A comprehensive assessment of environmental factors in aircraft cockpit based on fuzzy evaluation

Abstract

BACKGROUND:

The cockpit of an aircraft is the main place where the pilot controls the aircraft on a mission. An excellent cockpit environment not only ensures the pilot’s basic survival needs but also improves the comfort level and alleviates fatigue when performing missions.

OBJECTIVE:

On the basis of domestic and international airworthiness standards, a top-down refinement method is deployed to determine the initial goal, and the environmental criteria are fully discussed and balanced in a dynamic process to build a comprehensive evaluation system for environmental factors in the aircraft cockpit.

METHODS:

Based on the fuzzy comprehensive evaluation theory, an evaluation model for environmental factors is constructed by combining analytic hierarchical analysis (AHP) and particle swarm optimization (PSO). Then the feasibility of the evaluation model is verified by an illustrative example.

RESULTS:

The results suggest that the light environment gains the highest score among the 4 environmental criteria followed by the thermal environment, while both sound environment and microenvironment have relatively low scores.

CONCLUSION:

As for the 27 environmental sub-criteria, temperature, illumination, lighting clarity, light-color coordination, noise duration and pressure score the highest. The evaluation findings can provide important environmental control criteria for the subsequent environmental control system in the cockpit of the aircraft.

Keywords

Aircraft cockpit environmental factor index fuzzy comprehensive evaluation analytic hierarchy process index weight particle swarm optimization

1 Introduction

The cockpit belongs to a special man-environment system because of the particular nature of the job and working environment. For such a special man-environment system, “man” refers to the pilot in the aircraft cab; “environment” refers to the specific operating conditions of the aircraft cab where people and machines coexist, including e.g. noise, illumination and temperature [1]. As the only way of information interaction between the pilot and the aircraft, the cab environment’s comfort level not only has an effect on the pilot’s physical and mental activities but also has a direct impact on one’s work efficiency and the aircraft’s flight safety. At present, domestic and foreign scholars have carried out relevant research on the environmental factors of the aircraft cockpit. For example, scholar Hu Ying by analyzing the temperature, light, ventilation, and noise of the cabin, clarified the influence principle of the cabin environmental factors, upon which the fuzzy mathematics theory is introduced to establish and validate a comprehensive evaluation mathematical model [2]. Hu used a fuzzy comprehensive evaluation method to establish the evaluation model of light environment comfort, and established its relational function according to the various characteristics of different factors [3]. Park investigated the relationship between the local thermal feeling and the overall thermal feeling of passengers in the aircraft cabin [4]. Qu established a human heat regulation based on combined human temperature distribution with cabin thermal environment parameters [5].

Constrained by multiple environmental factors, various environmental indicators are needed to be evaluated comprehensively when assessing the aircraft cockpit. Since the multiple environmental indicators of the aircraft cockpit include both qualitative and quantitative indicators, it is a multi-indicator comprehensive assessment. Therefore, the evaluation method is also integrated with multiple systems. At present, the comprehensive evaluation methods that have been carried out at home and abroad are becoming more complicated, mathematical, and multidisciplinary. The multivariate statistical evaluation method, principal component analysis method [6], cluster analysis [7], fuzzy mathematics comprehensive evaluation method [8], and grey system evaluation method [9 –11] have been widely used. In recent years, new comprehensive evaluation methods such as data envelopment analysis (DEA) and artificial neural network (ANN) methods have emerged [12, 13]. In specific research, domestic and foreign scholars have also made relevant exploration. For example, Beijing University of Aeronautics and Astronautics has developed a military aircraft cockpit model and a pilot manikin, studied the modeling of the reachable domain and visual domain of the military aircraft cockpit, designed and analyzed the ergonomic design of the character coding of the display interface, and proposed a comprehensive evaluation index and evaluation method for the adaptability of man-machine control interface [14]. Zhang Hongbin and others established the evaluation index system of helicopter multi aircraft cooperative detection efficiency by using the analytic hierarchy process (AHP) according to the selection principle of efficiency index [15].

In summary, these modern comprehensive evaluation methods have a certain degree of advancement and practicability. However, most can only evaluate qualitative indicators based on the principle of fuzzy transformation and maximum membership because it is difficult to quantify multiple environmental indicators in the aircraft cockpit. Given that the fuzzy comprehensive evaluation method is a comprehensive evaluation method based on fuzzy mathematics theory, it is very suitable for solving vague evaluation problems and non-deterministic problems which are difficult to quantify [16].

2 Methods

2.1 Construction method of multi-environment index evaluation for aircraft cockpit

When it comes to establish a comprehensive evaluation index system for environmental factors in the aircraft cockpit (as shown in Fig. 1), a top-down gradual refinement method is usually used to determine the initial target level, and then gradually refine to finish the complete evaluation index system, so repeated scrutiny and comprehensive balance in the dynamic process [17]. The determination and selection of evaluation indicators are generally carried out by the researchers through the analysis of the various environmental systems of the aircraft to initially determine the evaluation indicators, and then extensively solicit the opinions of design experts and decision-makers in various fields, and carry out iterations, repeated revisions, and continuous improvements. Finally, an evaluation index system for the evaluation problem is established [18].

Fig. 1

Construction process of multi-environmental index assessment for aircraft cockpit.

