Dynamic Mode Decomposition Method Research Articles

Connections between propulsive efficiency and wake structure via modal decomposition

We present experiments on oscillating hydrofoils undergoing combined heaving and pitching motions, paying particular attention to connections between propulsive efficiency and coherent wake features extracted using modal analysis. Time-averaged forces and particle image velocimetry measurements of the flow field downstream of the foil are presented for a Reynolds number of $Re=11\times 10^3$ and Strouhal numbers in the range $St=0.16\unicode{x2013}0.35$ . These conditions produce 2S and 2P wake patterns, as well as a near-momentumless wake structure. A triple decomposition using the optimized dynamic mode decomposition method is employed to identify dominant modal components (or coherent structures) in the wake. These structures can be connected to wake instabilities predicted using spatial stability analyses. Examining the modal components of the wake provides insightful explanations into the transition from drag to thrust production, and conditions that lead to peak propulsive efficiency. In particular, we find modes that correspond to the primary vortex development in the wakes. Other modal components capture elements of bluff body shedding at Strouhal numbers below the optimum for peak propulsive efficiency and characteristics of separation for Strouhal numbers higher than the optimum.

Coherent structures decomposition of internal flow in the double-suction centrifugal pump impeller

Abstract In order to understand the unsteady flow phenomenon of the centrifugal pump, the dynamic mode decomposition method (DMD) is introduced to extract the three-dimensional coherent structure of the rotating flow field in the impeller passage under three different working conditions of the double-suction centrifugal pump. The time series collection of flow field is constructed by CFD numerical simulation, and the approximate matrix characteristic parameters and different modal data are solved. The analysis results show that the position, form and spatial-temporal evolution of the coherent structure can be accurately captured by DMD method corresponding to a single frequency in the double suction pump. For the temporal evolution, the coherent structure corresponding to low frequency is the most stable and dominate the unsteady flow. For the spatial evolution, the coherent structure corresponding to even-fold rotational frequency mostly occurs near the pressure side of the blade at the outlet of the impeller, and the coherent structure corresponding to odd-fold rotational frequency is mostly located in the flow field inside the impeller or near the blade surface.

Direct numerical simulation of shock wave/boundary layer interaction controlled by steady microjet in a compression ramp

Shock wave/boundary layer interaction in a 24° turning angle of the compression ramp at Mach number 2.9 controlled by steady microjet is investigated using direct numerical simulation. Three different jet spacings which are termed as sparse, moderate and dense are considered, and the induced vortex system and shock structures are compared. A moderate jet spacing configuration is found to generate counter-rotating vortex pairs that transport high-momentum fluid towards the vicinity of wall and strengthen the boundary layer to resist separation, reducing the separation region. The dense jet spacing configuration creates a larger momentum deficit region, reducing the friction downstream of the corner. Analysis of pressure and pressure gradient reveals that dense jet spacing configuration reduces the intensity of separation shock. The impact of varying jet spacings on the turbulent kinetic energy transport mechanism is also investigated by decomposing the budget terms in the transport equation. Furthermore, the spectral characteristics of the separation region are studied using power spectral density and dynamic mode decomposition methods, revealing that moderate jet spacing configuration suppresses low-frequency fluctuations in the separation region.

Data-driven modeling of unsteady flow based on deep operator network

Time-dependent flow fields are typically generated by a computational fluid dynamics method, which is an extremely time-consuming process. However, the latent relationship between the flow fields is governed by the Navier–Stokes equations and can be described by an operator. We therefore train a deep operator network (DeepONet) to learn the temporal evolution between flow snapshots. Once properly trained, given a few consecutive snapshots as input, the network has a great potential to generate the next snapshot accurately and quickly. Using the output as a new input, the network iterates the process, generating a series of successive snapshots with little wall time. Specifically, we consider two-dimensional flow around a circular cylinder at Reynolds number 1000 and prepare a set of high-fidelity data using a high-order spectral/hp element method as ground truth. Although the flow fields are periodic, there are many small-scale features in the wake flow that are difficult to generate accurately. Furthermore, any discrepancy between the prediction and the ground truth for the first snapshots can easily accumulate during the iterative process, which eventually amplifies the overall deviations. Therefore, we propose two alternative techniques to improve the training of DeepONet. The first one enhances the feature extraction of the network by harnessing the “multi-head non-local block.” The second one refines the network parameters by leveraging the local smooth optimization technique. Both techniques prove to be highly effective in reducing the cumulative errors, and our results outperform those of the dynamic mode decomposition method.

