Genetic Algorithm Based Fault Diagnosis and Repair Strategy in Computer Hardware System

In today’s information society, the rapid development of computer technology has made computer hardware an indispensable part of people’s daily life. However, just like any other mechanical equipment, computer hardware can also fail [1–4]. When computer hardware failure occurs, we need to carry out accurate fault diagnosis, and take corresponding repair measures. Fault diagnosis is a key technology, which plays an important role in various fields [5–8]. However, traditional fault diagnosis methods are often limited by the limitations of expert knowledge and cannot deal with complex fault situations. In recent years, genetic algorithms, as an emerging optimization method, have been gradually introduced into the field of fault diagnosis and have made significant research progress [9–12].

Genetic algorithm is a mathematical model that simulates the laws of biological evolution in nature, simulates the process of “gene” inheritance, mutation, and selection in the process of biological evolution, and solves a series of problems by expressing “gene” sequences as a set of numerical values, and gradually generating better “gene” sequences through random evolution and natural selection [13–16]. In the field of fault diagnosis, the fault diagnosis system based on genetic algorithm monitors the working state of the equipment, uses the data collected by the sensor as the diagnostic object, constructs the fault diagnosis model, and optimizes it through genetic algorithm to find the optimal solution so as to realize the fault diagnosis [17–20].

The study firstly proposes a method for computer hardware system fault feature extraction, i.e., using wavelet packet transform for model computer hardware system fault feature extraction. Then the genetic algorithm model and its algorithm implementation are discussed and utilized to improve the BP neural network operation efficiency and achieve the improvement of the function of the whole fault diagnosis system. Specifically, for the problem that the BP neural network is easy to fall into local minima in some regions, the initial of the weights and thresholds of the BP network are optimized with the help of the genetic algorithm. Finally, a model for diagnosing faults in computer hardware systems has been designed. In order to verify the feasibility and scientificity of the model proposed in this paper in computer hardware system fault diagnosis, the article concludes with simulation experiments and parametric experiments using the GA-BP neural network fault diagnosis model proposed in this paper.

2

Method

2.1

Wavelet Packet Based Fault Feature Extraction Method for Analog Computer Hardware Systems

According to the wavelet transform theory, it is known that the wavelet transform has poor frequency resolution in the high frequency band. The emergence of wavelet packets overcomes this shortcoming of the wavelet transform, and it is a signal processing method that can provide a more refined analysis of the signal. Wavelet packets are capable of further decomposing the high-frequency portion that is not subdivided by the multiresolution analysis, which allows for improved frequency resolution in the high-frequency band. Theoretically, for non-stationary signals such as computer hardware system failure signals, it would be more advantageous to use wavelet packets to analyze them.

2.1.1

Wavelet packet transform

The three-layer wavelet packet decomposition is shown in Figure 1. The wavelet packet technique clarifies the connection between multiresolution approximation and wavelets. In analog computer hardware system troubleshooting, the faulty signal is analyzed using wavelet packets in a process that can be viewed as filtering the signal using a set of high-pass and low-pass filters [21].

The wavelet packet decomposition process is illustrated by performing a three-layer wavelet packet decomposition of the signal, S0 denotes the original sample signal, which is decomposed by one layer of wavelet packet decomposition to obtain the low-frequency component L1 and the high-frequency component L2. Then by further decomposition of the low-frequency components and high-frequency components, the low-frequency components and high-frequency components on the next scale function can be obtained, and so on, the low-frequency components and high-frequency components can be obtained after the decomposition of the wavelet packet with N layers. Let the orthogonal wavelet function be φ(t) and the orthogonal scale functions be ϕ(t),φ(t) and ϕ(t) they satisfy the two-scale equation: 1 ${\begin{array}{l} ϕ (t) = \sqrt{2} \sum_{k \in Z} h (k) ϕ (2 t - k) \\ φ (t) = \sqrt{2} \sum_{k \in Z} g (k) φ (2 t - k) \end{array}$

Where: h(k) is the low-pass filter coefficient and g(k) is the high-pass filter coefficient. The next generalization of the two-scale equation defines the following recurrence relation: 2 $μ_{2 n} (t) = \sqrt{2} \sum_{k \in Z} h (k) μ_{n} (2 t - k)$ 3 $μ_{2 n + 1} (t) = \sqrt{2} \sum_{k \in Z} g (k) μ_{n} (2 t - k)$

From the above equation it is clear that when n = 0, μ₀(t) = ϕ(t),μ₁(t) = φ(t). The set of functions {μ_n(t)}, n = 0,1,2,… determined by Eq. is the wavelet packet determined by μ₀(t) = ϕ(t). It can be seen that the set of functions, wavelet packet {μ_n (t)}, n = 0,1,2,‥, includes the scale function ϕ(t) and the wavelet function φ(t), i.e., when n = 0, by Eq. and that they are somehow related.

Where the wavelet packet coefficients recursive formula is: 4 $d_{j + 1}^{2 n} = \sum_{k} h (k - 2 t) d_{j}^{n} (k)$ 5 $d_{j + 1}^{2 n + 1} = \sum_{k} g (k - 2 t) d_{j}^{n} (k)$

The reconstruction formula for wavelet packets is: 6 $d_{j}^{n} (k) = 2 [\sum_{τ} h (k - 2 τ) d_{j + 1}^{2 n + 1} (k) + \sum_{τ} g (k - 2 τ) d_{j + 1}^{2 n} (k)]$ $d_{j}^{n} (k)$ is the krd coefficient in node ( j, n) after wavelet packet decomposition, and node ( j, n) denotes the nth band in layer j after wavelet packet decomposition.

