Harmonic Approach Research Articles

Harmonising electronic health records for reproducible research: challenges, solutions and recommendations from a UK-wide COVID-19 research collaboration

BackgroundThe CVD-COVID-UK consortium was formed to understand the relationship between COVID-19 and cardiovascular diseases through analyses of harmonised electronic health records (EHRs) across the four UK nations. Beyond COVID-19, data harmonisation and common approaches enable analysis within and across independent Trusted Research Environments. Here we describe the reproducible harmonisation method developed using large-scale EHRs in Wales to accommodate the fast and efficient implementation of cross-nation analysis in England and Wales as part of the CVD-COVID-UK programme. We characterise current challenges and share lessons learnt.MethodsServing the scope and scalability of multiple study protocols, we used linked, anonymised individual-level EHR, demographic and administrative data held within the SAIL Databank for the population of Wales. The harmonisation method was implemented as a four-layer reproducible process, starting from raw data in the first layer. Then each of the layers two to four is framed by, but not limited to, the characterised challenges and lessons learnt. We achieved curated data as part of our second layer, followed by extracting phenotyped data in the third layer. We captured any project-specific requirements in the fourth layer.ResultsUsing the implemented four-layer harmonisation method, we retrieved approximately 100 health-related variables for the 3.2 million individuals in Wales, which are harmonised with corresponding variables for > 56 million individuals in England. We processed 13 data sources into the first layer of our harmonisation method: five of these are updated daily or weekly, and the rest at various frequencies providing sufficient data flow updates for frequent capturing of up-to-date demographic, administrative and clinical information.ConclusionsWe implemented an efficient, transparent, scalable, and reproducible harmonisation method that enables multi-nation collaborative research. With a current focus on COVID-19 and its relationship with cardiovascular outcomes, the harmonised data has supported a wide range of research activities across the UK.

Harmonic structure of wave loads on a surface piercing column in directionally spread and unidirectional random seas

We investigate the harmonic structure of wave-induced loads on vertical cylinders with dimensions comparable to those used to support offshore wind turbines. Many offshore wind turbines are designed, so the structural resonance is two or three times the fundamental wave loading period, which may be excited by higher harmonics of wave loading. The suitability of a ‘Stokes-type’ model for force is examined. We analyse experimental data for unidirectional and directionally spread sea-states. We demonstrate that approximate harmonic components may be extracted from a random time series, using a novel signal processing method. The extracted harmonics are shown to follow a ‘Stokes-like’ model, where the higher harmonics in frequency are proportional to the n-th power of the linear inline force component and its Hilbert transform. Results show that the third harmonic component of force is fitted less well by this model, which is consistent with the literature. A key new result is that the harmonic coefficients for spread and unidirectional seas are nearly identical when fitted as powers of the linear inline force and its Hilbert transform. This finding has the potential to greatly simplify the process of generating harmonic data for new wavelength to cylinder and wavelength to depth ratios. This also implies that the size of the inline component of the ntextrm{th} harmonic for force in a directional sea relative to the same component in a unidirectional sea scales as cos ^n sigma _theta , where sigma _theta is the rms directional spreading angle of the incident wave field. Hence, higher harmonics will be of less importance in directionally spread seas than unidirectional ones. We show that the computationally fast harmonic decomposition approach taken here can reproduce the shape and magnitude of the loading from non-breaking waves waves in a wide range of realistic unidirectional and directionally spread sea-states. The proposed force model has potential as an engineering tool for computationally fast prediction of nonlinear wave loads.

Influence of Reconstruction Algorithms on Harmonic Analysis in Electrical Impedance Tomography

Electrical Impedance Tomography (EIT) is a commonly used imaging technique for monitoring respiration on the bedside and it might have the potential for monitoring lung perfusion. Several signal processing approaches have been developed to separate respiration and perfusion. In this contribution we investigated whether different image reconstruction algorithms influence the separation results provided by the harmonic analysis approach. We compared the algorithms used by Dräger, the Gauss-Newton method with different regularizers as well as the GREIT algorithm. The comparison was carried out using a retrospective EIT dataset from a COVID-19 patient. The results gave insight that the harmonic analysis separation approach is dependent on the reconstruction algorithms. Both, the separation of the perfusion and the separation of the respiration showed differences between the reconstruction algorithms when carried out pixel-wise. On the other hand, the separations carried out on the global impedance only showed marginal differences for the separated perfusion.

Estimation of the work of adhesion between ITO and polymer substrates: a surface thermodynamics approach.

