Abstract Uncertainty is fundamental in modern power systems, where renewable generation and fluctuating demand make stochastic optimization indispensable. In stochastic optimization, chance constraints enable the representation of uncertainty in renewable energy sources that affect the dispatch and commitment of bulk generation. This is commonly known as the chance-constrained unit commitment problem (UCP), which rapidly becomes computationally challenging as the number of scenarios grows. Quantum computing has been proposed as a potential route to overcome such scaling barriers. In this work, we evaluate the applicability of quantum annealing platforms to the chance-constrained UCP. Focusing on a scenario approximation, we reformulate the problem as a mixed-integer linear program (MILP) and solve it using D-Wave’s hybrid quantum–classical solver alongside the classical solver Gurobi. The hybrid solver proves competitive under strict runtime limits for large scenario sets (15,000 in our experiments), while Gurobi remains superior on smaller cases. QUBO reformulations have also been tested, but current annealers cannot accommodate stochastic UCPs due to hardware limits, and deterministic cases suffer from embedding overhead. Our study delineates where chance-constrained UCPs can already be addressed with hybrid quantum–classical methods, and where current quantum annealers remain fundamentally limited.
In industry, defect detection is crucial for quality control. Non-destructive testing (NDT) methods are preferred as they do not influence the functionality of the object while inspecting. Automated defect detection is a growing field of research. In particular, machine learning approaches show promising results. To provide training data in sufficient amount and quality, synthetic data can be used. Rule-based approaches enable synthetic data generation in a controllable environment. Therefore, a digital twin of the inspected object including synthetic defects is needed. We present parametric methods to model 3d mesh objects of various typical defects in casting that can then be added to the object geometry to obtain synthetic defective parts. Synthetic data resembling the real inspection data can then be created by using a physically based Monte Carlo simulation of the respective testing method. Using our defect models, a variable and arbitrarily large synthetic data set can be generated with the possibility to include rarely occurring defects in sufficient quantity. Pixel-perfect annotation can be created in parallel.
Effective multi-attribute group decision-making (MAGDM) in complex scenarios often suffers from inherent challenges, which are unknown expert and attribute weights, and inherent information uncertainty. To overcome these limitations, this paper proposes a CRITIC-WASPAS method for solving MAGDM problems with unknown experts and attribute weights. The method integrates the Yager operator, expert weights, criteria importance through criteria correlation (CRITIC), and the weighted aggregate sum product assessment (WASPAS) decision-making method under interval-valued q-rung orthopair fuzzy sets (IVq-ROFS). Firstly, we extend the Yager weighted average operator (IVq-ROFYWA) and the Yager weighted geometric average operator (IVq-ROFYWG) under the IVq-ROFS framework. Secondly, we derive expert weights for different alternatives to avoid the deficiency of an overall decision-making perspective and attribute weights based on CRITIC under IVq-ROFS. Thirdly, the integrated CRITIC-WASPAS method based on the WASPAS method is introduced. Finally, two distinct domain cases are implemented to illustrate the effectiveness and broad applicability of the proposed CRITIC-WASPAS method. The implementation results across both domains are consistent with experts’ opinions, and the comparison and analysis results show that the CRITIC-WASPAS method is more effective and feasible.
Viscoelastic fluids have several applications in industry and technology, which has attracted a lot of investigation into their mathematical models. This paper presents the first-ever verifiable convergent second-order method, with complete theoretical analysis, for one-dimensional viscoelastic flow model. Existing studies have focused on first-order methods and without theoretical analysis. Here, the model is transformed into a form that involves the time derivative of spatial derivative. The convection and diffusion terms are discretized together by splitting the convection term into two parts and scaling with the diffusion coefficient, then combined with different terms of the diffusion approximation. The high-degree term is discretized with central difference spatial scheme and implicit-explicit time integrator, while the unsteady and external source terms are discretized implicitly. This yielded a positivity preserving numerical scheme which is second order accurate. We pose and prove several Lemmas and Theorems to establish consistency, boundedness and convergence of the method. Numerical experiments are then provided to verify the theoretical results, giving full confidence in the method. The results of this study provide a very useful tool for fluid dynamics simulations. The implication is that Researchers can now simulate 1D viscoelastic fluids, reliably, and without compromising some of the most important physics of the problem.
The implementation of thermally sprayed components in steel manufacturing presents challenges for production and plant maintenance. While enhancing performance through specialized surface properties, these components may encounter difficulties in meeting modified requirements due to standardization in the refurbishment process. This article proposes updating the established coating process for thermally spray coated components for steel manufacturing (TCCSM) by integrating real-time data analytics and predictive quality management. Two essential components–the data aggregator and the quality predictor–are designed through continuous process monitoring and the application of data-driven methodologies to meet the dynamic demands of the evolving steel landscape. The quality predictor is powered by the simple and effective multiple kernel learning strategy with the goal of realizing predictive quality. The data aggregator, designed with sensors, flow meters, and intelligent data processing for the thermal spray coating process, is proposed to facilitate real-time analytics. The performance of this combination was verified using small-scale tests that enabled not only the accurate prediction of coating quality based on the collected data but also proactive notification to the operator as soon as significant deviations are identified.
