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Abstract: In many applications of regression, the conditional average of the target variable is not sufficient for prediction. The dependencies between the explanatory variables and the target variable can be complex calling for modelling of the full conditional probability density. The ubiquitous problem with such methods is overfitting since due to the flexibility of the model the likelihood of any datapoint can be made arbitrarily large. In this paper a method for predicting uncertainty by modelling the conditional density is presented based on conditioning the scale parameter of the noise process on the explanatory variables. The model is constructed in such a manner that the unpredictability of the scale of the target distribution translates into a more robust predictive distribution. The overfitting problems are solved by learning the model using variational EM. The method is experimentally demonstrated with synthetic data as well as with real-world environmental data. The viability of the approach was put to test in the ‘Predictive uncertainty in environmental modelling’ competition held at WCCI’06. The proposed method won the competition. [Copyright &y& Elsevier]

Most of the scientific research is focused on KOH-based alkaline electrolysers, while NaOH-based ones are unexplored although they present interesting features. This paper presents a semi-empirical model developed in the Python environment to predict a NaOH-based alkaline electrolyser's performance to cover such a research gap and perform an optimisation procedure of electrochemical parameters. A sensitivity analysis has been carried out to study how its performance changes while varying the: i) NaOH content, ii) pressure, and iii) both. Separately, the best result has been obtained with a NaOH content and an operating pressure of 8% and 6.5 bar, respectively. Furthermore, the same values have been recorded even by varying both the NaOH content and the operating pressure. Specifically, a maximum average efficiency increase of 3.57% at 35 ° C , 0.17% at 40 ° C , and 3.74% at 35 ° C in the case of NaOH content, pressure, and both, respectively. [Display omitted] • A semi-empirical model of a NaOH-based alkaline electrolyser is developed. • Optimised electrochemical coefficients are obtained using non-linear regression. • A sensitivity analysis of a NaOH-based alkaline electrolyser is performed. • Optimal operating conditions, based on the cell temperature, are achieved. • Efficiency increase of 3.74% is obtained with NaOH content and pressure variation. [ABSTRACT FROM AUTHOR]

Aiming to address soft sensing model degradation under changing working conditions, and to accommodate dynamic, nonlinear, and multimodal data characteristics, this paper proposes a nonlinear dynamic transfer soft sensor algorithm. The approach leverages time-delay data augmentation to capture dynamics and projects the augmented data into a latent space for constructing a nonlinear regression model. Two regular terms, distribution alignment regularity and first-order difference regularity, are introduced during data projection to address data distribution disparities. Laplace regularity is incorporated into the nonlinear regression model to ensure geometric structure preservation. The final optimization objective is formulated within the framework of partial least squares, and hyperparameters are determined using Bayesian optimization. The effectiveness of the proposed algorithm is demonstrated through experiments on three public datasets. • Adaptive soft sensor combines unsupervised domain adaptation and dynamic PLS for variable conditions. • Leverages time-delay data augmentation to capture dynamics and constructs a nonlinear regression model in a latent space. • Introduces regular terms for distribution alignment and first-order differences, and incorporates Laplace regularity for geometric structure preservation. • Optimization within partial least squares framework, hyperparameters tuned by Bayesian optimization. [ABSTRACT FROM AUTHOR]

The thermal decomposition and sintering kinetics of microfine magnesite were investigated to inaugurate a new One-step process for preparing high-density sintered magnesia. The optimal parameters for the discharging particle size of magnesite through ball milling were determined using an orthogonal experiment and Three-Way Measures ANOVA. The model for the thermal decomposition process of microfine magnesite was established through TGA-DSC and nonlinear regression analysis. Meanwhile, by describing the sintering process of microfine magnesite in detail through microstructure and CTE, the kinetic mechanisms of grain growth at different sintering stages were obtained. The results revealed that increasing the ratio of ball to powder can quickly obtain microfine magnesite which the bulk density reaches 3.45 g·cm−3 after One-step sintering. The thermal decomposition process required an activation energy of only 124.98 kJ·mol−1, which is much lower than existing technology and followed the Two-dimensional phase boundary reaction mechanism R 2. Additionally, the densification process was dominated alternatively by grain boundary diffusion and volume diffusion. This paper provided a detailed theoretical basis and leads a new direction in the One-step preparation of high-density sintered magnesia. [ABSTRACT FROM AUTHOR]

• Machine learning (ML) techniques were pioneered to analyze non-linear relationships. • Algorithm's predictive power validated ML models, preventing spurious relations. • Recursive feature elimination explored predictor importance. • Presence of non-linear relationships is suggested, advising further investigation. • Acknowledgment of skepticism stresses rigorous analysis for long-term correlations. The Earth's climate is a complex system that can be influenced by various internal and external factors. Previous research has explored the relationship between climate and external forcings such as solar activity and GCR. However, the relations are intricate and intertwined into almost chaotic meteorological measurements. This paper delves deeper into understanding their interactions. GCR flux, Sunspot number (SSN), total solar irradiance (TSI), UV irradiance (UVI), and the Oceanic Niño Index (ONI) are the predictor variables, while total cloud amount (TCA) and low cloud amount (LCA) are the response variables. The analysis begins with standard statistical techniques and continues with multiple regression models including random forest, which is a machine learning (ML) method that can be used for non-linear regression. Subsequently, Recursive Feature Elimination (RFE) is employed to scrutinize the correlation among the predictor parameters. In the ML model, the final 25% of the dataset is held out and tested for validation, so, the predictive power of the algorithm is measured. Both geographical and temporal patterns have been investigated. This study suggests that a non-linear relationship might exist between the parameters, and should be investigated further, particularly in specific regions of the world. [ABSTRACT FROM AUTHOR]

Conventional convergence analysis on mini-batch learning is usually based on the stochastic gradient concept, in which we assume that the training data are presented in a random order. Also, some convergence results require that the learning rate should decrease with the number of training cycles, and that the objective function is a smooth function. Practically speaking, a deterministic presentation scheme with a fixed learning rate is more preferable. Hence, there is a gap between theoretical results and actual implementation. This paper aims at filling the gap. We use the radial basis function (RBF) model for nonlinear regression problems as an example to analyze the convergence properties of mini-batch learning. This paper considers a nonsmooth objective function, which consists of three terms. The coexistence of these three terms is able to handle a number of situations. The first term is a conventional training set error. The second term is a quadratic term which is used to suppress the effect of imperfections in the implementation. The last term is an ℓ 1 -norm term which is used to select important RBF nodes for the resultant network. Note that the ℓ 1 -norm term is a nonsmooth function. Although a nonsmooth ℓ 1 -norm is included and the mini-batch algorithm is deterministic, we are still able to derive the convergence properties, including the sufficient conditions for convergence and range of learning rate. With our results, we have a better theoretical understanding on the behaviour of mini-batch learning and obtain some guidelines on choosing the learning rate. The analysis results can be extended to other flat structural neural network models and other objective functions, which are with quadratic terms and ℓ 1 -norm. [ABSTRACT FROM AUTHOR]

Given the current maturity of hydrogen technologies, accurate and computationally efficient numerical models are crucial for improving their understanding and development. Traditional models are either computationally prohibitive or lack the capacity to assess the spatial distribution of critical variables. The present paper suggests a hybrid numerical model for Fuel Cells (FCs) and electrolysers, articulating the coupling between a 1D analytical model and a Computational Fluid Dynamics (CFD) model via a nonlinear regression. Results present an initial validation of the 1D analytical model and the CFD model, and, once the validation is proven successful, the hybrid model is evaluated with a relatively long and highly varying loading profile that covers a wide range of the potential operational points of a FC. The hybrid model shows promising results, showing fidelity levels similar to CFD models, including the capacity to assess the spatial distribution, and a low computational cost. Hence, this hybrid model is demonstrated to be an attractive tool for the design of FCs and electrolysers, optimisation of thermal management and control strategies, degradation analysis, and techno-economic analysis. [ABSTRACT FROM AUTHOR]

