Performance-driven Model Research Articles

Reduced-cost microwave modeling using constrained domains and dimensionality reduction

Development of modern microwave devices largely exploits full-wave electromagnetic (EM) simulations. Yet, simulation-driven design may be problematic due to the incurred CPU expenses. Addressing the high-cost issues stimulated the development of surrogate modeling methods. Among them, data-driven techniques seem to be the most widespread owing to their flexibility and accessibility. Nonetheless, applicability of approximation-based modeling for real-world microwave components is hindered by a high nonlinearity of the system characteristics, dimensionality issues, and broad ranges of operating parameters the model should cover to make it practically useful. Performance-driven modeling frameworks deliver a partial mitigation of these problems through appropriate spatial orientation of the metamodel domain, which only encapsulates high-quality designs and not the entire space. Unfortunately, the initial model setup cost is high, as defining the domain requires database designs that need to be a priori acquired. This paper introduces a novel approach, where the database designs are replaced by random observables, and dimensionality of the domain is reduced using spectral analysis thereof. The major contributions of the work include implementation of the explicit dimensionality reduction of the confined surrogate model domain and introducing this concept into a complete cost-efficient framework for modeling of microwave components. Comprehensive benchmarking demonstrates excellent performance of the introduced framework, both in terms of predictive power of the rendered surrogates, their scalability properties, as well as low computational overhead associated with the model setup.

Cost-Efficient Two-Level Modeling of Microwave Passives Using Feature-Based Surrogates and Domain Confinement

A variety of surrogate modeling techniques has been utilized in high-frequency design over the last two decades. Yet, the curse of dimensionality still poses a serious challenge in setting up reliable design-ready surrogates of modern microwave components. The difficulty of the modeling task is only aggravated by nonlinearity of circuit responses. Consequently, constructing a practically usable surrogate model, valid across extended ranges of material, geometry, and operational parameters, is far from easy. As a matter of fact, conventional modeling techniques are merely capable of building models for microwave structures featuring a relatively small number of designable parameters within reduced ranges thereof. One possible way of mitigating these obstacles may be the employment of the recently proposed two-stage performance-driven modeling approach. Therein, the surrogate model domain is narrowed down to the section of the space where the vectors of adequate quality are located, thereby permitting significantly reducing the cost of acquiring the training data. Seeking even further cost reduction, this work introduces a novel modeling framework, which exploits problem-specific knowledge extracted from the circuit responses to achieve substantial cost-savings of training data acquisition. In our methodology, the modeling procedure targets response features instead of the complete responses. The response features are the characteristic locations of the circuit response, such as relevant minima or maxima over selected frequency bands. The dependency of the coordinates of the said features on circuit dimensions is considerably less nonlinear than is observed for the complete characteristics, which enables sizable reduction of the data acquisition cost. Numerical validation of our procedure involving three microwave structures corroborates its remarkable efficiency, which allows for setting design-ready surrogates using only a handful of samples.

Dimensionality-reduced antenna modeling with stochastically established constrained domain

Over the recent years, surrogate modeling methods have become increasingly widespread in the design of contemporary antenna systems. On the one hand, it is associated with a growing awareness of numerical optimization, instrumental in achieving high-performance structures. On the other hand, considerable computational expenses incurred by massive full-wave electromagnetic (EM) analyses, routinely employed as a major design tool, foster the development of novel design techniques that exhibit practically acceptable costs while ensuring reliability. In this context, substituting EM simulations by fast surrogates is a profitable solution. Data-driven modeling is arguably the most popular approach owing to its versatility and the abundance of specific methods. Yet, a construction of approximation surrogates is severely encumbered by the curse of dimensionality, and even more so by the broad ranges of material and geometry parameters the model should cover to be applicable for solving practical design tasks. The recently reported performance-driven modeling paradigm offers workaround these obstacles by restricting the surrogate rendition to a small section of the parameter space, containing designs of sufficiently high quality according to performance requirements imposed on the system under study. Nevertheless, identification of this region is based on database designs that have to be pre-optimized, which is associated with significant CPU expenses. The usage of the reference designs can be replaced by stochastic domain identification, leading to considerable computational savings. This paper introduces a further advancement, where the metamodel domain is outlined based on the spectral analysis of the random observables pre-selected using an automated decision-making process. Our procedure retains the benefits of the prior techniques but also reduces the domain dimensionality, which translates into additional cost reduction of training data acquisition. These have been conclusively demonstrated through numerical validation involving three microstrip antennas and comprehensive comparisons with six state-of-the-art benchmark techniques.

