Closed-form Model Research Articles

Closed-form models for the cutting forces of general-helix cylindrical milling tools

Cutting force is the predictor of the performance indicators of machining processes, therefore, the measurement and modeling accuracy have received sustained research attention. The existing closed-form models for milling cutting force are useful for an analytical design process and optimization (over large parametric ranges) but the methods are not applicable to milling tools with arbitrary helix angle variation (general-helix). On the other hand, numerical methods are available for general-helix tools but are only applicable in an analytical design process and optimization when they are used to create surrogate models. The aim of this work is to develop closed-form models that retain the benefits of both approaches for computing the cutting forces of general-helix cylindrical milling tools by combining the properties of the analytical and numerical approaches. The proposed closed-form modeling approach is shown to be more accurate and more convergent than the numerical approach and checked using published experimental data for a fixed helix angle milling tool. For this illustrative case, the percentage error of a proposed closed-form model for the unsegmented (1-segment) tool model relative to the 500-segment model (considered exact) is 0.00% when the error for the equivalent numerical method is 1.90%. Higher accurate applicability of the proposed closed-form models to variable helix tools is also demonstrated for the harmonic case. The percentage error of a proposed closed-form model for the 1-segment tool model relative to the 500-segment model (considered exact) is 0.28% when the error of the equivalent numerical method is 1.05% for this illustrative case. The advantage in terms of generalized applicability and the disadvantage in terms of minor discretization error are highlighted against the backdrop of an existing close-form model for fixed helix angle tools.

Predicting Dissolution Kinetics of Tricalcium Silicate Using Deep Learning and Analytical Models

The dissolution kinetics of Portland cement is a critical factor in controlling the hydration reaction and improving the performance of concrete. Tricalcium silicate (C3S), the primary phase in Portland cement, is known to have complex dissolution mechanisms that involve multiple reactions and changes to particle surfaces. As a result, current analytical models are unable to accurately predict the dissolution kinetics of C3S in various solvents when it is undersaturated with respect to the solvent. This paper employs the deep forest (DF) model to predict the dissolution rate of C3S in the undersaturated solvent. The DF model takes into account several variables, including the measurement method (i.e., reactor connected to inductive coupled plasma spectrometer and flow chamber with vertical scanning interferometry), temperature, and physicochemical properties of solvents. Next, the DF model evaluates the influence of each variable on the dissolution rate of C3S, and this information is used to develop a closed-form analytical model that can predict the dissolution rate of C3S. The coefficients and constant of the analytical model are optimized in two scenarios: generic and alkaline solvents. The results show that both the DF and analytical models are able to produce reliable predictions of the dissolution rate of C3S when it is undersaturated and far from equilibrium.

Predictive ratio CUSUM (PRC): A Bayesian approach in online change point detection of short runs

The online quality monitoring of a process with low volume data is a very challenging task and the attention is most often placed in detecting when some of the underline (unknown) process parameter(s) experience a persistent shift. Self-starting methods, both in the frequentist and the Bayesian domain aim to offer a solution. Adopting the latter perspective, we propose a general closed-form Bayesian scheme, where the testing procedure is built on a memory-based control chart that relies on the cumulative ratios of sequentially updated predictive distributions. The theoretic framework can accommodate any likelihood from the regular exponential family and the use of conjugate analysis allows closed form modeling. Power priors will offer the axiomatic framework to incorporate into the model different sources of information, when available. A simulation study evaluates the performance against competitors and examines aspects of prior sensitivity. Technical details and algorithms are provided as supplementary material.

Modeling of bioprocesses via MINLP-based symbolic regression of S-system formalisms

Mathematical modeling helps guide experiments more effectively, support process monitoring and control tasks, stabilize product quality, increase consumer safety, or ease specific decision-making tasks for subject matter experts. However, constructing accurate process models can be challenging, especially with bioprocesses, due to complex metabolic mechanisms and data scarcity. This work proposes a method for building models combining a mass balance backbone with a canonical kinetic representation, i.e., the S-system formalism. The model structure and parameters that best describe the studied system are automatically identified by solving a mixed-integer nonlinear programming (MINLP) problem. Following an incremental approach, the integration of ordinary differential equations is avoided. Numerical examples show that our method performs similarly to models based on artificial neural networks, outperforming them in some cases while providing an analytical, closed-form model. Such expressions can be more easily interpreted and optimized in existing algebraic modeling systems.