Study on rotating stall characteristics of centrifugal pumps based on gamma transition model

The phenomenon of rotating stall in centrifugal pumps is closely associated with the evolution of the blade boundary layer. Aiming to accurately predict the characteristics of the boundary layer, this study investigates the phenomenon of rotating stall in centrifugal pump impellers using the gamma (γ) transition model. The accuracy of the numerical simulation was confirmed by comparing its conclusions with the results of the testing. In calculations considering transition characteristics, the distribution of low-pressure areas inside the impeller is relatively discontinuous, while the pressure distribution is more uniform. However, in calculations without considering transition, the low-pressure regions in neighboring flow channels exhibit a tendency to be interconnected, resulting in a more variable pressure distribution, and the pressure contour at the outlet is closer to parallel. The dynamic characteristics of the centrifugal pump impeller rotating stall were obtained through the dynamic mode decomposition method, including the frequency, structure, and dynamic evolution process of the stall vortex. Through modal reconstruction, it was discovered that the impeller's rotation causes the stall vortex to undergo periodic fluctuations. The stall vortex is not stationary but moves synchronously with the rotation of the blades. At different time points, the stall vortex exhibits periodic changes. At the blade suction entrance, the stall vortex initially appears. Subsequently, multiple vortex structures resulted in channel blockage. After a period of development, the excess vortex structures merge to generate a typical “8” shaped vortex structure and move toward the exit. Finally, the exit stall vortex disappears, and a new vortex structure is generated at the inlet of the blade suction surface.

Diagnosis of unsteady disturbance characteristics induced by the tip leakage vortex in a compressor based on data-driven modal decomposition methods

The structural information about the tip leakage vortex at the design point remains largely unknown. Here, the dynamic mode decomposition method is utilized to visualize the main coherent structures corresponding to unsteady disturbance frequencies induced by the tip leakage vortex of an isolated rotor at the design point. The results show that the tip clearance size has a significant impact on unsteady disturbance characteristics at the blade tip region. The flow field within the blade tip region can be categorized into four distinct regions: the formation region of the main tip leakage vortex (MTLV), the formation region of the secondary tip leakage vortex (STLV), the merging zone where the MLTV and the STLV interact, and the vortex shedding zone induced by the leakage vortex breakdown. The disturbance peak in the frequency domain decreases from 121.3 RF to 70.96 RF as the tip clearance size increases from 1.5% blade height to 2%, resulting in a reduction of 41.36%. The increase in the tip clearance size amplifies unsteady disturbances caused by the MTLV and STLV. The STLV exhibits more pronounced oscillatory characteristics than the MTLV. The unsteady disturbance induced by the MLTV mainly occurs at around 0.5 blade passing frequency (BPF). In contrast, high-frequency unsteady disturbances (>1 BPF) in the flow field are caused by vortex shedding resulting from the interaction and collision between the STLV and the MTLV. A better understanding of the unsteady disturbance characteristics induced by leakage vortex benefits the study of stall warning technology.