2.2 Index weight determination method

For multi-objective decision-making systems, some complex systems usually possess many variables, complex structures and uncertain factors. It is necessary to carry out a correct evaluation of the relative importance of the describing objectives to solve decision-making problems in these complex systems. The importance of each factor is different. In order to reflect the importance of the factor, the relative importance (weight) of each factor needs to be estimated. The weights of various factors compose the weight set. Weight is a relative concept, which refers to a certain index, refers to the relative importance of the index in the entire established evaluation index system, and is the result of subjective and objective comprehensive measurement. The methods for determining index weights mainly include analytic hierarchy process, expert estimation method, factor analysis weighting method, grey relational degree analysis method and more. The Analytic Hierarchy Process (AHP) in system engineering theory is a appropriate way to determine the weight [19]. It is a multi-objective and multi-criteria decision-making method that divides the factors of a complex problem into related and orderly levels to make it organized. It is an effective method that combines quantitative and qualitative analysis. Therefore, this study intends to use the analytic hierarchy process and particle swarm optimization algorithm to determine the index weight of each environmental factor.

2.2.1 Analytic hierarchy process

The analytic hierarchy process first puts the decision-making problem to be carried out in a large system. There are multiple factors that affect each other in this system [20]. These problems are to be hierarchized to form a multi-layered analysis structure model. After that, a combination of mathematical methods and qualitative analysis is used, through layered sorting, and finally calculated according to the weight of each plan to assist decision-making. The steps of AHP to determine the weights are as follows:

(1) Construct a judgment matrix. Let a denote the goal, u_i, u_j (i,j=1, 2, . . . , n) denote the factors. u_ij represents the relative importance value of u_ito u_j. And the A-U judgment matrix P is composed of u_ij. $P = [\begin{matrix} \begin{matrix} u_{11} & u_{12} \\ u_{21} & u_{22} \end{matrix} & \begin{matrix} \dots & u_{1 n} \\ \dots & u_{2 n} \end{matrix} \\ \begin{matrix} ⋮ & ⋮ \\ u_{n 1} & u_{n 2} \end{matrix} & \begin{matrix} ⋮ & ⋮ \\ \dots & u_{nn} \end{matrix} \end{matrix}]$ (1)

(2) Calculate importance ranking. According to the judgment matrix, find the eigenvector w corresponding to the largest eigenvalue λ_max. The equation is as follows: $P_{w} = λ_{\max} \cdot w$ (2)

The required feature vector w is normalized, that is, the importance of each evaluation factor is ranked, that is, the weight distribution.

(3) Consistency check. Whether the weight distribution obtained above is reasonable or not, the consistency test of the judgment matrix is also needed.

Test using formula: $CR = \frac{CI}{RI}$ (3)

CR is the random consistency ratio of the judgment matrix; CI is the consistency index of the judgment matrix. It is given by following formula: $CI = \frac{λ_{\max} - n}{n - 1}$ (4)

RI is the average random consistency index of the judgment matrix. When the CR of the judgment matrix P is less than 0.1 or λ_max = n, and CI = 0, P is considered to have a satisfactory consistency, otherwise the elements in P need to be adjusted to make it have a satisfactory consistency.

2.2.2 Particle swarm optimization algorithm

The combination of analytic hierarchy process (AHP) and fuzzy theory will lead to non-objectivity in the evaluation because of its strong subjectivity. Because the expert scoring of the analytic hierarchy process will be subjective, the scoring matrix will be inconsistent or omitted. At this time, we can use a particle swarm optimization algorithm to modify the expert scoring matrix. Under the condition that the original information of the decision-maker is maintained to the greatest extent and the judgment matrix is determined, the judgment matrix has better consistency and improves the weight value [21]. Particle Swarm Optimization (PSO) was proposed by Dr. Eberhart and Dr. Kennedy in 1995 [22]. Its basic core is to use the sharing of information by individuals in the group so that the movement of the entire group produces an evolutionary process from disorder to order in the problem-solving space, so as to obtain the optimal solution to the problem [23]. After finding these two optimal values, the particle uses the following formula to update its speed and position. $\begin{matrix} V_{i + 1} = V_{i} + c_{1} \times rand (0 \sim 1) \times ({pbest}_{i} - x_{i}) \\ + c_{2} \times rand (0 \sim 1) \times ({gbest}_{i} - x_{i}) \end{matrix}$ $x_{i + 1} = x_{i} + V_{i}$ (5)

i = 1, 2, . . . ,M, M is the total number of particles in the group; Vi is the velocity of the particles; pbest is the individual optimal value; gbest is the global optimal value; rand (0∼1) is a random number between (0, 1); xi is the current position of the particle. c1 and c2 are learning factors, usually c1 = c2 = 2. In each dimension, the particle has a maximum speed limit V_max. If the speed of a certain dimension exceeds the set V_max then the speed of this dimension is limited to V_max.

2.3 Fuzzy synthetic decision-making method

According to the factors involved in the evaluation, fuzzy comprehensive evaluation can be divided into one-level fuzzy comprehensive evaluation and multi-level fuzzy comprehensive evaluation [24]. Since the multi-environmental factor index system of the aircraft cockpit is multi-layered, the fuzzy comprehensive evaluation results of the lowest-level indicators are integrated together, and the fuzzy comprehensive evaluation is carried out layer by layer from low-level to high-level. The specific evaluation process is shown in Fig. 2.

