Automatic Relevance Determination Research Articles

Interpretable Recurrent Variational State-Space Model for Fault Detection of Complex Systems Based on Multisensory Signals

It is necessary to develop a health monitoring system (HMS) for complex systems to improve safety and reliability and prevent potential failures. Time-series signals are collected from multiple sensors installed on the equipment that can reflect the health condition of them. In this study, a novel interpretable recurrent variational state-space model (IRVSSM) is proposed for time-series modeling and anomaly detection. To be specific, the deterministic hidden state of a recursive neural network is used to capture the latent structure of sensor data, while the stochastic latent variables of a nonlinear deep state-space model capture the diversity of sensor data. Temporal dependencies are modeled through a nonlinear transition matrix; an automatic relevance determination network is introduced to selectively emphasize important sensor data. Experimental results demonstrate that the proposed algorithm effectively captures vital information within the sensor data and provides accurate and reliable fault diagnosis during the steady-state phase of liquid rocket engine operation.

State-of-Health prediction of lithium-ion batteries based on a low dimensional Gaussian Process Regression

An accurate determination of the condition of a battery is a key challenge in operation. As the performance of lithium-ion batteries is degrading over time, an accurate prediction of the State-of-Health would improve the overall efficiency and safety. This paper presents a prediction method for the State-of-Health based on a Gaussian Process Regression with an automatic relevance determination kernel in a single model for three different types of battery cells. After reducing the dimension of the problem and a sensitivity analysis of the features, the model is trained, validated, and further tested on unseen data. A minimum test error is obtained with a mean absolute error of 1.33%. Combined with the low uncertainty of the prediction results, this shows the applicability and the great potential of forecasting the condition of a battery using data-driven methods.

Pyaging: a Python-based compendium of GPU-optimized aging clocks.

Aging is intricately linked to diseases and mortality. It is reflected in molecular changes across various tissues which can be leveraged for the development of biomarkers of aging using machine learning models, known as aging clocks. Despite advancements in the field, a significant challenge remains: the lack of robust, Python-based software tools for integrating and comparing these diverse models. This gap highlights the need for comprehensive solutions that can handle the complexity and variety of data in aging research. To address this gap, I introduce pyaging, a comprehensive open-source Python package designed to facilitate aging research. pyaging harmonizes dozens of aging clocks, covering a range of molecular data types such as DNA methylation, transcriptomics, histone mark ChIP-Seq, and ATAC-Seq. The package is not limited to traditional model types; it features a diverse array, from linear and principal component models to neural networks and automatic relevance determination models. Thanks to a PyTorch-based backend that enables GPU acceleration, pyaging is capable of rapid inference, even when dealing with large datasets and complex models. In addition, the package's support for multi-species analysis extends its utility across various organisms, including humans, various mammals, and Caenorhabditis elegans. pyaging is accessible on GitHub, at https://github.com/rsinghlab/pyaging, and the distribution is available on PyPi, at https://pypi.org/project/pyaging/. The software is also archived on Zenodo, at https://zenodo.org/doi/10.5281/zenodo.10335011.

Operational Status Evaluation of Smart Electricity Meters Using Gaussian Process Regression With Optimized-ARD Kernel

Operational Status Evaluation (OSE) is essential for the health management of Smart Electricity Meters (SEM). This paper develops a machine learning-enabled OSE method for SEM. Specifically, the Gaussian Process Regression (GPR) is developed for modeling analysis, where an Optimized Automatic Relevance Determination (OARD) kernel is first used. Though the conventional ARD kernel structure can capture the potential mapping relationship between running time, temperature, humidity, and Measurement Error (ME), it cannot extract the influence degree of different stresses on the ME. To address this problem, an OARD kernel structure is proposed to identify the contribution of each part in ARD structure to the target data. Furthermore, the quartiles line instead of 95% confidence interval is exploited to enhance the performance of GPR for long-term prediction. Combining the two above improvements, a novel OSE model is established for the future-oriented long-term operation of the SEM. It is the first-known data-driven application that utilizes the GPR with OARD kernel to perform OSE for SEM. Actual SEM datasets collected from both dry and hot region are used for model validation and prediction. The results demonstrate that the proposed GPR model with OARD Matern52 kernel outperforms other conventional kernel approaches in the aspect of interpretability. More importantly, the operational status of the SEM in future can be assessed via the proposed OSE framework.

