Stochastic Method Research Articles

A penalty-free hybrid algorithm framework based on feasible stream matching principle for large-scale heat exchanger networks synthesis

In this work, a penalty-free hybrid stochastic-deterministic algorithm framework is proposed for large-scale heat exchanger networks (HENs) synthesis (HENS), formulated as a computationally-hard mixed-integer nonlinear programming (MINLP) problem. In the outer level, an improved genetic algorithm (GA) is developed to optimize process stream matches represented by integer variables whose values are generated by a unique heat exchanger vector. Unlike previous researches, the improved GA does not rely on any penalty terms, because we propose a feasible stream matching principle to exclude all infeasible process stream matches and only feasible matches are considered in optimization process. In the inner level, a reduced-size MINLP model is solved using deterministic methods to minimize total annualized costs (TACs), which are then used to evaluate the fitness of candidate HENs. Through this way, the proposed framework combines deterministic and stochastic methods to enhance optimization efficiency and global search capability. Illustrative tests on six benchmark cases demonstrate that the framework can efficiently achieve lower-cost solutions compared to deterministic, stochastic, or hybrid methods. The results show a decrease in TAC for all six cases and a reduction in solution time ranging from 11.1% to 97.2%. Importantly, the proposed framework can be extended to solve MINLP problems in other process networks.

Conceptual Design and Structural Performance Analysis of an Innovative Deep-Sea Aquaculture Platform

This paper proposes a conceptual design of an innovative deep-sea aquaculture platform that integrates a steel structural framework and high-density polyethylene (HDPE) floats. It aims to overcome the limitations of prevailing aquaculture equipment, including inadequate resistance to strong wind and waves, complex technologies, and prohibitively high costs. The design scheme and key parameters of the main platform, the netting system, and the mooring systems are presented. Based on the stochastic design wave method, the characteristic load response scenarios and design wave parameters are determined and analyzed. Strength analysis is conducted to assess the structural performance, vulnerabilities, and overall safety of the platform under various characteristic load conditions. The results indicate that the Von Mises stress levels across different sections of the platform conform to the allowable stress thresholds under various characteristic load conditions. However, the stress levels of the platform are notably higher when subjected to characteristic loads associated with vertical shear, vertical bending moments, and torsion about the horizontal axis, which requires further efforts in the design process to enhance the structural safety of the platform. The proposed design methodology and the presented research results can provide a wide range of references for the design and analysis of deep-sea fisheries aquaculture equipment.

Computer 3D Simulation of Proppant Particles

Proppants are one of the key materials for hydraulic fracturing, whose main role is to support fractures and create a channel through which oil and gas can flow. The nature of proppants is the most talked about feature besides their cost, for example, their sphericity, turbidity, particle size, or strength. The porosity, permeability, and fracture conductivity of proppants in fractures are also the main indicators to measure the performance of them. These indicators are usually obtained through physical experiments. However, experimental results often differ depending on the experimental scheme. Different stacking methods of proppant particles lead to this phenomenon. The nature of proppant particles in fractures varies with the way they accumulate. This paper will start with the microscopic arrangement of proppant particles. Considering the randomness and certainty of three-dimensional particle stacking and arrangement, the Monte Carlo stochastic method and an optimization model were used to conduct three-dimensional computer simulation of proppant particles. This lays an important foundation for revealing the randomness and regularity of the micro arrangement of proppant particles.

Stochastic Models for Cyber Attack Detection and Response: A Mathematical Approach to Intrusion Detection Systems