Fig. 2

Fuzzy comprehensive evaluation process of multi-environmental factors in aircraft cockpit.

To construct the fuzzy comprehensive evaluation model of multi-environmental factors in the aircraft cockpit, we should first determine the factor universe of the evaluation object, that is, P evaluation indicators u ={ u₁, u₂, ⋯⋯ , u_p }; secondly, it is necessary to determine the domain of the review rating, that is, the rating set v ={ v₁, v₂, ⋯⋯ , v_p }; each level can correspond to a fuzzy subset; then the fuzzy relationship matrix R is established. After constructing the hierarchical fuzzy subset, we quantify the evaluated items from each factor one by one u_i (i = 1, 2, ⋯⋯ , p). That is to determine the degree of membership of the rated thing to the fuzzy subset of the grade from the single factor (R|u_i), and then obtain the fuzzy relationship matrix: $R = [\begin{matrix} \begin{matrix} R | & u_{1} \\ R | & u_{2} \end{matrix} \\ \begin{matrix} \dots \\ \begin{matrix} R | & u_{p} \end{matrix} \end{matrix} \end{matrix}] = {[\begin{matrix} r_{11} & r_{12} & \dots & r_{1 m} \\ r_{21} & r_{22} & \dots & r_{2 m} \\ \dots & \dots & \dots & \dots \\ r_{p 1} & r_{p 2} & \dots & r_{pm} \end{matrix}]}_{p . m}$ (6)

The element in the row and column of the matrix represents the degree of membership of a certain thing to be evaluated to the fuzzy subset of the hierarchy in terms of factors. The performance of an evaluated object in a certain factor is described by the fuzzy vector (R|u_i) = (r_i1, r_i2, ⋯⋯ , r_im), while in other evaluation methods it is mostly described by the actual value of an indicator. Thirdly, the weight vector of the evaluation factor A = (a₁, a₂, ⋯⋯ , a_p) is determined. The elements in the weight vector A are essentially the membership degree of the factor to the fuzzy (The importance of the thing being evaluated). Finally, to synthesize the fuzzy comprehensive evaluation result vector, a suitable operator is used to synthesize A and each evaluated object to obtain the fuzzy comprehensive evaluation result vector of each evaluated object, namely: $\begin{matrix} A * R = (a_{1}, a_{2}, \dots \dots, a_{p}) [\begin{matrix} r_{11} & r_{12} & \dots & r_{1 m} \\ r_{21} & r_{22} & \dots & r_{2 m} \\ \dots & \dots & \dots & \dots \\ r_{p 1} & r_{p 2} & \dots & r_{pm} \end{matrix}] \\ = (b_{1}, b_{2}, \dots \dots, b_{m}) = B \end{matrix}$ (7)

Among vectors, the result is obtained by the operation of the column, which represents the degree of membership of the rated object to the fuzzy subset of the hierarchy as a whole. According to the above steps, the specific step-by-step framework is shown in Fig. 3.

Fig. 3

Step by step frame diagram.

3 Results

3.1 The result of index system construction

Since the aircraft cockpit is a special cabin, in addition to following the above principles when constructing the aircraft cockpit multi-environmental factor evaluation system, it is also necessary to refer to relevant standards given at home and abroad. Relevant requirements and guidance are given in national standard, national military standard, U.S. military standard, SAE standard, and ISO standard [26]. These standards are now organized and summarized, as shown in Table 1.

Table 1
Standard for environmental factors in aircraft cockpit

Related domestic standards Related foreign standards

GJB1193-91 General specification for aircraft environmental control system ISO 28803:2012 Ergonomics of the physical – Application of International Standards to people with special requirements

HB7788_2005 General specification for aircraft temperature control system ISO 15743:2008 Ergonomics of the thermal environment – Cold workplaces – Risk assessment and management

GJB 3101-97 General specification for aircraft heating and ventilation systems ISO 11079:2007 Ergonomics of the thermal environment – Determination and interpretation of cold stress when using required clothing insulation (IREQ) and local cooling effects

GJB1129_1991 Methods and physiological requirements for the temperature evaluation of military aircraft cockpit ISO 9920:2007 Ergonomics of the thermal environment – Estimation of thermal insulation and water vapour resistance of a clothing ensemble

GB/T18977-2003 Ergonomics of thermal environment use the subjective judgment scale to evaluate the impact of the thermal environment ISO 7730:2005 Ergonomics of the thermal environment – Analytical determination and interpretation of thermal comfort using calculation of the PMV and PPD indices and local thermal comfort criteria

GB/T18049-2017 Ergonomics of the thermal environment by calculating PMV/PPD, The local thermal comfort criterion analyzes, determines and explains thermal comfort ISO 9886:2004 Ergonomics – Evaluation of thermal strain by physiological measurements

GJB898A-2004 General medical requirements and evaluation of temperature environment in working cabins (rooms) ISO 7933:2004 Ergonomics of the thermal environment – Analytical determination andinterpretation of heat stress using calculation of the predicted heat strain

GB/T 18048-2008 Ergonomics of thermal environment determination of metabolic rate ISO 15265:2004 Ergonomics of the thermal environment – Risk assessment strategy for the prevention of stress or discomfort in thermal working conditions

