Samy Missoum
email: smissoum@email.arizona.edu

Christophe Vergez
email: vergez@lma.cnrs-mrs.fr

Jean-Baptiste Doc
email: jbdoc@lma.cnrs-mrs.fr

EXPLICIT MAPPING OF ACOUSTIC REGIMES FOR WIND INSTRUMENTS

This paper proposes a methodology to map the various acoustic regimes of wind instruments. The maps can be generated in a multi-dimensional space consisting of design, control parameters, and initial conditions. The boundaries of the maps are obtained explicitly in terms of the parameters using a support vector machine (SVM) classifier as well as a dedicated adaptive sampling scheme. The approach is demonstrated on a simplified clarinet model for which several maps are generated based on different criteria. Examples of computation of the probability of occurrence of a specific acoustic regime are also provided. In addition, the approach is demonstrated on a design optimization example for optimal intonation.

INTRODUCTION

Wind instruments (e.g., clarinets, oboes, trumpets) are nonlinear systems characterized by the presence of various acoustic regimes [START_REF] Mcintyre | On the oscillations of musical instruments[END_REF][START_REF] Noreland | The logical clarinet: numerical optimization of the geometry of woodwind instruments[END_REF]. The control of these regimes is typically tedious as exemplified by the difficulty for beginners to successfully produce a sound. In this case, the musician tries to reach the conditions discriminating the two following regimes: the occurrence or the lack of self-sustained oscillations in the instrument's resonator (i.e., a sound is produced or not). Beyond this simplified description, playing an instrument requires the selection of specific regimes (e.g., a given note) among many possible ones [START_REF] Wilson | Operating modes of the clarinet[END_REF].

Despite recent improvements in the understanding of the physics and the modeling of wind instruments [START_REF] Chaigne | Acoustique des instruments de musique[END_REF], there are still many open questions related to how the various regimes are reached. More specifically, it is not yet understood how the coupling between design and control parameters of the instrument will trigger a given regime. Such an understanding could help to not only understand the important features of a "good instrument" but also help, in the long term, modify the design of instruments for improved playability.

In order to understand the coupling between the various parameters and the acoustic behavior of the instrument, this paper proposes to generate maps defining the regions where specific acoustic regimes are reached. These maps are generated in a space of parameters that are known to govern the acoustic behavior of the instruments (e.g., mouth pressure and reed channel opening). The ability to construct such maps to associate specific acoustic behaviors with regions of the parameter space is of crucial importance for the analysis and design of wind instruments. In general, such a mapping is non intuitive and cannot be obtained through analytical developments arbitrarily far from the oscillation threshold. Alternative approach consists in performing the numerical continuation of solution branches [START_REF] Karkar | A high-order, purely frequency based harmonic balance formulation for continuation of periodic solutions: The case of non-polynomial nonlinearities[END_REF][START_REF] Cochelin | A high-order, purely frequency based harmonic balance formulation for continuation of periodic solutions[END_REF][START_REF] Doedel | AUTO-07P : Continuation and Bifurcation Software for Ordinary Differential Equations[END_REF] but only static or periodic solution branches are tractable [START_REF] Karkar | Oscillation threshold of a clarinet model: A numerical continuation approach[END_REF][START_REF] Terrien | Flute-like musical instruments: A toy model investigated through numerical continuation[END_REF]. More importantly, there are several parameters influencing the acoustic behavior of the instrument thus requiring the construction of a map in a multidimensional space. For this purpose, the most intuitive approach is the construction of maps using a cartesian grid [START_REF] Incio | Computational modelling of stringbody interaction for the violin family and simulation of wolf notes[END_REF][START_REF] Incio | A linearized modal analysis of the bowed string[END_REF][START_REF] Guettler | On the creation of the helmholtz motion in bowed strings[END_REF]. However, precisely identifying the boundaries between various regions of the map requires a large amount of simulation calls which increases exponentially as the dimensionality of the parameter space increases. For this reason, a dedicated approach such as the one proposed in this article is needed.

In this work, the map boundaries are constructed using a Support Vector Machine (SVM) [START_REF] Cristianini | An introduction to support Vector Machines: and other kernel-based learning methods[END_REF][START_REF] Cristianini | Support vector machines and kernel methods: The new generation of learning machines[END_REF] classifier. SVM is a so-called "machine learning" technique and defines an "optimal" boundary between two sets of data points differentiated by their "classes" (e.g., pass or fail ). That is, an SVM requires an initial training step such as a design of experiments [START_REF] Santner | The design and analysis of computer experiments[END_REF][START_REF] Montgomery | Design and Analysis of Experiments[END_REF]. The advan-tage of SVM stems from the construction of a boundary defined explicitly in terms of the parameters. In addition, the boundary generated can be highly nonlinear and defined in a high dimensional space. Because, the initial SVM constructed from a design of experiment might not be accurate, it is subsequently refined using a dedicated adaptive sampling scheme developed by the first author [START_REF] Basudhar | An improved adaptive sampling scheme for the construction of explicit boundaries[END_REF].

The flexibility of the approach allows one to study the regimes in a hybrid space including design, control parameters as well as initial conditions. The technique also enables the efficient propagation of uncertainties to estimate the probability of belonging to a specific regime [START_REF] Basudhar | A sampling-based approach for probabilistic design with random fields[END_REF]. In addition, because SVM is a classification technique, it is not sensitive to discontinuous behaviors. This is an essential aspect since this type of behavior can occur in wind instruments (e.g., discontinuities in playing frequencies due to changes in register). Another advantage of SVM is the possibility of handling several classification criteria simultaneously (e.g., frequency and amplitude).

The aim of this paper is to demonstrate the flexibility and advantages of the proposed methodology rather than to contribute to the understanding of the physics of a particular instrument. The capabilities of the new mapping approach are demonstrated through various numerical experiments based on the simplified reed instrument model. Two-and three-dimensional maps are presented for various choices of parameters, including initial conditions. In addition, examples of calculation of probability of obtaining a given frequency are provided. Finally, the approach is applied to a simple design optimization example for intonation.

The paper is structured as follows. The first section provides a background on the construction of the maps using SVM. The second section introduces the basic physics of a clarinet as well as the corresponding simplified model. Finally, the last section provides a set of numerical results in order to highlight the capabilities and potential of the methodology when applied to musical acoustics.

EXPLICIT DESIGN SPACE DECOMPOSITION

Support Vector Machines (SVMs)

In order to build maps, a technique referred to as explicit design space decomposition (EDSD) [START_REF] Basudhar | An improved adaptive sampling scheme for the construction of explicit boundaries[END_REF][START_REF] Basudhar | A sampling-based approach for probabilistic design with random fields[END_REF], is used. The basic idea is to construct the boundaries of an n-dimensional map using a Support Vector Machine (SVM) [START_REF] Cristianini | Support vector machines and kernel methods: The new generation of learning machines[END_REF][START_REF] Gunn | Support vector machines for classification and regression[END_REF], which provides an explicit expression of the boundary in terms of the chosen parameters.

SVM is a machine learning technique that is widely used for classification. In optimization and reliability assessment, SVMs are used to approximate highly nonlinear constraints and limit-state functions. The most important features of SVMs are their ability to handle multiple criteria using a single classifier, to be insensitive to discontinuities [START_REF] Missoum | Reliability-based design optimization of nonlinear aeroelasticity problems[END_REF], and to be computationally very efficient. The ability of an SVM to handle discontinuities is essential in the case of sudden changes of acoustic regimes (e.g., change of register). A schematic example of an SVM separating configurations with sounds and without sound is depicted in Figure 1. An SVM defines an explicit boundary that separates samples belonging to two classes labeled as +1 and -1. Given a set of N training samples x i in an n-dimensional space and the corresponding class labels y i = ±1, an SVM boundary is given as:

s(x) = b + N i=1 λ i y i K(x i , x) = 0 ( 1
)
where b is a scalar referred to as the bias, λ i are Lagrange multipliers , and K is a kernel function. The Lagrange multipliers and the bias are solved for using a quadratic programming optimization problem. The optimization problem is formulated so as to maximize the margin between samples of both classes [START_REF] Cristianini | Support vector machines and kernel methods: The new generation of learning machines[END_REF][START_REF] Gunn | Support vector machines for classification and regression[END_REF]. The training samples for which the Lagrange multipliers are non-zero are referred to as the support vectors. The predicted class of any arbitrary point x is given by the sign of s(x).