Achieving both high quality and cost-efficiency are two critical yet often conflicting objectives in manufacturing and maintenance processes. Quality standards vary depending on the specific application, while cost-effectiveness remains a constant priority. These competing objectives lead to multi-objective optimization problems, where algorithms are employed to identify Pareto-optimal solutions - compromise points which provide decision-makers with feasible parameter settings. The successful application of such optimization algorithms relies on the ability to model the underlying physical system, which is typically complex, through either physical or data-driven approaches, and to represent it mathematically. This paper applies three multi-objective optimization algorithms to determine optimal process parameters for high-velocity oxygen fuel (HVOF) thermal spraying. Their ability to enhance coating performance while maintaining process efficiency is systematically evaluated, considering practical constraints and industrial feasibility. Practical validation trials are conducted to verify the approximate theoretical solutions generated by the algorithms, ensuring their applicability and reliability in real-world scenarios. By exploring the performance of these diverse algorithms in an industrial setting, this study offers insights into their practical applicability, guiding both researchers and practitioners in enhancing process efficiency and product quality in the coating industry.
The micromachined beam fixed at both ends is an essential component of electrostatically-actuated Micro-Electro-Mechanical System (MEMS) based switches. The pull-in voltage and the response time are some of the most important parameters of this system. With physics-based approaches, the challenge of modelling and producing simplified representations comes from the strong nonlinearities involved and the interaction of more than one physical field. Data-driven methods based on recurrent neural networks can be used to obtain simplified, yet accurate models for predicting the minimum gap dynamics for different applied voltages. However, the solution of these black-box models lacks physical connection and can contradict the physical laws. Here, we propose using a hybrid approach, namely a physics-informed machine learning model, and we show the benefits of incorporating initial and boundary conditions into the training process in terms of accuracy without compromising the learning and simulation times. Our neural network models incorporating physics-based constraints are ten times more accurate than the classical neural network architectures for the same problem.
The Digital Twin, a virtual representation of a physical object that mimics its structure and behavior to inform decisions and optimize operational efficiency, is an established paradigm in industry. While Modelling, Simulation, and Optimization have been a standard practice in industry since long, the complementary role of models and data as well as a holistic and life cycle spanning approach distinguishes the Digital Twin paradigm. However, albeit nearly every industry is highlighting the potential and strategic importance of Digital Twins, they are by far not at a level of industrial practice as publicity suggests. A major hurdle is the effort associated with creating actionable and impactful Digital Twins. The reasons are multi-fold but novel algorithms and mathematical concepts will be key to overcome many of these. Within this article, we review the concept of the Digital Twin, major challenges of fostering its adoption, and highlight how research in Applied and Industrial Mathematics is key to address corresponding roadblocks.
The absence of a gap in pristine graphene is considered as hampering the possibility to realize an efficient field effect transistor (hereafter GFET). Nevertheless, in (Nastasi and Romano in Commun. Nonlinear Sci. Numer. Simul. 87:105300, 2020; Nastasi and Romano in IEEE Trans. Electron. Devices 68:4729–4734, 2021) a peculiar geometry has been proposed which seems to realize a robust GFET, at least according to the simulation results. One crucial aspect is the shape of the electrostatic potential. In (Nastasi and Romano in Commun. Nonlinear Sci. Numer. Simul. 87:105300, 2020; Nastasi and Romano in IEEE Trans. Electron. Devices 68:4729–4734, 2021) the electrostatic potential is simulated by distributing the charge in a volume surrounding the graphene sheet. In this work, we want to test the robustness of the GFET model proposed in (Nastasi and Romano in IEEE Trans Electron Devices 68:4729–4734, 2021). For this purpose we solve the Poisson equation by modeling the charge distribution in a different way, considering the graphene layer as a charge discontinuity surface and imposing the continuity of the electric displacement field. The two approaches give comparable results and furnish a further confirmation that the GFET in (Nastasi and Romano in IEEE Trans Electron Devices 68:4729–4734, 2021) does not stem from a spurious discretization of the Poisson equation for the electrostatic potential.
