Gasoline engine silencer design method based on multi-objective particle swarm optimization
By constructing a dual-objective function using a multi-objective particle swarm optimization method, the coupling contradiction between muffler and back pressure in the design of gasoline engine mufflers was resolved, achieving the global optimal solution for the muffler design, meeting engineering constraints and dynamic operating conditions, and improving the feasibility and stability of the design.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- CHINA AUTOMOTIVE ENG RES INST
- Filing Date
- 2026-01-23
- Publication Date
- 2026-05-08
AI Technical Summary
Existing gasoline engine muffler design methods have limitations due to their single-objective design, which cannot effectively resolve the coupling contradiction between muffler and back pressure. The objective function is incomplete, and the parameter coupling characteristics are ignored, resulting in a lack of engineering feasibility and cost balance, and failing to meet the comprehensive performance requirements under complex operating conditions.
A multi-objective particle swarm optimization method is adopted to construct a dual objective function that maximizes the transfer loss (TL) and minimizes the back pressure. By using particle swarm initialization, non-dominated sorting, and crowding screening, combined with a fuzzy logic dynamic matching mechanism, the design parameters of the muffler are optimized to ensure the global optimal solution under engineering constraints.
This method achieves the globally optimal solution for muffler design while satisfying noise reduction performance, back pressure, and cost constraints, avoids invalid solutions, improves the design success rate and the stability of actual vehicle operation performance, and breaks through the limitations of traditional methods.
Smart Images
Figure CN121997738A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of muffler design technology, and specifically to a gasoline engine muffler design method based on multi-objective particle swarm optimization. Background Technology
[0002] Driven by both automotive noise control and environmental regulations, gasoline engine muffler design has become a core technology for improving vehicle NVH performance and reducing emissions. However, existing gasoline engine muffler design methods have multiple technical limitations, making it difficult to meet the comprehensive performance requirements under complex operating conditions. The contradiction between single-objective and step-by-step design: Traditional solutions often adopt a step-by-step strategy of "silencing first - back pressure verification". After determining parameters such as silencer volume and expansion ratio through empirical formulas or single-objective optimization, the pipe size is then adjusted through fluid simulation to reduce back pressure. This mode leads to an irreconcilable strong coupling contradiction between silence and back pressure. For example, increasing the expansion ratio or the number of chambers can improve transmission loss (TL), but it will simultaneously increase the local drag coefficient and the resistance of the perforated pipe, resulting in excessive back pressure. Conversely, reducing back pressure may sacrifice silence performance, forming a zero-sum game of "silencing-back pressure".
[0003] Incomplete objective function: Existing optimization models often focus on the dual objective of "volume-transmission loss" or only consider the balance between "noise reduction performance and volume," without taking the back pressure threshold as a constraint or establishing an explicit mathematical model for back pressure and size parameters. This leads to invalid solutions in the Pareto solution set that "meet the volume and transmission loss requirements but exceed the back pressure requirements," or engineering-infeasible solutions that "optimize the transmission loss but have excessively high costs." For example, increasing the cavity diameter leads to a quadratic increase in material costs, and increasing the number of perforations leads to an increase in processing time.
[0004] Ignoring parameter coupling characteristics: Some methods employ a testing logic of "fixing other parameters and optimizing only a single variable." Therefore, we utilize electro-digital data processing technology to construct a muffler design optimization platform based on physical field coupling. For example, the independent tuning of the main pipe inner diameter and throat length completely ignores the strong interactions between various muffler design parameters. Such local optimization can only obtain the optimal parameter values under fixed operating conditions and cannot capture the global optimal solution under multi-parameter coupling, leading to significant performance fluctuations in actual operating conditions.
[0005] The lack of cost-performance balance: The objective function and constraints do not take cost factors into account, which means that some Pareto optimal solutions, although meeting the performance indicators, cannot be implemented in engineering due to excessive cost. Summary of the Invention
[0006] The present invention aims to provide a gasoline engine muffler design method based on multi-objective particle swarm optimization, so as to solve the technical problems that the existing technology cannot overcome the limitations of single-objective design and cannot cope with the contradiction between sound transmission loss and back pressure coupling.
