Uncertainty Reasoning Research Articles

Interface State Density Prediction between an Insulator and a Semiconductor by Gaussian Process Regression Models for a Modified Process.

During data-driven process condition optimization on a laboratory scale, only a small-size data set is accessible and should be effectively utilized. On the other hand, during process development, new operations are frequently inserted or current operations are modified. These accessible data sets are somewhat related but not exactly the same type. In this study, we focus on the prediction of the quality of the interface between an insulator and GaN as a semiconductor for the potential application of GaN power semiconductor devices. The quality of the interface was represented as the interface state density, Dit, and the inserted operation to the process was the ultraviolet (UV)/O3-gas treatment. Our retrospective evaluation of model-building approaches for Dit prediction from a process condition revealed that for the UV/O3-treated interfaces, data of interfaces without the treatment contributed to performance improvement. Such performance improvement was not observed when using a data set of Si as the semiconductor. As a modeling method, the automatic relevance vector-based Gaussian process regression with the prior distribution of the length-scale parameters exhibited a relatively high predictive performance and represented a reasonable uncertainty of prediction as reflected by the distance to the training data set. This feature is a prerequisite for a potential application of Bayesian optimization. Furthermore, hyperparameters in the prior distribution of the length-scales could be optimized by leave-one-out cross-validation.

Conversion of Induced Polarization Data and Their Uncertainty from Time Domain to Frequency Domain Using Debye Decomposition

The time-domain (TD) induced polarization (IP) method is used as an extension of direct current (DC) resistivity measurements to capture information on the ability of the subsurface to develop electrical polarization. In the TD, the transient voltage decay is measured after the termination of the current injection. To invert tomographic TD IP data sets into frequency-domain (FD) models of complex electrical resistivity, a suitable approach for converting TD IP transients and their corresponding uncertainties into the FD is essential. To apply existing FD inversion algorithms to TD IP measurements, a conversion scheme must transform the measured decay curves into FD impedances and also propagate the corresponding measurement uncertainty from the TD to the FD. Here, we present such an approach based on a Debye decomposition (DD) of the decay curve into a relaxation-time distribution and the calculation of the equivalent spectrum. The corresponding FD data error can be obtained by applying error propagation through all of these steps. To accomplish the DD we implement a non-linear Gauss–Newton inversion scheme. We test the conversion scheme in a synthetic study and demonstrate its application to field data on a tomographic TD IP data set measured on the Maletoyvaemskoie ore field (Kamchatka, Russia). The proposed conversion scheme yields accurate impedance data for relaxation processes, which are resolved by the TD measurements. The error propagation scheme provides a reasonable FD uncertainty estimate, as confirmed by a Monte Carlo analysis of the underlying parameter distributions.

Multi‐Objective Optimization Models for the Design of Water Distribution Networks by Exploring Scenario‐Based Approaches

AbstractDemand in a water distribution network (WDN) is an aleatory variable, owing to the unpredictable behaviors of water users. Therefore, it is one of the main reasons for uncertainty in the design of this infrastructure. The increasing number of water demand data sets offers opportunities to improve the traditional deterministic design approaches of WDNs by combining statistical and optimization methods. Robust optimization (RO) takes demand uncertainty into account by studying solutions that perform well under any possible demand scenario, that is, any possible realizations of this variable in the lifetime of a WDN. The right choice of scenario is therefore essential to ensure the reliability of the designed network. This paper presents a statistical methodology for generating scenarios to be used to solve a robust design optimization problem. It involves three steps: (a) descriptive analytics of historical data to derive the marginal distributions of peak hour demand in each node of the WDN, (b) generation of a very large number of snapshots by stratified sampling from the correlated marginal distributions of nodal peak demand, (c) generation of the peak demand scenarios by reducing the number of snapshots. Two heuristic techniques are proposed to reduce the number of snapshots, and for each of them, two different numbers of scenarios are derived. Two multi‐objective RO models are solved: the first model includes cost minimization and a mean‐variance Generalized Resilience and Failure index maximization objectives, and the second one additionally considers the minimization of the maximum undelivered demand, formalized using a regret function.

