MULTI-RULE DECISION METHOD FOR EVALUATING COMPREHENSIVE PERFORMANCE OF BATTERY STACK

TECHNICAL FIELD

The present disclosure relates to the field of battery stack technologies and in particular to a multi-rule decision method for evaluating comprehensive performance of a battery stack.

BACKGROUND

Solid Oxide Fuel Cell (SOFC) battery stack, as a location for directly converting fuel chemical energy into electric energy, is a key core functional component in fuel cell generation system. In the entire SOFC generation system, the performance of the SOFC battery stack directly determines the reliability and durability of the generation system. But, there are many evaluation rules for determining the performance of the battery stack (including open circuit voltage, power, long-term cycle durability, and cold and hot cycle durability and the like, totaling more than 20 performance indexes). Furthermore, there is relevance between different evaluation rules as well as different importances. Moreover, different evaluation rules of the battery stack determines different performances of the battery stack. Therefore, it is of great significance for evaluation of the comprehensive performance of the battery stack to determine an importance weight of each evaluation rule of the battery stack by using a multi-rule decision method.

The multi-rule decision refers to performing aggregation and sorting on multiple solutions to be evaluated based on rule values of multiple rules. The multi-rule decision includes two parts: performing evaluation on the importance weights of the rules and performing sorting on the priorities of the solutions to be evaluated. The methods for performing evaluation on the importance of the rules include Analytic Hierarchy Process (AHP), Decision-Making Trial and Evaluation Laboratory (DEMATEL), Analytic Network Process (ANP), least square method, ordering relation analysis method, and period-on-period ratio analysis method and the like. In 2015, Rezaei proposed an all-new method of evaluating an importance weight of a rule: Best Worst Method (BWM). Compared with the existing multi-rule decision method, the BWM method can generate more consistent pairwise comparison so as to generate a more reliable result. But, this model is only applicable to a decision of evaluation personnel for comprehensive performance of a single battery stack.

Afterwards, Mohammadi and Rezaei also established Bayesian-BWM group decision model. But, this model is based on probability distribution to determine a weight of a decision rule of a single performance of a battery stack based on many hypothetical factors. In practical applications, there are still some defects. Most of other BWM group decision methods are to obtain an arithmetic mean of weights of a decision rule of a single performance of a battery stack determined by multiple evaluation persons of comprehensive performance of the battery stack, so as to determine a final weight of the decision rule of the single performance of the battery stack. But, this method neglects the influence of a personal preference of each evaluation person of the comprehensive performance of the battery stack on the decision result, leading to a lower reliability of the decision result.

The present disclosure provides a multi-rule decision method for evaluating comprehensive performance of a battery stack. This method is based on the classical BWM method to determine a weight of a single-performance decision rule of the battery stack determined by each evaluation person of the comprehensive performance of the battery stack, and based on entropy theory and computer, perform iteration on an importance weight of the evaluation persons of the comprehensive performance of the battery stack, and aggregate a preference of each evaluation person of the comprehensive performance of the battery stack so as to obtain a final comprehensive weight of the decision rule of the single performance of the battery stack.

SUMMARY

The object of the present disclosure is to provide a multi-rule decision method of evaluating comprehensive performance of a battery stack, which effectively solves the problem in which the classical BWM method cannot allow multiple evaluation persons of the comprehensive performance of the battery stack to participate in decision and other BWM group decision models do not consider the contribution of each evaluation person of the comprehensive performance of the battery stack for a decision result.

In order to solve the above technical problems, the present disclosure adopts the following technical solution.

There is provided a multi-rule decision method of evaluating comprehensive performance of a battery stack, which is applied to evaluation of performance of an SOFC battery back and includes the following steps:

- at step S1, selecting multiple indexes from indexes affecting the performance of the battery stack, including but not limited to airtightness, open-circuit voltage, power, long-term cycle durability, cold and hot cycle durability, generation efficiency, fuel utilization rate, startup time, internal reforming efficiency, and stable running current, as a single-performance decision rule of the battery stack for evaluating the comprehensive performance of the battery stack to form a decision rule vector C_j=[c₁, c₂, . . . , c_n] of the comprehensive performance of the battery stack;
- at step S2, based on classical BWM method, obtaining a weight W^k_jof each evaluation person of the comprehensive performance of the battery stack for the single-performance decision rule of the battery stack in the decision rule vector C_j=[c₁, c₂, . . . , c_n] of the comprehensive performance of the battery stack, wherein j=1, 2, 3, . . . , n, k=1, 2, 3, . . . , m, j represents the j-th single-performance decision rule of the battery stack, and k represents the k-th evaluation person of the comprehensive performance of the battery stack;
- at step S3, based on entropy theory, aggregating a weight of the single-performance decision rule of the battery stack obtained by each evaluation person of the comprehensive performance of the battery stack to obtain an importance weight U_kof the k-th evaluation person of the comprehensive performance of the battery stack satisfying iteration stop condition and a final comprehensive weight W_jof the j-th single-performance decision rule of the battery stack, determine a comprehensive performance level of the battery stack and further determine reliability and durability of a fuel cell generation system.

