Highway sound barrier segmented deployment method based on multi-factor analysis

Abstract

The application relates to the technical field of traffic infrastructure engineering, and particularly discloses a highway sound barrier segmentation deployment method based on multi-factor analysis. The whole line is preliminarily segmented through construction feasibility; based on acoustic diffraction and noise propagation path analysis, key factors affecting the sound quantity of sensitive targets are obtained, including sound shadow area attenuation, atmospheric sound attenuation correction and dynamic spectrum of vehicle flow noise source intensity; the sensitive targets are graded according to the influence degree of the key factors, and the minimum noise reduction required to meet the standard is set; in each basic segmentation unit, a single-objective optimization model is established and solved by taking the constraint of the insertion loss being not less than the minimum noise reduction and the target of minimizing the total length of the sound barrier, so that the whole-line sound barrier segmentation deployment scheme is obtained. Through multi-factor fine analysis and optimization solving, the problems of the traditional method of length and height determination are solved, and the engineering economic cost is effectively reduced under the premise of ensuring noise reduction to meet the standard.

Description

Technical Field

[0001] This invention belongs to the field of transportation infrastructure engineering technology, and relates to a method for segmented deployment of highway sound barriers based on multi-factor analysis. Background Technology

[0002] With the continuous densification of China's highway network, a large number of newly built lines inevitably approach noise-sensitive areas such as residential areas, schools, and hospitals along the routes. Traffic noise pollution has become a prominent issue affecting the quality of life of residents along these routes. As the most widely used active noise reduction facility, sound barriers have seen rapid and sustained market growth in recent years, and the requirements for noise reduction effectiveness, structural safety, and economic efficiency throughout their entire life cycle are also constantly increasing.

[0003] Current industry practices for the planning, design, and deployment of sound barriers have long suffered from significant technical limitations, making them ill-suited to the complex and ever-changing conditions of highway sites. At the acoustic design level, existing solutions generally rely on standardized theoretical prediction models for parameter calculations. These designs often presuppose ideal conditions such as constant sound sources, flat terrain, and uniform weather conditions, which are significantly out of sync with actual on-site conditions. Furthermore, existing designs often simplify traffic flow into a uniform, steady-state model, failing to adequately consider the complex traffic characteristics in actual operation. This results in the preset average noise reduction being completely inaccurate during peak traffic hours, failing to consistently meet the acoustic environment standards for sensitive areas.

[0004] In determining the geometric parameters of sound barriers, existing deployment methods generally suffer from a crude approach: the industry has long relied on the empirical principle of extending the protection section of the sound barrier by four times based on geometric diffraction theory, without conducting detailed verification of the terrain undulations at both ends of different road sections and the sound wave reflection and scattering effects of surrounding buildings. This not only causes unnecessary waste of materials, but the excessively tall barrier structure also adds to the structural burden under wind load, significantly increasing the construction cost and the difficulty of later maintenance. Summary of the Invention

[0005] In view of the problems existing in the prior art, the present invention provides a segmented deployment method for highway sound barriers based on multi-factor analysis to solve the above-mentioned technical problems.

[0006] To achieve the above and other objectives, the technical solution adopted by the present invention is as follows: This invention provides a method for segmented deployment of highway sound barriers based on multi-factor analysis, the method comprising the following steps: Based on the feasibility analysis of sound barrier installation, the entire line was initially divided into several basic segment units. Based on acoustic diffraction calculation and noise propagation path analysis, the key factors affecting the actual sound received at each sensitive target are obtained. Based on the degree of influence of each of the key factors on the actual sound volume at the sensitive target, the sensitive targets are classified, and the minimum noise reduction required for each sensitive target to meet the standard is set according to the classification results. Within each of the basic segmented units, with the primary constraint that the sound barrier insertion loss value at the sensitive target is not less than the minimum noise reduction required to achieve the standard, and with the optimization objective of minimizing the total length of the sound barrier, a single-objective optimization model is established with the distribution location of the sensitive target and the boundary of the basic segmented unit as decision variables. The single-objective optimization model is solved to obtain the starting and ending station numbers and lengths of each segment of the sound barrier, thus forming a segmented deployment scheme for the entire line of sound barriers.

[0007] As described above, the segmented deployment method for highway sound barriers based on multi-factor analysis provided by the present invention has at least the following beneficial effects: This invention overcomes the technical limitations of existing methods that rely on standardized theoretical models and presupposed ideal premises, introducing a multi-factor comprehensive analysis framework at the acoustic design level. By incorporating actual working conditions such as traffic flow dynamics, terrain variations, and spatiotemporal differences in meteorological conditions into the sound barrier deployment decision-making process, the design scheme closely matches the actual sound propagation environment of the engineering site. Especially during peak traffic hours, this invention can accurately reflect the actual noise radiation characteristics under complex traffic flow conditions, avoiding the inaccuracy of noise reduction caused by existing uniform steady-state models, and ensuring that all sensitive targets stably meet the acoustic environment compliance requirements throughout the entire operating period.

[0008] This invention abandons the long-standing industry practice of using a 4x empirical principle for extensive extension based on geometric diffraction theory. Instead, it establishes a refined division mechanism of basic segmented units and candidate deployment micro-elements, refining sound barrier deployment decisions to the micro-element level. By combining acoustic prediction models with segment-by-segment quantitative evaluation of the noise reduction effect of each micro-element deployment combination, the starting and ending station numbers and length of the sound barrier are entirely driven by actual noise reduction needs, rather than simple extrapolation from empirical formulas. This refined deployment method eliminates unnecessary redundant lengths of the sound barrier at its source, effectively avoiding material waste. Attached Figure Description

[0009] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0010] Figure 1 This is a schematic diagram showing the connections between the steps of the method of the present invention.

[0011] Figure 2The flowchart shows the solution process for the single-objective optimization model using the branch and bound method.

[0012] Figure 3 A flowchart for pre-construction feasibility verification and basic segmentation unit division. Detailed Implementation

[0013] The following description, in conjunction with the implementation of the present invention, is merely an example and illustration of the concept of the present invention. Those skilled in the art can make various modifications or additions to the specific embodiments described, or use similar methods to replace them, as long as they do not deviate from the concept of the invention or exceed the scope defined in the claims, all of which should fall within the protection scope of the present invention.

[0014] Please see Figure 1-3 As shown, the segmented deployment method for highway sound barriers based on multi-factor analysis includes: Based on the feasibility analysis of sound barrier installation, the entire line was initially divided into several basic segment units. Before commencing construction in sections along the entire route, a preliminary feasibility study must be completed to ensure that all sections where sound barriers are to be installed meet the construction requirements. The study will include: First, site suitability verification. Based on the on-site survey data, the flatness of the terrain, the stability of the slopes, and the distribution of underground pipelines along the route were checked one by one to confirm that there were no unidentified communication and power lines, existing sign foundations, maintenance manholes, or other obstacles in all areas where sound barriers were to be installed, while also avoiding the risk of damage to existing road ancillary facilities.

[0015] Second, structural bearing capacity verification. Bearing capacity verification was carried out separately for the roadbed section and the bridge section: for the roadbed section, it was confirmed that the surface soil compaction degree met the foundation construction requirements, and the compaction degree was not less than 90%; for the bridge section, the bearing capacity of the bridge flange was verified simultaneously to ensure that the load of the newly added sound barrier foundation does not exceed the allowable range of the bridge's design bearing capacity.

[0016] Third, verify the construction conditions. Confirm the coverage of accessible construction access roads along the route, verify the clearance conditions for hoisting operations, investigate the noise reduction requirements for construction of sensitive buildings in the surrounding area, and clarify the time windows for operation to provide a basis for subsequent segmented and continuous operations.

[0017] After the feasibility study was approved, the entire line was divided into several independent basic segment units, prioritizing homogeneity, clear boundaries, and ease of construction. The operating parameters within each unit remained highly consistent. The specific division rules are as follows: First, the road is divided into three primary zones based on its road attributes: roadbed sections, bridge sections, and roadbed-bridge transition sections. The foundation types for each zone are completely independent: roadbed sections use shallow-buried concrete foundations, with the foundation depth determined based on geological conditions, generally not less than 0.8 meters; bridge sections use pre-embedded foundations with rebar anchorage, with the anchorage depth determined based on the bridge flange thickness; transition sections use gradually changing foundations to avoid uneven settlement caused by abrupt changes in foundation type.