An improved effective medium model for the electrical properties of granular rocks accounting for grain contact

SUMMARY Differential effective medium (DEM) model has been widely employed for the interpretation of electrical survey data. However, the contact of grains that is inevitably happening in reservoir rocks is not taken into account by the DEM model, making the model prediction underestimate the measured formation factor of clean granular rocks. We have developed a modified DEM model by introducing a geometric factor to account for the contact of grains that complicates the pore network and thus deviates the transportation of electrical current. The geometric factor is derived by fitting the measured formation factor from a large published data set of 111 clean sandstone samples, and is found to decrease exponentially with rock porosity. Comparison with laboratory data sets of various artificial and real clean sandstones shows that the modified DEM model improves the modelling results and fits satisfactorily the measured formation factor with varying porosity. The results illustrate the practical applicability of the developed closed-form model for the improved simulation of electrical properties of clean granular rocks, and suggest grain contact as a potential link for the joint elastic-electrical characterization of granular rocks through integrated seismic and electromagnetic surveys.

Connectivity and collision constrained opportunistic routing for emergency communication using UAV

Emergency communication is essential for search and rescue operations in the aftermath of natural disasters. Unmanned Aerial Vehicle (UAV)-assisted networking is emerging as a promising method for establishing emergency communication. UAVs can intelligently self-adjust their positions, communicate while moving at high speeds, and effectively capture and relay disaster site information to a Terrestrial Base Station (TBS). However, data forwarding from the UAVs to TBS is challenging because of the former’s dynamic network topology, high mobility and resource constraints. Designing efficient routing protocols is crucial in the context of these challenges. To the best of our knowledge, none of the previous works have integratively addressed the post-disaster routing concerns like coverage requirements, inter-UAV collision avoidance and reliable multi-hop routing in the absence of trajectory planning. This paper proposes a novel Multi-hop Opportunistic 3D Routing (MO3DR) algorithm for post-disaster data dissemination. The MO3DR algorithm employs coverage and inter-UAV collision constraints for selecting the next forwarding node to maximize the expected progress of data towards the TBS. Simulations validate the numerical results from closed-form analytical models. Results reveal that operating UAVs within the threshold inter-UAV distance meets the coverage and collision constraints while maximizing the expected progress of data towards the TBS.

Closed-form modeling of neuronal spike train statistics using multivariate Hawkes cumulants.

We derive exact analytical expressions for the cumulants of any orders of neuronal membrane potentials driven by spike trains in a multivariate Hawkes process model with excitation and inhibition. Such expressions can be used for the prediction and sensitivity analysis of the statistical behavior of the model over time and to estimate the probability densities of neuronal membrane potentials using Gram-Charlier expansions. Our results are shown to provide a better alternative to Monte Carlo estimates via stochastic simulations and computer codes based on combinatorial recursions are included.

Surface tension of nanoparticle dispersions unravelled by size-dependent non-occupied sites free energy versus adsorption kinetics

The surface tension of dispersions presents many types of behaviours. Although some models, based on classical surface thermodynamics, allow partial interpretation, fundamental understanding is still lacking. This work develops a single analytical physics-based formulation experimentally validated for the surface tension of various pure nanoparticle dispersions, explaining the underlying mechanisms. Against common belief, surface tension increase of dispersions appears not to occur at low but rather at intermediate surface coverage, owed by the relatively large size of nanoparticles with respect to the fluid molecules. Surprisingly, the closed-form model shows that the main responsible mechanism for the various surface tension behaviours is not the surface chemical potential of adsorbed nanoparticles, but rather that of non-occupied sites, triggered and delicately controlled by the nanoparticles ‘at a distance’, introducing the concept of the ‘non-occupancy’ effect. The model finally invites reconsidering surface thermodynamics of dispersions and provides for criteria that allow in a succinct manner to quantitatively classify the various surface tension behaviours.

Closed-form model for curved brittle substrates reinforced with FRP strips

Externally bonded Fiber Reinforced Polymer (FRP) strips have been proved to be effective for strengthening masonry structures. The role played by the bond between composite and substrate is crucial for transferring tensile stresses from masonry to the reinforcing system, thus has become the object of extensive investigation. When the reinforced components are curved, such as arches and vaults, which appear quite commonly in masonry buildings, the influence of the substrate curvature on the bonding cannot be ignored. The debonding mechanism can be studied with a concise model in which the substrate is rigid and the FRP plate is elastic, and the interface where the two are bonded is assumed to lump all the nonlinearities. In this paper, a fully analytical approach for FRP strengthened curved masonry prisms is proposed based on this model, providing closed-form solutions for different geometrical configurations. The interface cohesive law is assumed to be piecewise linear with elastic, softening and residual strength stages. The influence of the normal stress appearing at the interface due to the substrate curvature is considered in the cohesive law for both extrados and intrados strengthening cases. An extensive validation carried out considering both existing experimental results and alternative numerical approaches indicates that the procedure proposed is able to accurately predict the bond strength as well as to reproduce the global bond behavior, requiring few parameters and little calculation effort.