The kernel function K in Equation ( 1) can have several forms, such as polynomial or Gaussian radial basis kernel. The Gaussian kernel (Equation (2)) is used in this article:

K(x i , x j ) = exp - ||x i -x j || 2 2σ 2 , ( 2
)
where σ is the width parameter. An initial approximation of the map is obtained using a design of experiments (DOE) [START_REF] Montgomery | Design and Analysis of Experiments[END_REF][START_REF] Giunta | Overview of modern design of experiments methods for computational simulations[END_REF][START_REF] Sacks | Design and analysis of computer experiments[END_REF] such as Latin Hypercube Sampling (LHS) or Central Voronoi Tessellation (CVT) [START_REF] Romero | Comparison of pure and "latinized" centroidal voronoi tesselation against various other statistical sampling methods[END_REF]. These DOE techniques are tailored so as to provide information over the whole space using a reasonable number of samples in higher dimensions. From an implementation point of view, it is important that the variables be scaled for the construction of the SVM.

Refinement of the SVM boundary. Adaptive sampling.

The initial approximation of the boundary using a DOE might not be accurate and needs to be refined while maintaining a reasonable number of calls to the acoustic model. This refinement is performed using an adaptive sampling scheme that was developed by the first author and his team and is described in [START_REF] Basudhar | An improved adaptive sampling scheme for the construction of explicit boundaries[END_REF]. The basis of the scheme is to select a sample in the sparse regions of the space (i.e., as far away as possible from existing sample) and also in the regions of highest probability of misclassification by the SVM. The latter criterion is obtained by locating the samples on the SVM. In order to illustrate the foundation of the algorithm, Figure 2 depicts an SVM constructed from two classes of samples (circles and stars) which is subsequently refined using an adaptive sample located in the most sparse region on the boundary.

Formally, the sample is found by solving the following optimization problem: where x nearest is the closest training sample (i.e., the one with minimum distance). This is a global (non-smooth) "max-min" optimization problem that can either be solved using a global optimizer such as a Genetic Algorithm or using a local optimizer with different starting points. A gradient-based technique such as Sequential Quadratic Programming (SQP) can be used by reformulating the problem into a differentiable one as detailed in [START_REF] Basudhar | An improved adaptive sampling scheme for the construction of explicit boundaries[END_REF].

max x ||x -x nearest || (3)
s.t. s(x) = 0 x min ≤ x ≤ x max (4) x 1 x 2 x 1 x 2 a) b)

Probability estimates

Once an SVM boundary is constructed, the probability that a configuration belongs to a specific class (e.g., belongs to the region of the space corresponding to self-sustained oscillations) can be obtained through Monte-Carlo simulations [START_REF] Melchers | Structural Reliability Analysis and Prediction[END_REF]. Given the probability density functions of the parameters (e.g., the blowing pressure follows a normal distribution), the probability P f of belonging to the "positive" class is approximated using N M C samples p i :

P f = 1 N M C N M C i=1 I s (p i ), (5)
where I s is the indicator function defined as:

I s = 0 if s(p i ) ≤ 0 1 if s(p i ) > 0

CASE STUDY: THE CLARINET

In order to demonstrate the proposed methodology for the mapping of acoustic regimes and provide the reader with the necessary background, this section focuses on clarinets. It is an arbitrary choice and any other musical instrument could have been chosen. An explanation of the physics involved in the production of sound is first provided. A simplified clarinet model is subsequently described.

The physics -Fundamental equations

By blowing air into the instrument through the reed channel (Figure 3), the player destabilizes the reed from its rest position. The oscillations of the reed modulate the incoming air flow ũ(t), thus exciting the acoustic resonances of the air column inside the instrument. The resulting pressure fluctuations p(t) in the mouthpiece amplify the reed oscillations, thus contributing to an increased modulation of the incoming air flow. Therefore, the instability is amplified through a feedback loop. The self-sustained oscillations are expected to occur at a frequency close to a resonance frequency of the air column. However, the reed is a cane plate and has its own mechanical resonances : undesired squeak sounds may be produced if the instability occurs close to one of these mechanical resonance frequencies (usually the one corresponding to the first flexural mode for the reed). Clarinet players learn to avoid these squeak sounds by properly adjusting two main control parameters : the blowing pressure inside the mouth, and the force applied by the lower lip on the reed (which alters the position of the reed at rest, thus the height of the reed channel).

The model has been detailed and discussed in [START_REF] Silva | Simulation of single reed instruments oscillations based on modal decomposition of bore and reed dynamics[END_REF] and only the resulting fundamental equations are given in this section. For the sake of simplicity, the dynamic behavior of the reed has been omitted. Considering as a reference the pressure p M = KH required to close the reed channel in the non-oscillating case (where K is the reed surface stiffness and H is the height of the reed channel at rest), we introduce the following dimensionless quantities for pressure in the mouth and in the mouthpiece, and for volume flow.

p(t) = p(t) p M , γ = p m p M , u(t) = Z c ũ(t) p M , (6)
where Z c = ρc S is the characteristic impedance for plane waves inside the resonator of cross section S, ρ is the air density and c is the sound velocity. Likewise it is convenient to define a dimensionless reed position :

x(t) = y(t)/H + γ (7)
and

ζ = Z c W H 2(ρp M ) -1
where W is the width of the reed. The two dimensionless parameters controlled by the player for a given fingering are γ and ζ, the blowing pressure and an embouchure parameter respectively.

The air flow. Mainly based on Hirschberg's considerations [START_REF] Hirschberg | Aero-Acoustics of Wind Instruments[END_REF], an explicit expression for the air flow u is given below:

u = ζ(1 -γ + p) |γ -p|sgn(γ -p) if γ -p ≤ 1 (8) u = 0 if γ -p ≥ 1 (9)
The first equation corresponds to the case of an open reed channel. In that case, the incoming air flow depends only on the pressure drop γ-p(t) between the mouth and the mouthpiece. When the tip of the reed gets in contact with the lay, it completely closes the reed channel, therefore canceling the air flow. This is expressed by the second equation. In this case, it is noteworthy that the effect of the reed dynamics on the air flow is ignored. This approximation is valid at low frequency, i.e. when the frequency of the note played is much lower than the first resonance frequency of the reed.

Continuous time equations.. We consider a cylindrical bore (with length L) for the clarinet. The model is the wave equation inside the tube, with Neumann and Dirichlet boundary conditions at the input and output of the bore respectively, and a source term that accounts for the airflow blown inside the instrument.

Modal coordinates p n (t) of the mouthpiece pressure are calculated through the projection on each mode in the time domain. The expansion onto the modes is truncated to the m first modes:

d 2 p 1 (t) dt 2 + ω 1 Q 1 dp 1 (t) dt + ω 2 1 p 1 (t) = 2c L du(t) dt (10)
. . .

d 2 p m (t) dt 2 + ω m Q m dp m (t) dt + ω 2 m p m (t) = 2c L du(t) dt
where ω n = (2n -1) 2πc 4L are the resonance angular frequencies of the air column, and Q n are the quality factors of the resonances. In equation [START_REF] Incio | Computational modelling of stringbody interaction for the violin family and simulation of wolf notes[END_REF], u is calculated using equations ( 8) and ( 9) with the pressure p calculated as the sum of its modal components:

p(t) = m n=1 p n (t).
Equations [START_REF] Incio | Computational modelling of stringbody interaction for the violin family and simulation of wolf notes[END_REF] corresponds to an input impedance for the clarinet defined as:

Z(ω) = jω n 2c L 1 ω 2 n -ω 2 + jωω n /Q n (11)
The quality factors can be derived analytically [START_REF] Chaigne | Acoustique des instruments de musique[END_REF]. Assuming that the radius is small in comparison to the wavelength and the phase velocity is equal to the speed of sound, a good approximation of the quality factors is:

1 Q n ≈ 2α 1 R µL ργ n c + 1 2 (k n R) 2 γ n ( 12
)
where γ n = (2n-1)π 2 , k n = γn L , µ is the viscosity, ρ is the density. α 1 is related to the absorption coefficient and is equal to 1.044 in this work (see [START_REF] Chaigne | Acoustique des instruments de musique[END_REF] for details). Unless otherwise stated, the results presented in the remaining of this paper were obtained with a resonator length equal to L = 1m, an interior radius equal to R = 7mm, a viscosity µ = 1.708 × 10 -5 kg.m -1 s -1 , and a density ρ = 1.29 kg.m -3 .

Numerical Implementation

The system of equations ( 10) is solved using ode solvers. For this purpose, the second order odes are reformulated into a system of 2m first order odes. As multiple time scales are involved in the problem (duration of blowing pressure transient, bore resonance frequencies, reed resonance frequency and reed-lay contact duration), an ode solver designed for stiff problems, namely ode15s from the Matlab ode Suite was used. Note that in order to obtain consistent and robust pressure time series, the relative and absolute convergence tolerances were tightened to 10 -5 and 10 -7 respectively.

KEY FEATURES OF THE APPROACH IN PRACTICE

In this section, the key features and potential of the approach are presented in the context of musical acoustics. These features are demonstrated through several test cases based on the simplified single reed instruments model described in the previous section.