A novel approach for estimating lung tumor motion based on dynamic features in 4D-CT

Due to the high expenses involved, 4D-CT data for certain patients may only include five respiratory phases (0%, 20%, 40%, 60%, and 80%). This limitation can affect the subsequent planning of radiotherapy due to the absence of lung tumor information for the remaining five respiratory phases (10%, 30%, 50%, 70%, and 90%). This study aims to develop an interpolation method that can automatically derive tumor boundary contours for the five omitted phases using the available 5-phase 4D-CT data. The dynamic mode decomposition (DMD) method is a data-driven and model-free technique that can extract dynamic information from high-dimensional data. It enables the reconstruction of long-term dynamic patterns using only a limited number of time snapshots. The quasi-periodic motion of a deformable lung tumor caused by respiratory motion makes it suitable for treatment using DMD. The direct application of the DMD method to analyze the respiratory motion of the tumor is impractical because the tumor is three-dimensional and spans multiple CT slices. To predict the respiratory movement of lung tumors, a method called uniform angular interval (UAI) sampling was developed to generate snapshot vectors of equal length, which are suitable for DMD analysis. The effectiveness of this approach was confirmed by applying the UAI-DMD method to the 4D-CT data of ten patients with lung cancer. The results indicate that the UAI-DMD method effectively approximates the lung tumor’s deformable boundary surface and nonlinear motion trajectories. The estimated tumor centroid is within 2 mm of the manually delineated centroid, a smaller margin of error compared to the traditional BSpline interpolation method, which has a margin of 3 mm. This methodology has the potential to be extended to reconstruct the 20-phase respiratory movement of a lung tumor based on dynamic features from 10-phase 4D-CT data, thereby enabling more accurate estimation of the planned target volume (PTV).

The reduced-order model of 5 × 5 fuel rod bundles

The fuel rod bundles are the core part of pressurized water reactors (PWRs), and its heat transfer characteristics directly impact the safety of PWRs. A computational fluid dynamics (CFD) model of 5 × 5 fuel rod bundles with a spacer grid is established, and the numerical simulation results are in excellent agreement with the experimental results. Then, the effects of four turbulence models, namely shear stress transport model, standard k–ε model, re-normalization group k–ε model, and realizable k–ε model on the thermal-hydraulic characteristics of the 5 × 5 fuel rod bundles are systematically investigated. Furthermore, two data-driven methods, namely proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD), are used to analyze the flow fields of the 5 × 5 fuel rod bundles. The two methods can extract key modes or features to enhance the comprehension and description of the dynamic behaviors within the flow fields of 5 × 5 fuel rod bundles. Finally, two reduced-order models (ROMs), called the POD-radial basis function neural network surrogate model and DMD method, are constructed, which can enable rapid prediction of the flow fields for 5 × 5 fuel rod bundles with high accuracy. The CFD simulation results presented in this paper can provide valuable insights for studying the thermal-hydraulic characteristics of the 5 × 5 fuel rod bundles. The two ROMs proposed in this paper can significantly reduce the computational costs associated with studying the thermal-hydraulic characteristics of 5 × 5 fuel rod bundles.

Vehicle’s Lateral Motion Control Using Dynamic Mode Decomposition Model Predictive Control for Unknown Model

In this paper, we present a data-driven modeling method for lateral motion control of unknown vehicle models. Vehicle’s motion can be modeled linearly but this model has complex and nonlinear characteristic. Therefore, it is necessary to know the exact information of the car chassis and requires a knowledge and understanding of dynamics. To solve these drawbacks, we linearly represent full vehicle's lateral dynamics which include nonlinear behavior using dynamic mode decomposition (DMD), one of the data driven modeling methods. To determine the validity of the model obtained using the DMD method, we conducted a simulation of the comparison of the output states between the existing model and the model obtained through DMD modeling, using the scenario of a dynamic maneuver called a double line change during lateral motion of a vehicle. After determination of validation is completed, we designed a lane keeping system by applying a model predictive control to specifically evaluate the model of the proposed method. Performance was derived by comparing the error caused by the vehicle driving on the course with the controller of the simulation. The performance of the proposed approach has been evaluated through simulations and is useful when the model is inaccurate.