[0007] To achieve the above objectives, the present invention adopts the following technical solution: a gasoline engine muffler design method based on multi-objective particle swarm optimization, comprising: Collect the core parameters of the gasoline engine and set the design constraints of the muffler, including noise reduction performance, back pressure, muffler space and muffler structure manufacturing cost. The optimization variables and multiple optimization objectives of the muffler design are determined, and an objective function is constructed to quantitatively map the optimization variables and objectives. The multiple optimization objectives include maximizing transmission loss (TL) and total back pressure. minimize; Initialize the parameters of the multi-objective particle swarm optimization algorithm, including the number of particles, the number of iterations, and the external archive capacity; uniformly and randomly generate the initial particle swarm within the constraint space, and perform a feasibility check, retaining only the particles that simultaneously satisfy the constraint conditions; Perform non-dominated sorting on the particle swarm, divide the particle swarm into multiple layers according to the dominance relationship, and store the non-dominated solution of the first layer into an external archive; take the particle with the highest crowding in the external archive as the global leader g_best, update the particle's velocity and position, and perform constraint verification on the updated particle again. If the constraint is satisfied, update the individual optimal solution p_best; otherwise, discard it. Repeat the sorting and updating iteration of non-dominated solutions of particles until the number of iterations reaches the initially set maximum number of iterations. Based on the capacity of the external archive, overflowing inferior solutions are eliminated by non-dominated sorting, and the non-dominated solutions in the external archive are output as the Pareto optimal solution set. By using a fuzzy logic dynamic matching mechanism and combining the dynamic operating parameters of the gasoline engine, the optimal solution for dynamic operating conditions is obtained.
[0008] The principle and advantages of this solution are as follows: it transforms engineering constraints such as noise reduction performance (TL≥15dB), back pressure (≤3kPa), space (volume≤2.5L), and cost (cavity≤4) into mathematical boundaries, replacing the fuzzy limitations of traditional empirical design. It avoids invalid solutions such as "sound transmission loss meets standards but back pressure exceeds standards" or "volume complies with regulations but cost is too high," ensuring that all solutions meet engineering feasibility requirements and overcoming the limitations of incomplete objective functions in existing technologies.
[0009] We construct a dual objective function that maximizes TL and minimizes back pressure, and quantify the relationship between the two through a mathematical model. This breaks the "zero-sum game" caused by single-objective optimization. For example, in traditional methods, increasing the expansion ratio improves the noise reduction effect, but it affects engine power due to the surge in back pressure. This solution finds the optimal trade-off point between the two through dual objective synergy, achieving a balance between "efficient noise reduction and low back pressure".
[0010] Global optimization of multiple parameters is achieved through particle swarm initialization, non-dominated sorting, crowding screening, and iterative updates. This overcomes the local optimum trap of traditional "single-variable testing" and captures the global optimum under multi-parameter coupling. For example, the impact of the interaction between perforation rate and pipe diameter on back pressure is accurately quantified through global search of the algorithm.
[0011] Using real-time gasoline engine parameters, such as RPM, torque, and exhaust flow, as input, a fuzzy rule base is used to map these parameters to the Pareto solution set. The "best match" solution is then selected to dynamically adjust the muffler parameters. This achieves full-condition adaptive operation—emphasizing muffler control at idle and back pressure control during high-speed cruising. This addresses the pain point of static optimization failing to adapt to dynamic conditions and improves the stability of real-vehicle performance.
[0012] Preferably, as an improvement, the constraints include transmission loss TL ≥ 15dB and total back pressure of the muffler. ≤3kPa, silencer volume ≤2.5L, number of silencer chambers ≤4.
[0013] The beneficial effects of this improvement are: by explicitly quantifying engineering constraints, muffler design shifts from "experience-driven" to "data-driven." For example, a back pressure ≤3kPa ensures unrestricted engine power output, a volume ≤2.5L adapts to vehicle space limitations, and the number of chambers ≤4 avoids excessive complexity leading to a surge in manufacturing costs. It directly avoids generating "invalid solutions"—such as solutions that might occur in traditional methods, like "TL meets the standard but back pressure exceeds the standard" or "volume complies with regulations but costs are too high"—ensuring that all solutions meet engineering feasibility requirements and improving the design success rate.
[0014] Preferably, as an improvement, the objective function includes a first objective function and a second objective function. First objective function: ; Wherein, 2πf / c is the basic component of wave number k, which is fully expressed by multiplying by the geometric relationship of exhaust pipe length L, where f is the sound wave frequency; m is the muffler expansion ratio; This refers to the cross-sectional area of the exhaust pipe inlet. This refers to the number of silencer chambers; This refers to the volume of the muffler; Second objective function: ; Where K is a constant and ε is the perforation rate.
