CN112817784B - Soft error-oriented register reliability modeling and evaluating method - Google Patents
Soft error-oriented register reliability modeling and evaluating method Download PDFInfo
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Abstract
The invention discloses a soft error-oriented register reliability modeling and evaluating method, which comprises the following steps: calculating the vulnerability factor RVF and the damage rate RCR of a single register; based on a hierarchical modeling mode, establishing a reliability model ZRRM from registers with different functions to all registers of the system by using a Z language; converting the ZRRM model into a CTMC form, and establishing the CTMC model for different functional registers; calculating the instantaneous fragility of the registers with different functions according to the CTMC model of the registers, and evaluating the reliability of the registers with different functions; and performing reliability evaluation on the whole system by using the CTMC based on the relation between the reliability evaluation result and the state of the single register. The modeling process of the invention is processed in a grading way, is simple and clear, can not only evaluate the reliability of registers with different functions, but also strictly analyze and evaluate the reliability of the ZRRM model by using a model detection method.
Description
Technical Field
The invention belongs to the field of reliability and formal modeling and verification, and particularly relates to a soft error-oriented register reliability modeling and evaluating method.
Background
A Register (Register), which is an integral part of a Central Processing Unit (CPU), is a memory location that can be quickly accessed by the CPU. Memory is usually composed of a small amount of storage, and is relatively fast, and some registers may be read-only or write-only due to special hardware functions. Almost all computers with architectures load data in a larger memory into a register, perform calculation by using the data in the register under the control of machine instructions, write the data back to a main memory under the control of the instructions after the calculation is completed, and modern computer architectures often use a static or dynamic RAM as the main memory and access the main memory through one-level or multi-level caches. Registers are typically located at the top of such a multi-level memory hierarchy, providing the fastest access speed. Registers are usually measured in the number of bits they can hold and are implemented mostly as register arrays, but they may also be implemented using separate flip-flops, high-speed core memories, thin-film memories, and other means on a digital machine. Generally, according to the definition of an instruction set, a register generally refers to only a set of registers that are directly encoded as part of an instruction. However, it is common in modern high performance CPUs to have a copy of these "architectural registers" in order to improve performance through register renaming, thereby allowing parallel and speculative execution. By definition of the instruction set, the term generally refers only to a set of registers that are directly encoded as part of the instruction. However, modern high performance CPUs often have copies of these "architectural registers" in order to improve performance through register renaming, thereby allowing parallel and speculative execution.
In the aspect of embedded register modeling, the main modeling method at present describes the reliability information of the register from the aspects of components, circuit hierarchy, sensitivity to data silent errors and interaction between the system register and other hardware of the system. The evaluation of register reliability is described primarily from the two concepts of Architecture Vulnerability Factor (AVF), defined as the probability that an error in the processor architecture (including the registers) will result in a visible error in the final output of the program, and Register Vulnerability Factor (RVF), defined as the probability that a soft error in the registers will propagate into other components. The RVF concept was proposed primarily to compensate for the inability of AVFs to take advantage of the masking effect of write operations on soft errors in registers. The concepts of AVF and RVF can be combined with software technology, and can be optimized in hardware design and software compiling period to improve the reliability of a software system, but both concepts are static concepts and cannot take account of the correlation between the dynamic characteristic of register hardware reliability and time.
The technologies for studying register reliability include technologies such as register active intervals, program reliability static analysis, sequential logic and the like besides concepts of AVF and RVF, and a lot of achievements are obtained. However, as embedded registers become increasingly complex, register hardening techniques are becoming more and more popular, and it is increasingly difficult for conventional methods to describe their dynamic characteristics and reflect the dependency of embedded register reliability on time.
Disclosure of Invention
The invention aims to provide a register reliability modeling and evaluating method facing soft errors, which is based on basic elements of a Z language construction modeling and evaluating method, converts the description of the reliability of an embedded register into a predicate constraint form so as to be convenient for verifying a modeling result by using a formalized means, and the register modeling and evaluating method constructed based on the Z language has good expansibility.