[0018] Second, a two-level division is carried out based on the homogeneity of working conditions. Within the first-level division, areas with parameter differences exceeding 15% are separated by taking into account the distribution of noise source intensity, terrain slope, wind pressure load, and distribution of surrounding sensitive points along the route. This ensures that the design parameters within each basic segment unit are uniform, eliminating the need for frequent adjustments to the construction process.

[0019] Third, boundary avoidance rules. The boundaries of all segment units must avoid key nodes such as road expansion joints, existing drainage facilities, and cable wells. The boundary positions should be set in a flat area at least 2 meters away from the above-mentioned structures to reserve sufficient operating space for subsequent construction.

[0020] Based on acoustic diffraction calculation and noise propagation path analysis, the key factors affecting the actual sound received at each sensitive target are obtained. Preferably, the key factors include: the sound shadow zone attenuation amount determined by the route geometry and topography, the atmospheric sound attenuation correction amount determined by the wind speed and temperature gradient in real-time weather, and the dynamic spectrum of traffic noise source intensity determined by the vehicle type composition and time-varying flow in dynamic traffic flow.

[0021] Preferably, the sound shadow zone attenuation amount, which is jointly determined by the route geometry and topography, includes extracting the road longitudinal profile, cross profile and roadside slope angle from the route geometry, and the ground absorption coefficient from the topography. Based on the road longitudinal profile, cross-sectional shape, roadside slope angle, and ground absorption coefficient, the additional attenuation value of the sound shadow zone at each sound receiving point is calculated using the sound ray tracing method. Extracting route geometric features. Specifically, this includes: Road longitudinal profile alignment: Extract longitudinal profile design parameters for each sensitive target section from the highway design documents, including pavement elevation, longitudinal slope, vertical curve radius, and location of slope change points. For highways already in operation, acquire actual pavement elevation data using vehicle-mounted LiDAR scanning, with a scanning point spacing of no more than 5 meters.

[0022] Cross-sectional design parameters for each sensitive target road segment are extracted, including the number of lanes, single-lane width, median width, hard shoulder width, and the horizontal distance between the proposed location of the sound barrier and the lane centerline. For roadbed sections, the embankment height or cut depth is also extracted; for bridge sections, the bridge deck width and crash barrier height are extracted.

[0023] Roadside slope angle: Extract the topographic slope angle between the sound barrier location and the sensitive target. For high embankment sections, extract the slope ratio of the fill slope; for low cut sections, extract the slope ratio of the excavated slope. Slope angles are extracted through field measurements or digital elevation models.

[0024] Extracting topographic and geological features. Specifically, this includes: Ground absorption coefficient: The ground absorption coefficient G for each area is determined based on the ground type along the sound propagation path. Ground types are classified into three categories according to the classification standards in GB / T17247.2-1998 "Acoustics - Outdoor Sound Propagation Attenuation - Part 2: General Calculation Methods": hard ground, loose ground, and mixed ground. Hard ground includes asphalt pavement, concrete pavement, and water surfaces, with G set to 0; loose ground includes grassland, farmland, and snowfields, with G set to 1; for mixed ground, G is a value between 0 and 1, determined by the area ratio of hard ground to loose ground.

[0025] Based on the extracted road longitudinal profile, cross-sectional shape, roadside slope angle, and ground absorption coefficient distribution, the additional attenuation value of the sound shadow zone at each sound receiving point is calculated using the sound ray tracing method. The specific steps are as follows: The first step is to establish a three-dimensional geometric model of the sound propagation path. Taking the center line of the lane as the sound source line and the location 1 meter outside the window of the first floor of the sensitive target as the sound receiving point, a complete geometric model of the sound propagation path, including the sound source, sound barrier, ground, and slope, is constructed by combining the longitudinal profile, cross-sectional shape, and roadside slope angle.

[0026] The second step is to emit sound rays from the sound source in all directions of space. The emission angle of the sound rays covers 0 to 360 degrees in the horizontal direction and -90 to 90 degrees in the vertical direction.

[0027] The third step is to trace the propagation path of each sound ray. For each sound ray, trace it step by step along its propagation direction, determining the intersection of the sound ray with obstacles such as sound barriers, the ground, and slope structures. When a sound ray encounters an obstacle, handle it according to the acoustic properties of the obstacle: For a sound barrier, determine whether the sound ray diffracts from the top of the sound barrier to reach the receiving point. If the sound ray diffracts from the top of the sound barrier, calculate the path difference δ of the diffraction path and calculate the diffraction attenuation based on the Fresnel number N. If the sound ray diffracts from both sides of the sound barrier, calculate the corresponding diffraction attenuation accordingly.

[0028] For the ground, the change in sound energy caused by ground reflection or absorption is calculated based on the ground absorption coefficient G and the incident angle of the sound ray. When the sound ray propagates close to the ground at a grazing angle, the additional attenuation caused by the ground effect is considered.

[0029] For slopes, the slope is considered as an inclined ground. Based on the slope angle and the ground absorption coefficient of the slope material, the reflection or absorption effect of sound rays on the slope surface is calculated.

[0030] The fourth step is to calculate the additional attenuation value of the sound shadow zone at each receiving point. The sound energy of all effective sound rays reaching the receiving point is superimposed to obtain the total sound energy at that point. This total sound energy is compared with the sound energy under free-field conditions; the difference is the additional attenuation value of the sound shadow zone. In complex highway environments, sound propagation is influenced by a combination of factors, including route geometry, terrain and geology, meteorological conditions, and dynamic traffic flow. The energy ratio method described above comprehensively considers the impact of all these factors on sound energy, calculating from an overall energy perspective. For scenarios requiring a comprehensive assessment of sound attenuation, such as segmented deployment of sound barriers, this method more accurately reflects the actual situation. The specific calculation formula is as follows: ; in, The sound energy at the receiving point under free sound field conditions is calculated using a sound ray tracing model: ; in Here, is the sound power of the sound source, and dis is the straight-line distance from the sound source to the receiving point; The total sound energy at the receiving point after considering the sound shadow zone effect is the actual measured sound energy value, obtained by superimposing all effective sound ray energies that can reach the receiving point through sound ray tracing: ; E includes the effective sound energy after atmospheric reflection, ground refraction, and ground absorption; The aforementioned sound tracing method can accurately calculate the additional attenuation value of the sound shadow zone at each sound receiving point, which is determined by the geometric features of the route and the topography and geology, providing accurate basic parameters for subsequent calculation of actual sound reception.

[0031] Preferably, the atmospheric sound attenuation correction amount, determined by the wind speed and temperature gradient in real-time meteorological data, is specifically determined in the following manner: Obtain real-time meteorological monitoring data along the target highway, including at least wind speed profiles and temperature profiles at different heights above the ground; Based on the wind speed profile and temperature profile, calculate the sound ray bending correction caused by the refraction effect when the sound wave propagates in the atmosphere, and the sound scattering attenuation correction caused by atmospheric turbulence. Acquire real-time meteorological monitoring data along the target highway. Specifically, deploy micro-meteorological monitoring stations along the target highway. The spacing between monitoring stations is determined based on the terrain undulation and meteorological condition variation gradient along the route: no more than 5 kilometers between stations in plains and hilly areas, and no more than 3 kilometers between stations in mountainous and hilly areas. Spatial mapping rules from meteorological data to road micro-elements: Station influence range division: The mid-section between two adjacent meteorological monitoring stations is used as the boundary to divide the linear jurisdiction area corresponding to each meteorological station. All road micro-elements within the interval belong to the nearest meteorological station. Data assignment rules: All meteorological data, including air pressure, temperature, humidity, and turbulence parameters, obtained from actual measurements at a single meteorological station are directly assigned to all road micro-elements within its jurisdiction. Each monitoring station is equipped with multi-height wind speed and direction sensors and temperature sensors to acquire wind speed and temperature data at at least four heights: 1.5 meters, 3 meters, 5 meters, and 10 meters above the ground. The sampling frequency is no less than once per minute, and the data is transmitted back to the central processing platform in real time via a wireless transmission module.

[0032] For road sections along the transmission line corridor where local meteorological and environmental monitoring systems or highway meteorological stations have already been built, priority should be given to accessing existing monitoring data to avoid redundant construction. For road sections lacking ground monitoring stations, near-surface wind speed and temperature profile data from high-resolution numerical model forecast products should be obtained as supplementary data.

