With the development of industrial Internet, smart manufacturing information systems (SMISs) are faced with more uncertainties, dynamics, and complexity. These problems bring more challenges to the reliability operation of SMISs. To solve the above problem, a prediction model based on phase space reconstruction, chaos analysis, and back propagation (BP) neural network is proposed to predict SMISs reliability. First, we decompose failure data series into some subdata series components with strong regularity by using C‐C algorithm and Cao algorithm. On this basis, we use the maximum Lyapunov index to identify chaotic characteristics of failure data series. And then, we establish BP neural network prediction model by using reconstructing failure data to predict SMISs failure behaviors. Finally, we use two groups of failure data series to verify the effectiveness of chaotic BP neural network model, and the experiment results verify that chaotic BP neural network model has more accurate prediction results compared with BP network, support vector machine, long short term memory networks (LSTM), and autoregressive model (AR). LEAD PARAGRAPH SMISs are open and complex systems, human error and external environment cause the uncertainty of reliability. The threat of the external environment mainly comes from malicious attacks and the threat of the human error mainly comes from the wrong operation of the operator. Human error and external environment often cause frequent failures of software and hardware of the system or physical failures of devices. As an open complex system, the reliability operation of SMISs is very important for manufacturing enterprises. However, in the daily use of SMISs, the most common failures are time failure caused by human error and external environment. Therefore, it is very important to study the time failure of SMISs. Main points of this paper: (1) SMISs are complex and open systems, so we establish an interdependent network based on the characteristics of SMISs, and use the cascade effect of the complex network to point out that when SMISs fail, the system will easily fall into failure. (2) The phase space reconstruction method is used to restore the real data characteristics of failure data. (3) By using the reconstructed data and the neural network, the failure behavior can be predicted accurately. Compared with other popular prediction methods, it is found that general machine learning methods cannot predict data with chaotic characteristics. The research results of this paper find that when SMISs fail, the failure behavior can easily lead SMISs into chaos through the propagation of interdependent network. Therefore, when future scholars conduct fault analysis on SMISs, they should consider the chaos of the data, otherwise the systems fault analysis and diagnosis cannot be carried out accurately.

As the process of informatization progresses in an equipment manufacturing enterprise, its information system becomes a dissipative structure due to the nonlinear interaction of many factors. The objectives of this study were to help enterprises adopt intelligent manufacturing, realize sustainable development strategies, and understand the operation rules of information systems. For this purpose, this study analyzed an anomaly index time series of an information system in the process of integration. First, the embedding dimension, time delay, average period, and maximum Lyapunov exponent of the time series were calculated. The anomaly index with chaotic characteristics was denoised by combining phase space reconstruction with singular value decomposition (SVD). Finally, a radial basis function (RBF) neural network and local nonlinear method were used to predict the anomaly index of 79 test data points. The case simulation results verify that the anomaly index is affected by changes in basic data, system development, and online migration. One instance of local noise reduction can reveal hidden problems in the actual operations of enterprises, and multiple iterations can extract the actual information of the signals, avoid failures at isolated points, and show a clear attractor structure. Both the RBF neural network and local nonlinear approach are effective prediction methods with low relative errors, but the performance of the latter is superior.

When the chaotic characteristics of manufacturing quality level are studied, it is not practical to use chaotic methods because of the low speed of calculating the correlation integral. The original algorithm used to calculate the correlation integral is studied after a computer hardware upgrade. The result is that calculation of the correlation integral can be sped up only by improving the algorithm. This is accomplished by changing the original algorithm in which a single distance threshold-related correlation integral is obtained from one traversal of all distances between different vectors to a high-efficiency algorithm in which all of the distance threshold-related correlation integrals are obtained from one traversal of all of the distances between different vectors. For a time series with 3000 data points, this high-efficiency algorithm offers a 3.7-fold increase in speed over the original algorithm. Further study of the high-efficiency algorithm leads to the development of a super-high-efficiency algorithm, which is accomplished by changing the original and high-efficiency algorithms, in which the add-one operation of the Heaviside function is executed n times, such that the execution of the add-one operation occurs only once. The super-high-efficiency algorithm results in increases in the calculation speed by up to 109 times compared with the high-efficiency algorithm and by approximately 404 times compared with the original algorithm. The calculation speed of the super-high-efficiency algorithm is suitable for practical use with the chaotic method.

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