Fitting Error Research Articles

A novel multi-sensor data fusion enabled health indicator construction and remaining useful life prediction of aero-engine

Remaining useful life (RUL) prediction is vital to formulate a suitable maintenance strategy in manufacturing systems health management. Multisensor data fusion of complex engineering systems has attracted substantial attention due to the fact that a single sensor can only collect partial information. Health indicator (HI) construction plays a crucial role in multisensor data fusion and machinery prognostic, mainly because it attempts to quantify a history and ongoing degradation process by fusing the advantages of multiple sensors. However, large numbers of coefficients are involved for most of the existing HIs. Additionally, simplifications during modeling may inhibit the wide application of the constructed HI. To address these two challenges, a new multisensor data fusion method is proposed in this paper by constructing a HI for the characterization of the degradation process. Firstly, the sensors that collect invalid data or conflicting data are removed through a correlation coefficient operation. Then, principal component analysis (PCA) is adopted to reduce the number of coefficient before constructing the HI. Furthermore, the objective function is constructed under the comprehensive consideration of the three factors of the HI, that is, monotonicity, trendability, and fitting errors. The effectiveness of the proposed method is verified using the C-MAPSS dataset. Multiple comparison results show that the HI possesses excellent performance in both degradation characterization and remaining useful life prediction.

A Modified Regular Perturbation Model for the Single-Span Fiber Transmission Using Learnable Methods

In fiber optic communication systems, the dispersion and nonlinear interaction of optical signals are critical to modeling fiber optic communication, and the regular perturbation (RP) model is a simplified modeling method composed of parallel branches, which has obvious advantages in deep learning backpropagation. In this paper, we propose a simplified single-mode fiber signal transmission model based on the RP model, which significantly improves the fitting accuracy of the model for dispersion and nonlinear interactions at the same complexity by adding trainable parameters to the standard RP model. We explain in the paper that this improvement is applicable to dual-polarization systems and still effective under the conditions of large launch power, without dispersion management, and containing amplified spontaneous emission (ASE) noise. The model uses the standard split-step Fourier method (SSFM) to generate labels and updates parameters through gradient descent method. When transmitting a dual-polarization signal with a launch power of 13 dBm, the modified regular perturbation (MRP) model proposed in the paper can reduce the fitting errors by more than 75% compared to the standard RP model after transmitting through a 120 km standard single-mode fiber.

An extended Kalman filter with mixture kernel maximum correntropy criterion for GPS navigation applications

For enhancing the robustness of the Kalman filter in the presence of non-Gaussian noise or measurement outliers within a nonlinear state-space model, a robust filter based on mixed correlation entropy is proposed in this paper. The mixed correlation entropy cost function is utilized as a replacement for the second-order function used in the Kalman filter for measurement fitting errors in the Global Positioning System (GPS). Leveraging entropy theory with kernel functions, a novel robust filtering algorithm is designed by using the maximum correntropy criterion (MCC). While it has been demonstrated, the MCC-based robust filters are feasible for handling non-Gaussian noise and the default kernel in the original MCC, such as the Gaussian kernel, which may not be sufficient for dealing with more complex data encountered in many practical problems. The selection of kernel parameters for MCC-based filters becomes challenging when an adaptive kernel is not used. Therefore, there is a need to design algorithms, which are insensitive to kernel parameters for handling the measurement outliers. In this paper, the robust filters based on double-Gaussian mixture correntropy are proposed and combined with the nonlinear filtering algorithms, replacing filtering methods that rely solely on the minimum mean square criterion. Finally, the algorithm’s robustness is validated through simulation experiments under a certain degree of accuracy. The solutions suggested may outperform the current robust approaches, according to simulation findings, which can achieve better performance for GPS navigation applications.

