Normalized Mean Square Error Research Articles

Research on Sparse Denoising of Strong Earthquakes Early Warning Based on MEMS Accelerometers.

In view of the fact that the noise in the same frequency band as the useful signal in the MEMS acceleration sensor observation data cannot be effectively removed by traditional filtering methods, a denoising method for strong earthquake signals based on the theory of sparse representation and compressive sensing is proposed in this paper. This skillfully realized the separation of strong earthquake signals from noise by adopting a fixed dictionary and utilizing sparse characteristics. Furthermore, considering the weakness of the sparse denoising method based on the fixed dictionary in the high signal-to-noise ratio, a spare denoising method based on learning an over-complete dictionary is proposed. Through the initial given seismic data, the ideal over-complete dictionary is trained to achieve seismic data denoising. In addition, for the interference waves of non-seismic events, this paper proposes an idea based on sparse representation classification to remove such non-seismic interference directly. Combining the ideas of noise reduction and non-seismic event elimination, we can obtain a standard sparse anti-interference denoising model for earthquake early warning. It's innovative that this model implements the sparse theory into the field of earthquake early warning. According to the experimental results, in the case of heavy noise, the denoising model based on sparse representation can reach average SNR of 8.73 and an average MSE of 29.53, and the denoising model based on compression perception can reach average SNR of 7.29 and an average MSE 41.34, and the denoising model based on learning dictionary can reach average SNR 11.07 and average MSE 17.32. The performance of these models is better than the traditional FIR filtering method (average SNR -0.73 and average MSE 260.37) or IIR filtering method (average SNR 4.73 and average MSE 73.95). On the other hand, the anti-interference method of the sparse classification proposed in this paper can accurately distinguish non-seismic interference events from natural earthquakes. The classification accuracy of the method based on the noise category of the selected test data set reaches 100% and achieves good results.

Digital Predistortion Combined with Iterative Method for MIMO Transmitters

In this article, an auxiliary module is proposed to mitigate the crosstalk effect in multiple input–multiple output (MIMO) transmitters. Other branches do not need considering when linearizing the local branch, which reduces the complexity of the auxiliary module, and some branches can be linearized selectively to make the module application more flexible. In the end, the feasibility of the proposed algorithm is verified through the experimental platform. Experimental results demonstrate that for a 2 × 2 MIMO transmitter with −20 dB nonlinear crosstalk, the proposed DPD improves the adjacent channel power ratio (ACPR) more than 16 dB, and normalized mean square error (NMSE) more than 12.8 dB, which has similar performance to the PH model. The predistorter can be implemented with fewer coefficients by separating the crosstalk from the nonlinearity, enabling the technique to be used in 5G massive MIMO scenarios.

SDC-Net: End-to-End Multitask Self-Driving Car Camera Cocoon IoT-Based System

Currently, deep learning and IoT collaboration is heavily invading automotive applications especially in autonomous driving throughout successful assistance functionalities. Crash avoidance, path planning, and automatic emergency braking are essential functionalities for autonomous driving. Trigger-action-based IoT platforms are widely used due to its simplicity and ability of doing receptive tasks accurately. In this work, we propose SDC-Net system: an end-to-end deep learning IoT hybrid system in which a multitask neural network is trained based on different input representations from a camera-cocoon setup installed in CARLA simulator. We build our benchmark dataset covering different scenarios and corner cases that the vehicle may expose in order to navigate safely and robustly while testing. The proposed system aims to output relevant control actions for crash avoidance, path planning and automatic emergency braking. Multitask learning with a bird's eye view input representation outperforms the nearest representation in precision, recall, f1-score, accuracy, and average MSE by more than 11.62%, 9.43%, 10.53%, 6%, and 25.84%, respectively.