Efficiency of the adaptive sampling

In order to highlight the efficiency of the adaptive sampling, the first set of results is based on the separation between regimes producing sounds and the soundless ones. We first use a model of clarinet with one mode (Equation [START_REF] Incio | Computational modelling of stringbody interaction for the violin family and simulation of wolf notes[END_REF] with m = 1).

Soundless configurations are obtained if the initial oscillations die down and reach a static regime, as shown in Figure 4. On the other hand a sound is produced if self-sustained auto-oscillations are reached as depicted in Figure 5. In order to differentiate between the two states, a simple tentative criterion is used: the oscillation amplitude is averaged over the last third N 2/3 of the time series. For a large enough time, the average value is compared to an arbitrary value ǫ 1 . Formally, the criterion reads:

N 2/3 N 2/3 p(t i ) > ǫ 1 Oscillations (i.e., sound) (13)
1

N 2/3 N 2/3 p(t i ) ≤ ǫ 1 Static regime (i.e., no sound).
The first boundary is constructed in the (ζ, γ) space (adimensional reed channel opening and mouth pressure). For a given instrument design, these two parameters can be considered as the most influential control parameters. Figure 6 depicts the corresponding boundary constructed using 20 DOE samples and 30 adaptive samples.

The theoretical threshold for the soundless configurations can be derived analytically [START_REF] Chaigne | Acoustique des instruments de musique[END_REF]:

γ th = 1 3 + αL ζ 2 3 √ 3 ( 14
)
where α = π 2 16QL . Q is the quality factor set to 40 for this problem. The corresponding boundary is superimposed to the SVM approximation in Figure 6. In the case a total of 50 samples were used (20 DOE samples and 30 adaptive), there is a small difference between the theoretical and SVM boundary. This difference disappears in the case when 80 adaptive samples are used as showed in Figure 7. This result reveals an important and well known conclusion: for most of the reed channel opening (represented by ζ), a sound is obtained if the pressure in the mouth (represented by γ) is approximately larger than one third. For small values of ζ, this is no longer valid with a threshold asymptotically increasing.

The example is also used to show the importance of the adaptive sampling scheme. For this purpose, the same boundary was created using a static design of experiments with 50 samples (i.e., no adaptivity), thus leading to a rather inaccurate boundary (Figure 6 b). The advantage of the adaptive sampling scheme was shown to become more pronounced as the dimension increases [START_REF] Basudhar | An improved adaptive sampling scheme for the construction of explicit boundaries[END_REF].

The second boundary is constructed in the (ζ, γ, Q) space (Figure 8), which, in this case, is assumed to be freely imposed. The boundary is based on 50 DOE and 100 adaptive samples. As expected, it shows that the lower the quality factor is, the higher the oscillation threshold. This is due to the fact that more losses in the resonator should be compensated by an additional amount of energy (i.e. a larger blowing pressure).

Through the two previous simple problems, it appears that the approach proposed in this paper could be used as a new way of studying the oscillation threshold in musical instruments. Note that other approaches in the literature use analytic developments around the static solution [START_REF] Wilson | Operating modes of the clarinet[END_REF][START_REF] Silva | Interaction of reed and acoustic resonator in clarinet-like systems[END_REF][START_REF] Cullen | Brass instruments: linear stability analysis and experiments with an artificial mouth[END_REF], numerical continuation of Hopf points [START_REF] Karkar | Oscillation threshold of a clarinet model: A numerical continuation approach[END_REF] or regular sampling of the design space [START_REF] Incio | A linearized modal analysis of the bowed string[END_REF]. The proposed method generalizes these attempts by removing the restriction on the types of models (black-box models can be used) and by providing a sampling strategy more effective than a simple grid approach.

Ability to converge towards complex boundaries

To demonstrate the ability of the method to generate complex boundaries, this set of results provide examples related to the playing frequency. The frequency criterion is based on the difference between the actual frequency of the signal f act and a reference frequency f ref . It is typically expressed in cents. The number of cents N cents is defined as: The criterion chosen compares N cents to a user defined threshold ǫ 2 . The reference frequency can be the frequency of a note (e.g., 440Hz). In our work we have used the natural frequencies of the resonator as reference or notes from the equal-tempered scale. The actual frequency of the signal was obtained using the freely available code Yin [START_REF] De Cheveigné | Yin, a fundamental frequency estimator for speech and music[END_REF].

N cents = 1200log 2 f act f ref (
It is noteworthy that the frequency of the produced sound can, for instance, jump from one neighborhood of the resonators frequencies to another. That is, the signal frequencies can be discontinuous, thus requiring specific approaches such as the classification technique proposed for the construction of the maps. Figure [START_REF] Terrien | Flute-like musical instruments: A toy model investigated through numerical continuation[END_REF] depicts the frequency criterion along with possibility of a "jump".

The criterion is applied to the clarinet model with two modes (Equation [START_REF] Incio | Computational modelling of stringbody interaction for the violin family and simulation of wolf notes[END_REF] with m = 2). The quality factors where approximated using analytical expressions available in Equation [START_REF] Guettler | On the creation of the helmholtz motion in bowed strings[END_REF]. The criterion aims at separating the configurations within a given number of cents from a specific frequencies (e.g., the resonator's natural frequencies or a given pitch) and the other configurations, including the static regime configurations (i.e., soundless ones). As pointed previously, it is worth insisting on the fact that the use of a classification technique is justified by the fact that the frequencies are discontinuous.

In this experiment, the criterion is used to identify the playing frequencies that are within 5 cents of the first natural frequency of the resonator. The natural angular frequencies of the resonator are:

ω k = qπc 2L q = 1, 3, 5, .. (16)
For a resonator of length L = 1m, this leads to a first and second natural frequency of 85.75Hz and 257.25Hz respectively. Figure 10 depicts the corresponding map constructed from a design of experiments with 100 samples and 180 adaptive samples generated with the scheme described in Section 2. It is noteworthy that despite the apparent simplicity of the map, its accurate construction with a reasonable number of samples is highly dependent on the initial design of experiments. Specifically, in the narrow region of the map corresponding to large values of the opening, if no sample is initially present in this area, the adaptive sampling scheme would have difficulty (i.e., would exhibit a poor convergence rate) to construct the boundary.

Figure 10 shows that the reed opening ζ partly dictates the ease of play of a given note. If the opening is too large (little support of the reed by the lip, i.e. high values of ζ), the blowing pressure γ must be very precisely controlled to play in tune. On the contrary, when the lip reduces the opening of the reed channel, playing in tune becomes easier for the musician because a lower accuracy is required on the control of the blowing pressure. To the authors' knowledge, this has rarely been addressed in the literature with the exception of a very recent work [START_REF] Coyle | An attempt at predicting the variation in playing frequencies for clarinets[END_REF].

The same experiment is repeated for the second register. In order to increase the number of cases reaching the second register (i.e., the second natural frequency of the resonator), the initial condition of the second component of the adimensional pressure in the modal basis was set to 0.9 while the first component was set to 0.09. Figure 11 depicts the region of the (γ, ζ) space where the playing frequency is within 5 cents of the second register. The map was constructed using 50 initial DOE samples and 100 adaptive samples. In order to demonstrate the flexibility of the approach and study the influence of initial conditions, a variable was introduced whose purpose is to weigh differently the initial condition of the first and second components of the pressure in the modal basis. The weight β is chosen so that p 1 (t = 0) = β and p 2 (t = 0) = 1 -β. This represents of course an artificial problem whose only purpose is to demonstrate the various types of parameters that can be involved in the construction of the maps. On a side note, the ability to control the registers to be reached can be useful for sound synthesis.

In a three-dimensional space (β, γ, ζ), we wish to identify the region of the space leading to the second register within 5 cents as in the previous problem. Figure 12 depicts the results obtained with 100 initial DOE samples and 80 adaptive samples. As expected, when the initial condition on p 2 increases (i.e., β decreases), the region of the space within 5 cents of the second register also increases.

Figure 12 highlights the strong impact of initial conditions on the behavior of the dynamical system. If β is between 0.4 and 1, it is impossible to play in tune on the second register regardless of the parameter values γ and ζ.

Probability estimates

As explained in Section 2.3, SVM can be used for the calculation of probabilities of belonging to either the "positive" or "negative" region of the space. Given probability density functions for the parameters, the probability of belonging to a region of interest can be efficiently computed using Monte-Carlo simulations with Equation 5.

A probabilistic approach is particularly interesting in the context of analyzing or designing musical instruments since control parameters and design parameters follow statistical distributions and are subjected to uncertainties. For instance, the blowing pressure might be assumed to follow a specific statistical distribution (e.g., normal) or the manufacturing tolerances might introduce uncertainties that with influence the acoustic behavior of the instrument. As an example, consider the map depicted in Figure 13 describing the region where the playing frequency is within 5 cents of the first resonator frequency. We wish to evaluate the probability of satisfying the intonation criterion knowing that the parameter γ and ζ follow normal distributions with identical means and standard deviations: γ ∼ N (0.5, 0.05) and ζ ∼ N (0.5, 0.05). Figure 13 depicts the corresponding joint distribution over the map with 10 5 Monte-Carlo samples. The resulting probability of belonging to the region with an "acceptable frequency" is 6.3%. To the authors knowledge, it is the first time that uncertainty is introduced in the investigation of tuning or playability.

