Multi-step Prediction Error Research Articles

1D -FNO - Residual convolutional neural network autoregressive prediction model for deep water wave train evolution based on high-order spectral (HOS) data

Accurate prediction of deep-water wave dynamics is essential for ocean engineering, meteorology, and maritime safety. Traditional physical models, though effective, face significant computational and time challenges with complex nonlinear dynamics. This study introduces an autoregressive prediction model using a one-dimensional adaptive Fourier Neural Operator-Residual Convolutional Neural Network (1D-FNO-ResNet) to enhance prediction accuracy. We developed a high-precision single-step prediction model capable of capturing wave characteristics such as height and fluid particle velocity. A fine-tuning training strategy based on multi-step prediction errors was proposed for autoregressive evolution. Performance comparisons between the ResNet and FNO-ResNet models were made under various fine-tuning steps. A correction model was also introduced to control error accumulation, improving autoregressive prediction steps. The model's generalization performance was validated with modulated and random wave trains under different conditions, optimizing predictive stability and accuracy. This approach demonstrates efficient 1D deep-water wave evolution prediction, offering a novel deep learning solution for wave dynamics prediction in ocean engineering, supporting wave energy conversion device design and optimization.

Sample Efficient Deep Reinforcement Learning With Online State Abstraction and Causal Transformer Model Prediction.

Deep reinforcement learning (RL) typically requires a tremendous number of training samples, which are not practical in many applications. State abstraction and world models are two promising approaches for improving sample efficiency in deep RL. However, both state abstraction and world models may degrade the learning performance. In this article, we propose an abstracted model-based policy learning (AMPL) algorithm, which improves the sample efficiency of deep RL. In AMPL, a novel state abstraction method via multistep bisimulation is first developed to learn task-related latent state spaces. Hence, the original Markov decision processes (MDPs) are compressed into abstracted MDPs. Then, a causal transformer model predictor (CTMP) is designed to approximate the abstracted MDPs and generate long-horizon simulated trajectories with a smaller multistep prediction error. Policies are efficiently learned through these trajectories within the abstracted MDPs via a modified multistep soft actor-critic algorithm with a λ -target. Moreover, theoretical analysis shows that the AMPL algorithm can improve sample efficiency during the training process. On Atari games and the DeepMind Control (DMControl) suite, AMPL surpasses current state-of-the-art deep RL algorithms in terms of sample efficiency. Furthermore, DMControl tasks with moving noises are conducted, and the results demonstrate that AMPL is robust to task-irrelevant observational distractors and significantly outperforms the existing approaches.

BTPNet: A Probabilistic Spatial-Temporal Aware Network for Burn-Through Point Multistep Prediction in Sintering Process.

Burn-through point (BTP) is a very key factor in maintaining the normal operation of the sintering process, which guarantees the yield and quality of sinter ore. Due to the characteristics of time-varying and multivariable coupling in the actual sintering process, it is difficult for traditional soft-sensor models to extract spatial-temporal features and reduce multistep prediction error accumulation. To address these issues, in this study, we propose a probabilistic spatial-temporal aware network, called BTPNet, which is used to extract spatial-temporal feature for accurate BTP multistep prediction. The BTPNet model consists of two parts: an encoder network and a decoder network. In the encoder network, the multichannel temporal convolutional network (MTCN) is employed to extract the temporal features. Meanwhile, we also propose a novel architectural unit called variables interaction-aware module (VIAM) to extract the spatial features. In the decoder network, to reduce the accumulated errors of the last step prediction, a probabilistic estimation (PE) method is proposed to improve the performance of multistep prediction. Finally, the experimental results on a real sintering process demonstrate the proposed BTPNet model outperforms state-of-the-art multistep prediction models.