Expedited Variable-Resolution Surrogate Modeling of Miniaturized Microwave Passives in Confined Domains

The design of miniaturized microwave components is largely based on computational models, primarily, full-wave electromagnetic (EM) simulations. The EM analysis is capable of giving an accurate account for cross-coupling effects, substrate and radiation losses, or interactions with environmental components (e.g., connectors). Unfortunately, direct execution of EM-based design tasks, such as parametric optimization or uncertainty quantification (UQ), may turn prohibitively expensive in computational terms. A workaround has been offered by surrogate-assisted procedures that capitalize on replacing expensive EM simulations by fast metamodels, notably data-driven ones. However, the construction of general-purpose metamodels is impeded by the curse of dimensionality as well as a limited capability of approximation techniques to represent highly nonlinear responses of microwave devices. This article proposes a novel technique that integrates the performance-driven modeling paradigm as well as variable-resolution EM simulations. The former focuses on the construction of the surrogate in the parameter space subset encompassing high-quality designs, which effectively addresses the dimensionality issues. The latter—realized through co-kriging—contributes to further computational savings by executing the majority of circuit evaluations at the level of coarse-discretization EM analysis. Verification experiments conducted for three microstrip components demonstrate the superiority of the proposed approach over existing performance-driven techniques, let alone conventional modeling procedures, both with respect to accuracy and computational cost of the surrogate construction.

Two-stage variable-fidelity modeling of antennas with domain confinement

Surrogate modeling has become the method of choice in solving an increasing number of antenna design tasks, especially those involving expensive full-wave electromagnetic (EM) simulations. Notwithstanding, the curse of dimensionality considerably affects conventional metamodeling methods, and their capability to efficiently handle nonlinear antenna characteristics over broad ranges of the system parameters is limited. Performance-driven (or constrained) modeling frameworks may be employed to mitigate these issues by considering a construction of surrogates from the standpoint of the antenna performance figures rather than directly geometry parameters. This permits a significant reduction of the model setup cost without restricting its design utility. This paper proposes a novel modeling framework, which capitalizes on the domain confinement concepts and also incorporates variable-fidelity EM simulations, both at the surrogate domain definition stage, and when rendering the final surrogate. The latter employs co-kriging as a method of blending simulation data of different fidelities. The presented approach has been validated using three microstrip antennas, and demonstrated to yield reliable models at remarkably low CPU costs, as compared to both conventional and performance-driven modeling procedures.

Performance-Driven Yield Optimization of High-Frequency Structures by Kriging Surrogates

Uncertainty quantification is an important aspect of engineering design, as manufacturing tolerances may affect the characteristics of the structure. Therefore, the quantification of these effects is indispensable for an adequate assessment of design quality. Toward this end, statistical analysis is performed, for reliability reasons, using full-wave electromagnetic (EM) simulations. Still, the computational expenditures associated with EM-driven statistical analysis often turn out to be unendurable. Recently, a performance-driven modeling technique has been proposed that may be employed for uncertainty quantification purposes and can enable circumventing the aforementioned difficulties. Capitalizing on this idea, this paper discusses a procedure for fast and simple surrogate-based yield optimization of high-frequency structures. The main concept of the approach is a tailored definition of the surrogate domain, which is based on a couple of pre-optimized designs that reflect the directions featuring maximum variability of the circuit responses with respect to its dimensions. A compact size of such a domain allows for the construction of an accurate metamodel therein using moderate numbers of training samples, and subsequently, it is employyed to enhance the yield. The implementation details are dedicated to a particular type of device. Results obtained for a ring-slot antenna and a miniaturized rat-race coupler imply that the cost of yield optimization process can be reduced to few dozens of EM analyses.