MC_100_180adapt_5_cents_mode1_JbModif.pdf

A simple example of optimization for intonation

The ability to generate maps and to assess the probability of belonging to specific regions provides a framework to perform design optimization. As a demonstrative example, we wish to find the optimal length of a resonator so as to maximize the probability of having a playing frequency within 5 cents of the given note from the twelve-tone equal temperament scale. This "design for intonation" is of major practical importance in the world of musical instruments. As an example, consider the closest frequency in the equal temperament scale to the first natural frequency of a 1 m long resonator (85.75Hz). The corresponding frequency is found to be 87.30 Hz (note F2). The objective is to find the optimal length L * of the resonator that will maximize the probability of playing F2 within +/-5 cents as a function of γ and ζ. Formally, this can be written as:

L * = argmax L P ((γ, ζ) ∈ Ω), ( 17
)
where Ω is the region satisfying the intonation criterion. The region of interest is depicted in Figure 14. It was constructed using 100 DOE samples and 400 adaptive samples. Note that the region is rather thin and would not be easily obtainable without adaptive sampling. For a given value of the length, the probability can be estimated using Monte-Carlo simulations as in Section 2.3. In this work, the optimal value of L is searched within the interval [0.9, 1.10] m. Two cases of probability distributions are used for γ and ζ: normal N (0.5, 0.05) and uniform U (0, 1). The corresponding probabilities as a function of the length are depicted in Figure 15 as well as the corresponding optima. The optimal length is 0.97 m in the normally distributed case and 0.98 m for uniformly distributed variables.

Because this is a one dimensional optimization problem, the optimal length can be obtained by testing an array of cases. For higher dimen- sional optimization problems (including for instance side hole positions and sections), dedicated optimization techniques should be used.

CONCLUSION

A methodology was proposed to map the acoustic behaviors of wind instruments. A map of the acoustic regimes is accurately constructed using a technique referred to as explicit design space decomposition. This approach, based on an SVM classifier, enables one to accurately define explicit boundaries of the region of interest in terms of the selected parameters (e.g., blowing pressure and reed opening).

The results demonstrate the ability of the proposed approach to provide an understanding of the coupling between the parameters that could not be obtained otherwise. This difficulty stems from the highly nonlinear nature of the sound production in wind instruments. The maps produced for the two criteria are representative of the complexity of the phenomenon and the strong coupling between the parameters. In addition, these examples also demonstrate the potential high sensitivity of the acoustic behavior to small perturbations and uncertainties that the proposed technique is able to propagate. Finally, beyond analysis, this paper has demonstrated that the proposed mapping can be used as a tool for design. To the authors knowledge, this represents the first attempt to generate such maps.

The next steps of the research will include studies in higher dimensional spaces with more accurate models. In addition, the approach will also be tested to generate maps obtained experimentally with an artificial mouth [START_REF] Almeida | Clarinet parameter cartography: automatic mapping of the sound produced as a function of blowing pressure and reed force[END_REF][START_REF] Lopes | Control of an artificial mouth playing a trombone and analysis of sound descriptors on experimental data[END_REF] using a reasonable number of measurements. Finally, the mapping technique will be used to attempt instrument design optimization.

Figure 1 :

 1 Figure 1: Schematic depiction of an SVM boundary classifying sound producing configurations and soundless ones.

Figure 2 :

 2 Figure 2: Schematic representation of the EDSD adaptive sampling scheme before (a) and after adding one sample (b). The addition of a sample (red star) in the sparse region of the space on the SVM is the basis of EDSD. The red dashed boundary corresponds to the updated SVM.

Figure 3 :

 3 Figure 3: Schematic representation of a clarinet.

Figure 4 :Figure 5 :

 45 Figure 4: Soundless configuration. Static regime reached after a transient.

1

 1

Figure 6 :Figure 7 :

 67 Figure6: Boundary obtained using SVM with adaptive sampling (dashed blue curve) with a total of 50 samples (a). The SVM boundary separates sound producing regimes (blue triangles) and soundless ones (red squares). The solid red line is the theoretical boundary[START_REF] Chaigne | Acoustique des instruments de musique[END_REF]. For comparison, boundary created with 50 samples without adaptive sampling (b).

Figure 8 :

 8 Figure 8: Boundary constructed in the (ζ, γ, Q) space. The SVM boundary separates sound producing regimes (blue dots) and soundless ones (red dots).

Figure 9 :

 9 Figure 9: Depiction of the frequency criterion. The light green strip represents acceptable playing frequencies with a reference frequency chosen as f 1 . Possible jump from one peak of the frequency response function to another, thus leading to a discontinuity.

Figure 10 :

 10 Figure 10: SVM boundary identifying configurations within 5 cents of the first resonator natural frequency (red squares). The region of interest is surrounded by static solutions and the solutions with a difference larger than 5 cents (blue dots).

Figure 11 :

 11 Figure 11: SVM boundary identifying configurations within 5 cents of the second register (red squares).

Figure 12 :

 12 Figure 12: Region of the space within 5 cents of the second register (red squares). Inclusion of initial conditions through the parameter β.

Figure 13 :

 13 Figure 13: Example of probability estimates of belonging to the region where the playing frequency is within 5 cents of the first natural frequency of the resonator.

Figure 14 :

 14 Figure 14: Intonation map with respect to the length, γ and ζ. The reference frequency corresponds to the note F2 of the well-tempered scale.

Figure 15 :

 15 Figure 15: Probability of "good" intonation as a function of the length. Case of normally distributed (a) and uniformly distributed (b) γ and ζ.

ACKNOWLEDGMENTS

This study was performed during a visit of the first author to the CNRS in Marseille, France. This work was performed within the framework of the Labex MEC (ANR-11-LABX-0092) and has received support from the french National Research Agency (project AMidex (ANR-11-IDEX-0001-02), and project CAGIMA (ANR-11-BS09-0022)). The support of the National Science Foundation for the explicit design space decomposition part (grant CMMI-1029257) is gratefully acknowledged. The authors are also indebted to Dr. Jean Kergomard for priceless technical discussions.


Laetitia Dablanc
email: laetitia.dablanc@ifsttar.fr

Genevieve Giuliano
email: giuliano@usc.edu

Kevin Holliday
email: holliday@price.usc.edu

Thomas O'brien
email: thomas.obrien@csulb.edu

Best Practices in Urban Freight Management: Lessons from an International Survey

Freight movement is essential to the function of metropolitan areas, yet it generates many externalities, including congestion, air pollution, noise, and greenhouse gas emissions. Metropolitan areas around the world are seeking ways to manage urban freight and its impacts. This paper presents results from a comprehensive international survey of urban freight management strategies. Our purpose was to examine the effectiveness of alternative strategies and assess their transferability for broad US implementation. We use three categories to describe urban freight strategies: last mile/first mile deliveries and pickups, environmental mitigation, and trade node strategies. We find that there are many possibilities for better managing urban freight and its impacts including labeling and certification programs, incentive-based voluntary emissions reductions programs, local land use and parking policies, and more stringent national fuel efficiency and emissions standards for heavy duty trucks. More research is needed on intrametropolitan freight movements and on the effectiveness of existing policies and strategies.

INTRODUCTION

Commercial transport is crucial for the functioning of metropolitan areas. Trucks and vans provide local last mile deliveries and pickups, as well as most medium haul freight transport. In metro areas that serve as trade hubs, trucks are a major part of wholesaling, distribution, logistics and intermodal operations. Commercial traffic generates significant externalities in metro areas, including congestion, air pollution (small particulates, NOx, greenhouse gas emissions), noise, and traffic incidents. In addition, heavy duty vehicles affect pavements and generate additional demands for increased road capacity.

Metro areas are seeking ways to better manage goods movements. Researchers and local stakeholders have explored a range of strategies, such as better routing algorithms, smaller or newer trucks, consolidated local delivery stations, alternative modes, off-peak deliveries, low emission zones and freight partnerships. The purpose of this paper is to consider the state of research and practice in the US context. There are many interesting and innovative strategies being developed in Europe and other parts of the world. The extent to which these strategies are transferable to the US context depends on the complex governance arrangements in which urban freight policy takes place in the US.

This paper is organized as follows. We begin with a brief review of the urban freight literature. We then describe the sources of our research synthesis. We summarize the key findings of our study and lessons learned from our investigation of experiments with various policy measures. We consider whether these experiments are transferable in the US and may be identified as best practices. We close with some recommendations and suggestions for future research.

