Nonlinear System Identification Techniques Research Articles

Decoding Electroencephalography Signal Response by Stacking Ensemble Learning and Adaptive Differential Evolution.

Electroencephalography (EEG) is an exam widely adopted to monitor cerebral activities regarding external stimuli, and its signals compose a nonlinear dynamical system. There are many difficulties associated with EEG analysis. For example, noise can originate from different disorders, such as muscle or physiological activity. There are also artifacts that are related to undesirable signals during EEG recordings, and finally, nonlinearities can occur due to brain activity and its relationship with different brain regions. All these characteristics make data modeling a difficult task. Therefore, using a combined approach can be the best solution to obtain an efficient model for identifying neural data and developing reliable predictions. This paper proposes a new hybrid framework combining stacked generalization (STACK) ensemble learning and a differential-evolution-based algorithm called Adaptive Differential Evolution with an Optional External Archive (JADE) to perform nonlinear system identification. In the proposed framework, five base learners, namely, eXtreme Gradient Boosting, a Gaussian Process, Least Absolute Shrinkage and Selection Operator, a Multilayer Perceptron Neural Network, and Support Vector Regression with a radial basis function kernel, are trained. The predictions from all these base learners compose STACK's layer-0 and are adopted as inputs of the Cubist model, whose hyperparameters were obtained by JADE. The model was evaluated for decoding the electroencephalography signal response to wrist joint perturbations. The variance accounted for (VAF), root-mean-squared error (RMSE), and Friedman statistical test were used to validate the performance of the proposed model and compare its results with other methods in the literature, including the base learners. The JADE-STACK model outperforms the other models in terms of accuracy, being able to explain around, as an average of all participants, 94.50% and 67.50% (standard deviations of 1.53 and 7.44, respectively) of the data variability for one step ahead and three steps ahead, which makes it a suitable approach to dealing with nonlinear system identification. Also, the improvement over state-of-the-art methods ranges from 0.6% to 161% and 43.34% for one step ahead and three steps ahead, respectively. Therefore, the developed model can be viewed as an alternative and additional approach to well-established techniques for nonlinear system identification once it can achieve satisfactory results regarding the data variability explanation.

Data-based modeling and control of nonlinear process systems using sparse identification: An overview of recent results

This paper discusses recent developments in the data-based modeling and control of nonlinear chemical process systems using sparse identification of nonlinear dynamics (SINDy). SINDy is a recent nonlinear system identification technique that uses only measurement data to identify model dynamical systems in the form of first-order nonlinear differential equations. In this work, the challenges of handling time-scale multiplicities and noisy sensor data when using SINDy are addressed. Specifically, a brief overview of novel methods devised to overcome these challenges are described, along with modeling guidelines for using the proposed techniques for process systems. When applied to two-time-scale systems, to overcome model stiffness, which leads to ill-conditioned controllers, a reduced-order modeling approach is proposed where SINDy is used to model the slow dynamics, and nonlinear principal component analysis is used to algebraically “slave” the fast states to the slow states. The resulting model can then be used in a Lyapunov-based model predictive controller with guaranteed closed-loop stability provided the separation of fast and slow dynamics is sufficiently large. To handle high levels of sensor noise, SINDy is combined with subsampling and co-teaching to improve modeling accuracy. The challenges of modeling and controlling large-scale systems using noisy industrial data are then addressed by using ensemble learning with SINDy. After summarizing the advances, a nonlinear chemical process is used to provide an end-to-end demonstration of process modeling using sparse identification with guidelines for chemical engineering practitioners. Finally, several future research directions for the incorporation of SINDy into process systems engineering are proposed.

Multi-Area Distributed State Estimation in Smart Grids Using Data-Driven Kalman Filters

Low-latency data processing is essential for wide-area monitoring of smart grids. Distributed and local data processing is a promising approach for enabling low-latency requirements and avoiding the large overhead of transferring large volumes of time-sensitive data to central processing units. State estimation in power systems is one of the key functions in wide-area monitoring, which can greatly benefit from distributed data processing and improve real-time system monitoring. In this paper, data-driven Kalman filters have been used for multi-area distributed state estimation. The presented state estimation approaches are data-driven and model-independent. The design phase is offline and involves modeling multivariate time-series measurements from PMUs using linear and non-linear system identification techniques. The measurements of the phase angle, voltage, reactive and real power are used for next-step prediction of the state of the buses. The performance of the presented data-driven, distributed state estimation techniques are evaluated for various numbers of regions and modes of information sharing on the IEEE 118 test case system.