Accurate Modeling of Antenna Structures by Means of Domain Confinement and Pyramidal Deep Neural Networks

The importance of surrogate modeling techniques has been gradually increasing in the design of antenna structures over the recent years. Perhaps the most important reason is a high cost of full-wave electromagnetic (EM) analysis of antenna systems. Although imperative in ensuring evaluation reliability, it entails considerable computational expenses. These are especially pronounced when carrying out EM-driven design tasks such as geometry parameter tuning or uncertainty quantification, both requiring repetitive simulations. Conducting some of the design procedures, e.g., global search or yield optimization, directly at the level of simulation models may be prohibitive. The use of fast replacement models (or surrogates) may alleviate these difficulties; yet, accurate modeling of antenna structures faces its own challenges. The two major obstacles are the curse of dimensionality, manifesting itself in a rapid growth of the number of training data samples necessary to render a reliable model (as a function of the number of antenna parameters) and high nonlinearity of antenna characteristics. Recently, the concept of performance-driven modeling has been introduced, where the modeling process is focused on a small region of the parameters’ space, which contains high-quality designs with respect to the considered performance figures. The most advanced variation in this class of methods is nested kriging, where both the model domain and the surrogate itself are constructed through kriging interpolation. Domain confinement is realized using a set of preoptimized reference designs and allows for significant improvement of the model predictive power while using a limited number of training data samples. In this work, the constrained modeling concept is coupled with a novel pyramidal deep regression network (PDRN) surrogate, which offers improved handling of highly nonlinear antenna responses. Three examples of microstrip antennas are used to demonstrate the advantages of constrained PDRN metamodels over the nested kriging surrogates with the (average) accuracy improved by a factor of 2 without increasing the training dataset cardinality.

Low-Cost Modeling of Microwave Components by Means of Two-Stage Inverse/Forward Surrogates and Domain Confinement

Full-wave electromagnetic (EM) analysis is one of the most important tools in the design of modern microwave components and systems. EM simulation permits reliable evaluation of circuits at the presence of cross-coupling effects or substrate anisotropy, as well as for accounting for interactions with the immediate environment. However, repetitive analyses required by EM-driven procedures, such as parametric optimization or statistical analysis, may entail considerable computational expenditures, often prohibitive. Tackling the high-cost issue fostered the shift toward the incorporation of fast replacement models, including both physics-based surrogates and data-driven ones. While the latter is more popular and versatile, the construction of reliable approximation metamodels for microwave components is hindered by the curse of dimensionality and nonlinearity of system responses. The recent performance-driven modeling methodologies are capable of alleviating these difficulties by confining the surrogate domain to a vicinity of the optimum design manifold (i.e., the region that contains high-quality designs rather than the entire parameter space). Although setting up the model in a constrained domain requires small amounts of training data, domain definition itself requires a set of preoptimized reference designs, acquisition of which is an expensive endeavor. This work proposes a novel approach, which replaces the reference designs with a small set of random observables, thereby considerably reducing the overall cost of the model setup. Comprehensive verification involving several miniaturized microstrip structures demonstrates that our methodology is competitive to performance-driven frameworks both in terms of modeling accuracy and computational efficiency with an average savings of around 80%.

Knowledge-based performance-driven modeling of antenna structures

The importance of surrogate modeling techniques in the design of modern antenna systems has been continuously growing over the recent years. This phenomenon is a matter of practical necessity rather than simply a fashion. On the one hand, antenna design procedures rely on full-wave electromagnetic (EM) simulation tools. On the other hand, the computational costs incurred by repetitive EM analyses involved in solving common tasks (parameter tuning, uncertainty quantification, multi-criterial design, etc.), are often prohibitive. The replacement of full-wave simulations by fast surrogates may mitigate these issues; as a matter of fact, it is the only viable option for carrying out EM-driven design in many cases. Among available modeling approaches, data-driven surrogates are by far the most popular due to their accessibility and versatility. At the same time, a construction of reliable models is hindered by the curse of dimensionality, high nonlinearity of antenna characteristics, as well as broad ranges of parameters and operating conditions that the model has to cover to ensure its design utility. Recently proposed performance-driven modeling frameworks offer a workaround these issues by restricting the model domain to the parameter space regions that contain high-quality designs (w.r.t. the assumed performance metrics). However, the domain determination requires acquisition of a set of pre-optimized reference designs, which adds to the overall computational cost of the surrogate model setup in a significant manner. This work proposes a novel two-stage knowledge-based approach, where the confined domain is defined without using any reference designs. Instead, a preselected set of random observables is employed to establish an inverse regression model being a basis for domain determination of the final surrogate. Comprehensive numerical validation involving three antenna structures indicates that our methodology offers the computational benefits similar to those of the previous performance-driven methods while considerably reducing the initial setup cost, by a factor of sixty percent on the average, which has been achieved by exploiting the problem-specific knowledge.