Draw on advantages and avoid disadvantages by making a multi-step prediction

Reinforcement learning learns about the environment through the process of exploration, and the sufficient information collected during the interaction helps the agent to predict the future situation. However, uncontrolled exploration may cause the agent to stray into dangerous regions of the environment, leading to bad decisions and impairing the agent’s performance. In order to address the issue, a framework, referred to as the policy guided by multi-step prediction (PGMP), is proposed. PGMP utilizes a curiosity mechanism based on multi-step prediction errors to stimulate exploration. To encourage the agent to explore safe or task-relevant areas, a safety bonus model is designed to determine whether the exploration area is safe or not by predicting the possible reward that can be gained. The combination of two intrinsic rewards serves as a curiosity model to give high returns to unknown states and possible safe actions. In addition, to avoid possible dangers in a limited number of future steps during exploration, a looking-ahead model is introduced to predict future multi-step states, actions, and rewards, respectively. Then, future information is combined with the policy network and included in the loss function of the policy update, allowing the agent to optimize its policy for predicted future states. Experiments on several tasks demonstrated that the proposed PGMP framework significantly improves the agent’s performance.

PM2.5 Concentration Prediction Method Based on Temporal Attention Mechanism and CNN-LSTM

Accurately predicting PM2.5 concentration can effectively avoid the harm caused by heavy pollution weather to human health. In view of the non-linearity, time series characteristics, and the problem of large multi-step prediction errors in PM2.5 concentration data, a method combining Long Short-term Memory Network and Convolutional Neural Network with Time Pattern Attention mechanism (TPA-CNN-LSTM) is proposed. The method uses historical PM2.5 concentration data, historical meteorological data, and surrounding station data to predict the future 6-hour PM2.5 concentration of air quality monitoring stations. Firstly, CNN is used to obtain the spatial characteristics between multiple stations, secondly, LSTM is added after CNN to extract the temporal changes of non-linear data, and finally, to capture the key features of temporal information, Temporal Pattern Attention mechanism (TPA) is added. TPA can automatically adjust weights based on the input of each time step, and select the most relevant time step for prediction, thereby improving the accuracy of the model. An example analysis is conducted on the measured data of Beijing's air quality stations in 2018, and compared with other mainstream algorithms. The results show that the proposed model has higher prediction accuracy and performance.

Prediction of Battery SOH by CNN-BiLSTM Network Fused with Attention Mechanism

During the use and management of lead–acid batteries, it is very important to carry out prediction and study of the state of the health (SOH) of the battery. To this end, this paper proposes a SOH prediction method for lead–acid batteries based on the CNN-BiLSTM-Attention model. The model utilizes the convolutional neural network (CNN) to carry out feature extraction and data dimension reduction in the input factors of model, and then these factors are used as the input of the bidirectional long short-term memory network (BiLSTM). The BiLSTM is used to learn the temporal correlation information in the local features of input time series bidirectionally. The attention mechanism is introduced to assign more attention to key features in the input sequence with more significant influence on the output result by assigning weights to important features, and finally, multi-step prediction of the battery SOH is realized. Compared with the prediction results of battery SOH using other neural network methods, the method proposed in this study can provide higher prediction accuracy and achieve accurate multi-step prediction of battery SOH. Measured results show that most of the multi-step prediction errors of the proposed method are controlled within 3%.

Approaches for unsupervised identification of data-driven models for flow forecasting in urban drainage systems

Abstract In this work, an unsupervised model selection procedure for identifying data-driven forecast models for urban drainage systems is proposed and evaluated. Specifically, we consider the case of predicting inflows to wastewater treatment plants for activating wet weather operation (aeration tank settling, ATS) using Box–Jenkins models. The model selection procedure considers different model structures and different objective functions. The hyperparameter search space is constrained based on the time of concentration in the catchment. Objective function criteria that minimize one-step-ahead as well as multi-step prediction errors are considered. Finally, we consider two criteria for unsupervised selection of the best-performing model. These measure the agreement of observed and predicted hydrographs (persistence index), as well as the binary exceedance of critical flow thresholds (critical success index (CSI)). Our work shows that forecast models can be developed in an unsupervised manner, and ATS activation is correctly forecasted in 60–90% of the events. The selected model structures reflect the physical behaviour of the catchment. Models should not be selected on operational criteria like the CSI due to a risk of overfitting. The degree to which rainfall input improves forecasts depends on the specific catchment, and the objective function criterion that should be used for coefficient estimation depends on the application context.