Data-driven modeling of the thermal dynamics of a dual-spectral ultraviolet sterilizer and control of the output irradiance

Multi-channel LED light sources possess complicated nonlinear photo-electro-thermal (PET) dynamics. Modeling such PET dynamics is challenging, but important to ensure the performance of these light sources. Traditional first-principle modeling methods that have been reported in the literature yield either single-channel LED dynamic models, or multi-channel static models. On the other hand, system identification (SID) methods have also been applied, and lead to both single-channel nonlinear dynamic models and multi-channel linear time invariant (LTI) models. However, there are still few attempts given to build multiple-input-multiple-output (MIMO) nonlinear dynamic models of multi-channel LED systems. In this work, we try to model the PET dynamics of a dual-spectral ultraviolet (UV) light source, with a structured nonlinear system identification technique, i.e., linear parameter varying (LPV) SID technique. The experimental prototype contains a 280 nm UVC channel and a 365 nm UVA channel, respectively driven by two separate constant current sources, and is hence a MIMO system. Its nonlinear electro-thermal model is first identified from experimental data by the LPV-SID method, which is then integrated with the estimated photo-electro model to form a complete PET dynamic model. The experimental results have verified that the model can accurately predict the temperature variations at two representative points on the LED board. Moreover, the identified model has been applied in designing a feedforward-feedback controller to precisely track the reference radiation levels of the two UV channels, despite the strong nonlinearity caused by both the electro-thermal dynamics and the temperature-dependent lumen efficacy.

Comparing system identification techniques for identifying human-like walking controllers.

While human walking has been well studied, the exact controller is unknown. This paper used human experimental walking data and system identification techniques to infer a human-like controller for a spring-loaded inverted pendulum (SLIP) model. Because the best system identification technique is unknown, three methods were used and compared. First, a linear system was found using ordinary least squares. A second linear system was found that both encoded the linearized SLIP model and matched the first linear system as closely as possible. A third nonlinear system used sparse identification of nonlinear dynamics (SINDY). When directly mapping states from the start to the end of a step, all three methods were accurate, with errors below 10% of the mean experimental values in most cases. When using the controllers in simulation, the errors were significantly higher but remained below 10% for all but one state. Thus, all three system identification methods generated accurate system models. Somewhat surprisingly, the linearized system was the most accurate, followed closely by SINDY. This suggests that nonlinear system identification techniques are not needed when finding a discrete human gait controller, at least for unperturbed walking. It may also suggest that human control of normal, unperturbed walking is approximately linear.

Measurement and identification of the nonlinear dynamics of a jointed structure using full-field data, Part I: Measurement of nonlinear dynamics

Jointed structures are ubiquitous constituents of engineering systems; however, their dynamic properties (e.g., natural frequencies and damping ratios) are challenging to identify correctly due to the complex, nonlinear nature of interfaces. This research seeks to extend the efficacy of traditional experimental methods for linear system identification (such as impact testing, shaker ringdown testing, random excitation, and force or amplitude-control stepped sine testing) on nonlinear jointed systems, e.g., the half Brake–Reußbeam, by augmenting them with full-field data collected by high-speed videography. The full-field response is acquired using high-speed cameras combined with Digital Image Correlation (DIC), which enables studying the spatial–temporal dynamic characteristics of the system. As this is a video-based experiment, additional constraints are attached to the beam at the node points to remove the rigid body motion, which ensures that the beam is in the view of the camera during the entire test. The use of a video-based method introduces new sources of experimental error, such as noise from the high-speed camera’s fan and electrical noise, and so the measurement accuracy of DIC is validated using accelerometer data. After validating the DIC data, the measurements are recorded for several types of excitation, including hammer testing, shaker ringdown testing, fixed sine testing, and stepped sine testing. Using the DIC data to augment standard nonlinear system identification techniques, modal coupling and the mode shapes’ evolution are investigated. The suitability of videography methods for nonlinear system identification of nonlinear beams is explored for the first time in this paper, and recommendations for techniques to facilitate this process are made. This article focuses on developing an accurate data collection methodology as well as recommendations for nonlinear testing with DIC, which paves the way for video-based investigation of nonlinear system identification. In Part-II (Jin et al., 2021) of this work, the same data set is used for a rigorous assessment of nonlinear system identification with full-field DIC data.

