CN109241583B - Human-computer interaction system reliability solving method based on Markov - Google Patents
Human-computer interaction system reliability solving method based on Markov Download PDFInfo
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Abstract
The invention relates to a human-computer interaction system reliability solving method based on Markov, which comprises the following steps: the method comprises the following steps: analyzing a human-computer interaction system, an environment and a task scene, and analyzing fault logic to determine a bottom event set causing a human-computer system fault; step two: determining a complete set of state space, and drawing a system state transition diagram according to system fault logic; step three: calculating to obtain the transfer rate between states, and constructing a transfer rate matrix; step four: listing a state equation, and solving to obtain the instantaneous reliability of the human-computer system; through the steps, the fault logic in the human-computer interaction process is analyzed, the set of system fault bottom events is determined, and the instantaneous reliability of the human-computer system is finally solved, so that the effects of accurately solving the reliability of the human-computer system and searching system defects are achieved, and the problem that the multi-factor coupling characteristic of the human-computer system is difficult to describe in the conventional human-computer system reliability modeling is solved.
Description
Technical Field
The invention provides a Markov-based human-computer interaction system reliability solving method, which can deeply consider the cognitive characteristics, scene task characteristics and human-computer coupling characteristics of people and belongs to the field of human-computer interaction reliability quantitative modeling and prediction.
Background
The purpose of the human-computer interaction modeling is to describe a human-computer interaction dynamic process under a task requirement by taking human, machine and ring as a whole under the condition of fully considering the existence of environmental disturbance, system fault and human error, study information transmission between human and machine and analyze a potential risk scene possibly causing an accident. Human-computer interaction modeling is classified according to implementation modes and can be divided into a logic-based method and a simulation-based method. The first method is to model human-computer ring elements in the system and the influence relationship among the human-computer ring elements through logic analysis to obtain element combinations or sequences; the second method is to actually simulate a human-computer interaction process through a simulation technology, and add environmental disturbance, system faults and human errors into a human-computer system, so as to analyze human-computer interaction behaviors in abnormal states.
In terms of logic modeling, a Fault Tree Analysis (FTA) method is firstly proposed by a bell laboratory in 1961, and Dynamic logic gates such as a function-related gate, a priority gate and a spare part gate are introduced by Dugan, so that a Dynamic Fault Tree Analysis (DFTA) method is formed, and a markov model is proposed for quantitative Analysis, so that the defects of the method are improved and widely quoted by a plurality of scholars. However, the method only mistakenly considers the human as the bottom event and does not deeply consider the cognitive characteristics, the scene task characteristics and the man-machine coupling characteristics of the human. The Event Tree Analysis (ETA) method is a logically deduced Analysis method from bottom to top, can describe a human-computer interaction process from a causal logical relationship, is simple in modeling process, but can only be described in a linear chain manner but cannot analyze combined events (human-computer rings), and is insufficient in description capacity. In the aspect of simulation modeling, a risk and reliability center of Maryland university develops a class Information, decision and behavior response (IDAC) simulation analysis system; foreign research institutions such as taffy institute, university of labor in majors, university of chicago, university of birmingham, england, and the like, develop Multi Agent (MA) simulation technology research and develop corresponding platforms. The modeling method based on simulation needs to respectively construct simulation models aiming at multiple cognitive error models and fault mechanism models in different task scenes, and traversing event combination or time sequence is very time-consuming, so that the workload is huge, the universality is poor, and meanwhile, the simulation result is difficult to check.
At present, human-machine systems with complicated automation are widely applied to a plurality of important fields. To some extent, people have been converted from operators to monitors and controllers in general scenarios, handlers in important scenarios, and emergency handlers in emergency scenarios. In each scene, people often have different information acquisition channels, uninterruptedly acquire information from a highly dense information group in different perception modes, understand the information, screen and sort the information, analyze and process the information, make decisions and corresponding operations, and complete tasks and ensure safety. The complex cognitive processing activities in a certain time can cause the increase of the cognitive load of people, reduce the cognitive behavior ability and the operation performance level of people, and when the cognitive load is too high and the flight faces complex meteorological conditions, errors can be generated in information acquisition and analysis, and task failure or system failure can be caused and accidents can be caused. Therefore, the analysis of the reliability of the man-machine interaction of the complex system from the information cognition level is very important.