Function family {μ_n (t)}n = 0,1,2,… is the wavelet packet library derived from orthogonal scale function ϕ(t). The wavelet packet library contains many canonical orthogonal bases that become wavelet packet bases, and it can be seen from the formula that by selecting different mother wavelet functions, the wavelet coefficients of each frequency band obtained after wavelet packet decomposition of the signal will be different.

According to the wavelet packet theory, the use of wavelet packet analysis of the signal should first choose the appropriate wavelet filter, set the depth of wavelet packet decomposition for n, n layers of wavelet packet decomposition of the signal, the extraction of wavelet packet coefficients of the nth layer of each band, and finally reconstruct the wavelet packet coefficients. The signal’s wavelet packet analysis process is depicted in Figure 2.

2.1.2

Wavelet Packet Based Fault Feature Extraction Method for Analog Computer Hardware Systems

When the wavelet packet decomposition of the signal, the energy of the signal is preserved in the form of wavelet packet coefficients. When the computer hardware system fails, the energy of the output signal will change accordingly, using wavelet packet decomposition of the signal, the change of the signal energy is manifested in the wavelet coefficients of the wavelet packet of each frequency band wavelet coefficients change. Wavelet packet energy changes in the frequency bands can reflect the band coefficients have changed. Therefore, the wavelet packet energy in the frequency bands contains a large amount of feature information. When the simulation of computer hardware system failure, wavelet packet of a certain frequency band or several frequency band energy value will change, these changes indicate that the computer hardware system may be some components have failed [22]. The use of wavelet packet decomposition for simulated computer hardware system fault feature extraction does not require knowledge of the model structure of the simulated computer hardware system, as can be seen from the analysis. The fault state of the circuit can be characterized in terms of the energy change of each frequency band of the wavelet packet.

From the above, it can be seen that wavelet packets for fault feature extraction can be used to characterize the changes in the failure modes of the analog computer hardware system in terms of the changes in the energy of each frequency band. Wavelet packet for fault feature extraction can be divided into the following steps: 1)

Apply the excitation voltage to the analog computer hardware system, select the acquisition node, and acquire the signal f(t), which is denoised.

2)

Select the mother wavelet function and set the number of wavelet packet decomposition layers to j layers.

3)

Use wavelet packet to decompose the signal in j layers to get a wavelet packet decomposition structure with a full binary tree depth of j. Extract the decomposition coefficients of each frequency band of the jth layer, and the decomposition coefficients of each band are divided into a group, and there are 2^j groups in total, and you can express the decomposition coefficients of each frequency band of the jth layer as ${W_{j}^{0}, W_{j}^{1}, W_{j}^{2}, ..., W_{j}^{i}}$ where, i = 0,1,2,…,2^j – 1.

4)

Reconstruct the decomposition coefficients of each frequency band of the j th layer, and denote the reconstructed signal of $W_{j}^{i}$ by S_ij, then the signal S can be expressed as: 7 $S = \sum_{i = 0}^{2^{j} - 1} S_{j i}$

Calculate the total energy E_ji of the reconstructed signal S_ji : 8 $E_{j i} = \int | s_{j i} (t) |^{2} d t = \sum_{k = 1}^{n} | X_{i k} |^{2}$ where X_ik (k = 1,2,…,n) is the amplitude of the discrete points of the reconstructed signal S_ji, because the reconstructed signal S_ji is a discrete signal.

5)

Construct the eigenvector, taking the energy of each frequency band of layer j as a 2^j - dimensional eigenvector, the eigenvector can be expressed as: 9 $T = [E_{j 0}, E_{j 1}, E_{j 2}, ..., E_{j (2^{j} - 1)}]$

6)

Normalization. Normalization of the eigenvectors obtained in step (5) can avoid the calculation error caused by the fact that each eigenvalue is not of an order of magnitude due to an eigenvalue being too large. Let the total signal energy be E : 10 $E = \sqrt{\sum_{k = 0}^{2^{j} - 1} | E_{j k} |^{2}}$ 11 $T' = [E_{j 0} / E, E_{j 1} / E, E_{j 2} / E, \dots, E_{j (2^{j} - 1)} / E]$

Where: T' is the normalized fault feature vector.