Furthermore, in the step S2, a method of obtaining the weight W^k_jof the k-th evaluation person of the comprehensive performance of the battery stack for the j-th single-performance decision rule of the battery stack includes:

- (1) selecting the most important single-performance decision rule c_Bof the battery stack and the least important single-performance decision rule c_Wof the battery stack from the decision rule vector C_j=[c₁, c₂, . . . , c_n] of the comprehensive performance of the battery stack;
- (2) inviting each evaluation person of the comprehensive performance of the battery stack to use an importance value representation method of pairwise comparison to determine an importance of the most important single-performance decision rule of the battery stack relative to other single-performance decision rules of the battery stack and an importance of the other single-performance decision rules of the battery stack relative to the least important single-performance decision rule of the battery stack, and respectively establish a vector a_Bj=[a_B1, a_B2, . . . , a_Bj-1] of the importance of the most important single-performance decision rule of the battery stack relative to other single-performance decision rules of the battery stack and a vector a_jW=[a_1W, a_2W, . . . , a_j-1W] of the importance of the other single-performance decision rules of the battery stack relative to the least important single-performance decision rule of the battery stack;
- (3) based on the following linear optimization formula, obtaining the weight W^k_jof the single-performance decision rule of the battery stack determined by each evaluation person of the comprehensive performance of the battery stack;
- under the precondition that a target function ξ^Lis minimum, the following constraint conditions are to be satisfied:

$❘ w_{B}^{k} - a_{Bj} w_{j}^{k} ❘ \leq ξ^{L}; ❘ w_{j}^{k} - a_{jw} w_{W}^{k} ❘ \leq ξ^{L}; \sum_{j = 1}^{n} w_{j}^{k} = 1; w_{j}^{k} \geq 0;$

- when j=1,2,3, . . . , n, the above constraint conditions are all to be established;
- wherein w^k_Bis a weight of the most important single-performance decision rule of the battery stack determined by the k-th evaluation person of the comprehensive performance of the battery stack;
- w^k_Wis a weight of the least important single-performance decision rule of the battery stack determined by the k-th evaluation person of the comprehensive performance of the battery stack;
- w^k_jis a weight vector formed by the weight of the j-th single-performance decision rule of the battery stack determined by the k-th evaluation person of the comprehensive performance of the battery stack;
- ξ^Lis the target function of the linear optimization formula.

Furthermore, in the step S3, a method of obtaining the importance weight U_kof the k-th evaluation person of the comprehensive performance of the battery stack and the final comprehensive weight W of the j-th single-performance decision rule of the battery stack includes:

- (i) based on an optimal model aggregated relative to an entropy value in the group decision, aggregating a personal preference of each evaluation person of the comprehensive performance of the battery stack:

$W_{j}^{d} = \frac{\prod_{k = 1}^{m} {(W_{j}^{k})}^{U_{k}^{d - 1}}}{\sum_{j = 1}^{n} \prod_{k = 1}^{m} {(W_{j}^{k})}^{U_{k}^{d - 1}}}$

wherein W^k_jis a weight of the k-th evaluation person of the comprehensive performance of the battery stack for the j-th single-performance decision rule of the battery stack, W_j^dis a comprehensive weight of the j-th single-performance decision rule of the battery stack calculated in the d-th iteration, U_k^d-1is an importance weight of the k-th evaluation person of the comprehensive performance of the battery stack calculated in the (d−1)-th iteration, wherein j=1, 2, 3, . . . , n, k=1, 2, 3, . . . , m, d is a number of iterations, d=1,2,3, . . . , h, h is determined by a specific number of iterations;