Hydrogen bonding and Hirshfeld surface analysis of gallic acid and its monohydrate based on terahertz spectroscopy

The terahertz (THz) spectroscopy of gallic acid (GA) and gallic acid monohydrate (GAMD) in the frequency range of 0.2–3.0 THz were investigated using terahertz time-domain spectroscopy (THz-TDS) system. The THz absorption spectrum of GAMD exhibited a red-shift compared to that of GA. To resolve the absorption spectra of the two substances, density functional theory (DFT) was employed to calculate and simulate the theoretical spectra of the two substances in this frequency range, while the vibration mode automatic relevance determination (VMARD) method combined with GaussView and VMD software was utilized to determine the origin of each absorption peak. Additionally, Hirshfeld surface analysis and the Atoms-in-Molecules (AIM) topological analysis were conducted to explore the intermolecular interactions between GA and GAMD. The results revealed that the characteristic absorption peaks of both GA and GAMD are attributed to overall atomic and molecular motions, whereas those of GAMD are accompanied by water molecule translation. Furthermore, H…O/O…H hydrogen bonding was identified as the main contributor to the interaction between GA and GAMD. The addition of water molecules led to differentiation in the position and strength of intermolecular interactions; specifically, hydrogen bonding in GA primarily involved the carboxyl group with the hydroxyl group, while hydrogen bonding in GAMD occurred between the water molecule and the hydroxyl group of the central molecule.

Characteristic Analysis and Short-Impending Prediction of Aircraft Bumpiness over Airport Approach Areas and Flight Routes

Based on the Quick Access Recorder (QAR) data covering over 9000 routes in China, the monthly and intra-day distribution characteristics of aircraft bumpiness at different levels were analyzed, and the relationships between the eddy dissipation rate (EDR) and other aircraft flight status elements during bumpiness occurrence were also analyzed. Afterward, aircraft bumpiness routes were constructed using 19 machine learning models. The analyses show that (1) aircraft bumpiness was mainly concentrated between 0:00 a.m. and 17:00 p.m. Severe aircraft bumpiness occurred more frequently in the early morning in January, especially between 5:00 a.m. and 6:00 a.m., and moderate bumpiness always occurred from 3:00 a.m. to 11:00 a.m. (2) The relationship between the left and right attack angles and aircraft bumpiness on the routes was more symmetrical, with a center at 0 degrees, unlike in the approach area where the hotspots were mainly concentrated in the range of −5 to 0 degrees. In the approach area, the larger the Mach number, the more severe the bumpiness. (3) The performances of the Automatic Relevance Determination Regression (ARD), Partial Least Squares Regression (PLS), Elastic-Net Regression (ENR), Classification and Regression Tree (CART), Passive Aggressive Regression (PAR), Random Forest (RF), Stochastic Gradient Descent Regression (SGD), and Tweedie Regression (TWD) based models were relatively good, while the performances of the Huber Regression (HUB), Least Angle Regression (LAR), Polynomial Regression (PLN), and Ridge Regressor (RR) based models were very poor. The aircraft bumpiness prediction models performed best over the approach area of ZBDT (airport in Datong), ZULS (airport in Lhasa), ZPPP (airport in Kunming), and ZLQY (airport in Qingyang). The model performed best in predicting the ZLLL-ZBDT air route (flight routes for Lanzhou to Datong) with different prediction times.