Shrimp phenotypic data extraction and growth abnormality identification method based on instance segmentation

Shrimp phenotypic characteristics encompass externally or partially internally observable traits like body length, width, color, and morphology. These traits are vital for assessing shrimp health, growth, and environmental adaptability. The traditional manual sampling method is labor-intensive and inadequately reflects the overall growth status of cultured shrimp. Therefore, this paper proposes a shrimp phenotypic data extraction and growth abnormality identification method based on instance segmentation. Firstly, overhead images of shrimp are collected to form a dataset. Secondly, an improved YOLOv8 algorithm is utilized for instance segmentation of the shrimp. Then, shrimp phenotypic data is extracted through image processing techniques and reference object transformation. Finally, the Kolmogorov-Smirnov and Shapiro-Wilk tests are used to assess the growth and development status of the shrimp groups, while individual growth abnormalities are identified using the Z-value algorithm and the Interquartile Range method. Additionally, this paper optimizes shrimp farming processes such as grading, selective breeding, and feeding based on phenotypic data. On the self-built dataset, the proposed method achieves an average precision of instance segmentation of 99.5 % and an F1 score of 99.3 %. Comparing the shrimp lengths calculated by our model with manual measurements, the absolute error in shrimp length fitting is 4.63 mm, with a relative error of 4.58 %. The accuracy of detecting abnormal individuals in shrimp is 91 %. The results indicate that the proposed method can effectively evaluate shrimp growth status and identify abnormal growth patterns.

Self-supervised neural network for Patlak-based parametric imaging in dynamic [18F]FDG total-body PET.

The objective of this study is to generate reliable Ki parametric images from a shortened [18F]FDG total-body PET for clinical applications using a self-supervised neural network algorithm. We proposed a self-supervised neural network algorithm with Patlak graphical analysis (SN-Patlak) to generate Ki images from shortened dynamic [18F]FDG PET without 60-min full-dynamic PET-based training. The algorithm deeply integrates neural network architecture with a Patlak method, employing the fitting error of the Patlak plot as the neural network's loss function. As the 0-60min blood time activity curve (TAC) required by the standard Patlak plot is unobtainable from shortened dynamic PET scans, a population-based "normalized time" (integral-to-instantaneous blood concentration ratio) was used for the linear fitting of Patlak plot of t* to 60min, and the modified Patlak plot equation was then incorporated into the neural network. Ki images were generated by minimizing the difference between the input layer (measured tissue-to-blood concentration ratios) and the output layer (predicted tissue-to-blood concentration ratios). The effects of t* (20 to 50min post injection) on the Ki images generated from the SN-Patlak and standard Patlak was evaluated using the normalized mean square error (NMSE), and Pearson's correlation coefficient (Pearson's r). The Ki images generated by the SN-Patlak are robust to the dynamic PET scan duration, and the Ki images generated by the SN-Patlak from just a 10-minute (50-60min post-injection) dynamic [18F]FDG total-body PET scan are comparable to those generated by the standard Patlak method from 40-min (20-60min post injection) with NMSE = 0.15 ± 0.03 and Pearson's r = 0.93 ± 0.01. The SN-Patlak parametric imaging algorithm is robust and reliable for quantification of 10-min dynamic [18F]FDG total-body PET.

Inferring Word Class and Meaning From Spoken and Written Texts: A Comparison of Children With and Without Developmental Language Disorder.

The aim of the study was to determine the ability of children with developmental language disorder (DLD) to infer word class and meaning from text and to document variations by word class (noun, verb, adjective) and modality (listening, reading). We also asked whether the children could integrate global cues across the entire passage as well as local cues from the immediate sentence frame to support inferences. Fourth graders with DLD (n = 28) and typical language development (TLD; n = 41) read and listened to expository texts and guessed the noun, verb, and adjective removed from each. Adults (n = 20) completed the task to establish a baseline of correct responses. We used latent semantic analysis (LSA) to determine the semantic fit of the responses to the texts and to determine whether global cues were more difficult for children with DLD than local cues. The DLD group was 24% less accurate than the TLD group. In both diagnostic groups, accuracy varied by word class (nouns > adjectives > verbs) but not modality (reading = listening). Word class errors were rare, and errors of semantic fit were frequent. LSA cosines were higher for correct responses relative to the passage as a whole than the immediate sentence frame, suggesting that both groups mined the more extensive information in the global cues to support inferences. Compared to the TLD group, the DLD group tended to make "worse" errors: repeating words from the sentence frame or coming up with no response at all. Accuracy in the DLD group, but not the TLD group, was related to vocabulary knowledge. When the two groups were collapsed, scores on verbal short-term/working memory and sustained attention also predicted performance, but weaknesses in these aspects of executive function on the part of individuals with DLD did not fully explain the difference between the performance of the DLD and TLD groups. Whether listening or reading, fourth graders with DLD are less able to infer word meaning from texts than their age-mates. The problem reflects, in part, deficits in executive function and lexical semantic knowledge.

