A genetic algorithm approach for optimization of machinery noise calculations

Abstract

Noise produced by various noise sources in the mines is considered as a serious environmental problem. Exposure to such noise levels is considered as hazardous to workers working in such conditions. Noise assessment was exercised in a highly mechanized opencast bauxite mine, located in eastern India according to the Director General of Mines Safety Technical Circular No. 18 of 1975 and No.5 of 1990. There are numerous approaches in the literature on machinery noise prediction based on statistical models, soft computing techniques such as fuzzy inference system, artificial neural networks, support vector machines, adaptive neuro fuzzy inference system and other classification methods. The main drawback of statistical models, fuzzy inference system, artificial neural network, support vector machine and adaptive neuro fuzzy inference system is lack of interpretation for human and optimization issues. An attempt has been made to examine the applicability of a genetic algorithm, to take the advantage of genetic structures to find an optimal sound pressure level of the machinery noise taking into consideration the distance, directivity index, sound power level and other attenuation parameters under several noisy operating conditions according to ISO 9613-2:1996, ISO 6395:2008 and other related standards. Genetic algorithm used in this article has several advantages: it can be applied for low, high and dynamical system and uses a simple procedure to determine the order and the parameters with high accuracy. Genetic algorithm model is trained and tested in MATLAB to find the optimum parameters. Experimental results show that genetic algorithm is able to converge and find the optimum values faster along with acceptable computational time. By comparing the predicted values with the measured values, it proves the effectiveness of the proposed model as a useful and efficient method for machinery noise optimization problems.

Keywords

Genetic algorithm machinery noise CPU time sound pressure level mutation variants stochastic optimization

Introduction

Noise is considered as one of the most potential hazards and an environmental issue associated with the generation of higher noise levels from the workplaces. Noise produced from the industries is the most prevalent noise source and is considered as a global health issue.¹ Noise levels of the noise sources are measured to study the impact of noise on the miners at their working environments. Exposure to high noise levels at workplace is associated with hearing loss which at first causes temporary hearing problem termed as ‘Temporary Threshold Shift (TTS)’. It may result in permanent hearing damage termed as ‘Noise-Induced Permanent Threshold Shift (NIPTS)’ if exposure to higher noise levels is continuous over an extended period of time. In February 2011, the Central Government of India has announced noise-induced hearing loss (NIHL) as ‘notified disease’ under the Mines Act 1952. Henceforth, monitoring of noise sources is required, especially where heavy machineries are being utilized for a long period and producing high noise levels. Noise levels were calculated in decibels in A-weighted scale as recommended by the International Organization for Standardization (ISO) and Director General of Mines Safety (DGMS).

The impact of noise in the mines relies on sound power level (SWL) of the noise sources, mining conditions and meteorological parameters.² The sound pressure level (SPL) values should be considered as an integrated effect of the mentioned parameters. In mining situations, frequent change in the environment occurs due to mine advancement.³ Overall noise levels of the mine vary depending on the placement of the stationary and moving noise sources. Noise level at the receiver point is considered as the resultant SPL of all the noise sources, in all the noise prediction models. The need for predicting the SPL produced in the mines is well established. Data measured by sound level measurements can be examined, using various noise prediction models such as VDI-2714, ENM and ISO 9613-2. These statistical models are largely used to estimate noise in the mines and its allied industries.^3,4

Algorithm utilized as a part of these models depends for a larger part on measured data, which is a legitimate and beneficial method; however, their applications are constrained to sites which are more or less alike to those for which the measured data were integrated.³ Numerous models were developed and broadly utilized for the evaluation of SPL and their attenuation in and around industrial complexes.² The use of various noise prediction models was examined for numerous mines and petrochemical complexes, and it was reported that the ISO 9613-2 model was the better model vis-à-vis other models. VDI-2714 and ISO 9613-2 noise prediction models were utilized as a part of a cement plant of Egypt to predict noise.³ From the study, it was inferred that the prediction models could be utilized to distinguish the safe zones with respect to the SPL values in the mining and industries.^2–4 It was also concluded that the ISO 9613-2 model is the better model for prediction of noise in mining industries and other workplaces. All the noise prediction models consider noise as a function of distance, SWL and various attenuation factors. These parameters are measured at the mines and best models are applied to predict the machinery noise. Statistical models are complex and cannot be implemented in real-time systems as they fail to predict the future from present and previous measurements.² Soft computing techniques such as Mamdani fuzzy inference system (FIS), Takagi–Sugeno–Kang (TSK) FIS, artificial neural networks (ANNs) and adaptive neuro FIS (ANFIS) have been applied for prediction for a long time. This incredible development has enhanced traditional technologies in numerous engineering applications. Nanda et al.² worked on FIS-based noise prediction models for forecasting far-field noise levels of opencast mining machinery operations. Their results showed that the TSK-FIS model gave better results compared with Mamdani FIS model.²

