Proper Orthogonal Decomposition Method Research Articles

Three-dimensional particle image velocimetry experimental study of transient motion characteristics of different scale vortices in gasoline engine

The paper adopted three-dimensional (3D) Particle Image Velocimetry (PIV) combined with high-speed measurement technology to study the transient motion characteristics of tumble flow induced by small and medium-sized vortices on an optical gasoline engine. Meanwhile, the Proper Orthogonal Decomposition (POD) method was introduced to analyze the evolution of transient vortices, revealing the three-dimensional motion principle of vortices with different spatial scales within the cylinder. The results showed that increasing the engine speed can cause boosted in-plane and out-of-plane velocity, especially for the in-plane velocity. However, the average velocity in the plane was higher than that out of the plane with the difference generally within an order of magnitude. The strong intake jet was the main reason for bringing turbulent kinetic energy in the cylinder. The average kinetic energy and turbulent kinetic energy in the cylinder are both significantly improved at high engine speed. From the results of this experiment, it was revealed that there exists isotropic turbulent pulsation characteristics. Overall, the corresponding flow characteristics of different decomposed modes were different. The first mode section had the lowest average velocity ratio, while the other two had the highest. Due to the dissipation of large vortices into small vortices or the shear action between flow layers, new vortices were generated, leading to the intermittent phenomenon of the motion path of the vortex cluster in the target plane. The average vortex size and velocity circularity corresponding to two varied engine speeds presented a downward trend. The average vortex size was smaller at high engine speed, while the vortex intensity was higher. In addition, increasing the engine speed would decrease the vortex scale but increase the vortex strength. This work provided new fundamental insights into analyzing the characteristics of micro-scaled vortices in turbulent flow, as well as the organization of intake in the gasoline engine.

Direct numerical simulations of an airfoil undergoing dynamic stall at different background disturbance levels

Thin airfoil dynamic stall at moderate Reynolds numbers is typically linked to the sudden bursting of a small laminar separation bubble close to the leading edge. Given the strong sensitivity of laminar separation bubbles to external disturbances, the onset of dynamic stall on a NACA0009 airfoil section subject to different levels of low-amplitude free stream disturbances is investigated using direct numerical simulations. The flow is practically indistinguishable from clean inflow simulations in the literature for turbulence intensities at the leading edge of ${Tu} = 0.02\,\%$ . At slightly higher turbulence intensities of ${Tu} = 0.05\,\%$ , the bursting process is found to be considerably less smooth and strong coherent vortex shedding from the laminar separation bubble is observed prior to the formation of the dynamic stall vortex (DSV). This phenomenon is considered in more detail by analysing its appearance in an ensemble of simulations comprising statistically independent realisations of the flow, thus proving its statistical relevance. In order to extract the transient dynamics of the vortex shedding, the classical proper orthogonal decomposition method is generalised to include time in the energy measure and applied to the time-resolved simulation data of incipient dynamic stall. Using this technique, the dominant transient spatiotemporally correlated features are distilled and the wave train of the vortex shedding prior to the emergence of the main DSV is reconstructed from the flow data exhibiting dynamics of large-scale coherent growth and decay within the turbulent boundary layer.

Proper Orthogonal Decomposition Based Response Analysis of Inlet Distortion on a Waterjet Pump

This study addresses the challenge of performance degradation in waterjet pumps due to non-uniform suction flow. Utilizing the Proper Orthogonal Decomposition (POD) method, it decomposes and reconstructs the flow features within a waterjet pump under non-uniform inflow into a series of modes ranked in descending order of energy. By analyzing the modes with dominant energy, which contain complex information about the flow field, it is revealed that modes 1 and 2 predominantly represent the formation of a concentrated vortex, whereas modes 3 and 4 illustrate its spatial offset. Notably, in the hub section, mode 3 exhibits a delayed flow separation caused by the reduction of circumferential vortex (CV), with a consequent lift in blade loading at the leading edge and a higher head compared to mode 1. In the shroud section, the delayed flow separation in mode 3 suppressed reverse flow and the concentrated separation vortex (CSV) and then increased the blade loading, ultimately enhancing the pump head. The findings provide significant insights into optimizing waterjet pump performance by detailing the interactions between various flow structures and pump components, effectively filling a knowledge gap in applying dimensionality reduction techniques within the distorted flow fields of water jet pumps.