Numerical analysis of critical support stiffness in ring ribs of a sandwich composite pressure shell

ABSTRACT To study the hydro-static pressure carrying capability of a sandwich composite pressure shell with ring ribs, and explore a structure design method, we obtain an empirical formula of the ring rib segments critical support stiffness, which is defined as Dcr , via finite element simulation and theoretical analysis method. It was shown that, Dcr is of great significance in designing the sandwich composite pressure shell structure. On this basis, the parameters were dimensionless and the empirical formula was obtained by fitting serious independent simulated results. The fitting error of the empirical formula is within 2%. This fitting method has a certain theoretical value for the theoretical research of sandwich composite pressure shell structure. The obtained results are useful for desinging the bearing capacity of novel structure.

Thermal energy analysis using artificial neural network and particle swarm optimization approach in partially ionized hyperbolic tangent material with ternary hybrid nanomaterials

This investigation holds significant pragmatic implications for endeavors aimed at curbing energy losses stemming from diverse factors. A neural network propelled by artificial intelligence, employing the Levenberg-Marquardt technique (ANN-LMM) has been devised for integrating ternary hybrid nanoparticles into a partially ionized hyperbolic tangent liquid flowing over an extended melting surface (PIHTL-SMS). The substance motion equivalence is delineated, considering the rotational outcome. The heat energy is formulated by amalgamating viscous intemperance and Joule heat contributions. To streamline complexity, the resulting PDEs are transmuted into a series of ordinary differential equations (ODEs) through resemblance transformations. A reference dataset for ANN-LMM is produced encompassing diverse significant model permutations and pretending situations utilizing the Lobatto III-A statistical technique. This reference data undergoes verification, evaluation and training procedures to refine the estimated explanation towards achieving anticipated outcomes. The precision, constancy, capability and resilience of ANN-LMM are substantiated concluded mean squared error (MSE)-based fitness curves, error histograms, regression plots and absolute error evaluations. A relative examination elucidates the correctness of the suggested solver, exhibiting entire errors within the array of 10-10 to 10-06 for all significant constraints. Resulting differential equations are also solved using particle swarm optimization (PSO) approach. In PSO several parameters are optimized to enhance the performance of the algorithm. Optimizing these parameters help to improve the effectiveness and efficiency of the PSO algorithm for given problem. PSO converges quickly to optimal or near-optimal solutions, making it efficient for problems with large domain. Several pivotal graphs are constructed to illustrate the impact of emergent constraints on fluid temperature and velocity profiles. The outcomes underscore the numerical technique as a potent instrument for tackling the intricate conjoined ODEs system prevalent in fluid mechanism and allied intemperance presentations in technology. Additionally, improvements in the Forchheimer constraint and the Weissenberg number are deemed imperative for regulating fluid velocity. Unlike prior research that mostly concentrated on single or binary nanofluids, this work presents the integration of ternary hybrid nanoparticles into a partly ionized hyperbolic tangent liquid, a unique technique. Improved accuracy and processing efficiency are also provided by using an ANN-LMM neural network to solve the complicated transformed ODEs. Comparison of ANN, PSO results and existing results are done which shows validity of the current analysis. This work is unique in that it offers a deeper understanding of fluid behavior at advanced thermal settings by including emergent restrictions, viscous dissipation, and Joule heating.

