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Intelligent fault diagnosis (IFD) plays an indispensable role in protecting machinery from catastrophic accidents. Existing IFD methods are mainly developed in the framework of one-time learning. Therefore, they work under the hypothesis of complete dataset. Nevertheless, it is unrealistic to gain the complete dataset of machinery faults at once. More practically, new data will be progressively acquired over time. Therefore, it is urgently required to develop the incremental learning (IL) capabilities for IFD models to learn new knowledge continually from new data. For this purpose, this study proposes an improved broad learning system (IBLS) for lifelong learning IFD. Firstly, the initial IBLS is constructed based on the original broad learning system (BLS). Then, the IL capabilities of the IBLS are developed for three scenarios: increasing fault samples, increasing fault modes, and increasing running conditions. Based on these IL capabilities, the IBLS can be progressively updated to learn more and more diagnosis functions. Finally, the effectiveness of the proposed IBLS is verified using three experiments of high-speed train bearing, disc component, and Case Western Reserve University bearing. The results show that the IBLS is capable of learning continually new knowledge from new data. Besides, the diagnosis accuracy of the IBLS is 12.45%, 7.84%, and 5.10% higher than that of the original BLS in the three case studies. The satisfying results prove that the proposed IBLS is a useful method to solve the lifelong learning IFD problem. • An improved broad learning system (IBLS) is developed. • An IBLS based lifelong learning intelligent diagnosis framework is proposed. • Three case studies are carried out for validations. [ABSTRACT FROM AUTHOR]

Chaotic time series data is extensively applied in financial stocks, climate monitoring, and sea clutter, in which data fusion from various sources and multi-sensor information make accurate predictions of chaotic time series challenging under complex nonlinear conditions. Previous works focus on designing different model frameworks to capture the temporal dependence and extract richer nonlinear features to improve the accuracy of univariate chaotic time series prediction, which ignores the spatial dependence of multivariable. However, in this paper, we argue that spatial correlation among multiple variables is essential to improve the prediction accuracy of chaotic time series. To fill the gap, we innovatively propose a D ynamic A daptive G raph C onvolutional T ransformer with a B road L earning S ystem (DAGCT-BLS), a GCN and Transformer-based model utilizing multivariate spatial dependence for multi-dimensional chaotic time series forecasting. In DAGCT-BLS, the multivariate chaotic time series are reconstructed into the phase space, and the reconstructed data are rapidly feature-extracted using a cascade network BLS with frozen weights to maximize the retention of chaotic properties and nonlinear relationships. Then, the Dynamic Adaptive Graph Convolutional Network (DAGCN) is proposed to capture the spatial correlation among the multiple variables. Finally, improved multi-head attention of the Transformer Encoder is used to capture the temporal dependence of the phase point sequence. Experiments of our proposed model on three datasets (Lorenz, Rossler, and Sea clutter) show that DAGCT-BLS can achieve the best prediction performance and have strong interpretability, and multivariate-based joint modeling of chaotic time series helps to improve the prediction performance. • A novel DAGCT-BLS model is proposed to sovel multi-dimensional chaotic time series forecasting problem, unreported previously. • The multivariate chaotic time series are reconstructed into the phase space, which are rapidly feature-extracted using a cascade network BLS with frozen weights. • Improved multi-head attention is proposed to capture the temporal dependence of the phase point sequence. • DAGCN is proposed to model multivariate spatial relationships dynamically. [ABSTRACT FROM AUTHOR]

• A new feature extraction method which introduces the correlation coefficient and the dominant variable into the stacked autoencoder has been developed. • An adaptive algorithm which effectively determines the number of nodes of the broad learning system has been developed. • Two examples are used to demonstrate the effectiveness of the proposed method. In the actual soft sensor project, the complex industrial process leads to a large number of monitoring variables that lead to obvious problems of high dimension and data redundancy. To solve these problems, an adaptive cascade enhancement broad learning system combined with stacked correlation information autoencoder, referred to as SCIAE-ACEBLS, is proposed in this study. The latter is based on the broad learning system (BLS) and it includes two parts: feature node and enhancement node. In the feature node part, the correlation coefficient and the dominant variable are introduced into the stacked autoencoder (SAE), and all the hidden nodes are used as feature nodes. Both the correlation coefficient and the dominant variable are introduced to ensure that the information of feature nodes not only include the relevant information of the dominant variable in the auxiliary variables, but also in the dominant variable, and thus all the information related to dominant variables can be effectively used. In the enhancement node part, an adaptive cascade enhancement node algorithm is used to reduce the redundancy of effective information and solve the problems of node information redundancy and node number uncertainty caused by the randomness of the node parameters in BLS. Finally, two industrial examples show that the proposed model is effective and outperforms existing methods. [ABSTRACT FROM AUTHOR]

