CN112069045A - Cloud platform software performance prediction method based on hidden Markov - Google Patents

Cloud platform software performance prediction method based on hidden Markov Download PDF

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CN112069045A
CN112069045A CN202010817863.3A CN202010817863A CN112069045A CN 112069045 A CN112069045 A CN 112069045A CN 202010817863 A CN202010817863 A CN 202010817863A CN 112069045 A CN112069045 A CN 112069045A
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张彤
王仪
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Xian University of Technology
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Abstract

The invention discloses a software performance prediction method of a cloud platform based on hidden Markov, which is implemented according to the following steps: step 1, collecting parameters influencing performance from each business module of a cloud platform to be predicted to obtain an experimental sample characteristic set, and then preprocessing the experimental sample characteristic set; step 2, determining an initial hidden Markov model lambda as (A, B, pi); step 3, giving an observation sequence, and calculating the probability of the appearance of the observation sequence under the initial hidden Markov model determined in the step 2; and 4, knowing the hidden Markov model and the observation sequence, and solving a performance prediction result sequence. The software performance prediction method of the cloud platform based on the hidden Markov solves the problem that the unitary linear regression model in the prior art cannot effectively fit the complex and changeable load condition of the cloud platform software, so that the prediction precision cannot meet the requirement.

Description

Cloud platform software performance prediction method based on hidden Markov
Technical Field
The invention belongs to the technical field of computer virtualization, and relates to a software performance prediction method of a cloud platform based on hidden Markov.
Background
In recent years, cloud platform-based services are applied to many different fields including healthcare, public transportation, mobile communication, and the like, and are gradually becoming the mainstream trend of the development of the internet industry. However, the long uninterrupted operation of the cloud platform system may cause a phenomenon called software aging. The resulting brief system downtime or instability will severely impact the normal operation of the internet enterprise.
The performance degradation occurs because the software program is very complex and may not be forever and completely error free, and even if it is tested and verified sufficiently, it is not guaranteed that the software program will run smoothly and error free for a long time. Nowadays, software program development tends to be time-oriented development, that is, software programs have time effect, and need to be designed, developed and tested in the shortest time and quickly put into the market to preempt market share, which further aggravates the occurrence of imbalance in performance consumption, and the derivative problems of reliability, availability, safety and the like of software programs are followed.
If a "state" does not depend on "future states" nor on "previous states" and only on "present states", the evolution of this state is called markov chain. Hidden Markov is a statistical model describing the hidden nature of the system, based on a Markov chain. The traditional Markov chain is not ideal for predicting a non-stationary time sequence, the model convergence is poor, and the deviation of a prediction result is large. Two typical features of a hidden markov solution scenario are: the data set is time-varying based; the problem exists in two sequences, the internal property sequence and the monitoring value sequence of the system. Hidden Markov state transition chains describe associations between state sequences and observation sequences. Hidden states of hidden Markov are uncertain, a certain objective rule exists between the hidden states and an observation state, and a hidden state sequence can be described through a certain random process. The observable state and the system internal state are not in a one-to-one correspondence relationship, but the correlation between the two can be described by a probability distribution function.
In the traditional method for predicting the performance of the cloud platform software, a unary linear regression model and an improved model are mostly adopted to predict the performance change trend of the cloud platform software. The unary linear regression model is an analysis model with high practicability, but has the defect that the complex and variable load condition of cloud platform software cannot be effectively fitted due to an oversimplified form, so that the prediction precision cannot meet the requirement.
Disclosure of Invention
The invention aims to provide a hidden Markov-based cloud platform software performance prediction method, which solves the problem that the prediction precision cannot meet the requirement due to the fact that a unary linear regression model in the prior art cannot effectively fit the complex and changeable load condition of cloud platform software.
The technical scheme adopted by the invention is that the software performance prediction method of the cloud platform based on the hidden Markov is implemented according to the following steps:
step 1, collecting parameters influencing performance from each business module of a cloud platform to be predicted to obtain an experimental sample characteristic set, and then preprocessing the experimental sample characteristic set;
step 2, determining an initial hidden Markov model lambda as (A, B, pi);
step 3, giving an observation sequence, and calculating the probability of the appearance of the observation sequence under the initial hidden Markov model determined in the step 2;
and 4, knowing the hidden Markov model and the observation sequence, and solving a performance prediction result sequence.
The present invention is also characterized in that,
and 4, evaluating the performance prediction result sequence in the step 4 by adopting an average percentage error method.
The pretreatment in the step 1 specifically comprises the following steps: and carrying out normalization processing on all parameters in the experimental sample feature set to generate a data sequence with the length of N.