BACKGROUND AND LITERATURE REVIEW

Although there is increasing experimentation in solving urban freight problems, the relevant literature is limited and fragmented. A major challenge for research is the lack of appropriate data; studies have addressed data availability and promote more comprehensive data collection [START_REF] Ambrosini | Objectives, Methods and Results of Surveys Carried out in the field of Urban Freight Transport: An International Comparison[END_REF][START_REF]A Concept for a Freight Data Program[END_REF][START_REF] Wolpert | Status Quo of City Logistics in Scientific Literature. Systematic Review[END_REF]. Data on truck and van movements in US urban areas is almost non-existent; consequently the extent of the urban freight problem remains unknown. There is an extensive literature in logistics, with studies on truck routing, network optimization, and related topics [START_REF] Chassiakos | Selected papers from the second national urban freight conference, Long Beach, California[END_REF][START_REF] Dessouky | Selected papers from the National Urban Freight conference[END_REF][START_REF] Sonntag | A Computer Model of Urban Commercial Traffic, in Transport , Policy and Decision Making[END_REF]. This literature is not urban in the sense of considering the urban context (freight/passenger conflicts, externalities), but rather addresses routing and allocation problems that are common in the urban environment. Transport economists have examined the economic structure of the drayage trucking industry, shipper behavior, and responsiveness to pricing policies [START_REF] Holguín-Veras | The Impacts of Time of Day Pricing on the Behavior of Carriers in a Congested Urban Area: Implications to Road Pricing[END_REF][START_REF] Wang | Behavioral Analysis of Commercial Vehicular Mode Choice Decisions in Urban Areas Transportation Research Record[END_REF][START_REF] Kawamura | Evaluation of delivery consolidation in US urban areas using a logistics cost analysis[END_REF]. City logistics is an emerging field of study; it seeks to improve freight efficiency while minimizing both economic costs and social externalities, looking at city logistics in a broader sense than transportation [START_REF] Dablanc | City Logistics[END_REF]. This is also the conclusion achieved by [START_REF] Wolpert | Status Quo of City Logistics in Scientific Literature. Systematic Review[END_REF] in a recent review of city logistics in the academic literature. Researchers have examined spatial dynamics in freight activities, the transport geography of industry networks, and urban freight distribution systems [START_REF] Dablanc | Atlanta: A Mega Logistics Center in the Piedmont Atlantic Megaregion (PAM)[END_REF][START_REF] Rodrigue | The Geography of Global Supply Chains: Evidence from Third Party Logistics[END_REF][START_REF] Rodrigue | Comparative North American and European Gateway Logistics: The Regionalism of Freight Distribution[END_REF][START_REF] Cidell | Concentration and decentralization: the new geography of freight distribution in US metropolitan areas[END_REF][START_REF] Hesse | The City as a Terminal: The Urban Context of Logistics and Freight Transport[END_REF][START_REF] Hesse | The transport geography of logistics and freight distribution[END_REF].

There is a growing literature on the externalities associated with urban freight. The truck [START_REF]An Initial Assessment of Freight Bottlenecks on Highways[END_REF] and rail congestion [START_REF] Bryan | NCHRP REPORT 586: Rail Freight Solutions to Roadway Congestion-Final Report and Guidebook[END_REF] studies sponsored by USDOT show that freight bottlenecks are most prevalent in metropolitan areas, particularly where trade flows are concentrated, as in Los Angeles, Atlanta, Chicago and New York. Case studies document local congestion associated with truck parking and loading [START_REF] Bomar | Urban Freight Case Studies: New York[END_REF]. There is a growing number of studies of the health impacts of small particulates associated with diesel truck emissions, notably the longitudinal children s health study in Los Angeles [START_REF] Peters | Epidemiologic Investigation to Identify Chronic Effects of Ambient Air Pollutants In Southern California. Prepared for the California Air Resources Board and the California Environmental Protection Agency[END_REF]. Ports and intermodal terminals tend to be air pollution hot spots due the concentration of truck traffic and the prevalence of older, more polluting trucks in local delivery fleets. Trucks are also significant contributors to GHG emissions, accounting for about two-thirds of emissions from freight sources [START_REF]Freight and Climate Change Background Paper for the Oregon Freight Plan[END_REF].

There is an emerging literature on urban freight policy, much of it focused on environmental impacts and regulation [START_REF] Danielis | Urban freight policies and distribution channels: a discussion based on evidence from Italian cities[END_REF]. Studies of specific policy examples include off-hours deliveries in New York [START_REF] Holguín-Veras | The Impacts of Time of Day Pricing on the Behavior of Carriers in a Congested Urban Area: Implications to Road Pricing[END_REF], low emission zones [START_REF] Dablanc | Urban Goods Movement and Air Quality, Policy and Regulation Issues in European Cities[END_REF], and the container fee program in Los Angeles [START_REF] Giuliano | Extended gate operations at the Ports of Los Angeles and Long Beach: a preliminary assessment[END_REF]. These studies have not reached a point of synthesis or general understanding of what policies are effective, and what conditions are required for effective implementation [START_REF] Giuliano | NCFRP Project 36(05) Synthesis of Freight Research in Urban Transportation Planning[END_REF].

METHOD

Our synthesis is based on a review of the domestic and international literature [START_REF] Giuliano | NCFRP Project 36(05) Synthesis of Freight Research in Urban Transportation Planning[END_REF]. Our review includes journal publications, government reports, consultant reports, and unpublished papers and materials, resulting in 261 references of which 108 are academic papers and scientific books. We believe this review to be fairly comprehensive regarding academic publications in English, as it results from a search in the main publication databases covering transport engineering, transport geography, transport economics and logistics as well as transport planning. It matches the recent literature review on city logistics by (3). Our review is focused more on local sources, such as freight data collection in specific cities or national reports from ministries and institutions. These sources were identified from various contacts or previous work. Our literature review was supplemented with communications from project sponsors and data collected from secondary sources. A full list of references is available in Giuliano et al, 2013 [START_REF] Giuliano | NCFRP Project 36(05) Synthesis of Freight Research in Urban Transportation Planning[END_REF] and only the most significant ones have been referenced here. Our synthesis included: 1) an assessment of current knowledge on the impacts of freight in metropolitan areas; 2) a survey of mitigation strategies proposed, planned or implemented in metropolitan areas; 3) a discussion of the US governance and regulatory context; and 4) our evaluation of freight management strategies and their potential for implementation. In this paper we present an overview of mitigation strategies. We selected 63 practices based on their recurrence in the literature and, when available, their reported positive results. Half of them are from North America. The paper finally provides our assessment of the most promising strategies for broad implementation in the US.

RESULTS: BEST PRACTICES AND POLICY INITIATIVES

In response to growing urban freight problems, cities around the world have engaged in extensive experimentation. In this section we summarize findings, discuss effectiveness, and consider transferability to widespread implementation in the US.

We organize our discussion around three general categories of urban freight management problems: local last-mile/first-mile delivery and pick-up, environmental impacts, and trade node problems. Last mile strategies address local deliveries and pick-ups to or from urban businesses or residences (home deliveries). They aim towards making these trips more efficient. Strategies that reduce environmental impacts focus on reducing emissions and noise by regulation or offering incentives to use less polluting vehicles. Finally, we consider strategies related to trade nodes (i.e., cities that are hubs for national and international trade) where there are larges flows to and from ports, airports, or intermodal facilities.

Last mile strategies

One-third of urban truck traffic is goods pick-ups. The last mile (or rather miles) represents the final haul of a shipment to its end receiver, be it a shop, a business, a facility or a residence in case of home deliveries. (Collectively we will refer to these trips as the last mile. ) Serving local businesses and residences in cities is inefficient for several reasons. First, product is often delivered from vendor to establishment, so a given establishment (say department store) may receive multiple deliveries each day. Small deliveries across many destinations generate complex routing problems. If deliveries could be consolidated across vendors, more efficient routing and fewer trips would be possible (26). Second, deliveries may be restricted to certain routes or time periods, adding additional constraints on routing and scheduling. Restrictions on night deliveries, or the reluctance of urban business owners, force more trips to take place during peak hours, adding to congestion. Third, home delivery is inefficient due to the small size of products, the spatial dispersion of residences, competition within the local delivery industry, and the frequency of failed deliveries [START_REF] Xing | Physical Distribution Service Quality in Online Retailing[END_REF].