• This paper develops a noise/fault aware training objective for incremental ELM. • This paper uses two representative algorithms to develop two noise aware ELM. • The two proposed algorithms are much better than existing ones. • The multiple set concept can further enhance the performance. • We can make other non-noise tolerant algorithms to be noise tolerant. This paper investigates noise/fault tolerant incremental algorithms for the extreme learning machine (ELM) concept. Existing incremental ELM algorithms can be classified into two approaches: non-recomputation and recomputation. This paper first formulates a noise/fault aware objective function for nonlinear regression problems. Instead of developing noise/fault aware algorithms for the two computational approaches in a one-by-one manner, this paper uses two representative incremental algorithms, namely incremental ELM (I-ELM) and error minimized ELM (EM-ELM), to develop two noise/fault aware incremental algorithms. The proposed algorithms are called generalized I-ELM (GI-ELM) and generalized EM-ELM (GEM-ELM). The GI-ELM adds k hidden nodes into the existing network at each incremental step without recomputing the existing weights. To have a fair comparison, we consider a modified version of I-ELM as a comparison algorithm. The simulation demonstrates that the noise/fault tolerance of the proposed GI-ELM is better than that of the modified I-ELM. In the GEM-ELM, k hidden nodes are added into the existing network at each incremental step. Meanwhile, all output weights are recomputed based on a recursive formula. We also consider a modified version of EM-ELM as a comparison algorithm. The simulation demonstrates that the noise/fault tolerance of the proposed GEM-ELM is better than that of the modified EM-ELM. Moreover, we demonstrate that the multiple set concept can further enhance the performance of the two proposed algorithms. Following our research results, one can make some non-noise/fault tolerant incremental algorithms to be noise/fault tolerant. [ABSTRACT FROM AUTHOR]

This paper focuses on researching the various factors that influence the material melting rate during the hot air melting process. To achieve this purpose, the paper proposes a melting model for Acrylonitrile-Butadiene-Styrene (ABS) plastic under hot air heating based on Computational Fluid Dynamics (CFD). Orthogonal experiments were conducted based on the parameter range of each factor obtained in the pre-experiment. The results showed that the outlet distance, hot air velocity, hot air temperature, and their interaction items are important factors that affect the melting rate of ABS materials. Based on the simulation results, a multiple nonlinear regression model was constructed to predict the melting rate under different parameters. Comparing the simulation values with the predicted values of the multiple nonlinear regression model, the error between the two was no >10%, indicating the effectiveness of the prediction model. The research results can help guide the hot air welding melting process for different materials and characteristics, and provide a certain reference value for the development of hot air welding technology. • Welding of airbag labels was performed using hot air welding technology; • Realizes real-time monitoring of melt quality during the material melting process • Using CFD modeling to study the effects of outlet distance, hot air velocity, and hot air temperature on the melting rate. [ABSTRACT FROM AUTHOR]

Oil price forecasting is one of the most challenging issues since it is noisy, non-stationary, and chaotic. In this paper, we design a Bayesian Nonlinear Quantile method consisting of a Threshold Improved model and an Adaptive MCMC model to improve predicting performance. Specifically, the threshold improve model is introduced to solve the problems caused by the completely asymmetric distribution, and the Adaptive MCMC model is used to get the optimal threshold. Besides, the two-stage framework is applied to improve traditional methods' performance, including the Indirect GARCH model and Asymmetric Slope model. The experimental results show that our approach provides a promising alternative to oil price prediction, and the framework also improve the performance of the traditional methods. The contribution of this paper is to improve the accuracy of the oil price forecasting model, and the framework applies to other energy prices as well. [ABSTRACT FROM AUTHOR]

• New perturbed relative motion equations are derived. • Periodic orbits of deputy satellite are obtained numerically. • One, two, and three loops periodic orbits are analyzed. • The velocity and position of deputy satellite are also analyzed. • Single variable regression model developed to find the true anomaly initial value. This paper presents a novel dynamical system for the perturbed relative motion of deputy satellite. The governing equations are derived in the LVLH frame under the second zonal harmonic coefficient effect of the Earth on both chief and deputy satellites. An extended numerical analysis on the deputy satellite motion is performed, where the initial state vector of deputy satellite and eccentricity of chief satellite are used as initial conditions for finding its own periodic orbits. The interior loops of periodic orbits are obtained using numerical integrator RKEOM. Such orbits are analysed for different parameters and their stability are also discussed, where these orbits have considerable importance in the resonance analysis of motion The second zonal harmonic coefficient effect on the periodicity, initial position, initial true anomaly is studied, alongside exploring these orbits with one, two and three loops. Furthermore, a single variable nonlinear regression model is developed to predict initial true anomaly using eccentricity of chief satellite's orbit. [ABSTRACT FROM AUTHOR]

• A novel AI approach is applied to the transient stability prediction problem. • The mapping between bus voltage features and the CCT is modeled as an additive model. • Group Lasso algorithms are applied to solve the additive model. • Automatic feature selection is achieved in the process of the regression analysis. • For two fault cases in a 470-bus system, our modeling approach is compared with two other competing methods. In this paper, the problem of prediction of the transient stability boundary (TSB) of large-scale power systems is analyzed. For any given fault in a power system, whether a pre-contingency condition is considered as a stable operating point can be characterized by the critical clearing time (CCT). The mapping between the pre-contingency steady state and the CCT is in this paper modelled as additive multivariate regression of nonlinear functions of individual input features. Each individual univariate nonlinear function is approximated by an orthogonal polynomials representation, and then the Group Lasso as well as the adaptive Group Lasso algorithms are employed to estimate the original multivariate regression function. Although the original nonlinear structure is highly dimensional, it is shown in this paper that the final model exhibits a simple parsimonious form composed of only a few input features. This is due to the ability of the employed algorithms to recover the inherent sparsity in additive components of the proposed additive representation. This methodology is demonstrated by being applied to multiple fault cases in the context of a 470-bus power network. This approach is also compared with two competing methods recently applied in the dynamic security assessment literature: kernel ridge regression, as well as the Lasso method applicable to linear sparse models. [ABSTRACT FROM AUTHOR]

Seismic intensity measures are essential quantitative parameters for evaluating and predicting engineering structures' seismic risk and vulnerability. Various regional earthquake analysis and vulnerability models with evaluation and prediction capabilities have been developed using macroseismic and instrumental intensity measures. These results have significant positive implications for evaluating large-scale regional earthquake resilience and predicting earthquake risks. However, the traditional determination of seismic intensity measures is based on given seismic station detection data and macroscopic intensity standards, and the developed seismic risk models are relatively outdated, resulting in relatively low accuracy in assessing the vulnerability of regional structures. This paper proposed an improved instrumental intensity calculation equation and updated the model using 216,000 acceleration records monitored by nine typical seismic stations in China during the Jiuzhaigou earthquake on August 8, 2017. The proposed calculation model was combined with the latest version of China's macrointensity standard, and undamaged building samples were sufficiently considered. The vulnerability level of 1,499 buildings surveyed in the Jiuzhaigou earthquake was assessed. This paper innovatively proposed a membership index calculation model to estimate the impact relationship between different vulnerability levels. A comparative curve model was generated with the updated vulnerability databases of four typical regional structures, considering different vulnerability membership indices. Using the improved seismic intensity measures and nonlinear regression model, an improved vulnerability fitting model was developed to assess the seismic risk of regional structures. The model was analysed and verified using field survey data from the Jiuzhaigou earthquake. • This work improves old seismic intensity measures and proposes an instrument intensity model. • An index calculation model of vulnerability membership is innovatively proposed. • The outdated seismic vulnerability regression model has been improved. • A relatively reasonable optimized Gaussian distribution model is proposed. [ABSTRACT FROM AUTHOR]