The Unreasonable Effectiveness of Deep Evidential Regression

There is a significant need for principled uncertainty reasoning in machine learning systems as they are increasingly deployed in safety-critical domains. A new approach with uncertainty-aware regression-based neural networks (NNs), based on learning evidential distributions for aleatoric and epistemic uncertainties, shows promise over traditional deterministic methods and typical Bayesian NNs, notably with the capabilities to disentangle aleatoric and epistemic uncertainties. Despite some empirical success of Deep Evidential Regression (DER), there are important gaps in the mathematical foundation that raise the question of why the proposed technique seemingly works. We detail the theoretical shortcomings and analyze the performance on synthetic and real-world data sets, showing that Deep Evidential Regression is a heuristic rather than an exact uncertainty quantification. We go on to discuss corrections and redefinitions of how aleatoric and epistemic uncertainties should be extracted from NNs.

Insights into material recovery, revenue, and global warming potential of India’s end-of-life photovoltaic installations reveals the urgent need for blockchain-based solar passports

Growing photovoltaic (PV) panel waste is creating numerous environmental problems and an unfamiliar opportunity to add value and explore new business options in line with circular economy practices. As an immediate action, countries struggling with massive amounts of PV waste started exploring end-of-life management options, inventory analysis for PV waste, regulatory measures to handle, and asset monetization solutions for commissioning/decommissioning solar PV systems. Nevertheless, these actions have not been decisively implemented in many countries and have thus remained unfulfilled policy aspirations. In the context of India, it is worth noting that the country has established a set of industrial solid waste rules that are fairly comprehensive; however, they do not encompass the issue of PV waste. Hence, this study aims to understand India’s current stand on PV waste and provide a holistic solution for effective PV waste management in the long run. For this, a comprehensive look into India’s grid-connected PV plants was done to provide insights on the PV waste inventory potential, material recovery potential under various recycling approaches, possible revenues earned by selling recovered resources in the marketplace, and global warming potential for treated PV waste. Later, a survey-based discussion was done highlighting the reasons for uncertainties and potential pitfalls with installed solar inventory data considering ground reality situations. Lastly, based on the observed results and associated uncertainties, this study proposes the blockchain-based solar passports framework with a case illustrating the implementation as an urgent need in India to effectively monetize solar PV plant assets.

DeepSHARQ: hybrid error coding using deep learning

Cyber-physical systems operate under changing environments and on resource-constrained devices. Communication in these environments must use hybrid error coding, as pure pro- or reactive schemes cannot always fulfill application demands or have suboptimal performance. However, finding optimal coding configurations that fulfill application constraints—e.g., tolerate loss and delay—under changing channel conditions is a computationally challenging task. Recently, the systems community has started addressing these sorts of problems using hybrid decomposed solutions, i.e., algorithmic approaches for well-understood formalized parts of the problem and learning-based approaches for parts that must be estimated (either for reasons of uncertainty or computational intractability). For DeepSHARQ, we revisit our own recent work and limit the learning problem to block length prediction, the major contributor to inference time (and its variation) when searching for hybrid error coding configurations. The remaining parameters are found algorithmically, and hence we make individual contributions with respect to finding close-to-optimal coding configurations in both of these areas—combining them into a hybrid solution. DeepSHARQ applies block length regularization in order to reduce the neural networks in comparison to purely learning-based solutions. The hybrid solution is nearly optimal concerning the channel efficiency of coding configurations it generates, as it is trained so deviations from the optimum are upper bound by a configurable percentage. In addition, DeepSHARQ is capable of reacting to channel changes in real time, thereby enabling cyber-physical systems even on resource-constrained platforms. Tightly integrating algorithmic and learning-based approaches allows DeepSHARQ to react to channel changes faster and with a more predictable time than solutions that rely only on either of the two approaches.

