Herein, y is used to denote the actual space consumption of the FSCK tier, then the cost function J_θ(θ₀, θ₁) can be calculated by the following Equation (2) to measure the closeness between the predicted values and true values of the space consumption of the FSCK tier:

J
θ

(

θ
0

,

θ
1

)

=

1

2
⁢
n

⁢

∑

i
=
0

n

(

H
θ

(
x
)

(
i
)

-

y

(
i
)

)

2

(
2
)

In order to obtain the closest hypothetical value to the target output y, it is necessary to find the parameter pair (θ₀, θ₁) to minimize the value of the cost function J_θ(θ₀, θ₁). Given a random initial parameter pair (θ₀, θ₁), the partial derivatives

∂

J
θ

(

θ
0

,

θ
1

)

∂

θ
0

⁢

and
⁢

∂

J
θ

(

θ
0

,

θ
1

)

∂

θ
1

of the cost function J_θ(θ₀, θ₁) based on these two variables can be calculated by the following Equations (3) and (4) to update the variables θ₀and θ₁so as to obtain a relatively small loss in the next training iteration:

∂

J
θ

(

θ
0

,

θ
1

)

∂

θ
0

=

1
n

⁢

∑

i
=
0

n

(

H
θ

(
x
)

(
i
)

-

y

(
i
)

)

(
3
)

∂

J
θ

(

θ
0

,

θ
1

)

∂

θ
1

=

1
n

⁢

∑

i
=
0

n

(

H
θ

(
x
)

(
i
)

-

y

(
i
)

)

*

x

(
i
)

(
4
)

Herein, α is used to denote the learning rate of the linear regression model, then the parameter pair (θ₀, θ₁) can be updated simultaneously by the following Equations (5) and (6) after each round of training iterations:

θ
0

=

θ
0

-

α
*

∂

J
θ

(

θ
0

,

θ
1

)

∂

θ
0

(
5
)

θ
1

=

θ
1

-

α
*

∂

J
θ

(

θ
0

,

θ
1

)

∂

θ
1

(
6
)

FIG. 6A illustrates a schematic diagram of a loss function for a training phase of a linear regression model according to some embodiments of the present disclosure. As shown in FIG. 6A, having suitable values for the parameter pair (θ₀, θ₁) can minimize the loss function. In some embodiments, the learning rate a can be set to 0.0000001, and the values (0.856512, 0.348667) of the parameter pair (θ₀, θ₁) can be obtained by the training process described above. Thus, the predicted value H_θ(x) of the space consumption of the FSCK tier can be calculated by the following Equation (7):

H
θ

(
x
)

=

0.856512
+

0.348667
*
x

(
7
)

FIG. 6B illustrates a schematic diagram of a comparison of predicted values and true values for the training phase of a linear regression model according to some embodiments of the present disclosure. As shown in FIG. 6B, a straight line is used to represent the physical storage space occupation of the FSCK tier predicted based on the size of logical space, and x is used to denote the true value of the space consumption of the FSCK tier in the training data. From FIG. 6B, it can be seen that the prediction of the space consumption of the FSCK tier using the linear regression model has good accuracy.

By using the linear regression model to predict the space consumption of the FSCK tier, although certain data analysis is required in the training phase to determine the target features, the parameters of the linear regression model are transparent, and thus further analysis can be performed based on the above prediction function to determine whether the space reserved value given to the FSCK tool by the storage system is sufficient.

Herein, p is used to denote the total physical space of the storage system, and 1 is used to denote the actual size of logical space of the storage system. In some embodiments, the storage system may reserve 2.5% of the total physical space to the FSCK tool, then the following Inequality (8) should be met:

0.025
*
p

≥

H
θ

(
x
)

=

0.856512
+

0.348667
*
x

≈

0.35
*

(

l
/
64

)

(
8
)

Herein, the variable p′ is used to denote the actually used physical space of the storage system, and DRR is used to denote the overall data compression rate of the storage system, then the following Inequality (9) should be met:

0.025
*
p

≥

(

0.35
/
64

)

*

p
′

*
DDR

(
9
)

Thus, when the actually used physical space p′ reaches the total physical capacity p, the DRR is the factor that determines whether the space reserved value given by the storage system to the FSCK tool is sufficient. From Equation (9) above, it can be seen that when the reserved value is 2.5%, the DDR should not exceed 4.57.

In some embodiments, the machine learning model may also be a pre-trained neural network model. When using the neural network model to determine the space consumption of the FSCK tool, the first feature set or the second feature set may be used directly as an input to the model without prior data analysis of the features in the feature set.

In some embodiments, before inputting the first feature set or the second feature set into the neural network model, pre-processing such as data cleaning and normalization processing may be performed on the first feature set or the second feature set. The data cleaning can improve the quality of the data, thereby improving the training effect of the model; and the normalization processing can improve the comparability of the data, thereby improving the training efficiency of the model.