In this paper we provide the first solution to the challenging problem of designing a globally convergent estimator for the parameters of the standard model of a continuous stirred tank reactor. Because of the presence of non-separable exponential nonlinearities in the system dynamics that appear in Arrhenius law, none of the existing parameter estimators is able to deal with them in an efficient way and, in spite of many attempts, the problem was open for many years. To establish our result we propose a novel procedure to obtain a suitable nonlinearly parameterized regression equation and introduce a radically new estimation algorithm—derived applying the Immersion and Invariance methodology—that is applicable to these regression equations. A further contribution of the paper is that parameter convergence is exponential and is guaranteed with weak excitation requirements. To achieve this remarkable property we rely on the utilization of a recently introduced parameter estimator that seamlessly combines a classical least-squares search with the dynamic regressor extension and mixing estimation procedure. • A globally convergent estimator for the parameters of a CSTR. • A novel procedure to obtain a suitable nonlinearly parameterized regression equation of the CSTR. • Parameter convergence is guaranteed with extremely weak excitation requirements. [ABSTRACT FROM AUTHOR]

We proposed in a previous work a geometric framework to study a deep neural network, seen as sequence of maps between manifolds, employing singular Riemannian geometry. In this paper, we present an application of this framework, proposing a way to build the class of equivalence of an input point: such class is defined as the set of the points on the input manifold mapped to the same output by the neural network. In other words, we build the preimage of a point in the output manifold in the input space. In particular. We focus for simplicity on the case of neural networks maps from n –dimensional real spaces to (n − 1)–dimensional real spaces, we propose an algorithm allowing to build the set of points lying on the same class of equivalence. This approach leads to two main applications: the generation of new synthetic data and it may provides some insights on how a classifier can be confused by small perturbation on the input data (e.g. a penguin image classified as an image containing a chihuahua). In addition, for neural networks from 2D to 1D real spaces, we also discuss how to find the preimages of closed intervals of the real line. We also present some numerical experiments with several neural networks trained to perform non-linear regression tasks, including the case of a binary classifier. • The equivalence classes are sets of points that are mapped in the same way by the Neural Network. • We reconstruct equivalence classes of a given label in the NN input manifold. • We develop a strategy to step from an equivalence class to another in input manifold. • We apply the developed algorithms to thermodynamics and classification problems. [ABSTRACT FROM AUTHOR]

• A sensitive multi-gas sensing system is developed for CH 4 , NO 2 , and CO 2 gas detection. • A minimum cruciform photoacoustic cell is designed to allow multiple laser beams incident without combination. • The minimum detection limit of CH 4 , NO 2 , and CO 2 gas are 113 ppb, 2.1 ppm, and 1.6 ppm, respectively, with a 5 s integration time. Photoacoustic spectroscopy has the advantage of multi-gas sensing with only one sound detector because of its non-selectivity. A photoacoustic cell (PAC) is an important part of the system as it amplifies the intensity of sound pressure. In this paper, we report on the development of a multi-gas sensing system based on a specially designed cruciform photoacoustic cell (CF-PAC), whose structure contains two beam paths and is suitable for multiple laser beams incident from different directions independently. It is especially suitable where beams are not easy to combine due to large wavelength differences. The structure of the cell is carefully designed using the finite-element method (FEM) and the resonant frequency of it is about 5050 Hz and the external dimension is only 67×60×40 mm with the inner volume of about 24 cm3. We also present a contrast experiment between the CF-PAC and the conventional "H-type PAC" with similar parameters and the result shows that the former sacrifices only a small amount of performance, but adds beam path effectively. The sensor is designed to detect methane (CH 4), nitrogen dioxide (NO 2), and carbon dioxide (CO 2), and the minimum detection limit (MDL) with a 5 s integration time are 113 ppb, 2.1 ppm, and 1.6 ppm, respectively. The 1σ normalized noise equivalent absorption coefficients (NNEA) of the three gases are 2.54×10−9 cm−1 W Hz−1/2, 5.70×10−8 cm−1 W Hz−1/2, and 2.31×10−6 cm−1 W Hz−1/2, respectively. Modified formulas based on nonlinear regression will be given to make the detection results more accurate in the multi-component gas environment. [ABSTRACT FROM AUTHOR]

With the development of intelligentization and network connectivity of new energy vehicles, the estimation of power lithium-ion battery state of charge (SOC) using artificial intelligence methods is becoming a research hotspot. This paper proposes an optimized multi-segment long short-term memory (MSLSTM) network strategy for SOC estimation of powered lithium-ion batteries' adaptive wide temperatures. First, the multi-timescale electrochemical processes during the charging and discharging of power lithium-ion batteries are efficiently analyzed, and the analytically measurable external parameters are classified into subsets based on the analysis. Secondly, the idea of segment long short-term memory (SLSTM) estimation is proposed to enhance the data linkage between the SOC and the nonlinearly varying parameters and to improve the prediction accuracy. Finally, an optimized MSLSTM neural network is proposed for nonlinear regression prediction of SOC in subset intervals through a combination of segmented estimation idea and SLSTM neural network. The proposed algorithm is validated under a variety of temperatures and operating conditions, and the accuracy of the SOC estimation is improved by at least 66.770 % or more. It provides a solution idea for intelligent estimation of power lithium-ion battery SOC. • The subset estimation idea is established using battery intrinsic properties. • Subneural network for SOC estimation is proposed, using SLSTM. • An MSLSTM SOC estimation strategy is proposed for adaptive wide temperature. • The proposed MSLSTM algorithm realizes full SOC estimation with high accuracy. [ABSTRACT FROM AUTHOR]

• A digital twin model of pharmaceutical workshop with 3D visualization for solvent purification and recovery was designed. • The purity of product and solvent was effectively improved by multi-objective genetic algorithm and system evaluation. • The effectiveness of digital twin in predictive capability using CNN-LSTM regression model was demonstrated. Digital twin is to make full use of the physical model, sensor update, operation history and other data to integrate multidisciplinary, multi-physical quantity, multi-scale and multi-probability simulation process, and to complete the full life cycle process of the corresponding physical equipment in the virtual space. In this paper, digital twin technology was used to simulate the production process of a pharmaceutical workshop, thus realizing solvent recovery by an azeotrope system separation process. The separation was optimized by multi-objective genetic algorithm. separation process, wherein the polynomial curve fitting and entropy-weighted TOPSIS data evaluation algorithms were combined to optimize the operating parameters, then the solvent purity and yield reach 99.96 % and 77.9 %, respectively, which is much higher than the corporate requirements. In addition, the effectiveness of the digital twin in providing data-driven prediction capability was verified by a CNN-LSTM-based regression prediction model, and the CNN-LSTM model has an accuracy of more than 98.9 % for all prediction results. Finally, a 3D visualization model was built using the Unity engine, enabling researchers to visualize and explore changes in key metrics during the separation process. This study can provide some guidance for digital transformation and intelligent development in pharmaceutical industry. [Display omitted] [ABSTRACT FROM AUTHOR]

This paper presents a novel method for determining the fundamental frequency and modeling slender masonry structures, which is particularly relevant in the context of structural dynamics. This research evaluates the effectiveness of machine learning techniques, specifically artificial neural networks (ANN), and regression methods, including multiple linear regression (MLR) and multiple nonlinear regression (MNLR), in predicting the fundamental frequency of structures, considering both their geometrical and mechanical properties. The objective is to provide a comprehensive comparison of these methods, emphasizing their benefits, limitations, and potential applications in structural health monitoring. The ANN model demonstrated superior performance to linear and non linear regression methods. The findings could significantly impact both theoretical understanding and practical applications in this field. Moreover, this work paves the way for future research, potentially leading to the creation of more accurate and efficient predictive models for slender masonry structures. This methodology ensures a thorough understanding of the model's behavior and its responsiveness to variations in input parameters. • Comprehensive Database: Robust database of slender masonry structures' characteristics. • Empirical Formulations: New empirical formulas for predicting slender structure frequencies. • ANN Model: ANN model for frequency prediction of slender masonry structures. • Parametric Analysis: Study on geometrical/mechanical parameters' impact on frequency. • Future Research: Groundwork for refining models, ANN identified as the precise model. [ABSTRACT FROM AUTHOR]