Bubble transport during SGTR accident in lead-cooled fast reactor: A machine learning

Steam generator tube rupture (SGTR) is one of the safety issues for pool-type lead-cooled fast reactors (LFR). Accurately quantifying and predicting the bubble transport result is essential for evaluating the accident. This paper addresses tracking the bubble motion using an Eulerian-Lagrangian method in CFD based on the Europe Lead cooling System (ELSY) primary system model at 1/8 centrosymmetric structure. The steady and transient bubble distributions in the system under different leakage heights are obtained. Furthermore, the simulation results are predicted by machine learning, where Gaussian Process Regression (GPR) is employed for both steady conditions and transient conditions. The data-driven GPR model is established for the bubble transport prediction, which can capture complex non-linear relationships between input variables (i.e. bubble diameter, SG leakage height, final position, system contaminate) and output (reached bubble percentage) responses directly from data. For steady conditions, the prediction results by the kernel function of Automatic Relevance Determination (ARD) Rational Quadratic show the best accuracy in predicting the percentages of bubbles reaching the core, top of the steam generator, and staying in the system, with a total Root Mean Square Error (RMSE) of 3.22%. Four typical transient cases of bubble accumulation in the core are selected for prediction. All the cases are well predicted by the kernel function of ARD Matern 3/2 with low mean averaged error.

Generalized Variable Selection Algorithms for Gaussian Process Models by LASSO-Like Penalty

With the rapid development of modern technology, massive amounts of data with complex pattern are generated. Gaussian process models that can easily fit the nonlinearity in data become more and more popular nowadays. It is often the case that in some data only a few features are important or active. However, unlike classical linear models, it is challenging to identify active variables in Gaussian process models. One of the most commonly used methods for variable selection in Gaussian process models is automatic relevance determination, which is known to be open-ended. There is no rule of thumb to determine the threshold for dropping features, which makes the variable selection in Gaussian process models ambiguous. In this work, we propose two variable selection algorithms for Gaussian process models, which use the artificial nuisance columns as baseline for identifying the active features. Moreover, the proposed methods work for both regression and classification problems. The algorithms are demonstrated using comprehensive simulation experiments and an application to multi-subject electroencephalography data that studies alcoholic levels of experimental subjects. Supplementary materials for this article are available online.

Prediction of algal bloom using a combination of sparse modeling and a machine learning algorithm: Automatic relevance determination and support vector machine

Algae can produce odor substances and toxins that make the smell and taste of water unpleasant and impair the quality of human and aquatic life. Appropriate countermeasures can be implemented in advance in water purification processes to prevent algal disorders if the occurrence of algal blooms is accurately predicted. Several models have been developed to predict algal blooms. However, a comprehensive model that can be universally applied under various conditions is lacking. In this study, automatic relevance determination, a sparse modeling algorithm, and support vector machine were combined to construct prediction models for algal blooms in four Japanese dam reservoirs to predict their occurrence over 7 days. Automatic relevance determination was applied to a dataset consisting of monthly water quality data and daily hydraulic and meteorological data to identify variables relevant to the concentrations of Microcystis spp. and Dolichospermum spp., which are bloom-forming cyanobacteria and are dominant in freshwater ecosystems. A dataset of selected variables was used to train and validate the support vector machine models. The results of variable selection by automatic relevance determination revealed that the average concentration of total nitrogen in the past year and the average maximum temperature in the past 7 days may have an association with the algal concentration. Support vector machine models resulted in 92.3% accuracy and 86.4% precision for Microcystis spp. and 71.4% accuracy and 77.5% precision for Dolichospermum spp. on average in binary classification. The competitive relationship between Microcystis spp. and Dolichospermum spp., which differs according to the nutrient level and temperature, probably affects the prediction performance of the models. Our study suggests that the combination of sparse modeling and machine learning is applicable to the construction of a prediction model for site-specific algal bloom events in dam reservoirs.

Sparse Bayesian machine learning for the interpretable identification of nonlinear structural dynamics: Towards the experimental data-driven discovery of a quasi zero stiffness device

Data-driven discovery of governing laws for complex nonlinear structural dynamic systems remains a challenging issue of paramount importance. This work addresses the above issue by leveraging the available noisy data and integrating sparse Bayesian machine learning (ML) techniques to discover the governing equations. The problem of discovery is re-cast as the automatic relevance determination of models (model selection) from the library of potential candidate basis terms and their coefficients are determined (parameter identification) using sparse Bayesian linear regression. Two sparsity promoting ML algorithms based on relevance vector machines have been employed. Both these approaches use Bayesian statistics and quantify the uncertainty associated with the model predictions. Results from four representative numerical examples of nonlinear structural dynamics illustrate excellent performance of both proposed approaches. The results have been validated with the true governing equations and time response data. Comparison has also been made with a recent and popular sparse discovery approach. Finally, the proposed framework is applied to real datasets that were generated from an in-house designed experimental setup of a quasi zero stiffness device and good performance has been observed.