Verification and validation (V&V) for fast reactor system analysis code FASYS

The fast reactor system analysis code FASYS is developed by CIAE for transient accident analysis in CEFR. By referring to the application scope of FASYS, the basic requirements of FASYS and PIRT in CEFR are established. A comprehensive verification and validation for the accuracy of FASYS is performed, which consist of bottom-up assessment, top-down assessment and uncertainty assessment. The bottom-up assessment applies the static analysis and dynamic analysis to verify the basic function of FASYS. The separate effect tests and integral effect tests are employed in the top-down assessment to validate the availability to simulate model and system. The calculated results confirms that the basic function and model in FASYS are reasonable and credible. The uncertainty assessment results show that FASYS can still calculate IET under the reasonable uncertainty of input parameters, indicating that the FASYS can simulate and analyze the transient accident processes of sodium-cooled fast reactor.

Formic Acid in Hydrogen: Is It Stable in a Gas Container?

Formic acid is an intermediate of the steam methane reforming process for hydrogen production. According to International Standard ISO 14687, the amount fraction level of formic acid present in the hydrogen supplied to fuel cell electric vehicles must not exceed 200 nmol·mol−1. The development of formic acid standards in hydrogen is crucial to validate the analytical results and ensure measurement reliability for the fuel cell electric vehicles industry. NPL demonstrated that these standards can be gravimetrically prepared and validated at 4 to 100 µmol·mol−1, with a shelf-life of 1 year (stability uncertainty < 7%; k = 2). Stability was not affected over 1 year or by low temperature or pressure. At sub-µmol·mol−1 level, formic acid amount fraction was found to decrease due to adsorption on the gas cylinder surface; however, it is possible to certify the formic acid amount fraction after a period of 20 days and ensure the certified value validity for 1 year with an uncertainty below 7% (k = 1) confirmed by thermodynamic investigation. This study demonstrated that formic acid in hydrogen gas reference materials can be prepared with reasonable uncertainty (>7%, k = 1) and shelf life (>1 year). Potential applications include the calibration of analysers and for studying the impact of formic acid on future application with relevant traceability and accuracy.

Visual Reasoning for Uncertainty in Spatio-Temporal Events of Historical Figures.

The development of digitized humanity information provides a new perspective on data-oriented studies of history. Many previous studies have ignored uncertainty in the exploration of historical figures and events, which has limited the capability of researchers to capture complex processes associated with historical phenomena. We propose a visual reasoning system to support visual reasoning of uncertainty associated with spatio-temporal events of historical figures based on data from the China Biographical Database Project. We build a knowledge graph of entities extracted from a historical database to capture uncertainty generated by missing data and error. The proposed system uses an overview of chronology, a map view, and an interpersonal relation matrix to describe and analyse heterogeneous information of events. The system also includes uncertainty visualization to identify uncertain events with missing or imprecise spatio-temporal information. Results from case studies and expert evaluations suggest that the visual reasoning system is able to quantify and reduce uncertainty generated by the data.

Data-Driven Reconstruction of Dynamical Forces and Responses through Bayesian Expectation-Maximization and Modal Reduction Methods

This paper presents a new Bayesian approach for estimating input and state in linear structures using response-only measurements. The proposed approach benefits from a modally reduced state-space model, which circumvents the dimensionality of dynamical responses in complex structures through a low-dimensional subspace. It also substitutes unknown physical forces with a set of equivalent modal forces, which is beneficial when the magnitude and location of input forces are unknown. In this work, these forces are characterized through the conventional random walk model and a class of stationary Gaussian processes. Subsequently, an augmented state-space model is constructed to describe modal states and input loads. Based on this model, a Bayesian expectation-maximization (BEM) methodology is developed to identify the input, state, and noise parameters. This noise identification perspective activates uncertainty quantification in joint input-state estimation problems and enables quantifying the degree of confidence in the estimated quantities. When the proposed method is tested using numerical and experimental examples, accurate estimations and reasonable uncertainty bounds are acquired for the dynamical state and input forces. Although the literature reports the superiority of the Gaussian process latent force model over the random walk model without using a unified noise calibration strategy, this study, to our best knowledge, is the first effort to compare and interpret the results on a consistent basis where the noise and input characteristics are all identified from the data through BEM.