Given that blade machining errors can substantially degrade aeroengine performance and reliability, there is a critical imperative to implement stringent control over blade machining errors during the manufacturing process. Nevertheless, the prevailing complexity surrounding the numerous machining error types and their obfuscated interrelationships impedes the comprehensive control of blade profile errors. Consequently, unveiling the nonlinear relationships between the distinct machining errors represents a task of paramount importance. To uncover these nonlinear relationships, this work pioneers the application of factor analysis and Genetic Algorithm-optimized BP neural networks to enable nonlinear regression for diverse blade machining errors. Specifically, this paper first constructs an orthogonal factor analysis model to reduce the dimensionality of complex, high-dimensional blade machining error data and extract underlying correlations. This analysis reveals three distinct error groups, each dominated by a latent common factor. Building on these factor analysis outputs, GA-BP neural networks are then leveraged to perform nonlinear regression for intra-group errors. Guided by the Maximal Information Coefficients (MIC) between different errors, we identify control error types within each group to serve as network inputs, with other errors designated as outputs. To prevent overfitting and accelerate convergence of the neural network, Monte Carlo method is used to augment the limited raw error dataset. The augmented data trains the GA-BP network, establishing multivariate nonlinear models with control errors as independent variables and other errors as dependent variables. The model accuracy is validated by a separate validation set. The comparisons between the predicted and true values in the validation set reveal that the relative errors are around 5 %, indicating that the models achieve an accuracy of approximately 95 %. These results demonstrate the satisfactory performance of the established models. Overall, this work elucidates previously unclear relationships between distinct blade machining errors. These new insights establish the foundation for comprehensive error control and will directly benefit blade design, manufacturing, and performance. [ABSTRACT FROM AUTHOR]

In this paper, we develop a deterministic drag model for stationary spherical particles in a Stokes flow using a cascade of data-driven approaches. The model accounts for the variation in drag experienced by each particle within fixed random arrangements. The developed model is a symbolic expression that offers explainability, ease of implementation, and computational efficiency. Firstly, we generate particle-resolved direct numerical simulation data of the flow past periodic random arrangements of stationary spherical particles with volume fractions between 0.05 and 0.4 using the method of regularized Stokeslets. Secondly, we train graph neural networks (GNs) on the generated data to learn the pairwise influence of neighbouring particles on a reference particle. The GNs are converted to symbolic expressions using genetic programming (GP), unveiling repeated subexpressions. Finally, these subexpressions constitute the foundation of the proposed algebraic model, further refined via non-linear regression. The proposed model can qualitatively mimic the pairwise influences as predicted by the GN and can capture the drag variations with accuracy from 74% and up to 84.7% when compared to the particle-resolved simulations. Due to the interpretability of the proposed model, we are able to explore how neighbour positions alter the drag of a particle in an assembly. The proposed model is a promising tool for studying the dynamics of particle assemblies in Stokes flow. [Display omitted] • The method of regularized Stokeslets is used to perform PR-DNS of random arrangements of spherical particles. • A deterministic drag model is derived from the PR-DNS data using data-driven approaches. • The resulting drag model is a relatively simple algebraic expression, offering explainability and ease of implementation. • The model captures drag variations with an accuracy from 74% to 84.7%. [ABSTRACT FROM AUTHOR]

• Multivariate optimisation and statistical analyses were conducted on scaffold boards. • Effects of the selected wood defects on the performance of boards were investigated. • 0.3 TKAR and 0.1–0.17 MKAR were determined as the most critical values. • Failure is independent from knot defects for the low density and growth rate boards. The uncertainties involved in the prediction of scaffold material performance in the machine grading process have brought forth the necessity to identify the level of influence of wood defects on the scaffold performance required to be optimised for its intended use as a construction material. This paper tackled this important aspect by employing multivariate optimisation and statistical analyses on the previously reported experimental results in the literature on the machine graded scaffold boards from UK Sitka spruce (picea sitchensis) softwoods. Initially, nonlinear multivariate regression analyses were performed for the responses of such variables as failure load, displacement, extreme fibre stress and the critical failure distance to several wood characteristics as contributing factors. The extension of the statistical analysis to the multi-objective optimisation study was accomplished using Response Surface Method (RSM) by considering the mutual interactions between the factors including total and margin knot area ratios, density, rate of growth and slope of grain. This paper represented graphically how the load bearing capacity, the deformation characteristics and the critical failure location points are influenced by the considered factors. The significance of factors and their relative influence on the performance optimisation were finally discussed by providing the essential information on the future use of scaffold board products as construction material. [ABSTRACT FROM AUTHOR]

• The highly nonlinear and multi-modal response function for the day-to-day dynamics calibration is analyzed. • A surrogate-based approach is proposed to calibrate the day-to-day dynamics model. • The day-to-day dynamics model is validated with the license plate recognition data. This paper investigates the day-to-day dynamics model from the perspective of travelers' actual route choice behaviors, and calibrates and validates the route-based day-to-day dynamics model with the real-world license plate recognition (LPR) data. Due to the highly nonlinear and multi-modal response function in the calibration of the optimization problem, traditional gradient-based nonlinear regression algorithms or other analytical optimization approaches are inapplicable to deal with the calibration work. In this paper, a surrogate-based simulation optimization approach is proposed to deal with the expensive-to-evaluate response function in the day-to-day dynamics calibration work. More specifically, the kriging metamodel is adopted to surrogate the optimization function of the calibration process. With this meta-modeling approach, a sound solution can be achieved with only a few sampling points in a comfortably afforded computation burden, thus giving a valid estimation of the parameters in the day-to-day dynamics model. Finally, a case study based on the real-world LPR data is conducted to validate the proposed model and calibration method. [ABSTRACT FROM AUTHOR]

The construction of noise maps is of great significance for the management and control of urban noise and the protection of residents' physical and mental health. The European Noise Directive recommends using computational methods to construct strategic noise maps when possible. The current noise maps based on model calculation rely on complex noise emission and propagation models, and their huge number of regional grids needs to consume a lot of calculation time. This seriously restricts the update efficiency of noise maps, making it difficult to realize large-scale application and real-time dynamic update of noise maps. In order to improve the computational efficiency of noise maps, based on big data-driven technology, this paper combines the traditional CNOSSOS-EU noise emission modeling method with the multivariate nonlinear regression modeling method, and proposes an efficient calculation method of large-region dynamic traffic noise maps based on hybrid modeling method. First, this paper constructs the (daily and nightly) noise contribution prediction models of road sources with different classes, considering the daily and nightly periods and different urban road classes. Parameters of the proposed model are evaluated by using the multivariate nonlinear regression method to replace the complex nonlinear acoustic mechanism modeling. On this basis, in order to further improve the computational efficiency, noise contribution attenuations of the constructed models are parameterized and evaluated quantitatively. And then, the database containing the index table of the road noise sources-receivers and the corresponding noise contribution attenuations is constructed. The experimental results show that compared with the traditional calculation methods based on acoustic mechanism model, the noise map calculation method based on hybrid model proposed in this paper greatly reduces the model computations of noise map, improves the efficiency of noise mapping. It will provide technical support for constructing dynamic noise maps of large urban regions. Overall framework diagram of the proposed traffic noise mapping method. The schematic diagram of efficient update of the constructed dynamic noise map. [Display omitted] • A method of large-region traffic noise maps based on hybrid modeling is proposed. • The method is independent of acoustic calculation software and generous monitors. • The sound pressure level contribution prediction models are developed. • The method is applicable to hourly dynamic update of large-region noise maps. • The method is flexible, expandable and with great portability. [ABSTRACT FROM AUTHOR]

