Maximum Probability Research Articles

Reconfigurable intelligent surface-aided positioning-centered multi-LED integrated visible light communication and positioning system

This paper investigates a reconfigurable intelligent surface (RIS)-aided integrated visible light communication and positioning (VLCP) system, which aims to reduce sensitivity to line-of-sight (LoS) blockage in visible light and simultaneously achieve capabilities for both visible light communication (VLC) and visible light positioning (VLP). The framework of this system is divided into three parts: positioning, channel state information (CSI) estimation, and data transmission. When the LoS links are present, due to the potential adverse positioning effects RIS caused in this scenario, the RIS only plays a role in assisting the communication. Meanwhile, the positioning process is based on the received signal strength (RSS) information from the LoS transmission. If the LoS links are blocked, the RIS provides added non-line-of-sight (NLoS) positioning signals and achieves subsidiary communications accordingly. The Cramer-Rao lower bound (CRLB) on the positioning result is derived and the CSI estimation is conducted based on the results provided by the positioning schemes to reduce the pilot overhead. The achievable rate is evaluated based on the estimated CSI. The configurations of RIS parameters and the power allocated to positioning and communication are jointly optimized to minimize the CRLB while satisfying constraints on the maximum tolerable outage probability, RIS parameter acquisition, and total transmit power. To address this non-convex optimization problem, we proposed an alternative optimization (AO) algorithm to optimize the RIS assignment matrix and the power coefficient alternatively. We employ the worst-case distribution of the Conditional Value-at-Risk (CVaR) along with successive convex approximation (SCA) techniques to derive feasible solutions of the power coefficient optimization subproblem. Meanwhile, we optimize the RIS assignment matrix based on the principle of maximum received power chosen (MRPC). Simulation results demonstrate the influence of RIS in the positioning process in our proposed VLCP system with or without the presence of LoS links, and meanwhile, the relationship between communication performance and positioning performance is validated through the simulations. From the simulation results, the RIS-aided VLCP system can be verified as a viable option for the upcoming era of sixth-generation (6G) technology.

A Ratio-Type Weighted Geometric Distribution for Modelling Overdispersed Count Data

Weighted distributions have always been a popular approach in developing flexible distributions for data modelling. In this paper, we introduce a flexible ratio-type weighted geometric distribution by adopting the geometric distribution as a basic standard distribution and opting for weights, represented as . The proposed distribution is overdispersed and is capable of accommodating data with small mode values such as 0, 1 and 2. The proposed distribution has the following properties – unimodal, log-concave and has increasing failure rates. The moment estimator is obtained, and the resulting estimated parameter is utilized as the initial point in finding the estimators based on the maximum likelihood technique and probability generating function. A probability comparison between the typical geometric distribution and the proposed distribution is discussed as well. A collection of insurance claim datasets is utilized for model fitting, and it was found out that generally, the proposed distribution can adequately fit the datasets as opposed to other contending distributions.

Modeling the Inter-Arrival Time Between Severe Storms in the United States Using Finite Mixtures

When inter-arrival times between events follow an exponential distribution, this implies a Poisson frequency of events, as both models assume events occur independently and at a constant average rate. However, these assumptions are often violated in real-insurance applications. When the rate at which events occur changes over time, the exponential distribution becomes unsuitable. In this paper, we study the distribution of inter-arrival times of severe storms, which exhibit substantial variability, violating the assumption of a constant average rate. A new approach is proposed for modeling severe storm recurrence patterns using a finite mixture of log-normal distributions. This approach effectively captures both frequent, closely spaced storm events and extended quiet periods, addressing the inherent variability in inter-event durations. Parameter estimation is performed using the Expectation–Maximization algorithm, with model selection validated via the Bayesian information criterion (BIC). To complement the parametric approach, Kaplan–Meier survival analysis was employed to provide non-parametric insights into storm-free intervals. Additionally, a simulation-based framework estimates storm recurrence probabilities and assesses financial risks through probable maximum loss (PML) calculations. The proposed methodology is applied to the Billion-Dollar Weather and Climate Disasters dataset, compiled by the U.S. National Oceanic and Atmospheric Administration (NOAA). The results demonstrate the model’s effectiveness in predicting severe storm recurrence intervals, offering valuable tools for managing risk in the property and casualty insurance industry.