Development of machine learning-based solubility models for estimation of Hydrogen solubility in oil: Models assessment and validation

This research was done to build computational models for estimating solubility of hydrogen (S) in a given system based on the inputs of temperature (T) and pressure (P). In fact, multiples models were built considering double inputs and single output. To achieve this, three different regression algorithms were trained and tested on a comprehensive dataset using the optimization technique of Grey Wolf Optimization (GWO). The three models used were Elastic Net, Support Vector Regression (SVR), and Automatic Relevance Determination (ARD) Regression. R2 score, root mean square error (RMSE), and mean absolute error were just few of the measures used to assess the models' overall efficacy (MAE). The Elastic Net model achieved the highest R2 score of 0.965 with an RMSE of 8.84×10−2 and an MAE of 7.79×10−2. The SVR technique also performed well, indicated R2 of 0.949, an RMSE of 9.81×10−2, and an MAE of 7.79×10−2. The ARD Regression model revealed an R2 of 0.905 with an RMSE of 1.53×10−1 and an MAE of 1.32×10−1. These findings highlight the potential of machine learning models and metaheuristic algorithms such as GWO in accurately estimating gas solubility in oil, which can have significant implications for various industrial applications.

Sparse Bayesian Learning With Weakly Informative Hyperprior and Extended Predictive Information Criterion.

This article considers the regression problem with sparse Bayesian learning (SBL) when the number of weights P is larger than the data size N, i.e., P》 N. The situation induces overfitting and makes regression tasks, such as prediction and basis selection, challenging. We show a strategy to address this problem. Our strategy consists of two steps. The first is to apply an inverse gamma hyperprior with a shape parameter close to zero over the noise precision of automatic relevance determination (ARD) prior. This hyperprior is associated with the concept of a weakly informative prior in terms of enhancing sparsity. The model sparsity can be controlled by adjusting a scale parameter of inverse gamma hyperprior, leading to the prevention of overfitting. The second is to select an optimal scale parameter. We develop an extended predictive information criterion (EPIC) for optimal selection. We investigate the strategy through relevance vector machine (RVM) with a multiple-kernel scheme dealing with highly nonlinear data, including smooth and less smooth regions. This setting is one form of the regression task with SBL in the P》 N situation. As an empirical evaluation, regression analyses on four artificial datasets and eight real datasets are performed. We see that the overfitting is prevented, while predictive performance may be not drastically superior to comparative methods. Our methods allow us to select a small number of nonzero weights while keeping the model sparse. Thus, the methods are expected to be useful for basis and variable selection.

Development of machine learning-based models for describing processes in a continuous solar-driven biomass gasifier

The synergy of two renewable and efficient sources in producing clean fuels, i.e., solar energy and biomass, can result in high efficiency. In this regard, developing syngas production systems based on solar biomass gasification has attracted much attention. However, experimental setups on solar-driven gasifier processes are costly and time-intensive. In such a situation, an accurate and low-cost alternative is to develop data-driven machine learning (ML) models to predict the processes involved in solar-driven biomass gasifiers. In the present study, several ML models, including random forest (RF), RANdom SAmple Consensus (RANSAC), stochastic gradient descent (SGD), automatic relevance determination (ARD) regression, and elastic net linear (ENL) regression, were developed to accurately predict the various processing of a continuous solar-driven biomass gasifier, including CO production rate and H2 production rate (H2), carbon feeding rate, solar power input, thermochemical reactor efficiency, solar-to-fuel energy conversion efficiency, solar energy input, and carbon consumption rate. Using efficient ML methods, the eight formulas and the eight models for H2, CO production rate, carbon feeding rate, carbon consumption rate, solar energy input, solar power input, thermochemical reactor efficiency, and solar-to-fuel energy conversion efficiency are made in this study. Using the linear form can be reached the best R-Squared (R2) values for all formulas and the model, and the best R2 values are between 0.998 and 0.999 for the formulas by the elastic net and the ARD regression, and also the best R2 values are between 0.998 and 0.999 for the models by the RF and the RANSAC regressor. The R2 values for H2, CO production rate, carbon consumption rate, solar energy input, solar power input, thermochemical reactor efficiency, and solar-to-fuel energy conversion efficiency for formulas, respectively, are 0.998, 0.998, 0.999, 0.999, 0.999, 0.996, and 0.998 by the elastic net. For temperature of the carbon feeding rate, this value is 0.999 by the ARD regressor.