Nonlinear regression is frequently used to fit nonlinear relations between response variables and regressors, for process data. The procedure involves the minimization of the square norm of the residuals with respect to the model parameters. Nonlinear least squares may lead to parametric collinearity, multiple optima and computational inefficiency. One of the strategies to handle collinearity is model reparameterization, i.e. the replacement of the original set of parameters by another with increased orthogonality properties. In this paper we propose a systematic strategy for model reparameterization based on the response surface generated from a carefully chosen set of points. This is illustrated with the support points of locally K-optimal experimental designs, to generate a set of analytical equations that allow the construction of a transformation to a set of parameters with better orthogonality properties. Recognizing the difficulties in the generalization of the technique to complex models, we propose a related alternative approach based on first-order Taylor approximation of the model. Our approach is tested both with linear and nonlinear models. The Variance Inflation Factor and the condition number as well as the orientation and eccentricity of the parametric confidence region are used for comparisons. • The paper considers the model reparametrization to decrease ill-condition in nonlinear regression. • The support points of K-optimal designs are used for constructing a family of surface curves. • Semidefinite Programming is used to find K-optimal designs. • Two different approaches to handle the parameter's reversion are presented. • The methodology is demonstrated with various challenging nonlinear regression models. [ABSTRACT FROM AUTHOR]

Nonlinear regression plays a crucial role in various engineering applications. For the sake of mathematical tractability and ease of implementation, most of the existing inference procedures are derived under the assumption of independent and identically distributed (i.i.d.) Gaussian-distributed data. However, real-world situations often deviate from this assumption, with the true data generating process being a correlated, heavy-tailed and non-Gaussian one. The paper aims at providing the Misspecified Cramér–Rao Bound (MCRB) on the Mean Squared Error (MSE) of any unbiased (in a proper sense) estimator of the parameters of a nonlinear regression model derived under the i.i.d. Gaussian assumption in the place of the actual correlated, non-Gaussian data generating process. As a special case, the MCRB for an uncorrelated, i.i.d. Complex Elliptically Symmetric (CES) data generating process under Gaussian assumption is also provided. Consistency and asymptotic normality of the related Mismatched Maximum Likelihood Estimator (MMLE) will be discussed along with its connection with the Nonlinear Least Square Estimator (NLLSE) inherent to the nonlinear regression model. Finally, the derived theoretical findings will be applied in the well-known problem of time-delay and Doppler estimation for GNSS. • We focuses on lower bounds for nonlinear regression under non-iid, non-Gaussian data. • The Misspecified Cramér–Rao Bound has been derived and the efficiency of the NLLSE investigated. • The MCRB depends of the data autocorrelation function but not on their joint pdf. • The MCRB equates the Gaussian-based CRB for the parameter of interest under iid heavy-tailed data. [ABSTRACT FROM AUTHOR]

This paper introduces a novel approach to learn multi-task regression models with constrained architecture complexity. The proposed model, named RFF-BLR, consists of a randomised feedforward neural network with two fundamental characteristics: a single hidden layer whose units implement the random Fourier features that approximate an RBF kernel, and a Bayesian formulation that optimises the weights connecting the hidden and output layers. The RFF-based hidden layer inherits the robustness of kernel methods. The Bayesian formulation enables promoting multioutput sparsity: all tasks interplay during the optimisation to select a compact subset of the hidden layer units that serve as common non-linear mapping for every tasks. The experimental results show that the RFF-BLR framework can lead to significant performance improvements compared to the state-of-the-art methods in multitask nonlinear regression, especially in small-sized training dataset scenarios. [ABSTRACT FROM AUTHOR]

Highlights • The paper contributes set-membership regression (SMR), a new approach to nonlinear parameter estimation under measurement uncertainty. • Links between SMR and both guaranteed parameter estimation and classical statistical inference are investigated. • Several approaches to describing tight enclosures of the SMR regions using complete- search methods are developed. • Case studies are presented to illustrate various theoretical and computational aspects of SMR. Abstract This paper introduces set-membership nonlinear regression (SMR), a new approach to nonlinear regression under uncertainty. The problem is to determine the subregion in parameter space enclosing all (global) solutions to a nonlinear regression problem in the presence of bounded uncertainty on the observed variables. Our focus is on nonlinear algebraic models. We investigate the connections of SMR with (i) the classical statistical inference methods, and (ii) the usual set-membership estimation approach where the model predictions are constrained within bounded measurement errors. We also develop a computational framework to describe tight enclosures of the SMR regions using semi-infinite programming and complete-search methods, in the form of likelihood contour and polyhedral enclosures. The case study of a parameter estimation problem in microbial growth is presented to illustrate various theoretical and computational aspects of the SMR approach. [ABSTRACT FROM AUTHOR]

Highlights • Generating Pareto curves to show the optimal trade-off between Robustness and Performance. • Find the optimal PI and PID controller for First-Order and Integrating Plus Delay Processes. • Investigating the difference between ideal and serial PID, and the impact of filtering. • Comprehensive comparison between optimal-, SIMC- and "improved" SIMC-tuning. Abstract The first-order plus delay process model with parameters k (gain), τ (time constant) and θ (delay) is the most used representation of process dynamics. This paper has three objectives. First, we derive optimal PI- and PID-settings for this process. Optimality is here defined as the minimum Integrated Absolute Error (IAE) to disturbances for a given robustness level. The robustness level, which is here defined as the sensitivity peak (M s), may be regarded as a tuning parameter. Second, we compare the optimal IAE-performance with the simple SIMC-rules, where the SIMC tuning parameter τ c is adjusted to get a given robustness. The "original" SIMC-rules give a PI-controller for a first-order with delay process, and we find that this SIMC PI-controller is close to the optimal PI-controller for most values of the process parameters (k , τ , θ). The only exception is for delay-dominant processes where the SIMC-rule gives a pure integrating controller. The third objective of this paper is to propose and study a very simple modification to the original SIMC-rule, which is to add a derivative time τ d = θ /3 (for the serial PID-form). This gives performance close to the IAE-optimal PID also for delay-dominant processes. We call this the "improved" SIMC-rule, but we put "improved" in quotes, because this controller requires more input usage, so in practice the original SIMC-rule, which gives a PI-controller, may be preferred. [ABSTRACT FROM AUTHOR]

• The feasibility of CO2 foams added in tranditional grouts for synchronous grouting was examined. • Quadratic polynomial models were determined for predicting performance properties of CSG. • The mutual influence of independent variables on the grouting performance were illustrated by response plane diagrams. • The optimal mass ratio for achieving an optimal synchronous grout performance were established by NSGA-Ⅱ. • Effectiveness and economy characteristics were investigated by a real project study. A popular topic in the field of underground engineering is to find synchronous grouting materials with excellent performance and environmental protection characteristics. In this study, CO 2 -foamed synchronous grouting (CSG) materials are prepared with cement, water, CO 2 foams, fly ash, fine river sand and bentonite. The feasibility of the material is verified by a series of detailed tests and analyses. The properties and performance of the CSG materials are investigated. The effects of the ratios of water/binder (cement + fly ash), fly ash/cement, binder/fine river sand and bentonite/water on the response value of the synchronous grouting material performances are investigated with stepwise nonlinear regression analysis models and response plane diagrams. NSGA-II is used to solve the multiobjective problem to obtain an optimal mass ratio. The results indicate that the grout component proportion directly impacts the performance of CSG material. Under the optimal ratio conditions, the specific gravity of CSG is 19.42 % lower and the early strength is 52.46 % higher than that of traditional grouts, and other properties meet the basic performance requirements of grout. The microstructure and product analysis show that the presence of CO 2 foams causes the carbonation reaction of the hydration products in the cement mortar to form calcium carbonate and silica gel. The carbonation reaction consumes free water, decreasing the setting time. Calcium carbonate and silica gel effectively increase the mechanical properties of the material and achieve the storage of CO 2 in cement-based materials. The research strategy and optimal ratio proposed in this paper verify the effectiveness, practicality and environmental economy of CSG material as a synchronous grouting material, providing a new choice for tunnel excavation grouting. [ABSTRACT FROM AUTHOR]