[0033] Based on the acquired wind speed and temperature data at various altitudes, wind speed profiles and temperature profiles were constructed at each monitoring point. The wind speed profile was described using a logarithmic law wind profile model, i.e.: ; Where u(z) is the wind speed at a height z above the ground, and κ is the von Kármán constant, taken as 0.4, selected according to the recommended value in the appendix of GB / T28591-2012 "Wind Force Scale" based on the surface type along the route. Friction velocity: Vertical wind speed pulsation is directly measured using a three-dimensional ultrasonic anemometer. With horizontal wind speed fluctuations The calculation yielded: ; This refers to the surface roughness length. According to sources such as the "Encyclopedia of Earth Sciences," the following reference values ​​exist for different surfaces.

[0034] Table 1: Surface roughness length Z0 corresponding to different surface types; Very flat mud and ice surface 0.001cm Open water surface, snow surface 0.02~0.05cm Shallow grass, 1-10cm high 0.1~2.3cm Crops, height h Approximately h / 7 or h / 8 semi-desert 0.3cm Urban areas with dense housing 100cm Forests or high-density cities Up to 200cm The temperature profile was constructed using a linear piecewise interpolation method, with the temperature values ​​at each measured altitude level as nodes, creating a continuous profile showing the temperature variation with altitude.

[0035] Based on the constructed wind speed and temperature profiles, the sound ray bending correction caused by the refraction effect during sound wave propagation in the atmosphere is calculated. The propagation speed of sound waves in the atmosphere is affected by both temperature and wind speed, and the effective sound speed... Calculate using the following formula: ; in, The speed of sound in air under standard conditions is taken as 340 m / s. Let z be the absolute temperature at a height z above the ground. For reference temperature, take room temperature (293 Kelvin), and u(z) is the wind speed at height z. It is the angle between the wind direction and the sound propagation direction.

[0036] When temperature and wind speed gradients exist in the atmosphere, the speed of sound changes with altitude, causing sound rays to bend towards regions with lower sound speeds. During the day, when the surface temperature is higher, the speed of sound near the ground is greater, causing sound rays to bend upwards and creating a sound shadow zone at a distance from the sound source, thus lowering the sound level at the receiving point. At night, when the surface temperature is lower, the speed of sound near the ground is lower, causing sound rays to bend downwards, concentrating sound energy towards the ground, thus increasing the sound level at the receiving point.

[0037] Voice curvature correction amount The calculation employs a ray-tracing method based on Snell's law. The atmosphere is divided into several thin layers along the altitude, each no more than 0.5 meters thick, with the sound velocity within each layer considered constant. Starting from the sound source, sound rays are emitted at different elevation angles. The refraction and deflection angles of the sound rays are calculated layer by layer based on the differences in sound velocity, tracing the actual propagation path of the sound rays in a non-uniform atmosphere. The sound energy at the receiver location along the actual sound ray path is compared with the sound energy under the assumption of a uniform atmosphere; the difference is the sound ray bending correction. The expression is: ; in, To account for the sound energy at the point of reception after refraction, The sound energy at the point of sound reception is assumed to be in a uniform atmosphere.

[0038] Based on wind speed and temperature profiles, calculate the correction for sound scattering attenuation caused by atmospheric turbulence. Atmospheric turbulence causes sound waves to scatter during propagation, deviating some sound energy from its original direction of propagation, resulting in a decrease in sound level at the receiving point. Sound scattering attenuation correction amount. The calculation is based on an improved atmospheric sound scattering coefficient model, and the specific steps are as follows: A measurement system was deployed on-site. Representative measuring points were selected near the sensitive target, and temperature pulsation meters, humidity pulsation meters, and ultrasonic anemometers were installed. The three instruments were mounted at the same height, with a horizontal spacing of no more than 10 centimeters. The ultrasonic anemometer was used to measure average wind speed and direction, providing transformation parameters for Taylor's frozen hypothesis.

[0039] Temperature fluctuation time series, humidity fluctuation time series and wind speed data are collected synchronously at a sampling frequency of not less than 10 Hz, with a single sampling duration of not less than 10 minutes. Based on changes in atmospheric stability, multiple samplings are conducted at different times of the day to cover the fluctuation characteristics under different atmospheric conditions.

[0040] The original time series data is detrended by removing linear trend terms and retaining pulsation components. The stationarity of the data is checked, and outlier data segments clearly affected by external disturbances are removed.

[0041] Based on the acquired temperature fluctuation time series, the time series is converted into a spatial series using the Taylor freeze hypothesis. Based on the spatial temperature series, the temperature fluctuation structure function is calculated. For a given spatial interval r, calculate the average of the squared temperature differences between all pairs of points with a spacing of r: ,symbol This represents the overall average value. Within the inertial sub-region, and The relationship is linear. The calculated... and Perform a linear fit, and the slope of the fitted line is... .

[0042] Based on the collected humidity fluctuation time series, the time series is converted into a spatial series using the Taylor freeze hypothesis. Based on the spatial humidity series, the humidity fluctuation structure function is calculated. Calculate the average of the squared humidity differences between all pairs of points with a spacing of r: Within the inertial sub-region, and The relationship is linear. The calculated... and Perform a linear fit, and the slope of the fitted line is... .

[0043] Based on the collected synchronized temperature and humidity fluctuation time series, the Taylor freeze hypothesis was used to convert them into spatial sequences T(x) and q(x), respectively. The temperature and humidity-related fluctuation structure function was then calculated. Within the inertial subregion, for and Perform a linear fit, and the slope of the fitted line is... .

[0044] In a humid atmosphere: ; Where A and B are the partial derivatives of the acoustic refractive index with respect to temperature and humidity, respectively, determined based on atmospheric state parameters. The specific calculation process for A and B is as follows: Temperature and humidity measuring devices were deployed near the sensitive target to measure atmospheric state parameters at typical heights along the sound propagation path. The measured parameters included: actual atmospheric temperature T (Kelvin K); relative humidity RH (expressed as a percentage); and atmospheric pressure p (hPa, or standard atmospheric pressure 1013.25 hPa if not measured). The measurement period coincided with the time period of interest for the sound propagation attenuation calculation, with each measurement sampling duration not less than 10 minutes. The average value of each parameter within this time period was used as the calculation input.

[0045] Calculate the specific humidity q using the measured relative humidity RH and temperature T. Calculate the saturated vapor pressure. Using Magnus's formula: ; in, The unit of T is hPa, and the unit of K is K. 6.112 is the saturated vapor pressure at 0℃, in hPa. 17.67 is the temperature fitting coefficient of the Magnus empirical formula, a generally accepted fitting constant for the saturated vapor pressure of liquid water at temperatures between 0 and 100℃. 273.15 is the absolute temperature value corresponding to 0℃, a standard conversion constant between the thermodynamic temperature scale and the Celsius temperature scale. 29.65 is the empirical fitting constant of the Magnus formula, used to correct for calculation errors in the saturated vapor pressure at low temperatures.

[0046] Calculate the actual water vapor pressure e: ; Here, RH is substituted as a percentage.

[0047] Calculate the specific humidity q: q = 0.622e / p; Where p is atmospheric pressure in hPa, and 0.622 is the inherent constant of the specific humidity standard theoretical formula.

[0048] Calculate the acoustic refractive index n: ; in, For reference temperature, zero degrees Celsius (273.15 K) is used. 0.511 is derived from the theory of sound speed in moist air and represents the approximate proportionality constant of the influence of water vapor on sound speed.

[0049] The partial derivative coefficient A is the partial derivative of the acoustic refractive index n with respect to temperature T, and its calculation formula is as follows: ; The partial derivative coefficient B is the partial derivative of the acoustic refractive index n with respect to the wetted q, and its calculation formula is as follows: ; In dry atmospheres, the effect of humidity fluctuations is negligible. Determined solely by the temperature fluctuation term: ; according to Calculate the atmospheric sound scattering coefficient : ; Wherein, the continuous variable κ is the turbulent wavenumber: k=2π / ; in, The value of the turbulent vortex is within a certain range. , For the internal scale of turbulence, The external scale is selected based on empirically measured values ​​of near-surface atmospheric turbulence, and is conventionally taken as... =0.01m、 =10m. is the turbulence spectral function, with the integration range covering the wavenumber interval from the outer scale to the inner scale. 0.033 is the dimensionless synthesis coefficient derived based on Kolmogorov's turbulent acoustic scattering theory.

[0050] The specific expression for the turbulence spectral function is: ; Finally, based on the acoustic scattering coefficient Calculate the sound scattering attenuation correction amount based on the sound propagation distance r. : ; Where r is the sound propagation path length from the sound source to the receiving point, in meters. The unit is decibel. 4.343 is a fixed physical constant.

