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One problem in incremental product development is that geometric models are limited in their ability to explore radical alternative design variants. In this publication, a function modeling approach is suggested to increase the amount and variety of explored alternatives, since function models (FM) provide greater model flexibility. An enhanced function-means (EF-M) model capable of representing the constraints of the design space as well as alternative designs is created through a reverse engineering process. This model is then used as a basis for the development of a new product variant. This work describes the EF-M model's capabilities for representing the design space and integrating novel solutions into the existing product structure and explains how these capabilities support the exploration of alternative design variants. First-order analyses are executed, and the EF-M model is used to capture and represent already existing design information for further analyses. Based on these findings, a design space exploration approach is developed. It positions the FM as a connection between legacy and novel designs and, through this, allows for the exploration of more diverse product concepts. This approach is based on three steps – decomposition, design, and embodiment – and builds on the capabilities of EF-M to model alternative solutions for different requirements. While the embodiment step of creating the novel product's geometry is still a topic for future research, the design space exploration concept can be used to enable wider, more methodological, and potentially automated design space exploration.

Integrated circuit (IC) chip cards are commonly used in payment system applications since they can provide security and convenience simultaneously. More precisely, Europay, MasterCard, and VISA (EMV) are widely known to be well equipped with security frameworks that can defend against malicious attacks. On the other hand, there are other payment system applications at the national level. In the case of the Republic of Korea, standards for financial IC card specifications are established by the Korea Financial Telecommunications and Clearings Institute. Furthermore, security features defending against timing analysis, power analysis, electromagnetic analysis, and TEMPEST are required. This paper identifies side channel leakages in the financial IC cards of the Republic of Korea, although there may be side channel countermeasures. Side channel leakages in the financial IC cards of the Republic of Korea are identified for the first time since the side channel countermeasures were included in the standards. The countermeasure that is applied to the IC card from a black box perspective is estimated to measure security features against power analysis. Then, in order to investigate whether an underlying countermeasure is applied, first-order and second-order power analyses are performed on the main target, e.g., a S-box of the block cipher SEED that is employed in the financial system. Furthermore, the latest proposal in ICISC 2017 is examined to apply block cipher SEED to the financial IC card protocol. As a result, it is possible to identify some side channel leakages while expanding the lemma of the paper accepted in ICISC 2017. Algebraic logic is also constructed to recover the master key from some round keys. Finally, it is found that only 20,000 traces are required to find the master key.

The most general quantities of interest (called “responses”) produced by the computational model of a linear physical system can depend on both the forward and adjoint state functions that describe the respective system. This work presents the Fourth-Order Comprehensive Adjoint Sensitivity Analysis Methodology (4th-CASAM) for linear systems, which enables the efficient computation of the exact expressions of the 1st-, 2nd-, 3rd- and 4th-order sensitivities of a generic system response, which can depend on both the forward and adjoint state functions, with respect to all of the parameters underlying the respective forward/adjoint systems. Among the best known such system responses are various Lagrangians, including the Schwinger and Roussopoulos functionals, for analyzing ratios of reaction rates, the Rayleigh quotient for analyzing eigenvalues and/or separation constants, etc., which require the simultaneous consideration of both the forward and adjoint systems when computing them and/or their sensitivities (i.e., functional derivatives) with respect to the model parameters. Evidently, such responses encompass, as particular cases, responses that may depend just on the forward or just on the adjoint state functions pertaining to the linear system under consideration. This work also compares the CPU-times needed by the 4th-CASAM versus other deterministic methods (e.g., finite-difference schemes) for computing response sensitivities These comparisons underscore the fact that the 4th-CASAM is the only practically implementable methodology for obtaining and subsequently computing the exact expressions (i.e., free of methodologically-introduced approximations) of the 1st-, 2nd, 3rd- and 4th-order sensitivities (i.e., functional derivatives) of responses to system parameters, for coupled forward/adjoint linear systems. By enabling the practical computation of any and all of the 1st-, 2nd, 3rd- and 4th-order response sensitivities to model parameters, the 4th-CASAM makes it possible to compare the relative values of the sensitivities of various order, in order to assess which sensitivities are important and which may actually be neglected, thus enabling future investigations of the convergence of the (multivariate) Taylor series expansion of the response in terms of parameter variations, as well as investigating the range of validity of other important quantities (e.g., response variances/covariance, skewness, kurtosis, etc.) that are derived from Taylor-expansion of the response as a function of the model’s parameters. The 4th-CASAM presented in this work provides the basis for significant future advances towards overcoming the “curse of dimensionality” in sensitivity analysis, uncertainty quantification and predictive modeling.

