Statistical Laws Research Articles

B-TBM: A Novel Deep Learning Model with Enhanced Loss Function for HAZOP Risk Classification Using Natural Language Statistical Laws

HAZOP is a paradigm of industrial safety, and the introduction of deep learning-based HAZOP text categorization marks the arrival of an intelligent era of safety analysis. However, existing risk analysis methods have limitations in processing complex texts and extracting deep risk features. To solve this problem, this paper proposes a novel HAZOP risk event classification model based on BERT, BiLSTM, and TextCNN. The complexity of HAZOP text is revealed by introducing statistical laws of natural language, such as Zipf’s law and Heaps’ law, and the outputs of different levels of BERT are further combined linearly to collaborate with BiLSTM and TextCNN to capture long-term dependency and local contextual information for a more accurate classification task. Meanwhile, an improved loss function is proposed to effectively solve the deficiencies of the traditional cross-entropy loss function in the mislabeling process and improve the generalization ability of the model. It is experimentally demonstrated that the accuracy of the model is improved by 3% to 4% compared to the traditional BERT model in the task of severity and possibility classification of HAZOP reports. This study not only improves the accuracy and efficiency of HAZOP risk analysis, but also provides new ideas and methods for the application of natural language processing in industrial safety.

Dynamic Response and Damage Analysis of a Large Steel Tank Impacted by an Explosive Fragment

Abstract The fragments generated by explosions of storage tanks in chemical industrial parks may cause perforations or dents in adjacent tanks and trigger a domino effect. This paper determined reasonable fragment parameters based on the statistical laws of accidents and empirical formulas. The dynamic response process of large steel tanks impacted by fragments was simulated with ls-dyna. The typical impact process and results were analyzed in detail, and the damage laws of the tanks were discussed under various filling coefficients, volumes, fragment velocities, and impact angles. The results indicate that the inertial resistance of the inner liquid shortens the impact duration. Multiple collisions occur between the fragment and tank during impact, and the impact process involves three stages: initial collision, crushing and collision, and separation flight. The impact center displacement shows a fast and then slow reduction trend as the liquid level height increases, and the damage to the tank is negatively correlated with the liquid level height. The damage is lower when the tank volume is larger in an empty tank or at a high liquid level, while the damage instead increases when the volume exceeds 5000 m3 at a low liquid level. The peak impact force of the end-cap fragment is greatest when frontal impact occurs. Fragment flipping and curling occur at 45 deg and 90 deg impact, respectively. As the vertical impact angle increases from 0 deg to 90 deg, the fragment impact mode changes from initial frontal impact to flip detachment and finally to curling deformation.

Statistical Law between Areas and Perimeters Created by a Moving Trajectory

Based on our interest in properties of human movement, we investigated Japanese GPS data, and arrived at the following three observations: (1) there is a strong correlation between the area of polygons created by human movement trajectories and their perimeters; (2) short-distance movement trajectories less than 5 km tend to enclose a large area like a circle; and (3) long-distance movement trajectories over 5 km tend to be straight. We also clarified the following four observations on individual attributes and external factors related to long-distance movements: (1) women tend to travel more linearly than men; (2) linearity is stronger on weekends and national holidays in areas with a large theme park; (3) linearity is weaker on weekends and holidays in areas with many historical tourist attractions; and (4) these variations are created by people visiting such areas. These properties should be incorporated when modeling the movement trajectories of humans.

Is it Time to Demolish Current Mathematics?

Current mathematics in 3D geometric space plus real time t as an external control is incomplete and misleading. The dream of theoretical physicists and mathematicians to demolish all current mathematics and replace it with a single universal numerical statistical law in 4D is now within reach. In this paper, we first focus on the introduction and definition of the proposed unitary 4D space. Next, we introduce and explain what we call the modern Laplacian theorem in 4D unit space. Finally, we explain some unexpected and striking numerical results such as measuring the speed of sound in air at 330 m/s and that of light at 3 E8 m/s. There is an inherent relationship between the speed of sound in air and the diffusivity of sound waves in the sound room, similar to the relationship between the speed of light in a vacuum and the thermal diffusivity of metals when they all live two in a 4D unit. space.