Modeling of the control logic of a UASS based on coefficient of variation spraying distribution analysis in an indoor flight simulator.

In the past decade, unmanned aerial spraying systems (UASS) have emerged as an effective crop treatment platform option, competing with other ground vehicle treatments. The development of this platform has provided an effective spraying system that can be used on all crop types and in all weather conditions. However, related research has not been able to develop a UASS that can be operated in windy conditions with a low drift percentage. In this research, spraying was simulated in an indoor flight simulator by considering flight speed, altitude, wind speed, wind direction, rotor rotation, interval, spraying pattern, and nozzle type, which were used as the parameters affecting the output value of the coefficient of variation (CV) of spraying. These parameters were referenced as properties that occur in the field, and using machine learning methods, the CV value was used as a dataset to develop a model that can execute pump opening by controlling the flow rate. There are four machine learning methods used, i.e. random forest regression, gradient boosting, ada boost, and automatic relevance determination regression which are compared with simple linear regression and ridge regression as linear regression. The results revealed that the random forest regression model was the most accurate, with R2 of 0.96 and root mean square error (RMSE) of 0.04%. The developed model was used to simulate spraying with pump opening A, which connects two nozzles in front, and pump opening AB, which connects all four nozzles. Using the logic based on CV value and pesticide quantity, the model can execute the pump opening against the environment and UASS operation.

Correntropy-Based Logistic Regression with Automatic Relevance Determination for Robust Sparse Brain Activity Decoding.

Recent studies have used sparse classifications to predict categorical variables from high-dimensional brain activity signals to expose human's mental states and intentions, selecting the relevant features automatically in the model training process. However, existing sparse classification models will likely be prone to the performance degradation which is caused by the noise inherent in the brain recordings. To address this issue, we aim to propose a new robust and sparse classification algorithm in this study. To this end, we introduce the correntropy learning framework into the automatic relevance determination based sparse classification model, proposing a new correntropy-based robust sparse logistic regression algorithm. To demonstrate the superior brain activity decoding performance of the proposed algorithm, we evaluate it on a synthetic dataset, an electroencephalogram (EEG) dataset, and a functional magnetic resonance imaging (fMRI) dataset. The extensive experimental results confirm that not only the proposed method can achieve higher classification accuracy in a noisy and high-dimensional classification task, but also it would select those more informative features for the decoding tasks. Integrating the correntropy learning approach with the automatic relevance determination technique will significantly improve the robustness with respect to the noise, leading to more adequate robust sparse brain decoding algorithm. It provides a more powerful approach in the real-world brain activity decoding and the brain-computer interfaces.

