-The approach for cognitive processing of monitored data is proposed. An application for artificial intelligence systems (AIS) allows to use the possibilities of probabilistic modeling. There are described the models and methods for prediction a probability of “success” and/or a risk of “failure”, software tools to support them, techniques for solving the problems of rationale preventive measures against threats and effective risk control. The approach means practically a proactive commitment to excellence in uncertainty conditions. A suitability of the proposed models and methods is demonstrated by some practical examples.
INTRODUCTION
Today global trends in the development of modern systems
for various functional purposes indicate the need for a radical
turn from "manual" control of certain types of safety, based on
the implementation of established instructions and expert
estimations of emerging situations, to the implementation of
proactive measures based on prediction. This allows, on the
basis of a prognostic look ahead, to proactively take effective
managing actions. This idea runs like a red line through all
world concepts and the latest standards of systems engineering.
But how to do it remains behind the scenes. There is no
universal approach to the implementation of this idea yet. In
search – all the leading countries of the world. Special hopes
are connected with the use of AIS. Here AIS are understood as
systems, operating in uncertainty conditions by logic reasoning
on the base of processing the monitored data. In AIS practice
there are often used subjective expert estimations (for AIS
training), a regression analysis of collected data, a simulation
of processes [
Note. System is combination of interacting elements organized to achieve one or more stated purposes (according to ISO/IEC/IEEE 15288).
This paper focuses on applications that are critical from the point of view of safety depending on the structural complexity of systems, formal conditions of uncertainty, implemented methods of countering threats, as well as the conditions of elements operation. Available probabilistic methods in cognitive processing of monitored data are proposed. As a result the predicted probability of "success" or risk of "failure" is produced. The inputs for modeling are monitored data from current and previous states of compound elements.
The proposed ideas, models and methods are designed to
implement feedback to rationale requirements and conditions
that guarantee the non-exceeding of the specified acceptable
risks. The proposed probabilistic approach develops the
established probabilistic approaches [
II.
The monitored system may itself be a system of interest for analysis (for example, a dispatching intelligence center) or may be part of another, more comprehensive system of interest (for example, a complex of functionally oriented robots). To perform the functions of the system, current information is collected and processed. It is proposed to carry out probabilistic prediction of critical processes in order not only to act, but also to compare predictions and their coincidence with subsequent realities, to accumulate and use this knowledge. The cognitive decisions for AIS using monitoring data is in the accumulation, analysis and the use of emerging knowledge about the possible integrity of the system in the future.
When the system is operating in the conditions of heterogeneous threats, the degree of acceptability of events is proposed to be assessed by the probability of "success" and/or "failure" taking into account the consequences (risk of "failure") during a given period of prediction. In each case of modeling, the concept of "success" must be defined in terms of the acceptable state of the system concerned to perform the given or expected functions. The concept of "failure" means no "success".
It is proposed to carry out analytical prediction of risks on
the basis of probabilistic modeling. For practical application,
methods and models [
A complex system is decomposed to compound elements to solve problems with respect to each of the elements and subsystems with the possibility of integrating them into the system as a whole. Each of the elements is represented as a "black box", and various probabilistic models can be applied to it to calculate and construct the desired probability distribution function (PDF) for time between neighboring integrity losses, taking into account heterogeneous threats, the measures taken to control, monitor and integrity recovery. Below are some generalized models "black box" for the risk prediction.
III.
THE MODELS PROPOSED
In general case successful system operation (not only AIS) is connected with system counteraction against various dangerous influences on system integrity - these may be counteractions against failures, defects events, “human factors” events, etc. There are proposed the formalization for two general technologies of providing counteraction against threats: periodical diagnostics of system integrity (technology 1, without monitoring between diagnostics) and additionally monitoring between diagnostics (technology 2). As a rule these technologies are implemented by AIS.
Assumptions: for all time characteristic the PDF exists. It is supposed for technologies 1 and 2 that the used diagnostic tools allow to provide necessary system integrity recovery after revealing danger sources penetration into a system or consequences of influences.
The probability of system operation with required safety within the given prognostic period (i.e. probability of “success”) may be estimated as a result of modeling. Risk to lose integrity (R) is an addition to 1 for probability of correct system operation (P), i.e. R=1-P considering consequences. A. Model for the periodical diagnostics of system integrity
The model considers periodical diagnostics of system integrity, that is carried out to detect danger sources penetration into a system or consequences of negative influences (see Figure 1).
Dangerous influence on system is acted step-by step: at first a danger source penetrates into a system and then after its activation begins to influence. System integrity can’t be lost before a penetrated danger source is activated. A danger is considered to be realized only after a danger source has influenced on a system. The lost system integrity (after an accident event) can be detected only as a result of diagnostics. System recovery is started after detection.