ANNs are known to have the ability to be used as a part of data classification in addition to noise level predictors.^5–7 Genaro et al.⁸ demonstrated an immense potential in foreseeing environmental noise level with minute errors. They contemplated on noise data collected from various sources and utilized ANN in their investigation.⁹ Results obtained by them were enriched by ANN models as their error is less than 2% compared with standard model’s error which is above 5%.⁹ Kumar et al.¹⁰ considered the prediction of noise with numerous strategies and compared with ANN models. Results obtained by them showed that ANN models are more accurate and compelling than other deterministic and statistical models.¹⁰ Hashmienejad and Hasheminejad¹¹ found that ANNs and support vector machines (SVMs) outperform others in terms of accuracy and have a good ability to predict and classify the data. Numerous models were developed and extensively used for the assessment of SPL but less number of studies were carried out in finding the optimum noise levels.²,⁴,¹² One of the applicable techniques to analyse the measured data is to model the SPL of various noise sources using genetic algorithm (GA).¹³ Mahesh et al.¹⁴ found that optimization carried out using GA yields the best optimal solution. Recent studies conducted by Liu et al.,¹⁵ Majdi et al.¹⁶ and Rashidian et al.¹⁷ describe the efficiency of GA in enhancing the ANN performance and improving its drawbacks.

Evolutionary computing (EC) is an exciting development in computer science. It amounts to building, applying and studying algorithms based on Darwinian principles of natural selection. GAs are a family of computational models developed by Holland in 1975. In the last decade, approaches based on GA have received increased attention from the academic and industrial communities for dealing with optimization problems that have been shown to be intractable using conventional problem-solving techniques.¹⁸ A typical task of a GA is to find the best values of a predefined set of free parameters associated with either a process model or a control vector.¹⁹ Recent surveys of GAs, relating to improvements in the search process with respect to control system engineering problems, can be found. GA has also been used extensively to optimize nonlinear systems. GA is utilized to analyse the measured data and to model the SPL of various noise sources to address this nonlinear and non-convex problem. GAs are powerful global search optimization algorithms and have been used to solve various problems in control and system identification having the following advantages: it requires few control variables, global optimum value, fast convergence, easy to use and advances exceptionally well in parallel computation.¹²,^20,21 In this article, an attempt has been made to develop GA for optimization of noise levels of machineries used in a highly mechanized bauxite mine of India. The GA uses lower bounds and upper bounds of experimental data, which is an effective and advantageous technique for optimizing SPL in opencast mines.

The article is structured as follows. Study area is shown in section ‘Study area’. Materials and methods are presented in section ‘Materials and methods’. Optimization of SPL using GA is provided in section ‘GA: an overview’ followed by results and discussions in section ‘Experimental results’ and conclusion in section ‘Conclusion’.

Study area

The highly mechanized bauxite mine situated in eastern India is shown in Figure 1. It has produced 60 million tonnes of bauxite during 2015–2016 and has dispatched 58 million tonnes. It has a vast deposit containing over 300 million tonnes of reserve and is a leading front-runner for the bauxite exploitation in the east cost of India. Current annual production is about 6.3 million tonnes of bauxite per annum and is under expansion. There are three production benches of 6 m each. Shovels of 6.5 m³ capacity in combination with dumpers of 55 and 50 tonnes were deployed for loading and transportation of the blasted material to the crushing plants. The crushed ore was then conveyed with a downhill conveyor system to the refinery. Approximately 500 workers were involved in the mining-related activities in the opencast bauxite mine. There were three shifts, where each shift runs for about 8 h and the workers spend 6–8 h a day in the noisy work place.

Figure 1.

Location of highly mechanized bauxite mine in India.