Risk analysis of accident-causing evolution in chemical laboratory based on complex network

Chemical laboratories usually have many high risks from various dangerous chemicals, dangerous devices, and experimental operators involved in the laboratory. Once a severe accident occurs, the accident consequence will significantly impact scientific research innovation and social progress. Aiming at laboratory safety problems, an accident evolution model is established to reveal the critical accident-causing factors and the most likely evolutionary path of accidents in the process of accident evolution. Firstly, the 24 model is used to identify the cause factors of laboratory accidents and the causal relationship between factors. Then, the complex network model of laboratory accident evolution is constructed with accident-causing factors as nodes and causal relationships between factors as edges. Secondly, using the TOPSIS method, four typical complex network characteristic indexes, including degree centrality, betweenness centrality, closeness centrality, and eigenvector centrality, are constructed into a comprehensive evaluation index to reveal the key influencing factors in the accident evolution process. Finally, the fuzzy number is introduced to quantify the uncertainty of the accident evolution path. The most likely evolutionary path is obtained through the Dijkstra and risk entropy theory. Based on the data of 151 laboratory accidents from 2001 to 2022, the accident evolution analysis of chemical laboratories was carried out. The evolution results show that the maximum probability value is the evolution path of fire accidents, and the minimum probability value is the evolution path of electric shock accidents, which accords with the general statistical law of accidents. When applied to the actual laboratory, the safety management level of the laboratory can be effectively improved by controlling the key influencing factors and cutting off the accident evolution path.

Analyzing the Strelitzia Juncea Cellulosic Fibers Mechanical Properties’ Experimental Data Using Various Statistical Methods

ABSTRACT Manufacturing composites using natural fibers support the development of more ecologically friendly applications in many industrial areas, including sports equipment, wind turbine blades, construction materials, packaging, medical devices, and prosthetics. To investigate the tests’ number (N) impact on the fibers’ tensile behavior, newly developed fibers from the Strelitzia juncea (SJ) plant are being studied for their mechanical properties using various statistical laws. This study aims to assess the SJ fibers’ performance with a gauge length of 50 mm under quasi-static stress conditions. 150 SJ fibers were tensile tested in five groups (30, 60, 90, 120, and 150) to determine the N impact on the fibers’ tensile strength, break deformation, and Young’s modulus. Weibull and log-normal distributions were used to study statistically the mechanical properties results, and their dispersion was investigated and quantified using least squares and maximum likelihood prediction model with a confidence level of 95%.

Speckle denoising based on Swin-UNet in digital holographic interferometry

Speckle noise, mechano-physical noise, and environmental noise are inevitably introduced in digital holographic coherent imaging, which seriously affects the quality of phase maps, and the removal of non-Gaussian statistical noise represented by speckle noise has been a challenging problem. In the past few years, deep learning methods based on convolutional neural networks (CNNs) have made good progress in removing Gaussian noise. However, they tend to fail when these deep networks designed for Gaussian noise removal are used to remove speckle noise. Recently, numerous studies have employed CNNs to address the issue of degraded speckle images, yielding encouraging results. Nevertheless, the degradation of speckle noise that is simulated in isolation is limited and insufficient to encompass the increasingly complex DHI noise environment. This paper presents what we believe to be a novel approach to simulating complex noise environments by multiplexing simulated Gaussian noise and speckle noise. The noise resulting from aliasing does not adhere to the statistical laws of the noise prior to aliasing, which poses a more challenging task for the noise-reduction algorithms utilized in neural networks. Consequently, in conjunction with the capacity of the Swin Transformer to model multi-scale features, this paper proposes a DHI speckle denoising approach based on Swin-UNet. In this paper, Gaussian, speckle, and blending noise datasets with different noise densities are constructed for training and testing by numerical simulation, and generalizability tests are performed on 1,100 randomly selected open-source holographic tomography (HT) noise images at Warsaw University of Technology and 25 speckle images selected from DATABASE. All test results are quantitatively evaluated by three evaluation metrics: mean squared error (MSE), peak signal-to-noise ratio (PSNR), and structural similarity index (SSIM). All convolutional neural network (CNN) algorithms are evaluated qualitatively based on the number of parameters, floating point operations, and denoising time. The results of the comparison demonstrate that the denoising algorithm presented in this paper exhibits greater stability, accuracy, and generalizability.

