Sampled Time Series Research Articles

Self-Supervised Time Series Representation Learning via Cross Reconstruction Transformer.

Since labeled samples are typically scarce in real-world scenarios, self-supervised representation learning in time series is critical. Existing approaches mainly employ the contrastive learning framework, which automatically learns to understand similar and dissimilar data pairs. However, they are constrained by the request for cumbersome sampling policies and prior knowledge of constructing pairs. Also, few works have focused on effectively modeling temporal-spectral correlations to improve the capacity of representations. In this article, we propose the cross reconstruction transformer (CRT) to solve the aforementioned issues. CRT achieves time series representation learning through a cross-domain dropping-reconstruction task. Specifically, we obtain the frequency domain of the time series via the fast Fourier transform (FFT) and randomly drop certain patches in both time and frequency domains. Dropping is employed to maximally preserve the global context while masking leads to the distribution shift. Then a Transformer architecture is utilized to adequately discover the cross-domain correlations between temporal and spectral information through reconstructing data in both domains, which is called Dropped Temporal-Spectral Modeling. To discriminate the representations in global latent space, we propose instance discrimination constraint (IDC) to reduce the mutual information between different time series samples and sharpen the decision boundaries. Additionally, a specified curriculum learning (CL) strategy is employed to improve the robustness during the pretraining phase, which progressively increases the dropping ratio in the training process. We conduct extensive experiments to evaluate the effectiveness of the proposed method on multiple real-world datasets. Results show that CRT consistently achieves the best performance over existing methods by 2%-9%. The code is publicly available at https://github.com/BobZwr/Cross-Reconstruction-Transformer.

Nonlinear Transient Switching Filter for Automatic Buffer Window Adjustment in Short-term Ship Response Prediction

Online ship response prediction is one of the emerging interests in seakeeping due to the extensive range of applications for autonomous control of marine vehicles. In particular, the short-term prediction and online updates of ship response have received special attention. Despite a body of studies on different predictors, the asymptotic properties of estimators given the time series sample size have not been addressed specifically, so the predictors only have been analyzed for a fixed observation window regardless of the intrinsic statistical characteristics in the time series. To this end, the current research has explored the performance of two nonlinear and linear based regressors: support vector regression (SVR) and the adaptive Seasonal Auto-Regressive and Integrated Moving Average (SARIMA) model on the time series data obtained from a simulated semisubmersible platform in different sea states. The experiment demonstrated that the prediction accuracy depends significantly on the observation window length statistical properties with respect to the ship responses in various wave conditions. Therefore, an innovative filter using the weighted average of a proposed function has been introduced to adaptively adjust the buffer window based on the signal statistical characteristics. The encouraging outcomes underscore that the introduced filter not only holds the potential to enhance various predictors employed in autonomous onboard decision-making, guidance, and stabilization systems for both existing and forthcoming intelligent onboard control systems but also offers an avenue to bolster the autonomy of dynamic systems. More precisely, the proposed mechanism could extend its applicability to enhance cognitive systems and enable deterministic decision-making in diverse fields beyond the scope of present contribution.

SAR-Transformer-based decomposition and geophysical interpretation of InSAR time-series deformations for the Hong Kong-Zhuhai-Macao Bridge