[0015] The beneficial effect of this improvement is that it quantifies the "silencing-back pressure" coupling relationship through a mathematical model. The first objective function is based on the sound wave frequency f, exhaust pipe length L, and sound velocity c, constructing a wavenumber k expression for the transmission loss TL; the second objective function correlates back pressure and size parameters through a fluid dynamics model. This achieves synergistic optimization of the "silencing-back pressure" dual objectives, avoiding performance bias caused by single-objective optimization. For example, in traditional methods, increasing the expansion ratio improves TL but simultaneously increases back pressure; this scheme finds the optimal trade-off point between the two by balancing the dual objective functions.
[0016] Preferably, as an improvement, the initialization parameters of the multi-objective particle swarm optimization algorithm also include an inertial weight w and a learning factor; specifically, the number of particles is 80, the number of iterations is 80, the inertial weight w decreases linearly by 3 from 0.7 to 0.3 according to the number of iterations, the individual optimal weight and the global optimal weight are set to be equal to 2, the external archive capacity is 50, and the velocity boundary is a variable range of ±20%.
[0017] The beneficial effects of this improvement are: parameter settings are based on pre-experiment verification—80 particles ensure solution space coverage, and 80 iterations balance convergence speed and accuracy; the inertia weight w decreases linearly from 0.7 to 0.3, with a large w in the early stage enhancing global exploration and a small w in the later stage strengthening local convergence; c_1=c_2=2 ensures that particles refer equally to individual and group experiences, avoiding bias. This ensures a dynamic balance between "global exploration" and "local convergence" in the algorithm, avoiding premature convergence or getting trapped in local optima, and improving the quality and diversity of the Pareto solution set.
[0018] Preferably, as an improvement, in the non-dominated sorting layering of particles, the non-dominated sorting is divided into 3 layers, with the first layer having 22 non-dominated solutions, the second layer having 35 solutions, and the third layer having 23 solutions.
[0019] The beneficial effects of this improvement are as follows: Particles are divided into three layers through rapid non-dominated sorting: layer 1 contains 22 non-dominated solutions, layer 2 contains 35, and layer 3 contains 23. Layer 1 solutions are directly stored in an external archive set. When the archive exceeds 50 units, redundant particles are deleted based on their crowding level, with those having lower crowding levels being retained first. This layered mechanism prioritizes high-quality solutions, and the archive capacity limit avoids information overload. Crowding level filtering maintains the diversity of the solution set, ensuring a uniform distribution of the Pareto front and providing a high-quality solution pool for subsequent fuzzy matching.
[0020] Preferably, as an improvement, during the core parameter acquisition process, displacement... The error must be ≤ ±5%, and the error of the rated speed n must be ≤ ±100 rpm.
[0021] The benefits of this improvement are: High-precision sensors and calibration algorithms ensure the accuracy of input parameters, avoiding optimization deviations such as "garbage in, garbage out." It also enhances the reliability of optimization results—for example, excessive displacement errors may lead to muffler volume design deviations, affecting TL and back pressure calculations; precise parameter input ensures that the optimization model closely matches actual operating conditions.
[0022] Preferably, as an improvement, the core parameter includes displacement. Rated speed n, number of strokes T, number of cylinders N, speed of sound c, exhaust gas density ρ, and exhaust pipe inlet cross-sectional area .
[0023] The beneficial effects of this improvement are: it incorporates core parameters of the gasoline engine into the optimization model, constructing a full-link mapping relationship between "parameters and performance". For example, the speed of sound c and exhaust gas density ρ affect the sound wave propagation characteristics, thus affecting the TL calculation; the number of strokes T and the number of cylinders N are related to the engine exhaust characteristics, affecting the back pressure model. It achieves multi-parameter coupled optimization—traditional methods consider parameters in isolation, leading to local optima; this scheme, through parameter integration, captures the interactions between parameters to find the global optimal solution. Attached Figure Description
[0024] Figure 1 This is a flowchart of an embodiment of the present invention.
[0025] Figure 2 This is a schematic diagram of the internal pressure distribution of the silencer.
[0026] Figure 3 This is a schematic diagram of the velocity streamline distribution inside the muffler.