Materials and methods

Assessment of machinery noise level

Noise pollution is composed of many individual noise sources in the mines. Individual machinery noise can be attributed to its components, which can be classified into engine noise, exhaust noise, transmission, tyre–road interaction, aerodynamics, body and road rattle. Noise levels were calculated in decibels in A-weighted scale as recommended by the ISO 1996-2:2007 and DGMS standards.^22–24 Noise measurements were carried out according to ISO 9613-2:1996 (Acoustics − description, measurement and assessment of environmental noise) and other related standards.^25,26 The study was carried out at heavy noise level zones of the mine. The A-weighted SPLs were measured using Extech Type-1 real-time octave-band analyser with an accuracy of ±1 dB, with desired response set to slow (model: 407790) at various frequencies between 25 Hz and 10 kHz in A-weighted scale as recommended by the acoustic standard.^25,26 All the noise levels were measured in L_eq as specified by the 1996-2:2007, which has recognized L_eq as an international standard for measuring environmental noise in 1978.²⁶ The equivalent A-weighted L_Aeq has been calculated using the following equation

L_{A e q, T_{m e a s}} = 10 \log [\frac{1}{n} \sum_{(i = 1)}^{n} (10^{0.1 L_{p A i}})]

(1)

where $L_{p A i}$ is the A-weighted SPL in decibels for sample i, and n is the total number of samples collected within $T_{m e a s},$ the duration of the time intervals.

ISO 9613-2:1996 SPL objective function

The evaluation unit of standards for environmental noise in India is A-weighted equivalent sound level, L_eq. Noise measurement and SPL at a particular point with the necessary attenuation factors have been authenticated with ISO 9613-2:1996, using equation (2). The operation of the proposed algorithm has been explained and computed using the step-by-step procedure in Algorithm 1²²,^25–28

L_{f T} (D W) = L_{w} + D_{c} - A

(2)

where $L_{f T}$ is the equivalent continuous downwind octave-band SPL at any receiver point, $L_{w}$ is the octave-band SWL, $D_{c}$ is the directivity correction in decibels and A is the octave-band attenuation. The attenuation term A in equation (2) is given by equation (3)

A = A_{d i v} + A_{a t m} + A_{g r} + A_{b a r} + A_{m i s c}

(3)

where $A_{d i v}$ is the attenuation due to geometrical divergence, $A_{a t m}$ is the attenuation due to atmospheric divergence, $A_{g r}$ is the attenuation due to ground effect, $A_{b a r}$ is the attenuation due to barrier and $A_{m i s c}$ is the attenuation due to other miscellaneous effects.

Algorithm 1. SPL algorithm using ISO 9613-2:1996
Step 1: Determination of SWL
Step 2: Compute $D_{c}$
Step 3: Compute $A_{d i v}$
Step 4: Compute $A_{a t m}$
Step 5: Compute $A_{g r}$
Step 6: Compute $A_{b a r}$
Step 7: Compute $A_{m i s c}$
Step 8: Compute the resultant SPL using equation (1)
Step 9: End

GA: an overview

As traditional methods are not optimal to solve nonlinear and complex problems, GA is the best population search-based technique. It is different from traditional optimizations in the following ways:¹⁸

GA searches solution space through a group of points and not from a single point;

GA uses information of the objective or fitness function which influences the directions of search, not derivatives or other auxiliary knowledge;

GA uses probabilistic transition rules, not deterministic rules;

It is very likely that the expected GA solution will be a global solution.

GA is an evolutionary optimization approach based on random search algorithms and developed by Holland in 1975. GA is very popular combinatorial optimization method due to its robustness for complex and nonlinear problems. GA has numerous advantages over other classical optimization methods. In order to obtain better solutions, various genetic operators such as selection, mutation and crossover have been implemented in the algorithm. GA is a heuristic global optimization method based on the biological principle of natural selection, where the strongest individuals will survive and reproduce. In the GA, the individual parameters are encoded as strings of numbers called chromosomes, so, for example, one chromosome will contain a value for each of the parameters being investigated. The process starts by creating a random population of potential solutions; these are then evaluated using a fitness function. The algorithm can easily converge to good if not the best solution faster than other classical approaches. The basic steps of the GA working principle are as follows: First, the algorithm initializes a population of possible solutions and then applies the selection, crossover and mutation operators, respectively. The evaluation function is calculated for each candidate solution. After eliminating bad solution from population, new population is created again using GA operators and the working mechanism proceeds until stopping criterion is satisfied. GA requires defining of three parameters: population size (NP), mutation factor (F) and crossover ratio (C).²⁹ Convergence speed and CPU time play a vital role in evaluating the effectiveness of the algorithm and less number of studies have been done on this. Present work evaluates and compares the speed of convergence and performance characteristics among various mutation variants of GA algorithm. Figure 2 shows the various stages of the GA adopted for the present optimization purpose. In the sequel, each block in Figure 2 will be explained and expanded in more detail, to tailor the algorithm to the specific problem at hand. Algorithm 2 gives the pseudo-code of the GA.