Spacing Ratio Effects on the Evolution of the Flow Structure of Two Tandem Circular Cylinders in Proximity to a Wall

The flow around two tandem circular cylinders in proximity to a wall is investigated using particle image velocimetry (PIV) for Re = 2 × 103. The spacing ratios L/D are 1, 2, and 5, and the gap ratios G/D are 0.3, 0.6, and 1. The proper orthogonal decomposition (POD) method and λci vortex identification method are used to investigate the evolution of flow structure, and the influences of L/D and G/D on flow physics are shown. At L/D = 2 and G/D = 0.3, a “pairing” process occurs between the wall shear layer and the upstream cylinder’s lower shear layer, resulting in a small separation bubble behind the upstream cylinder. At L/D = 1, the Strouhal number (St) increases with decreasing G/D. At three gap ratios, the St gradually decreases as L/D increases. At G/D = 0.3, there is nearly a 49.98% decrease from St = 0.3295 at L/D = 1 to St = 0.1648 at L/D = 5, which is larger than the reductions in cases of G/D = 0.6 and G/D = 1. The effects of L/D on the evolution of flow structure at G/D = 0.6 are revealed in detail. At L/D = 1, the vortex shedding resembles that of the single cylinder. As L/D increases to 2, a squarish flow structure is formed between two cylinders, and a small secondary vortex is formed due to induction of the lower shear layer of the upstream cylinder. At L/D = 5, there is a vortex merging process between the upper wake vortices of the upstream and downstream cylinders, and the lower wake vortex of the upstream cylinder directly impinges the downstream cylinder. In addition, the shear layers and wake vortices of the upstream cylinder interact with the wake of the downstream cylinder as L/D increases, resulting in reductions in velocity fluctuations, and the production and turbulent diffusion of turbulent kinetic energy are decreased behind the downstream cylinder.

A preserving accuracy two-grid reduced-dimensional Crank-Nicolson mixed finite element method for nonlinear wave equation

In this paper, we mainly resort to a proper orthogonal decomposition (POD) method to study the reduced-dimension of unknown mixed finite element (MFE) solution coefficient vectors in the two-grid Crank-Nicolson MFE (TGCNMFE) method for the nonlinear wave equation and build a preserving accuracy reduced-dimension extrapolated TGCNMFE (RDETGCNMFE) method for the nonlinear wave equation. For this purpose, we first build a new TGCNMFE method for the nonlinear wave equation and demonstrate the existence, unconditional stability, and error estimates for the TGCNMFE solutions. From there, we build a preserving accuracy RDETGCNMFE method for the nonlinear wave equation by using the POD method to decrease the dimension of unknown TGCNMFE solution coefficient vectors and employ the matrix analysis to analyze the existence, unconditional stability, convergence, and errors for the RDETGCNMFE solutions. We finally make use of numerical experiments to verify our theoretical results and to show the advantages of RDETGCNMFE method.

Impact of Oxygen Content on Flame Dynamics in a Non-Premixed Gas Turbine Model Combustor

In this study, large eddy simulation (LES) was used to investigate the dynamic characteristics of diffusion flames in a swirl combustion chamber at an oxygen content of 11–23 wt% and temperature of 770 K. The proper orthogonal decomposition (POD) method was employed to obtain flame dynamic modes. The results indicate that oxygen content has a significant impact on the downstream flow and flame combustion characteristics of the swirl combustion chamber. With oxygen content increasing, the size of the recirculation zone is reduced, and the flame field fluctuations are intensified. The pressure and heat release fluctuations under different oxygen contents were analyzed using frequency spectrum analysis. Finally, the flame modes were analyzed using the POD method, and it was found that the coherent structures are asymmetric relative to the local coordinate system. At an oxygen content of 11 wt%, they exhibit larger coherent structures, while at an oxygen content of 23 wt%, they exhibit numerous turbulent structures.

Nonlinear reduction using the extended group finite element method

In this paper, we develop a nonlinear reduction framework based on our recently introduced extended group finite element method. By interpolating nonlinearities onto approximation spaces defined with the help of finite elements, the extended group finite element formulation achieves a noticeable reduction in the computational overhead associated with nonlinear finite element problems. However, the problem’s size still leads to long solution times in most applications. Aiming to make real-time and/or many-query applications viable, we consider model order reduction and complexity reduction techniques to reduce the problem size and efficiently handle the reduced nonlinear terms, respectively. For proof of concept, we focus on the proper orthogonal decomposition and discrete empirical interpolation methods. While similar approaches based on the group finite element method only focus on semilinear problems, our proposed framework is also compatible with quasilinear problems. Compared to existing methods, our reduced models prove to be superior in many different aspects as demonstrated in three numerical benchmark problems.