2.2

Genetic Algorithms and BP Neural Networks

2.2.1

Genetic algorithm models

Genetic Algorithm Modeling Discussion. First set up a hypothetical environment for the model, i.e., genetic modeling in a particular environment. Suppose there is an existing gene x_i (i = 1,2,⋯,n) and all the characteristics of this gene form a sequence string, let as X = x₁ x₂…x₃ [23]. Suppose the gene evolves t = 1.2.⋯.T times in the specified environment. Then the set of solutions formed by all possible values of this gene is: 12 $A = x_{1} \times x_{2} \times \dots \times x_{n} = \prod_{n = 1}^{n} x$

After evolution, a new population is created. Based on the above hypothetical environment, the tnd evolved population in any B(t) environment is A(t). A new population A(t+1) evolves through adaptations C(t) and d_i. 13 $A (t + 1) = d, (A (t), C (t))$

The environment used in the above evolutionary model is a specific environment, and in order to reflect the variable complexity of the environment, the pre-evolutionary relationship of the population to the environment can be described as E_ji(t) = 〈C(1),C(2),⋯,C(t–1)〉. Therefore, the new population evolutionary model is: 14 $A (t + 1) = d_{t} (A (t), C (t), E_{B} (t))$

Ditto for population evolution in relation to the corresponding environment under the combined effect of fitness C(t) and genetic mechanism d_i: 15 $E_{B} (t + 1) = d_{t} (E_{B} (t), C (t))$

In practice, genetic algorithms obtain evolved new populations by discrete computation. For the sample space X =[x₁,x₂,⋯,x_i,⋯,x_n], n =|X| of the population, the evolution of the population sample is analyzed using the probabilistic viewpoint when A(t) = x_j (j =1,2,⋯,n), the probability of the evolved population A(t + 1) = {x_q | q = 1,2,⋯,n} is: 16 $P (t) = {p_{i, q} (t) | \sum_{q = 1}^{n} p_{i, q} (t) = 1}$

With the help of probabilistic view one can optimize the genetic model as: 17 $P (t + 1) = d, (A (t), C (t), E_{B} (t))$

The model’s description of fitness, i.e., the degree to which a population A(t) corresponding to a dynamically changing environment B(t) is adapted to that environment. It is modeled as: 18 $μ_{B} (A (t)) = μ_{B, l} (A (t), B (t))$

In the above model, the relationship between the environment and the fitness of the population is represented. To show that the environment is not a single fixed environment, μ_R,l is used for the record. Regardless of any change in the environment or the population, the fitness will change dynamically, thus optimizing the population evolution: 19 $μ_{B, I + 1} = d_{t} (μ_{B J}, A (t), C (t))$

After t number of evolutions, the adaptive capacity C(t) of a population to its environment can be expressed as: 20 $C (t) = μ_{B, t} (A (t))$

Adaptation is not the only measure when A(t) and B(t) changes are made; selection and genetic mechanisms d_i are also important influences. As such, all need to be adjusted in the event of change. Adjustment to change in C(t) was discussed above for the analysis of adjustment to selection and genetic mechanisms d_i, which also requires an analysis of the past and present state of the population. It may be useful to introduce parameter E_ij(t) as a relationship between previous environmental and population interactions. Alternatively, updating the use of E_d (t) = 〈d(1),d(2).⋯,d(t–1),d(t)〉 to represent selection and genetic mechanisms, the model would be: 21 $d (t + 1) = g (A (t), C (t), E_{B} (t), E_{d} (t))$

Thus the entire process is a summation of each adaptive adjustment of the population: 22 $F (T) = \sum_{t = 1}^{T} μ_{B, t}$

The overall fitness of the population is: 23 $F (T, E_{d_{1}} (T)) = \sum_{i = 1}^{T} μ_{B, i} (d_{1} (t))$

In summary, after the detailed analysis of the population’s single adaptation to the changing adjustment of the environment and the overall adaptation adjustment throughout the evolutionary stage, the model about the evolutionary adaptation of the population is: 24 ${\begin{matrix} A (t + 1) = d_{t} (A (t), C (t), E_{t} (t)) \\ E_{B} (t + 1) = d_{t} (E_{B} (t), C (t)) \\ μ_{B} (A (t)) = μ_{B, t} (A (t), B (t)) \\ C (t) = μ_{B, t} (A (t)) \\ μ_{B, t + 1} = d_{t} (μ_{B, t}, A (t), C (t)) \\ d (t + 1) = g (A (t), C (t), E_{B} (t), E_{d} (t)) \\ F (T) = \sum_{t = 1}^{T} μ_{B, t} \end{matrix}$

The explanation of the parameters and notation in Eq. will not be repeated, as they are all described earlier.

2.2.2

Genetic Algorithm Implementation

1)

Coding scheme

Biological inheritance relies on gene realization. And the genetic algorithm, as a bionic technology, cannot directly recognize individual characteristic information by itself. This is similar to the computer not directlyrecognizing Chinese characters, English letters, and so on. We need to convert all the information into binary code for computer recognition through the conversion mechanism. Similarly, in order for the genetic algorithm to recognize the samples to be input, the coding scheme needs to be developed beforehand. The coding scheme is formulated based on a detailed analysis of the actual problem to simplify operations and improve efficiency.

2)

Population size

In the genetic algorithm, it is necessary to choose the appropriate population size for the actual problem. Usually, there is a certain misunderstanding of the population size, that is, a larger population size is conducive to achieving full training of the network and obtaining better genetic optimization results. In fact, large-scale population participation in network training will lead to a greater cost of the system, resulting in a decline in efficiency. However, if we are conservative and choose a smaller population size, from the actual effect of the algorithm sample selection, the population performance will be very homogeneous, and may not be able to complete the optimal convergence for network training. In general, the population size needs to be targeted to make a choice, will not repeat here, you can refer to the population size selection related research.