The technical solution for realizing the purpose of the invention is as follows: a soft error-oriented register reliability modeling and evaluation method comprises the following steps:
step 2, classifying the registers according to functions, and then establishing a reliability model ZRRM from the registers with different functions to all registers of the system by using a Z language based on a hierarchical modeling mode;
step 3, converting the ZRRM model into a Continuous Time Markov Chain (CTMC) form, and establishing CTMC models for different functional registers;
step 4, calculating the instantaneous fragility of the registers with different functions according to the CTMC model of the registers, and evaluating the reliability of the registers with different functions;
and 5, based on the relation between the reliability evaluation result and the state of the single register, carrying out reliability evaluation on the whole embedded register system by using a Continuous Time Markov Chain (CTMC).
Compared with the prior art, the invention has the remarkable advantages that: 1) The reliability model of the embedded system register is built step by taking a single register as a basic unit and adopting a hierarchical modeling mode, and the model built by using the modeling mode is easy to understand and is concise and clear; 2) The ZRRM model is built by depending on the Z language to describe basic elements, so that the model has strong data constraint capability and good expansibility; 3) The evaluation method converts and maps elements in a ZRRM model which is described by using Z language into elements in CTMC, so that cis-form reliability of transient basic elements of a single functional register in an embedded register model and probability of all registers of a system in various states can be described, and model elements related to reliability can be flexibly added to the ZRRM model; 4) The RVF is used for evaluating the reliability of the register, and the shielding effect of the write operation can be utilized to avoid the influence of invalid soft errors on the reliability of the evaluated register by using the concept, wherein the shielding effect of the write operation refers to that: soft errors between read and write or write intervals may be overwritten by the write without propagating to other components in the system.
The present invention is described in further detail below with reference to the attached drawing figures.
Drawings
FIG. 1 is a flow chart of a soft error oriented register reliability modeling and evaluation method.
Fig. 2 is a diagram of the embedded register ESR state transition relationship for two functional registers RFM.
Fig. 3 is a state transition diagram of an RFM, wherein (a) is a typical state transition diagram of the RFM and (b) is a state transition diagram obtained after simplifying the transient state existing in (a).
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the present application is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of and not restrictive on the broad application.
Because the Markov model can reflect the correlation of the state transition with time, and the state transition of hardware relative to time accords with the property of a Markov chain, the invention introduces the Markov theory to research the dynamic characteristics.
The Z language is the most widely used formal description language, which is used to describe and model the formal specification language of the computing system; the Z language can be used to generate structured mathematical descriptions that are applicable to the state of a system or component and the transaction under that state. The Z language is based on axiom set theory, lambda calculus and standard mathematical notation used in first order predicate logic. There are two languages for formalized description in the Z language: mathematical language and Schema (Schema) language. The mathematical language is used for describing objects and relations between the objects, and can be used for describing various characteristics of the system; and the pattern language is a semi-graphical language which can be used for sorting and packaging information so as to reuse the information. Furthermore, the expressions in the Z language are all typed, thereby avoiding some paradox of set theory. Therefore, the Z language is widely used in software formalized modeling.
In summary, in order to accurately describe the dynamic characteristics and the temporal correlation expressed by the Reliability of the Register and strictly evaluate the Reliability of the Register, the Reliability of the embedded Register is modeled in a hierarchical manner by adopting a Z language, and an evaluation Model ZRRM (Z-based embedded Register Reliability Model) of the Reliability of the Register is established by taking different functional registers as basic units of Reliability evaluation; then, describing the continuity characteristic of the state and the Time in the register by using a CTMC (Continuous Time Markov Chain), converting the ZRRM into the CTMC, and finally evaluating the reliability of the embedded register based on the CTMC.
With reference to fig. 1, the present invention provides a soft error-oriented register reliability modeling and evaluation method, which includes the following steps:
the register vulnerability factor is defined as the probability of the soft error in the register to propagate to other system components (such as a memory, a functional unit and the like), and can effectively measure the sensitivity of the register to the soft error; the damage rate of the register is the probability that the register is damaged in an irreparable way due to the single event effect at a certain moment.
Step 2, on the basis of using the register vulnerability factor as the reliability information of the embedded register, classifying the registers according to functions, and then establishing a reliability model ZRRM from registers with different functions to all registers of the system by using a Z language based on a hierarchical modeling mode;
step 3, converting the ZRRM model into a continuous time Markov chain CTMC form, and establishing CTMC models for different functional registers;
step 4, calculating the instantaneous fragility of the registers with different functions according to the CTMC model of the registers, and evaluating the reliability of the registers with different functions;
and 5, based on the relation between the reliability evaluation result and the state of the single register, carrying out reliability evaluation on the whole embedded register system by using a Continuous Time Markov Chain (CTMC).