Indium tin oxide (ITO) is one of the most widely used semiconductor among transparent conducting oxides (TCOs) due to their electrical conductivity and optical transparency properties. Since the development of low temperature deposition methods, coating of ITO on polymer substrates especially for use in flexible electronics has been a popular topic. The existence of adequate adhesion strength between ITO and polymer is critical in producing a successful film. Nowadays, polycarbonate (PC), poly(methyl methacrylate) (PMMA) and polyethyleneterephtalate (PET) are frequently used as substrates for such coatings. However, there may be other polymeric alternatives that have a potential to be used for this purpose in the future. To evaluate these alternatives, work of adhesion (Wa) knowledge between ITO and polymers is necessary, and it has not been handled systematically previously. In this study, the interphase interaction parameters and Wa values between ITO and various polymers were calculated based on the Dupré, Fowkes and Girifalco-Good equations. PC, PMMA, PET, polystyrene (PS), polyphenylene sulfide (PPS), Nylon 66, polypropylene (PP), polyvinylchloride (PVC), styrene-butadiene rubber (SBR), high density polyethylene (HDPE), low density polyethylene (LDPE), polyvinyl acetate (PVAc), polyvinyl fluoride (PVF), polyvinylidene fluoride (PVDF), polytetrafluoroethylene (PTFE), polytrifluoroethylene (PTrFE) and polyperfluoroalkylethyl acrylate (PPFA) were considered as substrate material. Surface free energy (SFE) components calculated by acid-base, geometric mean and harmonic mean approaches for polymeric substrates were used during the calculations. In the present study, the polymers that can be used as substrates were evaluated in terms of adhesion ability to ITO, the significance of calculation methods on Wa values were also investigated simultaneously. It was determined that the Wa between ITO and polymer substrates was directly related with the total SFE value of the polymers.

Stakeholders Conflicting Interest and Approach for Harmonization for Business Sustainability: Evidence from Limited Liability Companies in Nigeria.

Agitations for businesses to have respect for issues other than economic gains for their owners requires the alignment and maintaining equilibrium between the social and economic activities of business organization and its multiple stakeholders who have different interests. Thus, stakeholders’ management is considered critical to creating sustainable business. Therefore, this study examined impacts of the strategic approaches of stakeholders’ analysis, stakeholders’ integration and stakeholders’ engagement in achieving business sustainability. The study adopted survey research design and structured questionnaire was used to collect primary data from top management staff of twenty selected limited liability companies in Lagos and Ogun states, Nigeria. The research instrument was validated using Cronbach – Alpha to test the reliability of the instrument which showed a coefficient of 0.706 for stakeholders’ management approaches and 0.803 for business sustainability. Data collected were analyzed using descriptive and inferential statistics. The results of ordinary least square regression of analysis of Hypothesis 1 showed that stakeholders analysis significantly contributes to business sustainability in Nigeria where F=7.8717; p – value = 0.038 < 0.05, the result of Hypothesis 11showed that stakeholders integration significantly leads to business sustainability in Nigeria where F= 3.456; p – value= 0.001< 0.05 while the result of hypothesis 3 indicated that stakeholders engagement significantly leads to business sustainability with F = 11. 530 p – value =0.019 < 0.05. The study concluded that stakeholders analysis, stakeholders integration and stakeholders engagement are useful approaches for identification and harmonization of the varying interests of a business many stakeholders. The study recommended that business organizations should include in to their organizational culture, useful approaches necessary to establish positive collaborative relationships with their stakeholders.

CTFlow: Mitigating Effects of Computed Tomography Acquisition and Reconstruction with Normalizing Flows.

Mitigating the effects of image appearance due to variations in computed tomography (CT) acquisition and reconstruction parameters is a challenging inverse problem. We present CTFlow, a normalizing flows-based method for harmonizing CT scans acquired and reconstructed using different doses and kernels to a target scan. Unlike existing state-of-the-art image harmonization approaches that only generate a single output, flow-based methods learn the explicit conditional density and output the entire spectrum of plausible reconstruction, reflecting the underlying uncertainty of the problem. We demonstrate how normalizing flows reduces variability in image quality and the performance of a machine learning algorithm for lung nodule detection. We evaluate the performance of CTFlow by 1) comparing it with other techniques on a denoising task using the AAPM-Mayo Clinical Low-Dose CT Grand Challenge dataset, and 2) demonstrating consistency in nodule detection performance across 186 real-world low-dose CT chest scans acquired at our institution. CTFlow performs better in the denoising task for both peak signal-to-noise ratio and perceptual quality metrics. Moreover, CTFlow produces more consistent predictions across all dose and kernel conditions than generative adversarial network (GAN)-based image harmonization on a lung nodule detection task. The code is available at https://github.com/hsu-lab/ctflow.