[0027] Figure 4 This is a schematic diagram of the internal velocity streamlines of the muffler under another example operating condition.
[0028] Figure 5 This is a schematic diagram of the three-dimensional structure of the exhaust pipe.
[0029] Figure 6 This is a schematic diagram of a one-dimensional discrete model of the exhaust pipe.
[0030] Figure 7 A schematic diagram of the muffler structure model and a one-dimensional discrete model.
[0031] Figure 8 This is a schematic diagram of a system-level model showing the coupling of the engine and exhaust system. Detailed Implementation
[0032] The following detailed description illustrates the specific implementation method: Example The basics are as follows: Figure 1As shown, a gasoline engine muffler design method based on multi-objective particle swarm optimization includes: S1. Collect the core parameters of the gasoline engine, including displacement. Rated speed n, number of strokes T, number of cylinders N, speed of sound c, exhaust gas density ρ, and exhaust pipe inlet cross-sectional area The core parameters can be obtained from gasoline engine technical manuals or bench tests.
[0033] During parameter acquisition, control the acquisition accuracy of core parameters. Displacement The error must be controlled within ±5%, and the error of the rated speed n must be ≤ ±100 rpm. The acquisition accuracy of core parameters is optimized through dynamic measurement specifications and data verification mechanisms.
[0034] For example, to obtain displacement To obtain accurate values, high-precision flow measurement equipment was used to measure the engine's exhaust volume multiple times under different operating conditions. Outliers were removed using statistical methods, and the average value was taken to ensure accuracy. The accuracy.
[0035] For the rated speed n, a high-precision speed sensor is used to continuously monitor and record speed data during stable engine operation to ensure that its accuracy meets the requirements.
[0036] S2. Set design constraints for the muffler, including noise reduction, back pressure, space, and cost. Noise reduction parameter constraints are designed according to national standards to constrain the performance of muffler noise reduction. Specifically, in accordance with GB1495-2021 "Limits and Measurement Methods for Exterior Noise of Automobiles During Acceleration" standard, and based on the Class B muffler noise reduction specifications, the muffler noise reduction design covers the 100-2000Hz frequency band, and within this frequency band, the transmission loss TL must meet TL≥15dB.
[0037] Optimizing the noise reduction design of a muffler can be achieved by selecting appropriate materials and optimizing the chamber layout, ensuring that the muffler has sufficient noise reduction capability in the specific frequency band to meet the relevant national standards for limiting vehicle exterior noise.
[0038] Back pressure parameter constraints ensure that the total back pressure of the muffler... ≤3kPa, to ensure engine power loss is controlled within 30%. Engine output power and fuel economy are controlled by adjusting engine back pressure.
[0039] Optimizing muffler back pressure can be achieved by optimizing the combination of parameters such as pipe diameter, length, and internal structure to ensure smooth exhaust and keep back pressure within a reasonable range, thus maintaining the engine's efficient operation.
[0040] Controlling the volume of the muffler By actually measuring the available space in the engine compartment, 20% of the available space in the engine compartment was used as the muffler volume. The upper limit is, for example, in this embodiment, the actual measured usable space in the engine compartment is 12.5L. Considering that other components need to be arranged in the engine compartment, 20% of the space is reserved as the volume of the muffler. The design upper limit, that is, the requirement that the muffler volume must meet... ≤2.5L.
[0041] When designing the shape and internal structure of a muffler, it is necessary to rationally arrange components such as chambers and pipes within a limited space, so as to meet the requirements of noise reduction and back pressure, and also ensure that the muffler can be adapted to the engine compartment space.
[0042] Controlling the number of silencer chambers Research has shown that when the number of muffler chambers exceeds four, the manufacturing cost increases by more than 30%. Based on the principle of cost-effectiveness, the number of muffler chambers must meet certain requirements. ≤4.
[0043] During the design process, while ensuring the performance of the muffler, the number of chambers should be reduced as much as possible by optimizing the chamber structure and combination method to reduce production costs.
[0044] S3. Determine the optimization variables and optimization objectives, and construct an objective function that quantitatively maps the optimization variables and optimization objectives; Optimization parameters include muffler volume Expansion ratio m, number of silencer chambers Given the perforation rate ε, the optimization objective function includes maximizing the transfer loss TL and the total back pressure of the muffler. minimize.