An Optimization Coverage Strategy for Wireless Sensor Network Nodes Based on Path Loss and False Alarm Probability.

In existing coverage challenges within wireless sensor networks, traditional sensor perception models often fail to accurately represent the true transmission characteristics of wireless signals. In more complex application scenarios such as warehousing, residential areas, etc., this may lead to a large gap between the expected effect of actual coverage and simulated coverage. Additionally, these models frequently neglect critical factors such as sensor failures and malfunctions, which can significantly affect signal detection. To address these limitations and enhance both network performance and longevity, this study introduces a perception model that incorporates path loss and false alarm probability. Based on this perception model, the optimization objective function of the WSN node optimization coverage problem is established, and then the intelligent optimization algorithm is used to solve the objective function and finally achieve the optimization coverage of sensor nodes. The study begins by deriving a logarithmic-based path loss model for wireless signals. It then employs the Neyman-Pearson criterion to formulate a maximum detection probability model under conditions where the cost function and prior probability are unknown, constraining the false alarm rate. Simulated experiments are conducted to assess the influence of various model parameters on detection probability, providing comparative analysis against traditional perception models. Ultimately, an optimization model for WSN coverage, based on combined detection probability, is developed and solved using an intelligent optimization algorithm. The experimental results indicate that the proposed model more accurately captures the signal transmission and detection characteristics of sensor nodes in WSNs. In the coverage area of the same size, the coverage of the model constructed in this paper is compared with the traditional 0/1 perception model and exponential decay perception model. The model can achieve full coverage of the area with only 50 nodes, while the exponential decay model requires 54 nodes, and the coverage of the 0/1 model is still less than 70% at 60 nodes. According to the simulation experiments, it can be basically proved that the WSN node optimization coverage strategy based on the proposed model provides an effective solution for improving network performance and extending network lifespan.

Null method to estimate the maximal PA at subsaturating concentrations of agonist.

The maximal probability of being in an active state (PA,max) is a measure of gating efficacy for a given agonist acting on a given receptor channel. In macroscopic electrophysiological recordings, PA,max is typically estimated by comparing the amplitude of the current response to a saturating concentration of a test agonist to that of a reference agonist with known PA. Here, we describe an approach to estimate the PA,max for low-efficacy agonists at subsaturating concentrations. In this approach, the amplitude of the response to a high-efficacy control agonist applied alone is compared with the amplitude of the response to a control agonist coapplied with the low-efficacy test agonist that binds to the same site(s). If the response to the combination is larger than the response to the control agonist alone, then the PA,max of the test agonist is greater than the PA of the control response. Conversely, if the response to the control agonist is reduced upon exposure to the test agonist, then the PA,max of the test agonist is smaller than the PA of the control response. The exact PA,max of the test agonist can be determined by testing its effect at different concentrations of the control agonist to estimate the PA at which the effect changes direction. The main advantage of this approach lies in the ability to use low, subsaturating concentrations of the test agonist. The model-based predictions are supported by observations from activation of heteromeric and homomeric GABAA receptors by combinations of high- and low-efficacy orthosteric agonists.