[0051] The vocal ray bending correction amount calculated above With acoustic scattering attenuation correction amount The values ​​are superimposed to serve as the atmospheric sound attenuation correction. : ; This atmospheric sound attenuation correction reflects the additional impact of real-time meteorological conditions on sound propagation. When calculating the actual sound reception in subsequent calculations, it is included as a correction term to improve the adaptability of the segmented deployment scheme of the sound barrier to dynamic meteorological conditions.

[0052] Preferably, the dynamic spectrum of traffic noise source intensity, determined by the vehicle type composition and time-varying flow in dynamic traffic flow, includes: Real-time traffic flow and vehicle type classification data for each section of the target highway are collected according to the preset time granularity. Based on the vehicle classification data, the sound power level and frequency characteristics of each vehicle model were determined. Based on the real-time traffic flow and the sound power level of each vehicle type, the equivalent continuous sound level within each preset time granularity is calculated as the dynamic spectrum of traffic noise source intensity at that time granularity.

[0053] Real-time traffic flow and vehicle type classification data for each section of the target highway are collected according to a preset time granularity. The preset time granularity is determined comprehensively based on the intensity of traffic flow changes and the timeliness requirements of the segmented deployment of sound barriers. In this embodiment, the preset time granularity is 15 minutes. For nighttime periods with gentle traffic flow changes, it can be relaxed to 30 minutes; for periods of rapid traffic flow changes such as morning and evening rush hours, it can be increased to 5 minutes.

[0054] The specific data collection method is as follows: Traffic flow detection equipment, including but not limited to microwave vehicle detectors, video vehicle detectors, or loop detectors, is deployed at each section along the target highway. The detection equipment collects real-time information on the passage time, speed, length, and number of axles for each vehicle. Vehicle classification is based on the JT / T489-2019 standard "Vehicle Classification for Toll Roads," dividing vehicles into five categories: Category 1: Small passenger cars and small trucks; Category 2: Medium passenger cars and medium trucks; Category 3: Large passenger cars and large trucks; Category 4: Heavy trucks; and Category 5: Extra-large trucks and truck-trailers. For sections without dedicated detection equipment, vehicle data from the highway network toll collection system or ETC gantry system can be accessed to extract vehicle classification and traffic flow information.

[0055] Based on vehicle model classification data, the sound power level and frequency characteristics of each vehicle model were determined. Sound power level of each vehicle model. And spectral characteristics are determined comprehensively through the following methods: First, a basic database of noise source intensity for each vehicle type was established. Based on the measurement methods specified in GB1495-2002 "Limits and Measurement Methods for Exterior Noise of Automobiles During Acceleration" and GB16170-1996 "Limits for Stationary Noise of Automobiles," the sound power level and 1 / 3 octave band spectrum of representative vehicles for each vehicle type were measured under standard operating conditions. For Class I vehicles, a small gasoline passenger car was used as the representative model, with a sound power level reference value of 98 dB under a constant speed of 80 km / h; for Class II vehicles, a medium-sized diesel passenger car was used as the representative model, with a sound power level reference value of 102 dB; for Class III vehicles, a large diesel passenger car was used as the representative model, with a sound power level reference value of 105 dB; for Class IV vehicles, a heavy-duty diesel truck was used as the representative model, with a sound power level reference value of 108 dB; and for Class V vehicles, a truck-trailer was used as the representative model, with a sound power level reference value of 111 dB.

[0056] Secondly, a vehicle speed correction model is established. When there is a difference between the actual driving speed and the standard measured speed, the sound power level of each vehicle model is corrected for vehicle speed. The correction formula is as follows: ; in, The sound power level of vehicle model m at actual vehicle speed v. For vehicle model m at reference speed The sound power level reference value is below. For reference speed, 80 km / h is used in this embodiment, and the coefficient 30 is determined based on the acoustic test fitting law of road traffic noise standard vehicle noise changing with vehicle speed.

[0057] Next, the frequency characteristics of each vehicle model were determined. The noise spectrum characteristics of each vehicle model were characterized by the sound pressure level distribution in the frequency band from 50 Hz to 5000 Hz, with a center frequency of 1 / 3 octave band. The peak frequencies of the spectrum differ among different vehicle models: the noise energy of Class I vehicles and small passenger cars is mainly concentrated in the mid-to-high frequency range of 800 Hz to 1250 Hz; the noise energy of heavy trucks and truck trains is mainly concentrated in the low frequency range of 60 Hz to 250 Hz, and low-frequency noise has stronger penetrating and diffraction capabilities, thus having a more significant impact on the noise reduction effect of sound barriers.

[0058] Based on real-time traffic flow and the corrected sound power levels of each vehicle type, the equivalent continuous sound level within each preset time granularity is calculated, serving as the dynamic spectrum of traffic noise source intensity at that time granularity. The specific calculation steps are as follows: The first step is to calculate the hourly equivalent traffic flow for each vehicle type. The number of vehicles of each vehicle type passing through the cross-section within a preset time granularity Δt is converted into the hourly equivalent traffic flow. ; in, The hourly equivalent traffic flow for vehicle type m, expressed in vehicles per hour. This represents the number of vehicles of vehicle type m passing through within a preset time granularity Δt, where Δt is the preset time granularity in hours.

[0059] The second step is to calculate the sound level contribution of each vehicle model to the receiving point. Treating each vehicle model as a moving line sound source, the equivalent continuous sound level produced by vehicle model m at the receiving point is calculated. : ; in, For vehicle model m at its actual average speed The sound power level is given by d, where d is the horizontal distance from the lane centerline to the receiving point. =1m is the unit reference distance =1 vehicle / hour is the reference flow rate, and 16 is the formula for calculating the equivalent continuous sound level in JTGB03-2006 "Environmental Impact Assessment Specification for Highway Construction Projects": The empirical constant in the value is 16; The third step is to calculate the equivalent continuous sound level of the mixed traffic flow of multiple vehicle types. The energy of the sound levels contributed by each vehicle type is superimposed to obtain the total equivalent continuous sound level within the preset time granularity. The dynamic spectrum of traffic noise source intensity: ; The summation symbol iterates through all vehicle types.

[0060] The fourth step is to construct a frequency domain representation of the dynamic spectrum of traffic noise sources. This involves applying the total sound level calculated above... By combining the frequency characteristics of each vehicle type and weighting them according to the traffic flow ratio of each vehicle type, the frequency band sound pressure level at the center frequency of each 1 / 3 octave band is obtained, forming a complete dynamic spectrum of traffic noise source intensity: ; in, Center frequency The frequency band sound pressure level at that location, Let be the traffic flow proportion coefficient for vehicle type m, representing the proportion of traffic volume of vehicle type m at a certain cross-section of the road segment where the sound barrier is located during the statistical period, to the total traffic volume at that cross-section. For model m at the center frequency The frequency band sound pressure level at that location.

[0061] Through the above process, the dynamic spectrum of traffic noise source intensity under each preset time granularity, which varies with vehicle type and time-varying traffic flow, is obtained. This provides accurate sound source input parameters for the differentiated analysis of acoustic requirements at different time periods in the subsequent segmented deployment scheme of sound barriers.

[0062] Preferably, the sensitive targets are classified according to the degree of influence of each of the key factors on the actual sound volume at the sensitive target, and the minimum noise reduction amount required to achieve the target is set according to the classification results, specifically including: Obtain the predicted background noise values ​​at each sensitive target location, and determine the acoustic environment quality compliance limits for each sensitive target based on the acoustic environment functional zoning type to which the sensitive target belongs; For each sensitive target, the actual received sound amount is calculated under the combined effect of the sound shadow zone attenuation, the atmospheric sound attenuation correction, and the dynamic spectrum of the traffic noise source. The difference between the actual received sound level and the sound environment quality standard limit is used to obtain the minimum noise reduction required for the sensitive target.

[0063] Obtain the predicted background noise values ​​at each sensitive target location, and determine the acoustic environment quality compliance limits for each sensitive target based on the acoustic environment functional zoning type to which the sensitive target belongs.

[0064] First, sensitive targets along highways typically fall into three categories: Category 1, Category 2, and Category 4a. The functional zone type of a sensitive target can be determined by consulting the acoustic environment functional zoning map or related documents published by the local ecological and environmental authorities.

[0065] Secondly, the predicted background noise values ​​at each sensitive target location are obtained. Background noise refers to noise generated by all sound sources other than highway traffic noise. The predicted background noise values ​​are obtained in the following ways: For existing areas, automatic noise monitoring terminals are deployed at sensitive target locations, and continuous monitoring is conducted during the early morning hours when highway traffic volume is extremely low. The equivalent continuous sound level during this period is used as the background noise value. For planned construction areas, a combination of on-site investigation and comparison with similar functional areas is used, referring to the background noise statistics of similar functional areas in the local sound environment quality bulletin.