- (ii) establishing a formula U_k^d=αr_k^d-1+βe_k^d-1of the importance weight of the k-th evaluation person of the comprehensive performance of the battery stack calculated in the d-th iteration;

wherein,

$r_{k}^{d - 1} = \frac{1}{\sum_{j = 1}^{n} {(W_{j}^{d - 1} - W_{j}^{k})}^{2} \sum_{k = 1}^{m} \frac{1}{\sum_{j = 1}^{n} {(W_{j}^{d - 1} - W_{j}^{k})}^{2}}} e_{k}^{d - 1} = \frac{1 + \frac{1}{\log_{2} n} (\sum_{j = 1}^{n} (\frac{W_{j}^{d - 1}}{\sum_{j = 1}^{n} W_{j}^{k}} \log_{2} (\frac{W_{j}^{d - 1}}{\sum_{j = 1}^{n} W_{j}^{k}})))}{m + \sum_{k = 1}^{m} (\frac{1}{\log_{2} n} \sum_{j = 1}^{n} (\frac{W_{j}^{d - 1}}{\sum_{j = 1}^{n} W_{j}^{k}} \log_{2} (\frac{W_{j}^{d - 1}}{\sum_{j = 1}^{n} W_{j}^{k}})))}$

wherein r_k^d-1is a deviation weight obtained based on a total deviation amount of the comprehensive weight of the k-th evaluation person of the comprehensive performance of the battery stack calculated in the (d−1)-th iteration, e_k^d-1is an entropy weight of the k-th evaluation person of the comprehensive performance of the battery stack in the (d−1)-th iteration, U_k^dis an importance weight of the k-th evaluation person of the comprehensive performance of the battery stack in the d-th iteration, W^k_jis a weight of the k-th evaluation person of the comprehensive performance of the battery stack for the j-th single-performance decision rule of the battery stack, W_j^d-1is a comprehensive weight of the j-th single-performance decision rule of the battery stack calculated in the (d−1)-th iteration, wherein custom-character j=1,2,3, . . . , n, k=1,2,3, . . . , m, d is a number of iterations, d≥1, d=1,2,3, . . . , h, h is determined by a specific number of iterations, α and β are specified by the evaluation persons of the comprehensive performance of the battery stack based on actual situations, and α+β=1;

- (iii) based on aggregation algorithm of personal preferences of multiple evaluation persons of the comprehensive performance of the battery stack, performing iteration, by computer, on the formulas (i) and (ii), until

$\sqrt{\sum_{j = 1}^{n} {((W_{j}^{d - 1}) - (W_{j}^{d}))}^{2}} < ε,$

and stopping the iteration;

wherein ε is determined by the evaluation persons of the comprehensive performance of the battery stack based on actual situations, W_j^dis a comprehensive weight of the j-th single-performance decision rule of the battery stack calculated in the d-th iteration, and W_j^d-1is a comprehensive weight of the j-th single-performance decision rule of the battery stack calculated in the (d−1)-th iteration;

- (iiii) outputting the importance weight U_kof the k-th evaluation person of the comprehensive performance of the battery stack at the time of iteration stop and the final comprehensive weight W_jof the j-th single-performance decision rule of the battery stack, wherein W_j=W_j^d, U_k=U_k^d.

Furthermore, a flow of the aggregation algorithm of the personal preferences of multiple evaluation persons of the comprehensive performance of the battery stack includes:

- P1: inputting the weight W^k_jof the single-performance decision rule of the battery stack determined by each evaluation person of the comprehensive performance of the battery stack and an initial importance weight U_k⁰of each evaluation person of the comprehensive performance of the battery stack;
- P2: calculating a comprehensive weight value

$W_{j}^{1} = \frac{\prod_{k = 1}^{m} {(W_{j}^{k})}^{U_{k}^{0}}}{\sum_{j = 1}^{n} \prod_{k = 1}^{m} {(W_{j}^{k})}^{U_{k}^{0}}}$

of the single-performance decision rule of the battery stack obtained in the first iteration;

- P3: calculating an importance weight of each evaluation person of the comprehensive performance of the battery stack obtained in the first iteration;
- P4: based on the comprehensive weight value W_j¹of the single-performance decision rule of the battery stack and the importance weight U_k¹of each evaluation person of the comprehensive performance of the battery stack obtained in the first iteration, calculating a comprehensive weight value W_j²of the j-th single-performance decision rule of the battery stack in the second iteration and the importance weight U_k²of the k-th evaluation person of the comprehensive performance of the battery stack in the second iteration;
- P5: determining whether the iteration stop condition

$\sqrt{\sum_{j = 1}^{n} {((W_{j}^{d - 1}) - (W_{j}^{d}))}^{2}} < ε (d \geq 1)$

is satisfied; if the iteration stop condition is satisfied, stopping iteration and outputting W_j^d, i.e. the final comprehensive weight W_jof the j-th single-performance decision rule of the battery stack, and otherwise, repeating the iteration until the iteration stop condition is satisfied.