Abstract The main burden in treating human immunodeficiency virus (HIV) infection currently, is the side effects of the antiretroviral therapy (ART) used, because each treatment is toxic to the liver. This study uses optimal control theory applied to a mathematical model that describes the dynamics of HIV infection in the liver. The optimal controls are presented as therapy efficacy of reverse transcriptase inhibitors (RTIs), integrase inhibitors (INs) and protease inhibitors (PIs). An objective function is defined with an aim to investigate the optimal control strategy that minimises toxicity, viral load and cost of first-line and second-line HIV regimen. Results indicate that, in the first-line regimen with INs, a patient has to take medication for at least 98% of the treatment time and the regimen should be close to 100% efficacious regardless of the intervention cost. For second-line regimen, the period of drug administration of PIs largely depends on the weight constants. Inclusion of INs in the first-line regimen yields better HIV DNA suppression, as they are more efficacious than NRTIs. Of all drugs studied, nevirapine is highly efficacious but most toxic. The study recommends routine transaminase tests because results indicate liver enzyme elevation even with very low viral load. Numerical results with pharmacokinetic parameters further indicate an increase in HIV load at initiation of therapy, due to viral redistribution in plasma.
A stochastic 3D modeling approach for the nanoporous binder-conductive additive phase in hierarchically structured cathodes of lithium-ion batteries is presented. The binder-conductive additive phase of these electrodes consists of carbon black, polyvinylidene difluoride binder and graphite particles. For its stochastic 3D modeling, a three-step procedure based on methods from stochastic geometry is used. First, the graphite particles are described by a Boolean model with ellipsoidal grains. Second, the mixture of carbon black and binder is modeled by an excursion set of a Gaussian random field in the complement of the graphite particles. Third, large pore regions within the mixture of carbon black and binder are described by a Boolean model with spherical grains. The model parameters are calibrated to 3D image data of cathodes in lithium-ion batteries acquired by focused ion beam scanning electron microscopy. Subsequently, model validation is performed by comparing model realizations with measured image data in terms of various morphological descriptors that are not used for model fitting. Finally, we use the stochastic 3D model for predictive simulations, where we generate virtual, yet realistic, image data of nanoporous binder-conductive additives with varying amounts of graphite particles. Based on these virtual nanostructures, we can investigate structure-property relationships. In particular, we quantitatively study the influence of graphite particles on effective transport properties in the nanoporous binder-conductive additive phase, which have a crucial impact on electrochemical processes in the cathode and thus on the performance of battery cells.
In the domain of rotating machinery, bearings are vulnerable to different mechanical faults, including ball, inner, and outer race faults. Various techniques can be used in condition-based monitoring, from classical signal analysis to deep learning methods. Based on the complex working conditions of rotary machines, multivariate statistical process control charts such as Hotelling's T^2 and Squared Prediction Error are useful for providing early warnings. However, these methods are rarely applied to condition monitoring of rotating machinery due to the univariate nature of the datasets. In the present paper, we propose a multivariate statistical process control-based fault detection method that utilizes multivariate data composed of Fourier transform features extracted for fixed-time batches. Our approach makes use of the multidimensional nature of Fourier transform characteristics, which record more detailed information about the machine's status, in an effort to enhance early defect detection and diagnosis. Experiments with varying vibration measurement locations (Fan End, Drive End), fault types (ball, inner, and outer race faults), and motor loads (0-3 horsepower) are used to validate the suggested approach. The outcomes illustrate our method's effectiveness in fault detection and point to possible broader uses in industrial maintenance.
Low-discrepancy points (also called Quasi-Monte Carlo points) are deterministically and cleverly chosen point sets in the unit cube, which provide an approximation of the uniform distribution. We explore two methods based on such low-discrepancy points to reduce large data sets in order to train neural networks. The first one is the method of Dick and Feischl (J Complex 67:101587, 2021), which relies on digital nets and an averaging procedure. Motivated by our experimental findings, we construct a second method, which again uses digital nets, but Voronoi clustering instead of averaging. Both methods are compared to the supercompress approach of (Stat Anal Data Min ASA Data Sci J 14:217–229, 2021), which is a variant of the K-means clustering algorithm. The comparison is done in terms of the compression error for different objective functions and the accuracy of the training of a neural network.
We propose numerical algorithms for recovering parameters in eigenvalue problems for linear elasticity of transversely isotropic materials. Specifically, the algorithms are used to recover the elastic constants of a rotor core. Numerical tests show that in the noiseless setup, two pairs of bending modes are sufficient for recovering one to four parameters accurately. To recover all five parameters that govern the elastic properties of induction motors accurately, we require three pairs of bending modes and one torsional mode. Moreover, we study the stability of the inversion method against multiplicative noise; for tests in which the data contained multiplicative noise of at most 1%, we find that all parameters can be recovered with an error less than 10%.
