Gaussian Mixture Model Method Research Articles

A trajectory planning method for robotic arms based on improved dynamic motion primitives

Purpose Traditional robot arm trajectory planning methods have problems such as insufficient generalization performance and low adaptability. This paper aims to propose a method to plan the robot arm’s trajectory using the trajectory learning and generalization characteristics of dynamic motion primitives (DMPs). Design/methodology/approach This study aligns multiple demonstration motion primitives using dynamic time warping; use the Gaussian mixture model and Gaussian mixture regression methods to obtain the ideal primitive trajectory actions. By establishing a system model that improves DMPs, the parameters of the nonlinear function are learned based on the ideal primitive trajectory actions of the robotic arm, and the robotic arm motion trajectory is reproduced and generalized. Findings Experiments have proven that the robot arm motion trajectory learned by the method proposed in this article can not only learn to generalize and demonstrate the movement trend of the primitive trajectory, but also can better generate ideal motion trajectories and avoid obstacles when there are obstacles. The maximum Euclidean distance between the generated trajectory and the demonstration primitive trajectory is reduced by 29.9%, and the average Euclidean distance is reduced by 54.2%. This illustrates the feasibility of this method for robot arm trajectory planning. Originality/value It provides a new method for the trajectory planning of robotic arms in unstructured environments while improving the adaptability and generalization performance of robotic arms in trajectory planning.

Skilled analysts and earnings management in Chinese listed companies

The study finds that analyst skill plays a key factor to explain the complicated and chaotic relation between analyst coverage and external governance. We divide analysts into multiple skill groups by GMM (Gaussian mixture model) method, and explore the effect of skilled analysts on earnings management in Chinese listed companies. The results indicate that skilled analysts are significantly negatively correlated with both accrued and real earnings management, suggesting that skilled analysts play a genuine external monitoring role. Skilled analysts reduce earnings management primarily through decreasing agency costs within the company. In environments with weak regulatory by auditing firms, skilled analysts exhibit particularly pronounced restraints on earnings management. Our conclusion remains robust after considering endogeneity issues.

Impact analysis of bilateral trade openness and income inequality based on the system GMM method: A case study of transnational dynamic panel data

To analyze the impact of bilateral trade openness on income inequality, the study selected 16 countries with the highest global import and export trade rankings as research subjects, combined with cross-border dynamic panel data from 2005 to 2020, and used the Gaussian Mixture Model (GMM) to analyze the dynamic impact of natural and policy factors on domestic income inequality in the process of deepening bilateral trade openness. Empirical research has found that the policy-oriented expansion of openness in 16 countries has an inhibitory effect on domestic income inequality, while natural openness is influenced, to varying degrees, by different trading partners. High-quality education and sound infrastructure can help regulate income inequality. The results indicate that policy-based openness between 16 countries and those with weaker technological output, i.e., patent quantity, education level, i.e., higher education, and immigration, can suppress domestic income inequality, which is consistent with the expected hypothesis of the impact mechanism. The results indicate that in-depth research on the relationship between trade openness and income inequality can provide a basis for policymakers to adjust trade policies and provide recommendations to reduce income inequality. Meanwhile, the results and methods of this study can provide references for other scholars and promote research progress in related fields.

Morning Glory Flower Detection in Aerial Images Using Semi-Supervised Segmentation with Gaussian Mixture Models