Implementation of Parallel Cascade Identification at Various Phases for Integrated Navigation System

Global navigation satellite systems (GNSS) are widely used for the navigation of land vehicles. However, the positioning accuracy of GNSS, such as the global positioning system (GPS), deteriorates in urban areas due to signal blockage and multipath effects. GNSS can be integrated with a micro-electro-mechanical system (MEMS)–based inertial navigation system (INS), such as a reduced inertial sensor system (RISS) using a Kalman filter (KF) to enhance the performance of the integrated navigation solution in GNSS challenging environments. The linearized KF cannot model the low-cost and small-size sensors due to relatively high noise levels and compound error characteristics. This paper reviews two approaches to employing parallel cascade identification (PCI), a non-linear system identification technique, augmented with KF to enhance the navigational solution. First, PCI models azimuth errors for a loosely coupled 2D RISS integrated system with GNSS to obtain a navigation solution. The experimental results demonstrated that PCI improved the integrated 2D RISS/GNSS performance by modeling linear, non-linear, and other residual azimuth errors. For the second scenario, PCI is utilized for modeling residual pseudorange correlated errors of a KF-based tightly coupled RISS/GNSS navigation solution. Experimental results have shown that PCI enhances the performance of the tightly coupled KF by modeling the non-linear pseudorange errors to provide an enhanced and more reliable solution. For the first algorithm, the results demonstrated that PCI can enhance the performance by 77% as compared to the KF solution during the GNSS outages. For the second algorithm, the performance improvement for the proposed PCI technique during the availability of three satellites was 39% compared to the KF solution.

Entropy Fuzzy System Identification for the Heave Flight Dynamics of a Model-Scale Helicopter

This article studies nonlinear system identification of a small scale and flybar-free unmanned helicopter, the Trex450 chopper, built using commercial off-the-shelf components. We employ the real-time input-output data, obtained from human-controlled flight tests, operating the aircraft under severe ground effects during the vertical flight maneuvers. We highlight the efficacy of the entropy fuzzy system identification method with respect to the performance of several well-known nonlinear system identification techniques (i.e., a Takagi-Sugeno Fuzzy system, an adaptive neuro-fuzzy inference system (ANFIS), and a nonlinear autoregressive with exogenous (NARX) model) as our benchmarks. Our research confirms the benefits of the entropy fuzzy identification technique. Despite being nonlinear, the proposed fuzzy model is relatively simple, transparent, and highly accurate to represent the complex non-linear dynamic behaviors of our unmanned helicopter under severe ground effects. Another major advantage of the proposed system identification technique is its ability to avoid overfitting, an essential requirement in modeling. Overall, the fuzzy system is also capable of achieving a delicate balance between maximizing the accuracy while minimizing the complexity of the acquired model.

Applying polynomial decoupling methods to the polynomial NARX model

System identification uses measurements of a dynamic system’s input and output to reconstruct a mathematical model for that system. These can be mechanical, electrical, physiological, among others. Since most of the systems around us exhibit some form of nonlinear behavior, nonlinear system identification techniques are the tools that will help us gain a better understanding of our surroundings and potentially let us improve their performance. One model that is often used to represent nonlinear systems is the polynomial NARX model, an equation error model where the output is a polynomial function of the past inputs and outputs. That said, a major disadvantage with the polynomial NARX model is that the number of parameters increases rapidly with increasing polynomial order. Furthermore, the polynomial NARX model is a black-box model, and is therefore difficult to interpret. This paper discusses a decoupling algorithm for the polynomial NARX model that substitutes the multivariate polynomial with a transformation matrix followed by a bank of univariate polynomials. This decreases the number of model parameters significantly and also imposes structure on the black-box NARX model. Since a non-convex optimization is required for this identification technique, initialization is an important factor to consider. In this paper the decoupling algorithm is developed in conjunction with several different initialization techniques. The resulting algorithms are applied to two nonlinear benchmark problems: measurement data from the Silver-Box and simulation data from the Bouc-Wen friction model, and the performance is evaluated for different validation signals in both simulation and prediction.