3)

Initial population

After selecting the appropriate population size, it is necessary to determine the initial population. Similar to the input samples of BP neural network, as well as the input of the genetic algorithm, two aspects need to be noted when making the selection. Therefore, it is necessary to ensure its rich characteristics. And the distribution of individuals in the population can exactly make up for its lack of homogeneous traits, even if the population is dispersed throughout the search space. Experiments have shown that the search cost of the genetic algorithm will increase a lot if that distribution situation is satisfied. Therefore, the practice of utilizing time for space is not suitable for operation. In this paper, we utilize the golden section method to find the initial population, so that the initial population is more convenient for the execution of the algorithm.

4)

Degree of adaptation

According to the bionic principle, fitness is used to measure the ability of an individual in an algorithm to adapt. In the biological world, the organisms that are able to better fit into the environment in which they live have survived. Similarly, in genetic algorithms, the same is true for individuals in a population. In the process of biological evolution, history has shown that all evolution follows the rule that organisms evolve towards an environment to which they are better adapted. By analogy to genetic algorithms, a population that simulates biological evolution will also converge towards an objective function based on the actual laws of biological evolution. Let the fitness function be F(X), and in order to find the mapping relationship with its existence, let the objective function be f(X). Construct the following model.

Then the relationship between the two is: 25 $F (X) = {\begin{matrix} f (X) + C_{\min}, & f (X) + C_{\min} > 0 \\ 0, & f (X) + C_{\min} \leq 0 \end{matrix}$ where: C_min is a suitably relatively small number.

5)

Crossover operator

The crossover operator is what enables the genetic algorithm to continuously produce new individuals. The initial population just acts as an ancestor and according to the algorithm, the evolution continues and the new individuals generated according to the crossover operator will keep on joining the new population and participating in the calculation. In organisms, reproduction of the next generation is based on the corresponding genetic laws such as genetic inheritance. Therefore, individuals that combine with each other according to the agreed rules exchange genes with each other to realize inheritance and produce two new individuals. The new individuals continue to participate in the population computation, and in this way, the population is continuously updated until it converges to an optimal solution.

The specific steps for implementing this crossover operator to simulate biological reproduction of offspring are as follows:

(1)

Let, the number of individuals to be crossed be c = [P × p_c].

(2)

Let {p₁, p₂,⋯,p_c}∈[1,P–1], any c singular numbers be chosen from {p₁, p₂,⋯,p_c}, and similarly any c integers be chosen from {n₁,n₂,⋯,n_c}∈[1,n] in turn.

(3)

Let individuals X_p1 and X_p1+1 be selected as paired individuals. They perform an exchange operation on component n₁. 26 $F a t h e r_1 : X_{p 1} = (x_{n_{i} 1}, \dots, x_{n_{i} n_{i}}, \dots, x_{n_{i} n})$ 27 $F a t h e r_2 : X_{p_{1} + 1} = (x_{p_{1} + 1, 1}, \dots, x_{p_{1} + 1, n_{1}}, \dots, x_{p_{1} + 1, n})$

Two paired individuals exchange only some of their genes, and below find the new gene at the point of exchange: 28 ${\begin{matrix} x_{p_{1} n_{1}}^{'} = β * x_{p_{1} + 1. n_{1}} + (1 - β) * x_{p_{1} n_{1}} \\ x_{p_{1} + 1, n_{1}}^{'} = β * x_{p_{1} n_{1}} + (1 - β) * x_{p_{1} + 1, n_{1}} \end{matrix}, β \in [0, 1]$

(4)

Two new individuals are obtained after gene replacement: 29 $S o n_{1} : X_{p_{1} 1}^{'} = (x_{p_{1} 1}, \dots, x_{p_{1} n_{1}}^{^{'}}, \dots, x_{p_{1} n})$ 30 $S o n_{2} : X_{p_{1} + 1}^{'} = (x_{p_{1} + 1, 1}, \dots, x_{p_{1} + 1, p_{1}}^{^{'}}, \dots, x_{p_{1} + 1, n})$

6)

Mutation operator

In the biological world, mutations in the genes of organisms due to sudden changes in the environment around the organisms. Mutations are caused to individual organisms. Analogous to biological mutation, individual mutation in genetic algorithms is also similar. The mutation operator acts on the genes of an individual, causing a change in the characteristics of the individual and resulting in a new individual. Similar to the crossover operator above, when individuals exchange genes with each other, they only exchange part of each other’s genes. In this case, the mutation operator also triggers only a partial mutation.

The steps in which individual mutation occurs are as follows.

(1)

Let, the number of individuals to be mutated be c = [P × p_m].

(2)

Let {p₁,p₂,⋯,p_c}∈[1,P], choose c integers from {p₁, p₂,⋯,p_c}, and similarly choose c integers from {n₁,n₂,⋯,n_c}∈[1,n].

(3)

Let X_p1 be selected and X_p1 (x_p₁1,⋯,x_p₁n₁,⋯,x_p₁n) be the individual to be mutated. Let n₁ be the point of mutation. The new individual is $X_{p 1}^{'} (x_{p 1}, \dots, x_{p, n}^{'}, \dots, x_{p, n})$ , and $x_{p, n}^{'}$ can be expressed as: 31 $x_{p_{1} n_{1}} = x_{p_{1} n_{1}} + ε (d, y)$ 32 $ε (d . y) = y * a * (1 - \frac{d}{D})$ 33 $y = x_{p_{1} n_{1} \max} - x_{p_{1} n_{1} \min}$

Note that x_{p_in_imax}, x_{p_in_jmax} is the maximum and minimum value allowed for the gene values in an individual, respectively. α ∈ [0,1] is the maximum and minimum value allowed for the gene values in an individual. In the early stage of evolution, in order to increase the evolutionary activity of an individual, ε(d, y) takes a larger value to increase the individual mutation. In the late evolutionary stage, because the search range is close to the optimal solution, ε(d, y) takes a smaller value so that it strengthens the local optimization search.