Further, in one of the embodiments, the reliability model ZRRM in step 2 is represented as a triplet:
ZRRM RFM ＝(VRate RFM ，State RFM ，STR RFM )
in the formula, VRate RFM Representing the vulnerability of different functional registers RFM; state RFM State space representing the RFM, containing all possible states of the registers; STR RFM Representing the transition relationships between all possible states of the register;
wherein, the vulnerability of RFM is:
λ RFM ＝λ RVF +λ RCR
in the formula of lambda RFM Indicating vulnerability of RFM, λ RVF Indicating register fragility factor, λ RCR Indicating the register corruption rate.
Further, in one embodiment, the register fragility factor λ RVF Comprises the following steps:
in the formula, susceptibleTime (R) represents the time that the register R is in the sensitive interval mode, and LifeTime (R) represents the service life of the register R;
the register corruption rate λ RCR Comprises the following steps:
λ RCR ＝e ξt
in the formula, ξ is a constant.
Further, in one embodiment, the CTMC in step 3 is a five-tuple:
CTMC＝(S M ，S in ，A，T M ，t)
wherein the content of the first and second substances,
(1)S M representing the state space of the CTMC, which is a set of all possible states of the register;
(2)S in ∈S M the initial state of the CTMC is represented as the state of the register before being used;
(3)A＝[a ij ]is a matrix of n x n representing the state transition probability matrix of the CTMC, wherein a ij Indicating the slave state s of the register i ∈S M Transition to state s j ∈S M The probability of (d);
(4)
is the set of state transition relationships of CTMC,(s) i ，s j )∈T M Indicating that there is a branch to cause the register to slave state s i Becomes state s j ；
(5) t represents the time.
Further, in one embodiment, the ZRRM model is transformed in step 3 into a continuous time markov chain CTMC form, specifically by an element mapping rule between ZRRM and CTMC, which is shown in table 1 below:
table 1 element mapping rules between rrm and CTMC
Further, in one embodiment, the step 4 of calculating the instantaneous vulnerability of the different function registers according to the CTMC model of the registers and evaluating the reliability of the different function registers specifically includes:
step 4-1, defining the relationship between the RFM damage rate and time:
λ RCR (t)＝e ξt
in step 4-2, the typical state transition matrix A' of the register is:
the state probability equations for the different functional registers are thus obtained:
in the formula, P V (t) represents the probability that the RFM is in a vulnerable state at time t, P C (t) represents the probability that RFM is in a crash state at time t, P N-V (t) represents the probability that the RFM is in a non-vulnerable state at time t, λ Srrengthen Indicating a transition of RFM from a vulnerable to a non-vulnerable state, λ Weaken Indicating that the RFM is transitioning from a non-vulnerable state to a vulnerable state;
step 4-3, solving the formula in the step 4-2 to obtain the state probability distribution of the RFM at the time t, and then obtaining the reliability R of the RFM at the time t RFM (t) is:
R RFM (t)＝1-P V (t)-P C (t)。
further, in one embodiment, the step 5 of performing reliability evaluation on the whole embedded register system by using a continuous time markov chain CTMC based on the relationship between the reliability evaluation result and the state of the single register specifically includes:
step 5-1, describing the state spaces of all registers of the embedded register system:
the states of all registers form the state space, i.e. a institute, of the whole system of registers, i.e. the embedded register systemWith state sequences i of different functional registers n-1 i n-2 …i １ i 0 The state is one state in the whole system state space of the register, the whole system space of the register is formed by the state sequences, and n is the number of the registers; in the state sequence, i j =1 denotes the state i of register j j In a non-vulnerable state, i j =0 indicates that the state of the register j is in a fragile state or a destroyed state;
step 5-2, calculating a state transition probability matrix A of the whole embedded register system based on the relationship between the reliability evaluation result and the state of the single register;
and 5-3, obtaining the following equation according to the stable distribution property of the Markov chain, and utilizing the equation to carry out reliability evaluation on the whole embedded register system:
in the formula, P stable For the probability distribution, P, of a Markov chain corresponding to the ESR of an embedded register system in a stationary state stable Including the probability of ESR being in each state, P ESR (t) is the initial distribution of the Markov chain for ESR, m represents the number of transitions, and t represents the time at which the reliability of each BFM corresponds.
