Application Of Surrogate Models Research Articles

Application of a surrogate model for condition monitoring of a digital twin gas turbine

Condition monitoring technology plays a crucial role in ensuring the reliable operation of gas turbines. Digital twin has propelled condition monitoring research into a new phase. This paper established a surrogate model of gas turbines for condition monitoring based on Markov-projection approximation subspace tracking. Furthermore, it explores the application of surrogate model in developing digital twin for gas turbines. The study initially establishes a Markov matrix and acquires an observation vector, utilizing the framework of the linear model. Utilizing real-time measurement data of gas turbine, the signal subspace of the observation vector autocorrelation matrix is updated through the projection approximation subspace tracking. By aligning this signal subspace with the generalized observability matrix, the identification results of the surrogate model parameters are obtained online. Furthermore, a variable weight projection approximation subspace tracking method has been proposed to enhance the algorithm robustness. Simulation and real experiment demonstrate that the surrogate model output effectively tracks the real-time changes in gas turbine measurement data. When faults and degradation arise, condition monitoring can be achieved by analyzing the evolution of model parameters to obtain feedback information from the gas turbine. The proposed method maintains its robustness in the presence of impulsive noise. These features offer a novel approach for the development of gas turbine digital twin.

AsMODiTS: An application of surrogate models to optimize Time Series symbolic discretization through archive-based training set update strategy

The enhanced multi-objective symbolic discretization for time series (eMODiTS) uses an evolutionary process to identify the appropriate discretization scheme in the Time Series Classification (TSC) task. It discretizes using a unique alphabet cut for each word segment. However, this kind of scheme has a higher computational cost. Therefore, this study implemented surrogate models to minimize this cost. The general procedure is summarized below.•The K-nearest neighbor for regression, the support vector regression model, and the Ra- dial Basis Functions neural networks were implemented as surrogate models to estimate the objective values of eMODiTS, including the discretization process.•An archive-based update strategy was introduced to maintain diversity in the training set.•Finally, the model update process uses a hybrid (fixed and dynamic) approach for the surrogate model's evolution control.

Stochastic emulation with enhanced partial‐ and no‐replication strategies for seismic response distribution estimation

AbstractModern performance earthquake engineering practices frequently require a large number of time‐consuming non‐linear time‐history simulations to appropriately address excitation and structural uncertainties when estimating engineering demand parameter (EDP) distributions. Surrogate modeling techniques have emerged as an attractive tool for alleviating such high computational burden in similar engineering problems. A key challenge for the application of surrogate models in earthquake engineering context relates to the aleatoric variability associated with the seismic hazard. This variability is typically expressed as high‐dimensional or non‐parametric uncertainty, and so cannot be easily incorporated within standard surrogate modeling frameworks. Rather, a surrogate modeling approach that can directly approximate the full distribution of the response output is warranted for this application. This approach needs to additionally address the fact that the response variability may change as input parameter changes, yielding a heteroscedastic behavior. Stochastic emulation techniques have emerged as a viable solution to accurately capture aleatoric uncertainties in similar contexts, and recent work by the second author has established a framework to accommodate this for earthquake engineering applications, using Gaussian Process (GP) regression to predict the EDP response distribution. The established formulation requires for a portion of the training samples the replication of simulations for different descriptions of the aleatoric uncertainty. In particular, the replicated samples are used to build a secondary GP model to predict the heteroscedastic characteristics, and these predictions are then used to formulate the primary GP that produces the full EDP distribution. This practice, however, has two downsides: it always requires minimum replications when training the secondary GP, and the information from the non‐replicated samples is utilized only for the primary GP. This research adopts an alternative stochastic GP formulation that can address both limitations. To this end, the secondary GP is trained by measuring the square of sample deviations from the mean instead of the crude sample variances. To establish the primitive mean estimates, another auxiliary GP is introduced. This way, information from all replicated and non‐replicated samples is fully leveraged for estimating both the EDP distribution and the underlying heteroscedastic behavior, while formulation accommodates an implementation using no replications. The case study examples using three different stochastic ground motion models demonstrate that the proposed approach can address both aforementioned challenges.