European cities face more serious local delivery problems than US cities because of their older built form, higher average density, and greater share of small and independent businesses. European cities also have the apparent advantage of more regulatory control over truck access and roads. It is therefore not surprising that the majority of last mile experiments have come from overseas -Europe in particular. In the US, the few domestic policy experiments that do exist (like clean truck programs and off-peak deliveries) come from either of the two largest trade node cities: New York and Los Angeles. Other North American cities freight initiatives tend to center on new or improved infrastructure (such as grade separations, added highway capacity, or logistics parks) rather than operational changes

The main types of last miles strategies and some examples of each are presented in Table 1. The main sources of information are [START_REF] Holguín-Veras | The Impacts of Time of Day Pricing on the Behavior of Carriers in a Congested Urban Area: Implications to Road Pricing[END_REF][START_REF] Dablanc | Urban Goods Movement and Air Quality, Policy and Regulation Issues in European Cities[END_REF][START_REF] Sugar | City Logistics Best Practices: a Handbook for Authorities[END_REF][START_REF] Palmer | Time, cost and CO 2 effects of rescheduling freight deliveries[END_REF][START_REF] Ville | The limits of public policy intervention in urban logistics: lessons from Vicenza (Italy)[END_REF]. Table 1 clearly illustrates the preponderance of examples coming from outside the US.

[TABLE 1]

Labeling or other certification programs

Certification and labeling programs are examples of voluntary regulation. The public sector negotiates with private industry to develop a set of voluntary targets or operating rules that confer either recognition or special benefits like flexible delivery hours. Certification and labeling programs include the various green certification programs that promote use of cleaner vehicles, cleaner fuels, or operations during less congested periods of the day. Effectiveness depends on how much agreements change behavior. Certification programs that allow access to loading facilities, or extended delivery hours offer a significant benefit to shippers, and therefore make it easier to justify the purchase of new compliant vehicles. Certification programs are often the result of Freight Forums, or participatory processes including public and private stakeholders. Two well-known Freight Forums, in London and Paris, resulted in detailed Freight Plans.

The certification programs we reviewed were perceived as very successful both by the public sponsors and private participants. One potential problem is the buy-in and participation of all industry segments; for example the large shippers are more capable of negotiating program conditions with public sponsors, and hence programs may be designed to the advantage of larger shippers. Certification programs may increase trust and foster more collaborative relationships between industry and government. Shippers may also enjoy a competitive advantage when bidding for contracts, as more clients place value doing business with green firms. Finally, certification programs are relatively low cost, with most of the costs in the form of transactions costs establishing and maintaining public-private relationships. They may also evolve: as targets are reached, new targets are negotiated, leading to significant improvements over time.

Voluntary regulation is a good fit with the US context of decentralized governance and dispersed regulatory authority. In cases where direct regulation is either impossible (due to lack of authority) or infeasible, voluntary regulation may be the best available alternative.

Traffic and parking regulations

City efforts to manage last mile problems have focused on local traffic and parking regulations, because these tools are clearly within local authority. In theory traffic and parking regulations are effective as long as they are enforced. However, cities have no control over demand for pickups and deliveries, and consequently traffic and parking regulations are limited tools for managing last mile problems. In practice, highly restrictive regulations are costly to enforce and may lead to other problems. Restricting truck parking areas may result in trucks double-parking in the roadway or using curb space reserved for other purposes. When the demand for truck pickup and delivery greatly exceeds supply of loading and parking areas, enforcement becomes costly and increasingly difficult, as the risk of being cited becomes less costly than the delays incurred in waiting for a parking spot.

Traffic and parking regulations have a mixed record of success. Restrictions on truck access or the limit of truck deliveries to certain days of the week tend to shift truck traffic to smaller vehicles (generating a net increase in truck VMT), or concentrate traffic into shorter time periods (generating more congestion). Regulations that seek to use road resources as efficiently as possible tend to be successful. Barcelona s policy of allowing use of traffic lanes for pickup and delivery during off-peak hours is an example. San Francisco s recent implementation of dynamic parking charges is another. The lesson drawn from both US and international examples is that local freight demand must be accommodated, hence strategies that manage rather than restrict freight deliveries tend to be more effective.

Local planning policy

Local jurisdictions have land use planning authority, and hence may set policies and guidelines for incorporating freight deliveries into new developments, for the design of loading docks, and for parking and loading standards. With increased development in city cores and more frequent deliveries for each business, freight demand has increased, while the scarcity of road and curb space, as well as ever higher land values, increase the cost of managing demand. New development or redevelopment offers the opportunity to implement planning standards for onsite freight facilities. Examples include Tokyo s and New York s requirements for new commercial developments. Barcelona goes further, adding a requirement for minimum storage areas for new restaurants and bars. On-site facilities lessen the need for on-street loading zones, reducing conflicts with passenger demands. On-site facilities also add to building costs, and hence may be resisted by the development community.

Cities may also develop freight loading and parking standards for off-site activities (e.g., in a public right of way). There are more opportunities in developing areas, where the road infrastructure is still being constructed. However, standards can have an impact over time even in already developed areas if they are tied to future development and redevelopment.

Experiences with on-site planning policies have been largely positive. Although such requirements add to development costs, they also add to commercial property value by assuring that freight deliveries are accommodated. Shippers and truck drivers clearly benefit from having reliably available loading facilities. These policies are a good fit in the US context, where the authority of local governments to develop and implement planning and building guidelines is clearly established. The ability to negotiate through the zoning and approval process allows for flexibility in enforcement and is widely accepted.

City logistics and consolidation programs

Consolidation programs seek to reduce truck traffic by finding ways to combine pickups and deliveries of different shippers or difference receivers. They often focus on changing the supply chain, rather than on the final (or initial) step of the chain. The simplest (from a supply chain perspective) consolidation schemes are those that focus on final delivery or pickup, e.g. on the end of the chain, such as pick-up centers for online purchases. These common pick-up points reduce home deliveries (truck trips) but their impact on private vehicle trips is unknown and depends on how consumers access these centers.

Another version of consolidation is shared logistics spaces, where multiple shippers use an in-town facility to consolidate loads (typically from different, out of town logistics facilities) before final deliveries. The intent is to reduce truck VMT by more efficient routing of final deliveries (or initial pick-ups). The most ambitious version is the urban consolidation center, where goods from multiple shippers or vendors are combined and delivered by third-party trucking firms. Although shippers may benefit from the lower costs of consolidated deliveries, whether these benefits would offset the rental and added labor costs of trans-loading is unclear. In the many European experiments, consolidation centers were not feasible without public subsidies and many have since closed.

The transferability of consolidation schemes to the US context is limited. The required subsidies to freight operators would be politically difficult, even if local jurisdictions had the funding to provide. Any effort to force consolidation in the US via regulation (as in several European cities) would be very difficult due to interstate commerce laws.

Off-hours deliveries

Off-hours deliveries seek to shift truck activity out of the peak traffic periods and hence reduce congestion and emissions, yet few examples of off-hours delivery programs exist. Constraints on the trucking side include federal hours of service requirements, shift premium pay for unionized drivers, and possible efficiency losses associated with spreading shipments out across more hours of the day. Constraints on receivers include having to open receiving facilities early and to operate loading terminals more hours of the day, shift premium pay for terminal workers, and local zoning codes that prohibit after hours truck activities in residential neighborhoods.

There is only one permanent off-hours program in the US, the PierPass program at the Los Angeles/Long Beach ports. It was implemented due to unique circumstances that do not exist in other US metropolitan areas. A New York City demonstration was the first and only incity program. It has resulted in reduced congestion, energy consumption and emissions, and thus demonstrates the potential benefits of such programs. Off-hours delivery may have potential as a voluntary regulation. Shippers might be incentivized to purchase and use quieter trucks and handling equipment in exchange for being able to deliver off-hours.

Intelligent Transport Systems (ITS)

The use of ITS for monitoring or managing urban freight include technologies for providing realtime traffic (and parking) information, automated enforcement of parking or traffic regulations, toll collection, or automated access control. Use of ITS for monitoring truck traffic via license plate readers and other devices is extensive outside the US. Automated monitoring systems involve high upfront costs, and tend to be used either as part of road pricing systems or limited access zones. Once implemented, automated systems make possible continuous, low cost enforcement of tolls or access zones, and thus can be very effective.

Transferability in the US depends on the perceived acceptability of the policies to be implemented. So far, security at limited access facilities has proven to be an acceptable justification for semi-automated monitoring. The use of tolls to manage congestion in metropolitan areas is not yet widely accepted. The New York City congestion pricing proposal is illustrative; it included truck tolls that could be discounted by using clean trucks, and studies indicated that congestion and emissions reductions would be substantial. However, we expect that tolls will become more acceptable as congestion increases and funding from traditional sources to support capacity expansion declines.

A second implementation challenge in the US is the general resistance to automated monitoring by public authorities. An illustrative case is the conflict surrounding cameras used to enforce red light violations at intersections. Monitoring could provide comprehensive data on truck movements, which is greatly needed for better analysis of urban freight problems. However, these data may be perceived as proprietary and resisted by trucking companies and shippers. Use of ITS for truck tolls or automated monitoring outside limited access facilities appears to have limited transferability to the US context.