Atmospheric particulate matter pollution has attracted much wider attention globally. In recent years, the development of atmospheric particle collection techniques has put forwards new demands on the real-time source apportionments techniques. Such demands are summarized, in this paper, as how to set up new restraints in apportionment and how to develop a non-linear regression model to process complicated circumstances, such as the existence of secondary source and similar source. In this study, we firstly analyze the possible and potential restraints in single particle source apportionment, then propose a novel three-step self-feedback long short-term memory (SF-LSTM) network for approximating the source contribution. The proposed deep learning neural network includes three modules, as generation, scoring and refining, and regeneration modules. Benefited from the scoring modules, SF-LSTM implants four loss functions representing four restraints to be followed in the apportionment, meanwhile, the regeneration module calculates the source contribution in a non-linear way. The results show that the model outperforms the conventional regression methods in the overall performance of the four evaluation indicators (residual sum of squares, stability, sparsity, negativity) for the restraints. Additionally, in short time-resolution analyzing, SF-LSTM provides better results under the restraint of stability. [Display omitted] [ABSTRACT FROM AUTHOR]

[Display omitted] Fibrillar dry adhesives have shown great potential in many applications thanks to their tunable adhesion, notably for pick-and-place handling of fragile objects. However, controlling and monitoring alignment with the target objects is mandatory to enable reliable handling. In this paper, we present an in-line monitoring system that allows optical analysis of an array of individual fibrils (with a contact radius of 350 µm) in contact with a smooth glass substrate, followed by the prediction of their adhesion performance. Images recorded at maximum compressive preload represent characteristic contact signatures that were used to extract visual features. These features, in turn, were used to create a linear model and to train different linear and non-linear regression models for predicting adhesion force depending on the misalignment angle. Support vector regression and boosted tree models exhibited highest accuracies and outperformed an analytical model reported in literature. Overall, this new approach enables predictions in gripping objects by contact observations in near real-time, which likely improves the reliability of handling operations. [ABSTRACT FROM AUTHOR]

Numerical methods such as finite elements or finite differences to solve ordinary (ODEs) or partial differential equations (PDEs) are essential to computing in science and engineering. These discrete methods approximate the differential operators as matrices with non-zero coefficients for close-by degrees of freedom — the so-called stencil. For the computation of the stencil coefficients, the symbolic differential equation is generally required beforehand. In a recent work, we have demonstrated the usage of linear regression models for the accurate inference of stencil coefficients from spatial field data of linear, one- and two-dimensional PDEs with constant coefficients. In this paper, we introduce the propagation error, which may be used to evaluate regressed stencil coefficients with respect to the numerical stability of the induced system, which is a critical aspect for applications. Based on the propagation error, we continue by comparing several optimization techniques for variable selection that allow us to extend the applicability of linear models in stencil regression to non-linear PDEs. Finally, we highlight how a sliding-window approach may be utilized on spatio-temporal data to consider PDEs with non-constant coefficients. In summary, the analyses provided in this paper extend the use of linear regression models for the inference of stencil coefficients to a much broader class of applications. All source code associated with this study is publicly available at https://github.com/HSU-HPC/ESCO_OperatorInference_TimeDependentProblems. [ABSTRACT FROM AUTHOR]

In recent years, lithium-ion batteries have been widely used in the field of new energy, and the prediction of the remaining useful life (RUL) of lithium-ion batteries has become the focus in this field. There are few literatures about the fusion of multi-expert knowledge, integrated into the training process of the BP Neural Network, in RUL prediction based on small sample data, but it can improve the performance of the BP Neural Network and require less training sample data in non-linear regression model, which is the innovation of this paper. When there is a lot of expert knowledge, there is no general framework that can simultaneously integrate multiple pieces of expert knowledge. Therefore, this paper proposes a multi-expert knowledge processing method based on the Kreisselmeier-Steinhauser (KS) agglomeration function and applies it to the prediction of the remaining life of lithium-ion batteries. First, indirect health factors are extracted based on the NASA lithium-ion battery aging dataset. Secondly, the initial weights and thresholds of the Back-Propagation (BP) Neural Network are optimized by a genetic algorithm. The KS agglomeration function is used again to condense multiple pieces of expert knowledge into one. Finally, the expert knowledge is integrated into the training process of the BP Neural Network by the Augmented Lagrange multiplier method. The simulation results show that, compared with the mainstream algorithms, the improved algorithm proposed in this paper reduces the relative error (RE) and mean absolute error (MAE) obviously and has better prediction results. It means that the improved algorithm can the effectively improve the RUL prediction accuracy of lithium-ion batteries when there are many expert knowledges. • Indirect health factors are extracted based on the NASA lithium-ion battery aging dataset • The KS agglomeration function is used again to condense multiple pieces of expert knowledge into one • The expert knowledge is integrated into the training process of the BP Neural Network by the augmented Lagrange multiplier • Compared with the ALM-GA-BP neural network, the improved algorithm proposed in this paper reduces RE and MAE [ABSTRACT FROM AUTHOR]

This paper formulates a fuzzy logic neuron that uses n-uninorms to construct uni-nullneurons. A fuzzy neural network (FNN) composed of these neurons is easy to operate with nullnorms and uninorms at different times, which results in high accuracy of the model outputs and increases the flexibility in connecting the rule antecedents (enabling AND and OR connections within one rule). This, in turn, may allow experts/operators to extract more knowledge from data. The FNN uses a one-versus-rest classifier learning scheme for multi-class classification problems, where neuron activation levels construct the (indicator) regression matrix; this results in a non-linear regression by indicator, which can resolve the inherent class masking problem apparent in the linear case. We propose a specific neuron-selection strategy in the learning stage that applies Lasso to bootstrap replications in order to ensure that the rule base is as compact as possible and induced by a low number of neurons. To evaluate the new neuron acting in FNNs, we performed pattern classification, and regression tests. Compared with traditional FNN in the literature, our variant showed improved model accuracies for several high-dimensional real-world datasets in binary and multi-class classification and regression problems. Combined with the ability to generate human-readable rules, this offers the ability to generate parsimonious responses with a high degree of confidence. [ABSTRACT FROM AUTHOR]

One of the most versatile and powerful algorithms for the identification of nonlinear dynamical systems is the NARMAX (Nonlinear Auto-regressive Moving Average with eXogenous inputs) approach. The model represents the current output of a system by a nonlinear regression on past inputs and outputs and can also incorporate a nonlinear noise model in the most general case. In recent papers, one of the authors introduced a NARX (no noise model) formulation based on Gaussian Process (GP) regression and derived the corresponding expressions for Higher-order Frequency Response Functions (HFRFs). This paper extends the theory for the GP-NARX framework by providing a means of converting the GP prediction bounds in the time domain into bounds on the HFRFs. The approach is demonstrated on the Duffing oscillator. [ABSTRACT FROM AUTHOR]

Rheological study of powder flow is a hot topic in recent years. This paper aims to provide a novel alternative method for powder rheological characterization, instead of the conventional melt rheology. To achieve this goal, powders including glass beads, pulverized coal and alumina with different particle sizes were used as experimental materials. Powder flow properties were determined in terms of angle of repose, Hausner ratio, Carr's flowability index and permeability. Further, powders were discharged from the pressurized hopper to evaluate the effect of differential pressure on powder flow. The relationship between the differential pressure and the particle velocity was analyzed to reveal the non-Newtonian rheological behaviors of powders, which were further discussed from the perspective of the flow behavior index and the consistency coefficient. Based on the multivariate nonlinear regression analysis of the data, the flow behavior index was related to powder physical parameters and flow parameters, and the predictions agreed well with the experimental results. This study may provide a simple and feasible method for the rheological characterization of powder. [Display omitted] • This paper provides an alternative method for powder rheology characterization. • Flow characteristics of different powders was analyzed by different flow parameters. • Effect of the differential pressure on the powder discharge rate was discussed. • Non-Newtonian fluid-like properties of powders were revealed by rheological method. • An equation between flow behavior index and powder properties was established. [ABSTRACT FROM AUTHOR]