Research on uncertain multiple attribute decision making based on improved possibility degree relation model and its application

In this paper, we mainly focus on the triangular fuzzy number-based uncertain multiple attribute decision making problem, which not only attribute weights are unknown but also preference for decision-making objects do not exist, and give a new decision-making approach and consistency test method based on the improved possibility relation model. This method fully considers the influence of the comparison possibility degree measurement information between the measured values of the indicator attribute itself in the course of processing uncertain reasoning such as fuzziness and randomness, reconstructs a new and more optimized triangular fuzzy number-based decision making object improved possibility degree relation model (TFN-DMOIPDRM) to determine the attribute weight vector, and creatively designs a general formula to test the consistency of the improved possibility degree relation matrix. Next the criterion of consistency test is given to solve the remaining problem of the lack of consistency test in the construction of fuzzy number possibility degree relation model and fuzzy complementary judgment matrix. Moreover, another major contribution of this paper is to present the improved possibility degree relation theory of triangular fuzzy numbers on the basis of defining the comparative possibility degree of triangular fuzzy numbers, and fully study a series of its relevant properties and conclusions, as well as its application in constructing model to determine the attribute weight. By aggregating the improved possibility degree information measured by pairwise comparing decision objects, the overall improved possibility degree value of each decision object is obtained, and a new algorithm of the improved possibility relation model for triangular fuzzy number multi-attribute decision object is given, which improves and expands the application of fuzzy number possibility theory in the field of fuzzy uncertainty reasoning and intelligent computing of artificial intelligence.

Проблемы мировоззрения глазами обучающихся Крайнего Севера

The article reveals the concept of worldview, its significance in every person`s life as an individual. The purpose of the study consists in considering the problem of worldview, based on the view of the students of the Far North. In accordance with the goal, the researchers were assigned the following tasks: disclosure of the concept and types of worldview, identifying their differences; definition of the problem of the emergence of a worldview in the context of changes and the origin of significant events in the political sphere; conducting a sociological survey among students from the Far North, to identify the main problematic issues concerning the variability of their worldview, as well as its stability; research of the work of the founder of Yakut literature, the first of the researchers of Yakutia, whose works occupy a significant place in the formation of the worldview of every inhabitant of the Far North. In the process of forming a worldview, a person faces limitationsthat is, with what we call distinctiveness, which implies nationality, religion, territory of residence, age, upbringing; in addition, at this stage, the formation of a political worldview takes place. The political worldview itself is associated with the individual's search for his place in the political or social sphere, which is manifested in the individual and subjective aspects of the political worldview, the peculiarity of which lies in the values of a particular society, where there is more often the influence of the dominant view. Such influence exists due to the hypertrophied authority of one person (or a limited circle of personalities). The arguments of these opinion leaders in favor of their own points of view are sometimes convincing to large masses of people. Also, people can perceive the beliefs of one person as their own, without an assessment of correctness or it own analysis, which in most cases is connected with the search for simple solutions. Choosing the path of a kind of "energy saving", people take on faith the opinion of another person who seems more competent. Based on the results of the study, in the second part of the work, the authors formulated some conclusions. In the mechanics of a difficult choice, when a decision is not made automatically, one of the reasons for uncertainty is highlighted: the instinctive resistance of a person, the feeling that he is going against himself, violating personal attitudes. Persuasion is a powerful tool not only for management, but also for strengthening the personal stability of the worldview. A leader with sufficiently developed persuasion skills is able to convince almost any opponent of the truth of his worldview.

