the orchard environment, meets the demand for high-precision environmental mapping in the orchard environment, and provides technical support for promoting unmanned operation in the orchard environment.

The Importance of the Knowledge of Errors in the Measurements in the Determination of Copolymer Reactivity Ratios from Composition Data

AbstractOften the errors in the measurement of copolymerizations are not accurately determined or included in the calculation of reactivity ratios. Some knowledge of the errors in the initial monomer ratio, conversion, and copolymer composition is however essential to obtain reliable (unbiased) reactivity ratios with a realistic uncertainty. It is shown that the errors serve a trifold purpose; they can serve as weighing factors in the fit, they can be compared with the fit residues to decide whether the chosen model is adequate for the data and they can be used to construct a realistic joint confidence interval for the reactivity ratios. The best approach is to have an estimate of the individual errors in the copolymer composition, either from a thorough error propagation exercise or from replicate measurements. With these errors, the χ2‐joint confidence intervals can then be constructed which gives a realistic estimate of the errors in the reactivity ratios. Utilizing the Errors in Variables Method (EVM) is correct and useful, but only if the individual errors in all the variables in each experiment are more or less known.

Estimation and uncertainty quantification of magma interaction times using statistical emulation

The evolution of volcanic plumbing systems, which controls the style and size of eruptions, is largely determined by processes at depths that are not observable. Scientists use numerical models to simulate these processes and compare the outputs with data on erupted products to understand the plumbing system and eruption processes. However, our ability to explore the parameter space in order to match petrological and geophysical observations is limited by the computational cost required for such simulations. As an alternative, we present a statistical emulator that can reproduce the numerical results as a function of a set of input parameters. This approach can be used to invert the observed distribution of whole rock chemistry to determine the duration of interaction between magmas preceding an eruption and identify the best matching input parameters. This method intrinsically includes error propagation, thus providing reliable confidence intervals for the relevant parameters of the numerical simulations.

Error Propagation in Asymptotic Analysis of the Data-Driven (s, S) Inventory Policy

Estimating Optimal Inventory Policies: Moving Beyond SAA and Empirical Process Theory In “Error Propagation in Asymptotic Analysis of the Data-Driven (s,S) Inventory Policy,” Zhang, Ye, and Haskell dive into the class multiperiod stochastic inventory control in a data-driven setting. They investigate the statistical properties of the data-driven $(s, S)$-policy obtained by recursively computing the empirical cost-to-go functions. In this setting, the empirical cost-to-go functions for the estimated parameters are not i.i.d. sums because of the error propagation. They establish a novel asymptotic representation for multi-sample $U$-processes in terms of i.i.d. sums. This representation enables them to apply empirical process theory to derive the influence functions of the estimated parameters and to establish joint asymptotic normality. Based on these results, they also propose an entirely data-driven estimator of the optimal expected cost and derive its asymptotic distribution. They demonstrate some useful applications of their asymptotic results, including sample size determination and interval estimation.

A new autonomous positioning method of Baseline-RFMDR and Kalman filter solution

The development of intelligent positioning requires a new method of low-cost to meet the needs of autonomous positioning or emergency positioning underground. A new method of Baseline Radio Frequency Magnetic Dead Reckoning (Baseline-RFMDR) autonomous positioning is constructed in this paper, to solve the problems of low accuracy of geomagnetic matching positioning and large cumulative errors in Pedestrian Dead Reckoning (PDR) positioning, which provides a new approach for high-precision and stable autonomous positioning of underground personnel. This method combines PDR positioning and geomagnetic matching positioning, with the constraint of baseline distance, which is the distance from the Tag Pair to the reader. The Kalman Filter solution equation for this model is constructed, and the recursive equation for the covariance matrix under baseline constraints is derived. An underground positioning test was conducted using the self-developed Baseline RFMDR positioning device, the results showed that the accuracy of this combined positioning method is significantly better than PDR positioning or geomagnetic matching positioning. At normal speed, the MAE and RMSE of Baseline-RFMDR combined positioning can be kept within 0.12 m in the X direction and within 0.2 m in the Y direction. It is 88% more accurate in the X direction than PDR, 60% more than geomagnetic matching, 70% more in the Y direction than PDR, and 75% more than geomagnetic matching. At fast speed, the MAE and RMSE of Baseline-RFMDR combined positioning can maintain 0.2 m in the X direction and 0.61 m in the Y direction. It is 79% more accurate in the X direction than PDR, 21% more than geomagnetic matching, 49% more than PDR in the Y direction, and 46% more than geomagnetic matching. At the same time, Baseline-RFMDR positioning has good robustness. When the initial coordinate error or initial covariance error or Baseline-RFMDR partial failure, the MAE and RMSE of Baseline-RFMDR combined positioning can still be maintained within 0.24 m.