Time-series interferometric synthetic aperture radar (InSAR) provides a unique tool for measuring large-scale and long-term land surface deformation. Under the assumption of a single linear deformation model in conventional InSAR, it is difficult to quantify and interpret the impacts of multiple environmental factors that presumably induce nonlinear deformations. In this paper, we propose a SAR-Transformer method to decompose InSAR time-series signals into various physics-related components and apply the method to evaluate the deformation of the world's longest cross-sea bridge, the Hong Kong-Zhuhai-Macao Bridge (HZMB). We first developed an improved bridge geometry-based InSAR network to monitor the deformation of the HZMB using Sentinel-1 and COSMO-SkyMed images from 2019 to 2022, which were validated using the leveling and GPS data. The SAR-Transformer model was trained using synthetic InSAR time-series samples and applied to decompose the monitored InSAR measurements. Compared with that of conventional curve-fitting and seasonal-trend decomposition using LOESS, SAR-Transformer reduced the mean absolute error at least by 58.32% and mean absolute percentage error at least by 8.84% for time-series signal reconstruction. We evaluated the decomposed patterns according to the geotechnical, meteorological, and marine processes, and found that: 1) Seasonal thermal expansion owing to temperature changes was significant in all parts of the bridge, and deflection due to concrete shrinkage and creep was observed on cable-stayed bridges. 2) The artificial islands experienced evident ground subsidence with a decelerating trend. In particular, the newly adopted non-dredged reclamation method resulted in a lower decelerated settlement than that of fully-dredged reclamation areas. 3) The seawall showed linear horizontal movement from the outward stretching of the reclaimed soil consolidation and periodic displacement related to sea tidal loading. Furthermore, typhoons and coastal earthquakes had limited effects on the permanent movement of the bridge. These results improve the understanding of the interactions between artificial super-infrastructures and environmental factors, and provide valuable guidelines for the maintenance and management of the HZMB.

A CNN-LSTM model for road surface recognition of electric balance vehicles

In recent years, artificial intelligence has developed rapidly, and artificial intelligence equipment has greatly facilitated people's lives. During the operation of intelligent devices, accurate environmental perception is of great importance. To provide more accurate electric balance vehicle instructions, we collect the vibration signal data in different driving environments, and machine learning (ML) methods are adopted to extract and analyse the characteristics of the signal. Then, the classification of the road type is realized. In the study, a Bluetooth wireless acceleration-attitude sensor is used to collect acceleration, angular velocity and angle signal data of the balance vehicle in the X, Y and Z directions. Through analysis, the classification accuracy of using continuous time series data as learning samples is higher than that of using a single time step signal. In the classification based on continuous time series samples, three different models XGBoost, LSTM and 1D-ResNet, are used. XGBoost is applied on artificial feature extraction data and the other models are applied on original sequence data. The F1 scores of the three models are 0.80, 0.77 and 0.79, respectively. To mitigate overfitting, we propose a CNN-LSTM model, whose F1 score is 0.83, outperforming the previous three models.

Detecting Structural Changes in Time Series by Using the BDS Test Recursively: An Application to COVID-19 Effects on International Stock Markets

Structural change tests aim to identify evidence of a structural break or change in the underlying generating process of a time series. The BDS test has its origins in chaos theory and seeks to test, using the correlation integral, the hypothesis that a time series is generated by an identically and independently distributed (IID) stochastic process over time. The BDS test is already widely used as a powerful tool for testing the hypothesis of white noise in the residuals of time series models. In this paper, we illustrate how the BDS test can be implemented also in a recursive manner to evaluate the hypothesis of structural change in a time series, taking advantage of its ability to test the IID hypothesis. We apply the BDS test repeatedly, starting with a sub-sample of the original time series and incrementally increasing the number of observations until it is applied to the full sample time series. A structural change in the unknown underlying generator model is detected when a change in the trend shown by this recursively computed BDS statistic is detected. The strength of this recursive BDS test lies in the fact that it does not require making any assumptions about the underlying time series generator model. We ilustrate the power and potential of this recursive BDS test through an application to real economic data. In this sense, we apply the test to assess the structural changes caused by the COVID-19 pandemic in international financial markets. Using daily data from the world’s top stock indices, we have detected strong and statistically significant evidence of two major structural changes during the period from June 2018 to June 2022. The first occurred in March 2020, coinciding with the onset of economic restrictions in the main Western countries as a result of the pandemic. The second occurred towards the end of August 2020, with the end of the main economic restrictions and the beginning of a new post-pandemic economic scenario. This methodology to test for structural changes in a time series is easy to implement and can detect changes in any system or process behind the time series even when this generating system is not known, and without the need to specify or estimate any a priori generating model. In this sense, the recursive BDS test could be incorporated as an initial preliminary step to any exercise of time series modeling. If a structural change is detected in a time series, rather than estimating a single predictive model for the full-sample time series, efforts should be made to estimate different predictive models, one for the time before and one for the time after the detected structural change.