A Performance-Driven MPC Algorithm for Underactuated Bridge Cranes

A crane system often works in a complex environment. It is difficult to model or learn its true dynamics by traditional system identification approaches. If a dynamics model is created by minimizing its prediction error, its use tends to introduce inaccuracies and thus lead to suboptimal performance. Is it possible to learn the dynamics model of a crane that can achieve the best performance, instead of learning its true dynamics? This work answers the question by presenting a performance-driven model predictive control (P-MPC) algorithm for a two-dimensional underactuated bridge crane. In the proposed dual-layer control architecture, an inner-loop controller uses a proportional–integral–derivative controller to achieve anti-sway rapidly. An outer-loop controller uses MPC to ensure accurate trolley positioning under control constraints. Compared with classical MPC, this work proposes a data-driven method for plant modeling and controller parameter updating. By considering the control target at the learning stage, the method can avoid adjusting the controller to deal with uncertainty. We use Bayesian optimization in an active learning framework where a locally linear dynamics model is learned with the intent of maximizing control performance and then used in conjunction with optimal control schemes to efficiently design a controller for a given task. The model is updated directly based on the performance observed in experiments on the physical system in an iterative manner till a desired performance is achieved. The controller parameters and prediction models of the best closed-loop performance can be found through continuous experiments and iterative optimization. Simulation and experiment results show that we can explicitly find the dynamics model that produces the best performance for an actual system, and the method can quickly suppress swing and realize accurate trolley positioning. The results verified its effectiveness, feasibility, and superior performance on comparing it with state-of-the-art methods.

Expedited Acquisition of Database Designs for Reduced-Cost Performance-Driven Modeling and Rapid Dimension Scaling of Antenna Structures

Fast replacement models have been playing an increasing role in high-frequency electronics, including the design of antenna structures. Their role is to improve the computational efficiency of the procedures that normally entail large numbers of expensive full-wave electromagnetic (EM) simulations, e.g., parametric optimization or uncertainty quantification. Recently introduced performance-driven modeling methods, such as the nested kriging framework, alleviate some of the common difficulties pertinent to conventional modeling methods. These include the curse of dimensionality but also the need for rendering models to be valid for broad ranges of antenna parameters and operating conditions, as dictated by the design utility of the surrogates. The keystone of performance-driven methods is an appropriate confinement of the model domain so that the training data are only acquired in the regions containing high-quality designs. Identification of such regions is realized using a set of so-called reference designs preoptimized for selected ensembles of performance requirements. The CPU cost of generating the reference points may be considerable and compromise the savings obtained by operating in a constrained domain. In this article, a technique for automated, reliable and low-cost acquisition of the reference designs is proposed. Our methodology involves inverse sensitivities, iterative correction procedures, and accelerated feature-based gradient search with sparse Jacobian updates. It is validated using three microstrip antenna examples and demonstrated as an efficient tool for lowering the cost of building surrogate models within the nested kriging framework. The intended use of our approach is expedited construction of database designs for constrained modeling frameworks, construction of inverse surrogates, as well as procedures for rapid redesign and dimension scaling of antenna structures.