Figure 2.

Various stages of genetic algorithm.

Algorithm 2. Genetic algorithm
Input: Formalization of solution
Random initialization of a population of chromosomes (population size)
Evaluate the fitness of each chromosome
Select chromosomes for reproduction using a selection outline
Apply crossover and mutation operators
Replace several chromosomes in the existing population by the newly generated offspring via a replacement scheme.
Repeat steps 2–5 until the stopping criteria are met (e.g. the number of iterations is performed or the adequate fitness is reached)

Proposed solution approach using GA

A typical SPL string structure is presented in Figure 3. The parameters of GA are shown in Table 1. The flowchart for the overall optimization process using GA is shown in Figure 4. The operation of the proposed algorithm has been explained with a step-by-step procedure in Algorithm 3.

Figure 3.

A typical string for GA.

Table 1.

Parameters of genetic algorithm.

NP (population size)	D (size of the string)	F (mutation factor)	C (crossover ratio)	Generations
50	7	0.01	0.3–1.0	100

Figure 4.

Optimization process using genetic algorithm.

Population initialization

Initial population was randomly selected. Population size is the number of chromosomes in each generation and it was an important parameter to increase the performance of GAs.

Fitness function

The aim of this study is to make a prediction according to ISO 9613-2:1996, using equation (1) with minimum error. Authors have tried to minimize deviations from actual data, created the fitness function and calculated SPL using equation (1).

Selection

Selection is a significant part of the evolutionary algorithm to reach the best chromosomes. The selection operator chooses chromosomes from mating pool according to GA’s working principle, ‘the fittest individuals have a greater chance of survival than weaker ones’. Roulette wheel is utilized for a probabilistic selection.

Crossover

Crossover operator provides new offspring for the next generation by exchanging information between randomly selected two parent chromosomes which is represented in Figure 5. Diversification is very important in GA, and crossover provides much superiorities to GA in terms of exploration and diversification abilities to achieve global optimum point. In this work, we have used crossover with a crossover probability, C.

Figure 5.

Representation of crossover procedure for D = 7 parameters.

Mutation

Mutation operator was utilized to obtain new genetic information by modifying the genes of a chromosome selected with a mutation probability, F. Mutation is a divergence operation that provides avoiding local optima in the search space.

Termination

Authors used two different stopping criteria. The first termination criterion was selected using the maximum number of iterations, and the second was decided according to the improvement in the fitness function. If there is no improvement in the last improved solution’s fitness function after a prescribed number of iterations, then the algorithm is stopped.

Pseudo-code

The pseudo-code for Algorithm 3 is as follows.

Algorithm 3. GA optima for machinery noise
Input: Number of population/population size (NP), size of the string (D), maximum number of generations (maxgen), mutation factor (F), crossover ratio (C) and GA parameters Output: Best optimum solution
Begin
Initialize
Initialize the GA parameters: number of population/population size (NP), size of the string (D), maximum number of generations (maxgen), mutation factor (F), crossover ratio (C) and GA parameters; Initialize the number of population (NP) = 50, size of the string (D) = 7, maximum number of generations (maxgen) = 50, mutation factor (F) = 0.01 and crossover ratio (C) = 0.3;
Evaluate population
While (not termination condition) do
Selection: fitness proportionate selection
Crossover: with probability C
Mutation: with probability F
Optimum value reached Y/N
Get new population
Evaluate new population
End
Select the best optimal values of the specified parameters
End

Both the experimental data and the simulation data were sampled at 0.01 s intervals, and each point of the measurement data was compared against the corresponding point in the simulating data to find the difference between the two.

The mutation, crossover and selection operations were subjected to repetition in every generation till the population gets converged or reaches an optimum value. The control parameters of GA (NP, F and C) were chosen in advance and kept constant during the search of the algorithm.³⁰ The pseudo-code description of GA is presented in Algorithm 1.

