Parametric Methods Research Articles

Efficacy of targeted screening for familial hypercholesterolemia in children and adults aged <44 years: retrospective, prospective observational study

BACKGROUND: Considering the high cardiovascular risk in patients with familial hypercholesterolemia (FH), early diagnosis and treatment are the basis for the prevention of vascular accidents. In the absence of universal screening, the results of more targeted diagnostics are of interest — the search for lipid metabolism disorders in young relatives of patients with atherosclerotic vascular diseases.
 OBJECTIVE: To determine the effectiveness of targeted screening for identifying patients with FH, which will justify its widespread use in clinical practice.
 MATERIALS AND METHODS: At the start of the observational study, 584 patients were identified from the vascular centers of the Krasnoyarsk Regional Hospital, Krasnoyarsk Interdistrict Clinical Hospital No. 20 named after. I.S. Berzon, who had lipid profile data and early cardiovascular events (all forms of coronary heart diseases), including reconstructive vascular interventions up to 55 years in men and up to 60 years in women in the case of first-degree relatives and up to 50 years in second-degree relatives. The study examined patients’ relatives aged 44 years. To diagnose FH in participants aged 16 years, the scale developed by a network of Dutch lipid clinics was used; in participants aged 16 years, the S. Broome criteria were used. Targeted screening and lipid parameters in individuals with probable, possible, and definite FH were analyzed. Data processing was performed using Microsoft Excel and Statistica v. 12.0 (USA). Parametric (calculation of the median and 25th and 75th quartiles) and nonparametric (statistical significance of differences was determined using the Mann–Whitney and χ2 tests) methods were used.
 RESULTS: The study examined 70 children and 104 adults aged 44 years whose first- and/or second-degree relatives suffered premature vascular events. In the general group of participants, 42 (24.14%) patients had FH (of which 18 were 17 years old) and 37 (21.2%) had hyperlipoproteinemia (a). Definite FH was documented in 16 (9.1%) patients, probable in another 16, and possible in 9. Hyperlipoproteinemia (a) was found in 37 (21.2% of general group) patients, including 12 children (17.1% of pediatric group).
 CONCLUSION: Not more than 30% of the population are aware of the hereditary nature of lipid metabolism disorders and atherosclerotic diseases. Targeted screening is the least expensive and most effective tool for identifying patients with FH and hyperdipoproteinemia (a).

MR-Scout : Automated Synthesis of Metamorphic Relations from Existing Test Cases

Metamorphic Testing (MT) alleviates the oracle problem by defining oracles based on metamorphic relations (MRs), that govern multiple related inputs and their outputs. However, designing MRs is challenging, as it requires domain-specific knowledge. This hinders the widespread adoption of MT. We observe that developer-written test cases can embed domain knowledge that encodes MRs. Such encoded MRs could be synthesized for testing not only their original programs but also other programs that share similar functionalities. In this paper, we propose MR-Scout to automatically synthesize MRs from test cases in open-source software (OSS) projects. MR-Scout first discovers MR-encoded test cases (MTCs), and then synthesizes the encoded MRs into parameterized methods (called codified MRs ), and filters out MRs that demonstrate poor quality for new test case generation. MR-Scout discovered over 11,000 MTCs from 701 OSS projects. Experimental results show that over 97% of codified MRs are of high quality for automated test case generation, demonstrating the practical applicability of MR-Scout . Furthermore, codified-MRs-based tests effectively enhance the test adequacy of programs with developer-written tests, leading to 13.52% and 9.42% increases in line coverage and mutation score, respectively. Our qualitative study shows that 55.76% to 76.92% of codified MRs are easily comprehensible for developers.

Parametric Solid Models of the At-Term Uterus From Magnetic Resonance Images.