Further, in one embodiment, for an embedded register system including two BFMs, a general register GR and a stack register SR, the state transition probability matrix a is:
in the formula, λ GR 、λ SR Denotes the vulnerability status of GR and SR, respectively GR 、μ SR Representing the non-fragile probabilities of GR and SR, respectively.
The present invention will be explained in detail below.
The embedded register reliability evaluation model ZRRM provided by the invention is modeled by depending on Z language and then converted into a Continuous Time Markov Chain (CTMC) form for evaluation, the modeling and evaluation method is mainly divided into register models with different functions and all register reliability models of a system, wherein the evaluation model of all register reliability of the system is completed on the basis of the evaluation of all register reliability. The definition of the Z language template form of the ZRRM model is given below.
1. Register module RFM reliability model with different functions
The ZRRM model is defined in definition 1 with respect to the RFM submodel, and the modeling elements constituting the RFM reliability model are described in detail in this definition, which are specifically defined as follows:
define the RFM submodel ZRRM of 1.ZRRM RFM May be defined as a triplet form as shown in the following formula, wherein VRate RFM (Vulnerability Rate) indicates the Vulnerability, state, of the RFM RFM Representing the state space of the RFM, STR RFM (State Transfer Relationship) represents a State transition Relationship.
ZRRM RFM ＝(VRate RFM ，State RFM ，STR RFM )
ZRRM is described below RFM The specific meaning of the three elements in (a) and the Z-mode definition method of the element.
(1) Friability VRate RFM
The reliability of the RFM is defined by a register Vulnerability factor RVF and a register Corruption rate RCR, and when the register is in the WR and RR intervals, it can be regarded as that the current register is in a vulnerable (Vulnerability) state, and when the register is subjected to unrecoverable permanent Corruption, it can be regarded as that the register is in a corrupted state (Corruption), so that the following definition 2 can be given to the Vulnerability rate of the RFM.
Definitions 2. Vulnerability of RFM RFM Defined as the formula:
the RFM vulnerability rate VRate described using the Z mode is as follows:
wherein, S _ Time and L _ Time respectively represent SusceptibleTime (R) and Life Time (R), RFM _ VRate represents the vulnerability of RFM, and Corruption _ Rate represents the damage Rate of RFM as e ξt And the ESR has a plurality of RFMs, it is necessary to add in the name to distinguish these different registers<RFMName>。
(2) State space State RFM
The State space of the RFM includes a Normal State (NS), a fragile State (VS), a Non-fragile State (NVS), a strengthened State (strenghen State, SS), a weakened State (weak State, WS), and a damaged State (CS), wherein the Normal State is an initial State; vulnerability State is a State in which a register is in a vulnerable interval, i.e., WR or RR interval, strengthen State is a transient State, a State that is shifted from the vulnerable State to a non-vulnerable State, an intermediate State, when the register is shifted from the WR or RR interval to the RW or WW interval; the Weaken State is also a transient State, and the State transition process of the Weaken State is opposite to the intensified transition process; the corrmption State is a termination State indicating that a register is permanently damaged. Based on the above state relationships, an RFM typical state transition diagram as shown in fig. 3 (a) can be obtained, where the ellipses in the diagram represent states, the connecting lines with parameters represent the state transition relationships and their corresponding transition probabilities, and the parameters in the diagram are defined as shown in table 2, and if the transient state existing in the diagram 3 (a) is changed, the state transition diagram as shown in fig. 3 (b) can be obtained.
TABLE 2 exemplary RFM State transition parameters
Through the above steps, the state space of the RFM can be defined, and the Z-mode of the state space is defined as follows:
where isiinitial and isarive indicate whether the RFM is in the initial state and in the current state, respectively.
(3) State transition relationship STR RFM
Fig. 3 not only shows the state space of the RFM, but also describes the transition relationships between all states in the state space of the RFM. Any state transition must contain three elements, respectively: the starting point of the transition-the source state sState, the end point of the transition-the target state tState and the probability of the transition occurring-the transition probability parameter TRate, where the starting point sState and the end point tState of the transition must be states contained in the RFM state space, and TRate is the transition parameter listed in table 2. Their Z-mode is defined as follows:
after the Z-mode modeling of each reliability element attribute of the RFM is completed, in order to prevent the complex ESR from being established, the reliability constraints of the same RFM also need to be integrated, and after the number of RFMs expands, all the reliability attributes need to be managed in a hierarchical manner. In addition, soft errors in the register can be shielded by rewriting, so the reliability of the register can be improved by reducing the time of the register in the vulnerable interval through the techniques of code rearrangement, super-blocking and the like, so the vulnerability factor of the register can be related to the reliability of the register, which can be obtained by the following calculation, wherein μ represents the reliability of the RFM, susceptibleletime (R) represents the time of the register R in the sensitive interval mode, and LifeTime (R) represents the service life of the register R.