Attention-based spatio-temporal graph convolutional network considering external factors for multi-step traffic flow prediction

Traffic flow prediction is an important part of the intelligent transportation system. Accurate multi-step traffic flow prediction plays an important role in improving the operational efficiency of the traffic network. Since traffic flow data has complex spatio-temporal correlation and non-linearity, existing prediction methods are mainly accomplished through a combination of a Graph Convolutional Network (GCN) and a recurrent neural network. The combination strategy has an excellent performance in traffic prediction tasks. However, multi-step prediction error accumulates with the predicted step size. Some scholars use multiple sampling sequences to achieve more accurate prediction results. But it requires high hardware conditions and multiplied training time. Considering the spatiotemporal correlation of traffic flow and influence of external factors, we propose an Attention Based Spatio-Temporal Graph Convolutional Network considering External Factors (ABSTGCN-EF) for multi-step traffic flow prediction. This model models the traffic flow as diffusion on a digraph and extracts the spatial characteristics of traffic flow through GCN. We add meaningful time-slots attention to the encoder-decoder to form an Attention Encoder Network (AEN) to handle temporal correlation. The attention vector is used as a competitive choice to draw the correlation between predicted states and historical states. We considered the impact of three external factors (daytime, weekdays, and traffic accident markers) on the traffic flow prediction tasks. Experiments on two public data sets show that it makes sense to consider external factors. The prediction performance of our ABSTGCN-EF model achieves 7.2%–8.7% higher than the state-of-the-art baselines.

A Multi-Step Prediction Method for Wind Power Based on Improved TCN to Correct Cumulative Error

Wind power generation is likely to hinder the safe and stable operations of power systems for its irregularity, intermittency, and non-smoothness. Since wind power is continuously connected to power systems, the step length required for predicting wind power is increasingly extended, thereby causing an increasing cumulative error. Correcting the cumulative error to predict wind power in multi-step is an urgent problem that needs to be solved. In this study, a multi-step wind power prediction method was proposed by exploiting improved TCN to correct the cumulative error. First, multi-scale convolution (MSC) and self-attentiveness (SA) were adopted to optimize the problem that a single-scale convolution kernel of TCN is difficult to extract temporal and spatial features at different scales of the input sequence. The MSC-SA-TCN model was built to recognize and extract different features exhibited by the input sequence to improve the accuracy and stability of the single-step prediction of wind power. On that basis, the multi-channel time convolutional network with multiple input and multiple output codec technologies was adopted to build the nonlinear mapping between the output and input of the TCN multi-step prediction. The method improved the problem that a single TCN is difficult to tap the different nonlinear relationships between the multi-step prediction output and the fixed input. The MMED-TCN multi-step wind power prediction model was developed to separate linearity and nonlinearity between input and output to reduce the multi-step prediction error. An experimental comparative analysis was conducted based on the measured data from two wind farms in Shuangzitai, Liaoning, and Keqi, Inner Mongolia. As revealed from the results, the MAE and RMSE of the MMED-TCN-based multi-step prediction model achieved the cumulative mean values of 0.0737 and 0.1018. The MAE and RMSE metrics outperformed those of the VMD-AMS-TCN and MSC-SA-TCN models. It can be seen that the wind power prediction method proposed in this study could improve the feature extraction ability of TCN for input sequences and the ability of mining the mapping relationship between multiple inputs and multiple outputs. The method is superior in terms of the accuracy and stability of wind power prediction.

Optimal Construction of Koopman Eigenfunctions for Prediction and Control

This article presents a novel data-driven framework for constructing eigenfunctions of the Koopman operator geared toward prediction and control. The method leverages the richness of the spectrum of the Koopman operator away from attractors to construct a set of eigenfunctions such that the state (or any other observable quantity of interest) is in the span of these eigenfunctions and hence predictable in a linear fashion. The eigenfunction construction is optimization-based with no dictionary selection required. Once a predictor for the uncontrolled part of the system is obtained in this way, the incorporation of control is done through a multistep prediction error minimization, carried out by a simple linear least-squares regression. The predictor so obtained is in the form of a linear controlled dynamical system and can be readily applied within the Koopman model predictive control (MPC) framework of (M. Korda and I. Mezić, 2018) to control nonlinear dynamical systems using linear MPC tools. The method is entirely data-driven and based predominantly on convex optimization. The novel eigenfunction construction method is also analyzed theoretically, proving rigorously that the family of eigenfunctions obtained is rich enough to span the space of all continuous functions. In addition, the method is extended to construct generalized eigenfunctions that also give rise Koopman invariant subspaces and hence can be used for linear prediction. Detailed numerical examples demonstrate the approach, both for prediction and feedback control. <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">**</sup> Code for the numerical examples is available from https://homepages.laas.fr/mkorda/Eigfuns.zip.