Dam Breach Risk Analysis and Mapping: A Case Study of the Wala Dam, Jordan

This paper investigates the flood hazard related to dam breach analysis for Wala Dam in Jordan. Hydrologic modeling of probable maximum flood was conducted using the probable maximum precipitation values in the dam watershed. The peak probable maximum flood of the Wala dam watershed was about 2,621 m3/s. Two dam breach scenarios were investigated; namely, overtopping and piping failures, using empirical dam breach equations. A 2-dimensional unsteady hydraulic model (HEC-RAS) was used to route the breach flood downstream of the dam. The maximum peak flows for both the overtopping and piping scenarios were 12,435 m³/s and 5,962 m³/s, respectively. The results are used to generate inundation, flood hazard risk, duration, and velocity maps for areas downstream of the dam. Most inundated areas were classified as extreme hazard areas. The maximum depth of water for overtopping failure is approximately 43 m in some agricultural lands and about 8 m near the Dead Sea road. Flooded areas include farmhouses, roads and bridges, the Dead Sea road and other important public and private properties. Furthermore, the maximum velocities are 17.1 m/s and 15.8 m/s for overtopping and piping failures, respectively. This study demonstrates the importance of developing and regularly updating comprehensive emergency preparedness and enhancing the resilience of downstream communities by community-based disaster risk reduction programs. Keywords: Dam breach, Flood risk mapping, Wadi Wala dam, HEC-RAS modeling, Flood hydrology, Overtopping.

Asynchronous Control for Interval Type-2 Fuzzy Nonhomogeneous Markov Jump Systems Against Successive DoS Attacks.

This article is concerned with the problem of asynchronous control for Interval Type-2 (IT2) fuzzy nonhomogeneous Markov jump systems against successive denial-of-service (DoS) attacks. The system and the controller are assumed to be connected through a communication channel subject to malicious attacks. The maximum number and probability distribution of successive attacks are considered. Under the imperfect premise matching, a fuzzy asynchronous controller is constructed by the hidden Markov model. By means of the introduced transmission delay, a delay closed-loop system is constructed, where the stochastic description of the delay depends on the statistical characteristic of successive attacks. Then stability criteria together are derived in the form of linear matrix inequalities by the Lyapunov functional approach, as well as the condition on the existence of the fuzzy controller. Finally, the feasibility and effectiveness of the presented control scheme are demonstrated by simulation results.

Stochastic seepage stability analysis of the Pubugou clay core rockfill dam with potentially high permeability zone by integrating multi-source monitoring information

ABSTRACT One of the most important causes of the failure of a clay core rockfill dam (CCRD) is seepage failure caused by defects inside the clay core (e.g. a high permeability zone, HPZ for short). This study conducted a seepage stability analysis of the Pubugou CCRD with an HPZ, considering the uncertainty of dam parameters, including hydraulic conductivities, water level, and height of the HPZ. The reliability analysis methodology, both with and without the monitoring information, was first introduced. By inputting multi-source monitoring data, the probabilities of both the seepage failure and the dam parameters can be updated. The results show that the large monitoring values on 1 December 2010 have incurred an increase in the failure probability from 3.28 × 10−5 to 8.47 × 10−5, which was mainly caused by the increase of the hydraulic conductivity of the clay core (k 1). The failure probability then decreased from 8.47 × 10−5 to 7.46 × 10−6 when smaller monitoring values on 6 September 2011 were input. The maximum probability interval of the k 1 decreased from greater than 1.48 × 10−7 to between 4.18 × 10−8 and 7.86 × 10−8 due to long-term consolidation. However, the hydraulic conductivity of HPZ (k 2) slightly increased because of possible internal erosion caused by long-time seepage in HPZ.

A Novel Map Matching Method Based on Improved Hidden Markov and Conditional Random Fields Model

ABSTRACT Aiming at the inherent “labeling bias” problem of Hidden Markov Models (HMMs) in the process of low-frequency sampling rate GPS trajectory map matching, this paper proposes a map matching method that combines HMMs and Conditional Random Field Models (CRFs). Various features including vehicle driving direction, direction change between candidate roads, shortest path, and spatial localization accuracy of trajectory points are integrated to optimize the state transfer process in the HMM model. The Viterbi algorithm was then employed to calculate the joint probability values of all candidate paths and the path with maximum probability value was selected as the matching path. The proposed map matching method was validated using publicly available Global Positioning System (GPS) vehicle trajectories from Guangzhou, Dongguan, and field-collected vehicle trajectory data from Ganzhou, China. The results demonstrated that the proposed method achieves high matching accuracy while maintaining efficient matching efficiency. The percentage of correct matching of GPS sampling points remains above 95%, and the average calculation time for each candidate road segment is kept within 50 ms. These advancements can greatly benefit location-based services that rely on map matching technology.