[0066] Finally, the noise environmental quality standards were determined. Based on the functional zone type of the sensitive target, the daytime and nighttime noise environmental quality standard limits were determined by referring to tables. For Class 1 zones, the daytime limit was 55 dB and the nighttime limit was 45 dB; for Class 2 zones, the daytime limit was 60 dB and the nighttime limit was 50 dB; for Class 4a zones, the daytime limit was 70 dB and the nighttime limit was 55 dB. When the predicted background noise value exceeds the standard limit for the functional zone, sound barriers are installed along the entire length of the section of the highway within that functional zone.

[0067] For each sensitive target, the actual received sound volume is calculated under the combined effects of the sound shadow zone attenuation, the atmospheric sound attenuation correction, and the dynamic spectrum of the traffic noise source.

[0068] Actual sound volume The calculation is based on the dynamic spectrum of traffic noise source intensity. For the sound source input, subtract the additional attenuation value of the sound shadow zone in sequence. and superimposed atmospheric sound attenuation correction amount The calculation formula is: ; in, The aforementioned traffic noise source intensity dynamic spectrum is determined by the vehicle type composition and time-varying flow in dynamic traffic flow, i.e., the equivalent continuous sound level within the preset time granularity; An additional attenuation value is added to the sound shadow zone, which is determined by the geometric features of the route and the topography and geology, to reflect the sound attenuation caused by the combined effects of sound barrier diffraction, ground absorption and slope reflection; This is the atmospheric sound attenuation correction amount determined by the wind speed and temperature gradient in the real-time meteorological data. A positive value indicates that the atmospheric conditions increase the sound level at the receiving point, while a negative value indicates that the atmospheric conditions further attenuate the sound level at the receiving point.

[0069] In the above calculations, the additional attenuation value in the sound shadow zone and atmospheric sound attenuation correction amount All are frequency-dependent, therefore the actual sound received The calculation is performed band-by-band at 1 / 3 octaves.

[0070] For both day and night periods, the actual sound received during the day is calculated using the dynamic spectrum of traffic noise source intensity and the atmospheric sound attenuation correction for the corresponding time periods. and actual sound volume at night .

[0071] The minimum noise reduction required for the sensitive target is obtained by subtracting the actual received sound level from the standard limit for sound environment quality.

[0072] Minimum noise reduction required for the benchmark The calculation formula is: ; in, This represents the actual sound received at the sensitive target location. The acoustic environmental quality standards for sensitive targets are defined as follows. When the value is positive, it indicates that the actual sound received exceeds the standard limit, and noise reduction measures need to be taken. When the value is zero or negative, it indicates that the actual sound received has met the standard requirements and no additional noise reduction is needed.

[0073] Calculations were performed separately for day and night periods, taking the minimum noise reduction required as a daytime baseline. Minimum noise reduction required for nighttime benchmark The larger value in the range is taken as the minimum noise reduction required as the final benchmark for this sensitive target, so as to ensure that the sound environment quality requirements can be met both day and night.

[0074] Sensitive targets are classified according to the minimum noise reduction required for the baseline. In this embodiment, sensitive targets are divided into three levels: Level 1 Sensitive Targets: The minimum noise reduction required for the baseline is greater than 10 dB, indicating that the sensitive target is severely affected by traffic noise, the noise reduction requirement is urgent, and a high-performance acoustic barrier solution should be prioritized. Level 2 sensitive targets: The minimum noise reduction required is between 5 and 10 dB, indicating that the sensitive target is significantly affected by traffic noise and requires the deployment of a sound barrier solution with standard acoustic performance; Level 3 sensitive targets: The minimum noise reduction required for the benchmark is less than 5 dB, indicating that the sensitive target is relatively slightly affected by traffic noise. Sound barrier solutions with basic acoustic performance can be deployed, or auxiliary noise reduction measures such as green belts can be combined.

[0075] The classification results serve as an important basis for determining the height, length, materials, and structural form of each section of the sound barrier in the subsequent segmented deployment plan, ensuring that noise reduction resources are tilted towards high-demand sensitive targets, and maximizing the overall sound environment quality and investment benefits of the entire line.

[0076] Preferably, within each of the basic segmented units, a single-objective optimization model is established with the primary constraint that the sound barrier insertion loss value at the sensitive target is not less than the minimum noise reduction required to achieve the standard, and the optimization objective being to minimize the total length of the sound barrier. This model uses the boundaries of the basic segmented units as decision variables. Specifically, it includes: Each basic segment unit is discretized along the route direction into multiple equally spaced candidate deployment micro-elements. Each candidate deployment micro-element corresponds to a binary decision variable, which is used to indicate whether a sound barrier is deployed at that micro-element. Taking each of the aforementioned sensitive targets as the center, the effective acoustic range corresponding to each sensitive target is determined. The starting point and ending point of the effective acoustic range are determined by the position of the endpoint of the sound barrier section corresponding to the critical diffraction angle when the diffraction path difference between the sensitive target and the sound source is zero. When a certain micro-element is simultaneously within the acoustic effective range of multiple sensitive targets, the minimum noise reduction required by the highest level of sensitive target shall be the primary constraint. For any sensitive target, the actual insertion loss value at the sensitive target is calculated based on the combination of the deployment states of the candidate deployment micro-elements. The actual insertion loss value is calculated by Fresnel zone integration, and its magnitude is jointly contributed by all deployed sound barrier micro-elements located within the acoustic effective range of the sensitive target. The primary constraint is set as follows: for all sensitive targets, the actual insertion loss value is greater than or equal to the minimum noise reduction required to achieve the target for the sensitive target. The optimization objective is set as: minimizing the total length of the entire sound barrier; Using the boundaries of the basic segmented units as the forced segmentation boundaries, a single-objective optimization model is established within each basic segmented unit.

[0077] Specifically, taking the starting station of the basic segment unit as the origin, and following the direction of travel along the route, the basic segment unit is divided into M consecutive candidate layout micro-elements with a preset micro-element length Δx as the step size. The micro-element length Δx is determined comprehensively based on the minimum feasible length for sound barrier construction and the accuracy of optimization calculations. In this embodiment, Δx is set to 2 meters, which satisfies both the operability requirements of construction and ensures the precision of the optimization results.

[0078] For the j-th candidate placement element, define a binary decision variable. Its value is: =1 indicates that a sound barrier is installed at this micro-element location; =0 indicates that no sound barrier is installed at this micro-element location.

[0079] Therefore, the sound barrier deployment scheme within a basic segmented unit can be determined by a decision variable vector. In full, this vector represents the decision variables of the optimization model.

[0080] Taking each of the aforementioned sensitive targets as the center, the effective acoustic range corresponding to each sensitive target is determined. The starting point and ending point of the effective acoustic range are determined by the position of the endpoint of the sound barrier section corresponding to the critical diffraction angle when the diffraction path difference between the sensitive target and the sound source is zero.

[0081] The process for determining the effective acoustic range of the k-th sensitive target is as follows: First, establish the spatial geometric relationship between the sensitive target and the sound barrier. Using the location of the sensitive target's sound-receiving point as the origin, the road centerline as the sound source line, and the proposed location of the sound barrier as the diffraction boundary, construct a three-dimensional diffraction geometric model of the sound source, sound barrier, and sound-receiving point.

[0082] Secondly, the critical diffraction angle is calculated. The noise reduction effect of a sound barrier mainly comes from the diffraction attenuation of sound waves at the top of the barrier. When the sound rays emitted from the sound source diffract around the top of the barrier and reach the receiving point, the diffraction path difference δ is the difference in length between the diffraction path and the direct path. As the endpoint of the sound barrier moves further away from the sensitive target, the diffraction path difference gradually decreases. When the diffraction path difference decreases to zero, the sound barrier no longer has a noise reduction effect on the sensitive target. At this point, the angle formed by the line connecting the endpoint of the sound barrier and the receiving point of the sensitive target and the centerline of the road is the critical diffraction angle. .

[0083] Critical diffraction angle The calculation formula is: ; Where d is the horizontal distance from the sensitive target's sound receiving point to the location of the sound barrier, s is the three-dimensional spatial slant distance from the sensitive target's sound receiving point along the road direction to the end point of the sound barrier, and a and b are the straight-line distances from the sound source to the top of the sound barrier and from the top of the sound barrier to the sound receiving point, respectively.