Optimal operation of a natural gas sweetening plant

The most common method of removing acid gases from natural gas is through the use of solvent-based gas sweetening plants, which are energy-intensive. The present study aims to establish a plant-wide structure to operate natural gas sweetening plants optimally. Thus, a steady-state simulation of the Khangiran plant was carried out, and a 17% reduction in energy usage was achieved as a result of the optimization by the application of surrogate models. The self-optimizing method was applied to find the best set of controlled variables (CVs). There was found one unconstrained degree of freedom (DOF). The best CV for the remaining DOF was found to be the top stage temperature of the regenerator. Aspen Plus Dynamics was used to examine the performance of the proposed control structure utilizing simple traditional PIDs and compare it to modern feedback and feedforward MPCs.

A novel hybrid adaptive framework for support vector machine-based reliability analysis: A comparative study

This study presents an innovative hybrid Adaptive Support Vector Machine - Monte Carlo Simulation (ASVM-MCS) framework for reliability analysis in complex engineering structures. These structures often involve highly nonlinear implicit functions, making traditional gradient-based first or second order reliability algorithms and Monte Carlo Simulation (MCS) time-consuming. The application of surrogate models has proven effective in addressing computational challenges associated with a large number of simulations. Support Vector Machine (SVM), as an emerging machine learning method suitable for small-sample scenarios, offers a well-established theoretical foundation and presents an effective model substitution approach for reliability analysis in engineering structures. However, the existing literature lacks a comprehensive and thorough comparative analysis of SVM's hybrid adaptive modeling approach, encompassing initial sampling methods and learning functions, with regards to both computational efficiency and accuracy. Additionally, there is a gap in adaptive modeling methods capable of accommodating diverse types of input uncertainty, the nonlinearity of limit state functions, and various application scenarios. In response to these gaps, this article introduces the ASVM-MCS framework, which addresses these challenges by considering different types of input variables and various failure modes. Moreover, this study provides a comprehensive evaluation of the ASVM-MCS framework's performance, including its initial sampling methods and learning functions, across a range of application scenarios, such as scenarios involving only random variables, mixed variables, and the reliability of series-parallel systems.

Kriging, Polynomial Chaos Expansion, and Low-Rank Approximations in Material Science and Big Data Analytics.

In material science and engineering, the estimation of material properties and their failure modes is associated with physical experiments followed by modeling and optimization. However, proper optimization is challenging and computationally expensive. The main reason is the highly nonlinear behavior of brittle materials such as concrete. In this study, the application of surrogate models to predict the mechanical characteristics of concrete is investigated. Specifically, meta-models such as polynomial chaos expansion, Kriging, and canonical low-rank approximation are used for predicting the compressive strength of two different types of concrete (collected from experimental data in the literature). Various assumptions in surrogate models are examined, and the accuracy of each one is evaluated for the problem at hand. Finally, the optimal solution is provided. This study paves the road for other applications of surrogate models in material science and engineering.

Approaches for optimizing surrogate models considering uncertain parameters

AbstractSurrogate models are a common tool to perform expensive optimization or uncertainty analysis in a cost‐effective way. The structure and the application of surrogate models is well known, but there is still potential for improvement. The structure of the surrogate model can be divided into three parts, which can be considered separately. The sampling plan, the black box and the selection of the model itself. The optimization of the surrogate models in the sampling plan and the black box is presented on the basis of two case studies. In the sampling plans, the example of the FOSS method is used to show how sampling points are found for an optimized uncertainty analysis with a low number of sampling points. It is taken into account that the result space is not uniformly relevant for the uncertainty consideration with fuzzy parameters. If the black box is a problem from mechanics, known information can be used for an optimized surrogate modeling. For a Finite‐Element‐Method (FEM) black box, it makes sense to consider the maximum possible number of sampling points and maximum accuracy of the FEM‐black box with regard to the surrogate modeling. As the case study shows, a reduction of the accuracy in the FEM calculation, by using a lower mesh density, can lead to an increasing accuracy of the surrogate model.