For the simulation-based design of fiber melt spinning processes, the accurate modeling of the processed polymer with regard to its material behavior is crucial. In this work, we develop a high-speed elongational rheometer for Carreau-type materials, making use of process simulations and fiber diameter measurements. The procedure is based on a unified formulation of the fiber spinning model for all material types (Newtonian and quasi-Newtonian), whose material laws are strictly monotone in the strain rate. The parametrically described material law for the elongational viscosity implies a nonlinear optimization problem for the parameter identification, for which we propose an efficient, robust gradient-based method. The work can be understood as a proof of concept, a generalization to other, more complex materials is possible.
In the automotive industry, the absorption coefficient of a porous material layer is usually measured in an alpha cabin, a reverberant chamber of reduced dimensions where the operational frequency range is limited and the absorbent sample size is typically small. Those characteristics are well adapted to the requirements of automotive acoustics but far from the standard reverberant chambers used in building acoustics which ensures the conditions to perform measurements under a diffusive field. Since there are no standard norms to measure the absorption coefficient under non-diffusive fields, this work proposes a time-harmonic/time-domain hybrid approach to compute the absorption coefficient in alpha cabins. For this purpose, pointwise numerical predictions of the sound pressure level decay rate are used to calculate the absorption coefficient associated with a porous sample. To generate the pressure field acting inside the alpha cabin and, subsequently, approximate its decay rate, time-harmonic numerical simulations at a fixed frequency and a full time-dependent discretization of the wave problem have been considered. The proposed methodology is validated in a manufactured scenario where the exact solution is known in closed form. Finally, a realistic three-dimensional alpha cabin is deemed to predict the diffuse field absorption coefficient from the computed reverberation times using the proposed hybrid approach and the heuristic Sabine and Millington formulas.
The possibility to use diurnal temperature variations for nondestructive monitoring of growing tubers is investigated by numerically simulating the data collected with a grid of passive thermal sensors placed in the ground and sampled at regular intervals. A qualitative linear imaging algorithm that produces an approximate projected view of the tubers is proposed and an effective inversion method is applied to recover the volume fraction of tubers. In particular, it is shown that a correlation-based cost functional outperforms the usual least-squares metric, although, requiring additional steps to deal with the non-uniqueness of the solution.
AbstractElectric Circuit Element (ECE) boundary conditions (BC) defined for full-wave (FW) electromagnetic field allow a natural coupling between field devices and electric circuits. The novelty of this paper is that it shows how ECE BC can be implemented into a 3D-finite element method (FEM), when using A, a magnetic vector potential and φ, a scalar potential. Weak formulations are described and implemented in the free environment Open Numerical Engineering LABoratory(onelab). The validation is carried out on 3D examples solved both in frequency (FD) and time domain (TD), for FW formulations in potentials, as well as for corresponding Darwin approximations of Electromagneto-Quasistatic (EMQS) models. Results are compared with those obtained with a formulation in EV, where E is the electric field inside the domain and V is a scalar potential defined solely on the boundary. The results show that: 1) the use of potentials has some advantages over the EV formulation in TD only; 2) excitation type matters, the voltage excitation, here essential in FEM, proved to be the most robust one for the considered examples: a coplanar waveguide and a spiral inductor.
In this paper, we explore the effectiveness of strategies for mitigating urban warming from a numerical simulation standpoint. To achieve this, a reinterpretation of porosity on an urban context allows us to identify the urban surface covered by streets, and the urban surface covered by buildings as the fluid and solid phases of an urban-porous media, respectively. Using a Gaussian distribution we define the urban porosity at all points within an urban zone. Once the urban porosity is defined, a Darcy-Brinkman-Forchheimer type model is coupled with a thermal exchange model to obtain the wind field, and the air temperature. The convective nature of the model, and the porosity gradients lead us to use stabilized finite element methods in order to avoid the appearance of spurious oscillations in numerical solutions: we use a pressure stabilizer for the Darcy-Brinkman-Forchheimer model and a least-squares stabilizer for the thermal exchange model. Numerical experiments were conducted on a domain modeled after the Metropolitan Zone of Guadalajara City, Mexico, to evaluate strategies such as white roofs, concrete-paved streets instead of asphalt, and large urban parks. The results reveal significant differences in urban temperatures, which in turn helps to alleviate thermal stress for city inhabitants.
While interactive simulations have been mostly limited to Computer Graphics applications, new generations of Graphics Processing Units (GPUs) allow the realization of industrial-grade interactive 3D physics simulations. By combining an immersed boundary method with efficient GPU-based MINRES and CG solvers using a GPU-based geometric multigrid preconditioner, we demonstrate a fast industrial 3D computational mechanics solver. The various implementation aspects - specifically how they differ from similar concepts used in the Computer Graphics community - are discussed in detail. The proposed concept opens up new classes of industrial simulation applications allowing a democratization beyond today’s expert users, from designer centric simulation to operational and service decisions based on 3D simulations. To support this, we provide various benchmark cases including a real-world study of a simulation-based service decision for a damaged gear-box mount.