Birthing mechanics are poorly understood, though many injuries during childbirth are mechanical, like fetal and maternal tissue damage. Several biomechanical simulation models of parturition have been proposed to investigate birth, but many do not include the uterus. Additionally, most solid models rely on segmenting anatomical structures from clinical images to generate patient geometry, which can be time-consuming. This work presents two new parametric solid modeling methods for generating patient-specific, at-term uterine three-dimensional geometry. Building from an established method of modeling the sagittal uterine shape, this work improves the uterine coronal shape, especially where the fetal head joins the lower uterine wall. Solid models of the uterus and cervix were built from five at-term patients' magnetic resonance imaging (MRI) sets. Using anatomy measurements from MRI-segmented models, two parametric models were created-one that employs an averaged coronal uterine shape and one with multiple axial measurements of the coronal uterus. Through finite element analysis, the two new parametric methods were compared to the MRI-segmented high-fidelity method and a previously published elliptical low-fidelity method. A clear improvement in the at-term uterine shape was found using the two new parametric methods, and agreement in principal Lagrange strain directions was observed across all modeling methods. These methods provide an effective and efficient way to generate three-dimensional solid models of patient-specific maternal uterine anatomy, advancing possibilities for future research in computational birthing biomechanics.

Sustainable Energy Development and Sustainable Economic Development in EU Countries

Sustainable development is the subject of many economic analyses, but so far no attempt has been made to identify the main mechanism of interdependence between sustainable energy development and sustainable economic development in the second decade of the 21st century. The particular role of energy in achieving the Sustainable Development Goals is due to the fact that the production, supply and use of energy underpin economic growth. The article fills this research gap and spawns both a better understanding of the essence of sustainable development as well as practical conclusions. The aim is to assess sustainable energy development and sustainable economic development in EU member states and to determine the correlation between the two in the EU. Substantive and formal methods were used to select diagnostic variables, including: the parametric method, the standardized sums method, and correlation analysis. The analysis period covers the years 2014–2021. The conducted research demonstrated a significant variation in the level of sustainable energy development and sustainable economic development among EU countries.

HISTOCHEMICAL AND IMMUNOHISTOCHEMICAL FEATURES OF DIFFERENTIATED TROPHOBLAST IN CHORIONIC VILLI OF THE PLACENTA IN PRETERM LABOR

The importance of studying the histochemical and immunohistochemical features of the diff erentiated trophoblast in chorionic villi of the placenta in preterm labor is determined by the threatening nature of this condition for both mother and fetus, as well as its high prevalence and serious consequences for the health of both. The understanding of the damage to the trophoblast of chorionic villi in the placenta can be expanded by histochemical and immunohistochemical methods, which allow the assessment of the concentration of specifi c marker molecules in one way or another.Objective. To determine certain histochemical and immunohistochemical characteristics of proteins in the trophoblast of theintermediate and terminal chorionic villi of the placenta in preterm labor.Material and Methods. The obtained material (30 placentas from preterm deliveries and 30 placentas from normalpregnancies) was fi xed for 20-24 hours in 10 % neutral formalin solution buff ered in Lilly’s phosphate buff er. After tissue removal, the placental tissue was dehydrated in an ascending ethanol series and embedded in paraffi n at a temperature of approximately 58 °C. Serial histologic sections were cut at 5.0 μm thickness using an MS-2 sliding microtome. After deparaffi nization, histological sections were stained with hematoxylin and eosin, histochemical methods for total protein with bromophenol blue according to Bonhéme, and immunohistochemical techniques according to the manufacturer’s protocols (Dako, Denmark). In particular, immunohistochemical reactions were performed with monoclonal antibodies against trophoblast hormone- placental lactogen and placental alkaline phosphatase. Visualization of primary antibodies was performed using the Dako polymer visualization system with diaminobenzidine as chromogen (resulting in brown staining of the sites of studied antigens). In addition to the descriptive method of histopathologic research, computer morphometry of digital microphotographs of histologic sections was performed using a Delta Optical Evolution 100 microscope and an Olympus SP550UZ digital camera. Digital copies of the images were processed using a legitimate copy of the ImageJ v1.52f computer program developed for histometric studies (National Institutes of Health, USA). Specifi cally, the evaluation of staining intensity (optical density) was performed on digital microphotographs using the method of computer microdensitometry. For this purpose, a microprobe method was used to obtain a computer brightness value in an 8-bit analysis system with 256 gray levels – from black (0) to white (255).The obtained values were then transformed into relative optical density values (r.OD) by logarithmic transformation (naturallogarithm method). The relative optical density value ranges from 0 (absolute transparency of the object) to 1 (absolute opacity of the object). The obtained digital data were processed using statistical analysis methods. A legitimate copy of the statistical analysis computer program PAST v4.14 was used, with a preliminary check for normal distribution using the Shapiro- Wilk test. Since, according to this test, the hypothesis of normal distribution was not rejected for the statistical samples studied (at p=0.05), parametric methods of statistical analysis were applied: calculation of the mean and its standard error, Student’s t-test (two-tailed, unpaired). In addition, the non-parametric Mann- Whitney test was used for the reliability of the conclusions. The research was conducted as part of the scientifi c research project «Preservation and Restoration of Reproductive Health in Women and Girls with Obstetric and Gynecological Pathology» at the Department of Obstetrics and Gynecology of Bukovinian State Medical University (state registration number 0121U110020, duration 2021-2025).Results. Microscopic examination of histological sections stained with hematoxylin and eosin did not reveal any diff erencesin the structure of chorionic villus trophoblast in the placenta of preterm labor compared to normal pregnancy. However,histochemical and immunohistochemical methods of investigation revealed a number of features in the trophoblast of chorionic villi, where fundamental events related to substance exchange occur – intermediate immature, intermediate mature, terminal villi, including terminal «specialized villi».Conclusions. According to the obtained histochemical and immunohistochemical data, in preterm labor, compared to normalpregnancy, no changes are observed in the trophoblast of intermediate immature villi, while in intermediate mature and terminal villi, there is a decrease in histochemical staining for total protein and immunohistochemical staining for specifi c trophoblast proteins – placental lactogen hormone and placental alkaline phosphatase enzyme.