Strategies to reduce environmental impacts

Strategies to reduce environmental impacts seek to reduce truck emissions and energy consumption by improving engine performance, shifting to cleaner (and quieter) conventional diesel trucks or alternative fuel trucks, or shifting freight to more energy efficient modes. Our review makes clear that strategies that address the entire commercial fleet have the most impact, even if the impact is small on a per vehicle basis. Strategies that impose substantial costs on private industry will not be adopted unless industry is forced to do so, and strategies that seek to shift freight from trucks to slower modes are not attractive to industry without large subsidies, and may have little impact on emissions or energy consumption. Strategies to reduce environmental impacts are summarized in Table 2. The main sources of information are [START_REF]Freight and Climate Change Background Paper for the Oregon Freight Plan[END_REF][START_REF] Dablanc | Urban Goods Movement and Air Quality, Policy and Regulation Issues in European Cities[END_REF][START_REF] O Brien | Contested Trade and Policy Responses in Southern California[END_REF][START_REF]Clean Cities Guide to Alternative Fuels and Advances Medium-and Heavy-Duty Vehicles[END_REF][START_REF] Goevaers | PIEK low noise equipment, off peak hours transport[END_REF][START_REF] Maes | Low emission zones in Europe: their impact on sustainability and logistics, 4th METRANS national urban freight conference[END_REF][START_REF] Dablanc | Freight Transport, A Key for the New Urban Economy, Report for the World Bank as part of the initiative Freight Transport for Development: a Policy Toolkit[END_REF].

[TABLE 2]

Truck fuel efficiency and emissions standards

Truck fuel and efficiency standards have been demonstrated to be one of the most effective tools for reducing emissions. The recent changes in light truck CAFÉ standards will have a significant impact on the light truck portion of the freight vehicle fleet. The shift to cleaner diesel engines and fuels is having a similar impact on heavy duty trucks. The Los Angeles/Long Beach ports Clean Truck Program is by far the most ambitious emissions reduction program in the US, and in four years led to large reductions in diesel truck emissions. We expect fuel efficiency and emissions regulations to continue to be one of the most effective tools for reducing air pollution and CO 2 emissions in metro areas.

Alternative fuels and vehicles

Alternative fuel vehicles (AFVs) have been widely promoted in the US, but have achieved little market penetration due to higher capital and operating costs, the complexities of operating diverse fleets, limited range, and lack of fueling infrastructure. In Europe, even large subsidies have not prompted adoption of AFVs on any significant scale. AFVs are not yet sufficiently competitive with heavy duty diesel engines, and the progress being made in reducing diesel emissions may make it more difficult for AFVs to compete. However, the largest private delivery firms FedEx, DHL, and UPS are all experimenting with AFVs and have small numbers of electric and hybrid electric trucks operating in various cities.

In Europe we noted experiments with smaller AFVs, such as small vans and cargocycles for local deliveries. Niche markets may exist in the most dense US city centers (New York, Chicago, Boston), depending on the costs (labor, new vehicles) relative to conventional vans or small trucks. Lack of a potentially large market suggests that these strategies would have little impact on emissions reductions.

Low Emission Zones (LEZs)

Low emissions zones (LEZs) limit the types of vehicles that may enter a given part of the city. The limitation is based on emissions and energy consumption characteristics. LEZs have been established in several European cities LEZs have some obvious advantages: to the extent that performance standards are imposed on all trucks, the entire urban fleet is affected, and emissions reductions could be large. LEZs may generate secondary benefits by forcing the re-organization of the local trucking industry into larger and hence more efficient operations (we note that whether LEZs generate net benefits is uncertain, as the elimination of small operators would eliminate jobs and small businesses.).

Although a potentially effective strategy, the transferability of LEZs to the US context is low. In the absence of jurisdictional authority, a LEZ would have to be established as a voluntary program.

Alternative modes

Efforts to shift truck freight to slower but more energy efficient and cleaner modes have not been successful. Experiments in Europe using the regional rail system to ship goods to central areas for delivery show that large public subsidies are required. Studies of using commuter rail for package delivery failed to result in demonstrations or experiments. Efforts to shift freight to water have been similarly unsuccessful, both in the case of coastal shipping and river transport. Waterborne freight in the US continues to lose market share.

Mode shifting has large impacts on the supply chain. In order to use a slower mode, cargo owners must hold the inventory longer, and these inventory costs tend to exceed the higher costs of using faster modes. In addition, mixing modes adds to the number of times shipments must be handled, further increasing labor and facility costs. The most promising segments for mode shifting are through freight traffic (port or airport imports/exports) in large volumes, as for example increasing on-dock rail facilities to eliminate short drayage trips, or large volume, longer distance deliveries (say to distant distribution and warehouse centers) where rail is close to competitive with trucking.

Community environmental mitigation

The US has taken the lead in the incorporation of environmental justice as a performance measure for new freight projects. In part this is due to the socio-geography of US cities, where poor and minority populations tend to be concentrated near major freight facilities. The environmental review process provides a venue for environmental justice concerns. More recent research on the relationship between emissions and health has created an imperative for industry to find solutions to problems that might otherwise prevent them from securing the needed support of elected officials and regulatory agencies. Environmental justice considerations are therefore widely institutionalized in the transportation planning process and often involve industry-government partnerships. Examples include SCAG s Toolkit for Goods Movement, New York City s truck impact study, and Baltimore s industrial overlay zone study.

US ports have been particularly proactive in addressing environmental justice concerns. In addition to the extreme case of Southern California, clean truck programs, freight rail investments, and elimination of at-grade rail crossings are part of programs in New York/New Jersey, Seattle, and Oakland, as well as Chicago and Atlanta, two major intermodal hub cities.

Trade node strategies

Trade hubs and gateways places with large ports or airports, intermodal transfer points, or border crossings are the focus of freight flow associated with national and international trade. Trade hubs share the same last mile issues addressed in previous sections such as truck and van delivery and access issues, evening and weekend vehicle movements, and incompatible land uses. However, trade hubs are further defined by the scale and scope of operations that take place within them, particularly in the port, warehousing and distribution sectors. A combination of rising trade volumes, demand for larger facilities and the cost of land have pushed distribution centers (DCs) and warehouses to the periphery of metropolitan areas. These facilities generate freight-related activity that may pass through the urban core on their way from ports and airports to markets outside the region.

Unlike the last mile and environmental strategies outlined above, the majority of trade node strategies have been developed and tested in the US context. The largest trade nodes in particular Southern California have had the greatest influence in the development of strategies to address environmental problems. In the Southern California gateway, the threat of legislative mandates and rising trade volumes created a unique set of conditions that favored an industrydriven response to environmental pressures. The question is whether the same conditions exist in other places in the US. Both political pressure and competitive pressures exist in other parts of the world, but it is apparent from the research that the two in combination drive the environmental agenda in trade gateways. In the US, where good intermodal connections encourage the development of pass-through traffic transited through transload centers, the gateway plays a pivotal role in framing the debate surrounding the environmental impacts of trade. Trade node strategies are summarized in Table 3. The main sources of information are [START_REF] Holguín-Veras | The Impacts of Time of Day Pricing on the Behavior of Carriers in a Congested Urban Area: Implications to Road Pricing[END_REF][START_REF] Giuliano | Extended gate operations at the Ports of Los Angeles and Long Beach: a preliminary assessment[END_REF][START_REF] Davies | Container Terminal Reservation Systems (Power Point Presentation) Presented to the 3rd National Urban Freight Conference[END_REF][START_REF] Goodchild | Free and Secure Trade Commercial Vehicle Crossing Times at the Pacific Highway Port of Entry[END_REF][START_REF] Mu | Scheduling Freight Trains Traveling on Complex Networks[END_REF][START_REF] Le-Griffin | Container Terminal Productivity: Experiences at the Ports of Los Angeles and Long Beach[END_REF][START_REF] Roorda | Exclusive Truckways: Exploring Potential in Canada s Heartland[END_REF][START_REF] Woudsma | Innovation and Stakeholder Collaboration in West Coast Gateways: An Analysis of the Seaport and Freight Movement Industries[END_REF][START_REF] Giuliano | The terminal gate appointment systems at the Ports of Los Angeles and Long Beach: An Assessment[END_REF][START_REF] Giuliano | Extended gate operations at the Ports of Los Angeles and Long Beach: A preliminary assessment[END_REF][START_REF] Giuliano | Regulation and response at the San Pedro Bay Ports[END_REF].

[TABLE 3]

Appointments and pricing strategies at ports

These strategies attempt to spread the flow of truck traffic passing through terminal gates across more hours of the day. Appointments have been implemented at several ports. They have the potential to increase the efficiency of port operations and therefore reduce truck turn times (hence reducing truck idling), but to date there is little evidence that such efficiencies are being realized. Appointments require operational changes by terminal operators, so they are likely to be used effectively only when yard congestion makes it worthwhile.