Evaluation of GA optimization results

The selection of the parameters for optimization maximizes the SPL. In this study, an effort has been made to determine the optimum values of the parameters to obtain the best possible SPL value within the specified range. The maximization of the SPL using GA can be expressed as follows:

Maximize: SPL (SWL, $D_{c}$ , $A_{d i v}$ , $A_{a t m}$ , $A_{g r}$ , $A_{b a r}$ , $A_{m i s c})$

Within the ranges of the parameters: 70 ⩽ SWL ⩽ 130, 10 ⩽ $D_{c}$ ⩽ 50, 0.06 ⩽ $A_{d i v}$ ⩽ 0.07, 0 ⩽ $A_{a t m}$ ⩽ 4, −3 ⩽ $A_{g r}$ ⩽ 2, 0 ⩽ $A_{b a r}$ ⩽ 0 and 0 ⩽ $A_{m i s c}$ ⩽ 0

To obtain the best optimal results, the major consideration must be given to the number of the initial population size, type of selection function, crossover rate and mutation rate. No proper guidelines are given by the researchers, which could be followed to recommend the correct combination of the parameters for the best optimal result. By solving the optimization problem, GA predicted the optimum SPL as 118 dB (A) in the specified condition range. The GA-predicted SPL value (best fitness function) is expected to be very close to the optimized value of the experimental and regression models.

Validation of the model

The performance of the models developed for predicting L_eq using the soft computing methods has been evaluated using root-mean-square error (RMSE). RMSE is a measure of difference between the measured and the predicted values. It is a sample standard deviation of the differences between the observed values and those predicted by the model. These are called residuals when the differences are calculated for the sample (called in-sample) points that were used to make the model and prediction errors when the calculations are done for out-of-sample data points. RMSE is calculated using equation (4)

R M S E = \sqrt{\frac{1}{n} \sum_{i = 1}^{n} {(P r e d i c t e d - M e a s u r e d)}^{2}}

(4)

Figure 6 shows the comparison of predicted versus experimental value of the SPL. The GA-predicted optimum conditions were further validated with physical measurements. The percentage of error is found to be within ±1.5 dB (A) which shows the validity of the model. The experimental results of the SPL with the optimum parameters predicted by GA show good agreement. Figure 7 shows the performance of fitness value with generation and the best individual performances of variables in coded form.

Figure 6.

Graph showing the measured and predicted SPL values of a dozer.

Figure 7.

Convergence of GA during the first 50 generations for various crossover values.

Ten-fold cross validation

In this type of cross validation, generally known as k-fold cross validation, the data set is divided into k number of folds, also termed as sub-samples, which are used for prediction error. This is done 10 times in a 10-fold cross-validation exercise. So, all the data sets are used for calculating the prediction error. The 10-fold cross validation thus provides a measure for the stability of the model.

Experimental results

Training phase of the algorithm

Further to the fitness function and the coding scheme explained in the previous section, the performance of the GA in finding the best estimation for parameters of the developed model was heavily influenced by several other factors, namely, crossover rate, crossover type, mutation rate and population length. With the aim of finding the best estimate of parameters for the developed nonlinear model, it was necessary to train the GA and find the best possible parameters for this specific problem.

The reason for this was that it allows looking at the estimated value of the parameters outputted by the GA and shows how close they were to the real values. It also makes clear under what circumstances the algorithm has the capability to converge to the real values of the parameter, rather than getting stuck in a different global optimum point.

Evaluation of different crossover rates

The proposed algorithm was employed to determine the optimal value of the SPL. GA used the following parameters to find the global optimal value. Population size, NP, was set to 50; crossover ratio, C = 0.3; mutation factor, F = 0.01; number of parameters, D = 7; and maximum number of generations, maxgen = 50. When the programme is executed for various combinations of NP, C and F, the optimal set of parameters is determined based on three factors: objective function value, number of generations to reach the optimum value and CPU time.¹²,^20,21

The result of running the GA for different crossover values while the other parameters were set constant according to Table 10 is shown in Figure 7. As can be seen from Figure 7, the crossover rate has considerable effect on the speed of convergence of the GA. A crossover value of 1 means that at every iteration, all the parent chromosomes will create new child chromosomes, so every iteration will contain different chromosomes to the one before. Crossover values of 0.3 and 0.7 take almost the same time to converge, and despite 0.6 having the higher initial value of fitness, it converges to the lowest value, suggesting that a crossover value of 0.6 gives the best performance in this particular case. In fact, with this crossover value, the best compromise is to keep a balance between the diversity of populations and the need to force the output to determine the fittest individuals.