The invasive morning glory, Ipomoea purpurea (Convolvulaceae), poses a mounting challenge in vineyards by hindering grape harvest and as a secondary host of disease pathogens, necessitating advanced detection and control strategies. This study introduces a novel automated image analysis framework using aerial images obtained from a small fixed-wing unmanned aircraft system (UAS) and an RGB camera for the large-scale detection of I. purpurea flowers. This study aimed to assess the sampling fidelity of aerial detection in comparison with the actual infestation measured by ground validation surveys. The UAS was systematically operated over 16 vineyard plots infested with I. purpurea and another 16 plots without I. purpurea infestation. We used a semi-supervised segmentation model incorporating a Gaussian Mixture Model (GMM) with the Expectation-Maximization algorithm to detect and count I. purpurea flowers. The flower detectability of the GMM was compared with that of conventional K-means methods. The results of this study showed that the GMM detected the presence of I. purpurea flowers in all 16 infested plots with 0% for both type I and type II errors, while the K-means method had 0% and 6.3% for type I and type II errors, respectively. The GMM and K-means methods detected 76% and 65% of the flowers, respectively. These results underscore the effectiveness of the GMM-based segmentation model in accurately detecting and quantifying I. purpurea flowers compared with a conventional approach. This study demonstrated the efficiency of a fixed-wing UAS coupled with automated image analysis for I. purpurea flower detection in vineyards, achieving success without relying on data-driven deep-learning models.

The GAPS Programme at TNG

Context. Stellar activity is the most relevant types of astrophysical noise that affect the discovery and characterization of extrasolar planets. On the other hand, the amplitude of stellar activity could hint at an interaction between the star and a close-in giant planet. Progress has been made in recent years in understanding how to deal with stellar activity and search for observational evidence of star-planet interactions. Aims. The aim of this work is to characterize the chromospheric activity of stars hosting short-period exoplanets by studying the correlations between the chromospheric emission (CE) in the Ca II H&K and the planetary parameters. Methods. We measured CE in the Ca II H&K lines using more than 1900 high-resolution spectra of a sample composed of 76 targets, observed with the HARPS-N spectrograph between 2012 and 2020. We transformed the fluxes into bolometric- and photospheric-corrected chromospheric emission ratios, R′HK. Furthermore, we completed the sample of hosts digging for data in previous works. Stellar parameters Teff, B–V, and V were retrieved homogeneously from the Gaia DR3. Then, M★, R★, and ages were determined from isochrone fitting. We retrieved planetary data from the literature and catalogs. The search for correlations between the log(R′HK) and planetary parameters have been performed through both Spearman’s rank and its statistics as well as the more sophisticated Gaussian mixture model method. Results. We found that the distribution of log(R′HK) for the transiting planet hosts is different from the distribution of field main-sequence and sub-giant stars. The log(R′HK) of planetary hosts is correlated with planetary parameters proportional to the planetary radius to the power of n (RPn, indicating a common origin for the correlations. The statistical analysis has also highlighted four clusters of host stars with different behavior in terms of their stellar activity with respect to the planetary surface gravity. Some of the host stars have a value of log(R′HK) that is lower than the basal level of activity for main sequence stars. The planets of these systems are very close to filling their Roche lobe, suggesting that they evaporate through hydrodynamic escape under the strong irradiation of the host star, creating shrouds that absorb the core of the chromospheric resonance lines.

An entire life-cycle rolling bearing remaining useful life prediction method using new degradation feature evaluation indicators

The rolling bearing remaining useful life (RUL) prediction is a hot topic issue in the field of rail transportation. The existing RUL prediction methods for rolling bearing have problems such as unreasonable division of rolling bearing degradation stages and incomplete extraction of degradation features by feature selection indicators. In order to solve these problems, an entire life-cycle rolling bearing RUL prediction method using new degradation feature evaluation indicators is proposed. Firstly, the degradation feature evaluation indicator is designed to evaluate the stability of the degradation feature. Then, the combination of stability evaluation indicator and correlation evaluation indicator is used as the basis for feature selection. Secondly, the Gaussian Mixture Model (GMM) method is fused with the Support Vector Machine (SVM) to divide the bearing entire life-cycle into three stages: normal stage, early degradation stage, and degradation stage. Finally, the Long Short-Term Memory (LSTM) network model is trained separately to predict the rolling bearing RUL for different rolling bearing degradation stages. The effectiveness of the proposed prediction method based on different degradation stages of rolling bearing in predicting the RUL of rolling bearing is verified through PRONOSTIA bearing dataset. The comparison with existing methods shows that this approach demonstrates superior accuracy and predictive performance. For example, the Mean Square Error (MSE) evaluation metric has decreased by 60%. The Root Mean Square Error (RMSE) evaluation metric has decreased by 36.5%. The Mean Absolute Error (MAE) evaluation metric has decreased by 48.6%. The Mean Absolute Percentage Error (MAPE) evaluation metric has decreased by 36.9%.