Heart action monitoring from pulse signals using a growing hybrid polynomial network

Electrocardiogram (ECG) is a common used noninvasive test to quickly detect the heart problem with high precision. However, devices used to collect continuous ECG waveforms under free-living conditions have several operational difficulties. As an alternative, photoplethysmography (PPG) signals can be conveniently collected by pulse sensors, which can be mounted onto wearable devices. In this paper, we study the relation between ECG waveforms and PPG signals by proposing a novel growing hybrid polynomial network (GHPN)). Based on the projections between adjacent layers, the network is designed to approximate the target signals with the recorded inputs and the multi-scale dynamics of the input series are explored gradually through the growth of layers. Two public datasets are employed to evaluate the performance of the proposed approach on the accuracy of waveform reconstruction and heart rate (HR) detection with the widely used metrics. Compared with the reference ECG waveforms, the normalized mean square error (NMSE) of the proposed approach is 0.248 and 0.216 for PPG-Dalia and CapnoBase datasets, which is smaller than the comparison approaches. The average absolute value (AAE) between the detected HR and reference HR is 0.93 and 1.05 for PPG-Dalia and CapnoBase datasets, which exhibit higher HR detection accuracy. Experimental results obtained from benchmark datasets clearly show that the proposed method can achieve higher similarity on the reconstructed morphology with higher HR detection accuracy. Moreover, the proposed approach make it possible to employ PPG sensors for long-term monitoring of the heart actions with higher precision.

Segmented Spline Curve Neural Network for Low Latency Digital Predistortion of RF Power Amplifiers

At present, we are the dawn of a new era for wireless communication systems. The new dynamic approach to the operation of cellular networks requires an extension of the essential input–output hardware mechanisms, to include intelligence. Traditional neural network structures can be used to embed artificial intelligence into cellular network base stations; however, standard network structures are not an optimal solution for these use cases. In this article, we present a neural network structure, which is specifically designed to provide a more accurate and computationally efficient solution compared with the previous neural network solutions for predistortion of RF power amplifiers (PAs). The proposed network structure is directly compared with alternative neural network solutions, which have been successfully employed for digital predistortion (DPD). The operation of this network is validated for DPD with experimental measurements with wideband signals using the latest generation of commercially available RF hardware. The novel network structure proposed in this work is demonstrated, in practice, to have better performance for a normalized mean square error (NMSE), an adjacent channel leakage ratio (ACLR), and an error vector magnitude (EVM) compared with the most popular previously published neural network.

Environment information-based channel prediction method assisted by graph neural network

Recently, whether the channel prediction can be achieved in diverse communication scenarios by directly utilizing the environment information gained lots of attention due to the environment impacting the propagation characteristics of the wireless channel. This paper presents an environment information-based channel prediction (EICP) method for connecting the environment with the channel assisted by the graph neural networks (GNN). Firstly, the effective scatterers (ESs) producing paths and the primary scatterers (PSs) generating single propagation paths are detected by building the scatterer-centered communication environment graphs (SC-CEGs), which can simultaneously preserve the structure information and highlight the pending scatterer. The GNN-based classification model is implemented to distinguish ESs and PSs from other scatterers. Secondly, large-scale parameters (LSP) and small-scale parameters (SSP) are predicted by employing the GNNs with multi-target architecture and the graphs of detected ESs and PSs. Simulation results show that the average normalized mean squared error (NMSE) of LSP and SSP predictions are 0.12 and 0.008, which outperforms the methods of linear data learning.

Autonomous Short-Term Traffic Flow Prediction Using Pelican Optimization with Hybrid Deep Belief Network in Smart Cities