The present disclosure has the following beneficial effects:

The present disclosure is based on the classical BWM method to determine a weight of a single-performance decision rule of the battery stack determined by each evaluation person of the comprehensive performance of the battery stack, and based on entropy theory and computer, perform iteration on an importance weight of the evaluation persons of the comprehensive performance of the battery stack, and aggregate a preference of each evaluation person of the comprehensive performance of the battery stack so as to obtain a final comprehensive weight of the decision rule of the single performance of the battery stack. This method effectively solves the problem in which the classical BWM method cannot allow multiple evaluation persons of the comprehensive performance of the battery stack to participate in decision and other BWM group decision models do not consider the contribution of each evaluation person of the comprehensive performance of the battery stack for a decision result.

BRIEF DESCRIPTIONS OF THE DRAWINGS

The present disclosure will be further detailed below in combination with drawings and specific embodiments.

FIG. 1 is a technical flowchart of an aggregation algorithm of personal preferences of multiple evaluation persons of the comprehensive performance of a battery stack according to the present disclosure.

DETAILED DESCRIPTIONS OF EMBODIMENTS

There is provided a multi-rule decision method of evaluating comprehensive performance of a battery stack, which is applied to evaluation on performance of an SOFC battery stack and includes the following steps:

- at step S1, selecting multiple indexes from performance indexes affecting the performance of the battery stack, comprising but not limited to airtightness, open-circuit voltage, power, long-term cycle durability, cold and hot cycle durability, generation efficiency, fuel utilization rate, startup time, internal reforming efficiency, and stable running current, as a single-performance decision rule of the battery stack for evaluating the comprehensive performance of the battery stack to form a decision rule vector C_j=[c₁, c₂, . . . , c_n] of the comprehensive performance of the battery stack;
- at step S2, based on classical BWM method, obtaining a weight W^k_jof each evaluation person of the comprehensive performance of the battery stack for the single-performance decision rule of the battery stack in the decision rule vector C_j=[c₁, c₂, . . . , c_n] of the comprehensive performance of the battery stack, wherein j=1,2,3, . . . , n, k=1, 2, 3, . . . , m, j represents the j-th single-performance decision rule of the battery stack, and k represents the k-th evaluation person of the comprehensive performance of the battery stack;
- at step S3, based on entropy theory, aggregating a weight of the single-performance decision rule of the battery stack obtained by each evaluation person of the comprehensive performance of the battery stack to obtain an importance weight U_kof the k-th evaluation person of the comprehensive performance of the battery stack satisfying iteration stop condition and a final comprehensive weight W_jof the j-th single-performance decision rule of the battery stack, determine a comprehensive performance level of the battery stack and further determine reliability and durability of a fuel cell generation system.

In the step S2, a method of obtaining the weight W^k_j(j=1,2,3, . . . , n, k=1,2,3, . . . , m) of the k-th evaluation person of the comprehensive performance of the battery stack for the j-th single-performance decision rule of the battery stack includes:

- (1) selecting the most important single-performance decision rule c_Bof the battery stack and the least important single-performance decision rule c_Wof the battery stack from the decision rule vector C_j=[c₁, c₂, . . . , c_n] of the comprehensive performance of the battery stack;
- (2) inviting each evaluation person of the comprehensive performance of the battery stack to use an importance value representation method of pairwise comparison as shown in FIG. 2 to determine an importance of the most important single-performance decision rule of the battery stack relative to other single-performance decision rules of the battery stack and an importance of the other single-performance decision rules of the battery stack relative to the least important single-performance decision rule of the battery stack, and respectively establish a vector a_Bj=[a_B1, a_B2, . . . , a_Bj-1] of the importance of the most important single-performance decision rule of the battery stack relative to other single-performance decision rules of the battery stack and a vector a_jW=[a_1W, a_2W, . . . , a_j-1W] of the importance of the other single-performance decision rules of the battery stack relative to the least important single-performance decision rule of the battery stack;
- (3) based on the following linear optimization formula, obtaining the weight W^k_jof the single-performance decision rule of the battery stack determined by each evaluation person of the comprehensive performance of the battery stack;
- under the precondition that a target function ξ^Lis minimum, the following constraint conditions are to be satisfied:

$❘ w_{B}^{k} - a_{Bj} w_{j}^{k} ❘ \leq ξ^{L}; ❘ w_{j}^{k} - a_{jw} w_{W}^{k} ❘ \leq ξ^{L}; \sum_{j = 1}^{n} w_{j}^{k} = 1; w_{j}^{k} \geq 0;$

- when j=1,2,3, . . . , n, the above constraint conditions are all to be established;
- wherein w^k_Bis a weight of the most important single-performance decision rule of the battery stack determined by the k-th evaluation person of the comprehensive performance of the battery stack;
- w^k_Wis a weight of the least important single-performance decision rule of the battery stack determined by the k-th evaluation person of the comprehensive performance of the battery stack;
- w^k_jis a weight vector formed by the weight of the j-th single-performance decision rule of the battery stack determined by the k-th evaluation person of the comprehensive performance of the battery stack;
- ξ^Lis the target function of the linear optimization formula;
- wherein j=1,2,3, . . . , n, k=1,2,3, . . . , m.