As a novel neural network with efficient learning capacity, broad learning system (BLS) has achieved remarkable success in various regression and classification problems. Due to the broad expansion of nodes, however, BLS is known to have many redundant parameters and nodes, which will increase the memory and computation cost and is adverse to its deployment on equipment with limited resources. To optimize the number of neurons and parameters of BLS and then find the optimal sparse model under a given resource budget, in this paper, we introduce to train BLS through L0 regularization. The regularization constraint term of the BLS objective function is replaced by the L0 regularization method, and the normalized hard threshold iterative method is used to optimize the output weight. More concretely, the size of the model is fixed by controlling the number of output weights under given the resource size, and then parameters and nodes in the network are evaluated and selected from the node set in the training to obtain a BLS with controllable sparsity (CSBLS). Experiments on various data sets demonstrate the effectiveness of our proposed method. • An optimized method for Broad Learning System that is based on L 0 regularization. • Formulate the L 0 regularization problem mathematically to an optimization problem with the number of output weights as constraints. • Automatically find the best sparse BLS under a given resource budget. [ABSTRACT FROM AUTHOR]

As an efficient learning model, the broad learning system (BLS) has achieved great success in machine learning and various applications due to its outstanding performance. Differing from typical deep learning based models, the BLS has a more straightforward structure and few parameters. In this study, we focus on developing a decentralized version of the elastic-net BLS (D-ENBLS) with communication efficiency. The scenario we considered is that the training data is distributed throughout a network of interconnected agents, which prohibits sharing the raw data owing to resource limitations or privacy concerns. In such a distributed paradigm, the communication between agents is an important issue to investigate. From the perspective of saving communication resources, we introduce quantization and communication censoring strategies on the D-ENBLS algorithm to improve the communication procedure and minimize the communication cost with minimal performance degradation. The novel algorithm refers to as DQC-ENBLS, in which quantization reduces the number of bits for each transmission, whereas communication censoring reduces the total number of transmissions. By formulating the training problem as a finite-sum minimization, the alternating multiplication method (ADMM) is employed to solve the optimization problem in a decentralized manner. The experimental results verify that the DQC-ENBLS algorithm can reduce communication cost while maintaining similar performance on the test datasets. • A decentralized learning algorithm for elastic-net regularized BLS is developed. • The quantization and communication censoring strategies are introduced. • The performance of the proposed algorithm is verified by simulation experiments. [ABSTRACT FROM AUTHOR]

The observational 1-D signals available for realizing the highly accurate intrinsic attractor fitting of deep learning network approaches are often insufficient because of the complexity and nonlinearity of chaotic time series. Unlike deep models, a broad learning system (BLS) with the attention mechanism exhibits a unique and preeminent pattern prediction ability. Thus, this system has been applied as a practical trend in many fields. However, the application of multi-head attention fused manifold broad learning architecture to chaotic time series prediction remains inadequate. Thus, a multi-head attentional BLS (Multi-Attn BLS) for chaotic time series prediction is proposed in this study to improve the prediction accuracy of chaotic time series further. Our model develops a novel framework that combines the high computational efficiency of broad learning with the multi-head attention mechanism. First, the received data are reconstructed into fixed-size tuples. The multidimensional arrays with embedding dimensions and time delay are used as the input to a broad learning network. Subsequently, a robust BLS with a spatiotemporal multi-head attention mechanism is developed to depict the internal dynamic evolution. The Multi-Attn BLS model can capture key spatiotemporal feature information and achieve high predictive performance. It also has a good generalization ability in practical nonlinear complex systems. Comparative experiments with the traditional long short-term memory (LSTM) network and the primitive BLS show that its computing speed and generalization ability are improved. Furthermore, the network is good at capturing the spatiotemporal features of the sequence because of the multi-head attention mechanism. The experimental results show that our model outperforms BLS, ridge regression, and LSTM on the four main evaluation indicators (root mean square error, root mean square percentage error, mean absolute error, and mean absolute percentage error) in predicting classical systems (Lorenz and Rossler systems). Moreover, the model has an excellent prediction effect in the real-world chaotic system of sea clutter. • This paper proposes a multi-head attentional broad learning system (Multi-Attn BLS) for the prediction of chaotic time series. • Our model develops a novel framework that combines the high computational efficiency of broad learning with the multi-head attention mechanism of the Transformer. • The Multi-Attn BLS model can not only capture the key spatiotemporal feature information and achieve high predictive performance but also have a good generalization ability in practical nonlinear complex systems. • Experiments on three benchmarks show that our model framework is capable of advancing the state-of-the-art. It achieves an excellent prediction effect in chaotic time series, covering two widely used chaotic systems (Lorenz and Rossler) and a real-world chaotic system (sea clutter). [ABSTRACT FROM AUTHOR]