Large eddy simulation of non-premixed flame behavior and NOx emission characteristics in a staged combustor with multi-swirling flows

This study utilizes Large Eddy Simulation (LES) to investigate flame characteristics and NOx emission generation in a concentric staged combustor with three distinct pilot swirler arrangements. We examine the effects of multi-swirling flow on the instantaneous flow field and flame characteristics using the Proper Orthogonal Decomposition (POD) method, and assess how variations in swirler structures influence thermoacoustic instability. Furthermore, a comparison of NOx emissions between two pilot swirler configurations, with similar mean flow field and flame characteristics, highlights the precessing vortex core's role in NOx emissions. Compared to a single-swirler setup, a double-swirler configuration produces a more distinct single precessing vortex core, thereby amplifying thermoacoustic instability. The extended venturi structure in the double-swirler setup mitigates the development of the swirl-induced vortex core, reducing thermoacoustic instability. However, the expansion section in this setup impedes initial fuel and air mixing, leading to an extended flame length, which in turn results in higher NOx emissions due to a more concentrated temperature distribution. With similar mean flow field and flame structure, the double-swirler combustor proves more effective in reducing NO emissions than the triple-swirler combustor.

Experimental study on quantitative characterization of cavitation internal structure based on the distribution of void fraction in pressure relief valve

Accurately quantify the complex structure of cavitation in pressure relief valve by experiment remains a challenging task. In this research, a quantitative method for assessing the vapor volume fraction in cavitation images by void fraction experimentally is proposed, this method is less affected by environmental interference and could achieve rapid and accurate characterization of cavitation. The results show that void fraction effectively represents changes in vapor volume fraction under different conditions. The influence of the grid division numbers on the vapor volume fraction is investigated, the optimal number of grid division is 93 in X direction, with a misjudgment number of 130 and a misjudgment rate of 1.62 %. The effects of grid numbers on vapor volume fraction under different cavitation image pixels is also discussed, the optimal number of grid division is 112 in flow direction, with a misjudgment number of 144 and a misjudgment rate of 1.21 %. Through processing the vapor volume fraction image using the Proper Orthogonal Decomposition (POD) method under different cavitation numbers, the results show that the cavitation number has an important influence on the proportion of re-entrant jet area and cavitation collapse area, when the cavitation number decreases to 0.047, the proportion of re-entrant jet area and cavitation collapse area achieve the maximum that 6.41 % and 8.68 %, respectively. Such quantitative analysis of the cavitation degrees under various working conditions can contribute to a better understanding of the impact of cavitation on valve dynamics mechanisms.

Binocular reconstruction of breaking ship bow waves in circulating water channel

This study conducts an experiment on the bow waves generated by a 1:80 KRISO container ship (KCS) model in a circulating water channel. The Froude numbers (characterized by the length of perpendiculars) reach high conditions of 0.377, 0.424, and 0.471. A binocular imaging system is employed to reconstruct three-dimensional configurations of the bow wave surface. The dynamic characteristics of bow wave fields are investigated by observing the standard deviation and employing the Proper Orthogonal Decomposition (POD) method. The power spectral density function presents a power-law relationship with frequency. A novel technique referred as Stereoscopic Foam Image Velocimetry (SFIV) is developed to extract the instantaneous three-dimensional velocity of the foam in breaking area. The velocity field obtained through SFIV defines the nominal time-averaged velocity and nominal turbulent energy. A correlation mapping from pixel coordinates to world coordinates is established to evaluate the actual physical uncertainty. The results demonstrate the superior spatiotemporal accuracy and resolution of binocular imaging technology in measuring the characteristics of bow waves. This research provides significant experimental data of surface three-dimensional configurations for the bow waves breaking issues at high Froude numbers.