Efficient optimization design method of jacket structures for offshore wind turbines

With the gradual implementation of offshore wind energy production, the future tendency is to expand into the deeper water. The jacket foundations will take the place of the present monopile foundations when the water depth increases. The foundations account for the majority of the construction cost for offshore wind farms, and the structural optimization of jackets will bring lucrative economic benefits. Structural optimization is a complex iterative process that requires huge computing costs. Therefore, this paper proposes a structural optimization method based on surrogate models to solve this problem effectively and swiftly obtain optimized design schemes of lightweight jackets for offshore wind turbines. The structural responses of jacket wind turbine systems under the equivalent static extreme loads with a recurrence period of 50 years are mainly considered in structural optimization design, and the key optimization variables of jackets are determined by parameter sensitivity analysis. The finite element models of jackets are transformed into surrogate models, and the genetic algorithm is employed to optimize the surrogate models directly. The optimized jackets are additionally verified through coupled dynamic analysis, besides, buckling strength and fatigue life are also checked. And local refined optimizations are carried out for the failure members. According to the optimized design schemes of lightweight jackets for 30 m, 50 m and 70 m water depths, it is demonstrated that the structural optimization design method is adequate and efficient for jackets of wind turbines. Parameter sensitivity analysis can cut the number of optimization variables in half to improve the optimization efficiency. Furthermore, the application of surrogate models can significantly speed up the optimization process by saving about 98.61% of the original time consumed. The optimization design method of the jackets for offshore wind turbines proposed in this paper is suitable for practical engineering, with high precision and efficiency.

Application of surrogate models to stability analysis and transition prediction in hypersonic flows

To increase the efficiency and robustness of stability-based transition prediction in flow simulations, simplified methods are introduced to substitute direct stability analyses for rapid disturbance growth prediction. For low-speed boundary layers, these methods are mainly established based on self-similar assumptions, which are not applicable to non-similar boundary layers in hypersonic flows. The objective of this article is to investigate the application of surrogate models to stability analysis of non-similar flows over blunt cones, focused on parameterization of boundary-layer (BL) profiles. Firstly, correlations between BL edge and profile parameters are analyzed, along with self-similar flow parameters and discrete points on BL profiles, which present four groups of BL characteristic parameters. Secondly, using these parameters as inputs, surrogate models are built for disturbance growth prediction over an MF-1 blunt cone. Results show that, surrogate models using four BL edge parameters and a BL shape factor {Ue, Te, ρe, ηe, H12} for stability analysis can achieve comparable accuracy with those using 16 discrete BL profile parameters, which are more precise than those using merely self-similar parameters or BL edge parameters. Thirdly, the established surrogate models are validated by stability analysis and transition prediction over the MF-1 blunt cone in flight experiments at the instants of t = 17 s ~ 22 s. Compared with direct linear stability analyses, the mean relative error of predicted disturbance growth rates by surrogate models is 8.0% and the maximum relative error of N factor envelopes is 6.6%, which indicates feasible applications of surrogate models to stability analysis and transition prediction of non-similar boundary layers in hypersonic flows.

Application of Surrogate Models to the Multiphysics Sizing of Permanent Magnet Synchronous Motors

The application of surrogate models in engineering design is becoming popular due to their mimicking capabilities. In the design of electric motor drives for example, where a control-drive circuit is connected directly to the electric motor, the finite element simulations of the integrated motor drive system can be time-consuming. A complete motor simulation can run into several hours, if not days. Therefore, the main contribution of this article resides in the effort to address the computational burden associated with the design process by replacing the finite element models with surrogate models to achieve a faster design process. Briefly, the procedure involves filling the design space with multiple motor geometries created from an 8-pole 12-slot surface-mounted permanent magnet (SPM) synchronous motor. Then, a multiphysics performance evaluation is performed over the design space for different switching frequencies over a range of dc bus voltages. The design variables of the motor, the inverter, and the calculated performance objectives are used to train a collection of surrogate models to obtain the objective functions that could potentially be used as possible replacements for the finite element models in order to reduce the solution time.

Reduced-cost two-level surrogate antenna modeling using domain confinement and response features

Electromagnetic (EM) simulation tools have become indispensable in the design of contemporary antennas. Still, the major setback of EM-driven design is the associated computational overhead. This is because a single full-wave simulation may take from dozens of seconds up to several hours, thus, the cost of solving design tasks that involve multiple EM analyses may turn unmanageable. This is where faster system representations (surrogates) come into play. Replacing expensive EM-based evaluations by cheap yet accurate metamodels seems to be an attractive solution. Still, in antenna design, application of surrogate models is hindered by the curse of dimensionality. A practical workaround has been offered by the recently reported reference-design-free constrained modeling techniques that restrict the metamodel domain to the parameter space region encompassing high-quality designs. Therein, the domain is established using only a handful of EM-simulations. This paper proposes a novel modeling technique, which incorporates the response feature technology into the constrained modeling framework. Our methodology allows for rendering accurate surrogates using exceptionally small training data sets, at the expense of reducing the generality of the modeling procedure to antennas that exhibit consistent shape of input characteristics. The proposed technique can be employed in other fields that employ costly simulation models (e.g., mechanical or aerospace engineering).