With the global outbreak of COVID-19, there is an urgent need to develop an effective and automated detection approach as a faster diagnostic alternative to avoid the spread of COVID-19. Recently, broad learning system (BLS) has been viewed as an alternative method of deep learning which has been applied to many areas. Nevertheless, the sparse autoencoder in classical BLS just considers the representations to reconstruct the input data but ignores the relationship among the extracted features. In this paper, inspired by the effectiveness of the collaborative–competitive representation (CCR) mechanism, a novel collaborative–competitive representation-based autoencoder (CCRAE) is first proposed, and then collaborative–competitive broad learning system (CCBLS) is proposed based on CCRAE to effectively address the issues mentioned above. Moreover, an automated CCBLS-based approach is proposed for COVID-19 detection from radiology images such as CT scans and chest X-ray images. In the proposed approach, a feature extraction module is utilized to extract features from CT scans or chest X-ray images, then we use these features for COVID-19 detection with CCBLS. The experimental results demonstrated that our proposed approach can achieve superior or comparable performance in comparison with ten other state-of-the-art methods. [Display omitted] [ABSTRACT FROM AUTHOR]

• A novel hybrid model of broad-deep networks is proposed for data augmentation. • The highly similar features can be merged to generate new augmented features. • The method solves the problem of insufficient authenticity of EEG generated by GAN. Decades after data augmentation was first proposed in brain-computer interface (BCI), the authenticity and performance still do not meet rational requirements, which is directly related to the fact that the augmentation methods do not provide real electroencephalograph (EEG) trials. Here we show how to generate a numerous authentic EEG from the original calibrated EEG by using a novel hybrid model of broad-deep networks, which eliminates the lack of authenticity of data generated by GAN and other methods. First, we design an EEG evoked experiment with a complex boundary avoidance task to collect the EEG of different subjects. This experiment can effectively highlight the differences of EEG features of different subjects that makes the results more reliable when using our novel hybrid model to measure the similarity. A new hybrid model of broad-deep networks is proposed to measure the similarity of different subjects in this study. And the EEG features of the two subjects with the highest similarity are combined to generate an augmented feature set. On the condition of satisfying the authenticity of EEG, the augmented feature set is significantly better than the original feature set in data dimension and quality. Finally, we verify the classification effect of the augmented feature set, and the results show that the proposed method can effectively generate real EEG data and improve the classification performance to a high reliability level for complex boundary avoidance tasks under limited EEG conditions. In addition, we observe the obvious advantages of this model over traditional deep learning methods in terms of training time and memory overhead. [ABSTRACT FROM AUTHOR]