The step 2 specifically comprises the following steps:
step 2.1, defining the data sequence obtained in the step 1 as N hidden states of the model, wherein the hidden state at the time t is represented as qt, and then qt belongs to the [ S ]1,…,SN]，S1-SNRepresenting N hidden states;
step 2.2, determine the observation sequence O ═ (O)1,O2,...,OT)，OTThe state of the model at the time T is represented as Ot，t∈T；
Step 2.3, determining the state of the hidden Markov modelProbability distribution matrix a, a ═ aij}，1≤i，j≤N，aijRepresenting the probability from the ith state to the jth state, then at any time t, there is formula (1):
aij＝P[qt+1＝Sj|qt＝Si]，1≤N，j≤N (1)；
namely: a isijAt a time equal to t +1, the hidden state is SjThe probability of (d);
step 2.4, determining an observation probability distribution matrix B of the hidden Markov model, wherein B is ═ Bj(O)}，1≤j≤N，bj(O) represents the random observed output probability for state j, as in equation (2):
bj(O)＝P(Ot|qt＝Sj)，1≤j≤N (2)；
step 2.5, determining the probability distribution of the initial state as pi1＝P(q1＝S1)，1≤i≤N，π1Representing the initial hidden state q1The observation probability of the location;
step 2.6, according to the initial state probability distribution, the state transition probability distribution and the observation probability distribution determined in the steps 2.3-2.5, simplifying the hidden Markov model into a triple: λ ═ (pi, a, B).
The step 3 specifically comprises the following steps: the known observation sequence O ═ O (O)1,o2，...，oT) And (pi, a, B) the model λ determined in step 2, calculating the probability P [ O | λ ] of occurrence of the observation sequence]：
Figure BDA0002633379900000031
Wherein alpha isT(i) Is a forward factor.
Forward factor alphaT(i) Specifically, the calculation is performed as follows:
step 3.1, initialization, as formula (4):
a1(i)＝πi，bi(O1),1≤i≤N (4)；
πirepresenting a hidden state qiProbability of observation, bi＝(O1) Indicating that the current observation state O occurred at state i1The probability of (d);
step 3.2, the observation sequence (O) of the first t moments under the condition of the given model parameter lambda1,O2,...,Ot) The hidden state at the time t is qt＝SiProbability of (1), thent(i) As in equation (5):
αt(i)＝p(O1,O2...Ot,qt＝si|λ)，1≤t≤T (5)；
step 3.3, carrying out recursive calculation, calling a recursive formula of the forward probability, wherein the recursive formula is shown in (6):
Figure BDA0002633379900000041
step 3.4, progressively recurrently obtaining alphaT(i)。
Step 4 for a given observation sequence O ═ O (O)1,O2,...,OT) And model λ ═ (pi, a, B), the sequence of performance predictors
Figure BDA0002633379900000042
The preparation method comprises the following steps:
step 4.1, initialization, noting psi (i) as the status flag value,t(i) the probability of occurrence of the state sequence, when t is 1, and the state flag value are as shown in equations (7) and (8):
1＝πibi(O1),1＜i＜N (7)
ψ1(i)＝0,1＜i＜N (8)；
step 4.3, performing recursive operation, calling a recursion formula of the dimension bit algorithm, solving the probability of the state sequence at the time T in a recursion mode, wherein the recursion formula is shown as (9) and (10):
Figure BDA0002633379900000043
Figure BDA0002633379900000044
and 4.4, terminating: and (3) iteratively updating the probability of the calculated path, finding the path with the maximum probability as the path of the optimal state sequence, and stopping the recursion, wherein the conditional formula is shown in (11) and (12):
the recursion termination condition of equation (11) is: calculating maximum time TT(i) I.e. representing the probability of occurrence of the best state sequence, by P*Represents; the recursion termination condition of equation (12) is: is calculated at P*End point of sequence of best state under probability, using
Figure BDA0002633379900000051
Represents:
Figure BDA0002633379900000052
Figure BDA0002633379900000053
step 4.5, from
Figure BDA0002633379900000054
And (4) the end point starts to trace back the paths of T-1, T-2, 1 to obtain the optimal state sequence and record the optimal state sequence as
Figure BDA0002633379900000055
As shown in equation (13), the sequence is expressed such that P [ Q | λ [ ]]Maximum determined performance prediction sequence:
Figure BDA0002633379900000056
then: obtaining a performance prediction result sequence
Figure BDA0002633379900000057
The absolute average percentage error formula is as follows (14):
Figure BDA0002633379900000058
wherein, yiFor the actual data sequence obtained in step 1,
Figure BDA0002633379900000059
and 4, the smaller the error value of the performance prediction result sequence obtained in the step 4 is, the more accurate the prediction is.