Cyberattacks are a big problem in today's world because everything is linked online. They can damage the security, privacy, and access of private information. Intrusion Detection Systems (IDS) are very important for keeping networks safe because they quickly find and stop harmful activity. To successfully find and stop attacks, however, we need more advanced methods because online risks are always changing. This paper suggests a new mathematical approach for improving IDS that is based on random models. Traditional ways of finding intrusions often use signature- or anomaly-based methods, which might not be able to keep up with how attackers' strategies change all the time. By using random processes, our method provides a more flexible and adaptable way to find online threats. IDS can tell the difference between normal network traffic and hostile activities because stochastic models use a statistical framework to capture the uncertainty that comes with cyberattack behaviors. We use methods from probability theory, Markov chains, and queue theory to make models of how network traffic and possible cyberattacks might behave. Our random models can find differences that could mean someone is doing something bad by looking at the statistical features of different network factors, like the rate at which packets arrive, the length of a link, and the size of the payloads. Using Markov models, the IDS can also guess how likely it is that an attack will happen in the future based on past data, which helps with strategic strategies for reducing threats. Along with monitoring, our system includes ways to respond to cyberattacks and lessen their effects. By using stochastic optimization methods, we can change how resources are used and how reactions are prioritized based on how likely and how bad the threats are to be. This flexible method makes the network infrastructure more resistant to complex attack routes, which lowers the damage and downtime that can happen during cyber events. We show that our stochastic models can improve the performance of IDS in real-world situations by analyzing them theoretically and running simulations. Adopting a scientific approach to cyber security makes it possible for stronger and smarter defenses against cyber risks that are always changing.

A hybrid data- and model-driven learning framework for remaining useful life prognostics

The efficient and safe production of machinery equipment relies on the health of its mechanical components, making prognostics and health management (PHM) a critical aspect of production processes. One key PHM measure is the remaining useful life (RUL), which estimates the expected lifespan of a component in a production line before requiring repair or replacement. However, state-of-the-art RUL prediction methods, including data-driven, model-based, and hybrid approaches, face limitations such as incomplete/imprecise physical models, uncertainties in degradation processes, and measurement data noise. To address these limitations, this paper proposes a novel hybrid RUL prediction framework that combines the strengths of data-based and model-driven approaches. The framework includes an exponential model to leverage physical knowledge and a multi-head attention transformer to extract information from data. An extended Kalman filter is used to estimate unknown degradation process parameters and provide physical model information for the prediction process. A regression token is introduced to efficiently fuse the deep learning model and the stochastic filtering method. Numerical tests using real-world rolling bearing degradation datasets demonstrate the superiority of the proposed method over competitive alternatives.

Probabilistic Techno-Economic Assessment of Medium-Scale Photoelectrochemical Fuel Generation Plants.

Photoelectrochemical (PEC) systems are promising approaches for sustainable fuel processing. PEC devices, like conventional photovoltaic-electrolyzer (PV-EC) systems, utilize solar energy for splitting water into hydrogen and oxygen. Contrary to PV-EC systems, PEC devices integrate the photoabsorber, the ionic membrane, and the catalysts into a single reactor. This integration of elements potentially makes PEC systems simpler in design, increases efficiency, offers a cost advantage, and allows for implementation with higher flexibility in use. We present a detailed techno-economic evaluation of PEC systems with three different device designs. We combine a system-level techno-economic analysis based on physical performance models (including degradation) with stochastic methods for uncertainty assessments, also considering the use of PV and EC learning curves for future cost scenarios. For hydrogen, we assess different PEC device design options (utilizing liquid or water vapor as reactant) and compare them to conventional PV-EC systems (anion or cation exchange). We show that in the current scenario, PEC systems (with a levelized cost of hydrogen of 6.32 $/kgH2 ) located in southern Spain are not yet competitive, operating at 64% higher costs than the PV-driven anion exchange EC systems. Our analysis indicates that PEC plants' material and size are the most significant factors affecting hydrogen costs. PEC designs operating with water vapor are the most economical designs, with the potential to cost about 10% less than PV-EC systems and to reach a 2 $/kgH2 target by 2040. If a sunlight concentrator is incorporated, the PEC-produced hydrogen cost is significantly lower (3.59 $/kgH2 in the current scenario). Versions of the concentrated PEC system that incorporate reversible operation and CO2 reduction indicate a levelized cost of storage of 0.2803 $/kWh for the former and a levelized cost of CO of 0.546 $/kgCO for the latter. These findings demonstrate the competitiveness and viability of (concentrated) PEC systems and their versatile use cases. Our study shows the potential of PEC devices and systems for hydrogen production (current and future potential), storage applications, and CO production, thereby highlighting the importance of sustainable and cost-effective design considerations for future advancements in technology development in this field.