MRIS: A Multi-modal Retrieval Approach for Image Synthesis on Diverse Modalities.

Multiple imaging modalities are often used for disease diagnosis, prediction, or population-based analyses. However, not all modalities might be available due to cost, different study designs, or changes in imaging technology. If the differences between the types of imaging are small, data harmonization approaches can be used; for larger changes, direct image synthesis approaches have been explored. In this paper, we develop an approach based on multi-modal metric learning to synthesize images of diverse modalities. We use metric learning via multi-modal image retrieval, resulting in embeddings that can relate images of different modalities. Given a large image database, the learned image embeddings allow us to use k-nearest neighbor (k-NN) regression for image synthesis. Our driving medical problem is knee osteoarthritis (KOA), but our developed method is general after proper image alignment. We test our approach by synthesizing cartilage thickness maps obtained from 3D magnetic resonance (MR) images using 2D radiographs. Our experiments show that the proposed method outperforms direct image synthesis and that the synthesized thickness maps retain information relevant to downstream tasks such as progression prediction and Kellgren-Lawrence grading (KLG). Our results suggest that retrieval approaches can be used to obtain high-quality and meaningful image synthesis results given large image databases.

Traveling Subject-Informed Harmonization Increases Reliability of Brain Diffusion Tensor and Neurite Mapping.

Diffusion-weighted magnetic resonance imaging (dMRI) of brain has helped elucidate the microstructural changes of psychiatric and neurodegenerative disorders. Inconsistency between MRI models has hampered clinical application of dMRI-based metrics. Using harmonized dMRI data of 300 scans from 69 traveling subjects (TS) scanning the same individuals at multiple conditions with 13 MRI models and 2 protocols, the widely-used metrics such as diffusion tensor imaging (DTI) and neurite orientation dispersion and density imaging (NODDI) were evaluated before and after harmonization with a combined association test (ComBat) or TS-based general linear model (TS-GLM). Results showed that both ComBat and TS-GLM significantly reduced the effects of the MRI site, model, and protocol for diffusion metrics while maintaining the intersubject biological effects. The harmonization power of TS-GLM based on TS data model is more powerful than that of ComBat. In conclusion, our research demonstrated that although ComBat and TS-GLM harmonization approaches were effective at reducing the scanner effects of the site, model, and protocol for DTI and NODDI metrics in WM, they exhibited high retainability of biological effects. Therefore, we suggest that, after harmonizing DTI and NODDI metrics, a multisite study with large cohorts can accurately detect small pathological changes by retaining pathological effects.

MULTILINGUAL THEMATIC ANALYSIS USING VARIED TRANSLATIONS AND LINGUISTIC VALIDATION OF CODES: ADVANCING INCLUSION

Abstract Despite the widely acknowledged cultural diversity among older adults and family caregivers, the representation of people from different linguistic backgrounds in a single study is rare. Single language is a common inclusion criterion, limiting the diversity of samples. Performing cross-cultural qualitative research using several languages within a study requires a systematic data harmonization approach to assure the trustworthiness of the analysis. This paper describes strategies used to establish trustworthiness in the multi-lingual thematic analysis of a dyadic qualitative descriptive study of older adults hospitalized in general hospitals and family members who accompanied them during the hospitalization. Participant interviews (n=22) were conducted in English, Hebrew, and Russian according to individual preferences. Four of the dyads (8 participants) were interviewed in different languages. Based on the template analysis approach, we performed multiple multi-lingual translations and linguistic validation of an inductively identified high-level coding scheme. Each linguistic validation process included a reconciliation of two forward translations and harmonization using back translation, performed for each pair of languages. We describe the rationale for decisions regarding the translation process (the timing of translation after establishing a high-level coding scheme, using a hermeneutic translation approach to achieve conceptual equivalence, variability in the socio-demographic context of the translators, recruitment of both translators and linguists). This study provides principles of a feasible systematic approach to overcome linguistic barriers in caregiving research, providing an avenue for inclusive research among multi-cultural and multi-lingual study samples.