2.3

Optimization of BP network fault diagnosis model by improved GA

2.3.1

Optimization of Neural Networks by Genetic Algorithms

We found that BP networks can be applied in the fault diagnosis of computer hardware systems. The advantages of the BP algorithm’s simplicity and plasticity are also reflected in the fault diagnosis model of the BP network, but the diagnosis results of the BP neural network alone are not perfect, and often tend to fall into local minima. To summarize its cause, we finally placed the landing point on the backward transmission of the network. BP algorithm is based on the gradient method, and the gradient descent method itself is very susceptible to the influence of the local minima ah, often make the results fall into the local minima, which is the crux of the problem of the BP network in fault diagnosis is not ideal. The biggest advantage of the genetic algorithm is that it only needs a fitness function without other auxiliary information, and it is not subject to the limitations of function differentiability and function continuity, so that it will not fall into the local optimum, and can accurately achieve the global optimum. At the same time, the search of genetic algorithms always spreads over the entire solution space, so it is easier to obtain the global optimal solution. In conclusion, the emergence of genetic algorithms has given a new perspective to the training of neural networks.

In this paper, genetic algorithm is used to optimize the initial weights and thresholds of BP network with this method. The training process of neural network weights can be viewed as a function optimization problem, and the basic way to adjust it is to repeat adjustments and gradually seek the optimal solution. The overall distribution of the neural network weights contains all the knowledge of the neural network, and the traditional method is often used to determine a change in the rules, once the rules are determined and will not be changed, the distribution of the weights of the entire network is also determined. Gradient descent is a common method that has been widely used in BP networks. The initial weights play a crucial role for the whole BP network, if the initial weights are not set well, coupled with the original training process, some of the parameters are selected by experience, then the poor settings will cause the network is difficult to converge, or convergence is slow or even fall into the local optimum, which will affect the weight distribution of the whole network. Using genetic algorithms to optimize the connection weights of BP networks can effectively solve the above problems, and the evolutionary process can be expressed as follows: 1)

Encode the weights and randomly generate a set of distributions which correspond to a set of connection weights of the neural network.

2)

Input the training samples, calculate the value of the error function, and combine it with the fitness function to screen the advantages and disadvantages of the connection weights, and select the individuals among them with greater fitness.

3)

Use crossover, mutation and other operations to evolve the current population and, as a result, generate a new population for the next generation.

4)

Repeat steps 2)-3) to evolve the weights initially determined by the BP network until the training target is satisfied.

2.3.2

Optimization steps

Since a 3-layer BP network is chosen in this paper, the following settings are made first:

I(i) is the output of the ind cell in the input layer. H(i) is the output of the ith unit in the implicit layer. O(k) is the output of the kth unit in the output layer. W1(i, j) is the connection weight of the ith unit of the input layer to the jth unit of the implied layer. B1( j) is the threshold value of the jth unit of the implicit layer. W2(j,k) is the connection weight of the jth cell of the input layer to the kth cell of the implied layer. B2(k) is the threshold value of the kth unit of the implicit layer [24]. The flow of GA-BP algorithm is shown in Fig. 3.

1)

Initialize the population P, the cross size as well as for any one of W1(i, j), B1(j) and W2(j, k), B2(k). The population size is selected as 40, real numbers are used in coding, and the maximum number of iterations of the genetic algorithm is set to 200.

2)

According to the fitness function, each individual is ranked by its outcome and then selected according to the following probability: 34 $P_{i} = \frac{f_{i}}{\sum_{j = 1}^{N} f_{j}}$ where f is the fitness value of individual i. The following equation introduces the squared value of the error signal for measurement, which we call the evolutionary error squared, and the evolutionary error sum of squares is set to 0.5. E in the following equation is the error squared: 35 $f (i) = \frac{1}{E (i)}$ 36 $E (i) = \sum_{p} {\sum_{k} (V_{k} - T_{k})}^{2}$

Where, i= 1,2,⋯,N is the number of chromosomes. p = 1,2, 5 is the number of learning samples. k = 1,2,⋯,4 is the number of output layer nodes. T_k is the teacher signal.

3)

Fuzzy dynamic regulation P_c, with P_c probability, performs crossover operation on individuals G_i and G_i + 1, after which new individuals G_i ′ and G_i+1 ′ are produced, while for individuals without crossover, replication is performed directly: the same fuzzy dynamic regulation P_m, with that probability, performs mutation, and then produces individual G_j new individual $G_{j}^{'}$ .

4)

Place the new individuals into the population and compute the fitness function of the new individuals.

5)

Calculate the error sum of squares of the BP network and continue if the error allowance is satisfied, otherwise go to lesser step 3).

6)

Take the optimized initial value of the genetic algorithm as the initial weights of the BP network and input the samples to start the training, and stop when the accuracy load is required.