A distribution-free Max-EWMA scheme for multi-aspect process monitoring with industrial applications

In Statistical Process Monitoring, Distribution-free charting schemes play a vital role in Industry 4.0 for their superior effectiveness compared to parametric methods, especially in cases where the underlying process distribution is not well-defined or poses challenges in estimation. Traditional distribution-free charting schemes focus on surveilling only one process aspect: the location or scale parameter. The past two decades have also witnessed a rapid expansion of research on joint monitoring of the two aspects, location and scale, using combined bi-aspect charting schemes. However, there is a notable scarcity of methods that addressing complex industrial scenarios where multiple parameters (like location, scale, and shape) need simultaneous monitoring with high sensitivity and specificity. Our research is motivated by this challenge, and this paper describes a distribution-free tri-aspect monitoring procedure called the Maximum Exponentially Weighted Moving Average (Max-EWMA) scheme This scheme can effectively monitor shifts in three process characteristics, encompassing aspects related to process location, scale, and shape parameters. We utilize weighted versions of well-known statistical measures such as the Wilcoxon, Ansari-Bradley, and Savage-type statistics to construct the plotting statistics. An essential feature of our proposed Max-EWMA chart is its robustness under various continuous distributions, ensuring reliable performance in in-control situations. Competing schemes are compared via intensive computing techniques based on Monte Carlo using the Median Run Length metric, which evaluates the effectiveness of the proposed scheme. Finally, our proposed schemes are illustrated with two examples. Some concluding remarks and limitations of the study are noted.

Optimized parameterized Uzawa methods for solving complex Helmholtz equations

As we know that, the parameterized Uzawa (PU) method can be very efficient when used to solve the standard saddle point problem, especially, when we have good and accurate estimation of preconditioned Schur complement matrix. In this paper, by taking full use of the special structure of coefficient matrix arising from complex Helmholtz equations, two types of optimized PU (OPU) methods are discussed theoretically and experimentally. Specifically, the convergence factors of these two OPU methods are less than 0.172, and the optimal result of first OPU method can reach 0.0396 with σ1≥σ2>0, which is currently the best theoretical result in the literatures. Moreover, the second OPU method has better computational advantages compared with the first OPU method as it avoids the inverse computation of W at each step, indicating the less CPU time will be costed by the second OPU method. In addition, the optimal parameters involved in our algorithms consist of constants, reducing the computational complexity associated with parameter selection. Finally, numerical results are given, not only show the effectiveness of OPU methods, but also confirm the rationality of theoretical analysis.