The sole example of pricing-based terminal gate operations is the PierPASS program in Southern California. PierPASS was intended to reduce road congestion and it proved successful at shifting a significant amount of eligible cargo to the evening (approximately 40%). No other US metro area has the severity of congestion and air pollution to motivate use of peak fees, and no other port is inclined to take the risk of losing business in response to a fee. Shifting truck traffic at the ports generates changes along the rest of the supply chain, including distribution centers and retail establishments which presumably also operate on more traditional work schedules. The net benefits at the system level are not yet proven.

Road pricing and dedicated truck lanes

Despite the demonstrated effectiveness of congestion pricing in the few places where it has been implemented, pricing strategies in the US continue to be difficult to implement. There is more use of pricing strategies in Europe and Asia compared to the US, and at least a few examples of truck pricing, notably the weight-distance fees in Switzerland, Austria and Germany, and the cordon pricing scheme in London. There are numerous proposals for truck tolls in the US, including the New York bridge toll plan, and proposed tolled truck lanes in Atlanta, and in Los Angeles, but none of them have even reached the stage of being part of an accepted project.

Truck pricing may be more difficult than pricing passenger cars because of the competition between trucking and rail. The trucking industry argues that they already pay their fair share for using the roadways, and additional charges would reduce their competitiveness with rail. From an environmental perspective, if trucking generates more emissions per ton of freight carried, this shift would be socially beneficial despite the negative impact on the trucking industry. Despite their promise for managing congestion, implementation of pricing strategies will require extensive education and political leadership.

A second strategy (often linked with tolls to offer a funding mechanism) is truck-only lanes. They have been proposed in major metropolitan areas (most notably Atlanta) and included in regional transportation plans. They have failed due to lack of funding as well as a scarcity of land. Truck lanes are costly to build due to pavement and geometry requirements, and can rarely be justified on the basis of truck volumes. Given the fiscal constraints facing the US highway system, truck-only facilities do not appear to be a promising option for dealing with truck traffic.

Accelerated truck emissions reduction programs

Given the success in the US of national regulation to increase fuel efficiency and decrease emissions, a logical extension is to accelerate the introduction and use of cleaner vehicle at trade nodes. Several US ports have clean truck programs, which are intended to accelerate the use of cleaner diesel and alternative fuel vehicles in drayage trucking. The most aggressive effort is the Clean Truck Program (CTP) at the Los Angeles/Long Beach ports [START_REF] Giuliano | Regulation and response at the San Pedro Bay Ports[END_REF]. Seattle, Oakland, and New York/New Jersey have programs with more flexibility and less aggressive targets. These programs are examples of voluntary regulation: the targets are reached via negotiation and are beyond regulatory requirements. As voluntary, negotiated programs, they are a good fit in the US context.

Equipment management

Another potential source of reducing truck VMT is to use port-related freight equipment chassis and containers more efficiently. Ownership practices result in many extra trips for truckers, because they are required to match containers with the same owner s chassis. If management practices are modified by the owners, it becomes possible to share containers and chassis, reducing VMT associated with these movements. Equipment owners are motivated to experiment with different models due to the growing standardization of equipment characteristics (and therefore the declining value of branding one s own equipment), the costs of owning equipment that is idle much of the time, and the costs of storing equipment at land facilities. Public sector assistance may be necessary to assist with land assemblage for shared equipment facilities, and to sponsor studies.

Shared equipment offers a promising way to reduce truck trips while increasing the efficiency of port-related freight operations. Since it is industry motivated, it is a good fit in the US context.

Rail strategies

Efficient rail and intermodal facilities are critical to international trade. High volume rail corridors conflict with surface road traffic at at-grade rail crossings, and conflict with passenger commuter rail traffic. The main trade node city strategy to address these problems is capital investment to increase rail capacity and to eliminate at-grade rail crossings.

The major challenge to capital investment strategies is the lack of an obvious funding source. Railroads have little incentive to incur costs to solve a problem for road transport, and hence are typically unwilling to pay. Local jurisdictions have no authority to force railroads to incur these costs. They also have little incentive to pay, as they view the rail traffic as a national responsibility. At the national level there is no specific funding source for such projects.

Border crossings

Border crossing regions are a unique subset of trade nodes. Like port regions, border crossings generate truck traffic destined for local distribution or transfer facilities as well as markets beyond the immediate metropolitan area. This means last mile impacts as well as the passthrough impacts previously discussed. Border crossings provide a unique challenge with regard to managing regional freight capacity however because of the international context.

The US-Canadian border has provided a useful test bed for researchers investigating both the institutional and technological framework for freight flows across borders. In Washington State, the FAST Corridor was designed and supported by the USDOT, the state of Washington, the Puget Sound Regional Council, the three ports, three private freight carriers, 12 local cities and three counties. The FAST Corridor members identified highway/rail crossings as the most pressing concern, and proposed as a first phase, 15 projects: 12 grade separations and three truck access projects totaling $470 million.

US-Mexico border crossings, in many ways, operate in a more complex and uncertain environment. While the North American Free Trade Agreement (NAFTA) and other institutional and regulatory reforms have been designed to improve cross-border freight flows for the US, Canada, and Mexico, the lack of a truly open border results in further delays at crossings as goods are unloaded and reloaded on different vehicles on opposite sides of the gate. This has created a demand for technology-based solutions.

RECOMMENDATIONS 6.1 Urban freight management strategies

Our review and assessment suggests some promising options for better management of freight in US cities and metropolitan areas. Our findings are summarized in Table 4. The second column is our rating of effectiveness based on the literature as discussed in Section 5 above [START_REF] Giuliano | NCFRP Project 36(05) Synthesis of Freight Research in Urban Transportation Planning[END_REF]. The last column is our rating of applicability in the US context: given US institutional and governance structures, to what extent could such a strategy be implemented? The ratings for applicability were based on our judgment. The US context is quite different from that of Europe, and other developed parts of the world. For example, many aspects of urban freight are protected by interstate commerce, limiting the ability of local or state governments to regulate. There are also different perspectives on the extent to which private industry should be subsidized in order to achieve social benefits. Among the last-mile strategies, labeling and certification programs, land use planning (in the longer term), and off-hours deliveries are the most effective strategies. However, off-hours delivery programs are less transferable due to the many changes they require across the supply chain. Traffic and parking regulations are less effective, because they do not have an impact on the underlying demand for freight moves. We rate ITS strategies as medium due to their limited implementation feasibility and the need for more development of some of the most potentially beneficial applications, such as truck parking and loading information systems.

Within the category of environmental strategies, global fuel efficiency and emissions regulations have proven their effectiveness over several decades. Low emissions zones are the most effective to address local hot spots, but do not appear to be feasible under current national and state US policy. Alternative fuel vehicles may prove to be very effective long term, but the technology and market penetration are not sufficient to achieve significant reductions in emissions or energy consumption. Environmental justice efforts are more advanced in the US than in other countries; however environmental justice problems are challenging to solve.

Among the trade node strategies, pricing and accelerated emissions programs are among the most effective strategies. Despite the effectiveness of pricing, we rate it low on applicability because of the continuing strong political opposition from various stakeholder groups. Accelerated emission-reduction programs based on negotiation and voluntary targets have proven to be effective and are a better fit in the US context. Rail strategies can be effective, but involve high costs for which funding sources are not obvious.

[TABLE 4]

Future research needs

There are many opportunities for further research. First, most cities cannot answer the following questions: How many vehicles (be it a heavy-duty truck, a light-duty truck, a van, a car, or even, a bike) are engaged in freight transport activity? How many deliveries and pick-ups occur in a day, a week? Data accessible to planners and researchers on delivery characteristics is almost non-existent. Without these data it is hard to confirm or refute conventional wisdom such as, the rise of e-commerce means a net increase in commercial VMT.

Additionally, we find there is much research on system optimization, but little on how optimization methods work in practice. We need better data on, for example, real time route optimization that is based on actual fleet movements. Border crossings are a case in point. Similarly, the need for field tests in the area of technology deployment is great.

Second, one of the biggest problems associated with urban freight is truck emissions, and our review showed the many different approaches being taken to address this problem. We have limited information on the relative benefits and costs of certification systems or Low Emissions Zones (LEZs). Research is needed to better understand the effectiveness of these strategies. For example, in the case of LEZs, a) what are the costs associated both in terms of the government and logistics firms, b) what is the impact on trucking industry, c) are LEZs legally possible in the US, and if so, at what level of government?

Finally, there is a need for careful and systematic evaluation of existing policies and experiments. We are lacking analysis of the impacts of certification schemes, truck access restrictions, and requirements for alternative fuel trucks. Ongoing experimentation provides a rich resource for discovering whether these efforts have the expected results or have unintended consequences that reduce their benefits.

ACKNOWLEDGEMENTS

This paper is based on National Cooperative Freight Research Program Project 36(05) (25). The research was also supported by the METRANS Transportation Center, University of Southern California. The authors gratefully acknowledge the assistance of Jennifer Lieu. All errors and omissions are the responsibility of the authors.

List of tables