Improved Modeling of Microwave Structures Using Performance-Driven Fully-Connected Regression Surrogate

Fast replacement models (or surrogates) have been widely applied in the recent years to accelerate simulation-driven design procedures in microwave engineering. The fundamental reason is a considerable—and often prohibitive—CPU cost of massive full-wave electromagnetic (EM) analyses related to solving common tasks such as parametric optimization or uncertainty quantification. The most popular class of surrogates are data-driven models, which are fast to evaluate, versatile, and easy to handle. Notwithstanding, the curse of dimensionality as well as the utility demands (e.g., so that the model covers sufficiently broad ranges of the system operating conditions), limit the applicability of conventional methods. A performance-driven modeling paradigm allows for mitigating these issue by focusing the surrogate setup process in a constrained domain encapsulating designs being of high quality w.r.t. the assumed figures of interest. The nested kriging framework capitalizing on this idea, renders the constrained surrogate using kriging interpolation, and has been shown to surpass traditional approaches. In pursuit of further accuracy improvements, this work incorporates the performance-driven concept into the fully-connected regression model (FRCM). The latter has been recently introduced in the context of frequency selective surfaces, and combined deep neural networks with Bayesian optimization, the latter employed to determine the network architecture and hyper-parameters. Using two examples of miniaturized microstrip couplers, our methodology is demonstrated to outperform both conventional modeling techniques and nested kriging, with reliable models constructed over multi-dimensional parameters spaces using just a few hundreds of samples.

Nested Kriging with Variable Domain Thickness for Rapid Surrogate Modeling and Design Optimization of Antennas

Design of modern antennas faces numerous difficulties, partially rooted in stringent specifications imposed on both electrical and field characteristics, demands concerning various functionalities (circular polarization, pattern diversity, band-notch operation), but also constraints imposed upon the physical size of the radiators. Conducting the design process at the level of full-wave electromagnetic (EM) simulations, otherwise dictated by reliability, entails considerable computational expenses, which is another and a serious challenge. It is especially pronounced for the procedures involving repetitive EM analyses, e.g., parametric optimization. Utilization of fast surrogate models as a way of mitigating this issue has been fostered in the recent literature. Unfortunately, construction of reliable surrogates for antenna structures is hindered by their highly nonlinear responses and even more by the utility requirements: design-ready models are to be valid over wide ranges of operating conditions and geometry parameters. Recently proposed performance-driven modeling, especially the nested kriging framework, addresses these difficulties by confining the surrogate model domain to a region that encapsulates the designs being optimum with respect to the relevant figures of interest. The result is a dramatic reduction of the number of training samples needed to render a usable model. This paper introduces a variable-thickness domain, which is an important advancement over the basic nested kriging. The major benefit demonstrated using two antenna examples is a further and significant (up to seventy percent) reduction of the training data acquisition cost. It is achieved while ensuring that the model domain covers the regions containing optimum designs for various sets of performance specifications.

Low-cost performance-driven modelling of compact microwave components with two-layer surrogates and gradient kriging

Utilization of electromagnetic (EM) simulation tools has become indispensable for reliable evaluation of microwave components. As the cost of an individual analysis may already be considerable, the computational overhead associated with EM-driven tasks that require massive simulations (e.g., optimization) may turn prohibitive. One of mitigation methods is the employment of equivalent network models. Yet, they are incapable of accounting for cross-coupling effects that occur in devices of complex geometries. Another option are fast replacement models (surrogates), especially the data-driven ones: readily available, generic and problem independent. Unfortunately, due to the curse of dimensionality, their applicability is limited to low-dimensional parameter spaces and narrow parameter ranges. From the utility perspective, however, the surrogate has to be valid over broad ranges of parameters and operating conditions. The recently reported performance-modeling techniques (especially nested-kriging) allow for rendering such surrogates even for complex devices. Key concept is to carry out the modeling process within a confined domain, being a subset of the parameter space that encompasses the designs of high-quality regarding the performance figures of choice. The goal of this work is to reduce the cost of reference design acquisition, which adds up to the total cost of constructing the surrogate. Toward this end, gradient-enhanced kriging is incorporated into the performance-driven modeling framework. The predictive power of the surrogates rendered using our approach by far exceeds that of the conventional methods and is comparable to the original nested kriging technique while requiring a significantly smaller number of reference designs (thus, the CPU cost). These features are demonstrated using a three-section transformer and a rat-race coupler.

