Probability Density Function Of Normal Distribution Research Articles

A Comprehensive Approach to Fault Classification of Helicopter Engines with Adaboost Ensemble Model

This work is based on the PHM North America 2024 Conference Data Challenge’s datasets of Helicopter turbine engine performance measurements. These datasets were large and moderately imbalanced. For dealing with these challenges, we demonstrate significant tools covering feature engineering, augmentation and selection, model exploration, visualizations, model explainability and confidence margin estimation. This work was performed in its entirety using MATLAB. All these tools will be generally applicable to data-driven modeling and prediction of health to real life applications. Initially, we explored the 742k observations in the training set, noting a 60-40 split between healthy and faulty labels, and identified two major operational clusters within the data. We enhanced the dataset by removing duplicates and engineered new features based on domain knowledge, expanding the feature set to 242 dimensions. However for the torque margin estimation, we trained a regression model on a limited subset (18 features), which includes engineered features using domain knowledge, quadratic terms and linear interaction between all the terms. For the final submission, we utilized a stepwise linear regression model to optimize feature selection. This approach achieved a perfect regression score on test data, validated by a consistent torque margin residual range of +/- 0.5%. The model's RMSE and MAE metrics were optimal for employing a normal distribution probability density function. For , we reduced the feature set to 58 using dimensionality reduction techniques and balanced the data with upsampling and down-weighing the minority class. We employed ASHA (Asynchronous Successive Halving Algorithm) in conjunction with AutoML to efficiently determine the most suitable model family, significantly saving compute time. Subsequently, we trained ensemble models, including bagged tree and AdaBoost (Adaptive Boosting), which minimized false negatives and positives, achieving robust classification performance. This was particularly critical given the high penalty for false negatives in the data challenge. The MathWorks team score on Testing Data was 0.9686 at the close of competition. This was further improved to 0.9867. Our approach demonstrates the effectiveness of combining strategic data processing, feature engineering, and model selection to enhance predictive accuracy in complex operational datasets.

Underwater image enhancement using multi-task fusion.

Underwater images are often scattered due to suspended particles in the water, resulting in light scattering and blocking and reduced visibility and contrast. Color shifts and distortions are also caused by the absorption of different wavelengths of light in the water. This series of problems will make the underwater image quality greatly impaired, resulting in some advanced visual work can not be carried out underwater. In order to solve these problems, this paper proposes an underwater image enhancement method based on multi-task fusion, called MTF. Specifically, we first use linear constraints on the input image to achieve color correction based on the gray world assumption. The corrected image is then used to achieve visibility enhancement using an improved type-II fuzzy set-based algorithm, while the image is contrast enhanced using standard normal distribution probability density function and softplus function. However, in order to obtain more qualitative results, we propose multi-task fusion, in which we solve for similarity, then we obtain fusion weights that guarantee the best features of the image as much as possible from the obtained similarity, and finally we fuse the image with the weights to obtain the output image, and we find that multi-task fusion has excellent image enhancement and restoration capabilities, and also produces visually pleasing results. Extensive qualitative and quantitative evaluations show that MTF method achieves optimal results compared to ten state-of-the-art underwater enhancement algorithms on 2 datasets. Moreover, the method can achieve better results in application tests such as target detection and edge detection.

Whole Life Cycle Cost Analysis of Transmission Lines Using the Economic Life Interval Method

With the large-scale construction and commissioning of transmission lines over the past two decades, the grid is facing a large-scale centralized decommissioning of transmission lines. The transmission line’s economic life is crucial to rationalizing its construction and reducing the grid’s development costs. Based on the minimum economic life calculation principle, the static and dynamic transmission line economic life calculation model is established, considering the whole life cycle for transmission line cost. The improved gray GM (1,1) model is applied to forecast cost data during the economic life assessment of transmission lines with fewer samples. Considering the cost uncertainty in life-cycle costing, the interval cost model based on the coefficient of variation wave amplitude is proposed to determine the economic life intervals under different guarantees by using the normal distribution probability density function, which reduces the influence of cost fluctuations on the economic life calculation error. The economic life analysis of a 500 kV transmission line is used as a case study to verify the model’s accuracy and effectiveness. The method shows the economic life intervals under different guarantee degrees based on the most probable economic life determination, which provides theoretical support for calculating the economic life elasticity of transmission lines.