CRITERIA AND OBJECTIVE FUNCTIONS IN THE RATIONAL DESIGN OF TWO-SHAFT GEARBOXES

The relevance of the scientific and practical task of forming criteria and objective functions in the rational design of two-shaft gearboxes is described. This has made it possible to understand the need to highlight the topic and conduct relevant research and scientific discussions on the issue. The most significant mass and dimensional characteristics of two-shaft gearboxes from the perspective of vehicle design have been identified and used as criteria for optimal and rational design. Specifically: the center distance, which determines the placement of the gearbox shafts and its height; the length of the gearbox, which determines one of the main overall dimensions of the gearbox; the weight of the gearbox, the reduction of which may be dictated by the requirements for the technical object and also leads to a reduction in the material used and energy consumption; and the probability of reliable operation. Objective functions corresponding to the criteria of optimal and rational design are formulated, which are expressed by functional dependencies between geometric-constructive parameters and mass-dimensional characteristics, and also take into account the strength aspects of the main elements of two-shaft gearboxes. The objective function of the minimum center distance allows reducing the sum of the center distances of all gear meshes of the gearbox, and considering the condition of equality of the center distances of the gearbox gear meshes among themselves, to preserve the structural features and arrangement of the gear meshes. The objective function of minimum length accurately characterizes the linear dimension (length) of the gearbox. It considers not only the widths of the gear teeth but also other indicators (clearances, bearings, synchronizers, etc.), which are significant additions and increase the accuracy of calculations. The objective function of minimum weight of the gearbox consists of the weights of its main elements, namely: gears, shafts, bearings, synchronizers, and housing with the shifting mechanism. These elements make the main contribution to the mass characteristic, and the weights of other parts will be neglected due to their small sizes and inclusion in the error, which may be permissible for estimation calculations. The objective function of maximum reliability probability is presented as a certain «integral» value, which contains all calculated coefficients of stress levels for bending and contact stresses. Also design variables are defined

Probabilistic channel simulation using coherence

Channel simulation using coherence, which refers to realizing a target channel with coherent states and free operations, is a fundamental problem in the quantum resource theory of coherence. The limitations of the accuracy of deterministic channel simulation motivate us to consider the more general probabilistic framework. In this paper, we develop the framework for probabilistic channel simulation using coherence with free operations. When the chosen set of free operations is the maximally incoherent operations, we provide an efficiently computable semidefinite program (SDP) to calculate the maximal success probability and derive the analytic expression of success probability for some special cases. When the chosen set of free operations is the dephasing-covariant incoherent operations (DIO), we show that if the target channel is not a resource nonactivating channel then one cannot simulate it exactly both deterministically and probabilistically. The SDP for maximal success probability of simulating a channel by DIO is also given correspondingly. Published by the American Physical Society 2024

Seasonal-diurnal features of the medium-scale traveling ionospheric disturbances characteristics in the Asian Region of Russia During years of moderate solar activity

Based on data from a network of oblique-incidence sounding radio paths at mid-latitudes in the Asian region of Russia, a high (up to 40−50%) average-daily recording probability of the medium-scale traveling ionospheric disturbances in years of moderate solar activity has been identified. The daily variation in the recording probability of these disturbances at mid-latitude radio paths in the Asian region of Russia has a pronounced seasonal dependence. For the winter season, there is a daily maximum probability, reaching 100% on some days. In the summer season, it occurs at night hours of local time at the midpoint of the corresponding radio path. The most likely reason for this is the transition from winter to summer pattern of the atmosphere zonal circulation.