Accurate and timely traffic flow prediction not just allows traffic controllers to evade traffic congestion and guarantee standard traffic functioning, it even assists travelers to take advantage of planning ahead of schedule and modifying travel routes promptly. Therefore, short-term traffic flow prediction utilizing artificial intelligence (AI) techniques has received significant attention in smart cities. This manuscript introduces an autonomous short-term traffic flow prediction using optimal hybrid deep belief network (AST2FP-OHDBN) model. The presented AST2FP-OHDBN model majorly focuses on high-precision traffic prediction in the process of making near future prediction of smart city environments. The presented AST2FP-OHDBN model initially normalizes the traffic data using min–max normalization. In addition, the HDBN model is employed for forecasting the traffic flow in the near future, and makes use of DBN with an adaptive learning step approach to enhance the convergence rate. To enhance the predictive accuracy of the DBN model, the pelican optimization algorithm (POA) is exploited as a hyperparameter optimizer, which in turn enhances the overall efficiency of the traffic flow prediction process. For assuring the enhanced predictive outcomes of the AST2FP-OHDBN algorithm, a wide-ranging experimental analysis can be executed. The experimental values reported the promising performance of the AST2FP-OHDBN method over recent state-of-the-art DL models with minimal average mean-square error of 17.19132 and root-mean-square error of 22.6634.

Linear programming-aided power allocation for large OCDMA networks

To provide a suitable operation in optical code division multiple access (OCDMA) networks, it is paramount to balance the powers received at the destination optical node. This work presents a solution strategy for the power allocation (PA) problem in OCDMA by rewriting it as a linear programming (LP) problem and applying two LP methods based on the Simplex method and the Interior Point method (IPM). Such LP methods proposed in the PA OCDMA context were compared with two methods available in the literature: a) hybrid ALPSO PA method, which is based on the particle swarm optimization (PSO) strategy combined with the augmented Lagrangian (AL) analytical method and the solver GUROBI; b) the high-complexity benchmark solution matrix inversion method (MIM), which is used to verify the quality of the Simplex and IPM solutions. Numerical result reveal the effectiveness and efficiency of both LP methods when compared with other competitive methods. Numerical results in terms of floating-point operations (FLOPS), normalized mean squared error (NMSE), convergence, and the evolution of the allocated power reveal the effectiveness and efficiency of both LP methods when compared with the literature methods, mainly under higher network dimensions (K≥32 optical nodes), achieving better accuracy-complexity tradeoffs. For 32≤K≤512 users, the IPM has resulted in perfect feasibility (F=0) and little complexity, i.e., an order less in terms of Flops than Simplex, twice to five times less than MIM procedure, and at least four orders less complexity than the hybrid analytical-heuristic ALPSO method.

Machine Learning-Based Hearing Aid Fitting Personalization Using Clinical Fitting Data.

The initial software fitting prescribed by the fitting formula largely depends on the patient's hearing loss, which may not be the optimal preference for a particular user. Certain criteria must also be readjusted by an audiologist to meet the user-specific requirements. Therefore, this study focuses on the novel application of a neural network (NN) technique to build a suitable fitting algorithm with prescribed hearing loss and the corresponding preferred gain to minimize the gap between optimized fittings. The algorithm intended to learn the hearing preferences of an individual user such that the initial fitting may be optimized. These findings demonstrate the efficiency of the algorithm, with and without additional features. Using the clinical fitting data, the average mean square error (MSE) for the simple NN algorithm was 5.4183%. By adding additional features to the data, the algorithm performed better, and the average MSE was as low as 5.2530%. However, the algorithm outperformed Company A fitting software, as the MSE was the highest at 5.4748%. As the company's automatic fitting has a noticeable discrepancy with clinical fitting records, the impeccable results from this study can lead to a better path towards fitting satisfaction, thus benefiting the hearing-impaired community to a larger extent.

A Comparison of Surrogate Behavioral Models for Power Amplifier Linearization under High Sparse Data.

