Bayesian Theorem Research Articles

The Bayesian central limit theorem for exponential family distributions: a geometric approach

The Bayesian central limit theorem for exponential family distributions: a geometric approach

Simultaneous identification of propeller fluctuating forces and unknown parameters based on a Bayesian inversion approach

Accurate quantification of propeller excitation is essential for effective vibro-acoustic analysis and mitigation in marine vessels. This study introduces a Bayesian statistical framework that indirectly reconstruct uncertain forces and system parameters by fusing available prior information, forward modeling and measured vibration responses through Bayesian theorem. The Markov Chain Monte Carlo (MCMC) algorithm, enhanced with Polynomial Chaos Kriging (PC-Kriging) surrogates, is employed to facilitate efficient estimation of likelihood functions and robust uncertainty propagation, providing posterior probabilistic estimates and credible intervals for the identified forces. Additionally, the framework incorporates model class selection based on model evidence to determine the most plausible empirical spectrum model for the propeller broadband thrust spectrum. Specifically, this study proposes and evaluates two candidate empirical spectrum models, the Ornstein–Uhlenbeck (OU)-Gaussian and OU-Weibull models, which effectively capture the frequency–amplitude characteristics of unsteady thrust. Numerical results demonstrate substantial parameter uncertainty reduction, accurate thrust spectrum reconstruction, and effective quantification of statistical properties. Moreover, the OU-Gaussian model is revealed to be more plausible for characterizing the propeller thrust spectrum and response prediction. This framework may offer a practical solution for propeller excitation identification, enabling rapid vibro-acoustic performance assessments of marine vessels.

Bayesian modeling and optimization for split-plot experiments with multiple responses

In many industrial processes, cost or time constraints make some input variables harder to change or control than others. An appropriate experimental design method is restricted randomization, which results in split-plot experiments. Empirical models that connect multiple quality characteristics with input variables play a crucial role in robust parameter design for split-plot experiments. At present, many modeling methods typically adopt the single response model for analyzing industrial processes in the split-plot experiments without considering correlation among multiple responses, correlation among whole plots, and uncertainty of model parameters. However, ignoring these issues can lead to poor product or process design. To solve these issues, this paper suggests a novel Bayesian modeling and optimization approach. We first construct a Bayesian multi-response linear mixed-effects model and obtain the posterior distribution for model parameters by employing Bayesian theorem. Then, the Gibbs sampling procedure is employed for the estimation of model parameters. Finally, the overall weighted desirability optimization function meeting the specification is developed to avoid acquiring ideal input settings with outliers. A simulation and an engineering case study demonstrate the validity of the proposed method. In comparison to existing methods, the optimization results given the proposed method are more robust and reliable.

Methodologic procedure of beer competitions eliminating the problematic practices and based on the probabilistic approach

In beer competitions, there are some common problematic practices which ruin the final results, i.e. inappropriate distribution of samples into individual groups, inappropriate scoring of samples, comparison of results obtained from different sub-groups selecting better samples, inappropriate method of handling tied scores, and inappropriate numerical evaluation. To avoid these, the presented study aims to propose a methodologic procedure which eliminates these problematic practices and is based on the probabilistic approach. Further, it wishes to test and evaluate it by the Monte Carlo simulation. The procedure is based on a sensory evaluation of beer samples by assessors through ranking tests. Beer samples and assessors are randomly divided into groups in the lowest round of the competition. Data evaluation, which determines advancing samples or winners, is based on the application of the probability theory, namely the Bayesian theorem, so that the best-evaluated samples could be identified. This procedure achieves a higher probabilitiy of accurately recognised best-evaluated samples in comparison to the procedures involving the aforementioned problematic practices.

Hiddenly degrading performance prognosis based on recursive model incorporating double-layer rolling optimization strategy

An integrated and adaptive prognostic framework is proposed for hiddenly degrading actuator in the closed-loop system. Furthermore, the dual influence of degradation progress and operation time is considered in the established augmented model. It is important to obtain accurate and real-time distribution of degradation information under different degradation progress. Firstly, the expectation and variance of hidden index, unknown operation time parameter and degradation progress parameter are evaluated by designing a double-layer rolling optimization strategy. Then, the uncertainty distribution of degradation model is iteratively derived by employing Bayesian theorem. Finally, the distribution of remaining useful life (RUL) is calculated based on available distribution of degradation model and states. The effectiveness of proposed algorithm is demonstrated by a mold model of continuous casting driven by servo motor.