The average computational time is established on 50 different runs. As there is no single optimal solution which can simultaneously satisfy the goals, from test problems, it was found that strategy 4 performs better than the other strategies of GA and is shown in Tables 2 –10 and Figure 7.

Table 2.

Summary of GA during the different runs with crossover value 0.3 and mutation factor 0.01 (strategy 1).

S. no	Test condition	NP	D	C	F	Optimal value (dB (A))	No. of generations	Time taken (ms)
1	Run 1	50	7	0.3	0.01	118.070	17	0.81
2	Run 2	50	7	0.3	0.01	118.069	16	0.82
3	Run 3	50	7	0.3	0.01	118.068	16	0.81
4	Run 4	50	7	0.3	0.01	118.068	16	0.81
5	Run 5	50	7	0.3	0.01	118.068	16	0.81
6	Run 6	50	7	0.3	0.01	118.068	16	0.81
7	Run 7	50	7	0.3	0.01	118.068	16	0.81
8	Run 8	50	7	0.3	0.01	118.068	16	0.81
9	Run 9	50	7	0.3	0.01	118.068	16	0.81
10	Run 10	50	7	0.3	0.01	118.068	16	0.81

Table 3.

Summary of GA during the different runs with crossover value 0.4 and mutation factor 0.01 (strategy 2).

S. no	Test condition	NP	D	C	F	Optimal value (dB (A))	No. of generations	Time taken (ms)
1	Run 1	50	7	0.4	0.01	118.070	19	0.81
2	Run 2	50	7	0.4	0.01	118.069	19	0.82
3	Run 3	50	7	0.4	0.01	118.069	18	0.86
4	Run 4	50	7	0.4	0.01	118.067	18	0.82
5	Run 5	50	7	0.4	0.01	118.067	18	0.82
6	Run 6	50	7	0.4	0.01	118.067	18	0.82
7	Run 7	50	7	0.4	0.01	118.067	18	0.82
8	Run 8	50	7	0.4	0.01	118.067	18	0.82
9	Run 9	50	7	0.4	0.01	118.067	18	0.82
10	Run 10	50	7	0.4	0.01	118.067	18	0.82

Table 4.

Summary of GA during the different runs with crossover value 0.5 and mutation factor 0.01 (strategy 3).

S. no	Test condition	NP	D	C	F	Optimal value (dB (A))	No. of generations	Time taken (ms)
1	Run 1	50	7	0.5	0.01	118.071	19	0.88
2	Run 2	50	7	0.5	0.01	118.070	18	0.88
3	Run 3	50	7	0.5	0.01	118.070	18	0.86
4	Run 4	50	7	0.5	0.01	118.070	18	0.86
5	Run 5	50	7	0.5	0.01	118.070	18	0.86
6	Run 6	50	7	0.5	0.01	118.070	18	0.86
7	Run 7	50	7	0.5	0.01	118.070	18	0.86
8	Run 8	50	7	0.5	0.01	118.070	18	0.86
9	Run 9	50	7	0.5	0.01	118.070	18	0.86
10	Run 10	50	7	0.5	0.01	118.070	18	0.86

Table 5.

Summary of GA during the different runs with crossover value 0.6 and mutation factor 0.01 (strategy 4).

S. no	Test condition	NP	D	C	F	Optimal value (dB (A))	No. of generations	Time taken (ms)
1	Run 1	50	7	0.6	0.01	118.068	19	0.81
2	Run 2	50	7	0.6	0.01	118.067	19	0.82
3	Run 3	50	7	0.6	0.01	118.070	19	0.86
4	Run 4	50	7	0.6	0.01	118.068	18	0.79
5	Run 5	50	7	0.6	0.01	118.068	18	0.79
6	Run 6	50	7	0.6	0.01	118.068	18	0.79
7	Run 7	50	7	0.6	0.01	118.068	18	0.79
8	Run 8	50	7	0.6	0.01	118.068	18	0.79
9	Run 9	50	7	0.6	0.01	118.068	18	0.79
10	Run 10	50	7	0.6	0.01	118.068	18	0.79

Table 6.