An experimental study on monitoring of marine sediment transport by using a 3D sediment trap

The observation and analysis of sediment transport in oceans is an important means for the protection of the marine environment, resource development, construction engineering, and element cycling. However, traditional methods of observing sediment transport are either limited by the range of the instruments used or their own observational attributes, such that they cannot be used to accurately detect and analyze the process of transport of marine sediment. A 3D sediment trap has been proposed to compensate for the shortcomings of the various monitoring tools in our team, but no mature method for the analytical inversion of the data obtained from this device has been developed to date. In this paper, we developed analytical methods to invert sediment transport processes using corrected capture efficiency, sample inversion, and transport flux analysis. Through an annular flume test, we measured the turbidity, pressure, and particle size of the water stream and substituted them into the proposed analytical equations, thus verifying the applicability of the analytical methods. We used the slice experiment of the time series of the sediment samples, to determine the validity of the sample inversion, and establish the relationship between the particle size and concentration of the captured samples. We performed restoration tests on the process of sediment transport to establish a set of methods of flux analysis based on the velocity and turbidity of flow. And finally corrected for capture efficiency by particle size. The combination of analytical methods and 3D sediment trap could provide technological support for investigating the evolution of the sea, ecological cycle, and marine engineering.

Predicting net growth rates in boreal forests using Landsat time series and permanent sample plot data

Abstract Increasing temperature and changes in water dynamics are bringing uncertainty regarding the future productivity of boreal forests, even in the absence of stand-replacing disturbances. There is accumulating evidence that water deficits caused by warmer summer temperatures are linked to decreases in the growth rate of boreal tree species in some regions. In this context, it is essential to provide forest professionals with a means of monitoring net forest growth rates in undisturbed areas and at the scale of a management unit in order to determine where and when changes in growth are taking place. This is challenging using conventional forest inventory approaches. In this study, we use Landsat time series and data from permanent sample plots (PSP) to develop spatially explicit estimates of annual net basal area growth at a 30-m spatial resolution for a forest management unit in Canada. An ordinary least square regression model was developed using data from 120 PSPs and validated on an independent set of 60 PSPs, with R2 values of 0.61 and 0.58, respectively. Applying the model over a 586 607-ha study area revealed considerable temporal and spatial variability in the predicted growth rates and their evolution through time. There was an overall decline in predicted growth rates over time, with this trend corroborated by the PSP data and attributed to the ageing demographics of the forests in the study area. This variability was related to forest development stage, species composition, and structural attributes derived from light detection and ranging (LiDAR). The information generated by the suggested approach can help to improve yield predictions, optimize rotation lengths, and allow for the identification of target areas where silvicultural interventions aimed at maintaining or enhancing growth could be conducted.

Fault diagnosis of pressure relief valve based on improved deep Residual Shrinking Network

Pressure relief valves are widely used in hydraulic systems but often fail when operating in harsh environments. Developing effective and robust fault diagnosis models is essential for ensuring the reliable operation of hydraulic systems. In that study, we proposed a novel method for diagnosing clamping faults of pressure relief valve and addressing catastrophic forgetting under deep learning multi-task scenarios. Specifically, we combined the Elastic Weight Consolidation (EWC) algorithm with Deep Residual Shrinkage Network (DRSN) to achieve high diagnostic accuracy. Multiple time-series samples of pressure relief valve were collected and tested under hydraulic media with different pollutant particles. The proposed model achieves an average accuracy of 98.8% and an average loss of 0.095, which proves its effectiveness in the fault diagnosis of pressure relief valve. The main contribution of this study is the effective integration of the EWC algorithm with the DRSN, which provides an effective solution for the fault diagnosis of the pressure relief valve.