A probabilistic prediction method for mode I fatigue life of concrete based on the statistical laws of material parameters

Accurately predicting the mode I fatigue life of concrete is critical for evaluating the safety of structures. However, due to the stochasticity of fatigue life, it remains a challenge to the deterministic methods in the existing literature. This study presents a probabilistic method for predicting the mode I fatigue life of concrete. The method considers four concrete material parameters in the initial fracture toughness-based crack propagation criterion and the tension-softening constitutive relationship as random variables following a two-parameter Weibull distribution. The detailed procedure for the implementation of the method is elaborated using the notched three-point bending (TPB) beam as an example, and the effectiveness of the method is verified by comparing the predicted fatigue life with the experimental results collected from the literature. Furthermore, the sensitivity analysis shows that the stochasticity of the initial fracture toughness is the most important factor leading to the variability of the fatigue life. Tensile strength stochasticity is the second most important factor. The effects of other material parameters on fatigue life are negligible. The proposed method allows reasonable prediction of fatigue life based solely on prior knowledge of the statistical laws governing the two factors. Meanwhile, the calculation results suggest that the large scatter in fatigue life is due to the high sensitivity to the stochasticity of concrete material parameters. The proposed method is expected to enhance the understanding of the stochastic nature of fatigue life and achieve accurate predictions at different failure probabilities.

A Bayesian theory of market impact

Abstract The available liquidity at any time in financial markets falls largely short of the typical size of the orders that institutional investors would trade. In order to reduce the impact on prices due to the execution of large orders, traders in financial markets split large orders into a series of smaller ones, which are executed sequentially. The resulting sequence of trades is called a meta-order. Empirical studies have revealed a non-trivial set of statistical laws on how meta-orders affect prices, which include (i) the square-root behaviour of the expected price variation with the total volume traded, (ii) its crossover to a linear regime for small volumes and (iii) a reversion of average prices towards its initial value, after the sequence of trades is over. Here we recover this phenomenology within a minimal theoretical framework where the market sets prices by incorporating all information on the direction and speed of trade of the meta-order in a Bayesian manner. The simplicity of this derivation lends further support to the robustness and universality of market impact laws. In particular, it suggests that the square-root impact law originates from over-estimation of order flows originating from meta-orders.

Law of earthquake productivity in the Olami‒Feder‒Christensen‒Zhurkov model

The generalized cellular model based on the of Olami‒Feder‒Christensen cellular automaton model and modified by the allowance for the lifetime of the material on the basis of the kinetic concept for strength of solids by Academician S.N. Zhurkov is used to model and clarify the nature of the statistical law of earthquake productivity. The modified model is named Olami‒Feder‒Christensen‒Zhurkov model (OFCZ). The OFCZ model implements the main statistical regularities of seismicity: the Gutenberg‒Richter and Omori‒Utsu laws, the Bath’s law, fractal geometry of seismicity, and the law of earthquake productivity. It is shown that the clustering of model events (analogs of earthquakes), corresponding to the law of earthquake productivity, is due to the kinetic component of the OFCZ model. The productivity dependences on material strength and medium temperature are obtained. The influence of the Zhurkov parameter and the cell coupling parameter in the cellular model (the dissipativity of the model) on the productivity is considered. It is shown that the revealed dependences of productivity on strength and temperature are consistent with the empirical data.

Designing turbulence with entangled vortices

Matter entanglement is a common chaotic structure found in both quantum and classical systems. For classical turbulence, viscous vortices are like sinews in fluid flows, storing and dissipating energy and accommodating strain and stress throughout a complex vortex network. However, to explain how the statistical properties of turbulence arise from elemental vortical structures remains challenging. Here, we use the quantum vortex tangle as a skeleton to generate an instantaneous classical turbulent field with intertwined vortex tubes. Combining the quantum skeleton and tunable vortex thickness makes the synthetic turbulence satisfy key statistical laws, offering valuable insights for elucidating energy cascade and extreme events. By manipulating the elemental structures, we customize turbulence with desired statistical features. This bottom-up approach of designing turbulence provides a testbed for analyzing and modeling turbulence.