A new efficient parametric level set method based on radial basis function-finite difference for structural topology optimization

To overcome a significant challenge in traditional parameterized level set methods based on globally supported radial basis functions, we propose employing a local differentiation construction of radial basis functions using finite difference, a technique previously applied to solving partial differential equations but novel in the context of topology optimization. We present a novel parameterized level set method for structural topology optimization of compliance minimization and compliant mechanism, with the main aim of reducing computational costs associated with fully dense matrices when approximating systems with a large number of collocation points. The new scheme implemented with rectangular mesh elements and polygonal mesh generation accommodates both rectangular and complex design domains. Numerical results are provided to demonstrate the algorithm's effectiveness.

Verification of bile acid determination method and establishing reference intervals for biochemical and haematological parameters in third-trimester pregnant women.

The aims of this study were to verify the bile acids (BA) method and to establish reference intervals (RIs) for bile acids (BA) and biochemical and haematological parameters in Croatian pregnant women. BA spectrophotometric method verification was performed on Siemens Atellica Solution CH 930 automated analyser using Sentinel reagent. Stability, precision, trueness, linearity, and RIs, as well as lipemia interference were tested according to CLSI guidelines. BA, biochemical, and haematological parameters were measured in serum (BA, biochemical) and whole blood (haematological) samples of fasting healthy third-trimester pregnant women from Croatia (n=121). The establishment of the RIs was done a priori according to the CLSI EP28-A3C:2010 guideline. Selected reference individuals' data were analysed using parametric, non-parametric, and robust methods. Stability study showed that BA are stable in serum samples for 2days at 20 °C, 14days at 4-8 °C, and 22days at-20 °C. The precision study and adult RIs verification met the criteria. Linearity was verified for the concentration range of 3.5-172.1 μmol/L whereas the lipemia interference test showed a positive bias (%) in BA concentration. The determined reference limits generally exhibited better precision for haematological parameters, being lower than the upper recommended value 0.2, unlike biochemical parameters. Haematological parameters showed notable differences between pregnant and non-pregnant women, while many biochemical parameters' RIs remained similar. Only ALT and GGT showed lower non-comparable RI upper limits in the population pregnant women. Spectrophotometric BA method showed satisfactory performance and all examined parameters were within the set criteria. Moreover, RIs for key biochemical and haematological parameters, including BAs, have been established for the first time in the population of Croatian pregnant women.

A novel generative–predictive data-driven approach for multi-objective optimization of horizontal axis tidal turbine

Tidal turbines play a critical role in converting the kinetic energy of water into electricity, contributing significantly to energy conversion. However, the current optimization design of these turbines involves computationally intensive simulations, leading to higher design costs. Additionally, traditional parameterized modeling methods, constrained by predefined design parameters, limit the exploration of innovative designs. In response, this study introduces an innovative data-driven “generative–predictive” design approach comprising a generative model and a predictive model. The generative model autonomously learns feature representations from existing turbines and leverages this knowledge to generate a novel set of turbines with superior hydrodynamic performance. Subsequently, an efficient performance evaluation is conducted using a predictive model for the generated turbines. Compared to the current parameterized modeling approaches, the proposed approach is combined with multi-objective optimization algorithm to optimize the tidal turbine hydrodynamic performance. Research results demonstrate that the generative model, trained on gradients, can generate highly complex turbines with minimal latent vectors. Through transfer learning, the predictive model exhibits robustness and accuracy, effectively guiding the design process. In the final optimization comparison, the proposed generative–predictive design approach requires only 4% of the optimization time while achieving results similar to or surpassing traditional design approaches. This approach proves to be a powerful tool for guiding the efficient and optimized design of turbines.

Parametric learning of time-advancement operators for unstable flame evolution

This study investigates the application of machine learning, specifically Fourier neural operator (FNO) and convolutional neural network (CNN), to learn time-advancement operators for parametric partial differential equations (PDEs). Our focus is on extending existing operator learning methods to handle additional inputs representing PDE parameters. The goal is to create a unified learning approach that accurately predicts short-term solutions and provides robust long-term statistics under diverse parameter conditions, facilitating computational cost savings and accelerating development in engineering simulations. We develop and compare parametric learning methods based on FNO and CNN, evaluating their effectiveness in learning parametric-dependent solution time-advancement operators for one-dimensional PDEs and realistic flame front evolution data obtained from direct numerical simulations of the Navier–Stokes equations.

