The System Fault Evolution Process (SFEP) is a network topology composed of various events. In SFEP, the system function state is determined by the function states of all events, which involves both the representation and control of a single event function state, as well as the determination of the causal relationships between multiple event function states. Firstly, the feasibility of utilizing quantum superposition and entanglement to characterize the event function state is examined. Secondly, in the case of non-superposition and superposition of reliable and failed binary states, the influence of quantum strategy and binary strategy on state changes is studied, and encryption and decryption operators are provided accordingly; Subsequently, the significance of quantum state entanglement in event function states was analyzed. Finally, a quantum state entanglement degree algorithm for event function states is provided. Research has demonstrated that quantum strategy can achieve any desired event function state. The product of encryption and decryption operators for both non-overlapping and overlapping event function states remains constant. Multiple event function states can generate quantum state superposition. The superposition of two-event function states within the minimum unit of the SFEP is equivalent to a failure mode, where the squared probability amplitudes and probability density matrices of each superposition state represent the occurrence probability of each failure mode. The entanglement degree can comprehensively describe the fault modes and their occurrence probabilities, as well as determine the complexity of causal relationships between events and the challenges associated with obtaining them. This research aims to provide a fundamental theoretical framework for the comprehensive description and analysis of system function status.

Multimodal Streaming Data (MSD) has applications across various domains, particularly in data collection and analysis. The safety domain, with its emphasis on system safety and predictive analysis, stands to benefit significantly from the relevant theories and technologies associated with MSD. It is proposed that MSD can be conceptualized as a Basic Data Matrix (BDM) defined by three dimensions: time, factor, and object, which collectively represent the System Fault Evolution Process (SFEP). When MSD occurs under uncertain conditions, it can be represented as a BDM that serves as the foundational research framework. This proposal introduces the Optimal Lag Time Operator (OLTO) and an algorithm to assess the impact of time on SFEP. These lead to the derivation of the Optimal Lag Dynamic Matrix (OLDM) to identify MSD characteristics and reduce data volume. Furthermore, it is suggested that SFEP exhibits manifold characteristics, and exploring the influence of factors on SFEP can be accomplished through manifold learning techniques. Consequently, the study presents an analytical approach that accounts for the combined effects of time and factors on SFEP, offering a mathematical model and analytical procedure, supported by illustrative examples. The research outcomes present an effective methodology for leveraging MSD in safety applications, serving as a multimodal streaming learning technique within this domain.

In a smart system, the faults of edge devices directly impact the system’s overall fault. Further, complexity arises when different edge devices provide varying fault data. To study the Smart System Fault Evolution Process (SSFEP) under different fault data conditions, an intelligent method for determining the Smart System Fault Probability (SSFP) is proposed. The data types provided by edge devices include the following: (1) only known edge device fault probability; (2) known Edge Device Fault Probability Distribution (EDFPD); (3) known edge device fault number and EDFPD; (4) known factor state of the edge device fault and EDFPD. Moreover, decision methods are proposed for each data case. Transfer Probability (TP) is divided into Continuity Transfer Probability (CTP) and Filterability Transfer Probability (FTP). CTP asserts that a Cause Event (CE) must lead to a Result Event (RE), while FTP requires CF probability to exceed a threshold before RF occurs. These probabilities are used to calculate SSFP. This paper introduces a decision method using the information diffusion principle for low-data SSFP determination, along with an improved method. The method is based on space fault network theory, abstracting SSFEP into a System Fault Evolution Process (SFEP) for research purposes.