GB/T 17244-1998 Thermal environment evaluation of workers’ thermal load based on WBGT index ISO 13731:2001 Ergonomics of the thermal environment – Vocabulary and symbols

GB3096-2008 Acoustic environmental quality standards ISO 7726:1998 Ergonomics of the thermal environment – Instruments for measuring physical quantities

GB/T34828-2017 Acoustic free field environmental assessment test method ISO 11399:1995 Ergonomics of the thermal environment – Principles and application of relevant International Standards

GB9660-1988 Environmental standards for aircraft noise around airports ISO 10551:1995 Ergonomics of the thermal environment – Assessment of the influence of the thermal environment using subjective judgement scales

GB16710.1-1996 Construction machinery noise limit ISO 7243:1989 Hot environments – Estimation of the heat stress on working man, based on the WBGT-index (wet bulb globe temperature)

Related domestic standards	Related foreign standards
GJB1193-91 General specification for aircraft environmental control system	ISO 28803:2012 Ergonomics of the physical – Application of International Standards to people with special requirements
HB7788_2005 General specification for aircraft temperature control system	ISO 15743:2008 Ergonomics of the thermal environment – Cold workplaces – Risk assessment and management
GJB 3101-97 General specification for aircraft heating and ventilation systems	ISO 11079:2007 Ergonomics of the thermal environment – Determination and interpretation of cold stress when using required clothing insulation (IREQ) and local cooling effects
GJB1129_1991 Methods and physiological requirements for the temperature evaluation of military aircraft cockpit	ISO 9920:2007 Ergonomics of the thermal environment – Estimation of thermal insulation and water vapour resistance of a clothing ensemble
GB/T18977-2003 Ergonomics of thermal environment use the subjective judgment scale to evaluate the impact of the thermal environment	ISO 7730:2005 Ergonomics of the thermal environment – Analytical determination and interpretation of thermal comfort using calculation of the PMV and PPD indices and local thermal comfort criteria
GB/T18049-2017 Ergonomics of the thermal environment by calculating PMV/PPD, The local thermal comfort criterion analyzes, determines and explains thermal comfort	ISO 9886:2004 Ergonomics – Evaluation of thermal strain by physiological measurements
GJB898A-2004 General medical requirements and evaluation of temperature environment in working cabins (rooms)	ISO 7933:2004 Ergonomics of the thermal environment – Analytical determination andinterpretation of heat stress using calculation of the predicted heat strain
GB/T 18048-2008 Ergonomics of thermal environment determination of metabolic rate	ISO 15265:2004 Ergonomics of the thermal environment – Risk assessment strategy for the prevention of stress or discomfort in thermal working conditions
GB/T 17244-1998 Thermal environment evaluation of workers’ thermal load based on WBGT index	ISO 13731:2001 Ergonomics of the thermal environment – Vocabulary and symbols
GB3096-2008 Acoustic environmental quality standards	ISO 7726:1998 Ergonomics of the thermal environment – Instruments for measuring physical quantities
GB/T34828-2017 Acoustic free field environmental assessment test method	ISO 11399:1995 Ergonomics of the thermal environment – Principles and application of relevant International Standards
GB9660-1988 Environmental standards for aircraft noise around airports	ISO 10551:1995 Ergonomics of the thermal environment – Assessment of the influence of the thermal environment using subjective judgement scales
GB16710.1-1996 Construction machinery noise limit	ISO 7243:1989 Hot environments – Estimation of the heat stress on working man, based on the WBGT-index (wet bulb globe temperature)

The aircraft cockpit environmental factor index evaluation system constructed in this paper first divides the objects that affect the overall comfort of the cabin environment into three components (i.e., subsystems): thermal environment, light environment, and acoustic environment. And then each subsystem is divided into detail. Determine the indicators of each sub-level, including both quantitative indicators and qualitative indicators, and finally get a hierarchical structure diagram. Combined with the above domestic and international airworthiness standards, the first-level indicators of environmental factors in the aircraft cabin such as acoustic environment, light environment, thermal environment, and other micro-environments are summarized. The secondary indicators are summarized as: weighted sound pressure level, noise duration, equivalent continuous A sound level, speech interference level, noise evaluation level, noise pollution level, luminance level, brightness contrast, lighting clarity, lighting uniformity, prevention glare, emergency lighting, color temperature, diffuse reflection, light color coordination, light color adaptability, air temperature, air humidity, radiation temperature, PMV-PPD, air velocity, flow field velocity, airflow direction, pressure, gravity acceleration, ventilation, and air age. Based on the above indicators, an indicator system of environmental factors in the aircraft cockpit is constructed. As shown in Fig. 4.

Fig. 4

Aircraft cockpit environmental assessment index system.

3.2 The calculation result of index weight

In the comprehensive evaluation of the environmental factors of the aircraft cockpit, firstly, the weights of the multi-environmental factors in the cockpit are determined according to the analytic hierarchy process. Next, the questionnaires are made and the results are finally calculated by experts to obtain the weights of the various parameters of the multi-environmental factors in the cockpit. Because experts are required to score the relative importance of each index in the process of determining the weight, the members of the expert group for comprehensive evaluation should be determined first. Considering the specific situation of aircraft cockpit environmental assessment, 15 experts were invited from Northwest University of Technology and AVIC first aircraft design and Research Institute to form an expert group to analyze and score each index in the index system. When experts score, we draw the index weight information collection table of each index set for each layer of indicators. When filling in the form, experts should rank the importance of each index listed in the form according to their own understanding, and score the relative importance of each index after ranking according to Table 2 to complete the weight information collection of indicators at all levels.