UWB channel modeling and simulation with continuous frequency response

Ultra-wideband (UWB) technology is a prospective technology for high-rate transmission and accurate localization in the future communication systems. State-of-art channel modeling approaches usually divide the UWB channel into several sub-band channels and model them independently. By considering frequency-dependent channel parameters, a novel analytical UWB channel model with continuous frequency response is proposed. The composite effect of all frequency components within the UWB channel on the channel impulse response (CIR) of delay domain is derived based on the continuous channel transfer function (CTF) of frequency domain. On this basis, a closed-form simulation model for UWB channels and geometry-based parameter calculation method are developed, which can guarantee the continuity of channel characteristics on the frequency domain and greatly reduce the simulation complexity. Finally, the proposed method is applied to generate UWB channel with 2 GHz bandwidth at sub-6GHz and millimeter wave (mmWave) bands, respectively. The channel measurements are also carried out to validate the proposed method. The simulated CIR and power gain are shown to be in good agreement with the measurement data. Moreover, the comparison results of power gain and Doppler power spectral density (DPSD) show that the proposed UWB channel model achieves a good balance between the simulation accuracy and efficiency.

Analysis and Data-Based Modeling of the Photochemical Reaction Dynamics of the Induced Singlet Oxygen in Light Therapies.

The macroscopic singlet oxygen (MSO) model for quantifying the light-induced singlet oxygen ( 1O2) always contain a set of nonlinear dynamic equations and therefore are generally difficult to be applied. This work was devoted to analyze and simplify this dynamic model. Firstly, the nonlinearity of the MSO model was analyzed with control theory. The conditions, under which it can be simplified to a linear one, were derived. Secondly, in the case of ample triplet oxygen concentration, a closed-form exact solution of the 1O2 model was further derived, in a nonlinear algebraic form with only four parameters that can be easily fitted to experimental data. Finally, in vitro experiments of anti-fungal light therapies were conducted, where the fungi, Candida albicans, were irradiated respectively by the 385, 405, 415, and 450 nm wavelength light. The singlet oxygen concentration levels in the fungi were measured, and then used to fit the developed models. The parameters of the closed-form exact solution were estimated from both the simulated and the measured experimental data. Based on this model, a functional relationship between the photon energy, fluence rate and singlet oxygen concentration was also established. The fitting accuracy of this model to the data was satisfactory, which therefore demonstrates the effectiveness of the proposed modeling techniques. The results from simulating the closed-form model indicate that the photon energy within the range of either 2.7 ∼ 2.8 eV or 3.0 ∼ 3. 2 eV (388 ∼ 413 nm or 443 ∼ 459 nm in wavelength) is more effective in generating singlet oxygen in the fungi studied in this work. It is the first attempt of applying control theory to analyze the photochemical reaction dynamics of light therapies in terms of their nonlinearity. The proposed modeling techniques also offer opportunities for determining the light dosages in treating fungal infection diseases, especially those on the surface tissues of human body.

Assessing the quality of transmission of lightpaths in multiband C+L networks through Gaussian noise models

In an optical network scenario, wavelength division-multiplexing (WDM) channels are constantly being added and dropped, leading to dynamic traffic variations in the lightpaths. In this work, the impact of the network traffic load and spectral occupancy on the quality of transmission, namely on the normalized nonlinear interference (NLI) power, power transfer due to stimulated Raman scattering (SRS) and optical signal-to-noise ratio (OSNR) of the lightpaths in a C+L multiband optical network is assessed using the recently proposed closed-form interchannel SRS Gaussian noise model (ISRS GN-model). We show that, due to the dynamic traffic behavior, the normalized NLI power can oscillate up to 2 dB in the highest frequency channels due to NLI variations when the tested channels have unequal spacing along the spectrum. For the optimum channel launch power and by increasing the network traffic load, the power transfer between the outer channels can increase up to 5.1 dB due to the SRS effect. With 201 WDM channels, high traffic load and for the optimum channel power, we obtained a maximum OSNR variation along the channel frequencies of only about 0.7 dB. A comparison between the OSNR predictions of the closed-form ISRS GN-model and a closed-form Gaussian noise (GN) model that does not take into account the SRS effect is also performed. In all results obtained, the maximum difference between the OSNR predictions of GN (without SRS) and ISRS GN models is below 0.7 dB at optimum OSNR and maximum C+L band occupancy. For channel launch powers higher than the optimum, the OSNR differences increase up to 3 dB.