Development of Motorway Horizontal Alignment Databases for Accurate Accident Prediction Models

The safe and efficient operation of highways minimizes the environmental impact, reduces accidents, and promotes the reliability of the transportation infrastructure, all in support of sustainable transportation. The horizontal alignment of highways holds particular importance as it directly impacts driver behavior, vehicle stability, and overall road safety. In many cases, highway inventory data held by infrastructure operators may contain inaccurate or outdated information. The accuracy of the variables used in crash prediction models eliminates possible bias in the variable estimators. This research proposes a methodology to obtain accurate horizontal geometric features from digital imagery based on the analysis of the planimetry, feature geolocation and centerline azimuth sequence. The reliability of the method is verified by means of numerical and statistical procedures. This methodology is applied to 150 km of motorway segments in Portugal. Although it is found that the geometric characteristics of most of the inventory segments closely matched the extracted alignments, very significant differences are found in some sections. The results of the proposed procedure are illustrated with several examples. Finally, the propagation of error in the determination of the geometric design independent variables in the fitting of the statistical models is discussed based on the results.

CASCADE: Dataset of extant coccolithophore size, carbon content and global distribution

Coccolithophores are marine calcifying phytoplankton important to the carbon cycle and a model organism for studying diversity. Here, we present CASCADE (Coccolithophore Abundance, Size, Carbon And Distribution Estimates), a new global dataset for 139 extant coccolithophore taxonomic units. CASCADE includes a trait database (size and cellular organic and inorganic carbon contents) and taxonomic-unit-specific global spatiotemporal distributions (Latitude/Longitude/Depth/Month/Year) of coccolithophore abundance and organic and inorganic carbon stocks. CASCADE covers all ocean basins over the upper 275 meters, spans the years 1964-2019 and includes 33,119 gridded taxonomic-unit-specific abundance observations. Within CASCADE, we characterise the underlying uncertainties due to measurement errors by propagating error estimates between the different studies. This error propagation pipeline is statistically robust and could be applied to other plankton groups. CASCADE can contribute to (observational or modelling) studies that focus on coccolithophore distribution and diversity and the impacts of anthropogenic pressures on historical populations. Additionally, our new taxonomic-unit-specific cellular carbon content estimates provide essential conversions to quantify the role of coccolithophores on ecosystem functioning and global biogeochemistry.

Anti-windup strategies for biomolecular control systems facilitated by model reduction theory for sequestration networks.

Robust perfect adaptation, a system property whereby a variable adapts to persistent perturbations at steady state, has been recently realized in living cells using genetic integral controllers. In certain scenarios, such controllers may lead to "integral windup," an adverse condition caused by saturating control elements, which manifests as error accumulation, poor dynamic performance, or instabilities. To mitigate this effect, we here introduce several biomolecular anti-windup topologies and link them to control-theoretic anti-windup strategies. This is achieved using a novel model reduction theory that we develop for reaction networks with fast sequestration reactions. We then show how the anti-windup topologies can be realized as reaction networks and propose intein-based genetic designs for their implementation. We validate our designs through simulations on various biological systems, including models of patients with type I diabetes and advanced biomolecular proportional-integral-derivative (PID) controllers, demonstrating their efficacy in mitigating windup effects and ensuring safety.

Precision and bias of carbon storage estimations in wetland and mangrove sediments.