Multi-hazard stress testing under extreme rainstorms in the Shenzhen metropolitan area

ABSTRACT A severe rainstorm can trigger numerous natural hazards of multiple types in cities with hilly terrain, such as landslides, debris flows, and flooding. Such compound hazards may pose much greater risks than a single hazard to the safety of residents and infrastructures. This study focuses on a metropolitan area of Shenzhen, China and develops a multi-hazard stress testing method for hazard risk management against extreme rainstorms. The probable maximum precipitation in Shenzhen is first estimated using the storm transposition method considering orographic intensification and moisture maximisation, with the centre peak amount being 1441 mm in 24 hours at Tanglang Mountain. An integrated physically-based multi-hazard simulation model, EDDA, is then utilised to simulate the processes of initiation, propagation and transformation of landslides, debris flows and flooding in a unified manner. Under the designated extreme rainstorms of a 1000-year return period and 85% of probable maximum precipitation, deposit depths of landslides and debris flows can be large in some urban areas near the foot of Tanglang Mountain; flooding can be very extensive in the flat built-up regions, with 21.8% and 31.7% of the study area flooded, respectively. The produced multi-hazard maps can facilitate the design of risk mitigation measures against extreme rainstorms.

SYNCHRONIZATION OF EVENT-DRIVEN MANAGEMENT DURING DATA COLLECTION

The article considers an approach to implementing the architecture of a microservice system for processing large volumes of data based on the event-oriented approach to managing the sequence of using individual microservices. This becomes especially important when processing large volumes of data from information sources with different performance levels when the task is to minimize the total time for processing data streams. In this case, as a rule, the task is to minimize the number of requests for information sources to obtain a sufficient amount of data relevant to the request. The efficiency of the entire software system as a whole depends on how the microservices that provide extraction and primary processing of the received data are managed. To obtain the required amount of relevant data from diverse information sources, the software system must adapt to the request during its operation so that the maximum number of requests are directed to sources that have the maximum probability of finding the data necessary for the request in them. An approach is proposed that allows adaptively managing the choice of microservices during data collection and by emerging events and, thus, forming a choice of information sources based on an assessment of the efficiency of obtaining relevant information from these sources. Events are generated as a result of data extraction and primary processing from certain sources in terms of assessing the availability of data relevant to the request in each of the sources considered within the framework of the selected search scenario. Event-oriented microservice architecture adapts the system operation to the current loads on individual microservices and the overall performance by analyse the relevant events. The use of an adaptive event-oriented microservice architecture can be especially effective in the development of various information and analytical systems constructed by real-time data collection and design scenarios of analytical activity. The article considers the features of synchronous and asynchronous options in the implementation of event-oriented architecture, which can be used in various software systems depending on their purpose. An analysis of the features of synchronous and asynchronous options in the implementation of event-oriented architecture, their quantitative parameters, and features of their use depending on the type of tasks is carried out.

Unmanned-Aerial-Vehicle-Assisted Secure Free Space Optical Transmission in Internet of Things: Intelligent Strategy for Optimal Fairness.

In this article, we consider an UAV (unmanned aerial vehicle)-assisted free space optical (FSO) secure communication network. Since FSO signal is impossible to detect by eavesdroppers without proper beam alignment and security authentication, a BS employs FSO technique to transfer information to multiple authenticated sensors, to improve the transmission security and reliability with the help of an UAV relay with decode and forward (DF) mode. All the sensors need to first send information to the UAV to obtain security authentication, and then the UAV forwards corresponding information to them. Successive interference cancellation (SIC) is used to decode the information received at the UAV and all authenticated sensors. With consideration of fairness, we introduce a statistical metric for evaluating the network performance, i.e., the maximum decoding outage probability for all authenticated sensors. In particular, applying an intelligent approach, we obtain a near-optimal scheme for secure transmit power allocation. With a well-trained allocation scheme, approximate closed-form expressions for optimal transmit power levels can be obtained. Through some numerical examples, we illustrate the various design trade-offs for such a system. Additionally, the validity of our approach was verified by comparing with the result from exhaustive search. In particular, the result with DRL was only 0.3% higher than that with exhaustive search. These results can provide some important guidelines for the fairness-aware design of UAV-assisted secure FSO communication networks.