COMPARISON OF OPTIMIZATION STRATEGIES AND ESTIMATION TECHNIQUES FOR RADIO NETWORK PLANNING AND OPTIMIZATION PROBLEMS

Background. Radio network planning is one of the main phases of the cellular network lifecycle, as it determines capital and operating costs and allows system performance evaluation at any given time. An accurate and comprehensive analysis of existing network statistics is necessary for proper cell planning during network expansion. These statistics are collected throughout the life cycle of the cellular network and usually have certain imperfections (heterogeneity of statistics, which have different densities in different parts of the search space, up to the presence of significant voids, etc.) The system describing the functioning of the radio network can be represented as a black box because its internal processes are too complex to be defined by mathematical functions. This determines the need to use appropriate tools.
 Objective. The purpose of the paper is to create a toolkit that allows finding the proper relationships between network parameters to define target values that will help to build an effective network plan in terms of performance and costs for its creation and operation. The tools should be able to work efficiently using the minimum set of available statistical data, as well as taking into account their imperfections.
 Methods. Mathematical estimation and optimization methods are used, namely Ordinary Least Squares, Ridge Regression, Lasso, Elastic-net, LARS lasso, Bayesian Ridge Regression, Automatic Relevance Determination, Stochastic gradient descent, Theil-Sen estimator, Huber Regression, Quantile regression, Polynomial regression. We consider 12 estimation methods in combination with two optimization strategies. Additionally, the method of partial analysis of the search space with different number of configurations is considered.
 Results. A software package using the Python programming language has been created, which contains a practical implementation of all the considered estimation and optimization methods, as well as tools for evaluating arbitrary configurations of the software package (benchmark) and visualizing the results. The best estimation method is Ordinary Least Squares for finding the optimal configuration of the statistical parameters of the 4G radio network to maximize the download speed. To obtain satisfactory results, it is enough to consider 25 initial and 250 estimated points - a larger number of points will not significantly increase prediction accuracy.
 Conclusions. The results indicate the possibility of using the created software package for radio network planning tasks. Further research is aimed at expanding the created software package's functionality and considering additional estimation methods and optimization strategies.
 Keywords: radio network planning; radio network optimization; cellular networks; estimation techniques; optimization strategies; big data; 2G; 3G; 4G; CQI; capacity.

Implementing and tuning machine learning-based models for description of solubility variations of nanomedicine in supercritical solvent for development of green processing

Determination of drug solubility in supercritical solvents such as CO2 has been of great importance for preparation of nanomedicines. This study implements and tunes several machine learning models to describe the solubility of medicine and density of solvent at various pressure and temperature. The dataset used in this study consisted of the input variables, temperature, and pressure. The methods of AdaBoost algorithm to boost the performance of base regression models for predicting the mole fractions of rivaroxaban and the density of SC-CO2 were developed. The base models used include Theil-Sen Regression (TSR), Gaussian Process Regression (GPR), Automatic Relevance Determination Regression (ARD), and Linear Regression (LR). We employ the Hunter-Prey Optimization technique to tune the hyper-parameters of these models. The results indicated that the boosted models outperform their base counterparts. For the mole fraction predictions, AdaBoost with ARD achieves an R2 value of 0.95986, while AdaBoost with GPR obtains an R2 score of 0.99817. For the SC-CO2 density predictions, AdaBoost with GPR achieves an impressive R2 of 0.99906. Accordingly, the AdaBoost with GPR is the best model for both outputs. These results demonstrate AdaBoost strength and Hunter-Prey algorithm in enhancing the predictive accuracy of regression models for these chemical properties.

Probabilistic method for wind speed prediction and statistics distribution inference based on SHM data-driven

For wind-sensitive structures, such as long-span bridges, high-rise buildings, transmission towers, etc., the prediction of wind speed and its statistical distribution are vital steps in the design and operation stages. Specifically, wind speed prediction is directly related to the value of wind load in the next occurrence; the statistical distribution of wind speed has regular characteristics, which can represent the random characteristics of wind field. In this paper, a probabilistic prediction model of wind speed based on Bayes’ theorem is proposed and verified based on structural health monitoring (SHM) data. Firstly, the Gaussian process is derived and used as an a priori function in Bayes’ theorem. In addition, the influence of six covariance functions on the prediction performance are discussed, that is, squared exponential (SE), Matern-3/2 (MA-3/2), Matern-5/2 (MA-5/2), automatic relevance determination SE (ARDSE), ARDMA-3/2, and ARDMA-5/2. Secondly, the correlation between the next wind speed and the previous wind speed is discussed by using the moving window method. Finally, the parameters in the three wind speed probability distribution functions (PDF), that is, Gumbel distribution, Weibull distribution, Rayleigh distribution, are updated in real time by increasing the SHM data based on Bayes’ theorem.