Distributed Computation Offloading and Trajectory Optimization in Multi-UAV-Enabled Edge Computing

The Internet of Things (IoT) technology has expanded network space by interconnected devices, which has been widely used in various fields, such as environmental monitoring, object tracking, risk warning, etc. Due to insufficient computing capacity, limited battery life, and unreliable communication environment in IoT, unmanned aerial vehicle (UAV)-enabled edge computing has been recently utilized to provide enhanced coverage and efficient computational support in the scenarios with sparse or unreliable ground infrastructure, such as disaster rescue, emergency response, military fields, etc. However, UAV-enabled edge computing faces many challenges, such as low offloading efficiency, high energy consumption, high complexity, etc. In this article, a distributed computation offloading scheme is proposed to provide computational support to large-scale IoT nodes and optimize the energy efficiency of multiple UAVs. First, to provide accurate and efficient computational support, a real-time intelligent positioning algorithm is designed to obtain the precise location information of IoT nodes. Then, a distributed computation offloading and path planning algorithm is presented, which jointly optimizes the computation offloading of large-scale IoT nodes and trajectory planning of multiple UAVs to reduce the energy consumption of UAVs. Furthermore, we develop a closed-form theoretical analysis model to demonstrate that the algorithm enables a performance guarantee related to energy efficiency. Finally, extensive simulations have been conducted and show that the proposed scheme can greatly improve the system utility and energy efficiency.

In vitro prediction of the lower/upper-critical biofluid flow choking index and in vivo demonstration of flow choking in the stenosis artery of the animal with air embolism

<i>In vitro</i> prediction of the lower/upper-critical biofluid flow choking index and <i>in vivo</i> demonstration of flow choking in the stenosis artery of the animal with air embolism

Optimal Model Placement and Online Model Splitting for Device-Edge Co-Inference

Device-edge co-inference opens up new possibilities for resource-constrained wireless devices (WDs) to execute deep neural network (DNN)-based applications with heavy computation workloads. In particular, the WD executes the first few layers of the DNN and sends the intermediate features to the edge server that processes the remaining layers of the DNN. By adapting the model splitting decision, there exists a tradeoff between local computation cost and communication overhead. In practice, the DNN model is re-trained and updated periodically at the edge server. Once the DNN parameters are regenerated, part of the updated model must be placed at the WD to facilitate on-device inference. In this paper, we study the joint optimization of the model placement and online model splitting decisions to minimize the energy-and-time cost of device-edge co-inference in presence of wireless channel fading. The problem is challenging because the model placement and model splitting decisions are strongly coupled, while involving two different time scales. We first tackle online model splitting by formulating an optimal stopping problem, where the finite horizon of the problem is determined by the model placement decision. In addition to deriving the optimal model splitting rule based on backward induction, we further investigate a simple one-stage look-ahead rule, for which we are able to obtain analytical expressions of the model splitting decision. The analysis is useful for us to efficiently optimize the model placement decision in a larger time scale. In particular, we obtain a closed-form model placement solution for the fully-connected multilayer perceptron with equal neurons. Simulation results validate the superior performance of the joint optimal model placement and splitting with various DNN structures.

Simple analytical models and analysis of bistable vibration energy harvesters

In order to scavenge the energy of ambient vibrations, bistable vibration energy harvesters constitute a promising solution due to their large frequency bandwidth. Because of their complex dynamics, simple models that easily explain and predict the behavior of such harvesters are missing from the literature. To tackle this issue, this paper derives simple analytical closed-form models of the characteristics of bistable energy harvesters (e.g. power-frequency response, displacement response, cut-off frequency of the interwell motion) by mean of truncated harmonic balance methods. Measurements on a bistable piezoelectric energy harvester illustrate that the proposed analytical models allow the prediction of the mechanical displacement and harvested power, with a relative error below 10%. From these models, the influences of various parameters such as the inertial mass, the acceleration amplitude, the electromechanical coupling, and the resistive load, are derived, analyzed and discussed. The proposed models and analysis give an intuitive understanding of the dynamics of bistable vibration energy harvesters, and can be exploited for their design and optimization.