Design-Oriented Two-Stage Surrogate Modeling of Miniaturized Microstrip Circuits With Dimensionality Reduction

Contemporary microwave design heavily relies on full-wave electromagnetic (EM) simulation tools. This is especially the case for miniaturized devices where EM cross-coupling effects cannot be adequately accounted for using equivalent network models. Unfortunately, EM analysis incurs considerable computational expenses, which becomes a bottleneck whenever multiple evaluations are required. Common simulation-based design tasks include parametric optimization and uncertainty quantification. These can be accelerated using fast replacement models, among which the data-driven surrogates are the most popular. Notwithstanding, a construction of approximation models for microwave components is hindered by the dimensionality issues as well as high nonlinearity of system characteristics. A partial alleviation of the mentioned difficulties can be achieved with the recently reported performance-driven modeling methods, including the nested kriging framework. Therein, the computational benefits are obtained by appropriate confinement of the surrogate model domain, spanned by a set of pre-optimized reference designs, and by focusing on the parameter space region that contains high quality designs with respect to the considered performance figures. This paper presents a methodology that incorporates the concept of nested kriging and enhances it by explicit dimensionality reduction based on spectral decomposition of the reference design set. Extensive verification studies conducted for a compact rat-race coupler and a three-section impedance matching transformer demonstrate superiority of the presented approach over both the conventional techniques and the nested kriging in terms of modeling accuracy. Design utility of our surrogates is corroborated through application cases studies.

To aggregate or to eliminate? Optimal model simplification for improved process performance prediction

Operational process models such as generalised stochastic Petri nets (GSPNs) are useful when answering performance questions about business processes (e.g. ‘how long will it take for a case to finish?’). Recently, methods for process mining have been developed to discover and enrich operational models based on a log of recorded executions of processes, which enables evidence-based process analysis. To avoid a bias due to infrequent execution paths, discovery algorithms strive for a balance between over-fitting and under-fitting regarding the originating log. However, state-of-the-art discovery algorithms address this balance solely for the control-flow dimension, neglecting the impact of their design choices in terms of performance measures. In this work, we thus offer a technique for controlled performance-driven model reduction of GSPNs, using structural simplification rules, namely foldings. We propose a set of foldings that aggregate or eliminate performance information. We further prove the soundness of these foldings in terms of stability preservation and provide bounds on the error that they introduce with respect to the original model. Furthermore, we show how to find an optimal sequence of simplification rules, such that their application yields a minimal model under a given error budget for performance estimation. We evaluate the approach with two real-world datasets from the healthcare and telecommunication domains, showing that model simplification indeed enables a controlled reduction of model size, while preserving performance metrics with respect to the original model. Moreover, we show that aggregation dominates elimination when abstracting performance models by preventing under-fitting due to information loss.

Performance-driven modeling of compact couplers in restricted domains

Fast surrogate models can play an important role in reducing the cost of Electromagnetic (EM)-driven design closure of miniaturized microwave components. Unfortunately, construction of such models is challenging due to curse of dimensionality and wide range of geometry parameters that need to be included in order to make it practically useful. In this letter, a novel approach to design-oriented modeling of compact couplers is presented. Our method allows for building surrogates that cover wide range of operating conditions and/or material parameters, which makes them useful for design purposes. At the same time, careful definition of the model domain permits dramatic (volume-wise) reduction of the of the design space region that needs to be sampled, thus, keeping the number of training data samples at acceptable levels. The proposed technique is demonstrated using a compact rat-race coupler modeled for operating frequencies from 1 to 2 GHz and power split of −6 to 0 dB. Benchmarking and application examples for coupler design optimization as well as experimental validation are also provided.

モデル予測機能を有するパフォーマンス駆動型PID制御系の一設計

PID controllers have been widely used for various process control systems represented by chemical processes. Recently, from viewpoint of productivity improvement and cost reduction, it has demands to establish the PID controller retained a desirable performance over time on steady-state in spite of changes in the system property. In this paper, a design of performance-driven model predictive PID controller is proposed, which automatically adjusts the user-specified parameter within the GPC-PID controller based on the control performance assessment. According to the proposed algorithm, the PID controller is re-tuned in order to obtain desirable system performance only if the practically performance index to assess control loop exceeds a user-defined threshold. The effectiveness of the proposed control scheme is numerically evaluated by a computer simulation example.