Abnormality Determination of Spermatozoa Motility Using Gaussian Mixture Model and Matching-based Algorithm

Sperm analysis is an initial step in the examination conducted to identify infertility cases in humans. One aspect of sperm analysis involves observing the movement of spermatozoa and determining whether it is normal or abnormal. Normal spermatozoa movement is characterized by progressive motion at an average speed of 20 µm/second, while abnormal movement includes slow or non-motile spermatozoa. Traditional methods can be employed to assess the normality or abnormality of sperm movement, but they have drawbacks such as time-consuming procedures and diverse results depending on the expertise of the examiner. On the other hand, utilizing Computer-Assisted Sperm Analysis (CASA) equipment provides consistent results, albeit at a relatively high cost. Therefore, this research proposes an alternative method for determining sperm movement abnormalities using the Gaussian Mixture Model (GMM) for background subtraction and a matching-based algorithm to track and analyze the formed trajectories, distinguishing between normal and abnormal sperm movement. Human spermatozoa in real-time are used, and their movements are recorded in video format using a bright field microscope. The testing results for determining sperm movement abnormalities based on the GMM method and matching-based algorithm were successful, particularly in videos recorded at 50 fps recording speed, 20 minutes of liquefaction time, and 40x microscope lens magnification. This condition exhibited the highest average accuracy, with a tracking accuracy of 77.3% and an average accuracy for determining sperm motility abnormalities of 87.7%. Therefore, the combined tracking of sperm movement based on the GMM method and matching-based algorithm can be utilized to identify abnormalities in the movement of human spermatozoa.

Online Condition Monitoring of Industrial Loads Using AutoGMM and Decision Trees

Condition monitoring and fault management approaches can help with timely maintenance planning, assure industry-wide continuous production, and enhance both performance and safety in complex industrial operations. At the moment, data-driven approaches for condition monitoring and fault detection are the most attractive being conceived, developed, and applied with less of a need for sophisticated expertise and detailed knowledge of the addressed plant. Among them, Gaussian mixture model (GMM) methods can offer some advantages. However, conventional GMM solutions need the number of Gaussian components to be defined in advance and suffer from the inability to detect new types of faults and identify new operating modes. To address these issues, this paper presents a novel data-driven method, based on automated GMM (AutoGMM) and decision trees (DTree), for the online condition monitoring of electrical industrial loads. By leveraging the benefits of the AutoGMM and the DTree, after the training phase, the proposed approach allows the clustering and time allocation of nominal operating conditions, the identification of both already-classified and new anomalous conditions, and the acknowledgment of new operating modes of the monitored industrial asset. The proposed method, implemented on a commercial cloud-computing platform, is validated on a real industrial plant with electrical loads, characterized by a daily periodic working cycle, by using active power consumption data.

Using Deep-Learning for 5G End-to-End Delay Estimation Based on Gaussian Mixture Models

Deep learning is used in various applications due to its advantages over traditional Machine Learning (ML) approaches in tasks encompassing complex pattern learning, automatic feature extraction, scalability, adaptability, and performance in general. This paper proposes an end-to-end (E2E) delay estimation method for 5G networks through deep learning (DL) techniques based on Gaussian Mixture Models (GMM). In the first step, the components of a GMM are estimated through the Expectation-Maximization (EM) algorithm and are subsequently used as labeled data in a supervised deep learning stage. A multi-layer neural network model is trained using the labeled data and assuming different numbers of E2E delay observations for each training sample. The accuracy and computation time of the proposed deep learning estimator based on the Gaussian Mixture Model (DLEGMM) are evaluated for different 5G network scenarios. The simulation results show that the DLEGMM outperforms the GMM method based on the EM algorithm, in terms of the accuracy of the E2E delay estimates, although requiring a higher computation time. The estimation method is characterized for different 5G scenarios, and when compared to GMM, DLEGMM reduces the mean squared error (MSE) obtained with GMM between 1.7 to 2.6 times.