An Extremely Sparse Tomography Reconstruction of a Multispectral Temperature Field without Any a Priori Knowledge.

When undertaking optical sparse projection reconstruction, the reconstruction of the tested field often requires the utilization of a priori knowledge to compensate for the lack of information due to the sparse projection angle. In order to reconstruct the radiation field of unknown materials or in situations where a priori knowledge cannot be obtained, this paper proposes an extremely sparse tomography multispectral temperature field reconstruction algorithm that analyzes the similarity (the similarity here compares and calculates the Euclidean distance of the spectral emissivity values at various wavelengths between different spectral curves) of radiation characteristics of materials under the same pressure and concentration but different temperature, describes the similarity between the radiation information of the tested field using the dynamic time warping (DTW) algorithm, and uses the similarity sum of the radiation information among the subregions of the temperature field as the optimization objective. This is combined with the equation-constrained optimization algorithm and multispectral thermometry to establish the statistical law between the missing information and finally realize the reconstruction of the temperature field. Simulation experiments show that, without any a priori knowledge, the method in this paper can realize reconstruction of the temperature field with an accuracy of 1.53-12.05% under two projection angles and has fewer projection angles and stronger robustness than other methods.

Bose–Einstein distribution temperature features of quasiparticles around magnetopolaron in Gaussian quantum wells of alkali halogen ions

Abstract We have applied strong coupling unitary transformation method combined with Bose–Einstein statistical law to investigate magnetopolaron energy level temperature effects in halogen ion crystal quantum wells. The obtained results showed that under magnetic field effect, magnetopolaron quasiparticle was formed through the interaction of electrons and surrounding phonons. At the same time, magnetopolaron was influenced by phonon temperature statistical law and important energy level shifts down and binding energy increases. This revealed that lattice temperature and magnetic field could easily affect magnetopolaron and the above results could play key roles in exploring thermoelectric conversion and conductivity of crystal materials.

Extraction of vegetation disturbance range using aboveground biomass estimated from Sentinel-2 imagery in coal mining areas with high groundwater table.

Coal mining in regions characterized by high groundwater table markedly predisposes to surface subsidence and water accumulation, thereby engendering substantial harm to surface vegetation, soil, and hydrological resources. Developing effective methods to extract surface disturbance information aids in quantitatively assessing the comprehensive impacts of coal mining on land, ecology, and society. Due to the shortcomings of traditional indicators in reflecting mining disturbance, vegetation aboveground biomass (AGB) is introduced as the primary indicator for extracting the mining disturbance range. Taking the Huaibei Coal Base as an example, Sentinel-2 MSI imagery is firstly used to calculate spectral factors and vegetation indices. Multiple machine learning algorithms are coupled to perform remote sensing estimation and spatial inversion of vegetation AGB based on measured samples of vegetation AGB. Secondly, an Orientation Distance-AGB (OD-AGB) curve is constructed outward from the center of subsidence water areas (SWA), with the Boltzmann function used for curve fitting. According to the location of the inflection point of the curve, the boundary points of vegetation disturbance are identified, and then the disturbance range is divided. The results show that (1) the TV-SVM model, utilizing total variables and support vector machine, achieves the highest estimation accuracy, with σMAE and σRMSE values of 208.47g/m2 and 290.19g/m2, respectively, for the validation set. (2) Thirty-six effective disturbance areas, totaling 29.89 km2, are identified; the Boltzmann function provides a good fit for the OD-AGB curve, with an R2 exceeding 0.8 for typical disturbance areas. (3) Analysis of general statistical laws indicates that disturbance distance conforms to the general characteristics of normal distribution, exhibiting boundedness and directional heterogeneity. The research is expected to provide scientific guidance for hierarchical zoning management, land reclamation, and ecological restoration in coal mining areas with high groundwater table.