Study on prediction of ocean effective wave height based on hybrid artificial intelligence model

Accurate and effective wave height prediction plays a crucial role in harnessing marine energy, ensuring navigation safety, mitigating and preventing disasters, advancing scientific research, and so on. A hybrid Artificial Intelligence (AI) model Prophet_LSTM was proposed for effective wave height prediction in this study. First, the Prophet model is used to smooth the outliers in the original time series samples, and a large number of potential features were deeply mined. Then, the extracted information was used as a valuable source of augmented data, enhancing the training quality of the LSTM to improve its overall performance. Next, a sequence of procedures, encompassing normalization, grid search, and random search, was employed to identify the optimal parameters for the hybrid model in the wave height prediction. Finally, experiments were carried out based on seven years of data from station 44,025, 44,013, and 51,101 of the National Data Buoy Center (NDBC). The results show that the evaluation metrics of the Prophet_LSTM hybrid model are significantly improved compared with the traditional 1-h predictions technique and model.

Different Source Contributions of Bioactive Trace Metals in Sinking Particles in the Northern South China Sea

Time-series samples intercepted via three synchronized moored sediment traps, deployed at 1000 m, 2150 m, and 3200 m in the northern South China Sea (NSCS) during June 2009–May 2010, were analyzed to quantify the bioactive trace metal fluxes in sinking particles and investigate their different source contributions. Iron (Fe) primarily originated from lithogenic sources. Manganese (Mn), cobalt (Co), nickel (Ni), copper (Cu), and zinc (Zn) exhibited various degrees of enrichment over their continental crustal ratios. Since the sources of bioactive trace metals in sinking particles can be divided into lithogenic, biogenic, and excess fractions, mass conservation calculations were used to quantify the contribution of each source. The results showed that Fe, Mn, and Co had extremely low biogenic proportions (0.1–3.3%), while Ni, Cu, and Zn had higher proportions (2.7–17.3%), with the biogenic fraction decreasing with the depth. Moreover, excess sources accounted for a significant proportion of Mn (68–75%), Co (34–54%), Ni (60–62%), Cu (59–74%), and Zn (56–65%) in sinking particles at the three sampling depths. The excess fractions of Mn, Co, and Cu in sinking particles can be affected by authigenic particles. This is supported by their similar scavenging-type behavior, as observed via the increase in their fluxes and enrichment patterns with the increasing depth. Furthermore, the excess fractions of Ni, Cu, and Zn may have significant contributions from anthropogenic sources. The variability of Fe in sinking particles was mainly controlled via lithogenic matter. Notably, organic matter and opal were found to be pivotal carriers in the export of excess bioactive trace metals (Mn, Co, Ni, and Cu) via the water column, accompanied with the elevated ballast effect of lithogenic matter with the depth. However, the transportation of excess Zn was more complicated due to the intricate processes involved in Zn dynamics. These findings contribute to our understanding of the sources and transport mechanisms of bioactive trace metals in the marine environment.

Evaluating virtualization for fog monitoring of real-time applications in mixed-criticality systems