A new closed-form two-stage budgeting-based multiple discrete-continuous model

In this paper, we propose a multiple discrete-continuous (MDC) model approach that (a) does not need the total budget to be observed or predetermined, (b) allows for any finite or not-so-finite budget over the entire set of inside and outside goods, and (c) preserves a strong endogenous utility-theoretic link between inside good consumptions and the budget allocated to the inside goods (that is, to the product group of interest). We show that our proposed model, including a fractional MDC model at the lower level linked up to a Tobit model for the budget allocation to the inside goods, is strictly consistent with a two-stage budgeting utility theoretic structure. As importantly, by using reverse Gumbel distributional assumptions for the stochastic terms in the model system, we derive an incredibly simple closed-form model that, to our knowledge, is a first of its kind in the econometric literature. In doing so, we formally introduce a new distribution, which we label as the minLogistic distribution, to the statistical literature, and derive the properties of the distribution that is then used in the forecasting stage of the proposed model. An application of the proposed model to investigate the household vehicle fleet composition and usage demonstrates its potential relative to an unlinked and exogenously developed budget for the inside goods. The proposed model has the potential to open up a whole new world of MDC applications in general, and particularly for those cases with an unobserved total budget over the inside and outside goods.

Local postbuckling of omega-stringer-stiffened composite panels

In order to utilize the full lightweight potential of thin-walled stringer-stiffened composite panels, a new closed-form analytical solution for the buckling and postbuckling of omega-stringer-stiffened composite panels is introduced. Because of the high computational efficiency, it allows the analysis of the early postbuckling behaviour in the framework of preliminary design. The solution is derived based on the principle of the minimum of the total elastic potential. A suitable set of buckling shape functions models the buckling pattern and imperfection. The load is applied via prescribed displacements. The results of the closed-form model are compared and verified with finite element simulations and the implementation of another closed-form model found in the literature. An exemplary cross-ply laminated panel under uniaxial compression is investigated. The results show that the proposed model achieves excellent general agreement in the practically most relevant design space.

Novel extended C-m models of flow stress for accurate mechanical and metallurgical calculations and comparison with traditional flow models

Here, we developed novel extended piecewise bilinear power law (C-m) models to describe flow stresses under broad ranges of strain, strain rate, and temperature for mechanical and metallurgical calculations during metal forming at elevated temperatures. The traditional C-m model is improved upon by formulating the material parameters C and m, defined at sample strains and temperatures as functions of the strain rate. The coefficients are described as a linear combination of the basis functions defined in piecewise patches of the sample strain and temperature domain. A comparison with traditional closed-form function flow models revealed that our approach using the extended piecewise bilinear C-m model is superior in terms of accuracy, ease of use, and adaptability; additionally, the extended C-m model was applicable to numerical analysis of mechanical, metallurgical, and microstructural problems. Moreover, metallurgy-related values can be calculated directly from the flow stress information. Although the proposed model was developed for materials at elevated temperatures, it can be applied over a broad temperature range.

Symbolic Deep Learning for Structural System Identification

Closed-form model expression is commonly required for parametric data assimilation (e.g., model updating, damage quantification, and so on). However, epistemic bias due to fixing the model class is a challenging issue for structural identification. Furthermore, it is sometimes hard to derive explicit expressions for structural mechanisms such as damping and nonlinear restoring forces. Although existing model class selection methods are beneficial to reduce the model uncertainty, the primary issue lies in their limitation to a small number of predefined model choices. We propose a symbolic deep learning framework that alleviates the constraint of fixed model classes and lets the data more flexibly determine the model type and discover the symbolic invariance of the structural system. A design principle for symbolic neural networks has been developed to leverage domain knowledge and translate data to flexibly symbolic equations of motion with a good predictive capacity for new data. A two-stage model selection strategy is proposed to conduct adaptive pruning on network and equation levels by balancing the model sparsity and the goodness of fit. The proposed method’s expressive strengths and weaknesses have been analyzed in several numerical case studies, including systems with nonlinear damping, restoring force, and chaotic behavior. Results from an experimental case study revealed the potential of the proposed method for flexibly interpreting hidden mechanisms for real-world applications. Finally, we discuss necessary improvements to transfer this computational method for practical applications.