In the step S3, a method of obtaining the importance weight U_k(k=1,2,3, . . . , m) of the k-th evaluation person of the comprehensive performance of the battery stack and the final comprehensive weight W_j(j=1,2,3, . . . , n) of the j-th single-performance decision rule of the battery stack includes:

- (i) based on an optimal model aggregated relative to an entropy value in the group decision, aggregating a personal preference of each evaluation person of the comprehensive performance of the battery stack:

${W_{j}}^{d} = \frac{\prod_{k = 1}^{m} ({({W^{k}}_{j})}^{{U_{k}}^{d - 1}}}{\sum_{j = 1}^{n} \prod_{k = 1}^{m} {({W^{k}}_{j})}^{{U_{k}}^{d - 1}}}$

wherein W^k_jis a weight of the k-th evaluation person of the comprehensive performance of the battery stack for the j-th single-performance decision rule of the battery stack, W_j^dis a comprehensive weight of the j-th single-performance decision rule of the battery stack calculated in the d-th iteration, U_k^d-1is an importance weight of the k-th evaluation person of the comprehensive performance of the battery stack calculated in the (d−1)-th iteration, wherein j=1, 2, 3, . . . , n, k=1,2,3, . . . , m, d is a number of iterations, d=1,2,3, . . . , h, h is determined by a specific number of iterations;

- (ii) establishing a formula U_k^d=αr_k^d-1+βe_k^d-1(k=1,2,3, . . . , m, d=0, 1, 2, 3, . . . , h) of the importance weight of the k-th evaluation person of the comprehensive performance of the battery stack calculated in the d-th iteration;

wherein,

${r_{k}}^{d - 1} = \frac{1}{\sum_{j = 1}^{n} {({W_{j}}^{d - 1} - {W^{k}}_{j})}^{2} \sum_{k = 1}^{m} \frac{1}{\sum_{j = 1}^{n} {({W_{j}}^{d - 1} - {W^{k}}_{j})}^{2}}}$

${e_{k}}^{d - 1} = \frac{1 + \frac{1}{\log_{2} n} (\sum_{j = 1}^{n} (\frac{{W_{j}}^{d - 1}}{\sum_{j = 1}^{n} {W^{k}}_{j}} \log_{2} (\frac{{W_{j}}^{d - 1}}{\sum_{j = 1}^{n} {W^{k}}_{j}})))}{m + \sum_{k = 1}^{m} (\frac{1}{\log_{2} n} \sum_{j = 1}^{n} (\frac{{W_{j}}^{d - 1}}{\sum_{j = 1}^{n} {W^{k}}_{j}} \log_{2} (\frac{{W_{j}}^{d - 1}}{\sum_{j = 1}^{n} {W^{k}}_{j}})))}$

wherein r_k^d-1is a deviation weight obtained based on a total deviation amount of the comprehensive weight of the k-th evaluation person of the comprehensive performance of the battery stack calculated in the (d−1)-th iteration, e_k^d-1is an entropy weight of the k-th evaluation person of the comprehensive performance of the battery stack in the (d−1)-th iteration, U_k^dis an importance weight of the k-th evaluation person of the comprehensive performance of the battery stack in the d-th iteration, W^k_jis a weight of the k-th evaluation person of the comprehensive performance of the battery stack for the j-th single-performance decision rule of the battery stack, W_j^d-1is a comprehensive weight of the j-th single-performance decision rule of the battery stack calculated in the (d−1)-th iteration, wherein custom-character j=1, 2, 3, . . . , n, k=1,2,3, . . . , m, d is a number of iterations, d≥1, d=1,2,3, . . . , h, h is determined by a specific number of iterations, α and β are specified by the evaluation persons of the comprehensive performance of the battery stack based on actual situations, and α+β=1;

- (iii) based on aggregation algorithm of personal preferences of multiple evaluation persons of the comprehensive performance of the battery stack, performing iteration, by computer, on the formulas (i) and (ii), until

$\sqrt{\sum_{j = 1}^{n} {(({W_{j}}^{d - 1}) - ({W_{j}}^{d}))}^{2}} < ε$

(if the iteration stop condition is satisfied when proceeding to the h-th iteration, ε is determined by the evaluation persons of the comprehensive performance of the battery stack based on actual situations) and stopping the iteration;

wherein W_j^dis a comprehensive weight of the j-th single performance decision rule of the battery stack calculated in the d-th iteration, and W_j^d-1is a comprehensive weight of the j-th single-performance decision rule of the battery stack calculated in the (d−1)-th iteration;

- (iii) outputting the importance weight U_k(k=1,2,3, . . . , m) of the k-th evaluation person of the comprehensive performance of the battery stack at the time of iteration stop and the final comprehensive weight W_j(j=1, 2, 3, . . . , n) of the j-th single-performance decision rule of the battery stack, wherein W_j=W_j^d(j=1,2,3, . . . , n), U_k=U_k^d(k=1,2,3, . . . , m).