Technological advances in embedded systems and the advent of fog computing led to improved quality of service of applications of cyber-physical systems. In fact, the deployment of such applications on powerful and heterogeneous embedded systems, such as multiprocessors system-on-chips (MPSoCs), allows them to meet latency requirements and real-time operation. Highly relevant to the industry and our reference case-study, the challenging field of nuclear fusion deploys the aforementioned applications, involving high-frequency control with hard real-time and safety constraints. The use of fog computing and MPSoCs is promising to achieve safety, low latency, and timeliness of such control. Indeed, on one hand, applications designed according to fog computing distribute computation across hierarchically organized and geographically distributed edge devices, enabling timely anomaly detection during high-frequency sampling of time series, and, on the other hand, MPSoCs allow leveraging fog computing and integrating monitoring by deploying tasks on a flexible platform suited for mixed-criticality software, leading to so-called mixed criticality systems (MCSs). However, the integration of such software on the same MPSoC opens challenges related to predictability and reliability guarantees, as tasks interfering with each other when accessing the same shared MPSoC resources may introduce non-deterministic latency, possibly leading to failures on account of deadline overruns. Addressing the design, deployment, and evaluation of MCSs on MPSoCs, we propose a model-based system development process that facilitates the integration of real-time and monitoring software on the same platform by means of a formal notation for modeling the design and deployment of MPSoCs. The proposed notation allows developers to leverage embedded hypervisors for monitoring real-time applications and guaranteeing predictability by isolation of hardware resources. Providing evidence of the feasibility of our system development process and evaluating the industry-relevant class of nuclear fusion applications, we experiment with a safety-critical case-study in the context of the ITER nuclear fusion reactor. Our experimentation involves the design and evaluation of several prototypes deployed as MCSs on a virtualized MPSoC, showing that deployment choices linked to the monitor placement and virtualization configurations (e.g., resource allocation, partitioning, and scheduling policies) can significantly impact the predictability of MCSs in terms of Worst-Case Execution Times and other related metrics.

The asymptotic distribution of the permutation entropy.

Ordinal patterns serve as a robust symbolic transformation technique, enabling the unveiling of latent dynamics within time series data. This methodology involves constructing histograms of patterns, followed by the calculation of both entropy and statistical complexity-an avenue yet to be fully understood in terms of its statistical properties. While asymptotic results can be derived by assuming a multinomial distribution for histogram proportions, the challenge emerges from the non-independence present in the sequence of ordinal patterns. Consequently, the direct application of the multinomial assumption is questionable. This study focuses on the computation of the asymptotic distribution of permutation entropy, considering the inherent patterns' correlation structure. Furthermore, the research delves into a comparative analysis, pitting this distribution against the entropy derived from a multinomial law. We present simulation algorithms for sampling time series with prescribed histograms of patterns and transition probabilities between them. Through this analysis, we better understand the intricacies of ordinal patterns and their statistical attributes.

A study on pronunciation assessment of English learners based on temporal classification algorithm

Abstract This paper utilizes a time-series classification algorithm to classify samples, and the selected datasets are utilized to calculate the distance of time-series samples. The information gain is calculated using the information obtained, and the information entropy is determined collectively for the node datasets to generate time series features. The convolution operation is used to obtain the formal representation of the time series classification, and the extracted English pronunciation features are adaptively matched. The evaluation results were determined using a multilayer wavelet feature scale transformation method, and English learners achieved scores of 6 and above in all three tests using the time-series classification algorithm. To master standard English pronunciation, English learners should use the temporal classification algorithm.

Learning pharmacometric covariate model structures with symbolic regression networks

Efficiently finding covariate model structures that minimize the need for random effects to describe pharmacological data is challenging. The standard approach focuses on identification of relevant covariates, and present methodology lacks tools for automatic identification of covariate model structures. Although neural networks could potentially be used to approximate covariate-parameter relationships, such approximations are not human-readable and come at the risk of poor generalizability due to high model complexity.In the present study, a novel methodology for the simultaneous selection of covariate model structure and optimization of its parameters is proposed. It is based on symbolic regression, posed as an optimization problem with a smooth loss function. This enables training of the model through back-propagation using efficient gradient computations.Feasibility and effectiveness are demonstrated by application to a clinical pharmacokinetic data set for propofol, containing infusion and blood sample time series from 1031 individuals. The resulting model is compared to a published state-of-the-art model for the same data set. Our methodology finds a covariate model structure and corresponding parameter values with a slightly better fit, while relying on notably fewer covariates than the state-of-the-art model. Unlike contemporary practice, finding the covariate model structure is achieved without an iterative procedure involving manual interactions.