Feature Selection With Local Density-Based Fuzzy Rough Set Model for Noisy Data

Fuzzy rough set theory can model uncertainty in data and has been applied to feature selection for machine learning tasks. The existence of noise in data is one of the reasons for data uncertainty. However, most classical fuzzy rough set models are often sensitive to the noise in data, which somewhat degrades their applicability to process uncertainty of data. Furthermore, a robust feature evaluation function is nontrivial in a fuzzy rough set model as non-optimal feature subsets may be selected due to the perturbations from redundant features. In this paper, we delve into local density and indispensable features for fuzzy rough feature selection to address these challenges. We first propose a Local Density-based Fuzzy Rough Set (LDFRS) model to tackle noisy data. Mutual information is then plugged into the proposed LDFRS model to evaluate uncertainty in data. A joint feature evaluation function on the indispensability and relevance of features is constructed to evaluate the significance of features. On this basis, a fuzzy rough feature selection algorithm is built upon the LDFRS model. Experimental results using four typical classifiers demonstrate the robustness and effectiveness of the proposed model including our feature selection algorithm and its superiority against baseline methods.

Matrix-based approaches for updating three-way regions in incomplete information systems with the variation of attributes

As a commonly used framework for uncertainty reasoning, tolerance rough set has achieved remarkable success in handling incomplete information systems with missing values. Three-way regions generated from tolerance rough set model play an increasingly crucial role in decision making and intelligent data analysis. Nevertheless, the dynamic change of attributes often exists in incomplete information systems. With this dynamic characteristic, three-way regions must be effectively updated for potential decision-making processes. Therefore, we develop incremental algorithms for maintenance of three-way regions in incomplete information systems when adding or deleting attributes, accelerating the calculation by making use of prior information. First, we put forward an effective matrix-based approach to calculate three-way regions in incomplete data. With the dynamic change of attributes, we further investigate the updating strategies of related matrices for constructing three-way regions. Accordingly, matrix-based algorithms for incrementally updating three-way regions are developed and discussed while the attributes vary over time. In addition, the complexity comparisons of non-incremental and incremental algorithms are illustrated. Finally, empirical experiments are performed to reveal the efficiency of the incremental algorithms compared with matrix-based non-incremental and related incremental algorithms.

The conceptualization of acute bronchitis in general practice – a fuzzy problem with consequences? A qualitative study in primary care

BackgroundAcute bronchitis is one of the most frequent diagnoses in primary care. Scientifically, it is conceptualized as a viral infection. Still, general practitioners (GPs) often prescribe antibiotics for acute bronchitis. The explanation for this discrepancy may lie in a different conceptualization of acute bronchitis. Therefore, we wanted to know, how GPs conceptualize acute bronchitis, and how they differentiate it from common cold and pneumonia. Furthermore, we tried to find out the GPs’ reasons for prescribing antibiotics in those cases.MethodsTo answer our study questions, we conducted a qualitative study with GPs in Bavaria, Germany, by using semi-structured guided interviews. The analysis of the data was conducted using the documentary method according to Ralf Bohnsack. The transcripts were subdivided into categories. Analyzing each part by reflective interpretation, first manually, secondly with the help of RQDA, we extracted the most representative citations and main messages from the interviews.ResultsThe term acute bronchitis seems to be applied when there is neither certainty of the diagnosis common cold, nor of pneumonia. It seems it bridges the gap of uncertainty between supposedly harmless clinical pictures (common cold/viral), to the more serious ones (pneumonia/bacterial). The conceptual transitions between common cold and acute bronchitis on the one side, and acute bronchitis and pneumonia on the other are fluid. The diagnosis acute bronchitis cannot solve the problem of uncertainty but seems to be a label to overcome it by offering a way to include different factors such as severity of symptoms, presumed signs of bacterial secondary infection, comorbidities, and presumed expectations of patients. It seems to solve the pathophysiologic riddle of bacterial or viral and of decision making in prescribing antibiotics.ConclusionAcute bronchitis as an "intermediate category" proved difficult to define for the GPs. Applying this diagnosis leaves GPs in abeyance of prescribing an antibiotic or not. As a consequence of this uncertainty in pathophysiologic reasoning (viral or bacterial) other clinical and social factors tip the balance towards antibiotic prescribing. Teaching physicians to better think in probabilities of outcomes instead of pathophysiologic reasoning and to deal with uncertainty might help reducing antibiotic overprescribing.