White matter changes following electroconvulsive therapy for depression: a multicenter ComBat harmonization approach

ECT is proposed to exert a therapeutic effect on WM microstructure, but the limited power of previous studies made it difficult to highlight consistent patterns of change in diffusion metrics. We initiated a multicenter analysis and sought to address whether changes in WM microstructure occur following ECT. Diffusion tensor imaging (DTI) data (n = 58) from 4 different sites were harmonized before pooling them by using ComBat, a batch-effect correction tool that removes inter-site technical variability, preserves inter-site biological variability, and maximizes statistical power. Downstream statistical analyses aimed to quantify changes in Fractional Anisotropy (FA), Mean Diffusivity (MD), Radial Diffusivity (RD) and Axial Diffusivity (AD), by employing whole-brain, tract-based spatial statistics (TBSS). ECT increased FA in the right splenium of the corpus callosum and the left cortico-spinal tract. AD in the left superior longitudinal fasciculus and the right inferior fronto-occipital fasciculus was raised. Increases in MD and RD could be observed in overlapping white matter structures of both hemispheres. At baseline, responders showed significantly smaller FA values in the left forceps major and smaller AD values in the right uncinate fasciculus compared with non-responders. By harmonizing multicenter data, we demonstrate that ECT modulates altered WM microstructure in important brain circuits that are implicated in the pathophysiology of depression. Furthermore, responders appear to present a more decreased WM integrity at baseline which could point toward a specific subtype of patients, characterized by a more altered neuroplasticity, who are especially sensitive to the potent neuroplastic effects of ECT.

Stability Analysis of an Industrial Blade Accounting for a Blade-Tip/Casing Nonlinear Interface

Abstract This paper investigates the local stability analysis of periodic solutions corresponding to the nonlinear vibration response of an industrial compressor blade, NASA rotor 37, on which are applied different types of nonlinearities. These solutions are obtained using a harmonic balance method-based approach presented in a previous paper. It accounts for unilateral contact and dry friction of the rotating blade against a rigid casing through a regularized penalty law. A Lanczos filtering technique is also employed to mitigate spurious oscillations related to the Gibbs phenomenon thus enhancing the robustness of the solver. In addition, a component mode synthesis technique is used to reduce the dimension of the numerical model. Stability assessment of the computed solutions relies on Floquet theory. It is performed through the computation of the monodromy matrix as well as Hill's method. Both methodologies are applied and thoroughly compared as the severity of the nonlinearity is gradually increased from a cubic spring to three-dimensional contact conditions on a deformed casing. While the presented results underline the applicability of both stability assessment methodologies for all types of nonlinearities, they also put forward the much higher computational effort required when computing the monodromy matrix. Indeed, it is shown that Hill's method yields converged results for significantly lower values of both the number of retained harmonics and the considered number of time steps thus making it a far more efficient method when dealing with industrial models. It is also underlined that the presented results are in excellent agreement with reference solution points obtained with time domain solution methods. Specific implementation tweaks that were found to be of critical importance in order to efficiently assess the stability of computed solutions are also detailed in order to provide a comprehensive view of the challenges inherent to such numerical developments.

“Deep-Dive analysis of the latest Lithium-Ion battery safety testing standards and regulations in Germany and China”

Lithium-Ion batteries contribute a key technology for electric vehicles. Their production is being accelerated worldwide as electric vehicles become increasingly popular – not only because of the tremendous challenges of climate change. Currently, the homologation of Lithium-Ion batteries is subject to different regulations and authorities in different markets, provoking high efforts for battery testing in general. This comprehensive comparison of the latest updated Chinese regulation GB 38031–2020 with German as well as UN and ECE standards and regulations aims at exploring potentials for their harmonization. For this purpose, testing methods in the corresponding standards and regulations are systematically categorized, matched and evaluated. It is found that the testing methods for vibration, crush, altitude and pressure, thermal propagation and water immersion safety show the greatest differences. In corresponding deep dives, those testing methods are examined and challenged with regard to realistic vehicle usage situations and suggestions for further improvements are being derived. Finally, the authors discuss possible harmonization approaches, taking into account upcoming battery technological developments.