After the above steps, the optimization of BP network by GA is basically completed.

3

Results and discussion

3.1

Computer hardware system fault feature extraction results

In this section, the data of a computer hardware system is utilized for experiments, and F1~F9 are used as the codes for different fault types of the computer hardware system, and the different fault types of the computer hardware system are compared with the codes as shown in Table 1. As the computer hardware system has different values of action currents in different fault modes, the extracted fault eigenvalues are also different.

Table 1.

Different fault types are compared to the code

Code	Type
F₁	Energized insertion
F₂	Battery exhaustion
F₃	Virus attack
F₄	Insurance burn
F₅	CMOS error
F₆	BIOS error
F₇	Fan damage
F₈	Chip burn
F₉	Pin oxidation

In this paper, db3 wavelet basis is used to reconstruct the signal components of the original computer hardware system fault sample data after three-layer wavelet packet decomposition and single subband reconstruction to obtain the third layer of eight wavelet packet coefficients. As the overall action curve of the A, B and C phase currents of the computer hardware system is more consistent, the following wavelet packet decomposition process is described in detail, mainly taking the normal action current data as an example. The wavelet packet reconstruction diagram of A-phase current in normal state is shown in Fig. 4. In the figure, S3,0 represents the single subband reconstruction signal of wavelet packet decomposition node 1, S3,1 represents the single subband reconstruction signal of decomposition node 2, S3,2, S3,3…S3,7, and so on.

The wavelet packet energy spectrum of the computer hardware system in normal state and different failure modes is shown in Fig. 5, and the specific energy values are shown in Table 2. Observed as a whole, the wavelet packet energy values of all states in band 1 are very high, the phenomenon is due to the computer hardware system in the early stage of the 1DQJ suction up, 1DQJF also suction up, 2DQJ turn the pole when the action current curve rises abruptly to form a spike caused by the wavelet packet in the local current change is obvious, that is, there is an inrush signal of the place of the sensitivity of the stronger. The next band 2 energy value size are roughly ranked in the second place, is due to the action curve back behind the process of convergence to a stable value of the change compared to other stages of the process is a little larger, and the last band 3-7 energy value are relatively small, is due to the conversion stage of the computer hardware system current has been converted to a stable state.

Table 2.

Small wave packet signal energy values in different states

Type		E_{3, 0}	E_{3, 1}	E_{3, 2}	E_{3, 3}	E_{3, 4}	E_{3, 5}	E_{3, 6}	E_{3, 7}
F₁	A phase	20.89497	1.90092	0.53784	0.57775	0.631	0.06302	0.63374	0.56613
	B phase	20.29716	1.83883	0.49647	0.92937	0.38465	0.53339	0.00735	0.19315
	C phase	20.36814	2.03094	0.6404	1.20884	0.285	0.38776	0.8191	0.76402
F₂	A phase	21.74152	2.49463	0.55227	0.7002	0.06078	0.21492	0.06117	0.41162
	B phase	22.05262	2.80149	0.54056	0.82839	0.09295	0.01334	0.51159	0.09916
	C phase	21.35739	2.22552	0.3658	0.54142	0.30538	0.00799	0.29674	0.36698
F₃	A phase	52.9085	2.64749	0.64554	1.45001	0.59247	0.35469	0.63881	0.40664
	B phase	51.44517	2.24069	1.12016	1.18453	0.1002	0.32647	0.69766	0.73913
	C phase	51.50044	2.11677	0.60058	0.86984	0.05935	0.44582	0.83782	0.26125
F₄	A phase	23.78691	2.01025	0.35526	0.99227	0.04609	0.08815	0.61194	0.47845
	B phase	20.89412	2.09448	0.32138	0.79022	1.00049	0.66932	0.75864	0.92088
	C phase	19.18094	1.81479	0.18836	0.25097	0.06462	0.09428	0.26034	0.42114
F₅	A phase	25.44712	1.36955	1.07982	1.09213	0.68519	0.03638	0.16046	0.4368
	B phase	21.22982	1.59993	1.05251	1.27646	0.10855	0.6158	0.21551	0.24565
	C phase	24.47241	1.81635	0.55027	1.07477	0.13796	0.09511	0.51013	0.34002
F₆	A phase	22.14241	0.71841	0.41587	1.17691	0.45951	0.18965	0.30486	0.49869
	B phase	22.16743	0.59275	1.51896	1.55474	0.36249	0.33495	0.07684	0.63297
	C phase	21.64248	1.05406	1.49921	1.28476	0.71865	0.48852	0.51629	0.34018
F₇	A phase	11.47209	2.85734	0.91163	1.42704	1.08527	0.57577	0.26386	0.32958
	B phase	11.55484	2.4755	0.38902	1.56322	0.4103	0.14025	0.90733	0.6437
	C phase	11.70625	2.37743	0.51093	1.14821	0.38942	0.09546	0.90041	0.41444
F₈	A phase	21.94349	2.91297	0.50958	0.37141	0.11686	0.23509	0.11704	0.02484
	B phase	21.44111	2.54994	0.30436	0.37427	0.3814	0.61512	0.49593	0.84916
	C phase	20.85718	1.98473	0.6785	1.60634	0.45874	0.69275	0.14515	0.81491
F₉	A phase	15.61011	1.96101	0.2859	0.50719	0.28264	0.09245	0.13466	0.31414
	B phase	11.74552	1.69799	0.76886	0.63888	0.55513	0.61363	0.66487	0.7758
	C phase	15.57689	1.04778	0.47912	0.69852	0.40221	0.15222	0.26568	0.13442

Specifically to each different state of the computer hardware system, the distribution of its wavelet packet energy value has a certain difference, for the larger difference between the fault characteristics, can be directly screened out from it, for example, F3 (virus attack), the energy value of its band 1 is as high as 50, compared to other faults have a significant difference. For other fault features with smaller differences, it is necessary to identify them with the help of other fault diagnosis methods. The energy values of wavelet packet signals in different states are shown in Table 2.