Temperature and Frequency Dependence of Human Cerebrospinal Fluid Dielectric Parameters.

Accurate human cerebrospinal fluid (CSF) dielectric parameters are critical for biological electromagnetic applications such as the electromagnetic field modelling of the human brain, the localization and intensity assessment of electrical generators in the brain, and electromagnetic protection. To detect brain damage signals during temperature changes by electrical impedance tomography (EIT), the change in CSF dielectric parameters with frequency (10 Hz-100 MHz) and temperature (17-39 °C) was investigated. A Debye model was first established to capture the complex impedance frequency and temperature characteristics. Furthermore, the receiver operating characteristic (ROC) analysis based on the dielectric parameters of normal and diseased CSF was carried out to identify lesions. The Debye model's characteristic fc parameters linearly increased with increasing temperature (R2 = 0.989), and R0 and R1 linearly decreased (R2 = 0.990). The final established formula can calculate the complex impedivity of CSF with a maximum fitting error of 3.79%. Furthermore, the ROC based on the real part of impedivity at 10 Hz and 17 °C yielded an area under the curve (AUC) of 0.898 with a specificity of 0.889 and a sensitivity of 0.944. These findings are expected to facilitate the application of electromagnetic technology, such as disease diagnosis, specific absorption rate calculation, and biosensor design.

Numerical Simulation Study on the Stable Combustion of a 660 MW Supercritical Unit Boiler at Ultra-Low Load

To investigate the safe, stable, and economically viable operation of a boiler under ultra-low-load conditions during the deep peaking process of coal-fired units, a numerical simulation study was conducted on a 660 MW front- and rear-wall hedge cyclone burner boiler. The current research on low load conditions is limited to achieving stable combustion by adjusting the operating parameters, and few effective boiler operating parameter predictions are given for very low-load conditions, i.e., below 20%. Various burner operation modes under ultra-low load conditions were analyzed using computational fluid dynamics (CFDs) methods; this operation was successfully tested with six types of pulverized coal combustion in this paper, and fitting models for outlet flue gas temperature and NOx emissions were derived based on the combustion characteristics of different types of pulverized coal. The results indicate that under 20% ultra-low-load conditions, the use of lower burners leads to a uniform temperature distribution within the furnace, achieving a minimum NOx emission of 112 ppm and a flue gas temperature of 743 K. Coal type 3, with the highest carbon content and a calorific value of 22,440 kJ/kg, has the highest average section temperature of 1435.76 K. In contrast, coal type 1 has a higher nitrogen content, with a maximum cross-sectional average NOx concentration of 865.90 ppm and an exit NOx emission concentration of 800 ppm. The overall lower NOx emissions of coal type 3 are primarily attributed to its reduced nitrogen content and increased oxygen content, which enhance pulverized coal combustion and suppress NOx formation. The fitting models accurately capture the influence of pulverized coal composition on outlet flue gas temperature and NOx emissions. This control strategy can be extended to the stable combustion of many kinds of coal. For validation, the fitting error bar for the predicted outlet flue gas temperature based on the elemental composition of coal type 6 was 8.09%, whereas the fitting error bar for the outlet NOx emissions was only 1.45%.

Forecasting Grain Production in Hubei Province Based on Markov Modeling

Abstract. Grain production plays a crucial role in economic and social development. Accurate prediction of grain production can help agricultural decision-makers allocate resources rationally and do a good job at the next stage of the arrangements for the deployment of the work.This article used the production data, which was from 2023 Hubei Provincial Statistical Yearbook,to simulate and predict the grain production for several years,with the method of Markov prediction. It can be seen from the results that the average fitting error of the model is 3.47%. Using the text dataset of grain production from 2020 to 2022, the results show that the model can effectively improve the prediction accuracy of agricultural grain procuction. Finally, the model is used to predict the agricultural output value structure of China from 2023 to 2027. Markov prediction can improve the predictability and initiative of the work and provide scientific basis for the future decision-making of agricultural managers, and has guiding significance for the work of grain storage and distribution.