Parametric analysis of pollutant discharge concentration in non-Newtonian nanofluid flow across a permeable Riga sheet with thermal radiation

Proper wastewater disposal is crucial in various manufacturing and ecological systems. This study aims to prevent and regulate pollution in the water supply. It examines how the pollutant discharge concentration affects the flow of non-Newtonian nanofluids (NNNFs) over a porous Riga surface. Two different types of NNNFs, namely, Walter’s B and second-grade fluids, have been examined. The fluid flow is conveyed in the form of a system of partial differential equations (PDEs), which are first reduced to a non-dimensional set of ordinary differential equations (ODEs) and then to first-order differential equations. The numerical approach parametric continuation method is employed to solve these ODEs. It has been noticed that the energy curve declines with increasing numbers of TiO2-nanoparticles (NPs). The effect of the external pollutant source variation factor enriches the concentration of pollutants in both fluid cases. Furthermore, the viscoelastic parameter K1 plays a notable role in determining the behavior of the fluids. Particularly in NNNFs, the variation of K1 enhances the fluid flow, whereas the rise of second-grade fluid factor decreases the velocity of the fluid. Our findings indicate a substantial impact of the parameters under consideration on the concentration of pollutant discharge. Significantly, it was observed that an increase in the amount of NPs and the thermal radiation parameter led to an improvement in the thermal conductivity of the nanofluid, consequently decreasing the concentration of pollutants in the discharge. The nanofluid has greater efficiency in boosting the energy transfer rate of the base fluid. In the case of the second-grade fluid, the energy propagation rate increases up to 6.25%, whereas, in the case of Walter’s fluid B, it increases up to 7.85%.

Optimization of a high through-flow design turbine using response surface method

Enhancing the through-flow capability of the turbine facilitates the potential to decrease the external dimension of the engine, leading to a reduction in weight and an increase in the thrust-to-weight ratio. The optimization of blade profile in terms of aerodynamic design is an essential strategy to improve the overall performance of the high through-flow design turbine. This study aims to develop an automated optimization technique, utilizing the response surface method (RSM), to enable reliable prediction and rapid optimization of aerodynamic performance. A parametric modeling method is devised to generate blade profiles with continuous curvature throughout the automated optimization process. The Box–Behnken experimental design, in combination with Reynolds-averaged Navier–Stokes numerical calculation, is employed to construct a second-order polynomial RSM approximation model. The optimization process comprises two levels: improving the through-flow capability and reducing blade profile loss. The optimized profile, Opt1, achieves a substantial 13.19% improvement in through-flow capability at the cost of a 12.27% increase in blade profile loss. Thus, further optimization is performed to minimize blade profile loss based on the Opt1 scheme. Geometric constraints are applied to the most influential parameters affecting through-flow capability to mitigate their impacts. Compared to the Opt1, the final optimized profile, Opt2, achieves a substantial 31.83% decrease in blade profile loss with a negligible sacrifice of 0.23% in through-flow capability.

Transfer Learning Method from Parameter Scene to Physical Scene Based on Self-Game Theory

Due to the inherent challenges in meeting the comprehensive training requirements of combat scenarios within a digital environment, this paper proposes innovative solutions. Firstly, a parametric scene training method is introduced, aiming to enhance the adaptability of the training process. Secondly, the utilization of the digital environment as a test environment is suggested, which can significantly improve the efficiency of iterative virtual-to-real conversion. Additionally, employing digital simulation as a pre-test environment for the physical setting can effectively reduce deployment costs and enhance the safety of virtual reality migration experiments. The proposed approach involves constructing a training model based on the parameterized environment and implementing a feedback loop utilizing the digital environment agent model. This framework enables continuous verification of the environment’s parameters, ensuring the accuracy of decision-making strategies and evaluating the transferability of the decision-making model.