Stochastic iterative methods for online rank aggregation from pairwise comparisons

Stochastic iterative methods for online rank aggregation from pairwise comparisons

Прогнозирование углеводородоперспективных структур кольцевого вида в Баренцевоморском регионе по результатам применения стохастического метода при использовании совокупности геопараметров

The article presents the results of the application of the stochastic method used to predict hydrocarbon-prospective geostructures of a concentric type within the Barents Sea region. According to thecalculated values ofstochastic parameters for the 21 geostructures of aconcentric view in the waters of the Barents region, based on four different geoparameters a summary table of stochastic parameters was compiled and an encouraging forecast was made for 13 concentric geostructures promising for the search for new oil deposits within the Barents Sea region.

Dynamic characteristics of vertically irregular structures with random fields of different probability distributions based on stochastic homotopy method

Considering the uncertainty of elastic modulus in different materials as well as the strong nonlinearity between the structural frequency and elastic modulus, it is a great challenge for computing the dynamic characteristics of vertically irregular structures. In this research, a new stochastic homotopy approach is presented to compute the basic dynamic characteristics of the vertically irregular structures, where the elastic modulus of different materials are assumed as the random fields with different probability distributions. To obtain the dynamic characteristics of the vertically irregular structures, a stochastic eigenvalue equation is established firstly. Then the stochastic eigenvalue and eigenvector are represented by the homotopy series, and the stochastic residual error in relation to the stochastic eigenvalue equation is minimized to obtain the coefficients of the homotopy series. Afterwards, the basic dynamic characteristics, including stochastic natural frequencies and modal shapes, of the vertically irregular structures are obtained. In comparison to the sampling-based stochastic surrogate model methods like the Kriging and non-intrusive arbitrary polynomial chaos methods, the presented approach can efficiently yield more stable statistical moments of the natural frequencies. Meanwhile the proposed method can generate the statistical moments of the modal shapes, which is difficult to achieve with the stochastic surrogate model methods. Finally, the effectiveness of the suggested method is testified through two examples of a reinforced concrete-steel column and a realistic reinforced concrete-steel frame structure.

A stochastic approach for the solution of single and multi–objective optimisation problems of biological processes in sequencing batch reactor

This paper investigates the impact of implementing single and multi-optimisation solutions on the biological treatment process in a sequencing batch reactor (SBR). The research is based on a case study of the water resource recovery facility (WRRF) in Swarzewo, Northern Poland. The paper introduces the adaptive extremum seeking control (ESC) method for dissolved oxygen (DO) concentration control and places it in a layered control structure. Further, it presents the introduction of an optimisation layer for the structure and parameters of the SBR cycle, through the synthesis of stochastic methods: single-objective optimisation (SOO) using a genetic algorithm (GA) and multi-objective optimisation (MOO) using the NSGA-II algorithm. The results were compared to a classical approach with fixed cycle parameters. The paper shows the advantages of optimising cycle parameters, including the number of phases as well as the DO value, on the process flow. These control structures underwent simulation tests in the MATLAB environment with the Simba package. The biochemical processes occurring in the reactor are based on the Activated Sludge Model No. 2d (ASM2d). The optimising control system demonstrates tangible improvements in operational efficiency and significant reductions in electrical energy consumption, highlighting the effectiveness of the proposed methodologies. © 2017 Elsevier Inc. All rights reserved.

Implementation of unknown parameter estimation procedure for hybrid and discrete non‐linear systems

AbstractThe application of the hybrid extended Kalman filter (HEKF), hybrid unscented Kalman filter (HUKF), hybrid particle filter (HPF), and hybrid extended Kalman particle filter (HEKPF) is discussed for hybrid non‐linear filter problems, when prediction equations are continuous‐time and the update equations are discrete‐time, and also the discrete extended Kalman filter (DEKF), discrete unscented Kalman filter (DUKF), discrete particle filter (DPF), and discrete extended Kalman particle filter (DEKPF) for discrete‐time non‐linear filter problems, when prediction equations and update equations are discrete‐time. In order to assess the performance of the filters, the authors consider the non‐linear dynamics for a re‐entry vehicle. The filters are used in two hybrid and discrete states to estimate the position, velocity, and drag parameter associated with the re‐entry vehicle. Theoretical topics concerning estimating the drag parameter of a vehicle in re‐entry phase have been dealt with. Drag parameter estimation is carried out using a combination of hybrid filters and discrete filters as an effective estimator and fixed value, forgetting factor, and Robbins‐Monro stochastic approximation methods as the noise covariance matrix adjuster of the parameter.