[Display omitted] • Data on dilute acid pretreatment (DAP) of biomasses were aggregated from 63 papers. • Most DAP studies are in the ranges 0–30 min (70 %), 100–200 °C (83 %) and 0 %–2% (70 %). • The negative time–temperature relationship is not correlated with acid levels. • The time–temperature equivalences are quantified by nonlinear formulas. • Materials and methods standardization are needed to limit the variability of data. This review provides a critical analysis of the state of the art of dilute acid pretreatment applied to lignocellulosic biomass. Data from 63 publications were extracted and analysed. The majority of the papers used residence times of<30 min, temperature ranges from 100 °C to 200 °C, and acid levels between 0 % and 2 %. Yields are quantified directly after pretreatment (xylose content) or after enzymatic hydrolysis (glucose content). Statistical analyses allowed the time–temperature equivalence to be quantified for three types of biomass: they were formulated by non-linear expressions. In further works, investigating less explored areas, for example moderate temperature levels with longer residence times, is recommended. Pretreatment material (time–temperature kinetics, reactor type) and analytical methods should be standardized and better described. It becomes mandatory to promote the development of an open, findable, accessible, interoperable, and reusable data approach for pretreatments research. [ABSTRACT FROM AUTHOR]

To optimize the crushing chamber of the gyratory crusher, the discrete element method (DEM) is used to explore the influence of the concave curve height, concave curve radius, eccentric angle, and mantle shaft speed on the performance of the crushing chamber in this paper, here, the DEM analysis model of iron ore particle is established based on the bonded particle model. Based on this, a prediction model of the crushing chamber performance is established through the multiple nonlinear regression, and the multi-objective optimization is performed based on the genetic algorithm (GA). The corresponding optimization values are 450 mm, 950 mm, 0.2°, and 100 rpm, respectively. Finally, the validity of the optimization results is verified by DEM simulation, and the results show that productivity and power density is increased by 36% and 26%, respectively. The optimized crushing force is approximately twice the one before optimization. Both discharge granularity and power consumption are reduced to varying degrees. [Display omitted] • The crushing chamber performance is explored by the method of DEM and RSM. • The crushing chamber performance is analysed in axial and radial directions. • The multi-objective optimization based on GA is performed. • The power density is proposed to characterize power consumption. [ABSTRACT FROM AUTHOR]

As far as the calibration of bulk material for DEM simulations is concerned, it is necessary to adjust the properties of simulated bulk material until the behaviour of this digitally modelled material coincides with the behaviour of physical material tested in laboratory tests. One well-established parameter that is often used for this purpose is the so-called angle of repose, which can be described as the highest possible angle, with respect to the horizontal plane, at which bulk material can be heaped without collapsing. For the determination of this angle, various kinds of tests are applicable, such as the commonly used lifting cylinder test, in which a bottomless cylinder filled with bulk material is lifted off the ground. Digital bulk material calibration regarding the angle of repose is then performed using DEM simulations and adjusting the influencing material parameters correspondingly until the same angle of repose is obtained with the digital and thus calibrated bulk material model. Since the angle measurement is still mostly done by hand, which harbours the danger of errors, and the calibration process with altering angle measurement and parameter adjustment is rather time-consuming, the development of an algorithm for the evaluation of the angle of repose promises some significant advantages. To name a few: higher reproducibility and accuracy of measurements, by eliminating the factor human; faster calibration due to a well-defined evaluation process, also implementable as algorithms directly in calibration processes; and benefits due to statistically supported, time-efficient analysis of large amounts of data. This paper gives a step by step explanation of the methods behind the developed algorithm for the determination of the angle of repose, in particular, in order to enable the implementation of these methods as tools in custom software programs. Thus the developed algorithm is useful for applications ranging from simple angle determination to fully automated calibration procedures etc. [Display omitted] • The angle of repose is one of the most significant characteristics of bulk materials. • Its determination is essential for calibrating materials in DEM simulations. • A digitally implemented algorithm for this determination promises to be advantageous. • Computing the angle of repose by digitally analysing a bulk heaps outline curve. • Proposed methods for this computing: Using linear regression or a non-linear fit. [ABSTRACT FROM AUTHOR]

[Display omitted] • The DEM simulation model of the gyratory crusher is established based on the Ab - t 10 breakage model. • To explore the impact of influencing factors on performance of the gyratory crusher, the Analysis of Variance is performed based on the Box-Behnken design. • The prediction model of gyratory crusher performance is established by multiple nonlinear regression. • The concave is designed by a quartic equation and the optimal parameters are obtained using multi-objective optimization. To study and optimize the crushing chamber performance of the gyratory crusher, the impact of the crushing chamber shape on the gyratory crusher performance is explored in this paper. The discrete element method (DEM) analysis model of ore particle and gyratory crusher is established, where ore particle crushing is realized based on the Ab - t 10 breakage model, and its validity is verified based on actual working conditions. On this basis, the performance of the gyratory crusher under different crushing chamber shapes is studied by combining the DEM simulation with the response surface method (RSM), and the performance prediction model is obtained based on multiple nonlinear regression. Further, the productivity is considered as the main optimization objective, the mass percentage of effective particles and the crushing force are used as auxiliary optimization objectives. The multi-objective optimization is implemented and the optimized effects are analysed by DEM simulation, and the optimized quartic equation coefficients of the concave curve are obtained. Finally, the results show that the productivity, mass percentage of effective particles, and crushing force are increased to varying degrees. Meanwhile, the clogged layer area increases to some extent, which promotes the crushing of ore particles. [ABSTRACT FROM AUTHOR]

Accurate cluster photovoltaic power prediction (CPPP) is crucial for the operation and control of renewable energy grid-connected power systems. The traditional modeling strategies for CPPP such as direct aggregation (DA) and statistical upscaling (SU) have limitations such as error accumulation and upscaling factor uncertainty. To address these issues, this paper proposed a novel hybrid approach for CPPP by combining machine learning models with an improved SU technique. Firstly, a robust broad learning system (BLS) model, in which the Generalized Maximum Correntropy Criterion (GMCC) is used to replace the original mean square error (MSE) loss in BLS, is proposed to solve the problem of multiple outliers affecting the prediction accuracy of regional cluster stations, and it is called GBLS. Then, the Relevance Vector Machine (RVM) as an effective nonlinear regression model is further utilized to compensate for the prediction errors obtained by the GBLS to form the hybrid prediction model, namely GBLS-RVM. Moreover, to mitigate the uncertainty associated with scaling factors in traditional SU strategy, a new SU strategy is developed to refine the relationship between the reference station and the cluster sub-region, enabling direct modeling for regional power prediction. Finally, data from two PV clusters in different regions of China are used to validate the effectiveness of the proposed model, and the results show that under the improved SU strategy, the GBLS-RVM model, reduced RMSE by approximately 33.7% compared to the traditional BLS model, and the RMSE decreased by 12.89% and 30.2% when compared to traditional DA and traditional SU strategies. • A novel hybrid method for CPPP is developed by combining ML and improved SU technique. • A BLS with GMCC (GMCC-BLS) as a prediction model is developed to handle the outliers in measurement data. • An innovative error correction strategy based on RVM is proposed to improve prediction reliability. • A new SU technique is used to establish direct relationships between reference stations and subregions. [ABSTRACT FROM AUTHOR]