Therefore, the reliability constraint of the same RFM can be managed by using a Z mode, and the reliability of the RFM is expressed by using RFMRRate in the Z language mode, and the specific definition method is as follows:
the Z-mode < RFMName > RFM described above uses the definition included in the mode in the Z language.
2. Embedded register reliability model
In order to accurately model the reliability of System Register Hardware (RSH), the Hardware structure of RSH needs to be modeled first. The hardware in the RSH system can be divided into different Register Function Modules (RFM) according to functions, and the RFM is only in a vulnerable state, i.e., WR and RR intervals, and is sensitive to soft errors. Therefore, the reliability of RSH can be essentially modeled and analyzed from the vulnerability factors of RFM. RFM is the basic unit of ESR, so whether RFM is in a vulnerable state directly reflects the state of ESR. Registers can be divided by function into: general purpose registers, stack registers, link registers, program counters, and program status registers. Fig. 2 illustrates a state transition relationship of an ESR with two RFMs. As shown in fig. 2, the ESR has two RFMs, namely a general register GR and a stack register SR, and the circle in the figure represents one state of RSH, and the state "GRSR" represents that neither GR nor SR is in a vulnerable state; "GR" means GR is in a non-vulnerable state and SR is in a vulnerable state; "SR" indicates that GR is in a vulnerable state and SR is in a non-vulnerable state. Lambda [ alpha ] GR 、λ SR The vulnerability states of GR and SR are shown separately, and μ is used GR 、μ SR Respectively representing the non-fragile probabilities of both.
As shown in fig. 2, the ESR with two RFMs has 4 states, and the ESR contains the number of RFMs directly influencing the state space size of the ESR, and the specific relationship is that, assuming that the ESR contains n RFMs, the state space of the ESR contains n states. Therefore, the number of RFMs contained in the ESR and their number must be explicitly stated. For example, registers in a general-purpose ARM can be classified according to their functions: general purpose registers, stack registers, link registers, program counters and program status registers, the number of registers other than 13 general purpose registers is only 1, so n is 17 in the model of system registers on the general purpose ARM architecture. The Z-mode declaration of ESR is as follows:
in the above definition of Z-mode, RFM _ num indicates the number of RFMs contained in the ESR, and all RFMs belonging to the ESR are included in the mode declaration.
The reliability evaluation method based on the ZRRM model is described in detail below.
The state space changes in the ZRRM model are time dependent, but the state at the next time instant is only related to the current state, so the ZRRM model can be described using CTMC. The ZRRM model is defined below using CTMC:
ctmc is a five-membered group defined by the formula:
CTMC＝(S M ，S in ，A，T M ，t)
wherein, the first and the second end of the pipe are connected with each other,
(1)S M the state space representing the CTMC is a set of all possible states of the register;
(2)S in ∈S M the initial state of the CTMC is represented and is the state of the register before being used;
(3)A＝[a ij ]represents a state transition probability matrix, wherein a ij Indicating slave status s of register i ∈S M Transition to state s j ∈S M The probability of (d);
(4)
is a set of state transition relationships,(s) i ，s j )∈T M Indicating that there is a branch to make the register slave state s i Becomes state s j ；
(5) t represents time.
When the reliability evaluation is carried out on the ZRRM model by using the CTMC, the ZRRM model needs to be converted into an equivalent CTMC description, so in order to make the whole conversion process equivalent, the consistent reliability description needs to be maintained before and after conversion, and the elements contained in the two (CTMC and ZRRM model) need to be analyzed and compared, so that the equivalent mapping conversion of the same elements in the two is established. The conversion rules between the two elements are given below, and the mapping conversion rules between the two models are shown in table 3 below:
TABLE 3 ZRRM modeling and CTMC element mapping transformation rules
Using the mapping rule in the table above, all the reliability constraints in ZRRM are mapped to CTMC, and the whole transformation of the reliability constraints is not omitted, added, or modified during the transformation process, so that the whole transformation process is considered equivalent, and the elements before and after the transformation are also equivalent.