[0084] Finally, the starting and ending station numbers of the effective acoustic range are determined based on the critical diffraction angle. A perpendicular line is drawn from the sensitive target to the road centerline; the station number corresponding to the foot of the perpendicular is the center station number of the sensitive target. Using this center station number as a reference, lines are extended in both the forward and backward directions until the angle between the line connecting the endpoint of the sound barrier and the sound-receiving point of the sensitive target and the road centerline equals the critical diffraction angle. At this point, the two corresponding endpoint station numbers are the starting station numbers of the effective acoustic range of the sensitive target. and the final station number Length of the effective acoustic range .

[0085] For any sensitive target, the actual insertion loss value at the sensitive target is calculated based on the combination of the deployment states of the candidate deployment micro-elements. The actual insertion loss value is calculated by Fresnel zone integration, and its magnitude is jointly contributed by all deployed sound barrier micro-elements located within the acoustic effective range of the sensitive target.

[0086] For the k-th sensitive target, its actual insertion loss value The calculation process is as follows: First, effective micro-elements are selected. From all M candidate micro-elements of the basic segmented unit, those located within the effective acoustic range of the k-th sensitive target are selected. The infinitesimal elements within a given range are denoted as the effective set of infinitesimal elements. Only the set of effective infinitesimal elements The arrangement of micro-elements within the target affects the insertion loss value of the sensitive target.

[0087] Secondly, the diffraction path difference of each effective infinitesimal element is calculated. For the set of effective infinitesimal elements... The j-th infinitesimal element in the equation, if its decision variable... Then calculate the diffraction path difference of the sound barrier segment corresponding to the infinitesimal element to the k-th sensitive target. Diffraction path difference The spatial coordinates of the sound source, the midpoint of the top of the micro-element sound barrier, and the sound receiving point are calculated using geometric acoustics.

[0088] Next, calculate the Fresnel number of each effective infinitesimal element. This is based on the diffraction path difference. Given the wavelength λ of the sound wave, calculate the Fresnel number corresponding to the infinitesimal element. : ; Where λ is the wavelength of the sound wave. Based on the fact that the energy of highway traffic noise is mainly concentrated in the mid-frequency range of 400 to 600 Hz, the wavelength of 0.7 meters corresponding to the equivalent frequency of 500 Hz is used as the calculation wavelength.

[0089] Then, the Fresnel zone integral method is used to calculate the insertion loss value. For the k-th sensitive target, its actual insertion loss value is... The contribution is made jointly by all the acoustic barrier micro-elements located within the effective acoustic range, and the calculation formula is as follows: ; The integration range covers the set of effective infinitesimal elements. All The formula is based on the Fresnel number interval corresponding to the infinitesimal element, where i is the imaginary unit. It treats each infinitesimal sound barrier segment as an independent semi-infinite barrier and calculates the comprehensive diffraction attenuation effect of a finite-length sound barrier through the superposition of Fresnel integrals. The coefficients are used to represent the coefficients. Derived from the standard normalized amplitude correction term of the complex amplitude of diffraction of a semi-infinite barrier in Fresnel-Kirchhoff diffraction theory, it is an inherent theoretical constant of the analytical solution of the diffraction field of a single semi-infinite thin barrier.

[0090] The original integral of classical Fresnel-Kirchhoff diffraction uses the spatial physical coordinates of the barrier surface as the integration variable. In this case, the integration requires substituting the three-dimensional geometric distances of the sound source, barrier, and receiver to complete the phase term calculation. The integral kernel contains complex spatial distance expressions, and the geometric parameters are highly coupled. When optimizing and iterating a large number of discrete barrier elements along the highway, the amount of repetitive calculation is too large. After changing to Fresnel numbers, the dimensionless N is used to characterize the diffraction intensity of elements with different spatial layouts, eliminating the interference of different geometric scales and adapting to the parallel calculation of a large number of elements along the road.

[0091] In practical numerical calculations, the above integral is discretized into a summation form: ; in, = - .

[0092] The primary constraint is set as follows: for all sensitive targets, the actual insertion loss value is greater than or equal to the minimum noise reduction required to achieve the target for the sensitive target.

[0093] For all K sensitive targets within the basic segmented unit and those affected by it, the primary constraint is expressed as follows: ; in, This represents the actual insertion loss value at the k-th sensitive target. This is the minimum noise reduction required to achieve the target for the k-th sensitive target, and this value has been determined in the aforementioned sensitive target classification step.

[0094] When a sensitive target is simultaneously affected by the sound barriers within multiple basic segment units, the actual insertion loss value of the sensitive target is calculated by superimposing the contributions of the sound barriers within each basic segment unit. Each basic segment unit needs to be considered collaboratively during optimization.

[0095] The optimization objective is set as: minimizing the total length of the entire sound barrier.

[0096] Total length of sound barrier The objective function is obtained by summing the lengths of all the infinitesimal elements deployed within the basic segmented unit. It can be expressed as: ; Where Δx is the length of the infinitesimal element, and M is the total number of infinitesimal elements within the basic segmented unit.

[0097] Using the boundaries of the basic segmented units as the forced segmentation boundaries, a single-objective optimization model is established within each basic segmented unit.

[0098] In summary, the complete formulation of the single-objective optimization model established within a single basic segmented unit is as follows: Decision variables: ; Optimization goal: ; Constraints: ; in, ; This optimization model is a typical zero-one integer programming problem, solved using the branch and bound method. Since the number of infinitesimal elements M is typically in the tens to hundreds, the solution scale is moderate, allowing for the acquisition of the global optimum or near-optimal solution in a relatively short time. The resulting decision variable vector X represents the optimal sound barrier layout scheme within this basic segmented unit, clearly defining the start and end station numbers, layout length, and specific locations of the sound barriers.

[0099] Preferably, the single-objective optimization model is solved to obtain the start and end station numbers and lengths of each segment of the sound barrier, forming a segmented deployment scheme for the entire line of sound barriers, specifically including: The branch and bound method is used to solve the single-objective optimization model, and the solution process is as follows: The binary decision variables of each candidate placement micro-element within each basic segmented unit are used as the decision variables of the branch and bound method, where 1 indicates the placement of a sound barrier and 0 indicates the absence of a sound barrier.

[0100] The objective function of minimizing the total length of the sound barrier is used as the basis for calculating the lower bound of the branch and bound method. The insertion loss constraints at each sensitive target are relaxed, and the relaxed solution is used as the pruning basis of the branch and bound method to establish the branch and bound solution framework. Within the aforementioned branch-and-bound solution framework, the following steps are performed: Step A: Relax all constraints of the single-objective optimization model to linear constraints, solve the relaxed model using linear programming, and obtain the global lower bound. If all decision variables in the relaxed solution are integers and satisfy all original constraints, then the relaxed solution is the global optimal solution. Directly output the solution result and terminate the calculation. Step B: If the relaxed solution does not satisfy the integer condition, select a decision variable whose value is not an integer as a branch variable, and divide the current problem into two subproblems with the decision variable taking the values ​​of 0 and 1 as conditions, and add their respective branch constraints to each subproblem. Step C: Solve each of the subproblems using linear programming to obtain the lower bound of each subproblem. If the lower bound of a subproblem is not less than the objective function value of the currently known best integer feasible solution, then cut off that branch and do not continue to expand downwards. Step D: For the unpruned subproblems, repeat steps B and C to perform recursive branching until all branches are pruned. Select the solution with the smallest objective function value from all obtained integer feasible solutions as the global optimal solution. The values ​​of each decision variable in the global optimal solution are restored to the layout state of each candidate layout micro-element in the order of station number, and adjacent layout micro-elements with consecutive values ​​of 1 are merged into the same continuous sound barrier segment to obtain the starting and ending station numbers and length of each segment sound barrier. Boundary verification is performed on each of the obtained continuous sound barrier segments: if the length of any continuous sound barrier segment is less than the preset minimum effective length threshold, all decision variables corresponding to that segment are forcibly set to 0, and the forced constraint is added to the single-objective optimization model to re-solve the branch and bound problem. The iteration is performed until the length of all retained continuous sound barrier segments is not less than the preset minimum effective length threshold. Output the segmented deployment plan of the entire sound barrier after boundary verification. The plan includes the starting station number, ending station number and section length of each continuous sound barrier section.

[0101] The branch-and-bound method is used to solve the single-objective optimization model. The binary decision variables of each candidate placement element within each basic segmented unit are used as the decision variables for the branch-and-bound method, where 1 represents placing a sound barrier and 0 represents not placing a sound barrier. The objective function of minimizing the total length of the sound barrier is used as the lower bound calculation basis for the branch-and-bound method. The insertion loss constraints at each sensitive target are relaxed, and the relaxed solution is used as the pruning basis for the branch-and-bound method, establishing the branch-and-bound solution framework.