Cognitive overload and pattern confusion are two typical cognitive levels of human misbehavior. The cognitive overload refers to a state in which a person cannot perceive all required information due to limited cognitive resources on the premise of limited time. That is, cognitive overload failures are related to whether time is sufficient, cognitive resource limitations, and required sensory information, resulting in the selective abandonment of completing a task and sensing information related to the task, thereby failing to sense certain information or forgetting to perform an action. The mode confusion refers to a state in which a human makes an erroneous judgment on a system failure mode due to missing of perception information (information required for abandoning perception failure diagnosis due to cognitive overload or complete missing of information required for failure diagnosis due to equipment failure/harsh environment), incomplete perception information (partial missing, i.e., incomplete interactive information), or erroneous perception information (i.e., erroneous interactive information, including false alarms). The two human-computer error modes can explain most human-computer interaction faults, so that the reliability of the system can be more accurately analyzed if the two fault logics can be completely described during modeling analysis of a human-computer interaction system.
Disclosure of Invention
(1) The purpose is as follows:
the invention provides a method for solving the reliability of a man-machine interaction system based on Markov, which starts from the cognitive aspect of information by people in the man-machine interaction process, fully considers the cognitive characteristics, the scene task characteristics and the man-machine coupling characteristics of people, and perfects the fault logic of the system, thereby more accurately measuring the reliability of a complex man-machine system. Scenes and design defects which are easy to induce human errors can be found through analysis, and the method plays an important role in improving the performance capability level of personnel and enhancing the reliability and safety of a man-machine system.
(2) The technical scheme is as follows:
the invention relates to a human-computer system reliability solving method based on Markov, which comprises four steps of determining a system fault bottom event set, drawing a system state transition diagram, determining a state transition rate matrix and solving the system instantaneous reliability. The method can more accurately solve the reliability of the complex man-machine system, can find scenes and design defects which are easy to induce human errors, and has important effects on improving the performance capability level of personnel and enhancing the reliability and safety of the man-machine system.
The invention relates to a method for solving the reliability of a man-machine system based on Markov, which comprises the following specific steps:
the method comprises the following steps: analyzing a human-computer interaction system, an environment and a task scene, and analyzing fault logic to determine a bottom event set causing a human-computer system fault;
step two: determining a complete set of state space, and drawing a system state transition diagram according to system fault logic;
step three: calculating to obtain the transfer rate between states, and constructing a transfer rate matrix;
step four: listing a state equation, and solving to obtain the instantaneous reliability of the human-computer system;
through the steps, the fault logic in the human-computer interaction process is analyzed, the set of system fault bottom events is determined, and the instantaneous reliability of the human-computer system is finally solved, so that the effects of accurately solving the reliability of the human-computer system and searching system defects are achieved, and the problem that the multi-factor coupling characteristic of the human-computer system is difficult to describe in the conventional human-computer system reliability modeling is solved.