• A new Functional link broad learning system is used for solar irradiance prediction. • Large number of mapped feature nodes is created from expanded cluster of inputs. • Random weights and biases and suitable activation functions are used for these nodes. • Mapped feature nodes are used as inputs to enhancement nodes for FLBLS. • A new hybrid optimization technique is used for optimization of FLBLS parameters. A new machine learning approach for forecasting short-termsolar irradiance is presented in this paper considering different weather conditions and time horizon in a microgrid environment. Using historical solar irradiance, a short-term forecasting model known as Robust optimized functional link broad learning system (FLBLS) is developed. Here the original input comprising delayed historical solar irradiance samples is initially expanded by exponential trigonometric functions and the expanded features are then used to create a large number of feature nodes using random weights and biases. Further the newly created features are fed as inputs to the enhancement nodes forming a broad learning system (BLS). This newly formed flat FLBLS facilitates incremental learning in fast remodelling of the network if needed for efficient performance without a retraining process unlike deep neural networks using several hidden layers and filters, etc. The proposed approach is designed on the basis of the standard random vector functional link network (RVFLN), however unlike the traditional RVFLN that applies inputs directly and set up the enhancement nodes, in our proposed approach, initially the inputs are expanded and map the expanded inputs to generate a set of mapped features. It reduces the lengthy process unlike deep neural networks that involves the back propagation algorithm for error minimization. The proposed FLBLS approach simplifies the learning process with the proper choice of feature nodes as it can be implemented to a flat network or a simpler network such as ELM that requires only the simple calculation of the output weight and obtain the final output where retraining is not required for adding extra feature nodes or enhancement nodes like deep neural architectures. Also, the minimum variance strategy with the training samples is useful in rejecting the effects of noise and outliers in the system and make the network robust which gets reflected in computing output weights using generalized least square. The minimum variance strategy further enhances the performance of the proposed system. To improve the prediction accuracy, the FLBLS parameters are optimized using an efficient metaheuristic chaotic firefly-sine cosine levy flight algorithm. Also, to reject the effects of noise and outliers and make the network robust a minimum variance strategy is used with the training samples that gets reflected in computing output weights using generalised least squares. The suggested method is experimented rigorously and analysed with different time frames designed for 30 min and 60 min ahead solar irradiance prediction. The obtained results from experiments confirm that the proposed FLBLS approach outperforms other randomized neural network forecasting methods as well many state-of-the-art methods using solar irradiance data of Hyderabad, India collected from National Renewable Energy Laboratory (NREL). This approach exhibits with the lowest errors in different case studies among all the compared methods. This FLBLS designed approach is an efficient approach for the purpose of solar irradiance prediction with highly nonlinear data. [ABSTRACT FROM AUTHOR]

• An active broad learning system was proposed for ECG arrhythmia classification. • The sigmoid function was used to map the outputs in BLS into posterior probabilities. • ABLS has superior classification performance. • The ABLS can reduce the beats that need to be labeled and time-consumption. • The ABLS only needs to incrementally train the selected beats. This paper presents an active and incremental learning system called active broad learning system (ABLS) for ECG arrhythmia classification to reduce the time-consumption of training and labor cost of experts labeling beats. An effective strategy is designed to convert the actual outputs in broad learning system (BLS) into approximated posterior probabilities for active learning to select the most valuable beats from unlabeled beats. The proposed ABLS is first pre-trained with a small number of labeled beats and then incremental trained with the selected beats labeled by the expert to fine-tune the connection weight. Due to the structural characteristics, ABLS does not need to retrain all the beats, which can greatly reduce the time-consumption. The experimental results on the MIT-BIH arrhythmia database show ABLS can greatly reduce the number of beats that need to be labeled and consume very little training time while maintaining excellent performance compared to state-of-the-art methods. [ABSTRACT FROM AUTHOR]

The single-hidden-layer feedforward neural network (SLFN) exhibits an excellent approximation ability, despite its simple structure. This study examines two neural network models developed based on the general structure of the SLFN, i.e., the weights-and-structure-determination (WASD) neural network and broad learning system (BLS). The BLS and WASD neural networks exhibit many similarities in terms of their structure and algorithm, while BLS incorporates certain distinct ideas that render it an improved version of the WASD neural network. The research described in this paper is the first approach to establish a connection between the BLS and WASD neural networks. Moreover, pattern classification experiments on a foot dataset and several benchmark datasets are conducted using these two kinds of neural network models, and the performance of different models is compared and analyzed. Experimental results show that dividing the feature nodes into one group is the best choice for our foot dataset, and that the cross-layer connectivity and sparse coding of BLS can effectively improve the classification accuracy. In addition, it is shown that the dynamic update algorithm of BLS can improve the accuracy and save a lot of time when updating the model structure, but the final accuracy depends on the initial structure and parameters. Comparative experiments show that BLS achieves 89.12% classification accuracy for the foot dataset, which is the highest among all the demonstrated WASD neural networks and two other SLFN models. Finally, extended experiments on five benchmark datasets show that BLS can achieve satisfactory accuracy on multiple types of datasets, while WASD neural networks are possibly inadequate in processing image datasets in contrast. • It is the first attempt to establish a relation between BLS and WASD neural networks. • A novel structure for the BLS equivalent to the original structure is established. • Aspects that make BLS outperform WASD neural networks are clarified and demonstrated. • The effects of BLS and multiple WASD neural networks in real scenarios are compared. [ABSTRACT FROM AUTHOR]