There are possible the next variants for technologies 1 and 2: variant 1 – the given prognostic period Treq is less than established period between neighboring diagnostics (Treq < Tbetw.+Tdiag); variant 2 – the prognostic period Treq is more than or equals to established period between neighboring diagnostics (Treq ≥ Tbetw.+Tdiag). Here Tbetw. – is the time between the end of diagnostic and the beginning of the next diagnostic, Tdiag – is the diagnostic time.
The next formulas for PDF of time between the losses of
system integrity are proposed [
PDF for the model of technology 1, variant 1: Under the condition of independence for characteristics the probability of providing system integrity for variant 1 is equal to
P(1)(Treq) = 1 - Ωpenetr ∗ Ωactiv(Treq), (1) where Ωpenetr(t) – is the PDF of time between neighboring penetrations of dangers; Ωactiv(t) – is the PDF of activation time of penetrated danger. For different dangers a frequency of dangers for these PDF is the sum of frequencies of every kind of dangers.
PDF for the model of technology 1 , variant 2. Under the condition of independence for characteristics the probability of providing system integrity for variant 2 is equal to
P(2) (Treq) = N((Tbetw +Tdiag)/Treq) P(1)N(Tbetw +Tdiag) + +(Trmn/Treq) P(1)(Trmn), (2) where N=[ Тreq./(Тbetw.+ Тdiag.)] – may be real (for PDF) or the integer part (for estimation of deviations), Trmn = Treq N(Tbetw +Tdiag)). The probability of providing system integrity within the given time P(1)(Tgiven) is defined by (1).
B. Model for continuous monitoring between the periodical diagnostics of system integrity
Technology 2, unlike the previous one, implies that system integrity is continuously monitored between diagnostics by operator (operator functions may be performed by a man or special AIS component or their combination). In case of detecting a danger source an operator recovers system integrity. The ways of integrity recovering are analogous to the ways of technology 1.
Faultless operator’s actions provide a neutralization of a danger source trying to penetrate into a system. A penetration of a danger source is possible only if an operator makes an error but a dangerous influence occurs if the danger is activated before the next diagnostic. Otherwise the source will be detected and neutralized during the next diagnostic.
The next formulas for PDF of time between the losses of
system integrity are proposed [
PDF for the model of technology 2, variant 1. Under the condition of independence for characteristics the probability of providing system integrity is equal to .
Here A(τ) is the PDF of time between operator’s error. (3)
PDF for the model of technology 2, variant 2. Under the condition of independence of characteristics the probability of providing system integrity is equal to
P(2) (Treq) = N((Tbetw +Tdiag)/Treq) P(1)N(Tbetw +Tdiag) + +(Trmn/Treq) P(1)(Trmn), (4) where the probability of providing system integrity within the given time P(1)(Treq.) is defined by (3).
The final clear analytical formulas for modeling are received by Lebesque-integration of (3) expression. C. About a generation of probabilistic models for complex system
The basic ideas of correct integration of probability
metrics are based on a combination and development of
models. For a complex systems with parallel or serial
structure described there are proposed the method to generate
adequate probabilistic models described in [
1) time between losses of integrity for system combined from series connected independent elements is equal to a minimum from two times τi: failure of 1st or 2nd elements (i.e. the system goes into a state of lost integrity when either 1st, or 2nd element integrity is lost). For this case the PDF of time between losses of system integrity is defined by expression В(t) = Р[min (τ1,τ2)≤t]=1- Р[min (τ1,τ2)>t]=1-Р(τ1>t)Р(τ2 > t)= 1 – [1-В1(t)] [1- В2(t)], (4) 2) time between losses of integrity for system combined from parallel connected independent elements (hot reservation) is equal to a maximum from two times τi: failure of 1st and 2nd elements (i.e. the system goes into a state of lost integrity when both 1st and 2nd elements have lost integrity). For this case the PDF of time between losses of system integrity is defined by expression
В(t)=Р[max(τ1,τ2)≤t]=Р(τ1≤t)Р(τ2≤t)=В1(t)В2(t). (5) Applying recurrently expressions (4) – (5), it is possible to build PDF of time between losses of integrity for any complex system with parallel and/or series structure and theirs combinations.
Analytical modeling of complex systems is supported by
the software tools “Mathematical modeling of system life
cycle processes” – “know how” (registered by Rospatent
№2004610858), “Complex for evaluating quality of
production processes” (registered by Rospatent
№2010614145) and others [
IV MODELING TO THE RATIONALE OF PREVENTIVE MEASURES.