Forecasting Grain Production in Hubei Province Based on Markov Modeling

Abstract. Grain production plays a crucial role in economic and social development. Accurate prediction of grain production can help agricultural decision-makers allocate resources rationally and do a good job at the next stage of the arrangements for the deployment of the work.This article used the production data, which was from 2023 Hubei Provincial Statistical Yearbook,to simulate and predict the grain production for several years,with the method of Markov prediction. It can be seen from the results that the average fitting error of the model is 3.47%. Using the text dataset of grain production from 2020 to 2022, the results show that the model can effectively improve the prediction accuracy of agricultural grain procuction. Finally, the model is used to predict the agricultural output value structure of China from 2023 to 2027. Markov prediction can improve the predictability and initiative of the work and provide scientific basis for the future decision-making of agricultural managers, and has guiding significance for the work of grain storage and distribution.

Single Well Production Prediction Model of Gas Reservoir Based on CNN-BILSTM-AM

In the prediction of single-well production in gas reservoirs, the traditional empirical formula of gas reservoirs generally shows poor accuracy. In the process of machine learning training and prediction, the problems of small data volume and dirty data are often encountered. In order to overcome the above problems, a single-well production prediction model of gas reservoirs based on CNN-BILSTM-AM is proposed. The model is built by long-term and short-term memory neural networks, convolutional neural networks and attention modules. The input of the model includes the production of the previous period and its influencing factors. At the same time, the fitting production and error value of the traditional gas reservoir empirical formula are introduced to predict the future production data. The loss function is used to evaluate the deviation between the predicted data and the real data, and the Bayesian hyperparameter optimization algorithm is used to optimize the model structure and comprehensively improve the generalization ability of the model. Three single wells in the Daniudi D28 well area were selected as the database, and the CNN-BILSTM-AM model was used to predict the single-well production. The results show that compared with the prediction results of the convolutional neural network (CNN) model, long short-term memory neural network (LSTM) model and bidirectional long short-term memory neural network (BILSTM) model, the error of the CNN-BILSTM-AM model on the test set of three experimental wells is reduced by 6.2425%, 4.9522% and 3.0750% on average. It shows that on the basis of coupling the empirical formula of traditional gas reservoirs, the CNN-BILSTM-AM model meets the high-precision requirements for the single-well production prediction of gas reservoirs, which is of great significance to guide the efficient development of oil fields and ensure the safety of China’s energy strategy.

Modified REL-Based Piecewise Path Loss Modeling Approach for Shore-to-Ship Communication at 5.6 GHz

The need for reliable and uninterrupted communication systems in the marine environment has become critically important with increasing maritime activities, environmental monitoring, and the spread of autonomous systems. However, the complex structure of electromagnetic wave propagation in a sea environment limits the accuracy of the existing propagation models. Thus, the Modified Round Earth Loss (REL) model was first developed in this study to estimate the path loss more accurately in shore-to-ship communication. Subsequently, a piecewise modeling approach based on the principle of two-segment data modeling was proposed. In the Modified REL model, unlike the traditional REL model, the paths and gains of the direct and reflected waves were not considered equal in the calculations. Moreover, unlike in the classical approach, the receiver height was not taken as a fixed value; the estimated best receiver height value for each measurement was included in the calculations as a representation of the effect of roughness in the sea environment. Thus, the model is better adapted to various environmental conditions. In addition, the proposed piecewise model divides the propagation medium into two regions using a break point calculated by Fresnel zone theory. The Modified REL model was used for the first region and the log-distance model was used for the second region. This method allows for more accurate modeling of signal behaviors, especially at different distances. Experimental measurements and performance evaluations conducted using four different shore-to-ship communication scenarios show that the Modified REL model shows an average improvement of up to 3% in Root Mean Square Error (RMSE) values compared to the classical REL model. Additionally, the proposed piecewise model improves the fitting error of the Modified REL model, which models the data as a single whole, by an average of 22.25%. These findings emphasize the necessity of propagation models that are sensitive and adaptable to environmental changes for maritime communication.