Machine learning attack detection based-on stochastic classifier methods for enhancing of routing security in wireless sensor networks

Wireless Sensor Networks (WSNs) are vulnerable to attacks during data transmission, and many techniques have been proposed to detect and secure routing data. In this paper, we introduce a novel stochastic predictive machine learning approach designed to discern untrustworthy events and unreliable routing attributes, aiming to establish an artificial intelligence-based attack detection system for WSNs. Our methodology leverages real-time analysis of the features of simulated WSN routing data. By integrating Hidden Markov Models (HMM) with Gaussian Mixture Models (GMM), we develop a robust classification framework. This framework effectively identifies outliers, pinpoints malicious network behaviors from their origins, and categorizes them as either trusted or untrusted network activities. In addition, dimensionality reduction techniques are used to improve interpretability, reduce computation and processing time, extract uncorrelated features from network data, and optimize performances. The main advantage of our approach is to establish an efficient stochastic machine learning method capable of analyzing and filtering WSN traffic to prevent suspicious and unsafe data, reduce the large dissimilarity in the collected routing features, and rapidly detect attacks before they occur. In this work, we exploit a well-tuned data set that provides a lot of routing information without losing any data. The experimental results show that the proposed stochastic attack detection system can effectively identify and categorize anomalies in wireless sensor networks with high accuracy. The classification rates of the system were found to be around 83.65%, 84.94% and 94.55%, which is significantly better than the existing classification approaches. Furthermore, the proposed system showed a positive prediction value of 11.84% higher than the existing approaches.

π-Phase shift in a two-dimensional hardcore Bose-Hubbard model with imposed stripes

π-phase shift is crucial in strongly-correlated systems and plays a significant role in understanding the Hubbard model, which provides insights into the electronic structures and superconducting properties of the cuprate materials. In this paper, we present a comprehensive study to investigate the intriguing π-phase shift in the striped Bose-Hubbard model in a two-dimensional square lattice, as an extension of phenomena observed in the Hubbard model. The stochastic Green's function method is employed to investigate the model. By introducing stripes with higher potential energy, measurements of the density-density correlations reveal a distinct π-phase, where sublattices with higher and lower densities are reversed across the imposed stripes.

Predictive modelling of residual stress in turning of hard materials using radial basis function network enhanced with principal component analysis

This study proposes a hybrid machine learning (ML) model that combines a radial basis function network (RBFN) with principal component analysis (PCA) to predict residual stress (RS) in the machining process. Higher temperatures and plastic deformation can generate RS conditions in the machining of hard materials, significantly influencing the quality of machined parts, particularly their surface integrity. It is crucial to evaluate and guarantee machining conditions that ensure reliable surface integrity that yields compressive RS conditions. Incorrect parameter settings can lead to poor surface quality, resulting in tensile RS conditions that impact both the quality and lifetime of manufactured products. The methodology involved experimental machining trials for data acquisition, with conditions selected for hard material machining tests conducted using a computer numeric control (CNC) lathe under dry cutting conditions. The cutting force components were measured, and RS was evaluated using X-ray diffraction. A total of 60 trials were conducted. Data preprocessing, including normalization and removal of outliers, was executed before constructing the ML algorithm, leaving 59 valid tests for model training and testing. Separate datasets for training (70 % of the data) and testing (30 %) were randomly selected from the valid experimental tests. PCA enhanced the RBFN model’s generalization by reducing data dimensionality and providing the hidden units parameter. The eigenvectors obtained through PCA served as an efficient initial reference for RBF centroids, highlighting principal directions of variation. The PCA-RBFN model, using a multiquadric radial function, exhibited robust performance in capturing underlying patterns during training and demonstrated balanced results in the tests. In the PCA-RBFN model training stage, it exhibited a coefficient of determination (R2) of 76.66 %, a mean average error (MAE) of 72.15 MPa, and a root mean square error (RMSE) of 84.94 MPa. In the testing stage, the model showed increased metrics, indicating its ability to predict RS values accurately, with an R2 of 80.54 %, MAE of 51.25 MPa, and RMSE of 70.36 MPa. The evaluation between the training and testing stages highlighted the model’s coherence in performance, demonstrating its ability to generalize well to new data. A second comparative analysis was conducted with a conventional RBFN approach using stochastic method for centroid determination. The hybrid PCA-RBFN method exhibited lower computational effort, requiring only three iterations compared to 221,923 iterations in the conventional approach. Despite the conventional approach yielding better metrics in the training stage, it exhibited signs of overfitting, a common concern in machine learning models. The hybrid PCA-RBFN consistently outperformed it regarding generalization and fit during testing. The proposed methodology holds practical implications for the manufacturing industry, allowing the integration of a pre-trained predictive model into machine controllers or smart sensors. The hybrid PCA-RBFN’s computationally lightweight approach also supports incorporating real-time adaptive algorithms into production systems, enabling continuous real-time adjustments to the model factors and weights, thereby improving automated control.