A good approximation to power amplifier (PA) behavioral modeling requires precise baseband models to mitigate nonlinearities. Since digital predistortion (DPD) is used to provide the PA linearization, a framework is necessary to validate the modeling figures of merit support under signal conditioning and transmission restrictions. A field-programmable gate array (FPGA)-based testbed is developed to measure the wide-band PA behavior using a single-carrier 64-quadrature amplitude modulation (QAM) multiplexed by orthogonal frequency-division multiplexing (OFDM) based on long-term evolution (LTE) as a stimulus, with different bandwidths signals. In the search to provide a heuristic target approach modeling, this paper introduces a feature extraction concept to find an appropriate complexity solution considering the high sparse data issue in amplitude to amplitude (AM-AM) and amplitude to phase AM-PM models extraction, whose penalties are associated with overfitting and hardware complexity in resulting functions. Thus, experimental results highlight the model performance for a high sparse data regime and are compared with a regression tree (RT), random forest (RF), and cubic-spline (CS) model accuracy capabilities for the signal conditioning to show a reliable validation, low-complexity, according to the peak-to-average power ratio (PAPR), complementary cumulative distribution function (CCDF), coefficients extraction, normalized mean square error (NMSE), and execution time figures of merit. The presented models provide a comparison with original data that aid to compare the dimension and robustness for each surrogate model where (i) machine learning (ML)-based and (ii) CS interpolate-based where high sparse data are present, NMSE between the CS interpolated based are also compared to demonstrate the efficacy in the prediction methods with lower convergence times and complexities.

CT-free attenuation correction for dedicated cardiac SPECT using a 3D dual squeeze-and-excitation residual dense network

BackgroundAttenuation correction (AC) using CT transmission scanning enables the accurate quantitative analysis of dedicated cardiac SPECT. However, AC is challenging for SPECT-only scanners. We developed a deep learning-based approach to generate synthetic AC images from SPECT images without AC. MethodsCT-free AC was implemented using our customized Dual Squeeze-and-Excitation Residual Dense Network (DuRDN). 172 anonymized clinical hybrid SPECT/CT stress/rest myocardial perfusion studies were used in training, validation, and testing. Additional body mass index (BMI), gender, and scatter-window information were encoded as channel-wise input to further improve the network performance. ResultsQuantitative and qualitative analysis based on image voxels and 17-segment polar map showed the potential of our approach to generate consistent SPECT AC images. Our customized DuRDN showed superior performance to conventional network design such as U-Net. The averaged voxel-wise normalized mean square error (NMSE) between the predicted AC images by DuRDN and the ground-truth AC images was 2.01 ± 1.01%, as compared to 2.23 ± 1.20% by U-Net. ConclusionsOur customized DuRDN facilitates dedicated cardiac SPECT AC without CT scanning. DuRDN can efficiently incorporate additional patient information and may achieve better performance compared to conventional U-Net.

Learning How to Transfer From Uplink to Downlink via Hyper-Recurrent Neural Network for FDD Massive MIMO

In order to unlock the full advantages of massive multiple-input multiple-output (MIMO) in the downlink, the base station (BS) must leverage information about the downlink fading channels. However, in frequency division duplex (FDD) systems, full channel reciprocity does not hold, and acquiring information about the downlink channels generally requires downlink pilot transmission followed by uplink feedback. Prior work proposed to design pilot transmission, feedback, and channel state information (CSI) estimation, or directly downlink beamforming, via deep learning in an end-to-end manner. While previous work only used downlink pilots in a single slot, in this work, we introduce an enhanced end-to-end design that leverages partial uplink-downlink reciprocity and temporal correlation of the fading processes by utilizing jointly downlink and uplink pilots across multiple time slots. The proposed method is based on a novel deep learning architecture – HyperRNN – that combines hypernetworks and recurrent neural networks (RNNs) to optimize the transfer of long-term invariant channel features from uplink to downlink. Simulation results demonstrate that the HyperRNN achieves a lower normalized mean square error (NMSE) performance in terms of channel estimation, and that it attains a larger achievable sum-rate when applied to multi-user beamforming, as compared to the state of the art.