Web-based Clustering Application for Determining and Understanding Student Engagement Levels in Virtual Learning Environments

The increasing use of virtual learning environments (VLEs) in recent years has transformed teaching and learning methods. Universities now combine VLEs with traditional classrooms to accommodate hybrid teaching and learning approaches. However, student engagement with VLEs varies, and universities lack the tools to effectively determine and analyse VLE engagement. Consequently, data-driven decision-making regarding VLE usage remains a challenge for universities. This study thus proposed a user-friendly web-based application, using a R shiny framework, to determine and understand student engagement levels in VLEs. In this study, two clustering methods, K-means and Gaussian Mixture Model (GMM) were compared, to identify the most effective method for the proposed application. The results indicated that GMM outperforms K-means by generating more accurate and comprehensive groupings of student engagement levels. One key advantage of the GMM method is its ability to capture uncertainty and provide probabilities of student membership in each level of engagement, which enhances its usefulness for decision-making. Furthermore, the GMM method achieves these outcomes efficiently, saving valuable learning time. This research holds significant implications for education by providing valuable guidance for the development of Educational Data Mining (EDM) applications. Universities can leverage these applications to gain deep insights into VLE usage and enhance their understanding of student engagement. By adopting this web-based application, educators and administrators can make informed decisions and tailor interventions to optimize student learning experiences within VLEs. Keywords: Virtual Learning Environments, Student Engagement, Clustering.

Spatiotemporal distribution of precipitation and its characteristics under tropical atmospheric systems of Brazil: Insights from a large sub‐hourly database

AbstractThe study of rainfall properties at various spatiotemporal scales is deeply important for understanding a large range of socio‐environmental processes and variables (e.g., water resources, agriculture, socio‐ecosystemic services, natural risk assessment). However, such studies on rainfall characteristics, especially at sub‐hourly resolutions, are scarce in large areas of South America due to the lack of a high‐resolution temporal database. The Brazilian National Centre for Monitoring and Early Warning of Natural Disasters (CEMADEN) has gradually implemented, starting in 2013, a sub‐hourly monitoring network composed of approximately 3500 automated rain gauges distributed across Brazil, enabling access to new hydrological studies in this vast tropical country featuring a range of biomes. This study analysed the characteristics of rainfall events for the whole of Brazil on sub‐daily and sub‐hourly timescales, using 7 years of data (from 2014 to 2021) provided by CEMADEN. Rainfall events were defined by the minimum inter‐event time (MIT) and the minimum depth (1 mm). Seven MITs (30, 60, 120, 180, 360, 720, and 1440 min) were considered to evaluate the behaviour of rainfall event characteristics and their relationships. The Gaussian mixture model method was applied to identify regions with similar rainfall patterns according to the MIT. Six groups with homogeneous characteristics were identified, evidencing the climatic diversity of Brazil. The results show that the MIT strongly influences precipitation properties (especially the dry time and the number of events). The highest number of events occurred in the North‐east Coast region, which exceeded 200 events per year (MIT < 60 min), while the lowest number of events was observed in the Semiarid region, which reached only 38 events per year with an MIT of 1440 min. Moreover, the events with the highest rainfall intensities were found in the Central region. The results found in this study provide a better understanding of precipitation and its characteristics in Brazil, highlighting the climatological diversity of this country.