The invention has the beneficial effects that:
the method for predicting the software performance of the cloud platform based on the hidden Markov model breaks through the inherent idea of performance analysis of the original cloud platform software, explains the prediction principle by applying the forward and backward algorithm and the Vibert algorithm in the hidden Markov model, calculates the error of the prediction result, has good prediction effect, and achieves the purposes of solving the problem of hysteresis of the cloud platform software performance analysis and improving the high availability and reliability of the system.
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FIG. 1 is a flow chart of a software performance prediction method of a hidden Markov based cloud platform of the present invention;
FIG. 2 is a graph of the absolute average percentage error of the software performance prediction method of the cloud platform based on hidden Markov.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
The invention relates to a software performance prediction method of a cloud platform based on hidden Markov, the flow of which is shown in figure 1 and is specifically implemented according to the following steps:
step 1, collecting parameters influencing performance from each service module of a cloud platform to be predicted to obtain an experiment sample characteristic set, and then preprocessing, specifically: all parameters in the experimental sample feature set are subjected to normalization processing to generate a data sequence with the length of N;
step 2, determining an initial hidden Markov model lambda as (A, B, pi); the method specifically comprises the following steps:
step 2.1, defining the data sequence obtained in the step 1 as N hidden states of the model, wherein the hidden state at the time t is represented as qt, and then qt belongs to the [ S ]1,…,SN]，S1-SNRepresenting N hidden states;
step 2.2, determine the observation sequence O ═ (O)1,O2,...,OT)，OTThe state of the model at the time T is represented as Ot，t∈T；
Step 2.3, determining a hidden Markov model state probability distribution matrix A, A ═ aij}，1≤i，j≤N，aijRepresenting the probability from the ith state to the jth state, then at any time t, there is formula (1):
aij＝P[qt+1＝Sj|qt＝Si]，1≤N，j≤N (1)；
namely: a isijAt a time equal to t +1, the hidden state is SjThe probability of (d);
step 2.4, determining an observation probability distribution matrix B of the hidden Markov model, wherein B is ═ Bj(O)}，1≤j≤N，bj(O) represents the random observed output probability for state j, as in equation (2):
bj(O)＝P(ot|qt＝Sj)，1≤j≤N (2)；
step 2.5, determining the probability distribution of the initial state as pi1＝P(q1＝S1)，1≤i≤N，π1Representing the initial hidden state q1The observation probability of the location;
step 2.6, according to the initial state probability distribution, the state transition probability distribution and the observation probability distribution determined in the steps 2.3-2.5, simplifying the hidden Markov model into a triple: λ ═ (pi, a, B);
step 3, given the observation sequence, calculating the initial hidden Markov model determined in step 2The probability of occurrence of the observation sequence of (a); the method specifically comprises the following steps: the known observation sequence O ═ O (O)1,o2，...，oT) And (pi, a, B) the model λ determined in step 2, calculating the probability P [ O | λ ] of occurrence of the observation sequence]：
Figure BDA0002633379900000071
Wherein alpha isT(i) Is a forward factor;
wherein, the forward factor α t (i) is specifically calculated according to the following method:
step 3.1, initialization, as formula (4):
a1(i)＝πi，bi(O1),1≤i≤N (4)；
πirepresenting a hidden state qiProbability of observation, bi＝(O1) Indicating that the current observation state O occurred at state i1The probability of (d);
step 3.2, the observation sequence (O) of the first t moments under the condition of the given model parameter lambda1,O2,...,Ot) The hidden state at the time t is qt＝SiProbability of (1), thent(i) As in equation (5):
αt(i)＝p(O1,O2...Ot,qt＝si|λ)，1≤t≤T (5)；
step 3.3, carrying out recursive calculation, calling a recursive formula of the forward probability, wherein the recursive formula is shown in (6):
Figure BDA0002633379900000072
step 3.4, progressively recurrently obtaining alphaT(i)。
Step 4, knowing the hidden Markov model and the observation sequence, calculating a performance prediction result sequence, and obtaining a given observation sequence O ═ (O)1,O2,...,OT) And model λ ═ (pi, a, B), the sequence of performance predictors
Figure BDA0002633379900000081
The invention uses the dimension bit algorithm for solving, the dimension bit algorithm is also a dynamic programming method, is used for finding the optimal state sequence
Figure BDA0002633379900000082
The sequence is expressed such that P [ Q | λ]The maximum determined state sequence is obtained according to the following steps:
step 4.1, initialization, noting psi (i) as the status flag value,t(i) the probability of occurrence of the state sequence, when t is 1, and the state flag value are as shown in equations (7) and (8):