The dimension reduction method of two-grid Crank–Nicolson mixed finite element solution coefficient vectors for nonlinear fourth-order reaction diffusion equation with temporal fractional derivative

Herein, we mainly resort to a proper orthogonal decomposition (POD) to study the dimension reduction of unknown solution coefficient vectors in the two-grid Crank–Nicolson mixed finite element (CNMFE) (TGCNMFE) method for the nonlinear fourth-order reaction diffusion equation with temporal fractional derivative and establish a new reduced-dimension extrapolated TGCNMFE (RDETGCNMFE) method. For this purpose, we firstly retrospect the TGCNMFE method for the nonlinear fourth-order reaction diffusion equation and provide the existence, unconditional stability, and error estimates of the TGCNMFE solutions. Thereafter, we use the POD method to reduce the dimensionality of the unknown TGCNMFE solution coefficient vectors of the nonlinear fourth-order reaction diffusion equation and develop the new RDETGCNMFE method, and use matrix analysis to analyze the existence, unconditional stability, and errors of the RDETGCNMFE solutions. Finally, we perform numerical experiments to verify our theoretical results and show the advantages of the RDETGCNMFE method. It is worth noting that the RDETGCNMFE method herein is completely distinguished from the existing ones. Hence, the work in this paper is brand-new.

Spectral feature extraction of rocket exhaust plume using spectral proper orthogonal decomposition

The spectral characterization of flow-field parameters provides a new perspective for understanding the spatiotemporal evolution of unsteady supersonic exhaust plumes and for extracting typical structures. In this study, a large-eddy simulation is performed to calculate the three-dimensional unsteady supersonic plume flow field of rocket engines, and a spectral proper orthogonal decomposition (SPOD) method with a spatiotemporal separation is established. This approach is used to extract the coherent structural features of the unsteady exhaust plume flow field and analyze the mode space structure at different frequencies. The three-dimensional reconstruction and denoising of the exhaust plume flow-field parameters can be achieved via the frequency- and time-domain reconstructions of the SPOD algorithm and oblique projection method, respectively. The ground rocket exhaust plume of ballistic evaluation motor-II is analyzed. The results indicate that the SPOD method can effectively extract the single-frequency mode structure of the reactive supersonic flow field, and that low-order behavior appears in the m = 0 and m = 1 azimuth modes. The potential core exhibits a high-frequency wave-packet structure that is affected by shock waves and shear layers. Time-domain reconstruction based on the oblique projection method facilitates the capture of the dynamic characteristics of the flow field. For the first-order SPOD mode, the frequency- and time-domain reconstruction errors are 3.3% and 1.5%, respectively. The frequency-domain reconstruction method exhibits a 4% improvement in denoising ability compared to low-pass filters. This study provides a novel method for the spectral characterization and spatiotemporal feature extraction of supersonic exhaust plume flow fields.

A novel accelerated convergence method for solving adjoint equations based on modal reduction

The efficiency of adjoint-based aerodynamic shape optimization depends critically on the solution efficiency of adjoint equations. In this letter, we employ the Proper Orthogonal Decomposition (POD) method to analyze the adjoint field samples and project them from the physical space into a low-order modal space. Subsequently, the full-order adjoint equations are reduced to low-order equations using the POD modes. Thus, we can efficiently predict the initial values for pseudo-time marching, thereby accelerating the solution of adjoint equations. Results indicate that the high-order POD modes are crucial for constructing the low-dimensional system. Moreover, this method can be seamlessly integrated with our previously established Dynamic Mode Decomposition (DMD) acceleration method to form a POD+DMD acceleration approach. Application of this approach to the flow past a National Advisory Committee for Aeronautics 0012 airfoil demonstrates a noteworthy 80.9% reduction in iteration numbers when solving the adjoint equations. Even for the airfoil located on the upper boundary of sampling space, the number of iterations is still reduced by 72.6%. Therefore, we believe that the proposed method holds significant promise for improving the efficiency of adjoint-based aerodynamic shape optimization in future research.

Error analysis of a reduced order method for the Allen-Cahn equation⁎

In this paper we carry out an error analysis for a reduced order method for the Allen-Cahn equation. First, an ensemble of snapshots is formed from the numerical solutions at some time instances of the full order model, which is a time-space discretisation of the Allen-Cahn equation. The reduced order model is essentially a new spatial discretisation method by using low dimensional approximations to the original approximation space. The low dimensional approximation space is generated from the ensemble of snapshots by applying a proper orthogonal decomposition method. To determine the error between the exact solution and the solution of the reduced order model. We consider a time-space discretisation for which an error estimate of the full model solution is available. Specifically, the full discretisation is based on a stabilized auxiliary variable approach for the time stepping and a spectral Galerkin method for the spatial discretisation. The advantages of this full discretisation are its unconditional stability, the availability of error estimates and its ease of implementation. An estimate of the errors in the H1 seminorm is rigorously derived for both the full order model and the reduced order model, which is then verified by some numerical examples.