[0045] Based on acoustic theory and fluid dynamics formulas, an objective function is constructed. Acoustic theory provides the theoretical basis for analyzing the noise reduction performance of the muffler, while fluid dynamics formulas describe the flow characteristics of exhaust gas within the muffler. The intrinsic relationships between the parameters are expressed by combining the fluid dynamics formulas and the transmission loss (TL) formula.
[0046] Specifically, the expression for the relationship between the gas velocity inside the silencer and the geometric parameters of the silencer in the fluid mechanics formula is as follows: ; Where L is the effective length between the exhaust pipe inlet and the exhaust pipe outlet. For the volume of the muffler, The exhaust pipe outlet cross-sectional area is... This is the cross-sectional area of the exhaust pipe inlet. denoted by , where m is the number of silencer chambers and m is the silencer expansion ratio.
[0047] The cross-sectional area of the exhaust pipe inlet collected from S1 Substituting the speed of sound *c* into fluid dynamics formulas, we quantify the other geometric parameters of the muffler. Then, combining this with the transmission loss (TL) formula, we construct the first objective function: maximizing the muffler volume. First objective function: ; Here, 2πf / c is the basic component of the wave number k, which is fully expressed by multiplying it by the geometric relationship of the exhaust pipe length L, where f is the sound wave frequency (unit: Hz). In muffler design, f usually covers the main frequency band of engine exhaust noise, such as 100-2000Hz. The transmission loss TL varies with the frequency f, and the noise reduction effect of the muffler is different at different frequencies. TL needs to be optimized over a wide frequency range during design. The transmission loss formula reflects the mathematical relationship between the muffler's structural parameters and its noise reduction effect. By accurately substituting and calculating the parameters, the noise reduction performance of the muffler can be quantified.
[0048] In the first objective function, through The coefficient reconstruction deformation, compared with the traditional transmission loss formula In item, The linear term only reflects the effect of the expansion ratio, while the deformation term... The volume reduction is significantly amplified when m > 1.
[0049] For example, when m=4, the traditional term is 16, while the modified term reaches 14.06, an increase of approximately 10%. 1 / m approaches zero when m≈1, avoiding excessively low noise reduction under small expansion ratios, while enhancing the stability of noise reduction in the high-frequency band through the square term.
[0050] Through frictional loss Local losses and perforated tube resistance The summation constructs the second objective function, namely back pressure. Minimize. Specifically: Calculate friction loss Since the exhaust pipe is fixed, its value is also constant: ; in, Darcy friction factor is a dimensionless parameter used to quantify the frictional resistance loss of fluid flowing in a pipe. Its value depends on the flow state (Reynolds number Re) and the relative roughness (ε / D) of the pipe wall. According to the formula for calculating the Reynolds number: Based on the working environment in a gasoline engine muffler, the Reynolds number can typically be calculated to be around [value missing]. Even higher orders of magnitude, with a critical Reynolds number of 2300, it can be determined that the flow in the muffler of a gasoline engine is turbulent. The formula for calculating the Darcy friction factor in turbulent flow is typically: .
[0051] L is the effective length between the exhaust pipe inlet and the exhaust pipe outlet.
[0052] The diameter of a circular pipe is calculated using the following formula: =(4×A) / P; A is the cross-sectional area for fluid flow; P is the wetted perimeter (unit: m), which is the circumference of the fluid in contact with the solid wall. Careful 3D modeling is performed before manufacturing, so the diameter can be obtained from the model in 3D design software.
[0053] ρ is the density of the exhaust gas, ρ = p / (R) T), p is the exhaust (absolute) pressure (usually higher than ambient pressure); T is the exhaust (absolute) temperature; R is the specific gas constant of the exhaust gas.
[0054] v is the gas velocity. First, convert the displacement into the exhaust volume flow rate when the engine is running: ; This formula is for a four-stroke engine, where n is the engine speed variable; Engine displacement; This refers to the engine's volumetric efficiency, which is also a condition-dependent parameter. The formula for calculating the flow velocity is: v = Q_v / S_1; where S_1 is the cross-sectional area of the exhaust pipe inlet.
[0055] Due to frictional loss The calculation formula and the expansion ratio m = S_2 / S_1, where S_2 is the cross-sectional area of the expansion cavity, so S_2 = m × S_1; the cavity volume V_m = S_2 × L_m = m × S_1 × L_m, so L = V_m / (m × S_1). Circular cross section ,therefore According to the law of conservation of mass, the flow velocity inside the expansion cavity is v2 = v1 / m.