Generalized superimposed training for RIS-aided cell-free massive MIMO-OFDM networks

In this paper, a generalized superimposed training (GST) is proposed for an uplink cell-free multiple-input multiple-output orthogonal frequency-division multiplexing (mMIMO-OFDM) system, which is aided by reconfigurable intelligent surfaces (RISs) to enhance the spectral efficiency in the system. For the GST scheme, the pilots and data symbols are transmitted simultaneously in the coherence time. This scheme is different from traditional separate transmission methods, such as regular pilots (RP) transmission. In the OFDM multi-carrier case, a part of the subcarriers is based on the GST, whereas the other part of subcarriers is used for data transmission only. The channel and data estimations are carried out and the normalized mean-squared error (NMSE), bit error rate (BER), and sum-rate in different schemes are compared. Different receiver cooperation levels are analyzed in this case, including fully centralized processing and local processing. The distributed time processing and iterative process are also used to improve the performance of the data estimation in this system.

Mobility and Routing based Channel Estimation for Hybrid Millimeter-Wave MIMO WSNs

Recently, technological developments have enhanced, the use of Millimeter-wave (mm-Wave) Multiple Input Multiple Output (MIMO) system in various communication applications and wireless sensor networks as channel estimation efficiency can be immensely improved with the help of this technological developments in Millimeter-wave MIMO system and wireless sensor network as well. Moreover, they can improve quality of communication services to a great extent. However, cell interference in Millimeter-wave (mm-Wave) MIMO system can produce a massive impact on spectral efficiency. Therefore, a Routing Enabled Channel Estimation (RECE) technique is presented in this article to minimize interference between cells. The proposed Channel Estimation technique improves channel capacity as well as spectral efficiency. Moreover, Normalized Mean Square Error (NMSE) is minimized heavily using proposed RECE technique. Here, main aim of this article is to reduce cell interference and channel estimation inside a cell by using route selection, beam selection, and spatial frequency estimation. Here, different scenarios and parameters are considered to evaluate performance efficiency of proposed RECE technique in terms of spectral efficiency, NMSE and SNR and compared against varied traditional channel estimation techniques. Moreover, it is clearly evident from performance results that the proposed channel estimation technique performs better than the other two methods.

Leveraging Machine Learning for Fault-Tolerant Air Pollutants Monitoring for a Smart City Design

Air pollution has become a global issue due to its widespread impact on the environment, economy, civilization and human health. Owing to this, a lot of research and studies have been done to tackle this issue. However, most of the existing methodologies have several issues such as high cost, low deployment, maintenance capabilities and uni-or bi-variate concentration of air pollutants. In this paper, a hybrid CNN-LSTM model is presented to forecast multivariate air pollutant concentration for the Internet of Things (IoT) enabled smart city design. The amalgamation of CNN-LSTM acts as an encoder-decoder which improves the overall accuracy and precision. The performance of the proposed CNN-LSTM is compared with conventional and hybrid machine learning (ML) models on the basis of Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE) and Mean Square Error (MSE). The proposed model outperforms various state-of-the-art ML models by generating an average MAE, MAPE and MSE of 54.80%, 52.78% and 60.02%. Furthermore, the predicted results are cross-validated with the actual concentration of air pollutants and the proposed model achieves a high degree of prediction accuracy to real-time air pollutants concentration. Moreover, a cross-grid cooperative scheme is proposed to tackle the IoT monitoring station malfunction scenario and make the pollutant monitoring more fault resistant and robust. The proposed scheme exploits the correlation between neighbouring monitoring stations and air pollutant concentration. The model generates an average MAPE and MSE of 10.90% and 12.02%, respectively.

DuDoSS: Deep-learning-based dual-domain sinogram synthesis from sparsely sampled projections of cardiac SPECT.