[0102] Step A: Relax all constraints of the single-objective optimization model into linear constraints, and solve the relaxed model using linear programming to obtain the global lower bound.

[0103] Relaxation refers to the process of transforming a mathematical optimization problem that is difficult to solve directly into an approximate problem that is easier to solve by relaxing or eliminating some of its constraints. Its core mathematical definition can be summarized as follows: ; The key condition is ; Specifically, relaxation includes two aspects: first, relaxing the zero- and one-integer constraints of the decision variables into continuous variable constraints, that is, allowing... The first is to continuously take values ​​within the interval [0,1]; the second is to impose nonlinear constraints on the inserted loss value. Linearization is performed. The specific method of linearization is as follows: the insertion loss value... Perform a first-order Taylor expansion near the initial feasible solution: ; in, The initial feasible solution is obtained using the following greedy algorithm: Step 1: Initialize all =0, making the current feasible solution set empty; Step 2: Press Sort all sensitive targets from largest to smallest; Step 3: For each sensitive target k, sequentially within its acoustically effective range... Inside, one by one Set to 1 until Or all micro-elements within the interval have been deployed; Step 4: If all sensitive objectives have satisfied the constraints, then the initial feasible solution is obtained. If a sensitive target cannot satisfy the constraints even after being deployed throughout its entire effective acoustic range, then the basic segmented unit is determined to have no feasible solution.

[0104] This represents the insertion loss value corresponding to the initial feasible solution. The above-described insertion loss function is used in the initial feasible solution. For the j-th decision variable Taking the partial derivative, we get Let be the change of the j-th decision variable relative to the initial feasible solution; This first-order Taylor expansion is only applicable to relaxed linear programming problems with lower bounds, not for exact loss calculations, and has an upper bound on the error. satisfy: ; in, for of The neighborhood, based on the engineering quantification error reference, is taken as... When the value is 0.2, the relative error of the single sensitive target insertion loss is no more than 5%, which fully meets the accuracy requirements of the lower bound estimation. Solve the relaxed linear programming model to obtain the optimal objective function value. This is the global lower bound.

[0105] If all decision variables in the relaxed solution are integers and satisfy all original constraints, i.e., all If all values ​​are 0 or 1, and the insertion loss values ​​at each sensitive target meet the requirements, then the relaxed solution is the global optimal solution. The solution result is output directly and the calculation is terminated.

[0106] Step B: If the relaxed solution does not satisfy the integer condition, that is, some decision variables take the value of fractions, then select a decision variable whose value is not an integer as a branch variable, and divide the current problem into two subproblems with the condition that the decision variable takes the value of 0 or 1, and add their respective branch constraints.

[0107] The branch variable selection strategy adopts a strong branching strategy, which is as follows: for all decision variables with fractional values ​​in the current relaxation solution, calculate the change in the objective function value of the subproblem relaxation solution under the two cases of forcing each fractional variable to be 0 and 1 respectively, and select the variable with the largest change in objective function value as the branch variable, so as to facilitate subsequent pruning operations and accelerate convergence.

[0108] With selected branch variables Based on the original problem, two subproblems are generated: the left subproblem adds constraints to the original problem. =0, the right subproblem adds constraints to the original problem. =1. Add these two sub-problems to the list of nodes to be processed.

[0109] Step C: Solve each subproblem using linear programming to obtain the lower bound of each subproblem. For each subproblem, construct and solve the corresponding relaxed linear programming model according to the relaxation method in Step A. The relaxed optimal objective function value of the subproblem is the lower bound of the subproblem. .

[0110] If the lower bound of a certain subproblem is not less than the objective function value of the currently known best integer feasible solution, that is... ≥ If the branch is not found, then it should be pruned and will not continue to expand downwards. This represents the total length of the sound barrier corresponding to the currently found optimal integer feasible solution.

[0111] If the relaxation problem of the subproblem has no feasible solution, then the branch is also pruned.

[0112] Step D: For the unpruned subproblems, repeat steps B and C to perform recursive branching until all branches are pruned.

[0113] During the recursive branching process, whenever an integer feasible solution is found, that is, a solution where all decision variables are 0 or 1 and satisfy all original constraints, its objective function value is compared with the objective function value of the current best integer feasible solution. Compare the results. If the objective function value of the integer feasible solution is less than... Then update The objective function value is set, and the decision variable vector corresponding to the integer feasible solution is recorded as the current optimal solution.

[0114] When the list of nodes to be processed is empty, that is, after all branches have been pruned, the solution with the smallest objective function value is selected from all the obtained integer feasible solutions as the global optimal solution.

[0115] The values ​​of each decision variable in the global optimal solution are restored to the layout state of each candidate layout micro-element in the order of station number.

[0116] Specifically, the decision variable vector corresponding to the global optimal solution Arrange the micro-elements according to their corresponding station numbers from smallest to largest to obtain the sequence of sound barrier deployment status at each micro-element location along the route.

[0117] Adjacent and consecutively denoted micro-elements with a value of 1 are merged into the same continuous sound barrier segment. The merging method is as follows: starting from the first micro-element, traverse the sequence until a certain value is reached. When =1, record the starting station number corresponding to this infinitesimal element as the starting station number of the sound barrier section; continue traversing backwards until encountering... If the value is 0, iterate to the last micro-element and record the ending station number corresponding to the previous micro-element with a value of 1 as the ending station number of that sound barrier segment. This yields a complete continuous sound barrier segment. Repeat the above process until all micro-elements have been traversed, obtaining all continuous sound barrier segments within the basic segment unit.

[0118] For each continuous sound barrier segment, its segment length The number of continuously arranged micro-elements within the section is multiplied by the length of the micro-element Δx, and the starting and ending station numbers are determined by the station number range of the corresponding micro-elements.

[0119] Boundary checks are performed on each of the obtained continuous sound barrier segments. If the length of any continuous sound barrier segment is less than the preset minimum effective length threshold, all decision variables corresponding to that segment are forcibly set to 0, and this forced constraint is added to the single-objective optimization model for a new branch and bound solution. This process is repeated iteratively until the length of all retained continuous sound barrier segments is not less than the preset minimum effective length threshold.

[0120] The preset minimum effective length threshold is determined based on a combination of the minimum feasible length for sound barrier construction and acoustic effectiveness. In this embodiment, the preset minimum effective length threshold is set to 10 meters. When the length of a sound barrier section is less than 10 meters, its acoustic noise reduction effect is limited, and the construction is difficult and economical, making it unsuitable for deployment as an independent section.

[0121] The iterative process of boundary verification is as follows: The first step is to check all continuous sound barrier segments corresponding to the current optimal solution, identify all segments whose length is less than the minimum effective length threshold, and record them as the invalid segment set.

[0122] The second step is to proceed to step nine to output the final solution if the set of invalid segments is empty.

[0123] Third, if the set of invalid segments is not empty, for each invalid segment, force the decision variables corresponding to all infinitesimal elements contained therein to be set to 0, that is, add constraints. =0, for all infinitesimal elements j within this segment, these mandatory constraints are added to the original single-objective optimization model to form a new optimization model.

[0124] The fourth step is to re-execute the branch and bound solution process from step one to step seven on the new optimization model to obtain a new global optimal solution.

[0125] Fifth step, return to the first step and perform boundary verification on the new optimal solution again until the length of all retained continuous sound barrier segments is not less than the preset minimum effective length threshold.

[0126] Output the segmented deployment plan for the entire sound barrier after boundary verification. The plan includes the starting station number, ending station number, and length of each continuous sound barrier segment.

[0127] For multiple basic segment units along the entire line, the sound barrier segment deployment results obtained from solving each unit are summarized in order of station number to form a complete sound barrier segment deployment plan for the entire line. The plan is output in tabular form, including the following fields: segment number, starting station number, ending station number, segment length, corresponding sensitive target number, minimum noise reduction required to meet the standard, and design insertion loss value.

[0128] Simultaneously, the total length of the entire sound barrier, the predicted insertion loss value at each sensitive target, and the verification results of compliance status are output as a basis for verifying the rationality of the scheme.

[0129] It should be noted that the interval and threshold sizes are set for ease of comparison. The size of the threshold depends on the amount of sample data and the base number set by those skilled in the art for each set of sample data, as long as it does not affect the proportional relationship between the parameter and the quantized value. Furthermore, the above formulas are all dimensionless calculations, and the formulas are derived from software simulations using a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0130] It should be understood that in the various embodiments of this application, the order of the above-mentioned processes does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0131] It should be understood that determining B based on A does not mean determining B solely based on A; it also means determining B based on A and / or other information.