Wherein, the step one, namely determining the bottom event set causing the man-machine system fault, is the basis of the whole analysis and calculation process; when analyzing system fault logic, the method is divided into two parts of independent failure and man-machine interaction fault, bottom event sets of the two parts are respectively determined, and the bottom event set of the man-machine system fault can be obtained through a union set, and the method comprises the following steps:
step 1): determining a set of independent failure partial bottom events
The determination of the independent failure part bottom event set adopts a Fault Tree (FTA) method, which is widely applied in the engineering practice and is a mature method; combining the current man-machine system, environment and task situation, carrying out top-to-bottom logic analysis on system faults, and constructing an accident tree to obtain a bottom event set of an independent failure part; transmitting the man-machine interaction faults in the set to the next step as the basis of analysis;
step 2): determining a set of partial bottom events of human-computer interaction faults
The analysis of the part is established on the basis of Fault Tree (FTA) analysis, and human-computer interaction faults occurring under the current human-computer interaction system, environment and task situations are analyzed according to the definition and fault logic of cognitive overload and mode confusion of two human-computer interaction faults, so that a bottom event set of the human-computer interaction fault part is determined; firstly, determining a trigger event, namely a task of identifying a system mechanical fault born by a person under the current situation, and taking the trigger event as a bottom event of the cognitive overload fault; secondly, analyzing factors causing missing, error or incompleteness of human sensing information, and taking the factors and the equipment fault to be identified as a bottom event of mode confusion fault; the union set of the two events is a bottom event set of the human-computer interaction fault part; and finally, obtaining a bottom event set of the human-computer system fault by solving a union set of bottom event sets of the independent failure part and the human-computer interaction fault part.
Wherein, said "drawing the system state transition diagram" in the step two includes the following steps:
step 1): defining system states
The random combination of all the states of the bottom event constitutes the state of the system, so the state of the bottom event should be defined first; the occurrence states of the bottom events are generally defined as normal (indicated by 0) and fault (indicated by 1), then zero combination of the states of all the bottom events constitutes different states of the system, and the set of all the system states is called a state space;
step 2): drawing a system state transition diagram
Taking the number of faults of the bottom event as an abscissa, and sequentially listing all states of the system from top to bottom; then connecting the state points by using a directed line according to the state transition logic of the system, wherein the line represents the transition between the states;
the cognitive overload triggering condition is that the number a of input events is more than or equal to 2, and the occurrence probability of output events corresponding to different input events is different, so that the cognitive overload can be triggered for many times in the same chain in the Markov state transition diagram; for example, in a certain situation, cognitive overload faults occur when a person in a man-machine system undertakes A, B, C tasks, so that some tasks are abandoned or information D, E relevant to the tasks is abandoned, and the situation occurs and two cognitive overload faults are triggered;
the trigger condition of the mode confusion is that a condition judgment event occurs, so the occurrence of the trigger condition in the state transition diagram should be merged with the mode confusion; if a fault M occurs, a person erroneously recognizes the fault M as a fault N due to an event P; thereby finally forming a two-dimensional mesh structure diagram;
step 3): model simplification
Determining fault state points and non-fault state points of the system according to the analysis of the fault logic in the step one; combining a plurality of states in a system fault state set F and a non-fault state set NF, simplifying a model and reducing the number of system states; the simplified state space is marked with serial numbers from 0 to n and is input into the next step, so that the aim of simplifying the solving process is fulfilled.
Wherein, the step three includes "calculating the inter-state transition rate and constructing the transition rate matrix", which is performed as follows: calculating the transfer rate among the states, and classifying the transfer rate among the states according to the transfer form among the states, wherein the transfer rate includes three types of independent failure parts, cognitive overload faults and mode confusion faults; therefore, the transition rate between two different states should be discussed in a classification way; the transfer rate of the independent failure part between the states is given by experts according to actual experience and theoretical basis, and the state transfer rate of the human-computer interaction part is obtained by calculation; finally, expressing the transfer rate between states in a matrix form to construct a transfer rate matrix; the calculation steps of the transition rate between states are as follows:
step 1) solving the transition rate from the state i to the state j (i ≠ j)
If the state i is transferred to the state j, which is not related to the man-machine interaction fault logic, and i ≠ j, the transfer between the states only contains an independent failure part, and the transfer rate between the states is as follows:
q ij ＝λ ij (1)
in the formula: lambda ij State transition rate of independent failure part from state i to state j (i ≠ j);
if the state i is transferred to the state j and is related to the output event of the cognitive overload, and i is not equal to j, the inter-state transfer comprises an independent failure part and a cognitive overload related part, and the inter-state transfer rate is as follows:
in the formula: p c Outputting conditional probabilities of occurrence of an event when an input event occurs for cognitive overload;
if the state i is transferred to the state j and is related to the output event of the mode confusion, i is not equal to j, namely the output event is caused by the input event occurrence state corresponding to the output event, combining the state i and the state j, and calculating according to the formulas (1) (4.5);
step 2) solution of the transition rate from state i to state j (i = j)
When the state i is transferred to the remaining n states, there may be a plurality of state transfer processes related to cognitive overload, and then the transfer rate from the state i to the state j (i = j) is:
in the formula: m (m is less than or equal to n) is transferred to other n statesKnowing the number of overload-related processes; p cb The conditional probability that the cognitive overload output event occurs when the input event occurs in the process related to the cognitive overload for the b (i =1,2,3 Λ m);
therefore, the transition rate between all states is obtained, and the transition rate matrix Q is expressed in a matrix form and is in the form of:
wherein "list the state equation and solve to obtain the instantaneous reliability of the human-machine system" in step four is as follows: the solution of the system instantaneous reliability is actually to solve a linear differential equation, and the solution process comprises the following steps:
step 1): determining system initial state distribution
Let P denote the probability that the system is in state i at time t i (t), let P (t) = (P) 0 (t),P 1 (t),Λ,P n (t)), then there is P (t) = P (0) · e) according to the equation of state Qt (ii) a The transfer rate matrix Q has been determined in step two, so the initial state distribution of the system should be determined first, i.e. at time P when t =0 0 (t),P 1 (t),Λ,P n (t) to determine P (0), and then listing the system equation of state;
step 2): solving system state equations
Firstly, diagonalizing a transfer rate matrix Q as shown in formula (4), and recording each column in X as n +1 order column vectors A for simplifying expression 0 ,A 1 ,ΛA n Is mixing X -1 The middle lines are marked as n +1 order line vectors B 0 ,B 1 ,ΛB n ；
In the formula: q is a transfer rate matrix;
x is a transformation matrix;
X -1 an inverse matrix of X;
d is a diagonal matrix similar to Q;
A 0 ,A 1 ,ΛA n is n +1 rows in the matrix X;
B 0 ,B 1 ,ΛB n is a matrix X -1 N +1 columns of (1);
n is the order of the matrix Q minus 1;
d 0 ,d 1 ……d n n +1 characteristic roots for Q;
secondly, calculating the index e of the transfer rate matrix Qt ：
Then the instantaneous probability of each state is:
step 3): determining system instantaneous reliability
Obtaining instantaneous probability values of all states of the system through the solution of the step 2); summing all the state probabilities in the failure state set F of the system to obtain the instantaneous failure probability of the system; the probability of the system failing at time t is therefore:
wherein,
in the formula: p (t) is the instantaneous failure rate of the system;
t is time, unit s;
f is a fault set;
then the instantaneous reliability of the system is known as:
R(t)＝1-P(t) (8)
in the formula: r (t) is the instantaneous reliability;
the step is a process for solving the equation, the solving process is clear and simple, and manual solving can be replaced by MATLAB, VB, C language or C + + programming.
(3) Efficacy and advantages
The invention provides a Markov-based man-machine interaction system reliability calculation method, which considers the cognitive characteristics, scene task characteristics and man-machine coupling characteristics of people, completely describes the system fault logic and can adapt to the requirement of the reliability quantitative modeling analysis of a complex man-machine system. Meanwhile, a method for calculating the transfer rate between the system states is provided, and the reliability of the human-computer system can be calculated more accurately.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
FIG. 2 is a crash accident tree analysis diagram of a dual-engine ship-borne helicopter.
Fig. 3 is a simplified diagram of a crash accident tree of the double-engine carrier-based helicopter.
Figure 4 markov state transition diagram.
Figure 5 is a simplified diagram of markov state transitions.
Fig. 6 comparative graph of accident analysis results.