[0056] Substituting into the formula and simplifying, we get: ; Let constant The simplified formula is: ; Calculate local loss This loss is related to the muffler parameters: ; Perforated tube resistance This resistance is fitted by experiments: ; Where ε is the perforation rate.
[0057] Therefore, the second objective function is: ; S4. MOPSO algorithm initialization: Algorithm parameters were set using the Optimization Toolbox in Matlab R2023a. Parameter values were verified through three pre-simulations to ensure convergence. Particle generation and quantity setting: The particle swarm size is set to 80, and each particle is a 4-dimensional vector. .
[0058] Pre-simulation verification shows that the local optimum rate is 30% when the number of particles is 60, and drops to 5% when the number of particles is 80. Increasing the number of particles can expand the solution space coverage and reduce the risk of getting trapped in local optima, which is in line with the "exploitation-exploitation" balance theory.
[0059] Iteration count and inertia weight settings: The iteration count is set to 80, and the inertia weight w decreases linearly from 0.7 to 0.3.
[0060] When the archive set is incomplete after 60 iterations, it can cover all equilibrium states after 80 iterations, ensuring that the algorithm converges to the global optimum. In the early stage, a large w (0.7) enhances global exploration, and in the later stage, a small w (0.3) strengthens local convergence, balancing the "exploration" and "development" capabilities, which is in line with the dynamic adjustment strategy in particle swarm optimization theory.
[0061] Learning factor and external archive set: Set the learning factor to 2.0 and the external archive set capacity to 50.
[0062] The learning factors are specifically the individual optimal weight c_1 and the global optimal weight c_2. Setting the individual optimal weight c_1 and the global optimal weight c_2 to be equal avoids excessive bias in particles towards their own or group experience, enhancing the algorithm's stability and convergence. With a capacity of 30, non-dominated solutions are not fully stored; with a capacity of 50, the redundancy rate is <10%, ensuring sufficient storage of non-dominated solutions, reducing information loss, and conforming to the non-dominated sorting and crowding control mechanism.
[0063] Velocity boundary setting: Set the velocity boundary to a range of ±20%. Too high a velocity can cause particles to jump out of the feasible region, while too low a velocity will slow down the optimization process. A reasonable boundary balances the exploration efficiency and the effectiveness of the solution.
[0064] S5. Initial particle swarm generation: The initial particle swarm is generated using a uniform random generation and feasibility verification method. Eighty 4D vectors are uniformly and randomly generated within the design parameter constraints set in S2 using the `rand` function in Matlab. Design parameter constraints, namely the muffler volume. ≤2.5L, number of silencer chambers ≤4.
[0065] For each particle, substitute the two objective functions in S3: the first objective function is to maximize the propagation loss TL, and the second objective function is to maximize the total back pressure. Minimize, and select initial particles based on constraints. If TL≥15dB is satisfied, If the pressure is ≤3kPa, it is retained; otherwise, it is regenerated, resulting in 80 feasible first-generation particles. In this embodiment, the generation takes about 2 minutes.
[0066] S6. Non-dominated sorting and archiving; The performance values of each of the 80 feasible particles were calculated to establish a mapping between particles and their performance values. The performance values were used to calculate the transfer loss TL and total back pressure for each particle. The non-dominated sorting and archive updates are performed based on the performance values of each particle.
[0067] The particles are divided into three layers based on their dominance relationship using non-dominated sorting: Layer 1 has 22 non-dominated solutions, Layer 2 has 35, and Layer 3 has 23. Layer 1 contains all solutions not dominated by any other solution. Layer 2 consists of solutions dominated by solutions in Layer 1 but not by solutions in the same or lower layers. Layer 3 contains solutions dominated by solutions in Layers 1 and 2.
[0068] Add the 22 particles from layer 1 to the external archive set. Since the initial particle swarm archive set contains only 22 non-dominated solutions, there is no need to delete redundant particles.
[0069] S7, Particle Update; The velocity is updated for each dimension of each particle, and the velocity update formula is as follows: ; Where v_i(t) is the current velocity vector of particle i; v_i(t+1) is the updated velocity vector of particle i; w is the inertia weight, the inertia weight of the current iteration number = 7 + [(-0.4) / 79] * (current iteration number - 1); c_1 is the individual optimal weight 2.0; c_2 is the global optimal weight 2.0; r_1 and r_2 are uniform random numbers [0,1]; p_best is the individual optimal solution, that is, the best historical position of particle i; g_best is the global optimal solution, that is, the leader chosen from the external archive.