Using the Morgenstern–Price Method and Cloud Theory to Invert the Shear Strength Index of Tailings Dams and Reveal the Coupling Deformation and Failure Law under Extreme Rainfall

It is difficult to obtain reliable shear strength parameters for the stability analysis and evaluation of tailings dams in an unstable state. In this study, the sensitivity of the shear strength index to the safety factor of a tailings dam was evaluated. The cohesion C range of a tailings earth rock dam in an unstable state is determined by the safety factor, and the Morgenstern–Price method is used for inversion. During parameter inversion, uncertainty reasoning is established based on cloud theory, which overcomes the problem that the fuzziness and randomness of the quantitative cohesion value are transferred to the qualitative concept of the safety factor. The results show that the change in cohesion C has a greater influence on the safety factor Fs of the tailings dam, and the value of parameter inversion is 8.6901 kPa. The deformation and failure of tailings dams under extreme rainfall conditions are analyzed by using the modified cohesion C value. The dam toe becomes the main response area of plastic deformation and slowly expands to the interior, showing creep deformation. The displacement field gradually transfers from the accumulated tailings to the tailings dam with the flow direction, causing erosion damage. This study provides a new idea and method for parameter inversion of the shear strength index of tailings dams and provides a reference for the disaster prediction and prevention of tailings dams subjected to extreme rainfall.

Physics Considerations for Evaluation of Dose for Dose-Response Models of Pediatric Late Effects From Radiation Therapy: A PENTEC Introductory Review

We describe the methods used to estimate the accuracy of dosimetric data found in literature sources used to construct the Pediatric Normal Tissue Effects in the Clinic (PENTEC) dose-response models, summarize these findings of each organ-specific task force, describe some of the dosimetric challenges and the extent to which these efforts affected the final modeling results, and provide guidance on the interpretation of the dose-response results given the various dosimetric uncertainties. Each of the PENTEC task force medical physicists reviewed all the journal articles used for dose-response modeling to identify, categorize, and quantify dosimetric uncertainties. These uncertainties fell into 6 broad categories. A uniform nomenclature was developed for describing the "dosimetric quality" of the articles used in the PENTEC reviews. Among the multidisciplinary experts in the PENTEC effort, the medical physicists were charged with the dosimetric evaluation, as they are most expert in this subject. The percentage dosimetric uncertainty was estimated for each late effect endpoint for all PENTEC organ reports. Twelve specific sources of dose uncertainty were identified related to the 6 broad categories. The most common reason for organ dose uncertainty was that prescribed dose rather than organ dose was reported. Percentage dose uncertainties ranged from 5% to 200%. Systematic uncertainties were used to correct the dose component of the models. Random uncertainties were also described in each report and in some cases used to modify dose axis error bars. In addition, the potential effects of dose binning were described. PENTEC reports are designed to provide guidance to radiation oncologists and treatment planners for organ dose constraints. It is critical that these dose constraint recommendations are as accurate as possible, acknowledging the large error bars for many. Achieving this accuracy is important as it enables clinicians to better balance target dose coverage with risk of late effects. Evidence-based dose constraints for pediatric patients have been lacking and, in this regard, PENTEC fills an important unmet need. One must be aware of the limitations of our recommendations, and that for some organ systems, large uncertainties exist in the dose-response model because of clinical endpoint uncertainty, dosimetric uncertainty, or both.