1. Single RFM reliability assessment
Compared with other models for describing the register fragility rate, the exponential model has good advantages because the true curve of the register fragility rate has higher fitting degree. The vulnerability ratio versus time of the RFM is thus defined as follows:
definitions 4. The relationship between the vulnerability rate of RFM and time is shown as the following equation, λ RFM (t) represents the vulnerability rate of RFM at time t, and represents the vulnerability rate at initial time when t =0, i.e., ZRRM RFM VRate in model RFM RFM _ VRate asserted.
Let P RFM (t)＝(P N (t)，P V (t)，P N-V (t)) represents the state probability vector of RFM at time t, where P N (t)，P V (t) and P N-V (t) indicates the probability that RFM is in Normal State, vulnerability State, and Non-Vulnerability State, respectively, at time t. From the state transition equation of CTMC, the following state probability equation for RFM can be obtained:
P RFM (t′)＝P RFM (t)*A
wherein, P RFM (t′)＝(P N (t′)，P V (t′)，P N-V (t ')) represents the state probability vector of RFM at time t ', where t ' represents the time next to time t and A represents the state transition probability matrix of RFM, which can be derived from FIG. 3 (b), as follows, the transposed matrix of A.
The state probability equations for the different functional registers are thus obtained:
solving the above equation can obtain the state probability distribution of RFM at the time t, and the reliability of RFM at the time t is as follows:
R RFM (t)＝1-P V (t)-P C (t)
2. overall system register reliability evaluation
Combining the vulnerability rates and ZRRM of all different functional registers RFM In<RFMName>The RFMRRate defined by RFM is filled in fig. 3. Because all RFM reliability as a function of time has been calculated at this time, i.e., the probability of each state transition at any time in fig. 3 is determined, and the state transition relationships in fig. 3 satisfy the markov chain property.
For the embedded register, when only most RFMs are in the non-vulnerable state, the reliability of the whole system register is high, and thus the normal state of the embedded register requires more than general RFMs to be in the non-vulnerable state. Thus, the problem of evaluating the reliability of an embedded register translates into using a Markov chain to calculate the probability that the embedded register is in a non-state.
For the two RFM systems shown in fig. 2, the transition probability matrix can be expressed as:
wherein λ GR And λ SR Has been calculated to obtain GR And mu SR In ZRRM RFM As already defined in (1).
Since the state probability distribution of a Markov chain is independent of its initial distribution, the initial distribution can be set to P ESR (t), combining the smooth distribution nature of the Markov chain, the equation shown below can be derived:
wherein, P stable For the probability distribution, P, of a Markov chain corresponding to the ESR of an embedded register system in a stationary state stable Including the probability of ESR being in each state, P ESR (t) is the initial distribution of the Markov chain for ESR, and m represents the number of transitions. It is particularly noted that t in the above equation does not simply represent time, but represents the time corresponding to the reliability of each RFM, and the transition probability of the transition matrix is based on the reliability of the RFM, which in turn is time-dependent.
In conclusion, the modeling process is processed in a grading way, is simple and clear, can be used for evaluating the reliability of the registers with different functions, and can be used for strictly analyzing and evaluating the reliability of the ZRRM model by using a model detection method.