Development of a new framework based on Gaussian regression process for rapid fragility analysis of 2-DoF base-isolated structures

This paper develops metamodels (or surrogate models) to predict the fragility parameters of structures isolated with friction pendulum (FP) isolators. An equivalent inelastic two-degree-of-freedom (2DoF) system is utilized to model the base-isolated structures.6000 system simulations are initially established based on the probability distribution of input parameters. Then, incremental dynamic analyses are carried out to achieve structural data for the fragility function generation. The developed dataset of the fragility parameters (median and dispersion) is divided into training and testing sets to train and testthe efficiency of the developed metamodels, respectively.Powerful machine learning tool, namely, Gaussian Process Regression (GPR) is utilized for mapping structural input parameters to output (or target) parameters, i.e., median and dispersion of the fragility functions. GPRs are kernel-based probabilistic models, with kernel functions constituting their core components. In this study, the predictive quality of the GPR is evaluated considering different kernel functions to obtain the most accurate and reliable predictions. The results indicate that automatic relevance determination (ARD) kernel functions are much more efficient than isotropic kernel functions. Statistical performance metrics indicate that, among the implemented kernel functions, ARD Matern 3/2 is preferable for both the superstructure and FP isolator. The proposed GPR-based prediction metamodels exhibit excellent performance in the prediction of the fragility parameters of the superstructure and isolator for all considered limit states. Using the developed metamodels, conducting a rapid seismic fragility assessment on 2DoF systems that are representative of base-isolated structures is possible. At last, metamodels are exploited in seismic reliability analysis to assess their precision for further investigations. The results of seismic reliability-based performance and relationships between the displacement ductility demand and strength reduction factor reaffirm the efficiency, sufficiency, proficiency, and practicality of the GPR-based generated metamodels.

Estimation of Fv/Fm in Spring Wheat Using UAV-Based Multispectral and RGB Imagery with Multiple Machine Learning Methods

The maximum quantum efficiency of photosystem II (Fv/Fm) is a widely used indicator of photosynthetic health in plants. Remote sensing of Fv/Fm using MS (multispectral) and RGB imagery has the potential to enable high-throughput screening of plant health in agricultural and ecological applications. This study aimed to estimate Fv/Fm in spring wheat at an experimental base in Hanghou County, Inner Mongolia, from 2020 to 2021. RGB and MS images were obtained at the wheat flowering stage using a Da-Jiang Phantom 4 multispectral drone. A total of 51 vegetation indices were constructed, and the measured Fv/Fm of wheat on the ground was obtained simultaneously using a Handy PEA plant efficiency analyzer. The performance of 26 machine learning algorithms for estimating Fv/Fm using RGB and multispectral imagery was compared. The findings revealed that a majority of the multispectral vegetation indices and approximately half of the RGB vegetation indices demonstrated a strong correlation with Fv/Fm, as evidenced by an absolute correlation coefficient greater than 0.75. The Gradient Boosting Regressor (GBR) was the optimal estimation model for RGB, with the important features being RGBVI and ExR. The Huber model was the optimal estimation model for MS, with the important feature being MSAVI2. The Automatic Relevance Determination (ARD) was the optimal estimation model for the combination (RGB + MS), with the important features being SIPI, ExR, and VEG. The highest accuracy was achieved using the ARD model for estimating Fv/Fm with RGB + MS vegetation indices on the test sets (Test set MAE = 0.019, MSE = 0.001, RMSE = 0.024, R2 = 0.925, RMSLE = 0.014, MAPE = 0.026). The combined analysis suggests that extracting vegetation indices (SIPI, ExR, and VEG) from RGB and MS remote images by UAV as input variables of the model and using the ARD model can significantly improve the accuracy of Fv/Fm estimation at flowering stage. This approach provides new technical support for rapid and accurate monitoring of Fv/Fm in spring wheat in the Hetao Irrigation District.