Unveiling Malicious Network Flows Using Benford’s Law

The increasing proliferation of cyber-attacks threatening the security of computer networks has driven the development of more effective methods for identifying malicious network flows. The inclusion of statistical laws, such as Benford’s Law, and distance functions, applied to the first digits of network flow metadata, such as IP addresses or packet sizes, facilitates the detection of abnormal patterns in the digits. These techniques also allow for quantifying discrepancies between expected and suspicious flows, significantly enhancing the accuracy and speed of threat detection. This paper introduces a novel method for identifying and analyzing anomalies within computer networks. It integrates Benford’s Law into the analysis process and incorporates a range of distance functions, namely the Mean Absolute Deviation (MAD), the Kolmogorov–Smirnov test (KS), and the Kullback–Leibler divergence (KL), which serve as dispersion measures for quantifying the extent of anomalies detected in network flows. Benford’s Law is recognized for its effectiveness in identifying anomalous patterns, especially in detecting irregularities in the first digit of the data. In addition, Bayes’ Theorem was implemented in conjunction with the distance functions to enhance the detection of malicious traffic flows. Bayes’ Theorem provides a probabilistic perspective on whether a traffic flow is malicious or benign. This approach is characterized by its flexibility in incorporating new evidence, allowing the model to adapt to emerging malicious behavior patterns as they arise. Meanwhile, the distance functions offer a quantitative assessment, measuring specific differences between traffic flows, such as frequency, packet size, time between packets, and other relevant metadata. Integrating these techniques has increased the model’s sensitivity in detecting malicious flows, reducing the number of false positives and negatives, and enhancing the resolution and effectiveness of traffic analysis. Furthermore, these techniques expedite decisions regarding the nature of traffic flows based on a solid statistical foundation and provide a better understanding of the characteristics that define these flows, contributing to the comprehension of attack vectors and aiding in preventing future intrusions. The effectiveness and applicability of this joint method have been demonstrated through experiments with the CICIDS2017 public dataset, which was explicitly designed to simulate real scenarios and provide valuable information to security professionals when analyzing computer networks. The proposed methodology opens up new perspectives in investigating and detecting anomalies and intrusions in computer networks, which are often attributed to cyber-attacks. This development culminates in creating a promising model that stands out for its effectiveness and speed, accurately identifying possible intrusions with an F1 of nearly 80%, a recall of 99.42%, and an accuracy of 65.84%.

Statistical wave field theory.

In this paper, we introduce the foundations of the Statistical Wave Field Theory. This theory establishes the statistical laws of waves propagating in a closed bounded volume, that are mathematically implied by the boundary-value problem of the wave equation. These laws are derived from the Sturm-Liouville theory and the mathematical theory of dynamical billiards. They hold after many reflections on the boundary surface, and at high frequency. This is the first statistical theory of reverberation which provides the closed-form expression of the power distribution and the correlations of the wave field jointly over time, frequency, and space inside the bounded volume, in terms of the geometry and the specific admittance of its boundary surface. The Statistical Wave Field Theory may find applications in various science fields, including room acoustics, electromagnetic theory, and nuclear physics.

Research on charging monitoring method for lithium-ion batteries based on magnetic field sensing

With the rapid and continuous development of new energy vehicles, safety issues during charging have become increasingly prominent. Thus, there is an urgent need to strengthen charging safety management. However, current charging detection methods have limitations, such as difficulty in monitoring local battery pack currents, and indirect monitoring through temperature and gas sensors lead to lag. To address these limitations, this article proposes a safety monitoring method based on an improved lithium-ion battery magnetic field sensing model that covers the entire charging process. Specifically, thermal field analysis was introduced to the existing electric magnetic coupling model, resulting in an electric thermal magnetic multi-physical field coupling model. By conducting experiments, the study verified that the accuracy of the improved model has increased by 15.5 %. Based on this model, the study proposed a method for predicting and warning of abnormal currents using BP neural network and mathematical statistical laws. The results showed that the current prediction accuracy of this method reached 96.4 %. Such high accuracy ensures real-time comprehensive monitoring of the current information of lithium-ion battery packs, thereby eliminating the hidden dangers of charging safety accidents caused by the lack of local current detection.