1＝πibi(O1),1＜i＜N (7)
ψ1(i)＝0,1＜i＜N (8)；
step 4.3, performing recursive operation, calling a recursion formula of the dimension bit algorithm, solving the probability of the state sequence at the time T in a recursion mode, wherein the recursion formula is shown as (9) and (10):
Figure BDA0002633379900000083
Figure BDA0002633379900000084
step 4.3, performing recursive operation, calling a recursion formula of the dimension bit algorithm, solving the probability of the state sequence at the time T in a recursion mode, wherein the recursion formula is shown as (9) and (10):
Figure BDA0002633379900000085
Figure BDA0002633379900000086
and 4.4, terminating: and (3) iteratively updating the probability of the calculated path, finding the path with the maximum probability as the path of the optimal state sequence, and stopping the recursion, wherein the conditional formula is shown in (11) and (12):
the recursion termination condition of equation (11) is: calculating maximum time TT(i) I.e. representing the probability of occurrence of the best state sequence, by P*Represents; the recursion termination condition of equation (12) is: is calculated at P*End point of sequence of best state under probability, using
Figure BDA0002633379900000087
Represents:
Figure BDA0002633379900000088
Figure BDA0002633379900000091
step 4.5, from
Figure BDA0002633379900000092
And (4) the end point starts to trace back the paths of T-1, T-2, 1 to obtain the optimal state sequence and record the optimal state sequence as
Figure BDA0002633379900000093
As shown in equation (13), the sequence is expressed such that P [ Q | λ [ ]]Maximum determined performance prediction sequence:
Figure BDA0002633379900000094
then: obtaining a performance prediction result sequence
Figure BDA0002633379900000095
And (3) evaluating the performance prediction result sequence in the step (4) by adopting an average percentage error method, wherein the absolute average percentage error formula is as follows (14):
Figure BDA0002633379900000096
wherein, yiFor the actual data sequence obtained in step 1,
Figure BDA0002633379900000097
and 4, the smaller the error value of the performance prediction result sequence obtained in the step 4 is, the more accurate the prediction is.
The prediction aims at predicting the state of an object at a future moment, and in order to evaluate and measure the degree of deviation of a prediction result from an actual value, a reasonable index needs to be selected to evaluate the accuracy of the prediction result, wherein the accuracy refers to the fitting degree of the prediction value and the actual value, the error is directly reflected by the accuracy, and the smaller the error is, the higher the accuracy is. The average percentage error MAPE considers not only the error between the predicted value and the actual value, but also the comparison between the difference and the actual value, and from the average percentage error MAPE, as shown in fig. 2, it can be seen that all the calculated values are small in floating on the zero point, the prediction effect is very excellent, and the hidden markov prediction is very suitable for a computer system which depends on history, random nonlinearity and single-dimensional continuous change of various parameters.
The method carries out prediction through the hidden Markov model, the 'hidden' of the hidden Markov prediction is reflected in that all states are not visible, the most possible state sequence can be predicted according to the known observation sequence and the hidden Markov model, and the accurate prediction of the cloud platform software performance can be realized as long as the hidden Markov model of each state is accurately trained.

Claims (8)

1. The software performance prediction method of the cloud platform based on the hidden Markov is characterized by comprising the following steps:
step 1, collecting parameters influencing performance from each business module of a cloud platform to be predicted to obtain an experimental sample characteristic set, and then preprocessing the experimental sample characteristic set;
step 2, determining an initial hidden Markov model lambda as (A, B, pi);
step 3, giving an observation sequence, and calculating the probability of the appearance of the observation sequence under the initial hidden Markov model determined in the step 2;
and 4, knowing the hidden Markov model and the observation sequence, and solving a performance prediction result sequence.
2. The software performance prediction method of the cloud platform based on the hidden Markov is characterized in that the performance prediction result sequence in the step 4 is evaluated by adopting an average percentage error method.
3. The hidden markov based cloud platform software performance prediction method of claim 1, wherein the preprocessing in step 1 is specifically: and carrying out normalization processing on all parameters in the experimental sample feature set to generate a data sequence with the length of N.