Based on Wavelet and Windowed Multi-Resolution Dynamic Mode Decomposition, Transient Axial Force Analysis of a Centrifugal Pump under Variable Operating Conditions

This study analyzes the transient axial force of a centrifugal pump under variable operating conditions using wavelet analysis and a novel technique called windowed multi-resolution dynamic mode decomposition (wmrDMD). Numerically simulating the sampled time series allows the reconstruction of the impeller’s axial force information, providing validation for this innovative data-driven analysis technique. The comparison between the reconstructed results and the original axial force data demonstrates a remarkable agreement, as all data points exhibit error values below 2.49%. The wmrDMD technique systematically decomposes the impeller’s axial force field into dynamically significant modes across various time scales. Removing the mean flow field in this study resolves the transient motion of the impeller’s axial force, facilitating the identification of positions with high-frequency axial force oscillations and fluctuations in intensity amplitude. The high-frequency axial force of the impeller exhibits stable periodic variations within the operating range of 1.0nr-1.0Qr, whereas the changes are insignificant within the range of 0.4nr-0.4Qr. However, within the operating range of 1.0nr-0.4Qr, both the position and intensity amplitude of the axial force exhibit significant variations without a stable trend. Furthermore, cross-wavelet and wavelet coherence analyses reveal that within the operating range of 0.4nr-0.4Qr, the axial forces on the front and rear cover plates show the strongest correlation at the periodic scale. Within the operating range of 1.0nr-1.0Qr, the next highest correlation is observed, whereas the correlation is lowest within the 1.0nr-0.4Qr operating range.

Time pattern reconstruction for classification of irregularly sampled time series

Irregularly Sampled Time Series (ISTS) include partially observed feature vectors caused by the lack of temporal alignment across dimensions and the presence of variable time intervals. Especially in medical applications, because patients’ examinations depend on their health status, observations in this event-based medical time series are nonuniformly distributed. When using deep learning models to classify ISTS, most work defines the problem that needs to be solved as alignment-caused data missing or nonuniformity-caused dependency change. However, they only modeled relationships between observed values, ignoring the fact that time is the independent variable for a time series. In this paper, we emphasize that irregularity is active, time-depended, and class-associated and is reflected in the Time Pattern (TP). To this end, this paper focused on the TP of ISTS for the first time, proposing a Time Pattern Reconstruction (TPR) method. It first encodes time information by the time encoding mechanism, then imputes values from time codes by the continuous-discrete Kalman network, selects key time points by the conditional masking mechanism, and finally classifies ISTS based on the reconstructed TP. Experiments on four real-world medical datasets and three other datasets show that TPR outperforms all baselines. We also show that TP can reveal biomarkers and key time points for diseases.

Extraction of Spatiotemporal Distribution Characteristics and Spatiotemporal Reconstruction of Rainfall Data by PCA Algorithm

Scientific analyses of urban flood risks are essential for evaluating urban flood insurance and designing drainage projects. Although the current rainfall monitoring system in China has a dense station network and high-precision rainfall data, the time series is short. In contrast, historical rainfall data have a longer sample time series but lower precision. This study introduced a PCA algorithm to reconstruct historical rainfall data. Based on the temporal and spatial characteristics of rainfall extracted from high-resolution rainfall data over the past decade, historical (6 h intervals) rainfall spatial data were reconstructed into high-resolution (1 h intervals) spatial data to satisfy the requirements of the urban flood risk analysis. The results showed that the average error between the reconstructed data and measured values in the high-value area was within 15% and in the low-value area was within 20%, representing decreases of approximately 65% and 40%, respectively, compared to traditional interpolation data. The reconstructed historical spatial rainfall data conformed to the temporal and spatial distribution characteristics of rainfall, improved the granularity of rainfall spatial data, and enabled the effective and reasonable extraction and summary of the fine temporal and spatial distribution characteristics of rainfall.