Composite adaptive control with fast convergence for multilayer neural network

SummaryA composite adaptive control (CAC) that combines the benefits of direct and indirect adaptive controls has better parameter adaptation and control response. Multilayer neural networks (NNs) can be employed to enhance a model's representation capacity, but previous composite adaptive approaches cannot easily train the model due to its nonlinearities. A novel CAC is therefore developed in this study to tackle the above limitations. A modified robust version is adopted by focusing on the direct adaptive part to enhance robustness of adaption. Then, the indirect parameter adaptive law is improved by adopting a small learning rate in which a multistep adaption update is executed in one control interval. Moreover, multistep prediction errors are implemented to guarantee the consistency of the approximation errors, and an experience replay technique is adopted to attenuate the requirement of persistent excitation conditions. These improvements not only accelerate the convergence process but also smoothen the updating of NN parameters. Given that a nonlinear plant with MIMO strict‐feedback structure is considered, the proposed CAC is integrated into the backstepping framework. The uniformly bounded property of the tracking errors and the approximation errors is proven by Lyapunov theory. The superiority of the proposed method and the roles of these improvements are demonstrated by comparative simulations.

Adaptive Thermal Management of Implantable Device

The temperature increase in the surrounding tissue caused by the operation of neural prosthesis has raised growing concern as the device becomes more powerful. In this paper, a real-time adaptive thermal management method is developed for implantable devices to optimize their operation while maintaining a safe operating temperature. The method adopts a simplified thermal model for supporting real-time control and updates the model parameters online using a proposed recursive multi-step prediction error minimization method. The performance of the developed thermal management method is evaluated using simulation studies, and the results show that it can achieve longer operation time and better overall performance while maintaining the safe operating temperature. In addition, the developed thermal model is validated using both the COMSOL simulation and an in vitro experiment.

Adaptive Unscented Kalman Filter using Maximum Likelihood Estimation

The purpose of this study is to develop an adaptive unscented Kalman filter (UKF) by tuning the measurement noise covariance. We use the maximum likelihood estimation (MLE) and the covariance matching (CM) method to estimate the noise covariance. The multi-step prediction errors generated by the UKF are used for covariance estimation by MLE and CM. Then we apply the two covariance estimation methods on an example application. In the example, we identify the covariance of the measurement noise for a continuous glucose monitoring (CGM) sensor. The sensor measures the subcutaneous glucose concentration for a type 1 diabetes patient. The root-mean square (RMS) error and the computation time are used to compare the performance of the two covariance estimation methods. The results indicate that as the prediction horizon expands, the RMS error for the MLE declines, while the error remains relatively large for the CM method. For larger prediction horizons, the MLE provides an estimate of the noise covariance that is less biased than the estimate by the CM method. The CM method is computationally less expensive though.

Improving Multi-Step Prediction of Learned Time Series Models

Most typical statistical and machine learning approaches to time series modeling optimize a single-step prediction error. In multiple-step simulation, the learned model is iteratively applied, feeding through the previous output as its new input. Any such predictor however, inevitably introduces errors, and these compounding errors change the input distribution for future prediction steps, breaking the train-test i.i.d assumption common in supervised learning. We present an approach that reuses training data to make a no-regret learner robust to errors made during multi-step prediction. Our insight is to formulate the problem as imitation learning; the training data serves as a "demonstrator" by providing corrections for the errors made during multi-step prediction. By this reduction of multi-step time series prediction to imitation learning, we establish theoretically a strong performance guarantee on the relation between training error and the multi-step prediction error. We present experimental results of our method, DaD, and show significant improvement over the traditional approach in two notably different domains, dynamic system modeling and video texture prediction.