System identification technique for control of hybrid bio-system

Effective and accurate system parameters in physical system are crucial for the analysis and prediction of dynamic performance and to conduct control. A hybrid bio-system combined using solid and flexible bio-elements is adopted as the target system in this study. Each individual system has its own nonlinearity in nature. A flexible muscle is represented using a Hill-type model. In addition, the hybrid dynamic system exhibiting nonlinearity is modeled using the Hammerstein-Wiener model. These nonlinearities are characterized through piecewise linear approaches. The dynamics and control performance of the systems using the proposed nonlinear system identification are compared with those of linear system identification. Simulation results show the feasibility of the proposed nonlinear system identification technique in extracting effective system parameters with a varying piecewise linearity. Moreover, the possibility of bio-system control is qualitatively revealed. A sequential PID control scheme also shows its successful performance for a hybrid bio-system.

T2-ETS-IE: A Type-2 Evolutionary Takagi–Sugeno Fuzzy Inference System With the Information Entropy-Based Pruning Technique

We introduce a new nonlinear system identification technique, leveraging the benefits of the Type-2 Evolutionary Takagi–Sugeno (T2-ETS) fuzzy system. The major advantage of our proposed system identification technique is mainly due to its ability to learn-from-scratch while accommodating the footprint-of-uncertainties (FoUs). To support its mission to achieve a reasonably high prediction accuracy for uncertain nonlinear dynamic systems, we also introduce a new type reduction method to convert Type-2 fuzzy systems into their Type-1 counterparts. As a part of its efficient pruning strategy, the proposed system incorporates the concept of information entropy to avoid over fitting, which is a highly undesirable issue in modeling. We demonstrate the effectiveness of our system identification technique in achieving a delicate balance between minimizing the complexity of the acquired fuzzy model and maximizing the prediction accuracy. To highlight the efficacy of our algorithm, we employ a set of challenging pH neutralization data, known for its substantial nonlinearity, in addition to the dynamics of a nonlinear mechanical system. We conclude our research by conducting a rigorous comparative study to quantify the relative merits of our proposed technique with respect to the previous ETS algorithm (as its predecessor), the well-known KM-type reduction technique, and the higher-order discrete transfer functions, widely implemented in most conventional mathematical modeling techniques.

Comparison of nonlinear system identification methods for free decay measurements with application to jointed structures

Assembled structures are nonlinear. The sources of this nonlinearity could include the jointed interfaces, damage and wear, non-idealized boundary conditions, or other features inherent in real parts. To study these systems and to ascertain if they will be operating in a regime in which the nonlinearity is prominent, nonlinear system identification techniques are needed to assess and characterize the nature of the nonlinearity in the structure. Significant progress over the last few years has focused on using nonlinear system identification to identify damage and other deviations from idealized structures. This research reviews nine different methods for nonlinear system identification (restoring force surface, Hilbert transform, direct quadrature, zero-crossing, short-time Fourier transform, Gabor wavelet, Morlet wavelet, Morse wavelet, and a neural network-based algorithm) in order to assess their accuracy. The methods are compared by identifying characteristics of two systems: a single degree of freedom model of a Duffing oscillator and measured data from a jointed structure. As neural networks are not commonly used for system identification, multiple variations of the method are investigated to study its effectiveness. Perturbation analysis is conducted to see the efficacy of the different methods for identifying parameters across a large range of design spaces, and the advantages and disadvantages of each method are discussed. The primary contribution of this paper is a comparison on both analytical and experimental data of multiple widely used system identification methods, and an assessment of when each method is most and least applicable, specifically in the context of jointed structures.

Effect of two different therapeutic interventions: SRT in comparison to ERT on immune aspects and bone involvement in Gaucher disease

The flow-induced vibration of bluff bodies is an important problem of many marine, civil, or mechanical engineers. In the design phase of such structures, it is vital to obtain good predictions of the fluid forces acting on the structure. Current methods rely on computational fluid dynamic simulations (CFD), with a too high computational cost to be effectively used in the design phase or for control applications. Alternative methods use heuristic mathematical models of the fluid forces, but these lack the accuracy (they often assume the system to be linear) or flexibility to be useful over a wide operating range.In this work we show that it is possible to build an accurate, flexible and low-computational-cost mathematical model using nonlinear system identification techniques. This model is data driven: it is trained over a user-defined region of interest using data obtained from experiments or simulations, or both. Here we use a Van der Pol oscillator as well as CFD simulations of an oscillating circular cylinder to generate the training data. Then a discrete-time polynomial nonlinear state-space model is fit to the data. This model relates the oscillation of the cylinder to the force that the fluid exerts on the cylinder. The model is finally validated over a wide range of oscillation frequencies and amplitudes, both inside and outside the so-called lock-in region. We show that forces simulated by the model are in good agreement with the data obtained from CFD.