Estimation of Near-surface NO2 Concentration in Guangdong Province Based on Catboost Model

Nitrogen oxide （NOx） is an important air pollutant in the atmosphere, and nitrogen dioxide （NO2） is one of its main components. The monitoring and estimation of NO2 concentration is very important for environmental protection and public health. The near-real-time nitrogen dioxide concentration data （NRTI NO2）, ERA5 meteorological reanalysis data, and DEM data provided by Sentinel-5P atmospheric pollution monitoring satellite were used as estimation variables to estimate the near-surface NO2 concentration in Guangdong Province based on the Catboost model. The results showed that： ① The Catboost model estimated the near-surface NO2 concentration with the highest accuracy, with the coefficient of determination （R2）, root mean square error （RMSE）, and mean absolute error （MAE） of the model fit reaching 0.91, 4.89 μg·m-3, and 3.45 μg·m-3 and the cross-validated R2, RMSE, and MAE reaching 0.90, 4.91 μg·m-3, and 3.43 μg·m-3, with good stability on the monthly and quarterly scales. ② The monthly average NO2 concentration near the surface of Guangdong Province showed a U-shaped trend, with the highest value of 43.8 μg·m-3 in January and the lowest value of 14.37 μg·m-3 in July. The seasonal distribution of the near-surface NO2 concentration was characterized by "high during winter and low during summer and transitional during spring and autumn," and the NO2 concentration in each season was in the following order： winter （27.53 μg·m-3） > spring （20.77 μg·m-3） > autumn （18.77 μg·m-3） > summer （14.85 μg·m-3）. ③ From a spatial distribution perspective, areas with high near-surface NO2 values in Guangdong Province were mainly located in rapidly developing and densely populated areas, while areas with low values were mainly distributed in areas focusing on port economy, agriculture, and new energy sources.

Lifetime mapping using femtosecond time-resolved photoemission electron microscopy.

Time-resolved photoemission electron microscopy (PEEM) has established itself as a versatile experimental technique to unravel the ultrafast electron dynamics of materials with nanometer-scale resolution. However, the approach of performing PEEM-based, pixel-by-pixel lifetime mapping has not been reported thus far. Herein, we describe in detail the data pre-processing procedure and an algorithm to perform time-trace fittings of each pixel. We impose an energy cutoff for each pixel prior to spectral integration to enhance the robustness of our approach. With the energy cutoff, the energy-integrated time traces show improved statistics and lower fitting errors, thus resulting in a more accurate determination of the fit parameters, e.g., decay time constants. Our work allows us to reliably construct PEEM-based lifetime maps, which potentially shed light on the effects of local microenvironment on the ultrafast processes of the material and allow spatial distributions of lifetimes to be correlated with observables obtained from complementary microscopic techniques, hence enabling a more comprehensive characterization of the material.

Optimal Curve Fitting for Serial Chain in Six-Crease Origami Unit

Abstract Origami-inspired structures have been widely used in aerospace and robotics for three-dimensional (3D) symmetrical configurations using crease-symmetrical origami basic patterns. These patterns offer advantages in repeatable and systematic modeling and mass production. However, few studies have focused on 3D nonsymmetrical structures using symmetrical origami basic patterns due to their structure complexity, limiting their application. Therefore, we aim to analyze the folding behavior in 3D nonsymmetrical structures using a 6-crease symmetry origami base pattern. To achieve this goal, we first focus on behavior in a two-dimensional (2D) plane. This article presents a scheme for the behavior of origami units with an optimal curve-fitting algorithm. The curve can be any 2D space curve. The fitting curve, constructed by numerical analysis and an optimal approaching scheme, can satisfy error requirements and retain foldable origami unit features. The article verifies the feasibility of the curve-fitting scheme by presenting two curve examples, including a quadratic curve and a sin wave function. The results show that the fitting error is reduced by 99% when no boundary conditions are applied. This research provides valuable insights into understanding origami unit kinematic optimization through forward and inverse kinematics. It offers potential applications in the engineering design of foldable structures and precision origami-inspired mechanism, thereby opening avenues for further exploration of complex origami structures and their applications in emerging technologies.