Research on energy harvesting characteristics of a flapping foil with trailing edge jet flap

Flapping foils offer a potential means for extracting hydrokinetic energy from ocean and river flows by utilizing a combined pitching and heaving motion of the airfoil. In this paper, the effectiveness of trailing edge active flow control in enhancing the energy harvesting performance of the conventional flapping foil is examined through numerical simulations. In this approach, an injections slot is opened at the trailing edge of the flapping foil, from which a high velocity jet is discharged into ambient water. Since the water jet is issued vertically downwards perpendicular to the airfoil surface, it operates like a Gurney flap and thus is known as jet flap in aeronautics. Parametric studies show that the optimal injection position should be as far as possible from the leading edge of the flapping foil. In addition, it is also found when the width of the exit slot of jet equals to 2.6 % of the airfoil chord and the momentum coefficient of jet is 0.02, the flapping foil with the jet flap can increase the maximum net energy harvesting efficiency obtained after deducting the energy consumption for the flow control from 39.22 % to 47.6 % compared to its baseline counterpart, indicating the effectiveness of this method. Furthermore, the dynamic mode decomposition (DMD) method is also adopted to reveal the spatial-temporal features of the coherent structures in the wake flow behind the proposed flapping foil in an attempt to gain a deep understanding of the underlying flow mechanism involved in promoting its energy harvesting performance.

Analysis of axial force and pressure pulsation of centrifugal pump as turbine impeller based on dynamic mode decomposition

To investigate the spatiotemporal evolution mechanism of the axial force on a centrifugal pump acting as a turbine, this study focuses on a single-stage single-suction centrifugal pump and applies dynamic mode decomposition (DMD) to decompose the flow field of the turbine impeller's axial force. The axial force of the impeller under three flow conditions, namely, 1.0Qd, 1.3Qd, and 1.6Qd, is extracted and analyzed. Results show that the DMD method can accurately extract the spatiotemporal coherent structural characteristics of the main modes of axial force, with the first five modes accounting for more than 99.97% of the total mode energy. Under the 1.3Qd condition, the flow field is stable, and the axial force remains constant over time with a very small degree of pressure pulsation. However, under the 1.6Qd condition, the flow field inside the pump becomes complex and unstable, leading to larger changes in axial force compared to the 1.0Qd condition, with an increase in 2.13 times. The amplitude of the pressure pulsation gradually decreases from the impeller inlet to the outlet under both 1.0Qd and 1.6Qd conditions, with vibration caused by the axial force mainly occurring at the impeller inlet. These findings provide a reference basis for improving the stability of centrifugal pumps acting as turbines.

Influence of the Trailing Edge Shape of Impeller Blades on Centrifugal Pumps with Unsteady Characteristics

The flow field structure and pressure pulsation characteristics in two series of trailing edges of a centrifugal pump are investigated using the SST k-w turbulence model. Series 1 involves varying the impeller exit angle, and Series 2 involves varying the impeller exit shape. The entropy generation rate analysis method is used to evaluate the numerical simulation results. Vortex cores within the flow field are identified by applying the Ω criterion. The influence of different trailing edge configurations on the energy loss characteristics of the pumps is explored. The dynamic mode decomposition (DMD) method is used to analyze pressure pulsations at the volute considering unsteady flows in centrifugal pumps with different trailing edge shapes. The findings suggest that different trailing edge shapes can be used to adjust the energy loss proportions in various components of the pump. In Series 1, the efficiency remains nearly constant with changes in the outlet angle on both sides of the trailing edge. In Series 2, the efficiency is enhanced by 1.18% with the elliptical edge shape on both sides (EBS) compared to the original trailing edge (OTE) shape. In Series 1 and Series 2, greater entropy generation rates are accompanied by greater pressure pulsations at the pump outlet. The DMD results demonstrate a noticeable impact of the different trailing edges on the pressure distribution of various modes within the volute. Moreover, the impeller outlet pressure inhomogeneity coefficient changes under different modes. This study holds great significance for selecting the appropriate trailing edges for centrifugal pumps.