Nonlinear system identification from noisy measurements

A novel nonlinear system identification procedure using noisy measurements for health assessment of real civil infrastructure systems is presented. The important features of the procedure are that it can identify a structural system using only a limited number of highly noise-contaminated responses measured for a very short duration. To compensate for the use of very short duration response time-histories, multiple weighted global iteration (WGI) procedure is introduced in the unscented Kalman filter (UKF) algorithm to help the convergence process. It is denoted as UKF-WGI procedure. The algorithm is a finite element-based nonlinear system identification technique. It identifies not only the integrity of the whole structure, but also the locations and severity of the defects. Since no similar studies are reported in the literature, the superiority of UKF-WGI over the extended Kalman filter-based procedure in the presence of noise is established with the help of several illustrative examples.

Estimation of Time-Varying, Intrinsic and Reflex Dynamic Joint Stiffness during Movement. Application to the Ankle Joint.

Dynamic joint stiffness determines the relation between joint position and torque, and plays a vital role in the control of posture and movement. Dynamic joint stiffness can be quantified during quasi-stationary conditions using disturbance experiments, where small position perturbations are applied to the joint and the torque response is recorded. Dynamic joint stiffness is composed of intrinsic and reflex mechanisms that act and change together, so that nonlinear, mathematical models and specialized system identification techniques are necessary to estimate their relative contributions to overall joint stiffness. Quasi-stationary experiments have demonstrated that dynamic joint stiffness is heavily modulated by joint position and voluntary torque. Consequently, during movement, when joint position and torque change rapidly, dynamic joint stiffness will be Time-Varying (TV). This paper introduces a new method to quantify the TV intrinsic and reflex components of dynamic joint stiffness during movement. The algorithm combines ensemble and deterministic approaches for estimation of TV systems; and uses a TV, parallel-cascade, nonlinear system identification technique to separate overall dynamic joint stiffness into intrinsic and reflex components from position and torque records. Simulation studies of a stiffness model, whose parameters varied with time as is expected during walking, demonstrated that the new algorithm accurately tracked the changes in dynamic joint stiffness using as little as 40 gait cycles. The method was also used to estimate the intrinsic and reflex dynamic ankle stiffness from an experiment with a healthy subject during which ankle movements were imposed while the subject maintained a constant muscle contraction. The method identified TV stiffness model parameters that predicted the measured torque very well, accounting for more than 95% of its variance. Moreover, both intrinsic and reflex dynamic stiffness were heavily modulated through the movement in a manner that could not be predicted from quasi-stationary experiments. The new method provides the tool needed to explore the role of dynamic stiffness in the control of movement.

Nonlinear state-space modelling of the kinematics of an oscillating circular cylinder in a fluid flow

The flow-induced vibration of bluff bodies is an important problem of many marine, civil, or mechanical engineers. In the design phase of such structures, it is vital to obtain good predictions of the fluid forces acting on the structure. Current methods rely on computational fluid dynamic simulations (CFD), with a too high computational cost to be effectively used in the design phase or for control applications. Alternative methods use heuristic mathematical models of the fluid forces, but these lack the accuracy (they often assume the system to be linear) or flexibility to be useful over a wide operating range. In this work we show that it is possible to build an accurate, flexible and low-computational-cost mathematical model using nonlinear system identification techniques. This model is data driven: it is trained over a user-defined region of interest using data obtained from experiments or simulations, or both. Here we use a Van der Pol oscillator as well as CFD simulations of an oscillating circular cylinder to generate the training data. Then a discrete-time polynomial nonlinear state-space model is fit to the data. This model relates the oscillation of the cylinder to the force that the fluid exerts on the cylinder. The model is finally validated over a wide range of oscillation frequencies and amplitudes, both inside and outside the so-called lock-in region. We show that forces simulated by the model are in good agreement with the data obtained from CFD.