Uncertainties quantification for damage localization in concrete based on Bayesian method

The presence of defects in concrete can diminish load-bearing capacity of structures, giving rise to potential concerns regarding safety and durability. Thus, a method that enhances the sensitivity, resolution and robustness of damage localization is critically necessary to assess the condition of concrete structures. This research presents a damage localization method based on Bayesian probabilistic fusion, and uncertainties from measurement and identification process are considered and quantified. The likelihood function is constructed based on the hyperbola-based damage localization method, and the posterior distributions of unknown parameters are calculated via Bayesian theorem combined with measurement data. Furthermore, a meso-level finite element model is established, wherein the concrete medium is considered as a three-phase composite material consisting of polygonal aggregates, mortar matrix and interface transition zones. Owing to the meso-level modeling, the propagation behavior of stress waves within concrete and complicated interactions between stress waves and concrete internal structures can be better characterized. Finally, the damage information, time-difference-of arrival, is extracted from the response signals and the efficiency of the proposed method is verified numerically. The numerical results demonstrate that the proposed probabilistic fusion method outperforms the conventional hyperbola-based method in terms of achieving high spatial resolution and resilience in damage localization.

Ground Prediction by Markov-ANN Hybrid Analytics Using Baseline Geotechnical Data and Observed Field Data

ABSTRACT Geology along the tunnel length usually differs from the anticipated data as per Geotechnical Baseline Report (GBR), sometimes quite significantly. This has always led to the disruption of the planning, resource mobilisation, cost and duration of the project. One way to minimise this uncertainty is by exhaustive investigation like probe holes and geophysical prospecting. Forecasting or prediction of Geology can also be done by soft computing and analytical methods. Using the analytical tool of the Markov Model and the learning powers of Artificial Neural Networks (ANN) has been attempted in this study. The idea is to build a hybrid model that would combine both capabilities and do a probabilistic prediction of the ground condition ahead of the tunnel face in real time to better suit the site, accommodate complexities and can capture the associated uncertainties. The Geotechnical Baseline Report (GBR) having the initial survey details of the tunnel geology is used to build the Markov Model while the deterministic borehole data in the GBR is used to build the ANN model. Bayesian joint probability theorem is used to update the model with the face observed geological parameters. This hybrid model demonstrated to be a good complement to the physical forecasting methods and the geological uncertainty of a complex and challenging Himalayan region was well captured by the present approach. The window of the prediction was for a region of approximately 250m where it showed a very good prediction of ground class. The model can help in systematic planning and resource mobilisation in a better way and subsequent key decisions for the upcoming excavation method and corresponding support measures.

Machine learning-based characterization of friction stir welding in aluminum alloys

This research presents a machine learning (ML) approach that integrates Bayesian theorem to predict residual stress, plastic deformation, and peak temperature in friction stir welding (FSW) of different types of aluminum alloys. The training data was acquired from extensive numerical simulations of FSW conducted across various input parameter configurations. The regression analysis exhibits strong predictive performance for residual stress, peak temperature, and plastic deformation, achieving determination coefficients of 0.969, 0.955, and 0.919, respectively. The high prediction performance of the developed model is primarily attributed to Bayesian optimization, distinguishing it from other conventional ML methods. The results further demonstrate the efficacy of the proposed model in assessing the relevance of input features to prediction efficiency and output targets. For instance, concerning processing parameters, the predictive performance is closely correlated with the significance of preheating, traverse speed, and rotational speed in FSW, compared to welding force and plate thickness. On the other hand, considering material properties, it was observed that the hardness value of aluminum alloys emerged as a crucial predictor in the model so that alloys with moderate hardness values showed greater welding consistency and significantly enhanced prediction accuracy.

P‐16.2: A Method for Detection of Ink Droplet Volume Distribution Based on Bayesian Theorem

P‐16.2: A Method for Detection of Ink Droplet Volume Distribution Based on Bayesian Theorem

CGMGM: A Cross-Gaussian Mixture Generative Model for Few-Shot Semantic Segmentation