Proper orthogonal decomposition method of constructing a reduced-order model for solving partial differential equations with parametrized initial values

This paper proposes a novel proper orthogonal decomposition method for constructing a reduced-order model. This model effectively computes solutions for various initial conditions in time-dependent partial differential equations. The mode obtained from the proposed proper orthogonal decomposition captures both the fluctuating component and the mean-field of the time-dependent solution. In this mode, the eigenvalues representing the mean-field, are significantly larger than those representing the fluctuating component. Consequently, determining the number of modes required for representing a solution cannot rely solely on the cumulative contribution rate. Therefore, the proposed method gives a scalar weight to the mean-field and controls the magnitude of the mean-field energy. We propose a method that considers the magnitude of the scaler weight alongside the cumulative contribution ratio for determining the number of modes. This method was evaluated using the time-dependent Burgers equation with parametric initial values. Our proposed method selects the appropriate mode to represent the given dataset, unlike the conventional method. A reduced-order model based on the proposed method effectively computes the time evolutions of the solutions using datasets for several parameters by imposing a condition that the cumulative contribution ratio exceeds 98%.

Experimental investigation on the effects of transverse injection distribution scheme on dual flame dynamics subjected to flow disturbances

Combustion instability has become a major problem in low-emission annular gas turbine combustors. It is of practical importance to investigate the effects of transverse nozzle distribution scheme on multi-flame dynamics subjected to external acoustic perturbations. In this study, the responses of heat release rate perturbations from dual propane/air laminar premixed flames to axial acoustic perturbations have been experimentally measured. Specifically, the velocity disturbance upstream the flame base has been measured by two-microphone method and the flame heat release rate perturbation is obtained by the photomultiplier tube with CH* filter lens. The dynamic evolution of dual flames is captured by the high-speed camera and then analyzed with the proper orthogonal decomposition (POD) method. Results indicate that there is a critical distribution distance, where the peak gain of the dual flame transfer function is the largest. And the direct injection dual flame transfer function can behave as the low-pass filter. Furthermore, the dual flame transfer function behaves nonlinearly with the increase of the injection angle. The dual flame transfer function for large injection angle can behave as the hybrid mode of the low-pass filter and the band-pass filter. The POD analysis reveals that the coupling effect of gas thermal expansion and stretch effect would contribute to the interaction between dual flame front dynamics. The transverse injection distribution scheme (dual flame distance and injection angle) has a significant effect on the dual flame front dynamics, which in turn affects the flame heat release rate disturbance. The bulk mean flow velocity can enhance the interaction effect between dual flame front dynamics.

Data-driven identification and pressure fields prediction for parallel twin cylinders based on POD and DMD method

The mode analysis of parallel twin cylinders is conducted in this paper using two data-driven methods: proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD). First, a high-fidelity computational fluid dynamics (CFD) model of parallel twin cylinders is established, and numerical simulations of the model are carried out. Subsequently, the fundamental principles of the POD and DMD algorithms are systematically introduced. Utilizing snapshots obtained from the high-fidelity CFD model, the POD and DMD methods are employed to extract the dominant flow structures. Furthermore, a comparison between the two data-driven methods is conducted by analyzing modal frequencies, pressure distribution, and the reconstruction errors of pressure fields. Finally, the pressure fields of non-sample points are predicted based on the POD–backpropagation neural network (BPNN) surrogate model and the DMD method, and the predicted results are compared with the CFD simulation results. It found that (i) the DMD method is capable of extracting the main coherent structures of the pressure fields, directly obtaining flow modes and their corresponding frequencies, and assessing the stability of flow modes; (ii) the DMD method can capture the main flow features of the pressure fields in both spatial and temporal dimensions, while the POD method is primarily efficient at capturing the spatial features of the pressure fields; (iii) in contrast to the frequency-ranked DMD method, the energy-ranked POD method can reconstruct the pressure fields using a smaller number of modes, indicating that the POD method has an advantage in terms of mode reduction; (iv) in contrast to the energy-ranked POD method, the frequency-ranked DMD method has a wider applicability to the range of flow types and has more advantages in stability analysis of complex dynamic systems; (v) the predicted pressure fields around the cylinder using the first five-order POD modes or DMD modes closely align with CFD calculation results. Additionally, the evolution of pressure fields predicted by the POD–BPNN surrogate model with the first five-order POD modes or the DMD method with the first 200-order DMD modes significantly agrees with CFD simulation results; (vi) the combined use of the POD–BPNN surrogate model and DMD methods allows efficient interpolation and extrapolation of samples, delivering exceptional predictive performance. This study offers insight into the coherent structures in parallel twin cylinders.