Confident learning-based Gaussian mixture model for leakage detection in water distribution networks

Leakage detection in the water distribution system not only helps to reduce water waste but also decreases the risk of drinking water pollution. To reduce reliance on hardware devices and enable real-time detection, the water utilities are transitioning towards the data-driven based approach that relies on the analysis of the flow and pressure data collected from the supervisory control and data acquisition (SCADA) system. Due to the lack of leakage data, most of these methods are unsupervised methods that rely heavily on assumptions about the distribution of anomalies; whereas, the water utility's repair records contain much valid information about the leakage and normal characteristics. To convert this information into available labels and to address the lack of leakage data, this paper proposed a new leakage detection framework to infer the pressure characteristics under normal conditions based on historical data by combining a label cleaning method—confident learning (CL)—with an unsupervised method—Gaussian mixture model (GMM)—for leak detection. The methodology is validated with synthetic and real measured data. Comparisons with four unsupervised methods demonstrate that the GMM method has superior identification of leak features from pressure data. For a real-world water distribution system in K city containing 91 pressure sensors, the average true positive rate is 0.78 and the average false positive rate is 0.11. This methodology is a promising tool to identify signs of leakage in large-scale water distribution networks (WDNs).

Dynamic stationary subspace analysis based on Gaussian mixture models for ironmaking process monitoring

AbstractBlast furnace ironmaking process monitoring is an important and challenging task. Due to the influence of hot blast stove switching and large fluctuations in the quality of raw materials, the measurements of ironmaking processes show obvious non‐stationary characteristics, and in addition, the observed data are also characterized by time‐series dynamic and non‐Gaussian characteristics. In this paper, a dynamic stationary subspace analysis method based on the Gaussian mixture model (DSSA–GMM) is proposed to address the difficulties in blast furnace ironmaking process monitoring. The time‐series dynamic relationship of the data is conducted by introducing a sliding time window. The Gaussian mixture model (GMM) is used to deal with the non‐Gaussian characteristics of the data, and the parameters of the GMMs are estimated using the expectation–maximization algorithm. The stationary projection matrix is obtained by optimizing the Kullback–Leibler (K–L) divergence between GMMs of different periods to realize the stationary subspace separation. Finally, the convex hull of the stationary subspace is established for fault detection, thus realizing the monitoring for non‐stationary and non‐Gaussian dynamic processes. The effectiveness of the DSSA–GMM method is verified by a numerical simulation and a dataset collected from an actual blast furnace ironmaking process.

A Learning-Based Object Tracking Strategy Using Visual Sensors and Intelligent Robot Arm

This paper focuses on addressing the visual tracking problem using learning-based methods for object tracking tasks. This problem contains a major difficulty, i.e., how to acquire a satisfactory generalization ability of the developed system? In this paper, firstly, the object state tracking system, including a camera-in-hand, a 3D camera and a Rethink Baxter robot, is introduced. The problem formulation is also presented. Secondly, we propose a Kalman-based estimation strategy to acquire the object’s state. In addition, a learning-based tracking controller is developed using the Gaussian mixture models (GMM) method to steer the robot end-effector to track the mobile object. Thirdly, to guarantee system stability (i.e., the position and velocity errors between the object and end-effector will always converge to zeros), the controller parameter constraints are derived, which is a theoretical contribution of this paper. The controller parameter adjustment is avoided by the proposed training process. Thus, the proposed method becomes easy to implement, which is a practical contribution. Finally, the effectiveness of the proposed method is demonstrated by simulation and experimental examples, and the proposed method has satisfactory generalization ability. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper studies object tracking problems for different practical applications, such as industrial cutting, grasping and dynamic monitoring. Different trajectory tracking methods have been widely applied in the industrial area. However, users always complain that when the object or trajectory is changed, the tracking controller more or less needs to be re-adjusted. This re-adjust process always requires professional knowledge and programming experience, and thus a factory must employ some professional engineers. In addition, since the objects may be diverse in shape, color and size, to acquire the accurate object position and velocity, an appropriate solution is necessary. Motivated by the above introductions, this paper aims to develop a learning-based controller to track different complex trajectories without frequent and specific parameter adjustment processes. Firstly, a visual measurement system is developed to quickly find and estimate the position and velocity of an object. Secondly, with the object’s information, the learning from demonstration method (GMM method) is applied for the control policy design. Thirdly, the detailed system stability analysis is presented, and the corresponding controller parameter constraints are derived and considered in the proposed control policy. Subsequently, with the demonstration data, the packaged learning algorithm will automatically compute the controller parameters, and users can change the controller performance only by providing the desired demonstrations. In summary, this paper proposes a systematic object tracking solution, and it may bring a new idea to develop a practical object tracking system, using both the learning-based methods to improve the ability of generalization for tracking different objects.