Numerical Investigations of Outer-Layer Turbulent Boundary Layer Control for Drag Reduction Through Micro Fluidic-Jet Actuators

Drag reduction through turbulent boundary layer control (TBLC) is an essential way to develop green aviation technologies. Compared with traditional approaches for drag reduction, turbulence drag reduction is a relatively new technology, particularly for skin friction drag reduction, and it is becoming a hotspot problem worldwide. This paper focuses on the research of micro fluidic-jet actuators used for outer-layer boundary layer control with high-performance computing (HPC). This study aims to reduce turbulent drag by reshaping the flow structure within the turbulent boundary layer. To ensure the calculation accuracy of the core region and reduce the consumption of computing resources, a zonal LES/RANS strategy and WMLES method are proposed to simulate the effects of fluidic-actuators for outer-layer boundary control, in which high-performance computing has to be involved. The studies are performed on the classical zero-gradient turbulent flat plate cases, in which three different control strategies named “W-control,” “V-control,” and “VW-control” are used and compared to study the effects of drag reduction under a low Reynolds number at Reτ = 470 and a higher Reynolds number at Reτ = 4700. The mechanism for drag reduction is analysed via a pre-multiplied spectral method and a parallel dynamic mode decomposition (DMD) method. The results show that the present approach can effectively simulate the outer-layer turbulent boundary control where the “V-control” with the fluidic-jet actuator array behaves well to achieve an average drag reduction (DR) rate of more than 5% for the high Reynolds number case of the flat plate boundary layer. The high Reynolds shear stress and turbulent kinetic energy distribution in the boundary layer region show an obvious uplift under the effects of actuators, which is the main mechanism for drag reduction.

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.

Application of DMD method to eccentric self-excited vibration of tubular turbine runner

Tubular turbines are widely used in the development and utilization of low-head marine energy. The cantilever type runner inevitably leads to gap between the chamber and blade tip, and non-standard installation can easily lead to eccentric runner, affecting the safe and stable operation of turbine. The overall process of self-excited vibration is an obvious nonlinear process, so the applicability of traditional methods needs to be discussed. In recent years, reduced-order modelling methods based on linear dynamic systems have gradually been introduced into the analysis of hydraulic machinery, and have achieved certain results. Therefore, this study combines computational fluid dynamics (CFD) and dynamic mode decomposition (DMD) methods to conduct low-dimensional mode decomposition and comparative analysis of self-excited vibration caused by different runner eccentricities of tubular turbine. The research shows that as the runner eccentricity continues to increase, the modal frequency distribution of self-excited vibration becomes complex. The DMD method disassembles the low-level representations of self-excited vibration signals, greatly enriching the understanding of eccentric self-excited vibration of the runner, and providing assurance for the safe and stable operation of tubular turbines.

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.

Dynamic mode decomposition for Koopman spectral analysis of elementary cellular automata.

We apply dynamic mode decomposition (DMD) to elementary cellular automata (ECA). Three types of DMD methods are considered, and the reproducibility of the system dynamics and Koopman eigenvalues from observed time series is investigated. While standard DMD fails to reproduce the system dynamics and Koopman eigenvalues associated with a given periodic orbit in some cases, Hankel DMD with delay-embedded time series improves reproducibility. However, Hankel DMD can still fail to reproduce all the Koopman eigenvalues in specific cases. We propose an extended DMD method for ECA that uses nonlinearly transformed time series with discretized Walsh functions and show that it can completely reproduce the dynamics and Koopman eigenvalues. Linear-algebraic backgrounds for the reproducibility of the system dynamics and Koopman eigenvalues are also discussed.

EEG Detection and Prediction of Freezing of Gait in Parkinson's Disease Based on Spatiotemporal Coherent Modes.