Nonlinear System Identification Technique for a Base-Excited Structure Based on Modal Space Formulation

Most of the nonlinear system identification techniques described in the existing literature required force and response information at all excitation degrees-of-freedom (DOFs). For cases, where the excitation comes from base motion, those methods cannot be applied as it is not feasible to obtain the measurements of motion at all DOFs from an experiment. The objective of this research is to develop the methodology for the nonlinear system identification of continuous, multimode, and lightly damped systems, where the excitation comes from the moving base. For this purpose, the closed-form expression for the equivalent force also known as the pseudo force from the measured data for the base-excited structure is developed. A hybrid model space is developed to find out the nonlinear restoring force at the nonlinear DOFs. Once the nonlinear restoring force is obtained, the nonlinear parameters are extracted using “multilinear least square regression” in a modal space. A modal space is chosen to express the direct and cross-coupling nonlinearities. Using a cantilever beam as an example, the proposed methodology is demonstrated, where the experimental setup, testing procedure, data acquisition, and data processing are presented. The example shows that the method proposed here is systematic and constructive for nonlinear parameter identification for base-excited structure.

An evaluation of data-driven identification strategies for complex nonlinear dynamic systems

The development of suitable mathematical models on the basis of dynamic measurements from dispersed structural systems that may be undergoing significant nonlinear behavior is an important and very challenging problem in the field of Applied Mechanics that has drawn the attention of numerous investigators and motivated the development of many approaches for extracting reduced-order, reduced-complexity models from such systems. However, even though numerous nonlinear system identification techniques that are focused on the class of problems encountered in the structural dynamics field have been developed over the past decades, there are no systematic studies available that rigorously compare the performance and fidelity of such methods under similar operating conditions, and when encountering challenging nonlinear phenomena (such as hysteresis) that are present in physical systems, at different scales. This paper explores a variety of data-driven identification techniques for complex nonlinear systems and provides a much needed critical comparison of the accuracy and performance of each method. The Volterra/Wiener neural network (VWNN), a more recent development in nonlinear identification, is featured and compared against several existing methods, including polynomial-based nonlinear estimators and other artificial neural network systems. A representative three degree-of-freedom structure with nonlinear restoring force elements is used as the primary means of comparison for the different methods, and a variety of nonlinear models were investigated, including bilinear hysteresis, polynomial stiffness, and Bouc–Wen hysteresis. Performance comparisons were based on the ability to estimate the acceleration responses for both training and testing simulations. The results showed that, in general, the VWNN provided better accuracy in its estimates for each model. The VWNN also performed best when evaluated for scenarios in which numerical integration is required to find velocity and displacement information from measured accelerations or sensor noise is present in the measured responses.

Identification of discontinuous nonlinear systems via a multivariate Padé approach

We present a nonlinear system identification technique based on multi-dimensional rational polynomials. A multi-dimensional Padé–Legendre approximation is developed to circumvent challenges in dealing with sharp shocks. The purpose of this paper is to investigate the accuracy of such approximations for identification of various nonlinear systems, particularly systems with a non-smooth response surface. This identification approach utilizes the generalized form of a Padé–Legendre approximation for studying multivariable functions. In the studied problems, the nonlinearity is a function of state variables (displacement and velocity), which requires multi-dimensional formulation. Furthermore, a spatial filter is applied to minimize the effects of the singular points in the applicable rational function of the response surface. This study presents different types of nonlinearities including smooth, irregular, and hysteretic functions, in order to demonstrate the performance of the approach under different conditions. In order to study the robustness of the method in comparison to other identification techniques based on plain polynomial representation, a nonlinear system with a sharp discontinuous restoring force surface is considered. The performance of both approaches is investigated for different degrees of “sharpness”. In addition, the accuracy of the identified models to represent the nonlinear system is verified by comparing the output of the system (computed on the basis of the identified model) from data sets corresponding to different excitations than those used for identification purposes. It is shown that the proposed approach provides a robust identification technique for a broad class of highly-nonlinear systems, and it is particularly advantageous to use when dealing with systems incorporating discontinuous properties.

On the order reduction of the radiative heat transfer model for the simulation of plasma arcs in switchgear devices

An approach to derive low-complexity models describing thermal radiation, employed to simulate the behavior of electric arcs in switchgear systems, is presented. The idea is to approximate the (high dimensional) full-order equations, describing the propagation of the radiated heat intensity in space, with a model of much lower dimension, whose parameters are identified by means of nonlinear system identification techniques. The proposed order reduction approach is able to systematically compute the partitioning of the electromagnetic spectrum in frequency bands, and the related absorption coefficients, that yield the best matching with respect to the finely resolved absorption spectrum of the considered gaseous medium. In addition to the order reduction approach and the related computational aspects, an analysis by means of Laplace transform is presented, providing a justification to the use of very low orders in the reduction procedure as compared with the full-order model. Finally, comparisons between the full-order model and the reduced-order one are presented.