The numbers, symbols and codes in the figures are explained as follows:
FIG. 2 is a diagram of FIG. 3 showing English letters plus numerals as event codes, M representing an intermediate event, X representing a bottom event, and FDEP being a function-related logic gate in a fault tree;
in fig. 4 and 5, the number X plus the number represents the bottom event code, the oval box represents the state of the system formed by the bottom event, the numbers 0 and 1 represent the occurrence state of the bottom event, 0 represents the occurrence of the event, and 1 represents the non-occurrence of the event, the arrow represents the transfer direction of the system, the solid line represents the state transfer caused by the independent failure of the equipment, and the dotted line represents the state transfer caused by human error.
Detailed Description
The invention provides a man-machine system reliability solving method based on Markov, which is shown in figure 1; the method is sequentially carried out according to the following four steps; the invention adopts a double-engine carrier-borne helicopter as a case, in the case, the height of the airplane is lower in a landing stage, when an automatic throttle system is in a connected state and one engine of the helicopters has throttle jamming failure, the airplane automatically compensates the situation of asymmetric thrust caused by keeping the approach speed, the throttle handle of the other engine is automatically withdrawn, and simultaneously the parameters of the engine are rapidly reduced. The crew member easily judges the accelerator jamming fault of the engine as another engine fault, and manually shuts down the normal engine, so that the airplane crashes due to the loss of power.
The invention relates to a method for solving the reliability of a man-machine system based on Markov, which is shown in figure 1, and the detailed implementation mode is as follows:
the method comprises the following steps: determining a set of bottom events that cause a human machine system failure
The method comprises the following two steps:
step 1): determining a set of independent failure partial bottom events
And modeling and analyzing the system by using an FTA (fiber to the infrastructure) method to obtain an independent failure part bottom event set. In the example, a crash of a double-engine carrier-borne helicopter is taken as a top event, and an accident tree is constructed through top-down logic analysis, as shown in fig. 2, wherein two fault logics of cognitive overload and mode confusion are not included. To simplify the calculation process, the intermediate events (M4, M5, M9, M11) are omitted, and the simplified model is as shown in fig. 3. The available independent failure partial bottom events are shown in the following table:
table 1 independent failure partial bottom event table
| Numbering | Event(s) |
| X1 | Throttle blocking |
| X2 | Manual error shutdown No. 2 engine |
| X3 | Not looking at engine parameters |
| X4 | No. 2 engine throttle handle withdrawing |
Step 2): determining a set of partial bottom events of human-computer interaction faults
In this case, both cognitive overload faults and pattern confusion faults caused by cognitive overload are included. Firstly, overload fault logic is analyzed and cognized, in the case of the overload fault logic, a person undertakes normal flight tasks, communication tasks and tasks of identifying and recognizing mechanical faults, and the faults are characterized by being recovered from a No. 2 engine handle. The three tasks all need to occupy human cognitive resources, so that the occurrence of cognitive overload faults is caused, and people abandon the identification of engine parameters. In conjunction with the failure characterization, the occurrence of pattern confusion results in a person mistakenly considering engine failure No. 1 as an engine failure No. 2 and mistakenly shutting down engine No. 2. The bottom events of cognitive overload and pattern confusion are listed in table 2 according to their definitions:
TABLE 2 human-computer interaction failure part bottom event set
| Numbering | Event(s) |
| X4 | No. 2 engine throttle handle withdrawing |
Therefore, the system fault bottom event set is known as { X1, X4, X2, X3}.
Step two: drawing a system state transition diagram comprises the following steps
Step 1): defining system states
The system state is defined by firstly defining the state of a bottom event, recording the occurrence of the bottom event as state 1 and the non-occurrence of the bottom event as state 0, namely clearly distinguishing the states of the bottom event. In this case, there are four base events, and zero of these four event states constitutes a complete set of the state space of the system, and there are 16 state points in the set.
Step 2): drawing a system state transition diagram
Setting all the bottom events as initial state points, using the number of the bottom events as an abscissa, and listing the system states from top to bottom, and sequentially connecting the system state points by using directed lines according to the analysis of the fault logic in the first step to form a mesh logic diagram, as shown in fig. 4.