Investigation of the unsteady pressure fluctuation mechanism in a regenerative flow pump based on proper orthogonal decomposition

The regenerative flow pump (RFP) derives its name from the circular flow pattern akin to a vortex. However, the presence of numerous vortices results in highly turbulent flow and pressure fluctuation. This study delves into the characteristics of the internal unsteady flow in two distinct RFP models featuring different blade shapes. Numerical simulations are employed to obtain the pressure field, which is subsequently scrutinized using the proper orthogonal decomposition (POD) method. The results show that the average pressure in the peripheral direction undergoes minimal variation during the flow developing stage, experiences a sharp increase in the fully developed stage, and finally exhibits substantial changes in the stripper. The transient pressure in the time domain fluctuates periodically, and the dominant blade passing frequency in the frequency domain demonstrates a similar trend along the circumferential direction as the average pressure. Moreover, the fluctuating intensity of pressure diminishes along the impeller's rotating direction but intensifies significantly in the stripper. Comparative analysis indicates that the exchange intensity is influenced by the flow at different developmental stages, and the exchange flow conditions could reflect the fluctuating intensity. Furthermore, the study reveals that the frequency amplitude of the time coefficient gradually decreases as the mode order increases. The first and second modes exhibit a gradually changing trend associated with pressure increase patterns, whereas the third and fourth modes highlight the emergence of localized modulation phenomena linked to exchange flow. Thus, the POD method offers a unique perspective for comprehending the flow mechanisms within RFPs.

Experimental and numerical study on buffeting force characteristics of the π -shaped bridge deck

In this study, a π-shaped main beam with typical geometric characteristic parameters was selected for conducting wind tunnel tests, and the characteristics of the buffeting force were measured. Based on the measured results, numerical expansion research was conducted using the narrowband synthetic random flow generation (NSRFG) turbulent inlet method, and a grid strategy was provided. By changing the geometric characteristic parameters of the π-shaped girder, a comparative study was conducted using proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) methods, revealing the influence of cross-sectional geometric characteristic parameters on the buffeting force characteristics and analyzing their mechanism of action. The results indicate that the inlet wind parameters of the NSRFG need to be adapted to the grid size. The grid filter size at the front end of the model should be smaller than 0.193 of the along-wind turbulence integral scale, which can then be used to solve for 80% of the turbulent kinetic energy. The smaller the aspect ratio is, the larger the buffeting force spectrum is, and the smaller the opening ratio is, the smaller the buffeting force spectrum is. The opening ratio strongly influences the buffeting lift spectrum, and the aspect ratio strongly influences the buffeting drag spectrum. The POD decomposition indicates that the geometric characteristic parameters affect the shape, strength, position, and direction of vortices at the section opening. DMD decomposition indicates that geometric feature parameters affect the frequency and growth rate of dominant modes as well as the directionality and regularity of vortex distribution.

A physics merged deep neural network-based prediction method for jet turbulent mixing noise

Turbulent mixing noise is a vital component of jet noise, and its rapid, accurate prediction has always been persistently pursued. Recent advancement in machine learning has been applied to jet noise prediction. However, these applications are pure curve fitting and lack physical constraints. In this study, a physics-merged deep neural network (PMNN)-based prediction method was developed for turbulent mixing jet noise by merging the physics of the jet noise. This deep neural network (DNN)-based method employed recent advancements in jet turbulent mixing noise containing large- and fine-scale turbulence structures. Two simple rational functions for large- and fine-scale turbulent noise similarity spectra were proposed to replace the original complex similarity spectra functions and incorporated into the DNN-based prediction method. For comparison, we present two data-driven DNN-based prediction methods (DDNN). The first DDNN method used the sound pressure level (SPL) as the output of neural networks, directly establishing the nonlinear relationship between the input features and SPL. In the second DDNN method, the dominant modes of the jet noise spectra extracted using the proper orthogonal decomposition method were merged with DNN. These DNN-based methods were then trained using a set of experimental data over a wide range of jet operating conditions. Their performance was evaluated and compared. It was evident that all these DNN-based methods were capable of predicting turbulent mixing noise reasonably well. In contrast to the DDNN methods, the PMNN method could provide insights into the jet turbulent mixing noise components. It demonstrates that the turbulent mixing jet noise spectra at the mid polar angle is generated by the large-scale noise component at low-frequency range and by the fine-scale noise component at high-frequency range.