3.2

Effectiveness of computer hardware system fault diagnosis

In order to verify the diagnostic performance of the optimized computer hardware system fault diagnosis model and reflect the optimization effect of GA-BP network fault diagnosis model. The steps to design the verification experiment are as follows: 1)

Analyze the influence of genetic algorithm parameters on its optimization effect through experiments, and select the optimal parameters according to the experimental results to ensure the best optimization effect on the GA-BP network fault diagnosis model.

2)

After determining the parameters of the genetic algorithm, the computer hardware system fault diagnosis experiment. In order to reduce the experimental error, the fault data used in the experiment and the computer hardware system fault diagnosis model parameters are all the same as in the previous section of the experiment, to verify the optimization effect of the genetic algorithm.

3)

Compare the diagnosis correct rate of GA-BP network fault diagnosis model before and after optimization, and complete the verification analysis.

3.2.1

Experiments on Genetic Algorithm Parameters

The initial population size of the genetic algorithm determines the optimization effect of the computer hardware system fault diagnosis model, the population size is set too low, the algorithm may fall into the “precocious” and thus cause no solution, the population size is set too large, it will result in the complexity of the structure of the population relationship to increase the amount of computation, resulting in a reduction in the search speed. In order to avoid the above problems, the initial number of populations of the genetic algorithm, using the experimental method to determine the population value range from 10, in turn, plus 5 for the experiment. When choosing the initial population number, not only need to pay attention to the training error, but also to choose the population value with a smaller number of iterations, in order to achieve to meet the error requirements at the same time, to improve the processing efficiency of the network. The corresponding training parameters for different initial populations are shown in Table 3. Observing the data in the table, it is found that the difference in the number of training times is not very large with the change in the number of populations, indicating that the effect of the initial number of populations on the training efficiency is not very obvious in this model. Observing the trend of error change, it can be found that the error with the increase of the number of populations shows the change rule of decreasing and then increasing, in the initial population number of 30, the error is the lowest, and the number of training times is also within the acceptable range, so determine the initial population number of the genetic algorithm is 30.

Table 3.

Different initial population corresponding training parameters

Initial population (number)	Training step	error
10	25	0.0345
15	24	0.0269
20	19	0.0278
25	22	0.0209
30	20	0.0178
35	25	0.0252
40	28	0.0268

The crossover mutation process of chromosomes determines the diversity of the population in the genetic algorithm. Therefore the selection of crossover probability Pc and mutation probability Pm also has a certain impact on the training effect, and there is no uniform rule for the selection of the two, which are generally selected in the selected value interval. The selection of both parameters should not be too large or too small, choose 0.02 to 0.08 as the variation probability Pm interval, choose 0.4 to 0.8 as the crossover probability Pc interval, in turn, different crossover probability of variation experiments, Pc and Pm are taken to different values when the error performance of network training is shown in Table 4. Analyzing the data in the table, it can be seen that the influence of the variance probability on the training error is large, and the error is low in the interval of 0.04 to 0.06, and the training effect is excellent.

Table 4.

The error performance of network training in different values of Pc and Pm

Error		Pc
Error		0.4	0.5	0.6	0.7	0.8
Pm	0.02	0.158	0.0145	0.1021	0.0208	0.0577
	0.03	0.01266	0.0333	0.1047	0.0772	0.0685
	0.04	0.033	0.0224	0.0304	0.0148	0.035
	0.05	0.0735	0.1385	0.0392	0.0574	0.0749
	0.06	0.0083	0.0462	0.0065	0.0294	0.0263
	0.07	0.0258	0.1356	0.0634	0.0017	0.0026
	0.08	0.099	0.0018	0.0619	0.0024	0.0352

And the effect of cross probability training error has a high degree of randomness, and the error under different cross probabilities does not show an obvious pattern of change. The running parameters of the genetic algorithm are shown in Table 5. According to the data in the table, the crossover probability and variance probability corresponding to the lowest value of the training error are selected, i.e., the value of crossover probability is determined to be 0.3, and the value of variance probability is 0.05.

Table 5.

The genetic algorithm runs the parameters

Parameter name	Parameter setting
Population size	32
Maximum evolutionary frequency	48
Selection probability	0.92
Cross probability	0.3
Mutation probability	0.05

3.2.2

Diagnostic performance of optimized computer hardware system fault diagnosis model

In the experiment to verify the diagnostic performance of the optimized computer hardware system fault diagnostic model, in order to reduce the impact of experimental variables on the diagnostic results, the experimental design of GA-BP network fault diagnostic model parameters and experimental data are consistent with the previous section, the optimized computer hardware system fault diagnostic model parameters are shown in Table 6.