DDOFM: Dynamic malicious domain detection method based on feature mining

The domain name system is an essential part of the network, and target hosts are often attacked by malicious domain names to steal resources. Some traditional detection methods have low accuracy, poor generalization ability, and high resource overhead on model construction to deal with complex and variable malicious domain names. A three-level dynamic malicious domain detection method (DDOFM) is proposed in this paper. DDOFM only needs to combine a few high-order statistical features of benign domains with some DNS features, without flagging malicious samples and involving them in training. Firstly, the boundary recognition of passive DNS (PDNS) features extracted from DNS traffic is carried out to conduct an early- warning for some domains. Second, the Hidden Markov Model (HMM) forward algorithm and normal distribution probability density function are used to calculate the formation probabilities of the warned domains and their probability density values. Then the probabilities of every character in the warned domain name and the standard deviation between these probabilities are counted. Further, the probability density values and the standard deviations of these warned domain names are compared with their respective thresholds to identify the attribution of the warned domain names. Finally, if the domain name is not warned, the Jensen–Shannon divergence (JS divergence) between it and the previous domain name will be calculated. Then the local iterative threshold finding algorithm (LLTFA) proposed in this paper will be combined to determine its attribution and identify whether the host is connected to the command and control (C&C) server. Experiments show that the detection indexes of this method exceed 99% for multiple types of malicious domain names. The C&C servers can also be identified by DDOFM faster than similar methods.

Surface Dynamic Damage Prediction Model of Horizontal Coal Seam Based on the Idea of Wave Lossless Propagation.

According to traditional concepts, the movement of overlying strata and surface damage caused by coal mining in horizontal coal seams are symmetrical in terms of spatial distribution. However, in a lot of engineering practices, this symmetry has not been discovered. We often use the symmetry function to establish the profile prediction function of the surface damage, which results in a large difference between the prediction result and the actual situation. To solve this problem, this paper takes subsidence velocity as an example. Firstly, the spatial distribution functions of subsidence velocity on both sides were deduced theoretically. Through comparison, it is found that the change rate of the spatial distribution curve of the coal pillar side subsidence velocity is smoother than that of the goaf side and the subsidence velocity curves are skewed to the left. Secondly, based on the idea of lossless propagation of harmonic waves and idealizing the propagation environment, the spatial propagation relationship of surface subsidence velocity in the time domain is established. Then, the Box–Cox transform function is introduced to improve the normal distribution probability density function, and a new dynamic subsidence prediction model based on the Box–Cox transformation is obtained, which is suitable for the full mining stage. The model is tested by practical cases, the prediction accuracy is better than 7%, and the prediction results can meet the needs of engineering prediction accuracy (10%). The results of this research can enrich the existing subsidence prediction theory and provide theoretical and technical support for the prediction of dynamic surface damage caused by similar mining.

Design and implementation of human driving data-based lane-keeping assistance system for electric bus