Uncertainty-Based Calibration Method for Environmental Sensors—Application to Chlorine and pH Monitoring With Carbon Nanotube Sensor Array

Societal demands in the field of air and water pollution monitoring require the ability to simultaneously detect a wide variety of chemical elements at very low concentrations in complex environments using compact and low-cost sensor devices. Although nanomaterial-based sensors have long been proposed as a solution to these exacting requirements, their detection accuracy is generally degraded in real-world conditions compared to laboratory conditions due to the effects of various interferents. To manage the related uncertainties and to associate confidence to the estimations, it seems natural to formulate the calibration-estimation problem in a probabilistic framework. This probabilistic formulation and its successful application to the monitoring of pH and active chlorine in drinking water are the main contributions of this work. While other tested calibration methods only allowed the monitoring of active chlorine, our solution enables the monitoring of both active chlorine and pH with quantified and reasonable uncertainties. Its success relies mainly on two adaptations of standard calibration methods: the consideration of the sensor inputs measurement errors (and not only the errors associated with the sensor outputs as it is generally done), and the introduction of two sources of model error (ME), one accounting for the approximate character of the calibration model, the other for unmeasured—and possibly unknown—interferents in the calibration environment.

Information Fusion-Based Fault Diagnosis Method Using Synthetic Indicator

Multisensor information fusion technology plays an essential role in fault diagnosis. Uncertain reasoning is the core of information fusion, and the DS evidence theory (DSE) has founded a general and popular framework for uncertainty reasoning. Under this framework, a novel information fusion method is developed in this article, to solve the problems of counterintuitive results, poor robustness, and “one-vote veto” when fusing highly conflicting evidence using DSE. We proposed a new synthetic indicator, which can effectively eliminate the conflicts between evidences. This synthetic indicator is composed of two indexes: measurement index of indirect conflicts and that of the evidence’s information itself. First, the divergence is used to measure the degree of conflict between bodies of evidence, and the Decision-Making Trial and Evaluation Laboratory (DEMATEL) model is employed to deal with indirect conflicts. Second, the Deng entropy is utilized to quantitatively measure the uncertainty of evidences, and the relative credibility preference of the evidence is expressed by the fuzzy preference relation. Finally, the initial body of evidence frame is weighted and revised by synthetic indicator before adopting the Dempster Shafer (DS) fusion rule. The superiority of the developed method is illustrated by numerical examples and application cases. The results show that fault diagnosis using the developed information fusion method can have a higher diagnostic accuracy.

Uncertainty quantification of multimodal surface wave inversion using artificial neural networks

An inversion of surface wave dispersion curves (DCs) is a nonunique and ill-conditioned problem. The inversion result has a probabilistic nature, which becomes apparent when simultaneously restoring the S-wave velocity and layer thickness. Therefore, the problem of uncertainty quantification is relevant. Existing methods through deterministic or global optimization approaches of uncertainty quantification via posterior probability density (PPD) of the model parameters are not computationally efficient because they demand multiple solutions to the inverse problem. We have developed an alternative method based on a multilayer fully connected artificial neural network (ANN). We improve the current unimodal approach, which is known from publications, to multimodal inversion. We use Cox’s and Teague’s algorithm to determine optimal parameterization (number of layers) and the ranges of possible model parameters. We uniformly draw training data sets within estimated ranges and train the ANN. Saved ANN weights map the phase velocity DCs to values of the S-wave velocity and layers thickness. To estimate the uncertainties, we adapt the Monte Carlo simulation strategy, according to which the frequency dependent data noise and the inverse operator errors are projected onto the resulting velocity model. The inverse operator errors are evaluated by the prediction of the training data set. The proposed combination of surface wave data processing methods, configured with each other, provides a novel surface wave multimodal dispersion data inversion and uncertainty quantification approach. We first test our approach on synthetic experiments for various velocity models: a positive gradient velocity, a low-velocity layer, and a high-velocity layer. This is done considering unimodal inversion at first and then compared with the multimodal inversion. Afterward, we apply our approach to field data and compare the resulting models with the body S-wave processing by the generalized reciprocal method. The experiments indicate high-potential results — using ANN yields the possibility to accurately estimate the PPD of restored model parameters without a significant computational effort. The PPD-based comparison demonstrates the advantages of a multimodal inversion over a unimodal inversion. The trained ANN provides reasonable model parameters predictions and related uncertainties in real time.