Peaty sediments in coastal wetlands play an important role in the sequestration of atmospheric carbon dioxide and its belowground storage. Sediment cores are used to quantify organic matter (OM) density, estimated by multiplying the bulk density of a core segment by its OM fraction. This method can be imprecise, as repeated samples often differ widely. Recent studies have shown that sediment bulk density and OM fraction are not independent but tightly related by a function called the ideal-mixing model. Thus, the bulk density of the sediment can be directly estimated from its OM fraction. Statistical theory and simulations demonstrate that the high variance in the product estimation of OM density is the result of error propagation in the product of two functionally related variables with independent errors. Estimating OM density in wetland sediments using the ideal-mixing model is more precise than the traditionally used product estimate, especially in highly organic sediments.

CRISP-DM-Based Data-Driven Approach for Building Energy Prediction Utilizing Indoor and Environmental Factors

The significant energy consumption associated with the built environment demands comprehensive energy prediction modelling. Leveraging their ability to capture intricate patterns without extensive domain knowledge, supervised data-driven approaches present a marked advantage in adaptability over traditional physical-based building energy models. This study employs various machine learning models to predict energy consumption for an office building in Berkeley, California. To enhance the accuracy of these predictions, different feature selection techniques, including principal component analysis (PCA), decision tree regression (DTR), and Pearson correlation analysis, were adopted to identify key attributes of energy consumption and address collinearity. The analyses yielded nine influential attributes: heating, ventilation, and air conditioning (HVAC) system operating parameters, indoor and outdoor environmental parameters, and occupancy. To overcome missing occupancy data in the datasets, we investigated the possibility of occupancy-based Wi-Fi prediction using different machine learning algorithms. The results of the occupancy prediction modelling indicate that Wi-Fi can be used with acceptable accuracy in predicting occupancy count, which can be leveraged to analyze occupant comfort and enhance the accuracy of building energy models. Six machine learning models were tested for energy prediction using two different datasets: one before and one after occupancy prediction. Using a 10-fold cross-validation with an 8:2 training-to-testing ratio, the Random Forest algorithm emerged superior, exhibiting the highest R2 value of 0.92 and the lowest RMSE of 3.78 when occupancy data were included. Additionally, an error propagation analysis was conducted to assess the impact of the occupancy-based Wi-Fi prediction model’s error on the energy prediction model. The results indicated that Wi-Fi-based occupancy prediction can improve the data inputs for building energy models, leading to more accurate energy consumption predictions. The findings underscore the potential of integrating the developed energy prediction models with fault detection systems, model predictive controllers, and energy load shape analysis, ultimately enhancing energy management practices.

Visual Odometry in GPS-Denied Zones for Fixed-Wing Unmanned Aerial Vehicle with Reduced Accumulative Error Based on Satellite Imagery

In this paper, we present a method for estimating GPS coordinates from visual information captured by a monocular camera mounted on a fixed-wing tactical Unmanned Aerial Vehicle at high altitudes (up to 3000 m) in GPS-denied zones. The main challenge in visual odometry using aerial images is the computation of the scale due to irregularities in the elevation of the terrain. That is, it is not possible to accurately convert from pixels in the image to meters in space, and the error accumulates. The contribution of this work is a reduction in the accumulated error by comparing the images from the camera with satellite images without requiring the dynamic model of the vehicle. The algorithm has been tested in real-world flight experiments at altitudes above 1000 m and in missions over 17 km. It has been proven that the algorithm prevents an increase in the accumulated error.

Accuracy analysis and improvement methods for revolving parts in counter-rotating electrochemical machining with continuous radial feeding

Counter-rotating electrochemical machining (CRECM) stands out as an efficient and cost-effective method for machining aero-engine casings. To maintain stability in the CRECM process equilibrium state, continuous feeding of the cathode tool is essential. However, this continuous feeding approach with single direction of rotation may result in poor roundness and reduced machining accuracy. This paper aims to analyze the sources and rules of roundness error and asymmetry in CRECM. Based on simulation results, a method involving periodic reverse rotation of electrodes with continuous feeding is proposed for CRECM. This approach aims to mitigate the cumulative machining error, thereby significantly improving machining accuracy. Experimental results validate the efficacy of the proposed method at a rotation speed of 0.2 rpm. The roundness error is markedly reduced from 0.19 mm to 0.04 mm, resulting in a more symmetric convex structure. Additionally, the sidewall taper angle is reduced from 14.5 degrees to 6.4 degrees. This underscores the effectiveness of the proposed method in enhancing machining accuracy.