Myocardial perfusion imaging (MPI) using single-photon emission-computed tomography (SPECT) is widely applied for the diagnosis of cardiovascular diseases. In clinical practice, the long scanning procedures and acquisition time might induce patient anxiety and discomfort, motion artifacts, and misalignments between SPECT and computed tomography (CT). Reducing the number of projection angles provides a solution that results in a shorter scanning time. However, fewer projection angles might cause lower reconstruction accuracy, higher noise level, and reconstruction artifacts due to reduced angular sampling. We developed a deep-learning-based approach for high-quality SPECT image reconstruction using sparsely sampled projections. We proposed a novel deep-learning-based dual-domain sinogram synthesis (DuDoSS) method to recover full-view projections from sparsely sampled projections of cardiac SPECT. DuDoSS utilized the SPECT images predicted in the image domain as guidance to generate synthetic full-view projections in the sinogram domain. The synthetic projections were then reconstructed into non-attenuation-corrected and attenuation-corrected (AC) SPECT images for voxel-wise and segment-wise quantitative evaluations in terms of normalized mean square error (NMSE) and absolute percent error (APE). Previous deep-learning-based approaches, including direct sinogram generation (Direct Sino2Sino) and direct image prediction (Direct Img2Img), were tested in this study for comparison. The dataset used in this study included a total of 500 anonymized clinical stress-state MPI studies acquired on a GE NM/CT 850 scanner with 60 projection angles following the injection of 99m Tc-tetrofosmin. Our proposed DuDoSS generated more consistent synthetic projections and SPECT images with the ground truth than other approaches. The average voxel-wise NMSE between the synthetic projections by DuDoSS and the ground-truth full-view projections was 2.08%±0.81%, as compared to 2.21%±0.86% (p<0.001) by Direct Sino2Sino. The averaged voxel-wise NMSE between the AC SPECT images by DuDoSS and the ground-truth AC SPECT images was 1.63%±0.72%, as compared to 1.84%±0.79% (p<0.001) by Direct Sino2Sino and 1.90%±0.66% (p<0.001) by Direct Img2Img. The averaged segment-wise APE between the AC SPECT images by DuDoSS and the ground-truth AC SPECT images was 3.87%±3.23%, as compared to 3.95%±3.21% (p=0.023) by Direct Img2Img and 4.46%±3.58% (p<0.001) by Direct Sino2Sino. Our proposed DuDoSS is feasible to generate accurate synthetic full-view projections from sparsely sampled projections for cardiac SPECT. The synthetic projections and reconstructed SPECT images generated from DuDoSS are more consistent with the ground-truth full-view projections and SPECT images than other approaches. DuDoSS can potentially enable fast data acquisition of cardiac SPECT.

Selective Algorithm for Expanded Group Method of Data Handling Applied to Power Amplifier Modeling

Power amplifiers (PAs) are electronic devices commonly used in telecommunications that need to transmit information with high energetic efficiency. For this, it is necessary to use data manipulation methods that assist in the linearization of the output signal. Our previous conference paper presented two codes constructed based on the Group Method of Data Handling (GMDH) and which differ in their way of selecting the best coefficients to be used in the calculations of the neural network. The first method, called Embracing, assumes greater availability of data, while the second, called Selective, selects information from the beginning of the code. This work extends the previous GMDH models by expanding the PA inputs into Laguerre basis functions with a single real pole. The comparison among the different approaches employs experimental data collected from a GaN HEMT class AB PA and a Si LDMOS class AB. The most selective and computationally more complex structure, when searching for identification since from the first layers, expresses minor errors and the best results in the output for both Conventional and Expanded GMDH models, becoming a reasoned option for use in PAs. A normalized mean square error (NMSE) of -35.44 dB was obtained by Expanded GMDH with Selective algorithm and 5 inputs when using the GaN PA, whereas a NMSE of -40.35 dB was obtained by the Expanded GMDH with Selective algorithm and 4 inputs when calculated with the Si LDMOS PA data.