As shown in FIG. 1, a flow of the aggregation algorithm of the personal preferences of multiple evaluation persons of the comprehensive performance of the battery stack is further explained as follows:

- P1: inputting the weight W^k_j(j=1,2,3, . . . , n, k=1, 2, 3, . . . , m) of the single-performance decision rule of the battery stack determined by each evaluation person of the comprehensive performance of the battery stack and an initial importance weight U_k⁰(k=1,2,3, . . . , m) of each evaluation person of the comprehensive performance of the battery stack;
- P2: calculating a comprehensive weight value

${W_{j}}^{1} = \frac{\prod_{k = 1}^{m} {({W^{k}}_{j})}^{{U_{k}}^{0}}}{\sum_{j = 1}^{n} \prod_{k = 1}^{m} {({W^{k}}_{j})}^{{U_{k}}^{0}}}$

of the single-performance decision rule of the battery stack obtained in the first iteration;

- P3: calculating an importance weight of each evaluation person of the comprehensive performance of the battery stack obtained in the first iteration;
- P4: based on the comprehensive weight U_k^d-1of each evaluation person of the comprehensive performance of the battery tack in a last iteration and the comprehensive weight value W_j^d-1of the single-performance decision rule of the battery stack, calculating the importance weight U_k^dof each evaluation person of the comprehensive performance of the battery tack in a next iteration and the comprehensive weight value W_j^dof the single-performance decision rule of the battery stack, where d≥2;
- P5: determining whether a determination formula is satisfied; if not, repeating the step P4 to perform iterative calculation; if yes, stopping the iteration and outputting the final comprehensive weight W_j=W_j^dof the single-performance decision rule of the battery stack, where the determination formula is below:

$\sqrt{\sum_{j = 1}^{n} {(({W_{j}}^{d - 1}) - ({W_{j}}^{d}))}^{2}} < ε$

Embodiment 1

8 single-performance indexes are selected as the single-performance decision rule of the battery stack for determining the comprehensive performance of the battery stack: airtightness, open-circuit voltage, power, long-term cycle durability, cold and hot cycle durability, generation efficiency, fuel utilization rate and startup time.

1. Based on the classical BWM method, the weight W^k_j(j=1, 2, 3, . . . , 8, k=1, 2, 3, 4, 5) of the single-performance decision rule of the battery stack obtained by five evaluation persons of the comprehensive performance of the battery stack by performing pairwise comparison on the single-performance decision rule of the battery stack is obtained, where j represents the j-th single-performance decision rule of the battery stack, and k represents the k-th evaluation person of the comprehensive performance of the battery stack.

(1) The most important single-performance decision rule c_Bof the battery stack and the least important single-performance decision rule c_Wof the battery stack are selected from the decision rule vector C_j=[c₁, c₂, . . . , c_n] of the comprehensive performance of the battery stack; five evaluation persons of the comprehensive performance of the battery stack select the most important single-performance decision rule of the battery stack and the least important single-performance decision rule of the battery stack from the eight single-performance decision rules of the battery stack, as shown in Table 1.

TABLE 1

The most important single-performance decision

rule of the battery stack and the least important single-

performance decision rule of the battery stack determined

by each evaluation person of the comprehensive

performance of the battery stack

The most important
The least important

single-performance
single-performance

decision rule
decision rule of the battery

of the battery stack
stack

Evaluation person 1
Power
Startup time

Evaluation person 2
Power
Startup time

Evaluation person 3
Open-circuit voltage
Startup time

Evaluation person 4
Airtightness
Startup time

Evaluation person 5
Airtightness
Startup time

(2) Each evaluation person of the comprehensive performance of the battery stack is invited to use an importance value representation method of pairwise comparison as shown in Table 2 to determine an importance of the most important single-performance decision rule of the battery stack relative to other single-performance decision rules of the battery stack and an importance of the other single-performance decision rules of the battery stack relative to the least important single-performance decision rule of the battery stack, and respectively establish a vector a_Bj=[a_B1, a_B2, . . . , a_Bj-1] of the importance of the most important single-performance decision rule of the battery stack relative to other single-performance decision rules of the battery stack and a vector a_jW=[a_1W, a_2W, . . . , a_j-1W] of the importance of the other single-performance decision rules of the battery stack relative to the least important single-performance decision rule of the battery stack.