Uveitis complicated by phthisis bulbi: hemodynamic parameters in the prediction of anterior-posterior eye size reduction

Background. Phthisis bulbi is a serious complication of uveitis, causing vision loss and esthetic defects. Hemodynamic disorders can play an important role in the formation of this complication as a result of uveitis. We did not find data on predicting the progression of phthisis bulbi with a reduction in anterior-posterior size in the available literature. Aim. To analyze the possibility of predicting the reduction in the anterior-posterior size of the eye with uveitis, complicated by phthisis bulbi, based on hemodynamic parameters Materials and Methods. 33 patients aged 5–84 years, of them 19 male and 14 female patients, with unilateral endogenous uveitis, complicated by phthisis bulbi, were examined. 15 patients with uveitis complicated by phthisis bulbi, who had not received any treatment during this time, were examined in dynamics (for at least 1 year). All patients underwent Doppler ultrasound examination of the ophthalmic artery and short posterior ciliary arteries. In addition, all patients underwent biomicroscopic and tonometric examinations, ultrasound biomicroscopy, rheoophthalmography of eyeballs, A-scan and B-scan ultrasonography. The results of the examination of eyes with uveitis complicated by phthisis bulbi were compared with the results of the examination of paired (healthy) eyes of the same patients. Results. We have developed a multiple regression model that allows us to predict a reduction in the anterior-posterior size of the eye with phthisis bulbi due to uveitis. The dynamics of the disease in 15 patients not taking any treatment for uveitis, has been monitored for more than a year. The prediction of phthisis bulbi progression was confirmed in 13 patients, which amounts to 86.7% (p<0.05). Conclusions. We have proposed a model that allows predicting the progressive or stationary course of phthisis bulbi due to uveitis based on hemodynamic parameters. Keywords: infectious uveitis, noninfectious uveitis, phthisis bulbi hemodynamic disorders, anterior-posterior size of the eyeball.

Construction and evolutionary factors of spatial correlation network of China's provincial tourism resource conversion efficiency

Research objectiveTo explore the spatial correlation network characteristics and formation mechanisms of tourism resource conversion efficiency, and provide reference for the collaborative improvement of tourism resource conversion efficiency at the provincial level in China. Research methodsNon parametric SBM efficiency measurement method and social network analysis method. Research hypothesis: The spatial network correlation characteristics of tourism resource conversion efficiency are obvious, and regional connections are close. Research findings(i) during the research period, the spatial connection strength of China's tourism resource conversion efficiency continued to increase and the spatial network structure of tourism resource conversion efficiency tended to become more complex and significantly more stable. (ii) A spatially linked network with a stable tourism resource conversion efficiency structure formed in China. The number of network relations and density of the network fluctuated and increased, while the network efficiency continued to decrease; however, a strong small-world nature was observed. (iii) The economic development level difference matrix, tourism industry agglomeration difference matrix, human capital difference matrix, and marketization degree difference matrix significantly and positively affected spatial association relationship establishment, while the provincial adjacency matrix significantly and negatively affected such relationships.

A novel quasi-smooth tetrahedral numerical manifold method and its application in topology optimization based on parameterized level-set method

In this paper, a novel quasi-smooth tetrahedral numerical manifold method (NMM) and its two-dimensional (2D) counterpart are proposed. A new topology optimization method is established by combining the quasi-smooth manifold element (QSME) with the parameterized level set method (PLSM). The QSME introduces an innovative displacement function characterized by high accuracy and high-order continuity, effectively addressing the “linear dependence” (LD) issue inherent in traditional high-order NMM. To integrate QSME and PLSM, the corresponding optimization formulations and sensitivity analyses are provided. In order to fully utilize advantages of this novel quasi-smooth NMM and the PLSM, an element subdivision technique based on model recognition is proposed to accurately capture the physical boundaries. Additionally, a volume fraction update method based on element refinement is proposed. Taking advantage of the characteristics of the PLSM, a structure visualization method based on the sign distance function is developed to accurately describe curve boundary. This method allows for precise visualization of optimized structures. This study verifies high efficiency of the QSME-based PLSM for minimum compliance topology optimization problems in both 2D and 3D structures. Some representative structural optimization examples are tested to demonstrate effectiveness of the proposed method in both 2D and 3D problems, especially in complex design domain.