Three-Phase Load Prediction-Based Hybrid Convolution Neural Network Combined Bidirectional Long Short-Term Memory in Solar Power Plant

The economic renewable energy generations have been rapidly developed because of the sharp reduction in the costs of solar panels. It is imperative to forecast the three-phase load power for more effective energy planning and optimization in a smart solar microgrid installed on a building in the Linyuan District, Taiwan. To alleviate this problem, this article proposes a convolution neural network bidirectional long short-term memory (CNN-Bi-LSTM) to accurately predict the short-term three-phase load power in building the energy management system in the smart solar microgrid with the collected data from advanced metering infrastructure (AMI), which have not been investigated before. The three-phase load-predicting methodology is developed using weather parameters and different collected data from AMI. The project evaluates the performance of the CNN-Bi-LSTM model by utilizing hyper-parameter optimization to attain the optimum parameters. The prediction models are trained based on hourly historical input features, selected based on the Pearson correlation coefficient. The performances’ optimal structure CNN-Bi-LSTM are validated and compared with the bidirectional LSTM (Bi-LSTM), LSTM, the Gated Recurrent Unit (GRU), and the recurrent neural network (RNN) models. The obtained optimized structure of CNN-Bi-LSTM demonstrates the effectiveness of the proposed models in the short-term prediction of three-phase load power in a smart solar microgrid for building with a maximum enhancement of 68.36% and 8.81% average MSE, and 30.26% and 36.36% average MAE during the testing and validating operations.

A densely interconnected network for deep learning accelerated MRI

ObjectiveTo improve accelerated MRI reconstruction through a densely connected cascading deep learning reconstruction framework.Materials and methodsA cascading deep learning reconstruction framework (reference model) was modified by applying three architectural modifications: input-level dense connections between cascade inputs and outputs, an improved deep learning sub-network, and long-range skip-connections between subsequent deep learning networks. An ablation study was performed, where five model configurations were trained on the NYU fastMRI neuro dataset with an end-to-end scheme conjunct on four- and eightfold acceleration. The trained models were evaluated by comparing their respective structural similarity index measure (SSIM), normalized mean square error (NMSE), and peak signal to noise ratio (PSNR).ResultsThe proposed densely interconnected residual cascading network (DIRCN), utilizing all three suggested modifications achieved a SSIM improvement of 8% and 11%, a NMSE improvement of 14% and 23%, and a PSNR improvement of 2% and 3% for four- and eightfold acceleration, respectively. In an ablation study, the individual architectural modifications all contributed to this improvement for both acceleration factors, by improving the SSIM, NMSE, and PSNR with approximately 2–4%, 4–9%, and 0.5–1%, respectively.ConclusionThe proposed architectural modifications allow for simple adjustments on an already existing cascading framework to further improve the resulting reconstructions.

Fault Restoration of Six-Axis Force/Torque Sensor Based on Optimized Back Propagation Networks.

Six-axis force/torque sensors are widely installed in manipulators to help researchers achieve closed-loop control. When manipulators work in comic space and deep sea, the adverse ambient environment will cause various degrees of damage to F/T sensors. If the disability of one or two dimensions is restored by self-restoration methods, the robustness and practicality of F/T sensors can be considerably enhanced. The coupling effect is an important characteristic of multi-axis F/T sensors, which implies that all dimensions of F/T sensors will influence each other. We can use this phenomenon to speculate the broken dimension by other regular dimensions. Back propagation neural network (BPNN) is a classical feedforward neural network, which consists of several layers and adopts the back-propagation algorithm to train networks. Hyperparameters of BPNN cannot be updated by training, but they impact the network performance directly. Hence, the particle swarm optimization (PSO) algorithm is adopted to tune the hyperparameters of BPNN. In this work, each dimension of a six-axis F/T sensor is regarded as an element in the input vector, and the relationships among six dimensions can be obtained using optimized BPNN. The average MSE of restoring one dimension and two dimensions over the testing data is and , respectively. Furthermore, the average quote error of one restored dimension and two restored dimensions are and , respectively. The analysis of experimental results illustrates that the proposed fault restoration method based on PSO-BPNN is viable and practical. The F/T sensor restored using the proposed method can reach the original measurement precision.