Dynamic response of root-associated fungal community structure to nitrogen and phosphorus additions in a subtropical forest

The impacts of nitrogen (N) and phosphorus (P) additions on root-associated fungi (RAF) of mixed roots in forest soils remain poorly understood. We investigated how RAF communities respond to N and P inputs in a subtropical montane forest using a time-series sampling approach. Our results showed that sampling time had a significant effect on total fungal richness, while the N addition had significant impacts on symbiotrophic rather than saprotrophic fungal richness. RAF community composition was strongly influenced by P addition treatments regardless of sampling time. Furthermore, we found that RAF community structure was mainly affected by soil NO3–-N, C/N and N/P ratios. This influence could be ascribed to the direct control of fungal activities and the indirect effects of fertilization on soil properties. Together, our findings highlight the importance of considering temporal variation in RAF responses to fertilization for a more comprehensive understanding of fungal community dynamics.

Quantifying impacts of an environmental intervention using environmental DNA.

Environmental laws around the world require some version of an environmental-impact assessment surrounding construction projects and other discrete instances of human development. Information requirements for these assessments vary by jurisdiction, but nearly all require an analysis of the biological elements of ecosystems. Amplicon-sequencing-also called metabarcoding-of environmental DNA (eDNA) has made it possible to sample and amplify the genetic material of many species present in those environments, providing a tractable, powerful, and increasingly common way of doing environmental-impact analysis for development projects. Here, we analyze an 18-month time series of water samples taken before, during, and after two culvert removals in a salmonid-bearing freshwater stream. We also sampled multiple control streams to develop a robust background expectation against which to evaluate the impact of this discrete environmental intervention in the treatment stream. We generate calibrated, quantitative metabarcoding data from amplifying the 12s MiFish mtDNA locus and complementary species-specific quantitative PCR data to yield multispecies estimates of absolute eDNA concentrations across time, creeks, and sampling stations. We then use a linear mixed effects model to reveal patterns of eDNA concentrations over time, and to estimate the effects of the culvert removal on salmonids in the treatment creek. We focus our analysis on four common salmonid species: cutthroat trout (Oncorhynchus clarkii), coho salmon (Oncorhynchus kisutch), rainbow trout (Oncorhynchus mykiss), and sockeye salmon (Oncorhynchus nerka). We find that one culvert in the treatment creek seemed to have no impact while the second culvert had a large impact on fish passage. The construction itself seemed to have only transient effects on salmonid species during the two construction events. In the context of billions of dollars of court-mandated road culvert replacements taking place in Washington State, USA, our results suggest that culvert replacement can be conducted with only minimal impact of construction to key species of management concern. Furthermore, eDNA methods can be an effective and efficient approach for monitoring hundreds of culverts to prioritize culverts that are required to be replaced. More broadly, we demonstrate a rigorous, quantitative method for environmental-impact reporting using eDNA that is widely applicable in environments worldwide.

Weighted Dynamic Time Warping for Time Series

Recurrence network is a typical time series analysis method. However, irregular sampling may overshadow the dynamic features characterized by traditional recurrence network method, which makes the method ineffective. This paper introduces dynamic time warping method to determine the distance between time series segments. The method can match the features of time series segments and reduce the distortion of distances caused by irregular sampling. For points in sparse sampling area, many characteristics may not be collected and thus the matching results are unreliable. To overcome this problem, we further propose weighted dynamic time warping method which assigns small weights to matching points with sparse local sampling so as to reduce their influence on distance. A recurrence network constructed by weighted dynamic time warping method can effectively capture underlying nonlinear and nonstationary system dynamics from irregular sampling time series. The effectiveness of the proposed method is illustrated by two case studies: the discrimination of different dynamic behaviors and detection of system parameter perturbation from time series of Rössler system.