Table 2
r_kassignment

r _k Degree of importance

1.0 Index x_k-1 and index x_k is of equal importance

1.2 Index x_k-1 ratio index x_k is slightly more important

1.4 Index x_k-1 ratio index x_k is obviously important

1.6 Index x_k-1 ratio index x_k is strongly important

1.8 Index x_k-1 ratio index is extremely important

r _k	Degree of importance
1.0	Index x_k-1 and index x_k is of equal importance
1.2	Index x_k-1 ratio index x_k is slightly more important
1.4	Index x_k-1 ratio index x_k is obviously important
1.6	Index x_k-1 ratio index x_k is strongly important
1.8	Index x_k-1 ratio index is extremely important

The expert data obtains the bottom element result conclusion value (weight) through statistics as 1, and the matrix dimension n: n = 4. The calculation matrix A is as formula (8): $A : [\begin{matrix} 1 & 5.0587 & 7.1778 & 7.117 \\ 0.1977 & 1 & 4.9504 & 4.414 \\ 0.1393 & 0.202 & 1 & 0.4337 \\ 0.1405 & 0.2266 & 2.3058 & 1 \end{matrix}]$ (8)

Normalize matrix A by column to get a new matrix B as formula (9): $B : [\begin{matrix} 0.6768 & 0.7798 & 0.4651 & 0.549 \\ 0.1338 & 0.1541 & 0.3207 & 0.3405 \\ 0.0943 & 0.0311 & 0.0648 & 0.0335 \\ 0.0951 & 0.0349 & 0.1494 & 0.0771 \end{matrix}]$ (9)

Normalize the maximum eigenvector (weight) wT, calculate the geometric mean of each row of matrix A1, and then normalize to get the matrix: $[\begin{matrix} 0.636 & 0.2287 & 0.0527 & 0.0826 \end{matrix}]$ Where the process ranks Aw, [(A * w) T]: $[\begin{matrix} 2.759 & 0.9799 & 0.2233 & 0.3453 \end{matrix}]$ . Finally, a one-time CR solution, λmax = (∑(Aw/w))/n = 4.2602, RI = 0.89, n = 4, CI = (λmax-n)/(n-1)(4.2602-4)/(4-1) = 0.0867, CR = CI/RI = 0.0867/0.89 = 0.0975.

Through the above calculation, the original weight matrix of the multi-environment influencing factor index of the aircraft cockpit is obtained: λmax = 4.7165; CR = 0.2684; CI = 0.2388, the weight matrix used for calculation after correction: λmax = 10.1568; CR = 0.099; CI = 0.1446 after correction. Use the weight matrix as shown in Table 3.

Table 3

The initial weight value of each environmental factor in the aircraft cockpit

	Thermal	Light	Acoustic	Other	Weights
	environment	environment	environment	microenvironments
Thermal environment	1	5.0587	7.1778	7.117	0.636
Light environment	0.1977	1	4.9504	4.414	0.2287
Acoustic environment	0.1393	0.202	1	0.4337	0.0527
Other microenvironments	0.1405	0.2266	2.3058	1	0.0826

According to the above calculation method, the index of the factors affecting the thermal environment of the aircraft cockpit is obtained: λmax = 4.2561; CR = 0.0959; CI = 0.0854. The weight matrix for calculation after correction is shown in Table 4.

Table 4

Weights of thermal environment indicators in the aircraft cabin

	Air temperature	Air humidity	Radiation temperature	PMV-PPD	Weights (wi)
Air temperature	1	8.6991	7.6107	7.1646	0.7075
Air humidity	0.115	1	4.0022	2.2202	0.1524
Radiation temperature	0.1314	0.2499	1	1.229	0.0679
PMV-PPD	0.1396	0.4504	0.8137	1	0.0721

The index of the factors affecting the light environment of the aircraft cockpit is λmax = 11.3239; CR = 0.0987; CI = 0.1471. The weight matrix for calculation after correction is shown in Table 5.

Table 5

Weights of light environment indicators in the aircraft cockpit

	Illumination	Brightness	Illumination	Illumination	Anti-	Emergency	Color	Diffuse	Light and color	Light and color	Weights
	level	contrast	clarity	uniformity	glare	lighting	temperature	reflection	coordination	adaptability
Illumination level	1	3.3204	3.6514	7.2523	1.211	11.1445	8.4108	8.0405	8.4087	12.3148	0.289
Brightness contrast	0.3012	1	0.4169	4.638	0.7227	8.8341	9.7075	4.7786	9.1303	8.2437	0.1515
Illumination clarity	0.2739	2.3984	1	5.8868	3.7044	7.8873	7.3581	10.125	5.4875	11.8326	0.2202
Illumination uniformity	0.1379	0.2156	0.1699	1	0.2424	5.439	1.3997	5.1034	1.5424	8.1628	0.0558
Anti-glare	0.8257	1.3837	0.2699	4.1251	1	8.5958	8.8532	9.1908	7.7135	4.9778	0.1669
Emergency lighting	0.0897	0.1132	0.1268	0.1839	0.1163	1	0.5352	0.4581	0.3893	0.4686	0.0151
Color temperature	0.1189	0.103	0.1359	0.7144	0.113	1.8683	1	1.2887	5.1698	6.0244	0.0371
Diffuse reflection	0.1244	0.2093	0.0988	0.1959	0.1088	2.1829	0.776	1	1.4467	0.8553	0.0237
Light and color coordination	0.1189	0.1095	0.1822	0.6483	0.1296	2.5685	0.1934	0.6912	1	0.9851	0.0225
Light and color adaptability	0.0812	0.1213	0.0845	0.1225	0.2009	2.134	0.166	1.1692	1.0151	1	0.0183