[0070] Calculate the particle's position vector based on the updated velocity vector: ; Where x_i(t) is the current position vector, x_i(t+1) is the updated position vector, and v_i(t+1) is the updated velocity vector of particle i.
[0071] When updating the velocity vector, the particle crowding degree in the external archive is calculated, and the solution with the highest crowding degree is selected as g_best for the current iteration. A velocity boundary check is performed on the updated particle velocity vector to avoid updating the velocity beyond the ±20% variable range.
[0072] The updated particle position vector is verified for performance and constraints. If the updated position vector of the particle does not satisfy the constraints in S2, the individual optimal solution p_best of the particle is not updated; if the updated position vector of the particle satisfies the constraints in S2, the current position vector is updated to the individual optimal solution p_best of the particle.
[0073] S8. Repeat S6-S7. After each update of the external archive set, perform an overflow check on the non-dominated solutions in the external archive. If the number of external archive sets updated after the current non-dominated sort exceeds 50, truncate the non-dominated solutions after the 50th position according to the non-dominated sort. Keep the number of external archive sets below 50.
[0074] When the iteration reaches 80 times and the termination condition is met, the non-dominated solutions in the external archive set are output as the Pareto optimal solution set.
[0075] S9. Dynamically identify solutions using fuzzy logic; During actual vehicle operation, the "best match" solution is selected online from 50 Pareto optimal solutions through a fuzzy logic dynamic matching mechanism. This requires combining dynamic gasoline engine parameters, such as speed, torque, and exhaust flow, with the fuzzy inference system.
[0076] As attached Figure 2 The diagram shows the pressure distribution inside an exemplary muffler structure. As the gas flows in the exhaust direction, different pressure zones are formed in different chambers and connecting structures of the muffler, exhibiting a gradient change in pressure along the flow direction.
[0077] This pressure distribution is used to illustrate the relationship between the internal structural parameters of the muffler and the back pressure, providing a physical basis for the subsequent construction of the back pressure objective function.
[0078] like Figure 3 The diagram shows the velocity streamline distribution of gas flowing inside the muffler. It can be observed that the gas undergoes streamline rearrangement at the expansion chamber, connecting pipe sections, and locations of structural abrupt changes, forming localized backflow and acceleration zones.
[0079] These flow characteristics indicate that the structural parameters of the muffler have a significant impact on the internal flow state, providing a basis for the present invention to regulate the performance of the muffler through structural parameters.
[0080] like Figure 4 The image shows the internal velocity streamline distribution of the muffler under another exemplary structural parameter or operating condition. Figure 3 In contrast, the changes in the streamline distribution pattern in different regions indicate that the internal flow state of the muffler changes with changes in structural parameters or operating conditions.
[0081] Therefore, the method of the present invention is not limited to a single structural form and has good applicability.
[0082] like Figure 5 The figure shows a three-dimensional structural model of the exhaust pipe, which is used to describe the spatial structure and connections of the exhaust system. Establishing this three-dimensional model provides a geometric basis for subsequent discretization and system-level calculations.
[0083] like Figure 6 As shown, based on the three-dimensional structural model of the exhaust pipe, the exhaust pipe is discretized to construct a one-dimensional pipeline model. This one-dimensional model is used to describe the flow characteristics of gas in the exhaust system and can be combined with the system-level simulation model.
[0084] The above-described discrete process demonstrates that the method of the present invention is feasible in engineering.
[0085] like Figure 7 As shown, by modeling the internal structure of the muffler housing, straight pipes, baffles and perforated structures are set in the cavity to construct the structural model of the muffler, and further discretization is performed to obtain the corresponding one-dimensional muffler model.
[0086] This model can be used to parametrically describe the structural features of a muffler, providing a model basis for the design and optimization based on structural parameters in this invention.
[0087] like Figure 8 As shown, the discretized exhaust system model is coupled with the engine model to construct a system-level model of the engine-exhaust system, which is used to simulate the operating state of the exhaust system under actual engine conditions.
[0088] By using system-level modeling, the performance of the muffler can be analyzed under real boundary conditions, thereby improving the engineering applicability of the method of this invention.