This paper describes design, implementation, and evaluation of human driving data-based Lane Keeping Assistance System (LKAS) for electric bus equipped with a hybrid electric power steering system. The hybrid electric-power steering system used in this study means a steering system in which an Electric Power Steering (EPS) system and an Electro-Hydraulic Power Steering (EHPS) system are integrated into a ball-nut. A dynamic model of hybrid EPS system including EHPS system and EPS system has been developed to generate EPS torque and EHPS force corresponding to the input torque. In order to determine proper timing of LKAS intervention, driving data of electric bus drivers were collected and driving patterns were analyzed using a 2-D normal distribution probability density function. Lane information necessary for the lane-keeping assistance system is obtained from a vision camera mounted on the electric bus. Sliding mode control is used to get a Steering Wheel Angle (SWA) required for LKAS. A Proportional–Integral (PI) control is used to obtain an overlay torque required to track the target SWA. A proposed DLC threshold has been validated using vehicle simulation software, TruckSim, and MATLAB/Simulink. It is shown that the proposed DLC threshold shows good performance in both cases of slow lane departure and fast lane departure. The proposed algorithm has been successfully implemented on the electric bus and evaluated via real-world driving tests. Test scenario setting and the evaluation of performance were carried out by ISO 11270 criteria. It is shown that the algorithm successfully prevented the electric bus from unintended lane departure satisfying ISO 11270 criteria.

Research on the Evaluation Modeling Method of User Experience Quality under Uncertain Noise Environment

Experience economy is a trend of future economic development. Enterprises can only occupy the market more successfully by enhancing the user experience in product design. The user’s product experience is affected by uncertainty noises (such as the user’s environment and different users), rendering the user experience quality evaluation results highly variable. The purpose of this paper is to study the modeling method of user experience quality evaluations under uncertain environmental noises; inspired by normal ordered weighted averaging (OWA) operators, the normal distribution probability density function is implemented to improve the normal ordered weighted averaging (OWA) operators, and a new modeling method designed for the evaluation of user experience quality under uncertainty is proposed, which can overcome the disadvantage of unreasonable weight distribution when the data size and location are different, as well as weigh the importance of both the value and the location of the data. The simulation results show that this method is more effective, accurate, and feasible than the conventional order weighted synthesis operator method. The feasibility and validity of this method are proved by user experience and comparative experiments of multiattribute bread products.

Research and Application of Energy Storage Battery on Stabilizing Fluctuation Characteristics of Photovoltaic Power System

Photovoltaic power generation is clean, non-polluting, inexhaustible, but its characteristics of randomness, volatility and intermittent also produce its negative effects on power system economic, safe and reliable operation, which cannot be ignored. Storage battery in photovoltaic power generation system can not only absorb excess energy reserves, but also can stabilize the fluctuation, cut a peak to fill the valley and the stable voltage, it is very important and key part, At the same time, the energy storage capacity of the rational allocation of system not only for the photovoltaic power generation system of construction cost, also affects the performance and the service life of the system. This paper is based on the amount of solar radiation data of Liaoning area, proposed the hypothesis that PV fluctuation characteristics accord with normal distribution characteristics ,and fitted by normal distribution probability density function, verified the assumption of normal distribution, and proposed a selection strategy of energy storage power based on the normal distribution, Established mathematical model of battery energy storage capacity configuration, and regards the total power standard deviation, fluctuation of power capacity and power fluctuation rate as evaluation indicators to measure the effects of the long-term and short-term fluctuation of the storage battery on stabilizing fluctuation of photovoltaic power generation , through the examples and simulation proved that the model is correct and reasonable.

A Model of Fuzzy Normal Distribution

Nowadays fuzzy concepts are frequently used as statistical parameters, while the traditional normal distribution can only accept determinate variable. In order to design a practical model for fuzzy statistic events, this paper combines the fuzzy number, like “may-occur”, “very-likely-occur”, “rarely-occur”, to optimize the normal distribution probability density function, to provide a significant method in statistics.

Analysis on Difference of Contaminated Normal Distribution PDF

As a very important distribution, contaminated normal distribution play a great role in data processing. The probability density function (PDF) feature of the contaminated normal distribution was investigated. The Kullback-Leibler distance is suggested for measuring PDF difference between mean shift model and variance inflation model. Numerical calculations show that the PDF difference of two kinds of model is related to mean shift parameter λ and the variance inflation factor α closely when the main distribution is the standard normal distribution and the relationship is nonlinear proportional.