And step 3): model simplification
And determining fault state points and non-fault state points of the system according to the analysis of the fault logic in the step one. Multiple states in the system fault state set F and the non-fault state set NF are merged, and 12 state spaces remain, as shown in fig. 5. The simplified state space is marked with serial numbers from 0 to 11 and is input into the next step, so that the aim of simplifying the solving process is fulfilled.
Step three: calculating inter-state transition rates
The calculation of the inter-system state transition rate should first determine the state transition rate of the independently failing part. And the independent failure part of the system state transition is caused by the occurrence of the bottom event, so that the state transition rate of the independent failure part is equal to the occurrence rate of the bottom event causing the system state transition. The following assumptions were made:
λ X1 ＝λ X2 ＝λ X3 ＝λ X4 ＝1×10 -4 (9)
in the formula of X1 、λ X2 、λ X3 、λ X4 Are bottom events X1, X2, X3,Incidence of X4.
Step 1) solving the transition rate from the state i to the state j (i ≠ j)
Firstly, fault classification of system state transition is analyzed, in the case of the fault classification, an independent failure part and a man-machine interaction fault part are included, and two faults can be combined into a whole analysis due to cognitive overload confusion in the man-machine interaction fault part mode. The inter-system state transition relationships were analyzed and listed in table 3:
TABLE 3 intersystem State transition Classification
Then the rate of transitions between states containing only the independently failing part is:
q 01 ＝q 21 ＝q 39 ＝q 45 ＝q 65 ＝q 79 ＝q 8,11 ＝q 10,11 ＝λ X1
q 02 ＝q 37 ＝q 46 ＝q 8,11 ＝λ X4
q 03 ＝q 19 ＝q 27 ＝q 48 ＝q 5,11 ＝q 6,10 ＝λ X2
q 04 ＝q 15 ＝q 26 ＝q 38 ＝q 7,10 ＝q 9,11 ＝λ X2
for the part containing the man-machine interaction fault, the conditional probability of recognizing that the overload output event occurs at the input event is determined firstly. In the case, the overload input event is recognized as a normal flight task and a communication task which are assumed by people and a mechanical fault identifying task, and the output event is abandoned to identify engine parameters. Assuming this conditional probability P c And =0.8, the transition rate between states of the man-machine interaction fault part is as follows:
q 1,11 ＝(λ X2 +λ X3 )P c
q 2,10 ＝(λ X1 +λ X2 +λ X3 )P c
step 2) solution of the transition rate from state i to state j (i = j)
It is known that only state 1 and state 2 in all 12 states of the system have cognitive overload faults during transitions to the other states. The input event and the output event of the cognitive overload are the same in both processes, and the conditional probability is P c =0.8. There is an inter-state transition rate:
q 00 ＝-(λ X1 +λ X4 +λ X2 +λ X3 )
q 11 ＝-(λ X2 +λ X3 )(1-p c )
q 22 ＝-(λ X1 +λ X2 +λ X3 )(1-p c )
q 33 ＝-(λ X1 +λ X4 +λ X3 )
q 44 ＝-(λ X1 +λ X4 +λ X2 )
q 55 ＝-λ X2
q 66 ＝-λ X1 -λ X2
q 77 ＝-λ X1 -λ X3
q 88 ＝-λ X1 -λ X4
q 99 ＝-λ X3
q 10,10 ＝-λ X1
if the state transition rates between the other systems are all 0, the state transition rate matrix between the systems is:
step four: solving for system instantaneous reliability
First, the state distribution at the initial time of the system is determined, and in this case, the states in which all bottom events occur are defined as the initial state of the system, i.e., the state point (0000), so that the initial state distribution of the system is known as P (0) = (1,0, Λ, 0) 12 Can then utilizeThe programmed means solves for the system reliability. For the effect of the comparison method, the instant reliability of the system considering only the independent failure part is solved as follows:
a comparison of the instantaneous reliability of the system taking into account both the independent failure and the human-machine interaction failure and the instantaneous reliability of the system taking into account only the independent failure is plotted, as shown in fig. 6, where it can be seen that the former is significantly larger than the latter.