[0089] The above descriptions are merely embodiments of the present invention, and common knowledge such as specific technical solutions and / or characteristics are not described in detail here. It should be noted that those skilled in the art can make various modifications and improvements without departing from the technical solutions of the present invention, and these should also be considered within the scope of protection of the present invention. These modifications and improvements will not affect the effectiveness of the implementation of the present invention or the practicality of the patent. The scope of protection claimed in this application should be determined by the content of its claims, and the specific embodiments described in the specification can be used to interpret the content of the claims.
Claims
1. A method for designing a gasoline engine muffler based on multi-objective particle swarm optimization, characterized in that, include: Collect the core parameters of the gasoline engine and set the design constraints of the muffler, including noise reduction performance, back pressure, muffler space and muffler structure manufacturing cost. Determine the optimization variables and multiple optimization objectives for the muffler design, and construct an objective function that quantitatively maps the optimization variables to the optimization objectives. Multiple optimization objectives include maximizing transfer loss (TL) and total back pressure. minimize; Initialize the parameters of the multi-objective particle swarm optimization algorithm, including the number of particles, the number of iterations, and the external archive capacity; uniformly and randomly generate the initial particle swarm within the constraint space, and perform a feasibility check, retaining only the particles that simultaneously satisfy the constraint conditions; Perform non-dominated sorting on the particle swarm, divide the particle swarm into multiple layers according to the dominance relationship, and store the non-dominated solution of the first layer into an external archive; take the particle with the highest crowding in the external archive as the global leader g_best, update the particle's velocity and position, and perform constraint verification on the updated particle again. If the constraint is satisfied, update the individual optimal solution p_best; otherwise, discard it. Repeat the sorting and updating iteration of non-dominated solutions of particles until the number of iterations reaches the initially set maximum number of iterations. Based on the capacity of the external archive, overflowing inferior solutions are eliminated by non-dominated sorting, and the non-dominated solutions in the external archive are output as the Pareto optimal solution set. By using a fuzzy logic dynamic matching mechanism and combining the dynamic operating parameters of the gasoline engine, the optimal solution for dynamic operating conditions is obtained.
2. The gasoline engine muffler design method based on multi-objective particle swarm optimization according to claim 1, characterized in that: Constraints include transmission loss TL ≥ 15 dB and total back pressure of the muffler. ≤3kPa, silencer volume ≤2.5L, number of silencer chambers ≤4.
3. The gasoline engine muffler design method based on multi-objective particle swarm optimization according to claim 2, characterized in that: The objective function includes a first objective function and a second objective function. First objective function: ; Wherein, 2πf / c is the basic component of wave number k, which is fully expressed by multiplying by the geometric relationship of exhaust pipe length L, where f is the sound wave frequency; m is the muffler expansion ratio; This refers to the cross-sectional area of the exhaust pipe inlet. This refers to the number of silencer chambers; This refers to the volume of the muffler; Second objective function: ； Where K is a constant and ε is the perforation rate.
4. The gasoline engine muffler design method based on multi-objective particle swarm optimization according to claim 3, characterized in that: The parameters of the multi-objective particle swarm optimization algorithm are initialized, including the inertia weight w and the learning factor. Specifically, the number of particles is 80, the number of iterations is 80, the inertia weight w decreases linearly by 3 from 0.7 to 0.3 according to the number of iterations, the individual optimal weight and the global optimal weight are set to be equal to 2, the external archive capacity is 50, and the velocity boundary is ±20% of the variable range.
5. The gasoline engine muffler design method based on multi-objective particle swarm optimization according to claim 4, characterized in that: In the non-dominated sorting layering of particles, the non-dominated sorting is divided into 3 layers, with 22 non-dominated solutions in the first layer, 35 in the second layer, and 23 in the third layer.
6. The gasoline engine muffler design method based on multi-objective particle swarm optimization according to claim 5, characterized in that: During the collection of the core parameters, displacement The error must be ≤ ±5%, and the error of the rated speed n must be ≤ ±100 rpm.
7. The gasoline engine muffler design method based on multi-objective particle swarm optimization according to claim 6, characterized in that: The core parameters include displacement. Rated speed n, number of strokes T, number of cylinders N, speed of sound c, exhaust gas density ρ, and exhaust pipe inlet cross-sectional area .