Freezing of gait (FOG) in Parkinson's disease has a complex neurological mechanism. Compared with other modalities, electroencephalogram (EEG) can reflect FOG-related brain activity of both motor and non-motor symptoms. However, EEG-based FOG prediction methods often extract time, spatial, frequency, time-frequency, or phase information separately, which fragments the coupling among these heterogeneous features and cannot completely characterize the brain dynamics when FOG occurs. In this study, dynamic spatiotemporal coherent modes of EEG were studied and used for FOG detection and prediction. A dynamic mode decomposition (DMD) method was first applied to extract the spatiotemporal coherent modes. Dynamic changes of the spatiotemporal modes, in both amplitude and phase of motor-related frequency bands, were evaluated with analytic common spatial patterns (ACSP) to extract the essential differences among normal, freezing, and transitional gaits. The proposed method was verified in practical clinical data. Results showed that, in the detection task, the DMD-ACSP achieved an accuracy of 86.4 ± 3.6% and a sensitivity of 83.5 ± 4.3%. In the prediction task, 86.5 ± 3.2% accuracy and 86.7 ± 7.8% sensitivity were achieved. Comparative studies showed that the DMD-ACSP method significantly improves FOG detection and prediction performance. Moreover, the DMD-ACSP reveals the spatial patterns of dynamic brain functional connectivity, which best discriminate the different gaits. The spatiotemporal coherent modes may provide a useful indication for personalized intervention and transcranial magnetic stimulation neuromodulation in medical practices.

A data-driven reduced-order modeling approach for parameterized time-domain Maxwell's equations

<p>This paper proposed a data-driven non-intrusive model order reduction (NIMOR) approach for parameterized time-domain Maxwell's equations. The NIMOR method consisted of fully decoupled offline and online stages. Initially, the high-fidelity (HF) solutions for some training time and parameter sets were obtained by using a discontinuous Galerkin time-domain (DGTD) method. Subsequently, a two-step or nested proper orthogonal decomposition (POD) technique was used to generate the reduced basis (RB) functions and the corresponding projection coefficients within the RB space. The high-order dynamic mode decomposition (HODMD) method leveraged these corresponding coefficients to predict the projection coefficients at all training parameters over a time region beyond the training domain. Instead of direct regression and interpolating new parameters, the predicted projection coefficients were reorganized into a three-dimensional tensor, which was then decomposed into time- and parameter-dependent components through the canonical polyadic decomposition (CPD) method. Gaussian process regression (GPR) was then used to approximate the relationship between the time/parameter values and the above components. Finally, the reduced-order solutions at new time/parameter values were quickly obtained through a linear combination of the POD modes and the approximated projection coefficients. Numerical experiments were presented to evaluate the performance of the method in the case of plane wave scattering.</p>

Full Decoupling High-Order Dynamic Mode Decomposition for Advanced Static and Dynamic Synergetic Fault Detection and Isolation

Real industrial processes often present coupled static and dynamic characteristics, leading to significant challenges for fault detection and isolation. However, traditional dynamic modeling methods may lead to the coupling problem of statics and dynamics, which provide ambiguous process status descriptions and incorrect fault isolation results. In this work, a novel full decoupling high-order dynamic mode decomposition (FDHODMD) method is developed for fault detection and isolation of dynamic processes. Different from the existing dynamic methods, the proposed FDHODMD can separate the high-order dynamic information from static information. First, the static characteristics are separated by discarding the decomposed features corresponding to smaller singular values. Then, a high-order dynamic model is established to present the temporal relationships between variables. In this way, the effect of static characteristics on dynamics analysis can be eliminated. Accordingly, from both static and dynamic perspectives, multiple statistics are designed to comprehensively detect the anomalies and provide an explicit status identification. In addition to the static fault isolation strategy, a dynamic fault isolation strategy is designed to recognize the fault variables after detecting the deviation, which divides the complex dynamic system into several individual dynamic modes to avoid the interaction of dynamic characteristics. Thereupon, the contributions of different variables to each dynamic mode can be clearly presented to recognize the fault variables. Finally, the validity of the proposed method is illustrated through both a numerical case and a real industrial process. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —In industrial processes, the static and dynamic characteristics of data are often coupled. This work presents a FDHODMD method, which can be considered the high-order version of DMD, to achieve the decoupling of dynamics and statics while extracting high-order dynamic characteristics. Then the proposed fault detection strategy designs multiple statistics for monitoring the process from both dynamic and static perspectives, which ensures the safe operation of industrial processes. After detecting the anomaly, the proposed fault isolation strategy can recognize the fault variables separately dominating the dynamic and static deviation, which may help engineers locate the fault source.