Can structured integration of BI-RADS criteria by a clinical decision rule reduce the number of unnecessary biopsies in BI-RADS 4 lesions? A systematic review and meta-analysis.

This systematic review and meta-analysis investigate the added value of structured integration of Breast Imaging Reporting and Data System (BI-RADS) criteria using the Kaiser score (KS) to avoid unnecessary biopsies in BI-RADS 4 lesions. A systematic review and meta-analysis were conducted using predefined criteria. Eligible articles, published in English until May 2024, dealt with KS in the context of BI-RADS 4 MRI. Two reviewers extracted study characteristics, including true positives (TP), false positives (FP), true negatives (TN), and false negatives (FN). Sensitivity, specificity, negative likelihood ratio, and positive likelihood ratio were calculated using bivariate random effects. Fagan nomograms identified the maximum pre-test probability at which post-test probabilities of a negative MRI aligned with the 2% malignancy rate benchmark for downgrading BI-RADS 4 to BI-RADS 3. I² statistics and meta-regression explored sources of heterogeneity. p-values < 0.05 were considered significant. Seven studies with 1877 lesions (833 malignant, 1044 benign) were included. The average breast cancer prevalence was 47.3%. Pooled sensitivity was 94.3% (95%-CI 88.9%-97.1%), and pooled specificity was 68.1% (95%-CI 56.6%-77.7%) using a random effects model. Overall, 52/833 cases were FNs (6.2%). Fagan nomograms showed that KS could rule out breast cancer in BI-RADS 4 lesions at a pre-test probability of 20.3% for all lesions, 25.4% for masses, and 15.2% for non-mass lesions. In MRI-assessed BI-RADS 4 lesions, applying structured BI-RADS criteria with the KS reduces unnecessary biopsies by 70% with a 6.2% FN rate. Breast cancer can be ruled out up to pre-test probabilities of 20.3%. Question What, if any, value is added by structured integration of BI-RADS criteria using the Kaiser Score (KS) to avoid unnecessary biopsies in BI-RADS 4 lesions? Findings The structured integration of BI-RADS criteria using the Kaiser Score (KS) reduces unnecessary biopsies in BI-RADS 4 lesions by 70%. Clinical relevance The structured approach offered by the Kaiser Score (KS) avoids unnecessary recalls, potentially reducing patient anxiety, lessening the burden on medical personnel, and the need for further imaging and biopsies due to more objective and thus efficient clinical decision-making in evaluating BI-RADS 4 lesions.

Did Historical Storms Used in Probable Maximum Precipitation (PMP) Estimation Reach Maximum Efficiency? A Large Model Ensemble Approach

AbstractThe flood that would result from the greatest depth of precipitation “meteorologically possible”, or Probable Maximum Precipitation (PMP) is used in the design of dam spillways and other high‐risk structures. Historically, PMP has been estimated by scaling depth‐area‐duration relationships obtained from severe historical storms. Over the last decade, numerical weather prediction models have been used to instead simulate precipitation resulting from the addition of atmospheric moisture (called relative humidity maximization, or RHM). Despite the major improvement this represents, model‐based PMP relies on a key assumption, which this paper re‐evaluates in Oroville dam's Feather River watershed (California). Model‐based as well as earlier procedures assume that severe historical storms achieved maximum efficiency (moisture conversion to precipitation) and only maximize moisture. We examine the most severe storms found in the CESM2‐LE global climate model ensemble, which constitutes a very large artificial record (∼1,150 years) in comparison with the historical record, to understand the upper bounds of storm efficiency and precipitation. We downscale the 10 most severe CESM2‐LE storms (by precipitation totals), and identify key storm attributes (vertical motion, convection and convergence) that control precipitation efficiency. In comparison with historical storms, we find that CESM‐LE storms can have 30% higher efficiency and 32% higher precipitation, but produce only 8% higher PMP estimates, suggesting some convergence of model ensemble and historical storms in terms of PMP. The understanding of the controls on storm efficiency that our work provides leverages past work focused on moisture and supports the development of more reliable PMP storm amplification guidance.