The importance of the most important single-performance decision rule of the battery stack relative to other single-performance decision rules of the battery stack and the importance of the other single-performance decision rules of the battery stack relative to the least important single-performance decision rule of the battery stack are shown in Tables 3 and 4 respectively.

TABLE 2

Importance value representation of paired

comparison of pairwise decision rules

Importance value representation

1
2
3
4
5
6
7
8
9

TABLE 3

the importance of the most important single-performance decision rule of the

battery stack relative to other single-performance decision rules of the battery stack

Cold

Open-

Long-term
and hot

Fuel

circuit

cycle
cycle
Generation
utilization
Startup

Airtightness
voltage
Power
durability
durability
efficiency
rate
time

Evaluation
3
2
1
4
4
5
7
9

person 1

Evaluation
2
4
1
5
6
7
7
8

person 2

Evaluation
2
1
2
3
3
4
5
7

person 3

Evaluation
1
2
2
4
3
4
5
7

person 4

Evaluation
1
3
2
5
4
5
6
8

person 5

TABLE 4

The importance of other single-performance

decision rules of the battery stack relative to the least

important single-performance decision rule of the battery stack

Evaluation
Evaluation
Evaluation
Evaluation
Evaluation

person 1
person 2
person 3
person 4
person 5

Airtightness
6
7
7
7
9

Open-circuit
7
5
8
6
7

voltage

Power
8
8
7
6
8

Long-term
5
4
6
5
4

cycle

durability

Cold and hot
5
3
6
4
5

cycle

durability

Generation
4
2
5
5
4

efficiency

Fuel
2
2
3
3
2

utilization

rate

Startup time
1
1
1
1
1

(3) Based on the following linear optimization formula, the weight W^k_j(j=1, 2, 3, . . . , 8, k=1, 2, 3, 4, 5) of the single-performance decision rule of the battery stack determined by each evaluation person of the comprehensive performance of the battery stack is obtained; the weight W^k_jof the single-performance decision rule of the battery stack determined by each evaluation person of the comprehensive performance of the battery stack is as shown in Table 5.

Under the precondition that a target function ξ^Lis minimum, the following constraint conditions are to be satisfied:

$| {w^{k}}_{B} - a_{B j} {w^{k}}_{j} | \leq ξ^{L};$

$| {w^{k}}_{j} - a_{j w} {w^{k}}_{W} | \leq ξ^{L};$

$\sum_{j = 1}^{n} {w^{k}}_{j} = 1;$

${w^{k}}_{j} \geq 0;$

when j=1,2,3, . . . , n, the above constraint conditions are all to be established;

wherein w^k_Bis a weight (k=1, 2, 3, 4, 5) of the most important single-performance decision rule of the battery stack determined by the k-th evaluation person of the comprehensive performance of the battery stack; w^k_Wis a weight (k=1, 2, 3, 4, 5) of the least important single-performance decision rule of the battery stack determined by the k-th evaluation person of the comprehensive performance of the battery stack; w^k_jis a weight vector (j=1, 2, 3, . . . , 8, k=1, 2, 3, 4, 5) formed by the weight of the j-th single-performance decision rule of the battery stack determined by the k-th evaluation person of the comprehensive performance of the battery stack; ξ^Lis the target function of the linear optimization formula.

TABLE 5

the weight of the single-performance decision rule of the battery stack

determined by each evaluation person of the comprehensive performance of the battery stack

for each performance of the battery stack

Open-

Long-term
Cold and

Fuel

circuit

cycle
hot cycle
Generation
utilization
Startup

Airtightness
voltage
Power
durability
durability
efficiency
rate
time

Evaluation
13.19%
19.79%
29.26%
9.895%
9.90%
7.92%
5.65%
4.40%

person 1

Evaluation
22.06%
11.03%
32.61%
8.82%
7.35%
6.30%
6.30%
5.52%

person 2

Evaluation
16.67%
24.65%
16.67%
11.12%
11.12%
8.34%
6.67%
4.76%

person 3

Evaluation
24.46%
17.36%
17.36%
8.68%
11.57%
8.68%
6.94%
4.96%

person 4

Evaluation
29.24%
13.29%
19.93%
7.97%
9.97%
7.97%
6.64%
4.98%

person 5

2. Based on entropy theory, the preferences of five evaluation persons of the comprehensive performances of the battery stack are aggregated to obtain the importance weight of the k-th evaluation person of the comprehensive performance of the battery stack U_k(k=1, 2, 3, 4, 5) and the final comprehensive weight W_j(j=1, 2, 3, . . . , 8) of the j-th single-performance decision rule of the battery stack.