The index of the factors affecting the acoustic environment in the aircraft cockpit is λmax = 6.5936; CR = 0.0942; CI = 0.1187. The weight matrix for calculation after correction is shown in Table 6.

Table 6

Weights of acoustic environment indicators in the aircraft cockpit

	Weighted sound	Noise	Equivalent continuous	Speech	Noise evaluation	Noise pollution	Weights
	pressure level	duration	A sound level	jammer	level	level
Weighted sound pressure level	1	2.8385	6.5368	6.9869	7.0995	8.7413	0.4458
Noise duration	0.3523	1	7.4197	5.5819	7.7326	8.9519	0.3154
Equivalent continuous A sound level	0.153	0.1348	1	0.3285	0.6553	3.4417	0.0496
Speech jammer	0.1431	0.1791	3.0442	1	4.0438	6.5052	0.1123
Noise evaluation level	0.1409	0.1293	1.5259	0.2473	1	3.6165	0.0538
Noise pollution level	0.1144	0.1117	0.2906	0.1537	0.2765	1	0.0231

The microenvironment influencing factor index of the aircraft cockpit is λmax = 7.8146; CR = 0.0998; CI = 0.1358. The weight matrix for calculation after correction is shown in Table 7.

Table 7

Weights of micro-environment indicators in the aircraft cockpit

	Air velocity	Flow velocity	Airflow direction	Pressure	Acceleration of gravity	Ventilation	Air age	Weights
Air velocity	1	5.0117	0.9096	0.4838	0.5853	0.4447	4.8434	0.1231
Flow velocity	0.1995	1	0.5018	0.2339	0.3953	0.1488	4.8997	0.0521
Airflow direction	1.0994	1.9929	1	0.3375	0.5187	0.4109	5.9976	0.1056
Pressure	2.0669	4.2748	2.9628	1	3.2899	3.7171	9.8018	0.3361
Acceleration of gravity	1.7086	2.5299	1.928	0.304	1	4.4578	8.8779	0.2055
Ventilation	2.2486	6.7221	2.4335	0.269	0.2243	1	6.6898	0.1564
Air age	0.2065	0.2041	1/6	0.102	0.1126	0.1495	1	0.0211

Through the above calculation, the weight table of the middle layer can be obtained as shown in Table 8.

Table 8

Weight table of the middle layer of multiple environmental indicators in the aircraft cockpit

Node	Global weight	Sibling weight	Superior
Thermal environment	0.636	0.636	Airplane cockpit
Light environment	0.2287	0.2287	environment influencing
Acoustic environment	0.0527	0.0527	factors index
Other microenvironments	0.0826	0.0826
Air temperature	0.45	0.7075	Thermal environment
Air humidity	0.0969	0.1524
Radiation temperature	0.0432	0.0679
PMV-PPD	0.0459	0.0721
Illumination level	0.0661	0.289	Light environment
Brightness contrast	0.0346	0.1515
Illumination clarity	0.0503	0.2202
Illumination uniformity	0.0128	0.0558
Anti-glare	0.0382	0.1669
Emergency lighting	0.0034	0.0151
Color temperature	0.0085	0.0371
Diffuse reflection	0.0054	0.0237
Light and color coordination	0.0051	0.0225
Light and color adaptability	0.0042	0.0183
Weighted sound pressure level	0.0235	0.4458	Acoustic environment
Noise duration	0.0166	0.3154
Equivalent continuous A sound level	0.0026	0.0496
Speech jammer	0.0059	0.1123
Noise evaluation level	0.0028	0.0538
Noise pollution level	0.0012	0.0231
Air velocity	0.0102	0.1231	Other microenvironments
Flow velocity	0.0043	0.0521
Airflow direction	0.0087	0.1056
Pressure	0.0278	0.3361
Acceleration of gravity	0.017	0.2055
Ventilation	0.0129	0.1564
Air age	0.0017	0.0211

To verify the consistency of the total ranking: the aircraft cockpit environmental impact factor index:

CR = (0.636018*0.0854 + 0.228689*0.1471 +0.0527261*0.1187 + 0.0825672*0.1358)/(0.636018*0.89+ 0.228689*1.49 + 0.0527261*1.26 + 0.0825672* 1.36) = 0.0971. The thermal environment CR = 0.0, the light environment CR = 0.0, the acoustic environment CR = 0.0, and the microenvironment CR = 0.0.

Through the above calculation, the group decision weight table is obtained as shown in Table 9.