[0132] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

[0133] In conclusion, the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for segmented deployment of highway sound barriers based on multi-factor analysis, characterized in that, Includes the following steps: Based on the feasibility analysis of sound barrier installation, the entire line was initially divided into several basic segment units. Based on acoustic diffraction calculation and noise propagation path analysis, the key factors affecting the actual sound received at each sensitive target are obtained. Based on the degree of influence of each of the key factors on the actual sound volume at the sensitive target, the sensitive targets are classified, and the minimum noise reduction required for each sensitive target to meet the standard is set according to the classification results. Within each of the basic segmented units, a single-objective optimization model is established with the primary constraint that the sound barrier insertion loss value at the sensitive target is not less than the minimum noise reduction required to achieve the standard, and the optimization objective being to minimize the total length of the sound barrier. The single-objective optimization model is solved to obtain the starting and ending station numbers and lengths of each segment of the sound barrier, thus forming a segmented deployment scheme for the entire line of sound barriers.

2. The method for segmented deployment of highway sound barriers based on multi-factor analysis according to claim 1, characterized in that, Based on acoustic diffraction calculations and noise propagation path analysis, key factors affecting the actual sound reception at each sensitive target are identified. These key factors include: The noise attenuation amount is determined by the geometric features of the route and the topography and geology; the atmospheric noise attenuation correction amount is determined by the wind speed and temperature gradient in real-time weather; and the dynamic spectrum of traffic noise source intensity is determined by the vehicle type composition and time-varying flow in dynamic traffic flow.

3. The method for segmented deployment of highway sound barriers based on multi-factor analysis according to claim 2, characterized in that, The sound shadow zone attenuation, determined by the route's geometric features and topographical geology, includes: Extract the road longitudinal profile, cross section form, and roadside slope angle from the geometric features of the route, as well as the ground absorption coefficient from the topography and geology; Based on the road's longitudinal profile, cross-sectional shape, roadside slope angle, and ground absorption coefficient, the additional attenuation value of the sound shadow zone at each sound receiving point is calculated using the sound ray tracing method.

4. The method for segmented deployment of highway sound barriers based on multi-factor analysis according to claim 2, characterized in that, The atmospheric sound attenuation correction amount, determined by wind speed and temperature gradients in real-time meteorological data, is specifically determined in the following manner: Acquire real-time meteorological monitoring data along the target highway, including wind speed profiles and temperature profiles at different heights above the ground; Based on the wind speed profile and temperature profile, calculate the sound ray bending correction caused by the refraction effect when the sound wave propagates in the atmosphere, and the sound scattering attenuation correction caused by atmospheric turbulence. The sound ray bending correction amount is superimposed with the sound scattering attenuation correction amount to obtain the atmospheric sound attenuation correction amount.

5. The method for segmented deployment of highway sound barriers based on multi-factor analysis according to claim 2, characterized in that, The dynamic spectrum of traffic noise source intensity, determined by the vehicle type composition and time-varying flow rate in dynamic traffic flow, includes: Real-time traffic flow and vehicle type classification data for each section of the target highway are collected according to the preset time granularity. Based on the vehicle classification data, the sound power level and frequency characteristics of each vehicle model were determined. Based on the real-time traffic flow and the sound power level of each vehicle type, the equivalent continuous sound level within each preset time granularity is calculated as the dynamic spectrum of traffic noise source intensity at that time granularity.

6. The method for segmented deployment of highway sound barriers based on multi-factor analysis according to claim 1, characterized in that, The process of classifying sensitive targets based on the degree of influence of each key factor on the actual sound volume at the sensitive target, and setting the minimum noise reduction amount required for each sensitive target to meet the standard based on the classification results, specifically includes: Obtain the predicted background noise values ​​at each sensitive target location, and determine the acoustic environment quality compliance limits for each sensitive target based on the acoustic environment functional zoning type to which the sensitive target belongs; For each sensitive target, the actual received sound amount is calculated under the combined effect of the sound shadow zone attenuation, the atmospheric sound attenuation correction, and the dynamic spectrum of the traffic noise source. The difference between the actual received sound level and the sound environment quality standard limit is used to obtain the minimum noise reduction required for the sensitive target.

7. The method for segmented deployment of highway sound barriers based on multi-factor analysis according to claim 6, characterized in that, Within each of the aforementioned basic segmented units, a single-objective optimization model is established with the primary constraint that the sound barrier insertion loss at the sensitive target is not less than the minimum noise reduction required to achieve the target, and the optimization objective being to minimize the total length of the sound barrier. This model uses the boundaries of the basic segmented units as decision variables. Specifically, it includes: Each basic segment unit is discretized along the route direction into multiple equally spaced candidate deployment micro-elements. Each candidate deployment micro-element corresponds to a binary decision variable, which is used to indicate whether a sound barrier is deployed at that micro-element. Taking each of the aforementioned sensitive targets as the center, the effective acoustic range corresponding to each sensitive target is determined. The starting point and ending point of the effective acoustic range are determined by the position of the endpoint of the sound barrier section corresponding to the critical diffraction angle when the diffraction path difference between the sensitive target and the sound source is zero. For any sensitive target, the actual insertion loss value at the sensitive target is calculated based on the combination of the deployment states of the candidate deployment micro-elements. The actual insertion loss value is calculated by Fresnel zone integration, and its magnitude is jointly contributed by all deployed sound barrier micro-elements located within the acoustic effective range of the sensitive target. The primary constraint is set as follows: for all sensitive targets, the actual insertion loss value is greater than or equal to the minimum noise reduction required to achieve the target for the sensitive target. The optimization objective is set as: minimizing the total length of the entire sound barrier; Using the boundaries of the basic segmented units as the forced segmentation boundaries, a single-objective optimization model is established within each basic segmented unit.

8. The method for segmented deployment of highway sound barriers based on multi-factor analysis according to claim 7, characterized in that, Solving the single-objective optimization model yields the start and end station numbers and lengths of each segment of the sound barrier, forming a segmented deployment scheme for the entire line of sound barriers, specifically including: The branch and bound method is used to solve the single-objective optimization model, and the solution process is as follows: The binary decision variables of each candidate placement micro-element within each basic segmented unit are used as the decision variables of the branch and bound method, where 1 indicates the placement of a sound barrier and 0 indicates no placement of a sound barrier. The objective function of minimizing the total length of the sound barrier is used as the basis for calculating the lower bound of the branch and bound method. The insertion loss constraints at each sensitive target are relaxed, and the relaxed solution is used as the pruning basis of the branch and bound method to establish the branch and bound solution framework. Within the aforementioned branch-and-bound solution framework, the following steps are performed: Step A: Relax all constraints of the single-objective optimization model to linear constraints, solve the relaxed model using linear programming, and obtain the global lower bound. If all decision variables in the relaxed solution are integers and satisfy all original constraints, then the relaxed solution is the global optimal solution. Directly output the solution result and terminate the calculation. Step B: If the relaxed solution does not satisfy the integer condition, select a decision variable whose value is not an integer as a branch variable, and divide the current problem into two subproblems with the decision variable taking the values ​​of 0 and 1 as conditions, and add their respective branch constraints to each subproblem. Step C: Solve each of the subproblems using linear programming to obtain the lower bound of each subproblem. If the lower bound of a subproblem is not less than the objective function value of the currently known best integer feasible solution, then cut off that branch and do not continue to expand downwards. Step D: For the unpruned subproblems, repeat steps B and C to perform recursive branching until all branches are pruned. Select the solution with the smallest objective function value from all obtained integer feasible solutions as the global optimal solution. The values ​​of each decision variable in the global optimal solution are restored to the layout state of each candidate layout micro-element in the order of station number, and adjacent layout micro-elements with consecutive values ​​of 1 are merged into the same continuous sound barrier segment to obtain the starting and ending station numbers and length of each segment sound barrier. Boundary verification is performed on each of the obtained continuous sound barrier segments: if the length of any continuous sound barrier segment is less than the preset minimum effective length threshold, all decision variables corresponding to that segment are forcibly set to 0, and the forced constraint is added to the single-objective optimization model to re-solve the branch and bound problem. The iteration is performed until the length of all retained continuous sound barrier segments is not less than the preset minimum effective length threshold. Output the segmented deployment plan of the entire sound barrier after boundary verification. The plan includes the starting station number, ending station number and section length of each continuous sound barrier section.

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