The foregoing illustrates and describes the principles, general features, and advantages of the present invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (5)
1. A soft error-oriented register reliability modeling and evaluation method is characterized by comprising the following steps:
step 1, calculating a register vulnerability factor RVF and a register damage rate RCR of a single register in an embedded register system;
step 2, classifying the registers according to functions, and then establishing a reliability model ZRRM from the registers with different functions to all registers of the system by using a Z language based on a hierarchical modeling mode; the reliability model ZRRM is represented as a triplet:
ZRRM RFM ＝(VRate RFM ,State RFM ,STR RFM )
in the formula, VRate RFM Representing the vulnerability of different functional registers RFM; state RFM State space representing the RFM, containing all possible states of the registers; STR RFM Representing the transition relationships between all possible states of the register;
wherein, the vulnerability of the RFM is as follows:
λ RFM ＝λ RVF +λ RCR
in the formula, λ RFM Indicating vulnerability of RFM, λ RVF Indicating register fragility factor, λ RCR Representing the damage rate of the register;
the register fragility factor λ RVF Comprises the following steps:
in the formula, susceptibleTime (R) represents the time that the register R is in the sensitive interval mode, and LifeTime (R) represents the service life of the register R;
the register corruption rate λ RCR Comprises the following steps:
λ RCR ＝e ξt
in the formula, xi is a constant;
step 3, converting the ZRRM model into a continuous time Markov chain CTMC form, and establishing CTMC models for different functional registers;
step 4, calculating the instantaneous fragility of the registers with different functions according to the CTMC model of the registers, and evaluating the reliability of the registers with different functions;
step 5, based on the relation between the reliability evaluation result and the state of the single register, the reliability of the whole embedded register system is evaluated by utilizing a Continuous Time Markov Chain (CTMC); the method specifically comprises the following steps:
step 5-1, describing the state spaces of all registers of the embedded register system:
the states of all registers form the state space of the whole register system, i.e. the embedded register system, i.e. a state sequence i of all different functional registers n-1 i n-2 ...i 1 i 0 The state is one state in the whole system state space of the register, the whole system space of the register is formed by the state sequences, and n is the number of the registers; in the state sequence, i j =1 denotes the state i of register j j In a non-vulnerable state, i j =0 indicates that the state of the register j is in a fragile state or a destroyed state;
step 5-2, calculating a state transition probability matrix A of the whole embedded register system based on the relationship between the reliability evaluation result and the state of the single register;
and 5-3, obtaining the following equation according to the stable distribution property of the Markov chain, and utilizing the equation to carry out reliability evaluation on the whole embedded register system:
in the formula, P stable For the probability distribution, P, of the Markov chain corresponding to the ESR of the embedded register system in the stationary state stable Including the probability of the ESR being in each state, P ESR (t) is the initial distribution of the Markov chain for ESR, m represents the number of transitions, and t represents the time at which the reliability of each BFM corresponds.
2. The soft-error-oriented register reliability modeling and evaluation method of claim 1, wherein the CTMC in step 3 is a five-tuple:
CTMC＝(S M ,S in ,A,T M ,t)
wherein the content of the first and second substances,
(1)S M representing the state space of the CTMC, which is a set of all possible states of the register;
(2)S in ∈S M the initial state of the CTMC is represented as the state of the register before the register is not used;
(3)A＝[a ij ]is a matrix of n x n representing the state transition probability matrix of the CTMC, wherein a ij Indicating the slave state s of the register i ∈S M Transition to state s j ∈S M The probability of (d);
(4)
is the set of state transition relationships of CTMC,(s) i ,s j )∈T M Indicating that there is a branch to make the register slave state s i Change to state s j ；
(5) t represents the time.
3. The soft-error-oriented register reliability modeling and evaluation method according to claim 2, wherein the ZRRM model is transformed into a continuous time markov chain CTMC in step 3, specifically by an element mapping rule between ZRRM and CTMC, which is shown in table 1 below:
table 1 element mapping rules between ZRRM and CTMC
4. The soft-error-oriented register reliability modeling and evaluation method according to claim 3, wherein the step 4 of calculating the instantaneous fragility of the different functional registers according to the CTMC model of the registers and evaluating the reliability of the different functional registers specifically comprises:
step 4-1, defining the relationship between the RFM damage rate and time:
λ RCR (t)＝e ξt
in step 4-2, the typical state transition matrix A' of the register is:
the state probability equations for the different functional registers are thus obtained:
in the formula, P V (t) represents the probability that the RFM is in a vulnerable state at time t, P C (t) represents the probability that RFM is in a crash state at time t, P N-V (t) represents the probability that the RFM is in a non-vulnerable state at time t, λ Strengthen Indicating a transition of RFM from a vulnerable to a non-vulnerable state, λ Weaken Indicating that the RFM is transitioning from a non-vulnerable state to a vulnerable state;
step 4-3, solving the formula in the step 4-2 to obtain the state probability distribution of the RFM at the time t, and then obtaining the reliability R of the RFM at the time t RFM (t) is:
R RFM (t)＝1-P V (t)-P C (t)。
5. the soft-error-oriented register reliability modeling and evaluation method according to claim 1, wherein for an embedded register system including two BFMs, a general purpose register (GR) and a Stack Register (SR), the state transition probability matrix A is:
in the formula of lambda GR 、λ SR Denotes the vulnerability status of GR and SR, respectively GR 、μ SR Representing the non-fragile probabilities of GR and SR, respectively.
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