Summary of GA during the different runs with crossover value 0.7 and mutation factor 0.01 (strategy 5).

S. no	Test condition	NP	D	C	F	Optimal value (dB (A))	No. of generations	Time taken (ms)
1	Run 1	50	7	0.7	0.01	118.090	22	0.81
2	Run 2	50	7	0.7	0.01	118.091	23	0.82
3	Run 3	50	7	0.7	0.01	118.068	21	0.81
4	Run 4	50	7	0.7	0.01	118.068	21	0.81
5	Run 5	50	7	0.7	0.01	118.068	21	0.81
6	Run 6	50	7	0.7	0.01	118.068	21	0.81
7	Run 7	50	7	0.7	0.01	118.068	21	0.81
8	Run 8	50	7	0.7	0.01	118.068	21	0.81
9	Run 9	50	7	0.7	0.01	118.068	21	0.81
10	Run 10	50	7	0.7	0.01	118.068	21	0.81

Table 7.

Summary of GA during the different runs with crossover value 0.8 and mutation factor 0.01 (strategy 6).

S. no	Test condition	NP	D	C	F	Optimal value (dB (A))	No. of generations	Time taken (ms)
1	Run 1	50	7	0.8	0.01	118.078	16	0.86
2	Run 2	50	7	0.8	0.01	118.076	18	0.84
3	Run 3	50	7	0.8	0.01	118.070	16	0.82
4	Run 4	50	7	0.8	0.01	118.070	16	0.82
5	Run 5	50	7	0.8	0.01	118.070	16	0.82
6	Run 6	50	7	0.8	0.01	118.070	16	0.82
7	Run 7	50	7	0.8	0.01	118.070	16	0.82
8	Run 8	50	7	0.8	0.01	118.070	16	0.82
9	Run 9	50	7	0.8	0.01	118.070	16	0.82
10	Run 10	50	7	0.8	0.01	118.070	16	0.82

Table 8.

Summary of GA during the different runs with crossover value 0.9 and mutation factor 0.01 (strategy 7).

S. no	Test condition	NP	D	C	F	Optimal value (dB (A))	No. of generations	Time taken (ms)
1	Run 1	50	7	0.9	0.01	118.068	16	0.88
2	Run 2	50	7	0.9	0.01	118.067	18	0.87
3	Run 3	50	7	0.9	0.01	118.067	14	0.86
4	Run 4	50	7	0.9	0.01	118.067	14	0.86
5	Run 5	50	7	0.9	0.01	118.067	14	0.86
6	Run 6	50	7	0.9	0.01	118.067	14	0.86
7	Run 7	50	7	0.9	0.01	118.067	14	0.86
8	Run 8	50	7	0.9	0.01	118.067	14	0.86
9	Run 9	50	7	0.9	0.01	118.067	14	0.86
10	Run 10	50	7	0.9	0.01	118.067	14	0.86

Table 9.

Summary of GA during the different runs with crossover value 1.0 and mutation factor 0.01 (strategy 8).

S. no	Test condition	NP	D	C	F	Optimal value (dB (A))	No. of generations	Time taken (ms)
1	Run 1	50	7	1.0	0.01	117.076	16	0.81
2	Run 2	50	7	1.0	0.01	119.075	18	0.82
3	Run 3	50	7	1.0	0.01	116.925	12	0.89
4	Run 4	50	7	1.0	0.01	116.925	12	0.89
5	Run 5	50	7	1.0	0.01	116.925	12	0.89
6	Run 6	50	7	1.0	0.01	116.925	12	0.89
7	Run 7	50	7	1.0	0.01	116.925	12	0.89
8	Run 8	50	7	1.0	0.01	116.925	12	0.89
9	Run 9	50	7	1.0	0.01	116.925	12	0.89
10	Run 10	50	7	1.0	0.01	116.925	12	0.89

Table 10.

Summary of results.