• Single-layered 2D nanosheets of α-ZrP were obtained through exfoliation. • Free amine groups were covalently attached to the single-layered α-ZrP nanosheets. • AF-ZrP shows an extraordinarily high adsorption capacity for Pb2+ and Congo red dye. • Non-linear regression methods are more accurate compared to linear methods. This paper reports a facile route for preparing single-layered and crystalline 2D nanosheets of α-zirconium phosphate (α-ZrP), which were further functionalized through covalent attachment of amino organosilane on its exfoliated surfaces (AF-ZrP) to enhance their sorption capacity for Pb2+ and Congo red removal. Two possible surface arrangements of NH 2 groups were observed: one as free amine groups without bonding and the other as protonated or hydrogen-bonded amine groups. AF-ZrP exhibits extraordinary adsorption capacities of 1640 and 1213 mg g−1 for removing Pb2+ ions and CR dye. Further, linear and non-linear regression methods have been studied and compared for fitting four adsorption isotherm models and two kinetics models. Non-linear Freundlich isotherm and non-linear pseudo-second order kinetic models prove the most suitable. The high adsorption capacity, easy regeneration, and reusability rendered AF-ZrP a suitable adsorbent for removing Pb2+ ions and Congo red (CR) dye at industrial scale. [ABSTRACT FROM AUTHOR]

Deep neural operators, such as DeepONet, have changed the paradigm in high-dimensional nonlinear regression, paving the way for significant generalization and speed-up in computational engineering applications. Here, we investigate the use of DeepONet to infer flow fields around unseen airfoils with the aim of shape constrained optimization, an important design problem in aerodynamics that typically taxes computational resources heavily. We present results that display little to no degradation in prediction accuracy while reducing the online optimization cost by orders of magnitude. We consider NACA airfoils as a test case for our proposed approach, as the four-digit parameterization can easily define their shape. We successfully optimize the constrained NACA four-digit problem with respect to maximizing the lift-to-drag ratio and validate all results by comparing them to a high-order CFD solver. We find that DeepONets have a low generalization error, making them ideal for generating solutions of unseen shapes. Specifically, pressure, density, and velocity fields are accurately inferred at a fraction of a second, hence enabling the use of general objective functions beyond the maximization of the lift-to-drag ratio considered in the current work. Finally, we validate the ability of DeepONet to handle a complex 3D waverider geometry at hypersonic flight by inferring shear stress and heat flux distributions on its surface at unseen angles of attack. The main contribution of this paper is a modular integrated design framework that uses an over-parametrized neural operator as a surrogate model with good generalizability coupled seamlessly with multiple optimization solvers in a plug-and-play mode. • Generating an efficient and inexpensive surrogate model based on DeepONets. • The surrogate model is invariant to the low or high-dimensional parameterizations. • Prediction of flow field is used for various cost functions in the optimization loop. • Computing drag to lift ratio using the inferred high-dimensional flow field. • Integration of the Dakota optimization framework with the DeepONet surrogate. [ABSTRACT FROM AUTHOR]

In this paper, a novel adaptive stable backstepping controller(BSC) based on support vector regression (SVR) has been introduced for nonlinear dynamical systems. Stable BSC is designed over Lyapunov stability of the closed-loop system. The nonlinear system dynamics required to constitute the BSC architecture are identified via SVR. The prediction competency of SVR and the stable behavior of BSC are aggregated in this architecture for nonlinear systems. The performance evaluation of the proposed adaptive BSC has been examined on a nonlinear inverted pendulum(IP) and a nonlinear mass–spring–damper(NMSD) system. The acquired results provide a successful and stable BSC control performance for both nonlinear systems. [ABSTRACT FROM AUTHOR]

The inclusion of the geographic information into regression models is becoming increasingly popular due to the increased availability of corresponding geo-referenced data. In this paper, a novel framework for combining spatio-temporal regression techniques and artificial neural network (ANN) regression models is presented. The key idea is to use the universal approximation property of the ANN function to account for an arbitrary spatial pattern in the dependent variable by including geographic coordinate variables as regressors. Moreover, the implicit location-specific effects are allowed to exhibit arbitrary interaction effects with other regressors such as a time variable. In contrast to other machine learning approaches for spatio-temporal data, the likelihood framework of the classic (linear) spatio-temporal regression model is preserved. This allows, inter alia, for inference regarding marginal effects and associated confidence. The framework also allows for non-normal conditional distributions, conditional spatial correlation, arbitrary trend and seasonality. These features are demonstrated in a simulation section and two data examples, using linear spatio-temporal models as a reference. [ABSTRACT FROM AUTHOR]

Ultra-short-term wind power probabilistic forecasting is of significance for stable power grid operation; however, it is still challenging due to the inherent nonlinearity and uncertainty. Most state-of-the-art methods have focused on achieving quantile prediction using a combination of linear quantile regression and nonlinear complex deep neural networks. Yet, these methods struggle with several dilemmas. Quantile regression deep neural networks require a complete training once for each quantile. The multi-training mode and complex structure of quantile regression deep neural network can lead to extremely high computational complexity. Most of the training of quantile regression deep neural networks are guided by the loss of each quantile, and the weights are adjusted by gradient descent in which the gradient explosion and quantile crossover may be encountered. Therefore, this paper proposes a non-crossing multi-output quantile regression deep neural network optimized by chaotic particle swarm optimization. It designs a multi-output deep neural network to output all quantile estimations simultaneously through one training, effectively solving the structural complexity problem of traditional quantile regression deep neural networks. Since quantile regression produces a non-differentiable loss function which significantly hinders model training, the proposed neural network is trained by chaotic particle swarm optimization. It not only achieves the effect of optimizing all quantile losses simultaneously, but also can significantly alleviate the dilemma of training in traditional neural network weight optimization. In addition, several non-crossing constraints are designed for avoiding quantile crossover. The proposed model is trained and tested on two real-world wind power case studies. The experiment results show that the proposed model shows superiority in performance criteria, training speed, and avoiding quantile crossover. • A non-crossing multi-output quantile regression deep neural network is designed. • It is used to perform ultra-short-term wind power probabilistic forecasting. • Chaotic particle swarm optimization is used to avoid gradient explosion. • A set of constraints is designed for avoiding quantile crossover. • Proposed method performs better than other methods in wind power case studies. [ABSTRACT FROM AUTHOR]

• Two new computational algorithms are proposed for estimating the Lyapunov exponents from time series data in order to test the null hypothesis of a chaotic behavior. • The results obtained provide robust evidence that the Jacobian indirect methods provide better estimates than traditional direct methods in all the experiments we have conducted. • We have shown empirically that the algorithms proposed are robust to the presence of (small) measurement errors because the results obtained are comparable to those which are noise free. • The empirical size of the algorithms proposed decreased and the empirical power increased as the sample size increased which means that our hypothesis tests are consistent and reliable. • This paper opens a new research line where new contributions may appear considering new machine learning methods and deep learning algorithms for estimating the Lyapunov exponents from time series data. Most of the existing methods and techniques for the detection of chaotic behaviour from empirical time series try to quantify the well-known sensitivity to initial conditions through the estimation of the so-called Lyapunov exponents corresponding to the data generating system, even if this system is unknown. Some of these methods are designed to operate in noise-free environments, such as those methods that directly quantify the separation rate of two initially close trajectories. As an alternative, this paper provides two nonlinear indirect regression methods for estimating the Lyapunov exponents on a noisy environment. We extend the global Jacobian method, by using local polynomial kernel regressions and local neural net kernel models. We apply such methods to several noise-contaminated time series coming from different data generating processes. The results show that in general, the Jacobian indirect methods provide better results than the traditional direct methods for both clean and noisy time series. Moreover, the local Jacobian indirect methods provide more robust and accurate fit than the global ones, with the methods using local networks obtaining more accurate results than those using local polynomials. [ABSTRACT FROM AUTHOR]