Claims (2)
1. A human-computer interaction system reliability solving method based on Markov is characterized in that: the method comprises the following steps:
the method comprises the following steps: analyzing a human-computer interaction system, an environment and a task scene, and analyzing fault logic to determine a bottom event set causing a human-computer system fault;
step two: determining a complete set of state space, and drawing a system state transition diagram according to system fault logic;
step three: calculating to obtain the transfer rate between states, and constructing a transfer rate matrix;
step four: listing a state equation, and solving to obtain the instantaneous reliability of the human-computer system;
the step one of determining a bottom event set causing the man-machine system fault is the basis of the whole analysis and calculation process; when analyzing system fault logic, the method is divided into two parts of independent failure and man-machine interaction fault, bottom event sets of the two parts are respectively determined, and the bottom event set of the man-machine system fault can be obtained by solving a union set, and the method comprises the following steps:
step 1.1): determining a set of independent failure partial bottom events
Determining the independent failure part bottom event set by adopting a Fault Tree (FTA) method, and performing top-to-bottom logic analysis on system faults by combining the current man-machine system, environment and task situation to construct a fault tree, namely obtaining the independent failure part bottom event set; transmitting the man-machine interaction faults in the set to the next step to serve as a basis for analysis;
step 1.2): determining a set of partial bottom events of human-computer interaction faults
The analysis of the part is established on the basis of Fault Tree (FTA) analysis, and human-computer interaction faults occurring under the current human-computer interaction system, environment and task situations are analyzed according to the definition and fault logic of cognitive overload and mode confusion of two human-computer interaction faults, so that a bottom event set of the human-computer interaction fault part is determined; firstly, determining a trigger event, namely a task of identifying a system mechanical fault borne by a person under the current situation, and taking the trigger event as a bottom event of the cognitive overload fault; secondly, analyzing factors causing human perception information missing, errors and incompleteness, and taking the factors and equipment faults needing to be identified as bottom events of mode confusion faults; the union set of the two events is a bottom event set of the human-computer interaction fault part; finally, obtaining a bottom event set of the man-machine system fault by solving a union set of bottom event sets of the independent failure part and the man-machine interaction fault part;
the step two of drawing the system state transition diagram comprises the following steps:
step 2.1): defining system states
The random combination of all the states of the bottom event constitutes the state of the system, so the state of the bottom event should be defined first; the occurrence state of the bottom event is represented as normal by '0', and the occurrence state of the bottom event is represented as fault by '1', so that zero combination of the states of all the bottom events forms different states of the system, and a set of all the states of the system is called as a state space;
step 2.2): drawing a system state transition diagram
Taking the number of faults of the bottom event as an abscissa, and sequentially listing all states of the system from top to bottom; then, according to the state transition logic of the system, connecting state points by using a directed line, wherein the line represents the transition between states;
the cognitive overload triggering condition is that the number a of input events is more than or equal to 2, and the occurrence probability of output events corresponding to different input events is different, so that the cognitive overload is triggered for multiple times in the same chain in the Markov state transition diagram;
the trigger condition of the mode confusion is that a condition judgment event occurs, so the occurrence of the trigger condition in the state transition diagram should be merged with the mode confusion; if a fault M occurs, a person mistakenly identifies the fault M as a fault N due to an event P; thereby finally forming a two-dimensional mesh structure diagram;
step 2.3): model simplification
Determining fault state points and non-fault state points of the system according to the analysis of the fault logic in the step one; combining a plurality of states in a system fault state set F and a non-fault state set NF, simplifying a model and reducing the number of system states; the simplified state space is marked with serial numbers from 0 to n and is input into the next step, so that the aim of simplifying the solving process is fulfilled;