Few-shot semantic segmentation (FSS) aims to segment unseen objects in a query image using a few pixel-wise annotated support images, thus expanding the capabilities of semantic segmentation. The main challenge lies in extracting sufficient information from the limited support images to guide the segmentation process. Conventional methods typically address this problem by generating single or multiple prototypes from the support images and calculating their cosine similarity to the query image. However, these methods often fail to capture meaningful information for modeling the de facto joint distribution of pixel and category. Consequently, they result in incomplete segmentation of foreground objects and mis-segmentation of the complex background. To overcome this issue, we propose the Cross Gaussian Mixture Generative Model (CGMGM), a novel Gaussian Mixture Models~(GMMs)-based FSS method, which establishes the joint distribution of pixel and category in both the support and query images. Specifically, our method initially matches the feature representations of the query image with those of the support images to generate and refine an initial segmentation mask. It then employs GMMs to accurately model the joint distribution of foreground and background using the support masks and the initial segmentation mask. Subsequently, a parametric decoder utilizes the posterior probability of pixels in the query image, by applying the Bayesian theorem, to the joint distribution, to generate the final segmentation mask. Experimental results on PASCAL-5i and COCO-20i datasets demonstrate our CGMGM's effectiveness and superior performance compared to the state-of-the-art methods.

Aircraft turnaround time dynamic prediction based on Time Transition Petri Net.

Accurate aircraft turnaround time prediction is an important way to coordinate the operation time of airport ground service and improve the efficiency of airport operation. In this paper, by analyzing the aircraft turnaround operation process, a description model based on Time Transition Petri Net is proposed. The model describes the flight turnaround operation process and the logical relationship of the operation. According to the model, a dynamic prediction method of turnaround time based on Bayesian theorem is designed. According to the actual landing time of the flight, the aircraft turnaround time is predicted. The specific method is to obtain the prior probability distribution and joint distribution law of each operation link according to the flight history data, and use Shapiro-Wilke to test the prior probability distribution of each link. Based on the analysis and comparison between the actual turnaround data of a large airport in China and the forecast data proposed in this paper, the root-mean-square error 3.75 minutes and the mean absolute error 3.40 minutes can be calculated. This paper contributes to the improvement of flight punctuality rate and airport clearance level.

A New Fault Prognosis of MFS System Using Integrated Extended Kalman Filter and Bayesian Method

This paper presents a new fault prognosis approach for a multifunctional spoiler (MFS) system which employs an extended Kalman filter (EKF) and Bayesian theorem method for prognosis. The MFS is an important part of an aircraft spoiler control system (SCS), and thus, prognosis and health management (PHM) of this system improves the safety of the aircraft. To monitor the system, residual estimation based on the EKF method is utilized to observe the progress of the failure in the system. Then, a new measure is introduced by using a transformation to estimate degradation path (DP) of the failure in the system. Furthermore, a new recursive Bayesian method is invoked to predict the RUL of the system using the estimated DP data. Finally, for performance assessment, relative accuracy (RA) is utilized to evaluate the accuracy of the proposed method.

Enhancing investment performance of Black-Litterman model with AI hybrid system: Can it be done?

The B-L (Black-Litterman) model combines the subjective views of investors with the market's historical equilibrium return through the Bayesian theorem. This approach somewhat compensates for the limitations of the Mean-Variance model, making the asset allocation model attract significant attention. However, due to many investors lacking ample investment experience, they might struggle to provide appropriate subjective views. To address this issue, an Iaah (Industry Asset Allocation Hybrid) system based on the B-L model is proposed. First, a combined model is constructed, which simulates view return vectors and solves the problem of inaccurate view quantification. Then, the Iaah system introduces a dynamic condition correlation algorithm to optimize inherent parameters and explores asset allocation results in the time-varying effects. Next, it expands the types of objective functions and improves the deficiency of only considering the return and variance while ignoring the downside risk. Finally, based on a variety of performance metrics, the Iaah system is evaluated from multiple perspectives to test its practical value. The experiment results with the daily data of 10 SSE (Shanghai Stock Exchange) industry indexes show that the proposed system not only realizes the diversified allocation of industry assets and enhances the investment performance, but also exhibits strong robustness against changes in subjective parameters. It is conducive to managing personal wealth and achieving preservation and appreciation.

Gaussian process metamodel and Markov chain Monte Carlo-based Bayesian inference framework for stochastic nonlinear model updating with uncertainties