Due to the spatial variability of hydraulic properties, probabilistic slope seepage analysis becomes necessary. This study conducts a probabilistic analysis of slope seepage under rainfall, considering the spatial variability of saturated hydraulic conductivity. Through this, both the commonly used Monte Carlo simulation method and the proposed first-order stochastic moment approach are tested and compared. The results indicate that the first-order analysis approach is effective and applicable to the study of flow processes in a slope scenario. It is also capable of obtaining statistics such as mean and variance with a high enough accuracy. Using this approach, higher variabilities in the pressure head and the fluctuation of the phreatic surface in the slope are found with a higher value of the correlation length of the saturated hydraulic conductivity. The Monte Carlo simulation is found to be time-consuming: at least 10,000 realizations are required to reach convergence, and the number of realizations needed is sensitive to the grid density. A coarser grid case requires more realizations for convergence. If the number of realizations is not enough, the results are unreliable. Compared with Monte Carlo simulation, the accuracy of the first-order stochastic moment analysis is generally satisfied when the variance and the correlation length of the saturated hydraulic conductivity are not too large. This study highlights the applicability of the proposed first-order stochastic moment analysis approach in the slope scenario.

Two methods of reliability analysis of soil slopes are studied, and the representative flow charts of both methods are illustrated. Method 1 can predict the reliability index and the critical probabilistic slip surface directly and it is computational efficient, but it needs the development of new codes for integrating the reliability analysis code and the slope stability code. Method 2 makes the reliability analysis code call the slope stability analysis code directly, and each code can be considered as an intact part. The main result of Method 2 is the reliability index of soil slope. Combined with the proposed method for locating the critical slip surface, Method 2 can also predict the probabilistic slip surface. Although Method 2 needs much more callings of the subprogram of slope stability analysis code, it needs not the developing of new computer program. Thus, Method 2 is easy to use and can be applied to different reliability analysis methods and slope stability analysis methods.

This work presents the general mathematical frameworks of the “First and Second-Order Features Adjoint Sensitivity Analysis Methodology for Neural Integral Equations of Volterra Type” designated as the 1st-FASAM-NIE-V and the 2nd-FASAM-NIE-V methodologies, respectively. Using a single large-scale (adjoint) computation, the 1st-FASAM-NIE-V enables the most efficient computation of the exact expressions of all first-order sensitivities of the decoder response to the feature functions and also with respect to the optimal values of the NIE-net’s parameters/weights after the respective NIE-Volterra-net was optimized to represent the underlying physical system. The computation of all second-order sensitivities with respect to the feature functions using the 2nd-FASAM-NIE-V requires as many large-scale computations as there are first-order sensitivities of the decoder response with respect to the feature functions. Subsequently, the second-order sensitivities of the decoder response with respect to the primary model parameters are obtained trivially by applying the “chain-rule of differentiation” to the second-order sensitivities with respect to the feature functions. The application of the 1st-FASAM-NIE-V and the 2nd-FASAM-NIE-V methodologies is illustrated by using a well-known model for neutron slowing down in a homogeneous hydrogenous medium, which yields tractable closed-form exact explicit expressions for all quantities of interest, including the various adjoint sensitivity functions and first- and second-order sensitivities of the decoder response with respect to all feature functions and also primary model parameters.