4. The hidden markov based cloud platform software performance prediction method of claim 3, wherein the step 2 is specifically:
step 2.1, defining the data sequence obtained in the step 1 as N hidden states of the model, wherein the hidden state at the time t is represented as qt, and then qt belongs to the [ S ]1,…,SN]，S1-SNRepresenting N hidden states;
step 2.2, determine the observation sequence O ═ (O)1,O2,...,OT)，OTThe state of the model at the time T is represented as Ot，t∈T；
Step 2.3, determining a hidden Markov model state probability distribution matrix A, A ═ aij}，1≤i，j≤N，aijRepresenting the probability from the ith state to the jth state, then at any time t, there is formula (1):
aij＝P[qt+1＝Sj|qt＝Si]，1≤N，j≤N (1)；
namely: a isijEqual to the time at t +1Hidden state is SjThe probability of (d);
step 2.4, determining an observation probability distribution matrix B of the hidden Markov model, wherein B is ═ Bj(O)}，1≤j≤N，bj(O) represents the random observed output probability for state j, as in equation (2):
bj(O)＝P(Ot|qt＝Sj)，1≤j≤N (2)；
step 2.5, determining the probability distribution of the initial state as pi1＝P(q1＝S1)，1≤i≤N，π1Representing the initial hidden state q1The observation probability of the location;
step 2.6, according to the initial state probability distribution, the state transition probability distribution and the observation probability distribution determined in the steps 2.3-2.5, simplifying the hidden Markov model into a triple: λ ═ (pi, a, B).
5. The hidden markov based cloud platform software performance prediction method of claim 4, wherein the step 3 is specifically: the known observation sequence O ═ O (O)1,o2，...，oT) And (pi, a, B) the model λ determined in step 2, calculating the probability P [ O | λ ] of occurrence of the observation sequence]：
Figure FDA0002633379890000021
Wherein alpha isT(i) Is a forward factor.
6. The hidden Markov-based cloud platform software performance prediction method of claim 5, wherein the forward factor α isT(i) Specifically, the calculation is performed as follows:
step 3.1, initialization, as formula (4):
a1(i)＝πi，bi(O1),1≤i≤N (4)；
πirepresenting a hidden state qiProbability of observation, bi＝(O1) Indicating that the current observation state O occurred at state i1The probability of (d);
step 3.2, the observation sequence (O) of the first t moments under the condition of the given model parameter lambda1,O2,...,Ot) The hidden state at the time t is qt＝SiProbability of (1), thent(i) As in equation (5):
αt(i)＝p(O1,O2...Ot,qt＝si|λ)，1≤t≤T (5)；
step 3.3, carrying out recursive calculation, calling a recursive formula of the forward probability, wherein the recursive formula is shown in (6):
Figure FDA0002633379890000031
step 3.4, progressively recurrently obtaining alphaT(i)。
7. The hidden markov based cloud platform software performance prediction method of claim 5, wherein said step 4 is performed for a given observation sequence O ═ (O)1,O2,...,OT) And model λ ═ (pi, a, B), the sequence of performance predictors
Figure FDA0002633379890000032
The preparation method comprises the following steps:
step 4.1, initialization, noting psi (i) as the status flag value,t(i) the probability of occurrence of the state sequence, when t is 1, and the state flag value are as shown in equations (7) and (8):
1＝πibi(O1),1＜i＜N (7)
ψ1(i)＝0,1＜i＜N (8)；
step 4.3, performing recursive operation, calling a recursion formula of the dimension bit algorithm, solving the probability of the state sequence at the time T in a recursion mode, wherein the recursion formula is shown as (9) and (10):
Figure FDA0002633379890000033
Figure FDA0002633379890000034
and 4.4, terminating: and (3) iteratively updating the probability of the calculated path, finding the path with the maximum probability as the path of the optimal state sequence, and stopping the recursion, wherein the conditional formula is shown in (11) and (12):
Figure FDA0002633379890000035
Figure FDA0002633379890000036
the recursion termination condition of equation (11) is: calculating maximum time TT(i) I.e. representing the probability of occurrence of the best state sequence, by P*Represents; the recursion termination condition of equation (12) is: is calculated at P*End point of sequence of best state under probability, using
Figure FDA0002633379890000037
Represents:
step 4.5, ending, backtracking path to obtain the best state sequence
Figure FDA0002633379890000038
As shown in equation (13), the sequence is expressed such that P [ Q | λ [ ]]Maximum determined performance prediction:
Figure FDA0002633379890000041
then: the performance prediction result sequence is
Figure FDA0002633379890000042
8. The hidden markov based cloud platform software performance prediction method of claim 2, wherein the absolute mean percentage error formula is as follows (14):
Figure FDA0002633379890000043
wherein, yiFor the actual data sequence obtained in step 1,
Figure FDA0002633379890000044
and 4, the smaller the error value of the performance prediction result sequence obtained in the step 4 is, the more accurate the prediction is.
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CN112949742A (en) * 2021-03-22 2021-06-11 烽火通信科技股份有限公司 Method and electronic device for enhancing constellation data by using hidden Markov model
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