Performance Evaluation of Solar PV-Based Z-Source Cascaded Multilevel Inverter with Optimized Switching Scheme

AC loads may demand a fixed or variable voltage at their input terminals. When using inverters to power such loads, the response of the inverter must be precisely controlled to suit the demands of the AC loads. Inverters with higher efficiency and sensitivity will play an increasingly essential role as the need for solar PV applications in prospective green technology grows. To increase power quality and provide a reliable power source, an inverter architecture with harmonic reduction approaches is proposed. The multilevel inverter (MLI), unlike conventional inverters, is developed by cascaded single inverter units and is often used to connect renewable energy sources. As a result, they can be utilized to efficiently reduce harmonics. Among the three topologies, the most widely used in industries is the neutral-point clamped MLI. When the levels are raised, however, they demand a larger number of diodes. When the level of the flying capacitor exceeds three, several capacitors are necessary. As a result, the optimum option for synthesizing the right output voltage from several DC sources is a cascaded multilevel inverter (CMLI). Each link in a CMLI is connected by a single DC source; therefore, there is no voltage imbalance. However, getting equal DC voltages at the input of each unit is once again a limitation. In this work, various existing multilevel inverter topologies including hybrid topologies with different switching strategies are investigated and reported. The performance of a solar PV-based seven-level quasi-Z-source cascaded H-Bridge MLI (qZS-CHBMLI) has been thoroughly examined with the best switching scheme and best topology of multilevel inverters using MATLAB/Simulink.

Thermo-elastodynamic study of the nanocomposite circular sector plates exposed to swift thermal shock

Owing to ruinous effects of thermal shocks on the nanocomposite structures, this study scrutinizes the thermal shock resistance of the poroelastic nanocomposite circular sector plates in the scheme of elasticity theory and application of the harmonic differential quadrature approach (HDQA). Due to the fact that the related studies published priorly were just able to predict the response of the simply-supported plates, the current research would be considered as the first study on the transient thermal shock response of the above-mentioned plates with fully-clamped boundary conditions. To determine the system’s time-dependent response, differential equations are translated to the Laplace domain. Then, the modified declaration of the Dubner and Abate’s technique is exploited to derive the time realization of the system’s response from the Laplace domain. The validation procedure of the current analysis is performed by comparing the outcomes with those claimed in the published researches. In order to clearly assess the system’s shock resistance against the abrupt thermal load, effect of various parameters such as thermal relaxation time (TRT), different scattering models and volume fraction of the nano reinforcement, boundary conditions, intensity of the shock, poroelastic properties of the nanocomposite, and radius to thickness ratio of the sector plate on the thermo-elastodynamic response of the system are investigated. It is revealed that the sensitivity of the system’s response to increase of TRT subsides when TRT is over an upper bond.

Stochastic path-integral approach for predicting the superconducting temperatures of anharmonic solids

We develop a stochastic path-integral approach for predicting the superconducting transition temperatures of anharmonic solids. By defining generalized Bloch basis, we generalize the formalism of the stochastic path-integral approach, which is originally developed for liquid systems. We implement the formalism for ab initio calculations using the projector augmented-wave method, and apply the implementation to estimate the superconducting transition temperatures of metallic deuterium and hydrogen sulfide. For metallic deuterium, which is approximately harmonic, our result coincides well with that obtained from the standard approach based on the harmonic approximation and the density functional perturbation theory. For hydrogen sulfide, we find that anharmonicity strongly suppresses the predicted superconducting transition temperature. Compared to the self-consistent harmonic approximation approach, our approach yields a transition temperature closer to the experimentally observed one.

Scale-Shift and Harmonic analysis approach to the Mellin transform for Discrete-time signals

We investigate the scale-shift operator for discrete-time signals via the action of the hyperbolic Blaschke group. Practical implementation issues are discussed and given for any arbitrary scale, in the framework of very classical discrete-time linear filtering. Our group theoretical standpoint leads to a purely harmonic analysis definition of the Mellin transform for discrete-time signals. Explicit analytical expressions of the atoms of the discrete-time Fourier-Mellin decomposition are provided along with a simple algorithm for their computation. The so-defined scale-shift operator also allows us to establish a mathematical equivalence in between the discrete-time wavelet coefficients of a given discrete-time signal and the corresponding Voice-transform generated by a well-chosen unitary representation of the Hyperbolic Blaschke group, in the classical Hardy space of the unit disc.