The estimation of the posterior probability density function (PDF) of unknown parameters remains a challenge in stochastic nonlinear model updating with uncertainties; thus, a novel Bayesian inference framework based on the Gaussian process metamodel (GPM) and the advanced Markov chain Monte Carlo (MCMC) method is proposed in this paper. The instantaneous characteristics (ICs) of the decomposed measurement response, calculated using the Hilbert transform and the discrete analytical mode decomposition methodology, are extracted as nonlinear indices and further used to construct the likelihood function. Then, the posterior PDFs of structural nonlinear model parameters are derived based on the Bayesian theorem. To precisely calculate the posterior PDF, an advanced MCMC approach, i.e., delayed rejection adaptive Metropolis-Hastings (DRAM) algorithm, is adopted with the advantages of a high acceptance ratio and strong robustness. However, as a common shortage in most MCMC methods, the resampling technology is still applied, and numerous iterations of nonlinear simulations are conducted to ensure accuracy, thus directly reducing the computational efficiency of the DRAM. To address the abovementioned issue, a mathematical regression metamodel of the GPM with a polynomial kernel function is adopted in this paper instead of the traditional finite element model (FEM) to simulate a nonlinear response for the reduction of computational cost, and the hyperparameters are further estimated using the conjugate gradient optimization methodology. Finally, numerical simulations concerning a Giuffré–Menegotto–Pinto modeled steel-frame structure and a seven-storey base-isolated structure are conducted. Furthermore, a shake-table experimental test of a nonlinear steel framework is investigated to validate the accuracy of the Bayesian inference method. Both simulations and experiment demonstrate that the proposed GPM and DRAM-based Bayesian method effectively estimates the posterior PDF of unknown parameters and is appropriate for stochastic nonlinear model updating even with multisource uncertainties.

LOS compensation and trusted NLOS recognition assisted WiFi RTT indoor positioning algorithm

In previous studies, ranging errors in the line of sight (LOS) environment were often overlooked, resulting in an increase in positioning errors. In non-line of sight (NLOS) conditions, the measuring distance hardly participates in the location calculation, leading to the loss of useful positioning information. Thus, this paper proposes a WiFi RTT positioning approach based on LOS compensation and trusted NLOS recognition, which improves the performance of RTT positioning by using the compensated LOS distances and trusted NLOS ranges to estimate location. In the proposed approach, NLOS and LOS identification need to be implemented first. A support vector machine algorithm is used to construct a real-time model that recognizes NLOS and LOS distances based on the proposed classification features. Then, the distances under NLOS and LOS environments are evaluated and compensated, respectively, to obtain reliable NLOS ranges and calibrated LOS measurements. A least squares algorithm is utilized to build the LOS distance compensation model, and Bayesian theorem is applied to recognize the trusted NLOS ranges. The compensated LOS distances and credible NLOS ranges are used for estimating the location. The experimental results demonstrate that the proposed algorithm achieves excellent positioning accuracy, with a mean absolute error of 1.082 m. This signifies a substantial enhancement of 53.34% when compared to the least squares algorithm, a remarkable 60.24% improvement over the weighted centroid positioning algorithm, a significant 36.11% progress in comparison to the RTNLIA algorithm, and a noteworthy 32.82% boost relative to the NLRNB approach.

Analisa Perbandingan Metode Teorema Bayes Dan Case Based Reasoning Diagnosa Penyakit Pada Tanaman Tomat

Diseases in tomato plants have a significant impact on the agriculture industry as they can reduce crop yields and tomato quality. Therefore, this research aims to compare the Bayesian Theorem and Case-Based Reasoning (CBR) methods in diagnosing tomato plant diseases. The Bayesian Theorem is a statistical approach based on probability, while CBR uses knowledge from previous cases. This study includes an analysis of the performance of both methods in terms of diagnostic accuracy, result delivery speed, and resource efficiency. The research results have the potential to assist farmers and agricultural experts in choosing the most suitable method for diagnosing tomato plant diseases. Furthermore, the implementation of expert systems in agriculture can have a positive impact on tomato cultivation productivity and sustainability. This research aims to provide practical guidance for stakeholders in the agricultural field and contribute to sustainable agriculture improvement, with a specific focus on disease identification and management in tomato plants. The percentage values of the application of the Bayesian Theorem and Case-Based Reasoning methods show that Case-Based Reasoning has a lower success rate in diagnosing Fusarium Wilt and Bacterial Wilt compared to the Bayesian Theorem. However, Case-Based Reasoning excels in diagnosing Tomato Yellow Leaf Curl Virus (TYLCV), achieving a success rate of 100%, while the Bayesian Theorem reaches 63%.