Table 9

Weight table of multi-environmental indexes in aircraft cab

Node	Global weight	Sibling weight	Superior
Thermal environment	0.5588	0.5588	Airplane cockpit
Light environment	0.2293	0.2293	environment influencing
Acoustic environment	0.0933	0.0933	factors index
Other microenvironments	0.1186	0.1186
Air temperature	0.3799	0.6798	Thermal environment
Air humidity	0.0921	0.1648
Radiation temperature	0.0448	0.0801
PMV-PPD	0.0421	0.0753
Illumination level	0.0674	0.2942	Light environment
Brightness contrast	0.0376	0.1641
Illumination clarity	0.0502	0.219
Illumination uniformity	0.0168	0.0735
Anti-glare	0.0292	0.1275
Emergency lighting	0.0038	0.0166
Color temperature	0.0064	0.0279
Diffuse reflection	0.0058	0.0254
Light and color coordination	0.0065	0.0282
Light and color adaptability	0.0054	0.0237
Weighted sound pressure level	0.038	0.4068	Acoustic environment
Noise duration	0.0311	0.3329
Equivalent continuous A sound level	0.0035	0.0379
Speech jammer	0.0084	0.0899
Noise evaluation level	0.0088	0.0946
Noise pollution level	0.0035	0.0379
Air velocity	0.0159	0.1344	Other microenvironments
Flow velocity	0.0062	0.0522
Airflow direction	0.0105	0.0889
Pressure	0.0443	0.3736
Acceleration of gravity	0.0216	0.1825
Ventilation	0.0179	0.151
Air age	0.0021	0.0174

3.3 Results of the fuzzy comprehensive evaluation of indicators

According to the fuzzy comprehensive evaluation method given in 2.2.1 of this study, combined with the evaluation results of 20 questionnaires, the evaluation vector of each environmental factor is obtained. Determining the rating weighting vector is used to distinguish the difference between the good and the bad of the comprehensive evaluation result. This article uses a percentile system to determine (1,20) as unimportant, (20,40) as less important, (40,60) as general, (60,80) as more important, and (80,100) as important; take the median to get the rating weight vector F = (10,30,50,70,90).

The evaluation vector of the thermal environment is obtained by calculation: $\begin{matrix} B_{1} = a_{1} * R_{1} = (0.6798 0.1648 0.0801 0.0753) * \\ (\begin{matrix} 0.00 & 0.00 & 0.05 & 0.40 & 0.55 \\ 0.00 & 0.00 & 0.35 & 0.35 & 0.30 \\ 0.00 & 0.05 & 0.30 & 0.45 & 0.20 \\ 0.00 & 0.05 & 0.40 & 0.30 & 0.25 \end{matrix}) \end{matrix}$ (10)

Evaluation vector of light environment: $\begin{matrix} B_{2} = a_{2} * R_{2} = \\ (\begin{matrix} 0.2942 & 0.1641 & 0.219 & 0.0735 & 0.1275 \\ 0.0166 & 0.0279 & 0.0254 & 0.0282 & 0.023 \end{matrix}) \\ * (\begin{matrix} 0.00 & 0.00 & 0.10 & 0.50 & 0.40 \\ 0.00 & 0.00 & 0.30 & 0.55 & 0.15 \\ 0.00 & 0.00 & 0.20 & 0.50 & 0.30 \\ 0.00 & 0.05 & 0.30 & 0.45 & 0.20 \\ 0.00 & 0.10 & 0.25 & 0.40 & 0.25 \\ 0.00 & 0.15 & 0.10 & 0.55 & 0.20 \\ 0.00 & 0.25 & 0.25 & 0.40 & 0.10 \\ 0.00 & 0.20 & 0.35 & 0.30 & 0.15 \\ 0.00 & 0.00 & 0.20 & 0.50 & 0.30 \\ 0.00 & 0.10 & 0.35 & 0.45 & 0.10 \end{matrix}) \\ = (\begin{matrix} 0 & 0.03334 & 0.207835 & 0.483605 & 0.27532 \end{matrix}) \end{matrix}$ (11)

Evaluation vector of acoustic environment: $\begin{matrix} B_{3} = a_{3} * R_{3} = \\ (0.4068 0.3329 0.0379 0.0899 0.0946 0.0379) \\ * (\begin{matrix} 0.00 & 0.10 & 0.30 & 0.35 & 0.25 \\ 0.00 & 0.00 & 0.25 & 0.45 & 0.30 \\ 0.00 & 0.05 & 0.35 & 0.40 & 0.20 \\ 0.00 & 0.00 & 0.25 & 0.60 & 0.15 \\ 0.00 & 0.10 & 0.25 & 0.55 & 0.10 \\ 0.00 & 0.15 & 0.30 & 0.50 & 0.05 \end{matrix}) \\ = (00.057720.2760250.4322650.23399) \end{matrix}$ (12)

Evaluation vector of microenvironment: $\begin{matrix} B_{4} = a_{4} * R_{4} = \\ (0.1344 0.0522 0.0889 0.3736 0.1825 0.151 0.0174) \\ * (\begin{matrix} 0.05 & 0.10 & 0.35 & 0.50 & 0.00 \\ 0.00 & 0.10 & 0.20 & 0.65 & 0.05 \\ 0.10 & 0.10 & 0.40 & 0.35 & 0.05 \\ 0.00 & 0.00 & 0.25 & 0.55 & 0.20 \\ 0.00 & 0.05 & 0.20 & 0.60 & 0.15 \\ 0.00 & 0.15 & 0.30 & 0.45 & 0.10 \\ 0.15 & 0.05 & 0.80 & 0.00 & 0.00 \end{matrix}) \\ = (0.01822 0.060195 0.28216 0.515175 0.12425) \end{matrix}$ (13)