This work presents the “First-Order Features Adjoint Sensitivity Analysis Methodology for Neural Integro-Differential Equations of Fredholm-Type” (1st-FASAM-NIDE-F) and the “Second-Order Features Adjoint Sensitivity Analysis Methodology for Neural Integro-Differential Equations of Fredholm-Type” (2nd-FASAM-NIDE-F). It is shown that the 1st-FASAM-NIDE-F methodology enables the most efficient computation of exactly-determined first-order sensitivities of decoder response with respect to the optimized NIDE-F parameters, requiring a single “large-scale” computation for solving the 1st-Level Adjoint Sensitivity System (1st-LASS), regardless of the number of weights/parameters underlying the NIDE-F decoder, hidden layers, and encoder. The 2nd-FASAM-NIDE-F methodology enables the computation, with unparalleled efficiency, of the second-order sensitivities of decoder responses with respect to the optimized/trained weights, requiring only as many large-scale computations for solving the 2nd-Level Adjoint Sensitivity System (2nd-LASS) as there are non-zero feature functions of parameters. The application of both the 1st-FASAM-NIDE-F and the 2nd-FASAM-NIDE-F methodologies is illustrated in an accompanying work (Part II) by considering a paradigm heat transfer model.

Water-quality modeling and prediction is a complicated task because of inherent randomness and uncertainties associated with various processes and variables throughout the stream environment and the lack of appropriate data. Hence, the results of mathematical models are always approximate, lying within an uncertainty. This paper describes and demonstrates the application of the U.S. Environmental Protection Agency's water-quality model, QUAL2E-UNCAS, to the Zayandeh-Rood River in Iran. First-order reliability analysis is used to examine the variability of predicted water-quality parameters of total dissolved solids, dissolved oxygen, and biochemical oxygen demand. This analysis also determines key sources of uncertainty affecting prediction of the water-quality parameters. The results show that reliability analysis can help water-quality modelers and planners to quantify the reliability of the water-quality predictions and to carry out more efficiently planned sampling and data collection programs to reduce model-prediction uncertainty.

This article presents generalized finite element formulation for plastic hinge modeling based on lumped plasticity in the classical Euler–Bernoulli beam. In this approach, the plastic hinges are modeled using a special enrichment function, which can describe the weak discontinuity of the solution at the location of the plastic hinge. Furthermore, it is also possible to insert a plastic hinge at an arbitrary location of the element without modifying its connectivity or adding more elements. Instead, the formations of the plastic hinges are achieved by hierarchically adding more degrees of freedom to existing elements. Due to these features, the proposed methodology can efficiently perform the first-order plastic hinge analysis of large-frame structures. A generalized finite element solution technique based on the static condensation scheme is also proposed in order to reduce the computational cost of a series of linear elastic problems, which is in general the most time-consuming portion of the first-order plastic hinge analysis. The effectiveness and accuracy of the proposed method are verified by analyzing several representative numerical examples.

This work presents the “First-Order Features Adjoint Sensitivity Analysis Methodology for Fredholm-Type Neural Integral Equations” (1st-FASAM-NIE-Fredholm) and the “Second-Order Features Adjoint Sensitivity Analysis Methodology for Fredholm-Type Neural Integral Equations” (2nd-FASAM-NIE-Fredholm). It is shown that the 1st-FASAM-NIE-Fredholm methodology enables the efficient computation of exactly determined first-order sensitivities of decoder response with respect to the optimized NIE-parameters, requiring a single “large-scale” computation for solving the First-Level Adjoint Sensitivity System (1st-LASS), regardless of the number of weights/parameters underlying the NIE-net. The 2nd-FASAM-NIE-Fredholm methodology enables the computation, with unparalleled efficiency, of the second-order sensitivities of decoder responses with respect to the optimized/trained weights involved in the NIE’s decoder, hidden layers, and encoder, requiring only as many “large-scale” computations as there are first-order sensitivities with respect to the feature functions. The application of both the 1st-FASAM-NIE-Fredholm and the 2nd-FASAM-NIE-Fredholm methodologies is illustrated by considering a system of nonlinear Fredholm-type NIE that admits analytical solutions, thereby facilitating the verification of the expressions obtained for the first- and second-order sensitivities of NIE-decoder responses with respect to the model parameters (weights) that characterize the respective NIE-net.