Comparative study of electron temperature and ion energy in two different magnetic nozzle thruster designs

Conventional ion thruster technologies face challenges such as electrode and grid erosion and the need for additional neutralizer devices. In this article, we discuss two thruster concepts that achieve plasma acceleration by means of a magnetic nozzle, and thus avoid the need of a neutralizer device. The concept of a magnetic nozzle converting the thermal energy available in the electrons movement to ion kinetic energy is a well accepted model in the community. We discuss a novel thruster concept based on electrode-less electron cyclotron resonance plasma generation via a slot antenna design. The geometry of this thruster concept results in a converging-diverging character of the magnetic field topology along the plume direction. To this date it is not known in which way this new thruster design influences the electron dynamics and thus the ion energy. To understand the correlation between ion energy and electron temperature of this thruster system, it is compared with a well-known thruster prototype operating on similar principles, however, realizing microwave coupling and magnetic field topology in a different way. Both thruster designs operate within comparable power, frequency, and volume flow ranges. The ion energy with maximum probability is measured for both thrusters using a retarding potential analyzer in the same vacuum environment. Additionally, the electron temperature is measured with a Langmuir probe for various operation points of the thrusters, differing in input power level, volume flow, set excitation frequency, and argon or xenon as propellant.

Asymptotic estimation for statistical models of continuous-time discrete martingales

The paper deals with statistical experiments of the continuous-time discrete local martingales, including models of all types of point processes. The process of local density of the discrete local martingales is expressed by a stochastic exponent of the stochastic integral according to the compensated point measure. General conditions convenient for testing are determined to assure continuous validity of the maximum probability and Bayesian estimators, as well as the continuous asymptotic normality and the asymptotic minimaxity in each compact of the parametric set. The research applies the optimum Fréchet differentiation of random and parametric functions based on the probability in normed spaces in terms of a continuous compensator. It is demonstrated how the basic conditions become much simpler in the case of the renewal process with the continuous compensator.

Stochastic Risk Assessment Framework of Deep Shale Reservoirs by a Deep Learning Method and Random Field Theory

Risk assessment of deep shale reservoirs is very important for subsurface energy development. However, due to complex geological environments and physicochemical interactions, shale reservoir fabric parameters exhibit variability. Moreover, the actual investigation and testing information is very limited, which is a typical small-sample problem. In this paper, the heterogeneity and statistical characteristics of deep shale reservoirs are clarified by the measured mechanical parameters. A deep learning method for deep shale reservoirs with limited survey data information is proposed. The variability of deep shale reservoirs is characterized by random field theory. A variable stiffness method and stochastic analysis method are developed to evaluate the risk of deep shale reservoirs. The detailed workflow of the stochastic risk assessment framework is presented. The frequency distribution and failure risk of deep shale reservoirs are calculated and analyzed. The risk assessment of deep shale reservoirs under different model parameters is discussed. The results show that a stochastic risk assessment framework of deep shale reservoirs, using a deep learning method and random field theory, is scientifically reasonable. The scatter plots of the elasticity modulus (EM), cohesive force (CF), and Poisson ratio (PR) distribute along the 45-degree line. The different distributed variables of EM, CF, and PR have a positive correlation. The statistical properties of the measurement data and deep learning data are approximately the same. The principal stress of deep shale follows the normal distribution with significance level 0.1. Under positive copula conditions, the maximum failure probability is 5.99%. Under negative copula conditions, the maximum failure probability is 4.58%. Different copula functions under positive and negative copula conditions have different failure probabilities. For the exponential correlation structure, the minimum failure probability is 3.46%, while the maximum failure probability is 6.19%. The mean failure probability of the EM, CF, and PR of deep shale reservoirs is 4.85%. Different random field-related structures and parameters have different influences on the failure risk.