(1) based on an optimal model aggregated relative to an entropy value in the group decision, a personal preference of each evaluation person of the comprehensive performance of the battery stack is aggregated:

${W_{j}}^{d} = \frac{\prod_{k = 1}^{m} {({W^{k}}_{j})}^{{U_{k}}^{d - 1}}}{\sum_{j = 1}^{n} \prod_{k = 1}^{m} {({W^{k}}_{j})}^{{U_{k}}^{d - 1}}}$

wherein W^k_jis a weight of the k-th evaluation person of the comprehensive performance of the battery stack for the j-th single-performance decision rule of the battery stack, W_j^dis a comprehensive weight of the j-th single performance decision rule of the battery stack calculated in the d-th iteration, U_k^d-1is an importance weight (j=1, 2, 3, . . . , 8, k=1, 2, 3, 4, 5) of the k-th evaluation person of the comprehensive performance of the battery stack calculated in the (d−1)-th iteration.

(2) a formula U_k^d=αr_k^d-1+βe_k^d-1(k=1, 2, 3, 4, 5, d=0, 1, 2, 3, . . . , h) of the importance weight of the k-th evaluation person of the comprehensive performance of the battery stack calculated in the d-th iteration is established;

wherein,

wherein r_k^d-1is a deviation weight obtained based on a total deviation amount of the comprehensive weight of the k-th evaluation person of the comprehensive performance of the battery stack calculated in the (d−1)-th iteration, e_k^d-1is an entropy weight of the k-th evaluation person of the comprehensive performance of the battery stack in the (d−1)-th iteration, U_k^dis an importance weight of the k-th evaluation person of the comprehensive performance of the battery stack in the d-th iteration, W^k_jis a weight of the k-th evaluation person of the comprehensive performance of the battery stack for the j-th single-performance decision rule of the battery stack, W_j^d-1is a comprehensive weight of the j-th single-performance decision rule of the battery stack calculated in the (d−1)-th iteration, wherein custom-character j=1,2,3, . . . , n, k=1,2,3, . . . , m, d is a number of iterations, d=1,2,3, . . . , h, h is determined by a specific number of iterations. α and β are 0.6 and 0.4 respectively in this example.

(3) The weight of the single-performance decision rule of the battery stack determined by five evaluation persons of the comprehensive performance of the battery stack (as shown in Table 5) and the initial importance weight U_k⁰=0.2 (k=1, 2, 3, 4, 5) of five evaluation persons of the comprehensive performance of the battery stack are input. Based on the aggregation algorithm of personal preferences of multiple evaluation persons of the comprehensive performance of the battery stack and the formulas (1) and (2), iteration is performed until the iteration stop condition

$\sqrt{\sum_{j = 1}^{n} {(({W_{j}}^{d - 1}) - ({W_{j}}^{d}))}^{2}} < ε$

(ε=0.001 in this example) is satisfied, and then iteration is stopped;

wherein W_j^dis the comprehensive weight of the j-th single-performance decision rule of the battery stack in the d-th iteration, and W_j^d-1is the comprehensive weight of the j-th single-performance decision rule of the battery stack in the (d−1)-th iteration.

The importance weight U_k(k=1, 2, 3, 4, 5) of the k-th evaluation person of the comprehensive performance of the battery stack at the time of iteration stop and the final comprehensive weight W_j(j=1, 2, 3, . . . , 8) of the j-th single-performance decision rule of the battery stack are output as shown in Tables 6 and 7.

TABLE 6

the importance weight of each evaluation person of the

comprehensive performance of the battery stack

Evaluation
Evaluation
Evaluation
Evaluation
Evaluation

person 1
person 2
person 3
person 4
person 5

Importance
11.62%
11.14%
13.59%
45.95%
17.70%

weight

TABLE 7

The final comprehensive weight of the single-performance decision rule

of the battery stack

Open-

Long-term
Cold and

Fuel

circuit

cycle
hot cycle
Generation
utilization
Startup

Airtightness
voltage
Power
durability
durability
efficiency
rate
time

Final
22.42%
17.09%
20.62%
9.18%
10.65%
8.27%
6.74%
5.02%

comprehensive

weight

OF course, the above descriptions are not meant to limit the present disclosure and the present disclosure is also limited to the above embodiments. Various changes, variations, additions, or substitutions made by those skilled in the arts within the substantial scope of the present disclosure shall fall within the scope of protection of the present disclosure.

MULTI-RULE DECISION METHOD FOR EVALUATING COMPREHENSIVE PERFORMANCE OF BATTERY STACK

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