Application of Surrogate Models as an Alternative to Process Simulation for Implementation of the Self-Optimizing Control Procedure on Large-Scale Process Plants—A Natural Gas-to-Liquids (GTL) Case Study

High computational loads, time-consuming convergence, and simulation crashes are common when using process simulators for flowsheet optimization. In this paper, by replacing the large-scale physica...

Application of surrogate models in estimation of storm surge:A comparative assessment

Coastal storm surge hazard assessment has received increased attention due to major hurricane events in the last two decades. Robust hazard assessment requires accurate and efficient storm surge prediction models; however, existing numerical models are either high-fidelity but computationally demanding or low-fidelity but with real-time forecasting application. This dichotomy has prompted the development of surrogate models that leverage available synthetic/historical storm databases to build prediction models intended to better balance efficiency and accuracy. Despite numerous studies that have examined the application of various surrogate modeling methods in coastal response prediction, no study is available that compares all of the frequently used methods for storm surge prediction. Furthermore, in most of these studies, the discussion of the performance of these models is bounded to aggregated error metrics (e.g., RMSE, R). This study aims to provide a comprehensive framework for comparison and assessment of the performance of surrogate models based on Artificial Neural Network (ANN), Gaussian Process Regression (GPR) and Support Vector Regression (SVR) for predicting storm surge. The United States Army Corp of Engineers’ North Atlantic Coast Comprehensive Study (NACCS) database is used for developing the models at representative coastal locations. In this study, the performance of the models is explored by investigating the stability of performance across training sample sizes, identifying systematic trends in errors, assessing performance in predicting large target response quantities, and characterizing the distribution of error. The results indicate that the performance of surrogate models may be improved by use of physically-motivated parameter scaling and that the selection of a surrogate modeling method should be informed by factors such as consistency in performance under a range of target surge elevations. In particular, the results suggest that accuracy of the tested surrogate models may be a function of the target surge elevation. Furthermore, results suggest that model performance should be assessed using factors beyond aggregate error metrics because such measures (particularly when used without modification to focus on risk-significant events) may give incomplete information about performance of surrogate models.

Implementation of machine learning techniques into the Subset Simulation method

A hybrid reliability analysis procedure that combines the advantages of the Subset Simulation method, the application of surrogate models and clustering techniques is proposed to efficiently assess the failure probability of complex structural systems that may exhibit multiple failure modes. The proposed procedure, herein called SS-KK, integrates the Kriging surrogate modeling technique, K-means clustering algorithm into the original Subset Simulation (SS) method. The approach is found to not only improve the efficiency of the Subset Simulation method in finding the reliability of a structural system but to also help identify the important failure modes and controlling random variables. This information is important to aid engineers optimize the structural design process by focusing on the critical failures modes and design variables.The method consists of first constructing a relatively coarse global Kriging model at each subset level of SS by applying an appropriate active learning strategy. Subsequently, the initial global Kriging model is partitioned into several local Kriging models that coincide with the important failure modes identified by the K-means clustering algorithm. This partitioning, which helps identify the important failure modes, also gives a better representation of the entire failure region leading to improved estimates of the system reliability. Finally, FORM is implemented for each local Kriging to rank the importance of each identified failure mode based on its Hasofer-Lind reliability index and to use the associated design point and sensitivity coefficients to identify the most critical random variables.Several examples extracted from the available literature are analyzed to illustrate the advantages of the proposed SS-KK methodology and demonstrate its accuracy and efficiency.

Industrial application of surrogate models to optimize crude oil distillation units

This work presents a new approach to optimize existing crude oil distillation systems. The main features of this approach are its ability to provide key insights of the main factors affecting product yields and energy consumption; and the consideration of system limitations, such as crude oil changes, column flooding, heat transfer bottlenecks and product quality specifications. The new approach showcases sophisticated and systematic modelling and optimization methodologies, namely artificial neural networks and simulated annealing. The approach has been applied successfully in a debottlenecking study for yield optimization of a medium-scale Spanish refinery. The implementation of the optimization results was carried out successfully in the refinery; initial projections confirm predicted benefits of $7.2 million per year.