Strategy no.	Strategy	NP	D	C	F	Optimal value (dB (A))	No. of generations	Time taken (ms)
1	Strategy 1	50	7	0.3	0.01	118.068	16	0.81
2	Strategy 2	50	7	0.4	0.01	118.067	18	0.82
3	Strategy 3	50	7	0.5	0.01	118.070	18	0.86
4	Strategy 4	50	7	0.6	0.01	118.068	18	0.79
5	Strategy 5	50	7	0.7	0.01	118.068	21	0.81
6	Strategy 6	50	7	0.8	0.01	118.070	16	0.82
7	Strategy 7	50	7	0.9	0.01	118.067	14	0.86
8	Strategy 8	50	7	1.0	0.01	116.925	12	0.89

Final tune of the proposed algorithm

From the results achieved in the previous sections, it can be concluded that using the values in Table 4 should give the best performance for the GA. Figure 7 shows the final output after running the GA with these conditions. As the plot in Figure 6 shows, the measured values and the predicted values at various distances are nearly equal. However, further work is required to improve the estimation accuracy of the proposed algorithm.

Comparison between measured noise levels and predicted noise levels of dozer machinery noise was measured along straight line that could be viewed with a broad perspective from each measuring point. The straight line chosen for measurement had sound level metres measured at distances 1, 5, 10 and 25 m from the source. The height of microphones was 1.2 m from the ground level. Figure 6 shows the measured noise levels versus predicted noise levels. The solid straight line in the figure shows where the measured noise levels are equal to the predicted noise levels. And 95% of total data confirmed the error of this model to be within 1.5 dB (A).

Conclusion

Noise prediction and optimization of fixed or moving machineries is a class of interesting and essential problems in the mining sector. This article demonstrates the application of an ISO 9613-2 statistical model to GA, for SPL prediction and optimization of machinery operations in a bauxite mine. While conventional techniques work well with a few circumstances, they may fail miserably when the assumptions are not met. In the present work, a soft computing approach to develop machinery noise prediction model is presented. An overview of machinery noise parameters, the soft computing method used and the evaluation criteria of the model performance is also presented, for the benefit of the readers. The machinery noise prediction models are developed, with equivalent SPL, L_eq as the output (dependent variable) and the machinery noise variables, SWL, $D_{c}$ , $A_{d i v}$ , $A_{a t m}$ , $A_{g r}$ , $A_{b a r}$ and $A_{m i s c},$ as the independent variables. The 10-fold cross validation indicates the stability of the method. This article has exploited and refined a GA to estimate the parameters of the model using an output identification framework. This is accomplished in two steps. In the first step, the parameters of the GA, that is, coding scheme, crossover type, crossover rate, mutation rate and fitness function, are all tuned on the basis of simulation data. The results show that the developed GA has the capability to estimate the parameters of the dynamic model with a reasonable accuracy and the output of the model follows the simulated output closely. In the second step, the proposed GA is utilized to estimate the parameters of the model based on measured experimental data. Current study analysed the performance of various variants of GA, namely, strategy 1, strategy 2, strategy 3, strategy 4, strategy 5, strategy 6, strategy 7 and strategy 8, with the most commonly used and recommended setting for GA parameters. Based on the obtained results, it is evident from Tables 2 –10 and Figure 7 that the GA with strategy 4 variant enhances the working in terms of convergence, finding optimum value faster compared with the other variants without compromising the quality of the solution than the classical statistical ISO 9613-2 method.

This review utilized a cross-validation technique to assess the robustness of the algorithm. System robustness has vital managerial implications especially when the model is utilized for prediction purposes. The cross-validation procedure provides decision-makers with the best technique for examining predictive legitimacy. A significant part of the variety in results is related with the RMSE value. The accuracy of the developed prediction model is sufficient for practical use and will be used for environmental impact assessment in India. The accuracy of the model has been shown to be within 1.5 dB (A) range about 95% of the time and that it can predict the machinery noise level at a distance of 1–70 m and at a height of 1–5 m from the ground. Thus, the GA with strategy 4 seems to be a promising approach for engineering optimization problems. The soft computing approach for prediction modelling presented in this study has the potential of assisting the environmental managers in decision-making and policy formulation while dealing with various environmental problems. The model can also be useful in specific cases, for example, it can help mine planners and mine engineers in the design of suitable mitigation measures such as installing suitable barriers used for noise mitigating measures. The different methods presented in the study can be used for predicting the future scenario using the present data pertaining to an environmental problem of concern. The study also showcases the model which is more accurate, faster and cost effective. It can be used by environmental managers, policy- and decision-makers, and other stakeholders involved in environmental management.

Therefore, it is to suggest that the GA noise prediction model developed could be a valuable tool for engineers as a preparatory guide for assessing the environmental impacts of machinery operations.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship and/or publication of this article.

ORCID iD

DS Rao

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