Pengelompokkan kabupaten/kota di Pulau Sulawesi berdasarkan indikator indeks khusus penanganan stunting menggunakan Gaussian mixture model

Stunting or is a condition of growth failure in children under five years old (toddlers) who are malnourished. Children are called stunted if their height is below minus two standard deviations. The Special Index for Handling Stunting (IKPS) is one of the main indicators used as a measure of the achievement of handling the reduction in stunting rates. In implementing the 2024 development goals, namely setting a national stunting target that can decrease to 14%, it is necessary to identify based on the characteristics of a special index for handling stunting in each region. Method of Gaussian Mixture Model is a grouping with models that function to group a certain amount of data into a Gaussian distribution with mean and variance parameters. The main idea of model-based grouping is that object grouping is done using probabilities. This study was conducted with the aim of obtaining the results of grouping regencies/cities on Sulawesi Island based on the Special Index Indicator for Handling Stunting. The results of the study obtained different volume and shape models, coordinate axis orientation (VVI) with 4 optimum cluster. Cluster 1 with a low stunting handling index contains 24 districts/cities, cluster 2 with a medium stunting handling index contains 21 districts/cities, cluster 3 with a high stunting handling index contains 13 districts/cities, cluster 4 with a very high stunting handling index contains 23 districts/cities.Keywords: Four optimum cluster, low, medium, high and very highMSC2020: 62A09

Do controlling shareholders' equity pledges affect M&amp;A investment? Evidence from listed companies in China

As a new financing method, equity pledges are popular in China’s capital market. With the emergence of new financing models, will the relationship between financing and investment in corporate financial management change? The purpose of this study is to determine whether the controlling shareholders' equity pledges affect corporate merger and acquisition (M&amp;A) investment decisions. This paper uses data for listed companies from the China Stock Market &amp; Accounting Research (CSMAR) database, and Stata 17 is used as the data processing software. The M&amp;A variable is virtual and uses the logit model to study the relationship between controlling shareholders' equity pledges and M&amp;A investments. To test the robustness of the results, we replace the key variables, transform the model, and use the Gaussian Mixture Model (GMM) method to obtain the same results. The study found a positive correlation between controlling shareholders' equity pledges and M&amp;A investments. Further cross-sectional study shows that the positive correlation is stronger in state-owned companies, non-manufacturing companies, and companies with low pledge ratios. This study is conducive to standardizing the equity pledge behavior of listed companies and safeguarding the interests of investors.

Automated integration gate selection for Gaussian mixture model pulse shape discrimination

Pulse shapes differ between neutron and gamma particles when measured with detector devices employing pulse shape discriminating (PSD) scintillators. Digitized waveforms can be used in detection systems to perform pulse shape discrimination for this application. Prior Gaussian Mixture Model (GMM) methods require access to the pulse full-waveform. Reducing the waveform to a smaller set of combined samples reduces computational cost while affecting PSD performance. In this work, we develop a method for selecting the best performing combination of integration gates, or contiguous summed segments of the digitized pulse for PSD. The method uses a discrimination score based on the GMM PSD approach. The final selection is performed using Bayesian Optimization. PSD detection results are compared with varying numbers of selected gates on time-of-flight (TOF) data. This method can be used to fully automate the selection of gates in an unsupervised (without ground truth labels) setting.