Harmonic Analysis of the Relationship between GNSS Precipitable Water Vapor and Heavy Rainfall over the Northwest Equatorial Coast, Andes, and Amazon Regions

This study finds the relationship between increases in precipitable water vapor (PWV), and intense rainfall events in four different climatological regions of South America’s equatorial northwest: the coast, Andes valley, high mountains, and Amazon. First, the PWV was derived from tropospheric zenith delay measured by Global Navigation Satellite System (GNSS) instrumentation located near meteorological stations within the regions of interest using hourly data from the year 2014. A harmonic analysis approach through continuous wavelet cross-spectrum and coherence, as well as discrete wavelets, was used to determine a measure of the lags found between PWV and specific heavy rain events and then compared with satellite IR images and meteorological anomalies. The link between PWV peaks and rainfall was the most evident on the coast, and less discernible in the other stations possibly due to local dynamic factors. The results showed a lag of 11 h between the preceding PWV increase and an intense rainfall event. This was apparent in all of the stations, except in Amazon where it was 6 h, with the highest precision at the coast and with the largest dispersion in the high mountains. The interpretation of this lag for each region is also discussed.

Tensor-Based Harmonic Analysis of Distribution Systems

Over the past few decades, there have been rapid advances in solid-state technology as well as a reduction in cost. This, coupled with the functionality and efficiency improvements they afford, has resulted in a massive increase in the use of electronic devices. Where traditionally, there were a few well-known nonlinear loads that needed to be considered, now there are numerous low-power devices. Although individually insignificant, collectively, they are very significant. This paper presents a tensor-based harmonic analysis approach that is capable of capturing important interactions while being computationally efficient enough to model a large distribution system. Numerical experiments are used to highlight the advantages of the tensor framework. Numerous papers have investigated the tensor parametrisation or its mathematical equivalent—harmonically coupled admittance matrices (also known as frequency coupling matrices). However, this paper, for the first time, demonstrates how these models can be applied to perform harmonic modelling of a complete low voltage (LV) distribution system.

The impact of harmonization on radiomic features in Parkinson's disease and healthy controls: A multicenter study.

Radiomics is a challenging development area in imaging field that is greatly capturing interest of radiologists and neuroscientists. However, radiomics features show a strong non-biological variability determined by different facilities and imaging protocols, limiting the reproducibility and generalizability of analysis frameworks. Our study aimed to investigate the usefulness of harmonization to reduce site-effects on radiomics features over specific brain regions. We selected T1-weighted magnetic resonance imaging (MRI) by using the MRI dataset Parkinson’s Progression Markers Initiative (PPMI) from different sites with healthy controls (HC) and Parkinson’s disease (PD) patients. First, the investigation of radiomics measure discrepancies were assessed on healthy brain regions-of-interest (ROIs) via a classification pipeline based on LASSO feature selection and support vector machine (SVM) model. Then, a ComBat-based harmonization approach was applied to correct site-effects. Finally, a validation step on PD subjects evaluated diagnostic accuracy before and after harmonization of radiomics data. Results on healthy subjects demonstrated a dependence from site-effects that could be corrected with ComBat harmonization. LASSO regressor after harmonization was unable to select any feature to distinguish controls by site. Moreover, harmonized radiomics features achieved an area under the receiving operating characteristic curve (AUC) of 0.77 (compared to AUC of 0.71 for raw radiomics measures) in distinguish Parkinson’s patients from HC. We found a not-negligible site-effect studying radiomics of HC pre- and post-harmonization of features. Our validation study on PD patients demonstrated a significant influence of non-biological noise source in diagnostic performances. Finally, harmonization of multicenter radiomic data represent a necessary step to make analysis pipelines reliable and replicable for multisite neuroimaging studies.

A nonlinear seismic metamaterial lying on layered soils

To protect engineering structures from being destroyed by earthquakes, seismic metamaterials have been proposed for Rayleigh wave attenuation. Introducing nonlinearity may provide new design options for seismic metamaterials. Although nonlinear seismic metamaterials lying on homogeneous substrates have been reported, the real stratigraphy is a layered structure. In the present work, Rayleigh wave propagation through a nonlinear seismic metamaterial is studied. The seismic metamaterial consists of nonlinear resonators attaching on layered soils composed of clayey slit and sandy slit. First, an analytical model is established, and the closed-form solution for the dispersion of nonlinear Rayleigh wave is calculated via the leading-order harmonic balance approach. Then, finite element (FE) simulations are conducted to obtain the wave mode, dispersion, as well as transmission, and validate the analytical results. This study shows that the clayey slit reduces the phase velocity of Rayleigh wave. Due to the interaction of the resonators with Rayleigh wave propagating in the layered substrate, solutions in the form of surface wave vanish within a certain frequency band. This frequency band is the bandgap for Rayleigh wave. The FE simulations further show that in this frequency band, the energy of Rayleigh wave is converted into bulk wave. Moreover, the dispersion of nonlinear Rayleigh wave is amplitude-dependent, which enhances the designability of seismic metamaterials.