A robust and efficient structural reliability method combining radial-based importance sampling and Kriging

Simulation based structural reliability analysis suffers from a heavy computational burden, as each sample needs to be evaluated on the performance function, where structural analysis is performed. To alleviate the computational burden, related research focuses mainly on reduction of samples and application of surrogate model, which substitutes the performance function. However, the reduction of samples is achieved commonly at the expense of loss of robustness, and the construction of surrogate model is computationally expensive. In view of this, this paper presents a robust and efficient method in the same direction. The present method uses radial-based importance sampling (RBIS) to reduce samples without loss of robustness. Importantly, Kriging is fully used to efficiently implement RBIS. It not only serves as a surrogate to classify samples as we all know, but also guides the procedure to determine the optimal radius, with which RBIS would reduce samples to the highest degree. When used as a surrogate, Kriging is established through active learning, where the previously evaluated points to determine the optimal radius are reused. The robustness and efficiency of the present method are validated by five representative examples, where the present method is compared mainly with two fundamental reliability methods based on active learning Kriging.

Optimizing a Collision-Avoidance System for Closely Spaced Parallel Operations

The traffic alert and collision-avoidance system has been mandated worldwide to protect against aircraft midair collisions. One drawback of the current traffic alert and collision-avoidance system design is limited support for closely spaced parallel runway operations. The traffic alert and collision-avoidance system alerts, too frequently, leading pilots to often inhibit resolution advisories during approach. Research is underway on the Airborne Collision Avoidance System X, which is a next-generation collision-avoidance system that will support new surveillance systems and air traffic control procedures. The Airborne Collision Avoidance System X has been shown to outperform the traffic alert and collision-avoidance system for en route encounter scenarios. However, the design parameters that are tuned for the en route environment are not appropriate for closely spaced parallel landing operations. One concept to allow for closely spaced parallel landing operations is a procedure-specific mode of the logic that reduces the nuisance alert rate while still providing collision protection. This paper describes the application of surrogate modeling for the purpose of tuning Airborne Collision Avoidance System X for parallel landing operations. The performance of the tuned system is assessed using a data-driven blunder model and an operational performance model. The tuned Airborne Collision Avoidance System X logic is found to equal or outperform the traffic alert and collision-avoidance system for each model in terms of both safety and operational suitability.

Application of a surrogate modeling to the ship structural design

Multi-criteria design of complex engineering systems is methodologically and computationally demanding and time consuming process. Optimization algorithms, problem decomposition, surrogate modeling and methods for decision support are synthesis methods that are usually employed to solve the design problem. The objective of the research presented in this paper was to improve the design process of complex thin-walled ship structures through an application of surrogate modeling on this type of a problem. Methods considered are integrated into interactive computing environment for multi-criteria design in order to enable effective and efficient interaction between designer and design problem within given design timeframe. Surrogate modeling was applied for the approximation of structural responses in order to reduce a number of finite element method (FEM) calculations inside of optimization loop. Applicability of the proposed approach and suitability of different surrogate modeling methods for that purpose is extensively tested on the simple barge example.

Application of Surrogate Modeling to Design of A Compressor Blade to Optimize Stacking and Thickness

Surrogate modeling is applied to a compressor blade shape optimization to modify its stacking line and thickness to enhance adiabatic efficiency and total pressure ratio. Six design variables are defined by parametric curves and three objectives; efficiency, total pressure and a combined objective of efficiency and total pressure are considered to enhance the performance of compressor blade. Latin hypercube sampling of design of experiments is used to generate 55 designs within design space constituted by the lower and upper limits of variables. Optimum designs are found by formulating a PRESS (predicted error sum of squares) based averaging (PBA) surrogate model with the help of a gradient based optimization algorithm. The optimum designs using the current variables show that, to optimize the performance of turbomachinery blade, the adiabatic efficiency objective is improved substantially while total pressure ratio objective is increased a very small amount. The multi-objective optimization shows that the efficiency can be increased with the less compensation of total pressure reduction or both objectives can be increased simultaneously.

Cognitive technologies in adaptive models of complex plants

Abstract The paper deals with various aspects of the construction and application of surrogate models in CAD systems, outlines basic data analysis and simulation tasks essential for surrogate model construction, reviews the current state of the art and proposes innovative approaches based on cognitive data analysis and simulation technologies.