Multimodal modeling and identification study of a quadrotor robot

Abstract The flight control system of a flying robot plays a crucial role. Therefore, it is imperative to establish various flight mode control models. Traditional modeling methods face challenges in meeting the demands of rapid research and development due to the emergence of diverse aircraft shapes and load forms. To address these issues, this study focuses on multi-conditions modeling and system identification. Based on flight dynamics theory, a comprehensive quadrotor robot dynamics model along with its state space model was established. Flight tests were designed for system identification under different flight modes. The data obtained from the flight test was preprocessed using an extended Kalman filter algorithm based on flight path reconstruction technology to reduce constant deviation from airborne sensors. Frequency response identification technology was employed to identify control models for hovering mode and forward flight at 10m/s mode in the quadrotor robot. Model structures were determined based on precision index evaluation criteria. Time-domain validation method was utilized to simulate fitting error RMS for each channel model under multiple conditions using different signal excitations derived from datasets collected during experiments. The results confirmed that the proposed aircraft system identification method is effective and feasible.

HF Trimer: A New Full-Dimensional Potential Energy Surface and Rigorous 12D Quantum Calculations of Vibrational States.

HF trimer, as the smallest and the lightest cyclic hydrogen-bonded (HB) cluster, has long been a favorite prototype system for spectroscopic and theoretical investigations of the structure, energetics, spectroscopy, and dynamics of hydrogen-bond networks. Recently, rigorous quantum 12D calculations of the coupled intra- and intermolecular vibrations of this fundamental HB trimer (J. Chem. Phys. 2023, 158, 234109) were performed, employing an older ab initio-based many-body potential energy surface (PES). While the theoretical results were found to be in reasonably good agreement with the available spectroscopic data, it was also evident that it is highly desirable to develop a more accurate 12D PES of HF trimer. Motivated by this, here we report a new, and the first fully ab initio 12D PES of this paradigmatic system. Approximately 42,540 geometries were sampled and calculated at the level of CCSD(T)-F12a/AVTZ. The permutationally invariant polynomial-neural network based Δ-machine learning approach (J. Phys. Chem. Lett. 2022, 13, 4729) was employed to perform cost-efficient calculations of the basis-set-superposition error (BSSE) correction. By strategically selecting data points, this approach facilitated the construction of a high-precision PES with BSSE correction, while requiring only a minimal number of BSSE value computations. The fitting error of the final PES is only 0.035 kcal/mol. To assess its performance, the 12D fully coupled quantum calculations of excited intra- and intermolecular vibrational states of HF trimer are carried out using the rigorous methodology developed by us earlier. The results are found to be in a significantly better agreement with the available spectroscopic data than those obtained with the previously existing semiempirical 12D PES.

Structure Analysis for Plate Components Using an Advanced Boundary Element Method

Accurate and effective evaluation of physical variables is of great significance to the design safety and stability of plate structure. In this paper, an advanced boundary element method is developed to perform the structure analysis for plate components. The method is implemented as follows: Firstly, a novel interpolation method is developed to improve the simulation accuracy of the physical quantities on various structural models of plate components, which can improve the order of interpolation polynomials without changing the degrees of freedom of system equations, and eliminate the influence of the fitting error of physical variable in integral equation; And then an integral transformation frame is employed to remove the influence of the singular and nearly singular integrals in integral equation and ensure the accurate calculation of elastic parameters of plate components; Finally, several numerical examples (a porous plate, a deck framing and a propeller structure are included) are given to verify the feasibility of the proposed method. The results show that the proposed method can accurately evaluate the physical variables of the plate components.