the "calculating inter-state transition rates, constructing the transition rate matrix" described in step three is performed as follows: calculating the transfer rate among the states, and classifying the transfer rate among the states according to the transfer form among the states, wherein the transfer rate includes three types, namely an independent failure part, a cognitive overload fault and a mode confusion fault; therefore, the transition rate between two different states should be discussed in a classification way; the transfer rate of the independent failure part between the states is given by experts according to actual experience and theoretical basis, and the state transfer rate of the human-computer interaction part is obtained by calculation; finally, expressing the transition rate between states in a matrix form to construct a transition rate matrix; the calculation steps of the transition rate between states are as follows:
step 3.1) solving the transition rate from the state i to the state j;
if the state i is transferred to the state j which is not related to the man-machine interaction fault logic and i is not equal to j, the transfer between the states only comprises an independent failure part, and the transfer rate between the states is as follows:
q ij ＝λ ij (1)
in the formula: lambda ij The state transition rate of the independent failure part from the state i to the state j;
if the state i is transferred to the state j and is related to the output event of the cognitive overload, and i is not equal to j, the inter-state transfer comprises an independent failure part and a cognitive overload related part, and the inter-state transfer rate is as follows:
in the formula: p is c Outputting a conditional probability of an event occurring at the time of an input event for cognitive overload;
if the state i is transferred to the state j and is related to the mode-confused output event and i is not equal to j, namely the output event is generated because the input event generating state corresponding to the output event definitely causes the output event, combining the state i and the state j, and calculating according to a formula (1);
step 3.2) solving the transfer rate from the state i to the state j;
when the state i is transferred to the rest n states, a plurality of state transfer processes related to cognitive overload exist, and the transfer rate from the state i to the state j is as follows:
in the formula: m is the number of processes related to cognitive overload when the state i is transferred to the other n states, wherein m is less than or equal to n; i =1,2,3 … m; p cb The conditional probability of the cognitive overload output event occurring when the input event occurs in the process related to the cognitive overload is the b < th > process;
therefore, the transition rate among all states is obtained, and the transition rate matrix Q is expressed in a matrix form and is in the form of:
2. the markov-based human-computer interaction system reliability solution method of claim 1, wherein: "list the state equations and solve to get the instantaneous reliability of the human-machine system" described in step four, which is done as follows: the solution of the system instantaneous reliability is actually to solve a linear differential equation, and the solution process comprises the following steps:
step 4.1): determining system initial state distribution
Let P denote the probability that the system is in state i at time t i (t), let P (t) = (P) 0 (t),P 1 (t),…,P n (t)), then there is P (t) = P (0) · e) according to the equation of state Qt (ii) a The transfer rate matrix Q has been determined in step two, so the initial state distribution of the system should be determined first, i.e. at time P when t =0 0 (t),P 1 (t),…,P n (t) to determine P (0), and then listing the system equation of state;
step 4.2): solving system state equation
First, the transfer rate matrix Q is diagonalized as shown in formula (4), and each column in X is recorded as n +1 order column vectors A for simplifying expression 0 ,A 1 ,…A n Is mixing X -1 The middle lines are marked as n +1 order line vectors B 0 ,B 1 ,…B n ；
In the formula: q is a transfer rate matrix;
x is a transformation matrix;
X -1 an inverse matrix of X;
d is a diagonal matrix similar to Q;
A 0 ,A 1 ,…A n is n +1 rows in the matrix X;
B 0 ,B 1 ,…B n is a matrix X -1 N +1 columns of (1);
n is the order of the matrix Q minus 1;
d 0 ,d 1 ……d n n +1 characteristic roots for Q;
second, the index e of the transfer rate matrix is calculated Qt ：
Then the transient probability of each state is:
step 4.3): determining system instantaneous reliability
Obtaining instantaneous probability values of all states of the system through the solution of the step 4.2); summing all the state probabilities in the failure state set F of the system to obtain the instantaneous failure probability of the system; the probability of the system failing at time t is therefore:
wherein,
in the formula: p (t) is the instantaneous failure rate of the system;
t is time, unit s;
f is a fault set;
then the instantaneous reliability of the system is known as:
R(t)＝1-P(t) (8)
in the formula: r (t) is the instantaneous reliability.
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