Advancements in epidemiological modeling: Bayesian regularization neural networks for smoke dynamics

Using an artificial neural network and the Bayesian Regularization Technique (NNs-BRT), the stochastic method’s strength is used to analyze the differential system, illustrating a nonlinear smoke epidemic differential model (NSED). This allows for a more precise, dependable, cost-effective, dynamic calculating approach. In addition to experiments utilizing nonlinear mathematical structures through five distinct classes of differential operators-smokers contemplating quitting, infrequent smokers, regular smokers, those who have temporarily abstained from smoking, and those who have permanently quit smoking the NSED framework has been established. By allocating 25% of the data for testing and validation and 75% for training, the proposed NNs-BRT can determine the estimated solutions of five different examples based on the numerical computation of the NSED system employing Adams techniques. To prove the accuracy of the given NNs-BRTs, a comparison of the results from the dataset obtained using the Adam method for different scenarios reflecting variance in recruitment rate, effective contact rate between C and A, natural death rate, how quickly occasional smokers become regular smokers, contact rate between smokers, and temporary quitters, number of smokers quitting, and percentage of smokers who are still leaving for good is made. The use of error histograms, mean square error, regression, correlation, and state transitions is also examined in numerical replications of the NNs-BRTs to verify their competence, dependability, accuracy, consistency, and proficiency.

Probability model evolution laws and mechanisms of non-linear buckling capacity of single-layer spherical gridshells with topology-constrained initial imperfections

This research offers a detailed probability analysis of the non-linear buckling capacity (NBC) of single-layer gridshells (SLGs), impacted significantly by stochastic initial geometric imperfections during construction. Employing the constrained stochastic imperfection modal method, which adeptly incorporates topology constraints of actual initial imperfection scenarios. The key factors, such as the imperfection simulation method, imperfection amplitude, number of rings, and the rise-to-span ratio, are evaluated through systematic numerical analysis. The results reveal that the traditional random imperfection method cannot obtain the actual bimodal distribution of the NBC, and it can overestimate the maximum and minimum NBCs by 5.16 % and 52.49 %. Furthermore, the joint well-formedness is introduced to quantify the joint local stiffness, and it is found to have a highly intertwined correlation with the structural non-linear buckling mode. The evolution mechanism of probability models can be elucidated through the joint initial deviations leading to changes in joint well-formedness (i.e., local stiffness), based on which it is concluded that an imperfection amplitude of 1/1500 of the structural span should be recommended to be the imperfection amplitude acceptance limit to fully utilize the structural global buckling capacity; significant deviations in primary rib joints and inner ring joints markedly affect the NBC more than those in non-primary rib joints and outer ring joints. The aforementioned conclusions are essential for revising guidelines for permissible joint deviations and assessment methodologies for critical joints throughout the construction.

Analysis of stochastic probing methods for estimating the trace of functions of sparse symmetric matrices

We consider the problem of estimating the trace of a matrix function f ( A ) f(A) . In certain situations, in particular if f ( A ) f(A) cannot be well approximated by a low-rank matrix, combining probing methods based on graph colorings with stochastic trace estimation techniques can yield accurate approximations at moderate cost. So far, such methods have not been thoroughly analyzed, though, but were rather used as efficient heuristics by practitioners. In this manuscript, we perform a detailed analysis of stochastic probing methods and, in particular, expose conditions under which the expected approximation error in the stochastic probing method scales more favorably with the dimension of the matrix than the error in non-stochastic probing. Extending results from Aune, Simpson, and Eidsvik [Stat. Comput. 24 (2014), pp. 247–263], we also characterize situations in which using just one stochastic vector is always—not only in expectation—better than the deterministic probing method. Several numerical experiments illustrate our theory and compare with existing methods.