Non-probabilistic credible reliability analysis of the composite laminate

For the reliability analysis of composite laminate structures, there is a problem of difficult data acquisition. Traditional reliability analysis methods require a large amount of data to maintain calculation accuracy. Therefore, the traditional reliability analysis method is not applicable to composite laminates. For the above-mentioned problems, this paper presents a method to calculate the credible reliability of composite laminate structures using the Bayesian theorem. The method is distinguished from the traditional uncertainty analysis methods. The likelihood function and the newly introduced samples are first used to correct the prior distribution of the uncertain parameters. Furthermore, the posterior distribution, containing information from both the sample and prior distributions, can be obtained. Ultimately, based on the acquired posterior distribution, the probability density function can be updated with newly introduced samples. Using the Hashin failure criterion, the failure probabilities of the fibers and matrix of the composite laminate structure are quantified, respectively. Then, the credible reliability of the composite laminate is obtained. Numerical example results show the proposed method can maintain high accuracy with fewer samples and demonstrate the validity of the model. For the numerical calculations, the deterministic parameters of the distribution function and the functional distribution parameters were verified, composite laminates and aircraft wing structures were analyzed. The experimental results show that the error between the probability density function of the parameters and the probability density function predicted by the sample is less than 0.045. Compared with the traditional reliability analysis methods for composite structures, this method can effectively measure the credible reliability of composite laminate structures with fewer samples and similar accuracy. The method enables real-time updating of the parameter probability density function by newly introduced samples and improves the confidence level.

An Attribute-based Data Privacy Classification Through the Bayesian Theorem to Raise Awareness in Public Data Sharing Activity

The growth of the digital era with diverse existing electronic platforms offers information sharing and leads to the realization of a culture of knowledge. Vast amounts of data and information can be reached anywhere at any time, fingertips away. These data are public because people are willing to share them on digital platforms like social media. It should be noted that not all information is supposed to be made public; some is supposed to be kept private or confidential. However, people always misunderstand and are misled about which data needs to be secured and which can be shared. We proposed an attribute-based data privacy classification model using a Naïve Bayesian classifier in this work. It aims to identify and classify metadata (attributes) commonly accessible on digital platforms. We classified the attributes that had been collected into three privacy classes. Each class represents a level of data privacy in terms of its risk of breach. The public (respondent) is determined according to different ages to gather their perspective on the unclassified attribute data. The input from the survey is then used in the Naïve Bayesian classifier to formulate data weights. Then, the sorted privacy data in the class is sent back to the respondent to get their agreement on the class of attributes. We compare our approach with another classifier approach. The result shows fewer conflicting reactions from the respondents to our approach. This study could make the public aware of the importance of disclosing their information on open digital platforms.

Applicability of ocean wave measurements based on high-frequency radar systems in an estuary region

ABSTRACT The applicability of high-frequency (HF) radar systems for wave measurement in an estuary was explored by extracting the significant wave height ( H sr ) using a traditional Barrick equation from the Doppler spectra observed by three radar systems installed in Ise Bay, Japan. The minimum value of H sr estimated around each grid point was relatively consistent with the wave height observed with a wave gauge/buoy, except for a deterioration of wave measurement accuracy caused by a decrease in seawater conductivity from the freshwater inflow after flooding. Furthermore, the relationship between the accuracy and the signal-to-noise ratios for the first- and second-order peaks (SNR1 and SNR2, respectively) highlighted the difficulty in determining the threshold values of SNRs in the bay. Thus, we suggest the use of H sr as a criterion for quality control when applying a nonlinear inversion method for estimating ocean wave spectra based on the Bayesian possibility theorem (BIM). Our suggestion is to select the appropriate Doppler spectra and increase the acquisition rates of wave data with low relative error compared to BIMs using SNR1 and SNR2. These results can promote the applicability of the nonlinear inversion in estuary regions.

Malaria Disease Prediction and Grading System: A Performance Model of Multinomial Naïve Bayes (MNB) Machine Learning in Nigerian Hospitals

bstract: Malaria disease is the number one cause of death all over the Sub-Sahara world. Data mining can help extract valuable knowledge from available data in the healthcare sector. This allows training a patient health prediction model faster than in a clinical trial. Various implementation of machine learning algorithms such as Bayesian Theorem, Logistic Regression, K-Nearest Neighbor, Support Vector Machine and Multinomial Naïve Bayes (MNB), etc. have been applied on Public Hospital Malaria Disease datasets but there has been a limit to modeling using Multinomial Naïve Bayes Algorithm. This research applied MNB modeling to discover the relationship between 15 relevant attributes of the Public Hospitals data collected from Bwari General Hospital in Bwari Area Council and Maitama Hospital in Abuja Municipal Area Council, Abuja, FCT, and Nigeria. The goal is to examine how dependencies between attributes affect the performance of the classifier. The MNB produces a reliable and transparent graphical representation between the attributes with the ability to predict new scenarios. The model has an accuracy of 97%. It was concluded that the model outperformed the GNB classifier which has an accuracy of 100% and RF which also has an accuracy of 100%.