Finding a predictive value for the achievement of running the 800 m in terms of some biochemical indicators among female students of the College of Physical Education and Sports Sciences

The 800m event was discussed, and that some biochemical indicators have a direct impact on the students’ ability to continue performing with maximum effort and in the shortest possible time, as this event falls within the most difficult energy production systems, which is the lactic acid system. The importance of research is to find a predictive equation for the completion of this race in terms of some Biochemical indicators for them this equation will be a valuable tool for trainers. As for the problem of the research, and through the researcher’s follow-up of the local championships, he noticed that there is a difference in the completion of the 800 m event for women between high and low, and between one student and another, and one student and another. This may be one of the most important reasons for the quality and trends of the training provided to them or the study of the biochemical components of the female students. The research sample represents female students in the College of Education. Physical Education and Sports Sciences at the University of Dohuk used special tests and measurements and used statistical laws rather than extracting results. The researcher concluded that the contribution of the hemoglobin Hp index had the highest percentage of contribution to the completion of 800 meters among female students of the College of Physical Education and Sports Sciences. She recommended the need to pay attention to the percentages of the contribution that the study showed to the hemoglobin Hp index.

Model-data hybrid driven approach for remaining useful life prediction of cutting tool based on improved inverse Gaussian process

In the cutting process, reasonable evaluation of tool remaining useful life (RUL) is essential to ensure machining stability and safety. However, traditional data-driven methods rely on datasets with complete degradation data and prior knowledge, which are usually difficult to obtain in real scenarios. For these problems, this paper proposed a model-data hybrid driven approach for RUL prediction of cutting tool based on improved inverse Gaussian process. The tool wear degradation is considered as a random process, the cutting physical model and the data-driven stochastic process model are fused, so that the prior knowledge from the physical model and the statistical law of measured data are fully utilized to improve the accuracy of tool RUL prediction. The cutting physical model is established, and the prior knowledge of tool wear degradation is obtained based on physical simulation method. A data-driven random effects inverse Gaussian process model is constructed for tool RUL modeling and prediction. According to Bayesian method, the unknown parameters are estimated and updated integrating physical simulated and measured wear data, so as to obtain the probability density function for specific tool RUL, and quantify the prediction uncertainty. Finally, comparative experiments are conducted to validate the performance of the proposed method. The results suggest that the hybrid approach has the best performance in different tool RUL prediction.

Express Method for Assessing Performance of Lubricant Compositions Containing Nano-Additives Used for Wheel-Rail Pairs.

An express method for assessing the effectiveness of lubricating compositions with nano-additives of various chemical compositions is proposed, and a joint analysis of experimental data on the changes in the value of wear and the level of damage to the surface layers of metallic friction pairs was performed. The variation in the current relative hardness of the sample's surface, the variation in the current relative material damage level, the current value of wear, and the current level of the coefficient of friction were chosen as the key parameters to conduct a performance assessment. The level of material damage in the contact zone was determined using the parameters of the statistical law of hardness value scattering. Based on an analysis of data in the literature, it was observed that the structural changes occurring in metallic materials during long-term, cyclic, static, and frictional loading are correlated with changes in the statistical characteristics of the hardness scattering results. An experimental substantiation of the proposed method was carried out for steel-sliding friction pairs using lubricating compositions based on Greaseline Lithium BIO Rail 000 oil manufactured by AIMOL with nano-additives of copper, magnesium and aluminum alloys, graphite, and two grades of medium-carbon steel. According to the system of indicators presented in this research, the greatest efficiency (in terms of increasing the wear resistance of friction steel pairs) was achieved with lubricating compositions including nano-powder additives made of steel, which have lower hardness. For the friction experiments, where the determining factor was abrasive wear, such lubricants ensured minimal damage and wear to the friction surface, while the value of the friction coefficient was maintained at a level that is optimal for wheel-rail friction pairs.