Table 6.

The model parameters of the computer hardware system fault diagnosis

Parameter name	Parameter setting
Error threshold	0.001
Learning efficiency	0.02
Network topology	7-9-3
Implicit layer activation function	logsig
Output layer activation function	purelin
Training function	Trainlm
Maximum iteration number	1000

The GA-BP network fault diagnosis model is constructed in Matlab according to the parameters in Table 6, and still 70% of the total sample data is used as training data, and the remaining 30% of the data is used as test data for computer hardware system fault diagnosis experiments, and the training error of the optimized computer hardware system fault diagnosis model is shown in Figure 6. From the training error graph, it can be clearly seen that the number of iterations of the optimized GA-BP network fault diagnosis model has been reduced, and the convergence speed has been significantly accelerated. The model converges to complete the training process after 16 iterations, and the training error of the optimized GA-BP network fault diagnostic model decreases rapidly in the 1~10 iterations of the model training, which indicates that the GA-BP network fault diagnostic model has a higher learning rate, although the speed of error decrease also slows down in the subsequent training. However, in general, the convergence speed of the GA-BP network fault diagnosis model improved, the number of iterations decreased, and the error decreased. The final error stays around 0.003, which is lower compared to the pre-optimization model, indicating that the optimized GA-BP network fault diagnostic model has higher accuracy in identifying computer hardware system faults.

The BP network fault diagnosis model optimized by genetic algorithms shows the effectiveness of genetic algorithms by reducing the number of iterations by nearly one-third while obtaining lower errors.

From the training results, the optimized GA-BP network fault diagnosis model shows better learning efficiency, reduces the number of iterations, and decreases errors. However, the training results do not fully reflect the performance of the optimized model. Therefore, further optimization of the GA-BP network fault diagnosis model is needed. Fault diagnosis experiments are designed as follows: 100 groups of fault data are randomly selected and input into the optimized GA-BP network fault diagnosis model after normalization, fault diagnosis experiments are carried out, and diagnostic results are plotted to compare the diagnostic results with the confusion matrix in order to analyze the diagnostic performance of the diagnostic results of GA-BP network fault diagnostic model are shown in Figure 7. From the figure, it can be clearly seen that in 100 groups of fault data, only 4 groups of data were misdiagnosed, and the diagnostic accuracy of the optimized GA-BP network fault diagnosis model was 96%. The highest diagnostic accuracy is for fault type 1, fault type 3, fault type 4 and fault type 5, with 100% diagnostic accuracy. In fault type 2, 2 sets of faults 2 were misdiagnosed as fault 1, and 2 faults 2 were misdiagnosed as fault 3, with a diagnostic accuracy of 80%, respectively. Overall, the GA-BP network fault diagnosis model has a high diagnosis rate.

3.3

Rehabilitation strategy

Faulty maintenance strategies include three types, namely, regular maintenance, maintenance on a case-by-case basis, and after-the-fact maintenance.

Computer failure in the process of use but does not affect the use of the task to be implemented after the end of the implementation of the maintenance is called after-the-fact maintenance, the strategy can save maintenance costs, easy to operate, the disadvantage is that the rigid and unpredictable. Depending on the maintenance is focused on analyzing the causes of failure, based on test data to develop a maintenance plan, before the computer hardware damage to its overhaul, this strategy can make the hardware to get the maximum degree of application, the disadvantage is that it requires a higher level of technical requirements and capital investment. Regular maintenance is planned to determine the maintenance time interval, in the specified time interval overhaul hardware strategy, this strategy can improve computer uptime, the disadvantage is that the economic cost is higher. The comprehensive closeness index for each failure type is used to provide a corresponding maintenance strategy for each failure type.

4

Conclusion

Aiming at the current problem of not being able to effectively diagnose computer hardware systems, the study designed a GA-BP neural network fault diagnosis model. The research conclusions drawn are as follows: 1)

In the experiment of the error of network training when Pc and Pm take different values respectively. It has been found that the influence of variance probability on the training error is large, and the error value is low in the range of 0.04 to 0.06, indicating that the model training is good.

2)

In the GA-BP network fault diagnosis model diagnostic results experiment, it was found that after using the GA-BP network fault diagnostic model designed in this paper for computer hardware system fault diagnosis, only 4 groups of fault data in 100 groups of data were misdiagnosed, and the diagnostic accuracy rate was 96%.

3)

Synthesize the characteristics of regular maintenance, depending on the situation maintenance and aftermath maintenance, and carry out targeted fault repair for different computer system hardware failures.

Language:: English

Publication timeframe:: 1 times per year
Journal Subjects:: Life Sciences, Life Sciences, other, Mathematics, Applied Mathematics, General Mathematics, Physics, Physics, other

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Genetic Algorithm Based Fault Diagnosis and Repair Strategy in Computer Hardware System

Tao Wang

Peng Pan

Published Online: Mar 19, 2025

Received: Nov 01, 2024

Accepted: Jan 31, 2025

DOI: https://doi.org/10.2478/amns-2025-0438

KeywordsGA-BP neural network, Wavelet packet transform, Fault diagnosis model, Computer hardware system

© 2025 Tao Wang et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
GA-BP neural network, Wavelet packet transform, Fault diagnosis model, Computer hardware system