Statistical Learning Methods to Identify Nonwear Periods From Accelerometer Data

Background: Accelerometers are used to objectively measure movement in free-living individuals. Distinguishing nonwear from sleep and sedentary behavior is important to derive accurate measures of physical activity, sedentary behavior, and sleep. We applied statistical learning approaches to examine their promise in detecting nonwear time and compared the results with commonly used wear time (WT) algorithms. Methods: Fifteen children, aged 4–17, wore an ActiGraph wGT3X-BT monitor on their hip during overnight polysomnography. We applied Hidden Markov Models (HMM) and Gaussian Mixture Models (GMM) to classify states of nonwear and wear in triaxial acceleration data. Performance of methods was compared with WT algorithms across two conditions with differing amounts of consecutive nonwear. Clinical scoring of polysomnography served as the gold standard. Results: When the length of nonwear was less than or equal to WT algorithms’ predefined thresholds for consecutive nonwear time, GMM methods yielded improved classification error, specificity, positive predictive value, and negative predictive value over commonly used algorithms. HMM was superior to one algorithm for sensitivity and negative predictive value. When the length of nonwear was longer, results were mixed, with the commonly used algorithms performing better on some parameters but GMM with the greatest specificity. However, all approached the upper limits of performance for almost all metrics. Conclusions: GMM and HMM demonstrated robust, consistently strong performance across multiple conditions, surpassing or remaining competitive with commonly used WT algorithms which had marked inaccuracy when nonwear time periods were shorter. Of the two statistical learning algorithms, GMM was superior to HMM.

Comparison Approaches of the Fuzzy C-Means and Gaussian Mixture Model in Clustering the Welfare of the Indonesian People

We compared the previous study about clustering the welfare of the Indonesian people using the Fuzzy C-Means (FCM) approach to a recent study, the Gaussian mixture model (GMM). Both of which were soft clustering. The case analyzes by classifying 34 provincial data in Indonesia, based on eight welfare of people indicator variables in 2017, which the Central Statistics Agency had issued. We compared the FCM and the GMM approaches to determine a better level of accuracy in clustering data using the Silhouette index, the Davies-Bouldin index, and the Calinski-Harabasz index values as a validity test method. The FCM and GMM methods found that the optimal clusters were 2 and 6. When we observed the consistency of the three tests’ validity results, the GMM method was preferable to the FCM clustering method.&#x0D; Keywords: fuzzy, Gaussian mixture model, clustering

Forecasting and Uncertainty Analysis of Day-Ahead Photovoltaic Power Based on WT-CNN-BiLSTM-AM-GMM

Accurate forecasting of photovoltaic (PV) power is of great significance for the safe, stable, and economical operation of power grids. Therefore, a day-ahead photovoltaic power forecasting (PPF) and uncertainty analysis method based on WT-CNN-BiLSTM-AM-GMM is proposed in this paper. Wavelet transform (WT) is used to decompose numerical weather prediction (NWP) data and photovoltaic power data into frequency data with time information, which eliminates the influence of randomness and volatility in the data information on the forecasting accuracy. A convolutional neural network (CNN) is used to deeply mine the seasonal characteristics of the input data and the correlation characteristics between the input data. The bidirectional long short-term memory network (BiLSTM) is used to deeply explore the temporal correlation of the input data series. To reflect the different influences of the input data sequence on the model forecasting accuracy, the weight of the calculated value of the BiLSTM model for each input data is adaptively adjusted using the attention mechanism (AM) algorithm according to the data sequence, which further improves the model forecasting accuracy. To accurately calculate the probability density distribution characteristics of photovoltaic forecasting errors, the Gaussian mixture model (GMM) method was used to calculate the probability density distribution of forecasting errors, and the confidence interval of the day-ahead PPF was calculated. Using a photovoltaic power station as the calculation object, the forecasting results of the WT-CNN-BiLSTM-AM, CNN-BiLSTM, WT-CNN-BiLSTM, long short-term memory network (LSTM), gate recurrent unit (GRU), and PSO-BP models were compared and analyzed. The calculation results show that the forecasting accuracy of the WT-CNN-BiLSTM-AM model is higher than that of the other models. The confidence interval coverage calculated from the GMM is greater than the given confidence level.