Demand Response Power-Gas Interconnection Energy System and Power Metering Based on SOGA

Under the double background of global energy crisis and environmental pollution, China vigorously develops renewable energy while accelerating the construction of energy Internet. Taking demand response into account, this paper proposes the optimal design of power-gas interconnection energy system and power metering, and establishes the optimization research model of IEGES (integrated electricity-gas energy system) with demand response. Firstly, the structure model of the electric-gas interconnection energy system with CHP (Cogeneration, combined heat and power) as the core is constructed, and the energy conversion relationship and different energy flow directions of the coupling equipment are expounded from three aspects. The natural gas source point, pipeline equation, power side branch equation, voltage and current equation are modeled and sorted out, and the square term in the equation is linearized by second-order cone programming method, and the mixed integer nonlinear programming problem is transformed into mixed integer linear programming problem. A single objective genetic algorithm with “elite strategy” was selected to solve the equipment capacity optimization problem of IEGES system with system economy as the optimization objective. After a long time of parameter combination attempts, the current population size is 30, the number of iterations is 600, the crossover rate is 0.8, and the heritability is 0.3. The above parameters can obtain better convergence results on the basis of considering the operation time. Finally, a stochastic optimization method of energy Internet considering integrated demand response and uncertainty of wind power is proposed, which aims to meet the energy demand of end users while minimizing the operating cost of the system. The comprehensive demand response strategy including internal and external demand response is considered in the model. Internal demand response is realized by adjusting the internal operation mode of EH, while external demand response is implemented by the end user’s active response, and the load is time-shifted or interrupted under the guidance of external signals.

A subspace parameter identification method for nonlinear structures under oversampling conditions

In engineering practice, sampling frequencies much higher than the Nyquist frequency are often used to obtain accurate measurements of the dynamic characteristics of nonlinear systems. However, it may lead to oversampling when using the nonlinear subspace identification method (NSIM). This study proposes a subspace parameter identification method to address the identification of nonlinear structures under oversampling conditions. The proposed method first employs the prediction error method (PEM) to estimate the linear part of the state space model. In noisy environments, the PEM can achieve more accurate results than the NSIM by minimizing an error criterion function. The initial values fed into the PEM are obtained by the stochastic subspace identification method. The nonlinear part of the state space model is estimated by solving a linear regression equation. The proposed method effectively reduces the impact of high sampling frequencies on identification accuracy by combining data with different sampling frequencies to construct the linear regression equation. Among them, the low sampling frequency data is obtained by downsampling the high sampling frequency measurement data. The proposed method effectively reduces the effect of high sampling frequencies and environmental noise on identification accuracy by accurately estimating both the linear and nonlinear parts of the state space model. The identification accuracy of the proposed method is numerically verified by a chain-type structure with five degrees of freedom and a cantilever beam structure. Additionally, experimental verification is carried out on a two degrees of freedom floor structure with local nonlinearities. The results show that the proposed method achieves high identification accuracy in oversampling conditions and noisy environments.

A stochastic gradient method with variance control and variable learning rate for Deep Learning

In this paper we study a stochastic gradient algorithm which rules the increase of the mini-batch size in a predefined fashion and automatically adjusts the learning rate by means of a monotone or non-monotone line search procedure. The mini-batch size is incremented at a suitable a priori rate throughout the iterative process in order that the variance of the stochastic gradients is progressively reduced. The a priori rate is not subject to restrictive assumptions, allowing for the possibility of a slow increase in the mini-batch size. On the other hand, the learning rate can vary non-monotonically throughout the iterations, as long as it is appropriately bounded. Convergence results for the proposed method are provided for both convex and non-convex objective functions. Moreover it can be proved that the algorithm enjoys a global linear rate of convergence on strongly convex functions. The low per-iteration cost, the limited memory requirements and the robustness against the hyperparameters setting make the suggested approach well-suited for implementation within the deep learning framework, also for GPGPU-equipped architectures. Numerical results on training deep neural networks for multi-class image classification show a promising behaviour of the proposed scheme with respect to similar state of the art competitors.