EXAMPLES
The proposed practical way to forming input for modeling is explained in application to a parameter conditions.
Example 1. For each critical parameter (for which prognostic estimations are needed to do actions) the ranges of acceptable conditions can be established. The traced conditions of monitored parameters are data about a condition before and on the current moment of time. For example, the ranges of possible values of conditions may be established: “Working range inside of norm”, “Out of working range, but inside of norm”, “Abnormality” for each separate critical parameter. If the parameter ranges of acceptable conditions are not established in explicit form than for modeling purpose the may be implied and can be expressed in the form of average time value. These time values are used as input for probabilistic modeling. For example, for coal mine some of many dozens heterogeneous parameters are: for ventilation equipment - temperature of rotor and engine bearings, a current on phases and voltage of stator; for modular decontamination equipment - vacuum in the pipeline, the expense and temperature of a metano-air mix in the pipeline before equipment, pressure in system of compressed air, etc. It may be interpreted similarly by light signals – "green", "yellow", "red" - see Fig.2 and following Example 2.
Example 2. For avoiding the possible crossing a border of “Abnormality” a prediction of residual time, which is available for preventive measures, according to gathered data about parameter condition fluctuations considering ranges should be carried out. For prediction it is proposed: 1) a choice of probabilistic models for construction PDF of time before the next abnormality for one element (“black box”), 2) development of the algorithm of generation PDF of time before the next abnormality for complex system, 3) formalization of calculative methods of estimating the mean residual time before the next parameters abnormalities for monitored critical system.
The method allows to estimate residual time before the next parameter abnormality state (i.e. time before first next coming into “red” range) Tresid(1) for a given admissible risk Radm.(Treq) to lose integrity. The estimated Tresid(1) is the solution t0 of equation:
R(Tpenetr, t, Tbetw, Tdiag, Тerr., Treq.) = Radm.(Treq) (6) concerning of unknown parameter t, i.e. Tresid(1) = t0.
Here R(Tpenetr, t, Tbetw, Tdiag, Тerr., Treq.) is risk to lose integrity, it is addition to 1 for probability P(Treq) of providing system integrity (“probability of success”), for calculations the formulas (1)–(3), (6) are used. Tpenetr is the mathematical expectation of PDF Ωpenetr (τ ), it is defined by parameter statistics of transition from “green” into “yellow” range (see Fig.2). The others parameters Tbetw, Tdiag in (6) are known. The main practical questions are: what about Treq. and what about a given admissible risk Radm.(Treq)? For answering we can use the properties of function R(Tpenetr, t, Tbetw, Tdiag, Тerr.,
- if parameter t increases from 0 to ∞ for the same another parameters, the function R(…, t, …) is monotonously decreasing from 1 to 0, i.e. if the mean activation time of occurred danger (threat - from the 1-st input at the “yellow” range to the 1-st input in the “red” range) is bigger to lose integrity is less;
- if parameter Treq increases from 0 to ∞ for the same
another parameters, the function R(…,Treq) is monotonously
increasing from 0 to 1, i.e. for large Treq risk approaches to 1.
It means the such maximal x exists when t=x and Treq.=x and
0<R(Tpenetr, x, Tbetw, Tdiag, Тerr., x)<1. The residual time before
the next parameter abnormality (i.e. time before first next
coming into “red” range) is equal to defined x with confidence
level of admissible risk R(Tpenetr, x, Tbetw, Tdiag, Тerr., x). The
implementation see on Fig. 3 [
Author of this article took part in creation of the Complex of supporting technogenic safety on the systems of oil&gas transportation and distribution and have been awarded for it by the Award of the Government of the Russian Federation in the field of a science and technics. The AIS is a part of the created peripheral posts are equipped additionally by means of Complex to feel vibration, a fire, the flooding, unauthorized access, hurricane, and also intellectual means of the reaction, capable to recognize, identify and predict a development of extreme situations – see engineering decisions on Fig. 4.
The applications of this Complex for 200 objects in several
regions of Russia during the period 2009-2014 have already
provided economy about 8,5 Billions of Roubles. The
economy is reached at the expense of effective
implementation of the functions of risks prediction and
processes optimization [
The proposed approach for cognitive processing of monitored data develops the existing approaches to risk prediction, ensuring and improving the safety of systems with AIS. Probabilistic models and methods that allow predicting the probability of "success" and/or the risk of “failure”, supporting their software tools, methods for solving practical problems are presented. Application of the proposed approach allows to counteract threats by rationale preventive actions. A suitability of the approach is illustrated by practical examples.