Towards the real-life implementation of MPC for an office building: Identification issues

Modern control methods such as Model Predictive Control (MPC) are getting popular in recent years in many fields of industry. One of the branches that have witnessed great increase of interest in use of the MPC over the last few years is the building climate control area. According to the studies, the energy used in the building sector counts for 20–40% of the overall energy consumption. Almost half of this amount consists of heating, ventilation and air-conditioning (HVAC) costs which implies that energy consumption decrease in this area is one of the most interesting challenges today.Besides enormous potential in reduction of energy consumed by heating, ventilation and air conditioning (HVAC) systems brought by such controller, it suffers from a bottleneck being the necessity of having a reliable mathematical model of the building at disposal. By finding a mathematical model appropriate for the MPC, it is meant to obtain such a model that is able to predict the behavior of the building sufficiently accurately for several hours ahead, which is an especially delicate task. This task is getting even more complicated in case of a real-life application.In this paper, we are looking for a reliable model of a huge three-storey office building in Hasselt, Belgium. For parameter estimation, an advanced identification approach is used – its advantage is that it attacks the problem of minimization of multi-step prediction error and in this way, it corresponds to MPC requirements for a good multi-step predictor. Moreover, we discuss not only the identification approach itself but we also focus on accompanying problems with real-operation data acquisition, processing and special treatment which is an indispensable step for achieving satisfactory identification results. The chosen model is now used in real operation with MPC at Hollandsch Huys.

Improving performance and stability of MPC relevant identification methods

Model Predictive Control (MPC) Relevant Identification (MRI) methods are a good option for identification, if there is model structure mismatch. Herein a new MRI method, named Enhanced Multistep Prediction Error Method (EMPEM), is proposed. EMPEM combines the best characteristics of others MRI methods in a single algorithm. It was developed to identify either closed-loop or open-loop systems; its convergence and stability make it perform better than the other presented methods. To show the advantages of EMPEM, a comparison is made against two other methods (one MRI and one PEM). The statistical analysis indicates that in the cases studied, the performance and the robustness of the new method is equal or better than the other ones.

Study on Displacement Prediction Model of Foundation Pit

The prediction model is proposed in this paper to predict the displacement of foundation pit. In the model, genetic algorithms is applied to optimize the node function of the neural network (15 node function coefficients are optimized simultaneously). Next, do the further optimization to the model, and GA-transFcn3 Model is established whose fitness evaluation takes into account the multi-step prediction error. Finally, it is verified that the GA-transFcn3 Model created in this article has the desirable prediction accuracy through engineering examples. The establishment of GA-transFcn3 Model can provide researchers and engineers with ideas and methods for the displacement prediction of foundation pit, and can be popularized and applied in practical projects.

Multi-step prediction error approach for controller performance monitoring

Performance monitoring of model predictive control (MPC) systems has received a great interest from both academia and industry. In recent years some novel approaches for multivariate control performance monitoring have been developed without the requirement of process models or interactor matrices. Among them the prediction error approach has been shown promising, but it is based on single-step prediction and may not be compatible with the MPC objective that is based on multi-step prediction. This paper develops a multi-step prediction error approach for performance monitoring of model predictive control systems, and demonstrates its application in a real industrial MPC performance monitoring and diagnosis problem.

Toward optimal multistep forecasts in non-stationary autoregressions

This paper investigates multistep prediction errors for non-stationary autoregressive processes with both model order and true parameters unknown. We give asymptotic expressions for the multistep mean squared prediction errors and accumulated prediction errors of two important methods, plug-in and direct prediction. These expressions not only characterize how the prediction errors are influenced by the model orders, prediction methods, values of parameters and unit roots, but also inspire us to construct some new predictor selection criteria that can ultimately choose the best combination of the model order and prediction method with probability 1. Finally, simulation analysis confirms the satisfactory finite sample performance of the newly proposed criteria.

Multi-step Prediction Error Approach for MPC Performance Monitoring

Performance monitoring of model predictive control systems (MPC) has received a great interest from both academia and industry. In recent years some novel approaches for multivariate control performance monitoring have been developed without the requirement of process models or interactor matrices. Among them the prediction error approach has been shown to be a promising one, but it is k-step prediction based and may not be fully comparable with the MPC objective that is multi-step prediction based. This paper develops a multi-step prediction error approach for performance monitoring of model predictive control systems, and demonstrates its application in an industrial MPC performance monitoring and diagnosis problem.