Evaluation vector of fuzzy comprehensive evaluation: $\begin{matrix} z = (0.5588 0.2293 0.0933 0.1186) \\ * (\begin{matrix} 0.00000 & 0.00777 & 0.14582 & 0.388235 & 0.458175 \\ 0.00000 & 0.03334 & 0.207835 & 0.483605 & 0.27532 \\ 0.00000 & 0.05772 & 0.276025 & 0.432265 & 0.23399 \\ 0.01822 & 0.060195 & 0.28216 & 0.515175 & 0.12425 \end{matrix}) \\ = (0.002160892 0.024511141 0.18835809 \\ 0.429266424 0.355726383) \end{matrix}$ (14)

The fuzzy comprehensive evaluation score is: $\begin{matrix} Score = 10 \times 0.002160892 + 30 \times 0.024511141 \\ + 50 \times 0.18835809 + 70 \times 0.429266424 + 90 \\ \times 0.355726383 = 72.2388712 \approx 72.24 \end{matrix}$ (15)

The results show that the comprehensive assessment results of the environmental factors in the aircraft cockpit are more important. At the same time raccording to the above method rthe scores of the first-level indicators and the second-level indicators are calculated as shown in Table 10.

Table 10

Score table of level 1/level 2 environmental indexes of aircraft cockpit

First-level index	Score	Secondary indicators	Score
Thermal environment	75.9363	Air temperature	80
		Air humidity	69
		Radiation temperature	66
		PMV-PPD	65
Light environment	79.0249	Illumination level	76
		Brightness contrast	67
		Illumination clarity	72
		Illumination uniformity	66
		Anti-glare	66
		Emergency lighting	66
		Color temperature	57
		Diffuse reflection	58
		Light and color coordination	72
		Light and color adaptability	61
Acoustic environment	66.8505	Weighted sound pressure level	65
		Noise duration	71
		Equivalent continuous A sound level	65
		Speech jammer	68
		Noise evaluation level	63
		Noise pollution level	59
Other microenvironments	63.3408	Air velocity	56
		Flow velocity	63
		Airflow direction	53
		Pressure	69
		Acceleration of gravity	67
		Ventilation	60
		Air age	43

4 Discussion

Using the fuzzy comprehensive evaluation method based on AHP rthe scores of various environmental indicators are obtained rand the indicators with higher scores in the second-level indicators are: Air temperature rIllumination level rLight and color coordination. In the first index rthe light environment and thermal environment scored higher. Although the importance of microenvironment in the primary index evaluation is low rthe scores of secondary indexes atmospheric pressure and gravitational acceleration are high rwhich should still be paid attention to in the follow-up research.

5 Conclusion

This research is based on the fuzzy comprehensive evaluation theory rcombined with analytic hierarchy process (AHP) and particle swarm optimization (PSO) to build an environmental factor evaluation model rand obtain the important environmental impact factors of the aircraft cockpit through calculation rwhich can provide important environmental control indicators for the aircraft cockpit environmental control system. The main conclusions are as follows:

1) The multi environmental factor evaluation system of aircraft cockpit is constructed.

2) From the above evaluation results rit can be seen that it is more important to perform fuzzy comprehensive evaluation of multiple environmental factors in the aircraft cockpit. Among the four first-level environmental indicators rthe light environment is the most important rthe thermal and acoustic environment is second rand the microenvironment is the lowest degree.

3) Among the twenty-seven secondary environmental indicators rair temperature rluminance level rlighting clarity rlight and color coordination rnoise duration rand atmospheric pressure are of higher importance.

4) The results show that the fuzzy comprehensive evaluation method has a good predictive ability to evaluate the multi-environmental factors of the aircraft cockpit.

5) Through the above results rthe importance ranking of the environmental factors in the aircraft cockpit can be obtained rwhich can provide an analytical basis for the subsequent research on the environmental control of the aircraft cockpit rand at the same time can provide an index basis to improve pilot’s comfort and work efficiency.

Inadequacies remain in the consideration of some problems in the construction of the comprehensive evaluation index system and model of the aircraft cab environment rwhich need further study. In view of these deficiencies rthis paper proposes the following prospects: Firstly rthe multi-environment comprehensive evaluation index system of aircraft cab only evaluates the physical environment factors of aircraft cab rit does not consider the human-machine interface (HMI) environmental factors of aircraft cab. Secondly rthe dimension of the selected environmental grade index is low and the calculation amount is small. If there are too many indicators at a certain level rwhether this method can be used for real-time evaluation needs further research and testing. Finally rthe selected evaluation method is affected by the subjective knowledge and experience of experts. Due to persistence limitations in this study rfurther research could focus on optimization and addressing the limitations.

Footnotes

Acknowledgments

The authors have no acknowledgments.

Conflicts of interest

The authors declare that they have no conflict of interest.

Funding

This work was sponsored by the Fundamental Research Funds for the Central Universities (Project No. 31020190504004).

Ethical approval

Not applicable.

Informed consent

Not applicable.

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