Intelligent templates to prevent geometric parameterization failure in ship superstructure structural detail design

ABSTRACT Ship superstructures, as typical examples of non-standard design elements, require diverse structural geometric designs and frequent adaptations to meet evolving demands and simulation requirements during the detail design process. However, the utilization of current ship computer-aided design (CAD) systems for detail design presents several limitations, and traditional parametric methods often fall short in complex geometric parameterization. This paper proposed intelligent templates via knowledge-based engineering (KBE) to enhance CAD models' robustness and applicability. The study focused on three specific geometric problems that restrict the validity of parameterization: varying types of input conditions, multiple solutions in offsets and arc fillets, and non-topological transformations. Three representative structural component templates were developed on CATIA V6, showcasing effectiveness compared to traditional methods through a ship design task. Furthermore, this approach provides the basis for the implementation of modular design, design automation, and integrated design simulation.

A comparative study of methods for estimating model-agnostic Shapley value explanations

Shapley values originated in cooperative game theory but are extensively used today as a model-agnostic explanation framework to explain predictions made by complex machine learning models in the industry and academia. There are several algorithmic approaches for computing different versions of Shapley value explanations. Here, we consider Shapley values incorporating feature dependencies, referred to as conditional Shapley values, for predictive models fitted to tabular data. Estimating precise conditional Shapley values is difficult as they require the estimation of non-trivial conditional expectations. In this article, we develop new methods, extend earlier proposed approaches, and systematize the new refined and existing methods into different method classes for comparison and evaluation. The method classes use either Monte Carlo integration or regression to model the conditional expectations. We conduct extensive simulation studies to evaluate how precisely the different method classes estimate the conditional expectations, and thereby the conditional Shapley values, for different setups. We also apply the methods to several real-world data experiments and provide recommendations for when to use the different method classes and approaches. Roughly speaking, we recommend using parametric methods when we can specify the data distribution almost correctly, as they generally produce the most accurate Shapley value explanations. When the distribution is unknown, both generative methods and regression models with a similar form as the underlying predictive model are good and stable options. Regression-based methods are often slow to train but quickly produce the Shapley value explanations once trained. The vice versa is true for Monte Carlo-based methods, making the different methods appropriate in different practical situations.

Approximation of the Profile of Gas Turbine Engine Blades

Introduction. Increasing the durability of gas turbine engine (GTE) blades is achieved through the use of special protective coatings on their surface. For the development of such coatings, the basic source information is the geometric profile of the blade section. To transfer a given blade cross-section profile to the appropriate CAD/CAM system or engineering analysis package, parametric modeling methods are used to automate this operation. However, the known approaches to creating a parametric model of a blade profile are not without a number of disadvantages, and a generally accepted method for creating it does not currently exist. The research was aimed at creating a technique for approximating the profile of gas turbine engine blades, convenient for use in the subsequent analysis of the operating conditions of special coatings on the surface of the blades.Materials and Methods. When constructing parametric models of the profile of gas turbine engine blades, a method based on the orthogonal Legendre polynomials was used. This made it possible to provide high accuracy of approximation and construction of a continuous mapping for the parameters of the blade profile approximation. A Python application was created for automated processing of source profiles. It provided the calculation of the coefficients of approximating polynomials for the contour lines of the blade, visualization of the calculation results, and creation of a dxf file based on the points of approximating functions to transfer it to the CAD system. Next, geometric models of blades were used to solve the problem of a stationary aerodynamic flow around a blade. The results of solving this problem were used to study the effect of the blade profile on its cooling in an aerodynamic flow.Results. As an example, three options of blade profiles belonging to different types of GTE were considered. It was shown that for all three studied profiles, the proposed technique provided obtaining parametric models that maintained high accuracy in constructing approximating lines, which was confirmed by the values of the determination coefficients close to unity. To illustrate the possibility of using the obtained models, examples of solving the gas dynamic problem with a potential flow around a blade in a stationary aerodynamic flow were given. The distributions of pressure and temperature on the surface of the blade were calculated using the finite element method.Discussion and Conclusion. The calculation results show that the proposed technique of approximating the profile of the GTE blade, based on the use of orthogonal polynomials, is a convenient tool to automate the creation of a geometric model of the blade and compare different types and profiles of blades, solving the corresponding gas dynamic problems. At the same time, for a given blade profile and GTE operating conditions, it is possible to obtain the distribution of temperatures and forces acting on the surface of the blade, which is required for predicting the durability of special coatings.